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matrix method, rather than defining an RCWA-only structure (rcwa_structure)?" }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html", - "title": "Section 6a: Basic cell optics", + "objectID": "solcore-workshop/workshop2023.html", + "href": "solcore-workshop/workshop2023.html", + "title": "Solcore Workshop 2023 (SKKU)", "section": "", - "text": "In this script, we will build on the TMM model from example 1(a) and look at the effects of interference.\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer\nfrom solcore.absorption_calculator import calculate_rat, OptiStack\nimport seaborn as sns" - }, - { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#setting-up", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#setting-up", - "title": "Section 6a: Basic cell optics", - "section": "Setting up", - "text": "Setting up\nFirst, let’s define some materials:\n\nSi = material(\"Si\")\nSiN = material(\"Si3N4\")()\nAg = material(\"Ag\")()\n\nNote the second set of brackets (or lack thereof). The Solcore material system essentially operates in two stages; we first call the material function with the name of the material we want to use, for example Si = material(“Si”), which creates a general Python class corresponding to that material. We then call this class to specify further details, such as the temperature, doping level, or alloy composition (where relavant). This happens below when defining Si_n and Si_p; both are use the Si class defined above, and adding further details to the material. For the definitions of SiN and Ag above, we do both steps in a single line, hence the two sets of brackets.\n\nSi_n = Si(Nd=si(\"1e21cm-3\"), hole_diffusion_length=si(\"10um\"))\nSi_p = Si(Na=si(\"1e16cm-3\"), electron_diffusion_length=si(\"400um\"))\n\nTo look at the effect of interference in the Si layer at different thicknesses, we make a list of thicknesses to test (evenly spaced on a log scale from 400 nm to 300 um):\n\nSi_thicknesses = np.linspace(np.log(0.4e-6), np.log(300e-6), 8)\nSi_thicknesses = np.exp(Si_thicknesses)\n\nwavelengths = si(np.linspace(300, 1200, 400), \"nm\")\n\noptions = {\n \"recalculate_absorption\": True,\n \"optics_method\": \"TMM\",\n \"wavelength\": wavelengths\n }\n\nMake a color palette using the seaborn package to make the plots look nicer\n\ncolors = sns.color_palette('rocket', n_colors=len(Si_thicknesses))\ncolors.reverse()\n\ncreate an ARC layer:\n\nARC_layer = Layer(width=si('75nm'), material=SiN)" + "text": "Click here to view all the slides.\nOutline:\nDay 1:\n\nIntroduction to Solcore & computer modelling (lecture)\nIntegration for limiting current, limiting voltage model\nShockley-Queisser efficiency limit and detailed balance (DB) junction model (lecture)\n\nDay 2:\n\nIntroduction to drift-diffusion junction model, depletion approximation (lecture) & spectral irradiance\nThe depletion approximation: Si cell and GaAs cell\nOptical modelling using the transfer-matrix model (TMM):\n\nTMM introduction\nOptimizing an anti-reflection coating\n\nPlanar III-V on Si tandem solar cell\n\nDay 3:\n\nOptical absorption in textured Si: ray-tracing for pyramid textures, rigorous coupled-wave analysis (RCWA) for nano-scale gratings\nIII-V/Si cells with light-trapping structures:\n\nPlanar III-V wafer-bonded to silicon with planar front using e.g. epoxy\nPlanar III-V bonded to textured silicon with diffraction grating on rear\n\nConformal perovskite on silicon tandem cells" }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-si-thickness", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-si-thickness", - "title": "Section 6a: Basic cell optics", - "section": "Effect of Si thickness", - "text": "Effect of Si thickness\nNow we are going to loop through the different Si thicknesses generated above, and create a simple solar cell-like structure. Because we will only do an optical calculation, we don’t need to define a junction and can just make a simple stack of layers.\nWe then calculate reflection, absorption and transmission (RAT) for two different situations: 1. a fully coherent stack 2. assuming the silicon layer is incoherent. This means that light which enters the Si layer cannot interfere with itself, but light in the ARC layer can still show interference. In very thick layers (much thicker than the wavelength of light being considered) this is likely to be more physically accurate because real light does not have infinite coherence length; i.e. if you measured wavelength-dependent transmission or reflection of a Si wafer hundreds of microns thick you would not expect to see interference fringes.\nPLOT 1\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p) # silicon layer\n solar_cell = OptiStack([ARC_layer, base_layer]) # OptiStack (optical stack) to feed into calculate_rat function\n\n # Coherent calculation:\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False) # coherent calculation\n # For historical reasons, Solcore's default setting is to ignore reflection at the back of the cell (i.e. at the\n # interface between the final material in the stack and the substrate). Hence we need to tell the calculate_rat\n # function NOT to ignore this reflection (no_back_reflection=False).\n\n # Calculation assuming no interference in the silicon (\"incoherent\"):\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i']) # partially coherent: ARC is coherent, Si is not\n\n # Plot the results:\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1], label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(1) Absorption in Si with varying thickness\")\nplt.show()\n\n\n\n\nWe can see that the coherent calculations (solid lines) show clear interference fringes which depend on the Si thickness. The incoherent calculations do not have these fringes and seem to lie around the average of the interference fringes. For both sets of calculations, we see increasing absorption as the Si gets thicker, as expected." + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "", + "text": "The structure in this example is based on that of the previous example (9a), but with the planar bottom Si cell replaced by a Si cell with a pyramidal texture, bonded to the III-V top cells with a low-index epoxy/glass layer.\nWe could use the angular redistribution matrix method as in the previous example - however, because in this example we only need to use TMM and ray-tracing (RT), we can use the ray-tracing method with integrated RT directly (this is generally faster, because we do not need to calculate the behaviour of the surfaces for every angle of incidence)." }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", - "title": "Section 6a: Basic cell optics", - "section": "Effect of reflective substrate", - "text": "Effect of reflective substrate\nNow we repeat the calculation, but with an Ag substrate under the Si. Previously, we did not specify the substrate and so it was assumed by Solcore to be air (\\(n\\) = 1, \\(\\kappa\\) = 0).\nPLOT 2\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p)\n\n # As before, but now we specify the substrate to be silver:\n solar_cell = OptiStack([ARC_layer, base_layer], substrate=Ag)\n\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False)\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1],\n label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(2) Absorption in Si with varying thickness (Ag substrate)\")\nplt.show()\n\n\n\n\nWe see that the interference fringes get more prominent in the coherent calculation, due to higher reflection at the rear Si/Ag surface compared to Ag/Air. We also see a slightly boosted absorption at long wavelengths at all thicknesses, again due to improved reflection at the rear surface" + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#setting-up", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#setting-up", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Setting up", + "text": "Setting up\nWe load relevant packages and define materials, the same as in the previous example.\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.ray_tracing import rt_structure\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.textures import planar_surface, regular_pyramids\nfrom rayflare.options import default_options\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# download_db()\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nepoxy = material(\"BK7\")()\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nAlGaAs = material(\"AlGaAs\")\n\nAir = material(\"Air\")()\n\nGaAs = material(\"GaAs\")\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n234 main MgF2 Rodriguez-de_Marcos main/MgF2/Rodriguez-de Marcos.yml 1 1 0.0299919 2.00146 960\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n475 main Ta2O5 Rodriguez-de_Marcos main/Ta2O5/Rodriguez-de Marcos.yml 1 1 0.0294938 1.51429 212\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n2 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2835 other negative_tone_photoresists Microchem_SU8_2000 other/resists/Microchem SU-8 2000.yml 1 0 0.32 0.8 200\n2836 other negative_tone_photoresists Microchem_SU8_3000 other/resists/Microchem SU-8 3000.yml 1 0 0.32 1.7 200\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2 main Ag Jiang main/Ag/Jiang.yml 1 1 0.3 2.0 1701\n\n\nWe define the layers we will need, as before. We specify the thickness of the silicon (280 \\(\\mu\\)m) and epoxy (1 mm) at the top:\n\nd_Si = 280e-6 # thickness of Si wafer\nd_epoxy = 1e-6 # thickness of epoxy. In reality, the epoxy is much thicker, but the exact thickness doesn't matter \n # because the material is transparent and we will treat it incoherently.\n\nGaInP_total_thickness = 350e-9\nGaAs_total_thickness = 1200e-9\n\nARC = [Layer(110e-9, MgF2), Layer(65e-9, Ta2O5)]\n\nGaInP_junction = [Layer(20e-9, window), Layer(GaInP_total_thickness, GaInP(In=0.50))]\n\n# 100 nm TJ\ntunnel_1 = [Layer(100e-9, AlGaAs(Al=0.8)), Layer(20e-9, GaInP(In=0.5))]\n\nGaAs_junction = [Layer(20e-9, GaInP(In=0.5)), Layer(GaAs_total_thickness, GaAs()), Layer(70e-9, AlGaAs(Al=0.8))]\n\nspacer_ARC = [Layer(80e-9, Ta2O5)]" }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", - "title": "Section 6a: Basic cell optics", - "section": "Effect of polarization and angle of incidence", - "text": "Effect of polarization and angle of incidence\nFinally, we look at the effect of incidence angle and polarization of the light hitting the cell.\nPLOT 3\n\nangles = [0, 30, 60, 70, 80, 89] # angles in degrees\n\nARC_layer = Layer(width=si('75nm'), material=SiN)\nbase_layer = Layer(width=si(\"100um\"), material=Si_p)\n\ncolors = sns.cubehelix_palette(n_colors=len(angles))\n\nplt.figure()\n\nfor i1, theta in enumerate(angles):\n\n solar_cell = OptiStack([ARC_layer, base_layer])\n\n RAT_s = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='s',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n RAT_p = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='p',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n\n plt.plot(wavelengths*1e9, RAT_s[\"A\"], color=colors[i1], label=str(round(theta)))\n plt.plot(wavelengths*1e9, RAT_p[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"$\\theta (^\\circ)$\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(3) Absorption in Si with varying angle of incidence\")\nplt.show()\n\n\n\n\nFor normal incidence (\\(\\theta = 0^\\circ\\)), s (solid lines) and p (dashed lines) polarization are equivalent. As the incidence angle increases, in general absorption is higher for p-polarized light (due to lower reflection). Usually, sunlight is modelled as unpolarized light, which computationally is usually done by averaging the results for s and p-polarized light." + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-cell-layers", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-cell-layers", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Defining the cell layers", + "text": "Defining the cell layers\nThere are three interfaces in the cell which will define the structure to simulate:\n\nthe III-V/epoxy interface, where the epoxy itself will be treated as a bulk layer in the simulation\nthe epoxy/Si interface, where the Si has a pyramidal texture (the Si itself is another bulk layer in the simulation).\nthe rear surface of the cell, where the Si again has a pyramidal texture (and we assume there is a silver back mirror behind the cell)\n\nThese 3 interfaces are defined here, using the pre-defined textures for a planar surface or regular pyramids:\n\nfront_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + spacer_ARC\n\nfront_surf = planar_surface(interface_layers = front_layers, prof_layers=np.arange(1, len(front_layers)+1))\n\nSi_front = regular_pyramids(elevation_angle=50, upright=True)\n\nSi_back = regular_pyramids(elevation_angle=50, upright=False)\n\nNow we set relevant options for the solver. We set the number of rays to trace at each wavelength (more rays will make the result less noisy, but increase computation time) and whether to calculate the absorption profile in the bulk layers (no, in this case). The randomize_surface options determines whether the ray keeps track of its positions in the unit cell while travelling between surfaces; we set this to False to mimic random pyramids.\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl, output_units=\"photon_flux_per_m\")\n\noptions.wavelength = wl\noptions.project_name = \"III_V_Si_cell\"\n\n# options for ray-tracing\noptions.randomize_surface = True\noptions.n_rays = 1000\noptions.bulk_profile = False" }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#conclusions", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#conclusions", - "title": "Section 6a: Basic cell optics", - "section": "Conclusions", - "text": "Conclusions\nWe have now seen some effects of interference in layers of different thicknesses, and seen the effect of adding a highly reflective substrate. So we already have two strategies for light-trapping/improving the absorption in a solar cell: adding an anti-reflection coating (in example 1a), to reduce front-surface reflection and get more light into the cell, and adding a highly reflective layer at the back, to reduce loss through the back of the cell and keep light trapped in the cell." + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-structures", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-structures", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Defining the structures", + "text": "Defining the structures\nFinally, we define the ray-tracing structure we will use, using the interfaces, bulk materials, and options set above. Because we want to calculate the reflection/absorption/transmission probabilities at the front surface using TMM, we set the use_TMM argument to True. We also define a completely planar cell with the same layer thicknesses etc. to compare and evaluate the effect of the textures Si surfaces.\n\noptical_structure = rt_structure(\n textures=[front_surf, Si_front, Si_back],\n materials=[epoxy, Si()],\n widths=[d_epoxy, d_Si],\n incidence=Air,\n transmission=Ag,\n options=options,\n use_TMM=True,\n save_location=\"current\", # lookup table save location\n overwrite=True, # whether to overwrite any previously existing results, if found\n)\n\n# options for TMM\noptions.coherent = False\noptions.coherency_list = len(front_layers)*['c'] + ['i']*2\n\nplanar_optical_structure = tmm_structure(\n layer_stack = front_layers + [Layer(d_epoxy, epoxy), Layer(d_Si, Si())],\n incidence=Air,\n transmission=Ag,\n)\n\nINFO: Pre-computing TMM lookup table(s)\n\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded." }, { - "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#questions", - "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#questions", - "title": "Section 6a: Basic cell optics", - "section": "Questions", - "text": "Questions\n\nWhy are the interference fringes stronger when adding a silver back mirror, compared to having air behind the Si?\nWe modelled s and p-polarized light - how do we normally model unpolarized light?" + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#calculations", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#calculations", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Calculations", + "text": "Calculations\nCalculate the R/A/T for the planar reference cell:\n\ntmm_result = planar_optical_structure.calculate(options=options)\n\nGaInP_A_tmm = tmm_result['A_per_layer'][:,3]\nGaAs_A_tmm = tmm_result['A_per_layer'][:,7]\nSi_A_tmm = tmm_result['A_per_layer'][:,len(front_layers)+1]\n\nJmax_GaInP_tmm = q*np.trapz(GaInP_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs_tmm = q*np.trapz(GaAs_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_Si_tmm = q*np.trapz(Si_A_tmm*AM15G.spectrum()[1], x=wl)/10\n\nCalculate the R/A/T for the textured cell:\n\nrt_result = optical_structure.calculate(options=options)\n\nGaInP_absorption_ARC = rt_result['A_per_interface'][0][:,3]\nGaAs_absorption_ARC = rt_result['A_per_interface'][0][:,7]\nSi_absorption_ARC = rt_result['A_per_layer'][:,1]\n\nJmax_GaInP = q*np.trapz(GaInP_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_absorption_ARC*AM15G.spectrum()[1], x=wl)/10" }, { - "objectID": "solcore-workshop-2/schedule.html", - "href": "solcore-workshop-2/schedule.html", - "title": "Schedule", - "section": "", - "text": "Day 1 (Wednesday 22/11)\n\nDay 2 (Thursday 23/11)\n\nDay 3 (Friday 24/11)\n\n\n\n\nThemes:\nIntroduction, efficiency limits & fitting data\n\nJunction models & planar optics\n\nAdvanced light-trapping structures\n\n\n1.00 - 1.30\nIntroduction to computer modelling & Solcore\n1.00 - 1.30\nIntroduction to different junction models\n1.00 - 1.20\nIntroduction to RayFlare & different optical methods\n\n\n1.30 - 2.15\nLimiting current & voltage models\n1.30 - 2.00\nPlanar Si cell using depletion approximation junction\n1.20 - 2.00\nEffect of diffraction grating (RCWA) and ray-tracing (RT) on a silicon wafer\n\n\n2.15 - 2.45\nBreak\n2.00 - 2.45\nIntroduction to the transfer-matrix method: interference and anti-reflection coatings\n2.00 - 2.30\nGaInP/GaAs/Si triple-junction cell with rear diffraction grating\n\n\n2.45 - 3.30\nShockley-Queisser efficiency limit\n2.45 - 3.15\nBreak\n2.30 - 3.00\nBreak\n\n\n3.30 - 4.00\nChanging irradiance spectra\n3.00 - 3.45\nPlanar Si cell using drift-diffusion junction\n3.00 - 3.45\nEpoxy-bonded GaInP/GaAs//Si triple-junction cell with pyramidally textured silicon\n\n\n4.00 - 4.15\nBreak\n3.45 - 4.15\nBreak\n3.45 - 4.30\nPerovskite on silicon tandem cell with pyramidcal texturing\n\n\n4.15 - 5.00\nTwo-diode model fits to experimental data\n4.15 - 5.00\nOptical model of a planar III-V on Si tandem cell\n4.30 - 5.00\nUsing the Katana HPC" + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#plotting-the-results", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#plotting-the-results", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Plotting the results", + "text": "Plotting the results\nFinally, we plot the results; the solid lines show the results for the textured Si cell (calculated using ray-tracing), the dashed lines for the planar cell (calculated using TMM). The maximum possible currents are shown in the plot, with the value in brackets for Si being for the planar cell.\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_absorption_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_absorption_ARC, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_absorption_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, GaInP_A_tmm, \"--k\")\nplt.plot(wl * 1e9, GaAs_A_tmm, \"--b\")\nplt.plot(wl * 1e9, Si_A_tmm, \"--r\")\nplt.plot(wl * 1e9, rt_result['R'], '-', color='grey', label=\"Reflected\")\nplt.plot(wl * 1e9, tmm_result['R'], '--', color='grey')\n\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(870, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.text(870, 0.45, r\"({:.1f} mA/cm$^2)$\".format(Jmax_Si_tmm))\n\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.tight_layout()\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html", - "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html", - "title": "Section 6b: Optimizing an ARC", - "section": "", - "text": "In the previous example, we introduced a simple one-layer anti-reflection coating (ARC); ARCs are a standard feature of all high-efficiency solar cells. But how do you find out the right thickness for the anti-reflection coating layer(s) (or the right dimensions for a light-trapping grating, or some other structure in your cell)? This is where optimization comes in. Here, we will look at a very simple ‘brute-force’ optimization for a single or double-layer ARC.\nimport numpy as np\nimport os\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer, SolarCell\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.light_source import LightSource\nfrom solcore.absorption_calculator import search_db, download_db\nfrom solcore.absorption_calculator import calculate_rat\nfrom solcore.state import State\n\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.options import default_options\nimport seaborn as sns\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The Poisson - Drift-Diffusion solver will not be available because the ddModel fortran library could not be imported.\nname 'dd' is not defined\n\n\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/registries.py:73: UserWarning: Optics solver 'RCWA' will not be available. An installation of S4 has not been found.\n warn(" + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#questionschallenges", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#questionschallenges", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Questions/challenges", + "text": "Questions/challenges\n\nDoes it make sense to do a ray-tracing calculation for short wavelengths? For this structure, can you speed up the calculation and avoid the random noise at short wavelengths?\nHow much current is lost to parasitic absorption in e.g. tunnel junctions, window layers etc.?\nHow can we reduce reflection at the epoxy interfaces?\nIf the epoxy/glass layer is much thicker than the relevant incident wavelengths, and not absorbing, does the exact thickness matter in the simulation?\nWhat happens if only the rear surface is textured? Would a structure without the front texture have other advantages?\nWhy does the Si have lower absorption/limiting current in this structure compared to the previous example?" }, { - "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#setting-up", - "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#setting-up", - "title": "Section 6b: Optimizing an ARC", - "section": "Setting up", - "text": "Setting up\nWe set some options, as in previous examples, setting the wavelengths and defining the incident spectrum. We are going to do a partially coherent calculation, treating the ARC as a coherent layer and the thick Si layer as incoherent (no thin-film interference).\n\nopts = State()\n\nwavelengths = np.linspace(300, 1200, 800)*1e-9\n\nAM15g = LightSource(source_type=\"standard\", version=\"AM1.5g\", output_units=\"photon_flux_per_m\")\nspectrum = AM15g.spectrum(wavelengths)[1]\nnormalised_spectrum = spectrum/np.max(spectrum)\n\nopts.wavelength = wavelengths\nopts.coherency_list = ['c', 'i']\nopts.optics_method = 'TMM'\nopts.position = 100e-6\nopts.no_back_reflection = False\n\nSi = material(\"Si\")()\nSiN = material(\"Si3N4\")()\nAg = material(\"Ag\")()\nAir = material(\"Air\")()" + "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#electrical-calculation", + "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#electrical-calculation", + "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "section": "Electrical calculation", + "text": "Electrical calculation\nNow we can also use RayFlare’s optical results to run an electrical simulation in Solcore. To use the depletion approximation (DA) or drift-diffusion (PDD) solvers, we need the front surface reflectivity, and a depth-dependent absorption/generation profile. While so far we have been plotting total absorption per layer, RayFlare can calculate depth-dependent profiles too.\nWe need to import some more things, and set some options for solar_cell_solver, as we did before. We must set the optics_method option to 'external', since we want to pass the values calculated by RayFlare into Solcore.\n\nfrom solcore.solar_cell import SolarCell, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom rayflare.utilities import make_absorption_function\nfrom solcore.state import State\n\noptions = State(options) # convert the RayFlare options to Solcore options object so Solcore will recognise it\nV = np.linspace(-3, 0, 100)\noptions.optics_method = 'external'\noptions.voltages = V\noptions.internal_voltages = np.linspace(-4, 1, 200)\noptions.light_iv = True\noptions.mpp = True\noptions.light_source = AM15G\noptions.recalculate_absorption = True\n\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/registries.py:73: UserWarning: Optics solver 'RCWA' will not be available. An installation of S4 has not been found.\n warn(\n\n\nNow, previously we only calculate total reflection/absorption/transmission. Now we want to calculate depth-dependent absorption (generation) profiles at every wavelength. We set some options for RayFlare for this (we can use the same options object) and then ask RayFlare to calculate the absorption profile:\n\noptions.bulk_profile = True\noptions.depth_spacing = 1e-9\noptions.depth_spacing_bulk = 10e-9\n\nprofile_data = optical_structure.calculate_profile(options)\n\nWe not only want to calculate the absorption profile in the bulk layers (the Si) but also the front surface layers, since the GaInP and GaAs junctions are defined as part of the front interface. This was the reason for defining the surface as:\nfront_surf = planar_surface(interface_layers = front_layers, prof_layers=np.arange(1, len(front_layers)+1))\nnear the start of the script. The prof_layers argument tells RayFlare we want to calculate the absorption profile in the surface layers, in addition to the total absorption.\nIn order for Solcore to use the information we just calculated, it must be in the right format. We need to provide Solcore with two things: the reflectance, and a function which describes the depth-dependent absorption. This function expects an argument which is an array of positions, and returns the generation (units of \\(m^{-1}\\)) at each position and each wavelength. Fortunately, RayFlare has a function which takes your layer structure, results, and user options, and creates such a function for you:\n\ndepths, external_optics_func = make_absorption_function(profile_data, optical_structure, options)\n\noptions.position = depths\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\nPreviously, we defined RayFlare rt_structure and tmm_structure objects to do the optical calculation. For the cell calculation, we need a Solcore SolarCell object, which needs different information (such as doping levels) to perform the electrical calculation. Here we create the junctions, making sure that the total layer thicknesses of each material are the same as they were in the ray-traced structure.\n\nGaInP_emitter_thickness = 100e-9\nGaAs_emitter_thickness = 200e-9\nSi_emitter_thickness = 1e-6\n\nGaInP_base_thickness = GaInP_total_thickness - GaInP_emitter_thickness\nGaAs_base_thickness = GaAs_total_thickness - GaAs_emitter_thickness\nSi_base_thickness = d_Si - Si_emitter_thickness\n\nGaInP_junction = Junction([\n Layer(20e-9, material(\"AlInP\")(Al=0.52), Nd=si(\"1e18cm-3\"), role=\"window\"), # window\n Layer(GaInP_emitter_thickness, GaInP(In=0.50, Nd=si(\"1e18cm-3\"), hole_diffusion_length=si(\"200nm\")), role=\"emitter\"), # emitter\n Layer(GaInP_base_thickness, GaInP(In=0.50, Na=si(\"1e17cm-3\"), electron_diffusion_length=si(\"300nm\")), role=\"base\"), # base\n ], kind=\"DA\") # TJ\n\nGaAs_junction = Junction([\n Layer(20e-9, GaInP(In=0.5, Nd=si(\"1e18cm-3\")), role=\"window\"), # window\n Layer(GaAs_emitter_thickness, GaAs(Nd=si(\"1e18cm-3\"), hole_diffusion_length=si(\"250nm\")), role=\"emitter\"), # emitter\n Layer(GaAs_base_thickness, GaAs(Na=si(\"9e16cm-3\"), electron_diffusion_length=si(\"1000nm\")), role=\"base\"), # basee\n Layer(70e-9, AlGaAs(Al=0.8, Na=si(\"4e18cm-3\")), role=\"bsf\") # BSF\n ], kind=\"DA\")\n\nSi_junction = Junction([\n Layer(Si_emitter_thickness, Si(Nd=si(\"1e19cm-3\"), hole_diffusion_length=si(\"1000nm\")), role=\"emitter\"),\n Layer(Si_base_thickness, Si(Na=si(\"1e16cm-3\"), electron_diffusion_length=si(\"250um\")), role=\"base\")],\n kind=\"DA\")\n\nsolar_cell = SolarCell(\n ARC + [GaInP_junction] + tunnel_1 + [GaAs_junction] + spacer_ARC + [Layer(d_epoxy, epoxy)] + [Si_junction],\n external_reflected=rt_result[\"R\"],\n external_absorbed=external_optics_func)\n\nFinally, we are ready to the our cell calculations; first, we calculate and plot the light I-V:\n\nsolar_cell_solver(solar_cell, 'iv', options)\n\nplt.figure(2)\nplt.plot(-V, -solar_cell.iv['IV'][1]/10, 'k', linewidth=3, label='3J cell')\nplt.plot(-V, solar_cell(0).iv(V)/10, 'b', label='InGaP sub-cell')\nplt.plot(-V, solar_cell(1).iv(V)/10, 'g', label='GaAs sub-cell')\nplt.plot(-V, solar_cell(2).iv(V)/10, 'r', label='Si sub-cell')\nplt.text(1.5, 5,f'Jsc= {abs(solar_cell.iv.Isc/10):.2f} mA.cm' + r'$^{-2}$')\nplt.text(1.5, 4,f'Voc= {abs(solar_cell.iv.Voc):.2f} V')\nplt.text(1.5, 3,f'FF= {solar_cell.iv.FF*100:.2f} %')\nplt.text(1.5, 2,f'Eta= {solar_cell.iv.Eta*100:.2f} %')\n\nplt.legend()\nplt.ylim(-10, 15)\nplt.xlim(0, 3)\nplt.ylabel('Current (mA/cm$^2$)')\nplt.xlabel('Voltage (V)')\nplt.show()\n\nINFO: Solving optics of the solar cell...\n\n\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\n\n\n\nAnd now the QE (we also plot the total absorption in each junction for comparison with the EQE):\n\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nplt.figure(1)\nplt.plot(wl * 1e9, solar_cell(0).eqe(wl) * 100, 'b', label='GaInP QE')\nplt.plot(wl * 1e9, solar_cell(1).eqe(wl) * 100, 'g', label='GaAs QE')\nplt.plot(wl * 1e9, solar_cell(2).eqe(wl) * 100, 'r', label='Si QE')\nplt.fill_between(wl * 1e9, GaInP_absorption_ARC * 100, 0, alpha=0.3,\n label='GaInP Abs.', color='b')\nplt.fill_between(wl * 1e9, GaAs_absorption_ARC * 100, 0, alpha=0.3,\n label='GaAs Abs.', color='g')\nplt.fill_between(wl * 1e9, Si_absorption_ARC * 100, 0, alpha=0.3,\n label='Ge Abs.', color='r')\n\nplt.plot(wl*1e9, 100*(1-solar_cell.reflected), '--k', label=\"100 - Reflectivity\")\nplt.legend()\nplt.ylim(0, 100)\nplt.ylabel('EQE (%)')\nplt.xlabel('Wavelength (nm)')\nplt.show()\n\nINFO: Solving optics of the solar cell...\n\n\nSolving QE of the solar cell..." }, { - "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#single-layer-arc", - "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#single-layer-arc", - "title": "Section 6b: Optimizing an ARC", - "section": "Single-layer ARC", - "text": "Single-layer ARC\nHere, we will calculate the behaviour of a single-layer SiN anti-reflection coating on Si while changing the ARC thickness between 0 and 200 nm. We will consider two values to optimize: the mean reflectance mean_R, and the reflectance weighted by the photon flux in an AM1.5G spectrum (weighted_R). The reason for considering the second value is that it is more useful to suppress reflection at wavelengths where there are more photons which could be absorbed by the cell (up to the cell’s bandgap).\nWe will loop through the different ARC thicknesses in d_range, build the structure for each case, and then calculate the reflectance. We then save the mean reflected and weighted mean reflectance in the corresponding arrays. We also plot the reflectance for each 15th loop (this is just so the plot does not get too crowded).\n\nd_range = np.linspace(0, 200, 200)\n\nmean_R = np.empty_like(d_range)\nweighted_R = np.empty_like(d_range)\n\ncols = sns.cubehelix_palette(np.ceil(len(d_range)/15))\n\nplt.figure()\njcol = 0\n\nfor i1, d in enumerate(d_range):\n\n struct = SolarCell([Layer(si(d, 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\n solar_cell_solver(struct, task='optics', user_options=opts)\n\n if i1 % 15 == 0:\n plt.plot(wavelengths*1e9, struct.reflected, label=str(np.round(d, 0)), color=cols[jcol])\n jcol += 1\n\n mean_R[i1] = np.mean(struct.reflected)\n weighted_R[i1] = np.mean(struct.reflected*normalised_spectrum)\n\nplt.legend()\nplt.show()\n\nWe now find at which index mean_R and weighted_R are minimised using np.argmin, and use this to print the ARC thickness at which this occurs (rounded to 1 decimal place).\n\nprint('Minimum mean reflection occurs at d = ' + str(np.round(d_range[np.argmin(mean_R)], 1)) + ' nm')\nprint('Minimum weighted reflection occurs at d = ' + str(np.round(d_range[np.argmin(weighted_R)], 1)) + ' nm')\n\nMinimum mean reflection occurs at d = 67.3 nm\nMinimum weighted reflection occurs at d = 74.4 nm\n\n\nWe see that the values of \\(d\\) for the two different ways of optimizing are very similar, but not exactly the same, as we would expect. The minimum in both cases occurs around 70 nm. We can also plot the variation of the mean and weighted \\(R\\) with ARC thickness \\(d\\):\n\nplt.figure()\nplt.plot(d_range, mean_R, label='Mean reflection')\nplt.plot(d_range[np.argmin(mean_R)], np.min(mean_R), 'ok')\nplt.plot(d_range, weighted_R, label='Weighted mean reflection')\nplt.plot(d_range[np.argmin(weighted_R)], np.min(weighted_R), 'ok')\nplt.xlabel('d$_{SiN}$')\nplt.ylabel('(Weighted) mean reflection 300-1200 nm')\nplt.legend()\nplt.show()\n\n\n\n\nNow, to see what the reflectance looks like for the optimized structure, we make new tmm_structures with the optimal values and calculate and plot the reflectance:\n\nstruct_1 = SolarCell([Layer(si(d_range[np.argmin(mean_R)], 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\nsolar_cell_solver(struct_1, task='optics', user_options=opts)\nR_1 = struct_1.reflected\n\nstruct_2 = SolarCell([Layer(si(d_range[np.argmin(weighted_R)], 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\nsolar_cell_solver(struct_2, task='optics', user_options=opts)\nR_2 = struct_2.reflected\n\nplt.figure()\nplt.plot(wavelengths*1e9, R_1, label='Mean R minimum')\nplt.plot(wavelengths*1e9, R_2, label='Weighted R minimum')\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"R\")\nplt.show()\n\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\n\n\n\n\n\nWe see that the two reflectance curves are very similar, as expected because the layer thicknesses are very similar." + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "", + "text": "This example shows how you can simulate a perovskite-Si tandem cell with pyramidal surface textures, where the perovskite and other surface layers are assumed to be deposited conformally (i.e., also in a pyramid shape) on top of the Si. The perovskite optical constants are from this paper, while the structure is based on this paper We will calculate total reflection, transmission and absorption per layer as well as the wavelength-dependent absorption profiles in the perovskite and Si, which can be used in e.g. device simulations. We will look at the effect of treating the layers deposited on Si (including the perovskite) coherently or incoherently.\nFirst, import relevant packages and RayFlare functions:\nimport numpy as np\nimport os\n\nfrom solcore.structure import Layer\nfrom solcore.constants import q\nfrom solcore import material\nfrom solcore.absorption_calculator import search_db, download_db\nfrom solcore.light_source import LightSource\n\nfrom rayflare.textures import regular_pyramids\nfrom rayflare.options import default_options\nfrom rayflare.ray_tracing import rt_structure\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\nfrom cycler import cycler\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nNow we set some relevant options. We will scan across 20 x 20 surface points of the pyramid unit cell between 300 and 1200 nm, for unpolarized, normally-incident light. The randomize_surface option is set to True to prevent correlation between the incident position on the front and rear pyramids. The n_jobs option is set to -1, which means that all available cores will be used. If you want to use all but one core, change this to -2 etc. We also need to provide a project_name to save the lookup tables which will be calculated using TMM to use during ray-tracing.\nwavelengths = np.linspace(300, 1200, 40) * 1e-9\n\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wavelengths,\n output_units=\"photon_flux_per_m\")\n\noptions = default_options()\noptions.wavelength = wavelengths\noptions.nx = 20\noptions.ny = options.nx\noptions.n_rays = 4 * options.nx**2\noptions.depth_spacing = 1e-9\noptions.pol = \"u\"\noptions.I_thresh = 1e-3\noptions.project_name = \"perovskite_Si_rt\"\noptions.randomize_surface = True\noptions.n_jobs = -1 # use all cores; to use all but one, change to -2 etc." }, { - "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#double-layer-arc", - "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#double-layer-arc", - "title": "Section 6b: Optimizing an ARC", - "section": "Double-layer ARC", - "text": "Double-layer ARC\nWe will now consider a similar situation, but for a double-layer MgF\\(_2\\)/Ta\\(_2\\)O\\(_5\\) ARC on GaAs.\nSolcore can directly interface with the database from www.refractiveindex.info, which contains around 3000 sets of data for a large number of different materials. Before the first use, it is necessary to download the database. This only needs to be done once, so you can comment this line out after it’s done:\n\ndownload_db(confirm=True) # only needs to be done once\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaking request to https://refractiveindex.info/download/database/rii-database-2021-07-18.zip\nDownloaded and extracting...\n\n\nWe search for materials in the refractiveindex.info database, and use only the part of the solar spectrum relevant for absorption in GaAs (in this case, there is no benefit to reducing absorption above the GaAs bandgap around 900 nm). We will only consider the weighted mean \\(R\\) in this case. Since all the layers in the structure are relatively thin compared to the wavelengths of light, we do a coherent calculation.\n\npageid_MgF2 = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0]\npageid_Ta2O5 = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0]\n\nGaAs = material(\"GaAs\")()\nMgF2 = material(str(pageid_MgF2), nk_db=True)()\nTa2O5 = material(str(pageid_Ta2O5), nk_db=True)()\n\nMgF2_thickness = np.linspace(50, 100, 20)\nTa2O5_thickness = np.linspace(30, 80, 20)\n\nweighted_R_matrix = np.zeros((len(MgF2_thickness), len(Ta2O5_thickness)))\n\nwavelengths_GaAs = wavelengths[wavelengths < 900e-9]\nnormalised_spectrum_GaAs = normalised_spectrum[wavelengths < 900e-9]\n\nopts.coherency_list = None\nopts.wavelength = wavelengths_GaAs\nopts.position = 20e-6\n\nWe now have two thicknesses to loop through; otherwise, the procedure is similar to the single-layer ARC example.\n\nfor i1, d_MgF2 in enumerate(MgF2_thickness):\n for j1, d_Ta2O5 in enumerate(Ta2O5_thickness):\n struct = SolarCell([Layer(si(d_MgF2, 'nm'), MgF2), Layer(si(d_Ta2O5, 'nm'), Ta2O5),\n Layer(si('20um'), GaAs)],\n substrate=Ag)\n solar_cell_solver(struct, 'optics', opts)\n R = struct.reflected\n\n weighted_R_matrix[i1, j1] = np.mean(R * normalised_spectrum_GaAs)\n\n# find the row and column indices of the minimum weighted R value\nri, ci = np.unravel_index(weighted_R_matrix.argmin(), weighted_R_matrix.shape)\n\nWe plot the total absorption (\\(1-R\\)) in the structure with the optimized ARC, and print the thicknesses of MgF\\(_2\\) and Ta\\(_2\\)O\\(_5\\) at which this occurs:\n\nplt.figure()\nplt.imshow(1-weighted_R_matrix, extent=[min(Ta2O5_thickness), max(Ta2O5_thickness),\n min(MgF2_thickness), max(MgF2_thickness)],\n origin='lower', aspect='equal')\nplt.plot(Ta2O5_thickness[ci], MgF2_thickness[ri], 'xk')\nplt.colorbar()\nplt.xlabel(\"Ta$_2$O$_5$ thickness (nm)\")\nplt.ylabel(\"MgF$_2$ thickness (nm)\")\nplt.show()\n\nprint(\"Minimum reflection occurs at MgF2 / Ta2O5 thicknesses of %.1f / %.1f nm \"\n % (MgF2_thickness[ri], Ta2O5_thickness[ci]))\n\nFor these two examples, where we are only trying to optimize one and two parameters respectively across a relatively small range, using a method (TMM) which executes quickly, brute force searching is possible. However, as we introduce more parameters, a wider parameter space, and slower simulation methods, it may no longer be computationally tractable; in that case, using for example differential evolution or other types of numerical optimization may be more appropriate (see this example)." + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#adding-custom-materials", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#adding-custom-materials", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "Adding custom materials", + "text": "Adding custom materials\nWe define our materials. Note that some of these are custom materials added to the database; we only need to do this once. We then define the front layer stack (i.e. all the materials which are on top of the Si, excluding Si itself, which will be the ‘bulk’ material) and the rear layer stack. Layer stacks are always defined starting with the layer closest to the top of the cell.\n\n# Can comment out this block after running once to add materials to the database\nfrom solcore.material_system import create_new_material\n\ncreate_new_material(\"Perovskite_CsBr_1p6eV\", \"data/CsBr10p_1to2_n_shifted.txt\",\n \"data/CsBr10p_1to2_k_shifted.txt\")\ncreate_new_material(\"ITO_lowdoping\", \"data/model_back_ito_n.txt\",\n \"data/model_back_ito_k.txt\")\ncreate_new_material(\"aSi_i\", \"data/model_i_a_silicon_n.txt\",\n \"data/model_i_a_silicon_k.txt\")\ncreate_new_material(\"aSi_p\", \"data/model_p_a_silicon_n.txt\",\n \"data/model_p_a_silicon_k.txt\")\ncreate_new_material(\"aSi_n\", \"data/model_n_a_silicon_n.txt\",\n \"data/model_n_a_silicon_k.txt\")\ncreate_new_material(\"C60\", \"data/C60_Ren_n.txt\",\n \"data/C60_Ren_k.txt\")\ncreate_new_material(\"IZO\", \"data/IZO_Ballif_rO2_10pcnt_n.txt\",\n \"data/IZO_Ballif_rO2_10pcnt_k.txt\")\n# Comment out until here\n\n\n# download_db()\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nSi = material(\"Si\")()\nAir = material(\"Air\")()\nMgF2 = material(str(MgF2_pageid), nk_db=True)()\nITO_back = material(\"ITO_lowdoping\")()\nPerovskite = material(\"Perovskite_CsBr_1p6eV\")()\nAg = material(str(Ag_pageid), nk_db=True)()\naSi_i = material(\"aSi_i\")()\naSi_p = material(\"aSi_p\")()\naSi_n = material(\"aSi_n\")()\nLiF = material(\"LiF\")()\nIZO = material(\"IZO\")()\nC60 = material(\"C60\")()\n\n# stack based on doi:10.1038/s41563-018-0115-4\nfront_materials = [\n Layer(100e-9, MgF2),\n Layer(110e-9, IZO),\n Layer(15e-9, C60),\n Layer(1e-9, LiF),\n Layer(440e-9, Perovskite),\n Layer(6.5e-9, aSi_n),\n Layer(6.5e-9, aSi_i),\n]\n\nback_materials = [Layer(6.5e-9, aSi_i), Layer(6.5e-9, aSi_p), Layer(240e-9, ITO_back)]\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n234 main MgF2 Rodriguez-de_Marcos main/MgF2/Rodriguez-de Marcos.yml 1 1 0.0299919 2.00146 960\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2 main Ag Jiang main/Ag/Jiang.yml 1 1 0.3 2.0 1701" }, { - "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#questions", - "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#questions", - "title": "Section 6b: Optimizing an ARC", - "section": "Questions", - "text": "Questions\n\nApart from varying the thickness of the layers, what else could we change?\nHow do we know where to start when designing an ARC (layer thickness/material)?" + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#defining-the-interfaces-and-structure", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#defining-the-interfaces-and-structure", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "Defining the interfaces and structure", + "text": "Defining the interfaces and structure\nNow we define our front and back surfaces, including interface_layers. We will use regular pyramids for both the front and back surface; these pyramids point out on both sides, but since the direction of the pyramids is defined relative to the front surface, we must set upright=True for the top surface and upright=False for the rear surface. We also gives the surfaces a name (used to save the lookup table data) and ask RayFlare to calculate the absorption profile in the 5th layer, which is the perovskite.\n\ntriangle_surf = regular_pyramids(\n elevation_angle=55,\n upright=True,\n size=1,\n interface_layers=front_materials,\n name=\"coh_front\",\n prof_layers=[5],\n)\n\ntriangle_surf_back = regular_pyramids(\n elevation_angle=55,\n upright=False,\n size=1,\n interface_layers=back_materials,\n name=\"Si_back\",\n coherency_list=[\"i\"] * len(back_materials),\n)\n\nNow we make our ray-tracing structure by combining the front and back surfaces, specifying the material in between (Si) and setting its width to 260 microns. In order to use the TMM lookuptables to calculate reflection/transmission/absorption probabilities we must also set use_TMM=True.\n\n%%capture\n\nrtstr_coh = rt_structure(\n textures=[triangle_surf, triangle_surf_back],\n materials=[Si],\n widths=[260e-6],\n incidence=Air,\n transmission=Ag,\n use_TMM=True,\n options=options,\n overwrite=True,\n save_location=\"current\",\n)\n\n# calculate:\nresult_coh = rtstr_coh.calculate(options)\n\nINFO: Pre-computing TMM lookup table(s)\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\n\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.WARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found." }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "", - "text": "In this first set of examples, we will look at simple planar Si solar cell.\nIn this script, we will look at the difference between Beer-Lambert absorption calculations, using the Fresnel equations for front-surface reflection, and using the transfer-matrix model.\nFirst, lets import some very commonly-used Python packages:\nimport numpy as np\nimport matplotlib.pyplot as plt\nNumpy is a Python library which adds supports for multi-dimensional data arrays and matrices, so it is very useful for storing and handling data. You will probably use it in every Solcore script you write. Here, it is imported under the alias ‘np’, which you will see used below. matplotlib is used for making plots, and is imported under the alias ‘plt’. Both the ‘np’ and ‘plt’ aliases are extremely commonly used in Python programming.\nNow, let’s import some things from Solcore (which will be explained as we use them):\nfrom solcore import material, si\nfrom solcore.solar_cell import SolarCell, Layer, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.interpolate import interp1d" + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#incoherent-calculation", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#incoherent-calculation", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "Incoherent calculation", + "text": "Incoherent calculation\nNow we define the same front surface and structure again, except now we will treat all the layers incoherently (i.e. no thin-film interference) in the TMM.\n\n%%capture\n\ntriangle_surf = regular_pyramids(\n elevation_angle=55,\n upright=True,\n size=1,\n interface_layers=front_materials,\n coherency_list=[\"i\"] * len(front_materials),\n name=\"inc_front\",\n prof_layers=[5],\n)\n\nrtstr_inc = rt_structure(\n textures=[triangle_surf, triangle_surf_back],\n materials=[Si],\n widths=[260e-6],\n incidence=Air,\n transmission=Ag,\n use_TMM=True,\n options=options,\n overwrite=True,\n save_location=\"current\",\n)\n\nresult_inc = rtstr_inc.calculate(options)\n\nINFO: Pre-computing TMM lookup table(s)\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\n\n\nNow we plot the results for reflection, transmission, and absorption per layer for both the coherent and incoherent cases.\n\npal = sns.color_palette(\"husl\", n_colors=len(front_materials) + len(back_materials) + 2)\n# create a colour palette\n\ncols = cycler(\"color\", pal)\n# set this as the default colour palette in matplotlib\n\nparams = {\n \"axes.prop_cycle\": cols,\n}\n\nplt.rcParams.update(params)\n\nfig = plt.figure(figsize=(8, 3.7))\nplt.subplot(1, 1, 1)\nplt.plot(wavelengths * 1e9, result_coh[\"R\"], \"-ko\", label=\"R\")\nplt.plot(wavelengths * 1e9, result_coh[\"T\"], mfc=\"none\", label=\"T\")\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_layer\"][:, 0], \"-o\", label='Si')\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_interface\"][0], \"-o\",\n label=[None, \"IZO\", \"C60\", None, \"Perovskite\", None, None])\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_interface\"][1], \"-o\",\n label=[None, None, \"ITO\"])\n\nplt.plot(wavelengths * 1e9, result_inc[\"R\"], \"--ko\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"T\"], mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_layer\"][:, 0], \"--o\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_interface\"][0], \"--o\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_interface\"][1], \"--o\", mfc=\"none\")\n\nplt.plot([300, 301], [0, 0], \"-k\", label=\"coherent\")\nplt.plot([300, 301], [0, 0], \"--k\", label=\"incoherent\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"R / A / T\")\nplt.ylim(0, 1)\nplt.xlim(300, 1200)\nplt.legend(bbox_to_anchor=(1.05, 1))\nplt.tight_layout()\nplt.show()\n\n\n\n\nCalculate and print the limiting short-circuit current per junction:\n\nJmax_Pero_coh = q*np.trapz(result_coh[\"A_per_interface\"][0][:,4]*AM15G.spectrum()[1],\n x=wavelengths)/10\nJmax_Si_coh = q*np.trapz(result_coh[\"A_per_layer\"][:, 0]*AM15G.spectrum()[1],\n x=wavelengths)/10\n\nprint(\"Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:\"\n \".2f}\".format(Jmax_Pero_coh, Jmax_Si_coh))\n\nJmax_Pero_inc = q*np.trapz(result_inc[\"A_per_interface\"][0][:,4]*AM15G.spectrum()[1],\n x=wavelengths)/10\nJmax_Si_inc = q*np.trapz(result_inc[\"A_per_layer\"][:, 0]*AM15G.spectrum()[1],\n x=wavelengths)/10\n\nprint(\"Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:\"\n \".2f}\".format(Jmax_Pero_inc, Jmax_Si_inc))\n\nLimiting short-circuit currents in coherent calculation (mA/cm2): 19.27 / 21.47\nLimiting short-circuit currents in coherent calculation (mA/cm2): 18.67 / 20.98" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-materials", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-materials", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Defining materials", - "text": "Defining materials\nTo define our solar cell, we first want to define some materials. Then we want to organise those materials into Layers, organise those layers into a Junction (or multiple Junctions, for a multi-junction cell, as we will see later), and then finally define a SolarCell with that Junction.\nFirst, let’s define a silicon material. Silicon, along with many other semiconductors, dielectrics, and metals common in solar cells, is included in Solcore’s database:\n\nSi = material(\"Si\")\n\nThis creates an instance of the Si material. However, to use this in a solar cell we need to do specify some more information, specifically the doping level and the minority carrier diffusion length. The ‘si’ function comes in handy here to convert all quantities to base units e.g. m, m\\(^{-3}\\)…\n\nSi_n = Si(Nd=si(\"1e21cm-3\"), hole_diffusion_length=si(\"10um\"))\nSi_p = Si(Na=si(\"1e16cm-3\"), electron_diffusion_length=si(\"400um\"))" + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#absorption-profiles", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#absorption-profiles", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "Absorption profiles", + "text": "Absorption profiles\nWe can also plot the absorption profiles, for wavelengths up to 800 nm, in the perovskite (since we asked the solver to calculate the profile in the perovskite layer above).\n\nwl_Eg = wavelengths < 800e-9\n\npal = sns.cubehelix_palette(sum(wl_Eg), reverse=True)\ncols = cycler(\"color\", pal)\nparams = {\n \"axes.prop_cycle\": cols,\n}\nplt.rcParams.update(params)\n\npos = np.arange(0, rtstr_coh.interface_layer_widths[0][4], options.depth_spacing*1e9)\n\nfig, (ax1, ax2) = plt.subplots(1,2)\nax1.plot(pos, result_coh[\"interface_profiles\"][0][wl_Eg].T)\nax1.set_ylim(0, 0.02)\nax1.set_xlabel(\"z (nm)\")\nax1.set_ylabel(\"a(z)\")\nax1.set_title(\"Coherent\")\nax2.plot(pos, result_inc[\"interface_profiles\"][0][wl_Eg].T)\nax2.set_ylim(0, 0.02)\nax2.yaxis.set_ticklabels([])\nax2.set_xlabel(\"z (nm)\")\nax2.set_title(\"Incoherent\")\nplt.show()\n\n\n\n\nWe see that, as expected, the coherent case shows interference fringes while the incoherent case does not. We can also plot the absorption profile in the Si (> 800 nm):\n\npos_bulk = pos = np.arange(0, rtstr_coh.widths[0]*1e6, options.depth_spacing_bulk*1e6)\n\nfig, (ax1, ax2) = plt.subplots(1,2)\nax1.semilogy(pos, result_coh[\"profile\"][~wl_Eg].T)\nax1.set_ylim(1e-8, 0.00015)\nax1.set_xlabel(\"z (um)\")\nax1.set_ylabel(\"a(z)\")\nax1.set_title(\"Coherent\")\nax2.semilogy(pos, result_inc[\"profile\"][~wl_Eg].T)\nax2.set_ylim(1e-8, 0.00015)\nax2.yaxis.set_ticklabels([])\nax2.set_xlabel(\"z (um)\")\nax2.set_title(\"Incoherent\")\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-layers", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-layers", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Defining layers", - "text": "Defining layers\nNow we define the emitter and base layers we will have in the solar cell; we specify their thickness, the material they are made of and the role they play within the cell (emitter or base). We create a junction which is a total of 200 \\(\\mu\\)m thick, with a 1 \\(\\mu\\)m junction depth.\n\nemitter_layer = Layer(width=si(\"1um\"), material=Si_n, role='emitter')\nbase_layer = Layer(width=si(\"199um\"), material=Si_p, role='base')\n\nNow we create the p-n junction using the layers defined above. We set kind=“DA” to tell Solcore to use the Depletion Approximation in the calculation:\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")" + "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#questions", + "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#questions", + "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "section": "Questions", + "text": "Questions\n\nWhy do you think the total absorption is slightly lower in the incoherent calculation?\nEven though the layers on top of the Si are not very thick compared to the wavelength, and they are the first thing encountered by the light, why might it make sense to treat them incoherently?\nCan you improve the current-matching (at least in terms of limiting currents) between the perovskite and the Si?" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#setting-user-options", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#setting-user-options", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Setting user options", - "text": "Setting user options\nWavelengths we want to use in the calculations; wavelengths between 300 and 1200 nm, at 200 evenly spaced intervals:\n\nwavelengths = si(np.linspace(300, 1200, 200), \"nm\")\n\nNote that here and above in defining the layers and materials we have used the “si()” function multiple times: you can use this to automatically convert quantities in other units to base SI units (e.g. nanometres to metres).\nNow we specify some options for running the calculation. Initially we will use the Beer-Lambert absorption law (\\(I(z) = I_0 e^{-\\alpha*z}\\)) to calculate the optics of the cell (“BL”). We set the wavelengths we want to use, and we set “recalculate_absorption” to True so that further down in the script when we try different optics methods, Solcore knows we want to re-calculate the optics of the cell rather than re-using previous results. We can specify the options in a Python format called a dictionary:\n\noptions = {\n \"recalculate_absorption\": True,\n \"optics_method\": \"BL\",\n \"wavelength\": wavelengths\n }" + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html", + "title": "Section 8: Textured Si", + "section": "", + "text": "This example is based on Figures 6, 7 and 8 from this paper. This compares three different structures, all based on a 200 micron thick slab of silicon with different surface textures:\nThe methods which will be used to calculate the redistribution matrices in each case are given in brackets. If case 1 and 2 are calculated first, then case 3 does not require the calculations of any additional matrices, since it will use the rear matrix from (1) and the front matrix from (2)." }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#running-cell-simulations", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#running-cell-simulations", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Running cell simulations", - "text": "Running cell simulations\nDefine the solar cell; in this case it is very simple and we just have a single junction:\n\nsolar_cell = SolarCell([Si_junction])\n\nNow we use solar_cell_solver to calculate the QE of the cell; we can ask solar_cell_solver to calculate ‘qe’, ‘optics’ or ‘iv’.\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nPLOT 1: plotting the QE in the Si junction, as well as the fraction of light absorbed in the junction and reflected. Because we are using the Beer-Lambert absorption law and we did not specify external reflectance, the reflectance = 0 over the whole wavelength range.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell[0].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell[0].layer_absorption, label='Absorptance (A)')\nplt.plot(wavelengths*1e9, 100*solar_cell.reflected, label='Reflectance (R)')\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.title(\"(1) QE of Si cell - Beer-Lambert absorption\")\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#setting-up", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#setting-up", + "title": "Section 8: Textured Si", + "section": "Setting up", + "text": "Setting up\nFirst, importing relevant packages:\n\nimport numpy as np\nimport os\n\n# solcore imports\nfrom solcore.structure import Layer\nfrom solcore import material\nfrom solcore import si\n\nfrom rayflare.structure import Interface, BulkLayer, Structure\nfrom rayflare.matrix_formalism import process_structure, calculate_RAT\nfrom rayflare.utilities import get_savepath\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.angles import theta_summary, make_angle_vector\nfrom rayflare.textures import regular_pyramids\nfrom rayflare.options import default_options\n\nimport matplotlib.pyplot as plt\nimport matplotlib as mpl\nimport seaborn as sns\nfrom sparse import load_npz\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\nSetting options (taking the default options for everything not specified explicitly):\n\nangle_degrees_in = 8 # same as in Fraunhofer paper\n\nwavelengths = np.linspace(900, 1200, 20) * 1e-9\n\nSi = material(\"Si\")()\nAir = material(\"Air\")()\n\noptions = default_options()\noptions.wavelength = wavelengths\noptions.theta_in = angle_degrees_in * np.pi / 180 # incidence angle (polar angle)\noptions.n_theta_bins = 30\noptions.c_azimuth = 0.25\noptions.n_rays = 5e4 # number of rays per wavelength in ray-tracing\noptions.project_name = \"OPTOS_comparison\"\noptions.orders = 60 # number of RCWA orders to use (more = better convergence, but slower)\noptions.pol = \"u\" # unpolarized light\noptions.only_incidence_angle = True\noptions.RCWA_method = \"Inkstone\"" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-fresnel", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-fresnel", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Adding front-surface reflection: Fresnel", - "text": "Adding front-surface reflection: Fresnel\nNow, to make this calculation a bit more realistic, there are a few things we could do. We could load some measured front surface reflectance from a file, or we could calculate the reflectance. To calculate the reflectance, there are many approaches we could take; we are going to explore two of them here.\nIf we assume the silicon is infinitely thick (or at least much thicker than the wavelengths of light we care about) then the reflectance will approach the reflectivity of a simple air/Si interface. We can calculate what this is using the Fresnel equation for reflectivity.\n\ndef calculate_R_Fresnel(incidence_n, transmission_n, wl):\n # return a function that gives the value of R (at normal incidence) at the input wavelengths\n\n Rs = np.abs((incidence_n - transmission_n)/(incidence_n + transmission_n))**2\n\n return interp1d(wl, Rs)\n\nThe transmission_n is the complex reflective index of Si at our wavelengths for the transmission medium (Si), which we can extract easily from the Si material object in Solcore. The incidence_n = 1 (air). Note that the function above is specifically for normal incidence.\n\ntrns_n = Si_n.n(wavelengths) + 1j*Si_n.k(wavelengths)\nreflectivity_fn = calculate_R_Fresnel(1, trns_n, wavelengths)\n\nWe define the solar cell again, with the same layers but now supplying the function for the externally-calculated reflectivity, and calculate the optics (reflection, absorption, transmission) again:\n\nsolar_cell_fresnel = SolarCell([Si_junction], reflectivity=reflectivity_fn)\n\nsolar_cell_solver(solar_cell_fresnel, 'optics', options)" + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#defining-the-structures", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#defining-the-structures", + "title": "Section 8: Textured Si", + "section": "Defining the structures", + "text": "Defining the structures\nNow, set up the grating basis vectors for the RCWA calculations and define the grating structure. These are squares, rotated by 45 degrees. The halfwidth is calculated based on the area fill factor of the etched pillars given in the paper.\n\nx = 1000\n\nd_vectors = ((x, 0), (0, x))\narea_fill_factor = 0.36\nhw = np.sqrt(area_fill_factor) * 500\n\nback_materials = [\n Layer(width=si(\"120nm\"), material=Si,\n geometry=[{\"type\": \"rectangle\", \"mat\": Air, \"center\": (x / 2, x / 2),\n \"halfwidths\": (hw, hw), \"angle\": 45}],\n )]\n\nNow we define the pyramid texture for the front surface in case (2) and (3) and make the four possible different surfaces: planar front and rear, front with pyramids, rear with grating. We specify the method to use to calculate the redistribution matrices in each case and create the bulk layer.\n\nsurf = regular_pyramids(elevation_angle=55, upright=False)\n\nfront_surf_pyramids = Interface(\n \"RT_Fresnel\",\n texture=surf,\n layers=[],\n name=\"inv_pyramids_front_\" + str(options[\"n_rays\"]),\n)\n\nfront_surf_planar = Interface(\"TMM\", layers=[], name=\"planar_front\")\n\nback_surf_grating = Interface(\n \"RCWA\",\n layers=back_materials,\n name=\"crossed_grating_back\",\n d_vectors=d_vectors,\n rcwa_orders=20,\n)\n\nback_surf_planar = Interface(\"TMM\", layers=[], name=\"planar_back\")\n\nbulk_Si = BulkLayer(200e-6, Si, name=\"Si_bulk\")\n\nNow we create the different structures and ‘process’ them (this will calculate the relevant matrices if necessary, or do nothing if it finds the matrices have previously been calculated and the files already exist). We don’t need to process the final structure because it will use matrices calculated for SC_fig6 and SC_fig7.\n\n%%capture\n\nSC_fig6 = Structure(\n [front_surf_planar, bulk_Si, back_surf_grating], incidence=Air, transmission=Air\n)\nSC_fig7 = Structure(\n [front_surf_pyramids, bulk_Si, back_surf_planar], incidence=Air, transmission=Air\n)\nSC_fig8 = Structure(\n [front_surf_pyramids, bulk_Si, back_surf_grating], incidence=Air, transmission=Air\n)\n\nprocess_structure(SC_fig6, options, save_location='current') # if you want to overwrite previous results, add overwrite=Trues\nprocess_structure(SC_fig7, options, save_location='current')\n\nINFO: Making matrix for planar surface using TMM for element 0 in structure\nINFO: Existing angular redistribution matrices found\nINFO: Existing angular redistribution matrices found\nINFO: RCWA calculation for element 2 in structure\nINFO: Existing angular redistribution matrices found\nINFO: Ray tracing with Fresnel equations for element 0 in structure\nINFO: Existing angular redistribution matrices found\nINFO: RT calculation for wavelength = 947.3684210526316 nm\nINFO: RT calculation for wavelength = 915.7894736842105 nm\nINFO: RT calculation for wavelength = 931.578947368421 nm\nINFO: RT calculation for wavelength = 994.7368421052631 nm\nINFO: RT calculation for wavelength = 1010.5263157894736 nm\nINFO: RT calculation for wavelength = 900.0000000000001 nm\nINFO: RT calculation for wavelength = 1026.3157894736842 nm\nINFO: RT calculation for wavelength = 978.9473684210526 nm\nINFO: RT calculation for wavelength = 1042.1052631578948 nm\nINFO: RT calculation for wavelength = 963.1578947368421 nm\nINFO: RT calculation for wavelength = 1057.8947368421054 nm\nINFO: RT calculation for wavelength = 1073.6842105263158 nm\nINFO: RT calculation for wavelength = 1089.4736842105265 nm\nINFO: RT calculation for wavelength = 1105.2631578947369 nm\nINFO: RT calculation for wavelength = 1121.0526315789475 nm\nINFO: RT calculation for wavelength = 1136.842105263158 nm\nINFO: RT calculation for wavelength = 1152.6315789473683 nm\nINFO: RT calculation for wavelength = 1168.421052631579 nm\nINFO: RT calculation for wavelength = 1184.2105263157896 nm\nINFO: RT calculation for wavelength = 1200.0000000000002 nm\nINFO: Making matrix for planar surface using TMM for element 2 in structure\n\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.WARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found." }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-tmm", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-tmm", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Adding front surface reflection: TMM", - "text": "Adding front surface reflection: TMM\nFinally, we do the same again but now instead of supplying the external reflectivity we ask set the optics_method to “TMM” (Transfer Matrix Method), to correctly calculate reflection at the front surface. We will learn more about the transfer matrix method later.\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")\n\nsolar_cell_TMM = SolarCell([Si_junction])\n\nSet some more options for the cell calculation:\n\noptions[\"optics_method\"] = \"TMM\"\nvoltages = np.linspace(-1.1, 1.1, 100)\noptions[\"light_iv\"] = True\noptions[\"mpp\"] = True\noptions[\"voltages\"] = voltages\noptions[\"internal_voltages\"] = voltages\n\nwe calculate the QE and the IV (we set the light_iv option to True; if we don’t do this, Solcore just calculates the dark IV). We also ask Solcore to find the maximum power point (mpp) so we can get the efficiency. Note that the sign convention used by Solcore means that an n-on-p cell with have a negative open-circuit voltage.\n\nsolar_cell_solver(solar_cell_TMM, 'iv', options)\nsolar_cell_solver(solar_cell_TMM, 'qe', options)\n\nPLOT 2: here we plot the reflection, transmission, and absorption calculated with the Fresnel equation defined above, and with the TMM solver in Solcore, showing that for this simple situation (no anti-reflection coating, thick Si junction) they are exactly equivalent.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, color='firebrick', label = \"R (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.reflected, '--', color='orangered', label = \"R (Fresnel)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.absorbed, color='dimgrey', label = \"A (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.absorbed, '--', color='lightgrey', label = \"A (Fresnel)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, color='blue', label = \"T (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.transmitted, '--', color='dodgerblue', label = \"T (Fresnel)\")\nplt.ylim(0, 100)\nplt.legend()\nplt.title(\"(2) Optics of Si cell - Fresnel/TMM\")\nplt.show()\n\nPLOT 3: As above for the TMM calculation, plotting the EQE as well, which will be slightly lower than the absorption because not all the carriers are collected. Comparing to plot (1), we can see we now have lower absorption due to the inclusion of front surface reflection, which is ~ 30% or more over the wavelength range of interest for a bare Si surface.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].layer_absorption, label='A')\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, label=\"R\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, label=\"T\")\nplt.title(\"(3) QE of Si cell (no ARC) - TMM\")\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.ylim(0, 100)\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#calculating-rat", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#calculating-rat", + "title": "Section 8: Textured Si", + "section": "Calculating R/A/T", + "text": "Calculating R/A/T\nThen we ask RayFlare to calculate the reflection, transmission and absorption through matrix multiplication, and get the required result out (absorption in the bulk) for each cell. We also load the results from the reference paper to compare them to the ones calculated with RayFlare.\n\n%%capture\n\nresults_fig6 = calculate_RAT(SC_fig6, options, save_location='current')\nresults_fig7 = calculate_RAT(SC_fig7, options, save_location='current')\nresults_fig8 = calculate_RAT(SC_fig8, options, save_location='current')\n\nRAT_fig6 = results_fig6[0]\nRAT_fig7 = results_fig7[0]\nRAT_fig8 = results_fig8[0]\n\nsim_fig6 = np.loadtxt(\"data/optos_fig6_sim.csv\", delimiter=\",\")\nsim_fig7 = np.loadtxt(\"data/optos_fig7_sim.csv\", delimiter=\",\")\nsim_fig8 = np.loadtxt(\"data/optos_fig8_sim.csv\", delimiter=\",\")\n\nINFO: After iteration 1: maximum power fraction remaining = 0.2955034746873003\nINFO: After iteration 2: maximum power fraction remaining = 0.24735134017097984\nINFO: After iteration 3: maximum power fraction remaining = 0.2163507471365699\nINFO: After iteration 4: maximum power fraction remaining = 0.19159890069625435\nINFO: After iteration 5: maximum power fraction remaining = 0.17095529483161526\nINFO: After iteration 6: maximum power fraction remaining = 0.15344062600062974\nINFO: After iteration 7: maximum power fraction remaining = 0.1384291294436452\nINFO: After iteration 8: maximum power fraction remaining = 0.12547688890130715\nINFO: After iteration 9: maximum power fraction remaining = 0.11424326382940328\nINFO: After iteration 10: maximum power fraction remaining = 0.10445704654991224\nINFO: After iteration 11: maximum power fraction remaining = 0.09589761402726735\nINFO: After iteration 12: maximum power fraction remaining = 0.0883830436692257\nINFO: After iteration 13: maximum power fraction remaining = 0.08176193170317834\nINFO: After iteration 14: maximum power fraction remaining = 0.07590744044348399\nINFO: After iteration 15: maximum power fraction remaining = 0.07071278644058707\nINFO: After iteration 16: maximum power fraction remaining = 0.06608771669781371\nINFO: After iteration 17: maximum power fraction remaining = 0.0619556977477\nINFO: After iteration 18: maximum power fraction remaining = 0.05825164073869242\nINFO: After iteration 19: maximum power fraction remaining = 0.05492004211445781\nINFO: After iteration 20: maximum power fraction remaining = 0.05191345343864926\nINFO: After iteration 21: maximum power fraction remaining = 0.04919121562204323\nINFO: After iteration 22: maximum power fraction remaining = 0.046718407568182026\nINFO: After iteration 23: maximum power fraction remaining = 0.044464969858259776\nINFO: After iteration 24: maximum power fraction remaining = 0.042404972041952975\nINFO: After iteration 25: maximum power fraction remaining = 0.04051599822739152\nINFO: After iteration 26: maximum power fraction remaining = 0.038778630473564266\nINFO: After iteration 27: maximum power fraction remaining = 0.03717601330766723\nINFO: After iteration 28: maximum power fraction remaining = 0.03569348574421198\nINFO: After iteration 29: maximum power fraction remaining = 0.034318269637635124\nINFO: After iteration 30: maximum power fraction remaining = 0.03303920518123784\nINFO: After iteration 31: maximum power fraction remaining = 0.031846525969740455\nINFO: After iteration 32: maximum power fraction remaining = 0.030731667346668046\nINFO: After iteration 33: maximum power fraction remaining = 0.029687102821135403\nINFO: After iteration 34: maximum power fraction remaining = 0.028706204208766243\nINFO: After iteration 35: maximum power fraction remaining = 0.027783121866022602\nINFO: After iteration 36: maximum power fraction remaining = 0.026912681975976842\nINFO: After iteration 37: maximum power fraction remaining = 0.026090298330296663\nINFO: After iteration 38: maximum power fraction remaining = 0.025311896455915424\nINFO: After iteration 39: maximum power fraction remaining = 0.024573848270729514\nINFO: After iteration 40: maximum power fraction remaining = 0.023872915732924625\nINFO: After iteration 41: maximum power fraction remaining = 0.023206202183040037\nINFO: After iteration 42: maximum power fraction remaining = 0.022571110274614448\nINFO: After iteration 43: maximum power fraction remaining = 0.02196530555470288\nINFO: After iteration 44: maximum power fraction remaining = 0.021386684895000417\nINFO: After iteration 45: maximum power fraction remaining = 0.02083334909208419\nINFO: After iteration 46: maximum power fraction remaining = 0.020303579054949197\nINFO: After iteration 47: maximum power fraction remaining = 0.019795815082497975\nINFO: After iteration 48: maximum power fraction remaining = 0.019308638805378607\nINFO: After iteration 49: maximum power fraction remaining = 0.018840757427562815\nINFO: After iteration 50: maximum power fraction remaining = 0.018390989954995544\nINFO: After iteration 51: maximum power fraction remaining = 0.01795825514292941\nINFO: After iteration 52: maximum power fraction remaining = 0.017541560931354713\nINFO: After iteration 53: maximum power fraction remaining = 0.017139995170233478\nINFO: After iteration 54: maximum power fraction remaining = 0.016752717463871532\nINFO: After iteration 55: maximum power fraction remaining = 0.016378951987414226\nINFO: After iteration 56: maximum power fraction remaining = 0.01601798114871917\nINFO: After iteration 57: maximum power fraction remaining = 0.01566913998624118\nINFO: After iteration 58: maximum power fraction remaining = 0.015331811208484045\nINFO: After iteration 59: maximum power fraction remaining = 0.015005420793388834\nINFO: After iteration 60: maximum power fraction remaining = 0.014689434077044667\nINFO: After iteration 61: maximum power fraction remaining = 0.014383352270584045\nINFO: After iteration 62: maximum power fraction remaining = 0.014086709352282257\nINFO: After iteration 63: maximum power fraction remaining = 0.013799069288907425\nINFO: After iteration 64: maximum power fraction remaining = 0.013520023546425057\nINFO: After iteration 65: maximum power fraction remaining = 0.013249188855386125\nINFO: After iteration 66: maximum power fraction remaining = 0.012986205200837965\nINFO: After iteration 67: maximum power fraction remaining = 0.01273073401049334\nINFO: After iteration 68: maximum power fraction remaining = 0.012482456518260769\nINFO: After iteration 69: maximum power fraction remaining = 0.012241072283152531\nINFO: After iteration 70: maximum power fraction remaining = 0.012006297846108658\nINFO: After iteration 71: maximum power fraction remaining = 0.011777865509460205\nINFO: After iteration 72: maximum power fraction remaining = 0.011555522225649468\nINFO: After iteration 73: maximum power fraction remaining = 0.011339028583468616\nINFO: After iteration 74: maximum power fraction remaining = 0.011128157881506017\nINFO: After iteration 75: maximum power fraction remaining = 0.010922695279730358\nINFO: After iteration 76: maximum power fraction remaining = 0.010722437021222662\nINFO: After iteration 77: maximum power fraction remaining = 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After iteration 10: maximum power fraction remaining = 0.21840401464945428\nINFO: After iteration 11: maximum power fraction remaining = 0.19583800968944132\nINFO: After iteration 12: maximum power fraction remaining = 0.17344166256983365\nINFO: After iteration 13: maximum power fraction remaining = 0.15530793273842505\nINFO: After iteration 14: maximum power fraction remaining = 0.13789731413300393\nINFO: After iteration 15: maximum power fraction remaining = 0.12335775256871925\nINFO: After iteration 16: maximum power fraction remaining = 0.10971979419070547\nINFO: After iteration 17: maximum power fraction remaining = 0.09808315863565356\nINFO: After iteration 18: maximum power fraction remaining = 0.08734240233208478\nINFO: After iteration 19: maximum power fraction remaining = 0.0780417094944075\nINFO: After iteration 20: maximum power fraction remaining = 0.06955082453103606\nINFO: After iteration 21: maximum power fraction remaining = 0.06212436763500962\nINFO: After iteration 22: maximum power fraction remaining = 0.05539475523478134\nINFO: After iteration 23: maximum power fraction remaining = 0.04946888092506737\nINFO: After iteration 24: maximum power fraction remaining = 0.04412586351647957\nINFO: After iteration 25: maximum power fraction remaining = 0.03939959150147595\nINFO: After iteration 26: maximum power fraction remaining = 0.035152466756422904\nINFO: After iteration 27: maximum power fraction remaining = 0.03138417210722542\nINFO: After iteration 28: maximum power fraction remaining = 0.02800549474394666\nINFO: After iteration 29: maximum power fraction remaining = 0.025001662835576158\nINFO: After iteration 30: maximum power fraction remaining = 0.022336528444980536\nINFO: After iteration 31: maximum power fraction remaining = 0.019970345021341422\nINFO: After iteration 32: maximum power fraction remaining = 0.017850251895806992\nINFO: After iteration 33: maximum power fraction remaining = 0.01595879897926111\nINFO: After iteration 34: maximum power fraction remaining = 0.014265341950741119\nINFO: After iteration 35: maximum power fraction remaining = 0.012753479233909213\nINFO: After iteration 36: maximum power fraction remaining = 0.01140055750519969\nINFO: After iteration 37: maximum power fraction remaining = 0.010192162654957652\nINFO: After iteration 38: maximum power fraction remaining = 0.009111167021520275\nINFO: After iteration 1: maximum power fraction remaining = 0.7673983435875205\nINFO: After iteration 2: maximum power fraction remaining = 0.6372585557661392\nINFO: After iteration 3: maximum power fraction remaining = 0.5414879294120498\nINFO: After iteration 4: maximum power fraction remaining = 0.46198278041320184\nINFO: After iteration 5: maximum power fraction remaining = 0.39433973016867285\nINFO: After iteration 6: maximum power fraction remaining = 0.33676090679898063\nINFO: After iteration 7: maximum power fraction remaining = 0.28761095693740824\nINFO: After iteration 8: maximum power fraction remaining = 0.2456437571054792\nINFO: After iteration 9: maximum power fraction remaining = 0.20980167029275584\nINFO: After iteration 10: maximum power fraction remaining = 0.17918990119472689\nINFO: After iteration 11: maximum power fraction remaining = 0.15304474763794992\nINFO: After iteration 12: maximum power fraction remaining = 0.13071442653724563\nINFO: After iteration 13: maximum power fraction remaining = 0.11164227220874255\nINFO: After iteration 14: maximum power fraction remaining = 0.09535288871681696\nINFO: After iteration 15: maximum power fraction remaining = 0.08144024158383945\nINFO: After iteration 16: maximum power fraction remaining = 0.06955754767323634\nINFO: After iteration 17: maximum power fraction remaining = 0.059408621208283954\nINFO: After iteration 18: maximum power fraction remaining = 0.05074049344792487\nINFO: After iteration 19: maximum power fraction remaining = 0.04333710537780831\nINFO: After iteration 20: maximum power fraction remaining = 0.03701392274486675\nINFO: After iteration 21: maximum power fraction remaining = 0.03161333608191989\nINFO: After iteration 22: maximum power fraction remaining = 0.02700073227373622\nINFO: After iteration 23: maximum power fraction remaining = 0.02306113917976735\nINFO: After iteration 24: maximum power fraction remaining = 0.0196963598948841\nINFO: After iteration 25: maximum power fraction remaining = 0.016822525118259837\nINFO: After iteration 26: maximum power fraction remaining = 0.014368002659713427\nINFO: After iteration 27: maximum power fraction remaining = 0.012271611959434315\nINFO: After iteration 28: maximum power fraction remaining = 0.010481099123494625\nINFO: After iteration 29: maximum power fraction remaining = 0.008951834461485581\n\n\nFinally, we use TMM to calculate the absorption in a structure with a planar front and planar rear, as a reference.\n\nstruc = tmm_structure([Layer(si(\"200um\"), Si)], incidence=Air, transmission=Air)\noptions.coherent = False\noptions.coherency_list = [\"i\"]\nRAT = tmm_structure.calculate(struc, options)" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-an-arc", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-an-arc", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Adding an ARC", - "text": "Adding an ARC\nThe reflectance of bare Si is very high. Let’s try adding a simple anti-reflection coating (ARC), a single layer of silicon nitride (Si\\(_3\\)N\\(_4\\)):\n\nSiN = material(\"Si3N4\")()\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")\n\nsolar_cell_TMM_ARC = SolarCell([Layer(width=si(75, \"nm\"), material=SiN), Si_junction])\n\nsolar_cell_solver(solar_cell_TMM_ARC, 'qe', options)\nsolar_cell_solver(solar_cell_TMM_ARC, 'iv', options)\n\nPLOT 4: Absorption, EQE, reflection and transmission for the cell with a simple one-layer ARC. We see the reflection is significantly reduced from the previous plot leading to higher absorption/EQE.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].layer_absorption, label='A')\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.reflected, label=\"R\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.transmitted, label=\"T\")\nplt.legend()\nplt.title(\"(4) QE of Si cell (ARC) - TMM\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.ylim(0, 100)\nplt.show()\n\nPLOT 5: Compare the IV curves of the cells with and without an ARC. The efficiency is also shown on the plot. Note that because we didn’t specify a light source, Solcore will assume we want to use AM1.5G; in later examples we will set the light source used for light IV simulations explicitly.\n\nplt.figure()\nplt.plot(-voltages, solar_cell_TMM[0].iv(voltages)/10, label=\"No ARC\")\nplt.plot(-voltages, solar_cell_TMM_ARC[1].iv(voltages)/10, label=\"75 nm SiN\")\nplt.text(0.5, 1.02*abs(solar_cell_TMM.iv[\"Isc\"])/10, str(round(solar_cell_TMM.iv[\"Eta\"]*100,\n 1)) + ' %')\nplt.text(0.5, 1.02*abs(solar_cell_TMM_ARC.iv[\"Isc\"])/10, str(round(solar_cell_TMM_ARC\n .iv[\"Eta\"]*100, 1)) + ' %')\nplt.ylim(0, 38)\nplt.xlim(-0.8, 0.8)\nplt.legend()\nplt.xlabel(\"V (V)\")\nplt.ylabel(r\"J (mA/cm$^2$)\")\nplt.title(\"(5) IV curve of Si cell with and without ARC\")\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#plotting", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#plotting", + "title": "Section 8: Textured Si", + "section": "Plotting", + "text": "Plotting\nPlot everything together, including data from the reference paper for comparison:\n\npalhf = sns.color_palette(\"hls\", 4)\n\nfig = plt.figure()\nplt.plot(sim_fig6[:, 0], sim_fig6[:, 1],\n \"--\", color=palhf[0], label=\"OPTOS - rear grating (1)\")\nplt.plot(wavelengths * 1e9, RAT_fig6[\"A_bulk\"][0],\n \"-o\", color=palhf[0], label=\"RayFlare - rear grating (1)\", fillstyle=\"none\")\nplt.plot(sim_fig7[:, 0], sim_fig7[:, 1],\n \"--\", color=palhf[1], label=\"OPTOS - front pyramids (2)\",)\nplt.plot(wavelengths * 1e9, RAT_fig7[\"A_bulk\"][0],\n \"-o\", color=palhf[1], label=\"RayFlare - front pyramids (2)\", fillstyle=\"none\")\nplt.plot(sim_fig8[:, 0], sim_fig8[:, 1],\n \"--\", color=palhf[2], label=\"OPTOS - grating + pyramids (3)\")\nplt.plot(wavelengths * 1e9, RAT_fig8[\"A_bulk\"][0],\n \"-o\", color=palhf[2],label=\"RayFlare - grating + pyramids (3)\", fillstyle=\"none\",)\nplt.plot(wavelengths * 1e9, RAT[\"A_per_layer\"][:, 0], \"-k\", label=\"Planar\")\nplt.legend(loc=\"lower left\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorption in Si\")\nplt.xlim([900, 1200])\nplt.ylim([0, 1])\nplt.show()\n\n\n\n\nWe can see good agreement between the reference values and our calculated values. The structure with rear grating also behaves identically to the planar TMM reference case at the short wavelengths where front surface reflection dominates the result, as expected. Clearly, the pyramids perform much better overall, giving a large boost in the absorption at long wavelengths and also reducing the reflection significantly at shorter wavelengths. Plotting reflection and transmission emphasises this:\n\nfig = plt.figure()\nplt.plot(wavelengths * 1e9,RAT_fig6[\"R\"][0],\n \"-o\", color=palhf[0], label=\"RayFlare - rear grating (1)\", fillstyle=\"none\")\nplt.plot(wavelengths * 1e9, RAT_fig7[\"R\"][0],\n \"-o\", color=palhf[1], label=\"RayFlare - front pyramids (2)\", fillstyle=\"none\")\nplt.plot(wavelengths * 1e9, RAT_fig8[\"R\"][0],\n \"-o\", color=palhf[2], label=\"RayFlare - grating + pyramids (3)\", fillstyle=\"none\")\n\nplt.plot(wavelengths * 1e9, RAT_fig6[\"T\"][0], \"--o\", color=palhf[0])\nplt.plot(wavelengths * 1e9, RAT_fig7[\"T\"][0], \"--o\", color=palhf[1])\nplt.plot(wavelengths * 1e9, RAT_fig8[\"T\"][0], \"--o\", color=palhf[2])\n\n# these are just to create the legend:\nplt.plot(-1, 0, \"k-o\", label=\"R\", fillstyle=\"none\")\nplt.plot(-1, 0, \"k--o\", label=\"T\")\n\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Reflected/transmitted fraction\")\nplt.xlim([900, 1200])\nplt.ylim([0, 0.6])\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#conclusions", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#conclusions", - "title": "Section 5a: Planar Si solar cell using DA", - "section": "Conclusions", - "text": "Conclusions\nWe see that the cell with an ARC has a significantly higher \\(J_{sc}\\), and a slightly higher \\(V_{oc}\\), than the bare Si cell. In reality, most Si cells have a textured surface rather than a planar surface with an ARC; this will be discussed later in the course.\nOverall, some things we can take away from the examples in this script:\n\nThe Beer-Lambert law is a very simple way to calculate absorption in a cell, but won’t take into account important effects such as front-surface reflection or the effects of anti-reflection coatings.\nUsing the transfer-matrix method (TMM), we can account for front surface reflection and interference effects which make e.g. ARCs effective. In the simple situation of a thick cell without any front surface layers, it is equivalent to simply calculating the reflection with the Fresnel equations and assuming Beer-Lambert absorption in the cell.\nAdding a simple, one-layer ARC can significantly reduce front-surface reflection for a single-junction cell, leading to improved short-circuit current. To correctly account for interference in this layer, which is what causes its anti-reflective properties, we most use the transfer-matrix method (TMM) optical solver." + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#redistribution-matrices", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#redistribution-matrices", + "title": "Section 8: Textured Si", + "section": "Redistribution matrices", + "text": "Redistribution matrices\nPlot the redistribution matrix for the rear grating (summed over azimuthal angles) at 1100 nm:\n\ntheta_intv, phi_intv, angle_vector = make_angle_vector(\n options[\"n_theta_bins\"], options[\"phi_symmetry\"], options[\"c_azimuth\"])\n\npath = get_savepath(save_location='current', project_name=options.project_name)\nsprs = load_npz(os.path.join(path, SC_fig6[2].name + \"frontRT.npz\"))\n\nwl_to_plot = 1100e-9\nwl_index = np.argmin(np.abs(wavelengths - wl_to_plot))\n\nfull = sprs[wl_index].todense()\n\nsummat = theta_summary(full, angle_vector, options[\"n_theta_bins\"], \"front\")\nsummat_r = summat[: options[\"n_theta_bins\"], :]\nsummat_r = summat_r.rename({ r\"$\\theta_{in}$\": r\"$\\sin(\\theta_{in})$\",\n r\"$\\theta_{out}$\": r\"$\\sin(\\theta_{out})$\"})\n\nsummat_r = summat_r.assign_coords({r\"$\\sin(\\theta_{in})$\": np.sin(summat_r.coords[r\"$\\sin(\\theta_{in})$\"]).data,\n r\"$\\sin(\\theta_{out})$\": np.sin(summat_r.coords[r\"$\\sin(\\theta_{out})$\"]).data})\n\npalhf = sns.cubehelix_palette(256, start=0.5, rot=-0.9)\npalhf.reverse()\nseamap = mpl.colors.ListedColormap(palhf)\n\nfig = plt.figure()\nax = plt.subplot(111)\nax = summat_r.plot.imshow(ax=ax, cmap=seamap, vmax=0.3)\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#questions", - "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#questions", - "title": "Section 5a: Planar Si solar cell using DA", + "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#questions", + "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#questions", + "title": "Section 8: Textured Si", "section": "Questions", - "text": "Questions\n\nWhich parameters could we change which would affect the EQE and/or IV of the cell?\nWhy can’t we just use the Fresnel equations to calculate the effect of an anti-reflection coating?" + "text": "Questions\n\nIf you can add only one of the textures (pyramids or a grating), which one is better? Why?\nWhy do the structures with a front-surface texture have high reflection at long wavelengths? The anti-reflection properties of pyramids (treated with ray optics) are mostly independent of the wavelength, so why does apparent reflection increase near the bandgap of Si?\nCan you explain any of the features present in the angular redistribution matrix of the rear grating surface?" }, { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html", + "title": "Section 7: Planar GaInP//Si tandem cell", "section": "", - "text": "SPCTRAL 2 is a clear-sky spectral irradiance model that accounts for variations in the atmospheric conditions and air-mass. Developed at NREL in 1984, it generates terrestrial spectral irradiance from 300nm to 4um with a resolution of approximately 10nm.\n“Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres”, R. Bird, C. Riordan, December 1984\nThe Solcore implementation accomodates the following inputs (stated values are defaults):\nAll the inputs are numeric other than the aod_model whose options are: ‘rural’, ‘urban’, ‘maritime’ and ‘tropospheric’." + "text": "This example is partly based on the structure presented in this paper, but with planar interfaces instead of a textured Si surface. This is a four-terminal GaInP/Si device which uses an epoxy and glass to bond the two cells together mechanically. First, we will do optical-only calculations to look at the effect of an intermediate anti-reflection coating (on top of the epoxy/glass) on the absorption in the bottom Si cell, and then we will use the results of the optical calculation to do a device simulation and calculate external quantum efficiency and current-voltage under AM1.5G.\nNote: the paper linked above has a GaInP/AlGaInP heterojunction as the top junction. Because we do not have AlGaInP built in to Solcore’s database, this is replaced by a GaInP homojunction in this example.\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver, default_options\nfrom solcore.solar_cell import SolarCell\nfrom solcore.light_source import LightSource\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/registries.py:73: UserWarning: Optics solver 'RCWA' will not be available. An installation of S4 has not been found.\n warn(" }, { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#comparison-between-spctral2-with-default-parameters-and-am1.5g", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html#comparison-between-spctral2-with-default-parameters-and-am1.5g", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", - "section": "Comparison between SPCTRAL2 with default parameters and AM1.5G", - "text": "Comparison between SPCTRAL2 with default parameters and AM1.5G\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\n\n# Setup the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 #wl contains the x-ordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl*1e9, version='AM1.5g')\n\nspc2default = LightSource(source_type='SPECTRAL2', x=wl * 1e9)\n\nplt.figure()\nplt.title(\"Comparing SPCTRAL 2 vs AM1.5G\")\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()" - }, - { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#adjusting-the-precipitable-water-value", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html#adjusting-the-precipitable-water-value", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", - "section": "Adjusting the precipitable water value", - "text": "Adjusting the precipitable water value\nThe default SPCTRAL2 parameters results in almost no atmospheric absorption. This suggests the precipitable water column thickness is much too low, the default is 0.00142 cm. Let’s increase that value to 1cm to roughly match AM1.5G:\n\nspc2pc = LightSource(source_type='SPECTRAL2', precipwater=1.0, x=wl * 1e9)\n\nplt.figure()\nplt.title('Comparions between SPCTRAL2 defaults, 1cm precipitable water & AM1.5G')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')\nplt.plot(*spc2pc.spectrum(wl*1e9), label='PC water')\n\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()" + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#defining-materials-layers-and-junctions", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#defining-materials-layers-and-junctions", + "title": "Section 7: Planar GaInP//Si tandem cell", + "section": "Defining materials, layers and junctions", + "text": "Defining materials, layers and junctions\nThe paper referenced above uses a double-layer anti-reflection coating (ARC) made of MgF\\(_2\\) and ZnS. As in the previous example, we use the interface to the refractiveindex.info database to select optical constant data from specific sources, and define Solcore materials using this data. The III-V materials are taken from Solcore’s own material database.\nNote that for the epoxy/glass layer, we use only a single material (BK7 glass). The epoxy and glass used in the paper have the same refractive index (n = 1.56), so we can use a single material with an appropriate refractive index to represent them.\n\ndownload_db(confirm=True) # uncomment to download database\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaking request to https://refractiveindex.info/download/database/rii-database-2021-07-18.zip\nDownloaded and extracting...\nWrote /var/folders/wh/w5k56r_927j4yp3mh91bggfc0000gq/T/tmpxl4nacr8/database from https://refractiveindex.info/download/database/rii-database-2021-07-18.zip\nLOG: 2746,other,PtAl2,Chen : Bad Material YAML File.\n***Wrote SQLite DB on /Users/z3533914/.solcore/nk/nk.db\n\n\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/material_data/refractiveindex_info_DB/dbmaterial.py:278: RuntimeWarning: invalid value encountered in sqrt\n n = numpy.sqrt(nsq)\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/material_data/refractiveindex_info_DB/dbmaterial.py:299: RuntimeWarning: invalid value encountered in sqrt\n n = numpy.sqrt(n)\n\n\n\n%%capture\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nZnS_pageid = search_db(os.path.join(\"ZnS\", \"Querry\"))[0][0];\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nZnS = material(str(ZnS_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nBSF = material(\"AlGaAs\")(Al=0.5)\n\nepoxy = material(\"BK7\")()\n\nFor the Si cell, the front surface has both a low-index and high-index SiN\\(x\\) layer. The rear surface uses Al\\(2\\)O\\(3\\), and the cell has Al at the rear surface.\n\nSiOx = material(\"SiO\")()\nSiN_191_pageid = search_db(\"Vogt-1.91\")[0][0];\nSiN_213_pageid = search_db(\"Vogt-2.13\")[0][0];\nSiN_191 = material(str(SiN_191_pageid), nk_db=True)();\nSiN_213 = material(str(SiN_213_pageid), nk_db=True)();\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2816 other SiN Vogt-1.91 anti-reflective coatings/SiN/Vogt-1.91.yml 1 1 0.25 1.7 146\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2818 other SiN Vogt-2.13 anti-reflective coatings/SiN/Vogt-2.13.yml 1 1 0.25 1.7 146\n\n\nWe now define the layers used in the top cell stack: the ARC and window layer for the top cell, and the GaInP junction itself. The ARC and window layers are not involved in the electrical calculation using the depletion approximation, so they are defined as simple layers, while the GaInP emitter and base are defined as part of a Junction object.\n\nARC_window = [\n Layer(97e-9, MgF2),\n Layer(41e-9, ZnS),\n Layer(17e-9, window, role=\"window\"),\n]\n\nGaInP_junction = Junction([\n Layer(200e-9, GaInP(In=0.50, Nd=si(\"2e18cm-3\"), hole_diffusion_length=si(\"300nm\")),\n role=\"emitter\"),\n Layer(750e-9, GaInP(In=0.50, Na=si(\"1e17cm-3\"), electron_diffusion_length=si(\n \"800nm\")),\n role=\"base\"),\n Layer(500e-9, BSF, role=\"bsf\")], kind=\"DA\", sn=1, sp=1\n)\n\nWe now define the spacer layer, with and without a ZnS anti-reflection coating, so we can compare their performance in the cell stack. Note that we set the epoxy thickness here to be 10 microns, although the real thickness is much higher - this is because the epoxy/glass is not absorbing at the wavelengths which are able to reach it (which are not absorbed in the GaInP top cell), and we will treat it incoherently (no thin-film interference), so the exact thickness does not matter.\n\nspacer = [\n Layer(82e-9, ZnS),\n Layer(10e-6, epoxy), # real thickness is much higher, but since this layer is\n # non-absorbing at the relevant wavelength (> 650 nm) and treated incoherently,\n # this does not matter\n]\n\nspacer_noARC = [\n Layer(10e-6, epoxy),\n]\n\nNow we define the layer stacks for the Si cell, including the front SiO\\(_x\\)/SiN\\(_x\\) stack, the junction itself, and the back dielectric layers.\n\nSi_front_surf = [\n Layer(100e-9, SiOx),\n Layer(70e-9, SiN_191),\n Layer(15e-9, SiN_213),\n ]\n\nSi_junction = Junction([\n Layer(1e-6, Si(Nd=si(\"2e18cm-3\"), hole_diffusion_length=2e-6), role=\"emitter\"),\n Layer(150e-6, Si(Na=si(\"2e15cm-3\"), electron_diffusion_length=150e-6), role=\"base\"),\n], kind=\"DA\", sn=0.1, sp=0.1)\n\nSi_back_surf = [\n Layer(15e-9, Al2O3),\n Layer(120e-9, SiN_191)\n]" }, { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#atmospheric-turbidity", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html#atmospheric-turbidity", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", - "section": "Atmospheric Turbidity", - "text": "Atmospheric Turbidity\nThe short wavelength is attenuated which is likely due to a high level of aerosol loading in the default spectrum. To address this atmospheric turbidity can be reduced to around 0.05.\n\nspc2high = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2, x=wl * 1e9)\nspc2med = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.1, x=wl * 1e9)\nspc2low = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.05, x=wl * 1e9)\n\nplt.figure()\nplt.title('Spectral Irradiance Plotted for Different Aersol Models')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2high.spectrum(wl*1e9), label='Turbidity = 0.2')\nplt.plot(*spc2med.spectrum(wl*1e9), label='Turbidity = 0.1')\nplt.plot(*spc2low.spectrum(wl*1e9), label='Turbidity = 0.05')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()" + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#comparing-the-optical-performance-with-and-without-intermediate-arc", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#comparing-the-optical-performance-with-and-without-intermediate-arc", + "title": "Section 7: Planar GaInP//Si tandem cell", + "section": "Comparing the optical performance with and without intermediate ARC", + "text": "Comparing the optical performance with and without intermediate ARC\nNow we will run the calculation. We will treat some of the layers (those above the epoxy) with a coherent TMM calculation, and the epoxy and the layers below it using incoherent TMM. We will discuss the difference this makes, why this is important, and when to use coherent and incoherent layers.\n\nn_coh_layers = len(ARC_window + GaInP_junction)\nn_inc_layers = 1 + len(Si_front_surf + Si_junction + Si_back_surf)\n\nwl = np.linspace(300, 1200, 600) * 1e-9\n\noptions = default_options\noptions.recalculate_absorption = True\noptions.wavelength = wl\noptions.optics_method = 'TMM'\n\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl*1e9,\n output_units=\"photon_flux_per_nm\")\n\nNow we define two versions of the cell for optical calculations, without and with the ZnS anti-reflection coating on the epoxy. Note that we also set the substrate for the calculation (aluminium) here.\n\ncell_no_ARC = SolarCell(\n ARC_window + GaInP_junction + spacer_noARC + Si_front_surf + Si_junction +\n Si_back_surf,\n substrate=Al,\n)\n\ncell_with_ARC = SolarCell(\n ARC_window + GaInP_junction + spacer + Si_front_surf + Si_junction + Si_back_surf,\n substrate=Al,\n)\n\nWe set the appropriate coherency list for the structure (a list with entry ‘c’ for a coherent layer or ‘i’ for an incoherent layer), and solve for the cell optics of the cell without the intermediate ARC. We get the total absorption in the GaInP and Si junctions.\n\n%%capture\n\noptions.coherency_list = ['c']*(n_coh_layers) + ['i']*n_inc_layers\nsolar_cell_solver(cell_no_ARC, \"optics\", options)\n\nGaInP_A = cell_no_ARC[3].layer_absorption + cell_no_ARC[4].layer_absorption\nSi_A = cell_no_ARC[10].layer_absorption + cell_no_ARC[11].layer_absorption\n\nTreating layer(s) 11 incoherently\nCalculating RAT...\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/ZnS/Querry.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/ZnS/Querry.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial anti-reflective coatings/SiN/Vogt-1.91.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial anti-reflective coatings/SiN/Vogt-1.91.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial anti-reflective coatings/SiN/Vogt-2.13.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial anti-reflective coatings/SiN/Vogt-2.13.yml loaded.\nCalculating absorption profile...\n\n\nAs above, but for the cell with an intermediate ARC:\n\noptions.coherency_list = [\"c\"]*(n_coh_layers + 1) + ['i']*n_inc_layers\nsolar_cell_solver(cell_with_ARC, \"optics\", options)\n\nGaInP_A_ARC = cell_with_ARC[3].layer_absorption + cell_with_ARC[4].layer_absorption\nSi_A_ARC = cell_with_ARC[11].layer_absorption + cell_with_ARC[12].layer_absorption\n\nTreating layer(s) 12 incoherently\nCalculating RAT...\nCalculating absorption profile...\n\n\nNow we plot the GaInP and Si absorption, and the reflectance of the whole structure, for both cells:\n\nplt.figure()\n\nplt.plot(wl * 1e9, GaInP_A_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, Si_A_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, cell_with_ARC.reflected, '-b', label=\"R\")\n\nplt.plot(wl * 1e9, GaInP_A, \"--k\", label=\"No middle ARC\")\nplt.plot(wl * 1e9, Si_A, \"--r\")\nplt.plot(wl * 1e9, cell_no_ARC.reflected, '--b')\n\nplt.legend(loc='upper right')\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance/Reflectance\")\nplt.tight_layout()\nplt.show()\n\n\n\n\nWe see that the cell without an ARC on the epoxy shows much stronger interference fringes (due to the thickness of the top stack), and higher reflectance overall in the long-wavelength region (at short wavelengths, light is absorbed before it is able to reach the epoxy at all). Before doing an actual electrical calculation, we will calculate the limiting current in both of the sub-cells (assuming all the generated charge carriers can be collected):\n\nJ_GaInP = q*np.trapz(GaInP_A * AM15G.spectrum()[1], wl*1e9)\nJ_Si = q*np.trapz(Si_A * AM15G.spectrum()[1], wl*1e9)\n\nprint(\"Limiting short-circuit currents without ARC (mA/cm2): {:.1f} / {:.1f}\".format(\n J_GaInP/10, J_Si/10))\n\nJ_GaInP_ARC = q*np.trapz(GaInP_A_ARC * AM15G.spectrum()[1], wl*1e9)\nJ_Si_ARC = q*np.trapz(Si_A_ARC * AM15G.spectrum()[1], wl*1e9)\n\nprint(\"Limiting short-circuit currents with ARC (mA/cm2): {:.1f} / {:.1f}\".format(\n J_GaInP_ARC/10, J_Si_ARC/10))\n\nLimiting short-circuit currents without ARC (mA/cm2): 16.4 / 15.5\nLimiting short-circuit currents with ARC (mA/cm2): 16.4 / 17.4\n\n\nAs expected from the reduced reflection and increased absorption in the Si, the cell with an intermediate ARC has significantly higher maximum current in the bottom Si cell." }, { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#variation-with-aerosol-models", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html#variation-with-aerosol-models", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", - "section": "Variation with Aerosol models", - "text": "Variation with Aerosol models\nSeveral standard aerosol models are implemented in SPCTRAL 2 that were established by Shettle & Fenn.\nShettle, E. P., and R. W. Fenn, “Models of the Atmospheric Aerosol and Their Optical Properties, II Proceedings of the Advisory Group for Aerospace Reseach and Development Conference No . 183, Optical Propagation in the Atmosphere, 1975, pp. 2.1-2.16. Presented at the Electromagnetic Wave Propagation Panel Symposium, Lyngby, Denmark; 27-31 October 1975.\nHere we plot some of them with a turbidity of 0.2 to emphasise the different spectral behaviour:\n\nspc2rural = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='rural', x=wl * 1e9)\nspc2marit = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='maritime', x=wl * 1e9)\nspc2tropo = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='tropospheric', x=wl * 1e9)\n\nplt.figure(1)\nplt.title('Spectral Irradiance Plotted for Different Aersol Models')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2rural.spectrum(wl*1e9), label='rural')\nplt.plot(*spc2marit.spectrum(wl*1e9), label='maritime')\nplt.plot(*spc2tropo.spectrum(wl*1e9), label='tropospheric')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()" + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#eqe-and-iv-calculation", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#eqe-and-iv-calculation", + "title": "Section 7: Planar GaInP//Si tandem cell", + "section": "EQE and IV calculation", + "text": "EQE and IV calculation\nNow, just taking the structure with an intermediate ARC, we do a cell calculation using the depletion approximation.\n\noptions.mpp = True\noptions.light_iv = True\noptions.voltages = np.linspace(-1.9, 0.1, 100)\noptions.light_source = AM15G\n\nsolar_cell = SolarCell(\n ARC_window + [GaInP_junction] + spacer + Si_front_surf + [Si_junction] +\n Si_back_surf,\n substrate=Al,\n)\n\nFirst, we calculate and plot the external quantum efficiency (EQE):\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nplt.figure()\nplt.plot(wl * 1e9, GaInP_A_ARC, \"--k\", label=\"GaInP only absorption\")\nplt.plot(wl * 1e9, Si_A_ARC, \"--r\", label=\"Si only absorption\")\nplt.plot(wl*1e9, solar_cell[3].eqe(wl), '-k')\nplt.plot(wl*1e9, solar_cell[9].eqe(wl), '-r')\nplt.legend(loc='upper right')\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance/EQE\")\nplt.ylim(0,1)\nplt.tight_layout()\nplt.show()\n\nTreating layer(s) 12 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving QE of the solar cell...\n\n\n\n\n\nAnd the current-voltage under AM1.5G:\n\nsolar_cell_solver(solar_cell, 'iv', options)\n\nplt.figure()\nplt.plot(-options.voltages, -solar_cell.iv['IV'][1]/10, 'k', linewidth=3,\n label='Total (2-terminal)')\nplt.plot(-options.voltages, solar_cell[3].iv(options.voltages)/10, 'b',\n label='GaInP')\nplt.plot(-options.voltages, solar_cell[9].iv(options.voltages)/10, 'g',\n label='Si')\nplt.text(0.1, 18, r\"2-terminal $\\eta$ = {:.2f}%\".format(solar_cell.iv[\"Eta\"]*100))\nplt.legend()\nplt.ylim(0, 20)\nplt.xlim(0, 1.9)\nplt.ylabel('Current (mA/cm$^2$)')\nplt.xlabel('Voltage (V)')\nplt.tight_layout()\nplt.show()\n\nTreating layer(s) 12 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell..." }, { - "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#changing-the-time-of-day", - "href": "solcore-workshop-2/notebooks/4-Spectral2.html#changing-the-time-of-day", - "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", - "section": "Changing the time of day", - "text": "Changing the time of day\nOne of the most common uses for a spectral irradiance model such as SPCTRAL2 is to calculate how a particular solar cell technology behaves under varying spectral conditions during the day. This is particularly important whan working with series connected tandem solar cells where the current matching condition will vary according to the incident spectrum. Here we plot the spectral irradiance at 12pm, 2pm, 3pm, 4pm, 5pm, 6pm and 7pm. Note the strong relative loss in short-wavelength light relative to the infrared as the air-mass increases throughout the afternoon.\n\nimport datetime\n\nplt.figure(1)\nplt.title('Spectral Irradiance plotted from 12pm-7pm')\nhours=[12, 14, 15, 16, 17, 18, 19]\n\nfor h in hours:\n spc2 = LightSource(source_type='SPECTRAL2', dateAndTime=datetime.datetime(2011, 6, 30, h, 00),\n precipwater=1.0, turbidity=0.05, x=wl * 1e9)\n plt.plot(*spc2.spectrum(wl*1e9), label='hour '+ str(h))\n\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()" + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#two-vs.-four-terminal-efficiency", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#two-vs.-four-terminal-efficiency", + "title": "Section 7: Planar GaInP//Si tandem cell", + "section": "Two vs. four-terminal efficiency", + "text": "Two vs. four-terminal efficiency\nBy default, Solcore assumes any SolarCell object is a two-terminal device, and will thus calculate the total I-V curve assuming the cells are connected in series and that the current is limited by the lowest-current sub-cell. However, it will also calculate the I-V curves of the individual cells, so we can use this information to calculate the possible power output in a 4-terminal configuration where the cells operate independently from an electrical point of view:\n\nV = np.linspace(0, 1.3, 100)\nP_GaInP = V*solar_cell[3].iv(V)\nP_Si = V*solar_cell[9].iv(V)\n\nP_MPP_GaInP = max(P_GaInP)\n\nP_MPP_Si = max(P_Si)\n\neta_4T = (P_MPP_GaInP + P_MPP_Si)/AM15G.power_density\n\nprint('4-terminal efficiency: {:.1f} %'.format(eta_4T*100))\n\n4-terminal efficiency: 39.6 %" }, { - "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html", - "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html", - "title": "Section 5b: Planar Si solar cell using PDD", - "section": "", - "text": "In the previous example, we looked at a silicon cell using the depletion approximation. Here, we will instead use Solcore’s Poisson drift-diffusion (PDD) solver, which is can handle doping profiles (not just constant doping levels). Note that Solcore actually has two PDD solvers: a built-in one which was developed in Fortran specifically for cells with quantum wells, and an interface to the Sesame package, which was written in Python and developed for silicon-based cells. Here, we will use the Sesame solver.\nThe script starts of in much the same way as the DA cell in the previous example: we import relevant external packages and Solcore features, define some of the materials we will use, and set user options for solar_cell_solver.\n\nfrom solcore.solar_cell import SolarCell, Junction, Layer\nfrom solcore.state import State\nfrom solcore.solar_cell_solver import solar_cell_solver\nimport numpy as np\nfrom solcore.light_source import LightSource\nfrom scipy.special import erfc\n\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\n\nAir = material(\"Air\")()\nMgF2 = material(\"MgF2\")()\nAg = material(\"Ag\")()\nTCO = material('ITO2')()\n\nwavelengths = np.linspace(280, 1200, 100)*1e-9\n\noptions = State()\noptions.wavelength = wavelengths\noptions.optics_method = 'TMM'\noptions.light_iv = True\noptions.T = 298\noptions.light_source = LightSource(source_type=\"standard\",\n version=\"AM1.5g\", x=options.wavelength)\n\noptions.voltages = np.linspace(0, 0.8, 40)\noptions.internal_voltages = options.voltages\noptions.mpp = True\noptions.no_back_reflection = False\noptions.position = 1e-9\n\nThe Sesame PDD solver which we will be using can affect doping profiles (although you can also still set constant doping, like in the previous example, for each layer). Because we are going to pass a doping profile rather than distinct p and n-type materials, we just define one Si material which will be used for the whole junction, with electron and hole mobilities and lifetimes.\nOf course, there are many other material parameters which the PDD solver must have access to; these are stored in Solcore’s material database, but they can always be overridden by user-specified values when calling the material function.\n\nSi_pn = material(\"Si\")(electron_mobility=si(\"1e4cm2\"), hole_mobility=si(\"1e3cm2\"),\n electron_minority_lifetime=0.001, hole_minority_lifetime=0.001)\n\nNow we will define the doping profile. We will define a p-n junction, with the highly-doped region (the emitter) at the rear and an ‘erfc’ profile at the front and rear surfaces. Note that Solcore expects the doping to be provided in base Si units (per m3). Solcore expects the doping profile information in the form of a function which returns the doping at a given depth (in m) in the junction. Positive values are n-type doping, negative values are p-type.\n\nnD = si(\"1e20cm-3\")\nnA = si(\"1e19cm-3\")\nbulk_doping = si(\"5e15cm-3\") # n type bulk\n\nd_bulk = 100e-6 # Si thickness, in m\n\n# rear junction (n-type)\ndef doping_profile_func(x):\n\n L = d_bulk\n\n doping_profile = - nA * erfc(x/150e-9) # characteristic depth of 150 nm\n\n doping_profile_rear = nD * erfc((L - x)/200e-9) # characteristic depth of 200 nm\n\n return doping_profile + doping_profile_rear + bulk_doping\n\nTo check it looks reasonable, let’s plot this doping profile:\n\ndepth = np.linspace(0, d_bulk, int(1e5))\n\nplt.figure()\nplt.semilogy(depth*1e6, doping_profile_func(depth))\nplt.xlabel(r\"Depth ($\\mu$m)\")\nplt.ylabel(r\"Doping (m$^{-3}$)\")\nplt.show()\n\n\n\n\nWe will add transparent conducting oxides (TCOs) and an anti-reflection coating. Note that a real Si cell would have a more complicated layer structure (for example, for a heterojunction cell, the amorphous Si layers). In this case, these layers will be outside the junction: this means they will have optical effects but will not be included in the drift-diffusion calculation.\n\nfront_materials = [Layer(80e-9, MgF2), Layer(55e-9, TCO)]\n\nback_materials = [Layer(55e-9, TCO),\n Layer(120e-9, MgF2)]\n\nAnother important cell parameter, for both the depletion approximation and the drift-diffusion solvers, is the surface recombination. This is passed to Solcore as a surface recombination velocity (SRV). With the Si_pn material, the doping profile function, and the SRVs, we define the Junction. We set the kind of junction to sesame_PDD, so that Solcore knows to use the Sesame PDD solver.\n\nSi_junction = [Junction([Layer(d_bulk, Si_pn)],\n doping_profile=doping_profile_func, kind='sesame_PDD',\n sn=2, sp=1 # SRVs. Note these should be in m/s, not cm/s! sn refers to the n-type region (can be at the back or the front!), sp to the p-type.\n )]\n\nNow we combine the surface layers and the junction into a solar cell, with 2% shading and a silver back mirror.\n\nSi_cell = SolarCell(front_materials +\n Si_junction +\n back_materials,\n shading=0.02,\n substrate=Ag,\n )\n\nNow we ask Solcore to solve both the light IV and QE of the cell:\n\nsolar_cell_solver(Si_cell, 'qe', options)\nsolar_cell_solver(Si_cell, 'iv', options)\n\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving QE of the solar cell...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\nPlot the results:\n\nresult_stack = np.vstack([Si_cell.reflected, [layer.layer_absorption for layer in Si_cell]])\n\nfig, (ax, ax2) = plt.subplots(1, 2, figsize=(10, 3.5))\nax.stackplot(wavelengths * 1e9, 100 * result_stack[::-1], linewidth=0.5, alpha=0.5,\n labels=['MgF2 (rear)', 'TCO (rear)', 'Si bulk', 'TCO (front)', 'MgF2 (front)',\n 'Reflection'])\nax.plot(wavelengths * 1e9, 100 * Si_cell(0).eqe(wavelengths), '-k', linewidth=2,\n label='EQE')\n\nax.set_xlim(280, 1200)\nax.set_ylim(0, 100)\nax.set_xlabel(\"Wavelength (nm)\")\nax.set_ylabel(\"R / A / EQE (%)\")\nax.set_title('a) EQE and cell optics', loc='left')\nax.legend()\n# plt.show()\n\njsc = Si_cell.iv.Isc / 10\n\nax2.plot(Si_cell.iv['IV'][0], Si_cell.iv['IV'][1] / 10, '-', label='IV',\n linewidth=2, color='k')\n\nax2.set_ylim(0, 1.03 * jsc)\nax2.set_xlim(np.min(options.voltages), np.max(options.voltages))\nax2.set_xlabel('Voltage (V)')\nax2.set_ylabel('Current density (mA/cm$^2$)')\nax2.set_title('b) IV characteristics and power output', loc='left')\n\nax3 = ax2.twinx()\nax3.plot(options.voltages, Si_cell.iv['IV'][0] * Si_cell.iv['IV'][1],\n '-r', label='Power', linewidth=2)\nax3.set_ylabel('Power density (W m$^{-2}$)')\nax3.set_ylim(0, 1.03 * jsc * 10)\n\nax3.spines['right'].set_color('r')\nax3.yaxis.label.set_color('r')\nax3.tick_params(axis='y', colors='r')\n\nax2.set_axisbelow(True)\nax3.set_axisbelow(True)\n\nax2.text(0.02, 0.9 * jsc, r'$J_{SC}$', zorder=5)\nax2.text(0.02, 0.8 * jsc, r'$V_{OC}$')\nax2.text(0.02, 0.7 * jsc, 'FF')\nax2.text(0.02, 0.6 * jsc, r'$\\eta$')\nax2.text(0.02, 0.5 * jsc, r'$J_{MPP}$')\nax2.text(0.02, 0.4 * jsc, r'$V_{MPP}$')\n\nax2.text(0.1, 0.9 * jsc, r'= {:.2f} mA/cm$^2$'.format(jsc))\nax2.text(0.1, 0.8 * jsc, r'= {:.3f} V'.format(Si_cell.iv.Voc))\nax2.text(0.1, 0.7 * jsc, '= {:.2f} %'.format(Si_cell.iv.FF * 100))\nax2.text(0.1, 0.6 * jsc, r'= {:.2f} %'.format(Si_cell.iv.Eta * 100))\nax2.text(0.1, 0.5 * jsc, r'= {:.2f} mA/cm$^2$'.format( Si_cell.iv.Impp / 10))\nax2.text(0.1, 0.4 * jsc, r'= {:.3f} V'.format(Si_cell.iv.Vmpp))\nax2.grid(which='major', alpha=0.35)\n\nax3.grid(False)\nplt.tight_layout()\n\nplt.show()\n\n\n\n\nRecently, record-efficiency silicon cells have been optimized to such a level that Auger recombination (rather than Shockley-Read-Hall recombination) becomes the dominant recombination mechanism. SRH recombination is parameterized in the PDD solver through the minority lifetimes. Here, we will scan through different minority carrier lifetimes between 1e-4 s to 0.1 s and look at the effect on cell parameters. Other cell parameters are assumed to stay the same.\n\nlifetime_exp = np.linspace(-4, -1.5, 6) # exponent for the lifetimes\n\nlifetimes = 10.0**lifetime_exp # lifetimes which are linearly spaced on a log scale\n\ncell_results = np.zeros(([len(lifetimes), 4])) # make an array to store the efficiency, FF, Voc, Jsc for each lifetime\n\nfor i1, lt in enumerate(lifetimes): # loop through the lifetimes\n\n options.recalculate_absorption = True\n\n Si_pn = material(\"Si\")(electron_mobility=si(\"1e4cm2\"), hole_mobility=si(\"1e3cm2\"),\n electron_minority_lifetime=lt, hole_minority_lifetime=lt)\n\n Si_junction = [Junction([Layer(d_bulk, Si_pn)],\n doping_profile=doping_profile_func, kind='sesame_PDD',\n sn=2, sp=1)]\n\n Si_cell = SolarCell(front_materials +\n Si_junction +\n back_materials,\n shading=0.02,\n substrate=Ag,\n )\n\n solar_cell_solver(Si_cell, 'iv', options)\n\n cell_results[i1] = np.array([100*Si_cell.iv.Eta, 100*Si_cell.iv.FF, Si_cell.iv.Voc, Si_cell.iv.Isc/10])\n\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\nNow we plot the results. The points are labelled with the lifetime in ms in the left-hand plot.\n\nfig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.5))\n\nax1.plot(cell_results[:, 2], cell_results[:, 1], 'ko')\n\nfor i, lt in enumerate(lifetimes):\n ax1.annotate(str(np.round(1000*lt,2)), (cell_results[i, 2] - 0.001, cell_results[i, 1]), ha='right')\n\nax1.set_xlabel(r'V$_{oc}$ (V)')\nax1.set_ylabel('FF (%)')\nax1.set_xlim(0.69, 0.75)\n\nax2.semilogx(lifetimes, cell_results[:, 0], 'o', color='k')\nax2.set_ylabel('Efficiency (%)')\nax3 = ax2.twinx()\nax3.plot(lifetimes, cell_results[:, 3], 'o', color='r', markerfacecolor='none')\nax3.set_ylim(33, 34)\nax3.set_ylabel(r'$J_{sc}$ (mA/cm$^2$)', color='r')\n\nax2.set_xlabel(r'$\\tau$ (s)')\n\nplt.tight_layout()\nplt.show()\n\n\n\n\nAs the lifetimes become very long, the fill factor shoots up rapidly, while the open-circuit voltage saturates. This increase in FF is faster than would be expected with an ideality factor of 1 (for SRH recombination) in the diode equation, and occurs because recombination becomes increasingly dominated by Auger recombination (ideality factor = 2/3). Compare the plot on the left with Figure 1b in this paper, where much the same behaviour is observed with data from real record efficiency devices.\n\n1000*lifetimes\n\narray([ 0.1 , 0.31622777, 1. , 3.16227766, 10. ,\n 31.6227766 ])" + "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#questionschallenges", + "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#questionschallenges", + "title": "Section 7: Planar GaInP//Si tandem cell", + "section": "Questions/challenges", + "text": "Questions/challenges\n\nWhat causes the strange, sharp fringes in the simulation data of Fig. 1 in the reference paper? Can you reproduce them by modifying this code? Which version of the simulation do you think is more correct, and why?\nHow could you increase the current in one or both of the sub-cells (remember, unlike the paper, we assumed all the layers in the cell are planar!).\nOnce the light encounters an ‘incoherent’ (thick) layer, does it make sense to treat any layers below that as coherent?" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", "section": "", - "text": "In this example, we will build two structures similar to those described in this paper. These are both triple-junction, two-terminal GaInP/GaAs/Si cells; one cell is planar, while the other has a diffraction grating deposited on the rear of the bottom Si cell to boost its current." + "text": "Tuesday 1 August 2023" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#setting-up", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#setting-up", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Setting up", - "text": "Setting up\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.options import default_options\nfrom rayflare.structure import Interface, BulkLayer, Structure\nfrom rayflare.matrix_formalism import process_structure, calculate_RAT\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\nAs before, we load some materials from the refractiveindex.info database. The MgF\\(_2\\) and Ta\\(_2\\)O\\(_5\\) are the same as the ARC example; the SU8 is a negative photoresist which was used in the reference paper The optical constants for silver are also loaded from a reliable literature source. Note that the exact compositions of some semiconductor alloy layers (InGaP, AlInP and AlGaAs) are not given in the paper and are thus reasonable guesses.\n\n# download_db() # only needs to be run once\n# commented out because this should have already been done in a previous example. Uncomment if necessary.\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")(In=0.5)\nAlGaAs = material(\"AlGaAs\")(Al=0.8)\nGaAs = material(\"GaAs\")()\nSi = material(\"Si\")\n\nAir = material(\"Air\")()\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()" + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#trivich-flinn-efficiency-limit", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#trivich-flinn-efficiency-limit", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "Trivich-Flinn Efficiency limit", + "text": "Trivich-Flinn Efficiency limit\nIn 1955 Trivich & Flinn published a model for limiting efficiency. The limit it produces is too high, but it represents a good place to start with a computer model.\nTrivich D, Flinn PA. Maximum efficiency of solar energy conversion by quantum processes. In Solar Energy Research, Daniels F, Duffie J (eds). Thames and Hudson: London, 1955.\nTrivich & Flinn assumed that the ideal solar cell would absorb all photons with energy above the band-gap energy \\(E_g\\) and that the maximum voltage that could ever be attained in a solar cell is the band-gap energy. The latter assumption is incorrect unless the solar cell is operating at absolute zero temperature.\nTo develop a model for the Trivich & Flinn efficiency limit the first step is to calculate what the limit to the photocurrent is in a solar cell." }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#defining-the-cell-layers", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#defining-the-cell-layers", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Defining the cell layers", - "text": "Defining the cell layers\nNow we define the layers for the III-V top junctions, and the Si wafer, grouping them together in a logical way. In this example, we will only do optical simulations, so we will not set e.g. diffusion lengths or doping levels.\n\nARC = [Layer(110e-9, MgF2), Layer(65e-9, Ta2O5)]\n\nGaInP_junction = [Layer(17e-9, window), Layer(400e-9, GaInP), Layer(100e-9, AlGaAs)]\n\ntunnel_1 = [Layer(80e-9, AlGaAs), Layer(20e-9, GaInP)]\n\nGaAs_junction = [Layer(17e-9, GaInP), Layer(1050e-9, GaAs), Layer(70e-9, AlGaAs)]\n\ntunnel_2 = [Layer(50e-9, AlGaAs), Layer(125e-9, GaAs)]\n\nSi_junction = [Layer(280e-6, Si(Nd=si(\"2e18cm-3\"), hole_diffusion_length=2e-6), role=\"emitter\")]\n\ncoh_layers = len(ARC) + len(GaInP_junction) + len(tunnel_1) + len(GaAs_junction) + len(tunnel_2)\n\nAs for Example 7, to get physically reasonable results we must treat the very thick layers in the structure incoherently. The coh_layers variable sums up how many thin layers (which must be treated coherently) must be included in the coherency_list options." + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#limits-to-the-short-circuit-current", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#limits-to-the-short-circuit-current", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "Limits to the short-circuit current", + "text": "Limits to the short-circuit current\n\nSolar Spectrum\nThe solar spectrum defines the ultimate current that a solar cell can produce. First we will plot the AM1.5G solar spectrum \\(b(\\lambda)\\) as a spectral irradiance, meaning that the y-axis has units of \\(W.m^{-2}.nm^{-1}\\)\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\nimport seaborn as sns\n\n# Setup the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 # wl contains the x-coordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl*1e9, version='AM1.5g',\n output_units=\"power_density_per_nm\")\n\nplt.figure()\nplt.title('Spectral Irradiance')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\n<matplotlib.legend.Legend at 0x175783150>\n\n\n\n\n\nLet us now integrate the solar spectrum to provide the total irradiance in units of [\\(W.m^{-2}\\)]. The code below performs the following operation \\(b=\\int^{\\infty}_{0} b(\\lambda) d\\lambda\\)\n\n# Since .spectrum function returns a tuple (x,y) but np.trapz requires data in format (y,x) these are extracted into separate 1D np arrays.\nyval = am15g.spectrum()[1]\nxval = am15g.spectrum()[0]\nintegrated_value = np.trapz(yval,xval) # Perform integration using trapezium rule\nb = integrated_value # Save the integrated power density for the sun for later.\nprint('b = ', integrated_value)\n\nb = 1000.3974821197136\n\n\nLet’s take the opportunity to learn how to format numbers nicely in Python. Here we use the command “%.0f” % to display the value to zero decimal places.\n\nprint('b = ',\"%.0f\" % integrated_value,\"W.m-2\")\n\nb = 1000 W.m-2\n\n\nSolcore performs this integration for us internally. Let’s try the same exercise but for the extraterrestrial solar spectrum, AM0\n\nam0 = LightSource(source_type='standard', x=wl*1e9, version='AM0')\nprint(\"AM0 integrates to\", \"%.0f\" % am0.power_density, \"W.m-2\")\n\nAM0 integrates to 1348 W.m-2\n\n\n\n\nSpectral Photon Flux\nTo calculate a short-circuit current it is convenient to change the units. Two changes are necessary : 1. Since we specify band-gap energies in electron volts (eV) we need to transform the x-axis from nm to eV 2. Photocurrent is proportional to the incident photon flux (number of photons per second) not the irradiance (watts) so we need to convert the y-axis from energy to photon number.\nNote: The conversion is performed internally within the software but be aware that because the transformation from wavelength is non-linear, changing the x-axis from nm to eV also changes the y-values of the data. This is known as a Jacobian transformation and discussed in more detail in an article “Getting the basics right: Jacobian Conversion of Wavelength and Energy Scales for Quantatitive Analysis of Emission Spectra”, Journal of Physical Chemistry, 4(19) 3316 (2013)\n\nev = np.linspace(0.02,4,4000)\nflux = LightSource(source_type='standard', version='AM1.5g', x=ev, output_units='photon_flux_per_ev')\n\nplt.figure()\nplt.title('Spectral Photon Flux')\nplt.plot(*flux.spectrum(), label='AM1.5G')\nplt.xlim(0.2, 4)\nplt.xlabel('Photon Energy (eV)')\nplt.ylabel('Photon flux N ($ph.s^{-1}m^{-2}eV^{-1}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x177da5050>\n\n\n\n\n\n\n\nCalculating the short-circuit current\nIntegrating the photon flux can provide an upper limit to the short-circuit current [A.m-2]. We can integrate the spectrum over the entire spectral range using \\(J_{sc}=q\\int_{0}^{\\infty}N(E)dE\\)\n\nq = 1.60217662E-19\nyval = flux.spectrum()[1]\nxval = flux.spectrum()[0]\nyint = q*np.trapz(yval,xval) # Perform integration using trapezium rule\n\nprint(\"%.0f\" % yint)\n\n690\n\n\nA more useful calculation is to calculate the current that a solar cell would produce with a particular band-gap energy. To do this requires a bit more coding, since we now wish to integrate between limits: \\(J_{sc}=q\\int_{Eg}^{\\infty}N(E)dE\\)\nLet’s do this for a band-gap of 1.42 eV:\n\nq = 1.60217662E-19\neg = 1.42\nyval = flux.spectrum()[1]\nxval = flux.spectrum()[0]\n\nyval[xval < eg] = 0 # set photon flux to zero for photon energies below the band-gap\n\nyint = q*np.trapz(yval,xval) # Perform integration using trapezium rule\n\nprint(\"%.0f\" % yint)\n\n321\n\n\nLet’s reproduce the \\(J_{sc}\\) vs \\(E_g\\) graph that is shown on p. 87 of Martin Green’s Solar Cells book:\n\nq = 1.60217662E-19\n\ndef getJsc(eg):\n yval = flux.spectrum()[1] # Start with the solar spectrum in yval & xval\n xval = flux.spectrum()[0]\n yval[xval < eg] = 0 # set photon flux to zero for photon energies below the band-gap\n return q*np.trapz(yval,xval) # return the integrated value\n\neg = np.linspace(0.5,2.5,100)\njsc = np.vectorize(getJsc)(eg)\n\nplt.figure()\nplt.title('Limit to the short-circuit current $J_{sc}$')\nplt.plot(eg, jsc/10, label='AM1.5G') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('$J_{sc}$ ($mA.cm^{-2}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x177dde090>\n\n\n\n\n\n\n\nCalculating the Trivich-Flinn Efficiency limit\nNow that the limit to \\(J_{sc}\\) is known, we can estimate the power of delivered by the solar cell by evaluating \\(\\frac{Eg J_{sc}}{b}\\)\n\nplt.figure()\nplt.title('Trivich-Flinn Single Junction Efficiency Limit')\nplt.plot(eg, 100*eg*jsc/b,label='AM1.5G') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x177edb150>" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#planar-cell", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#planar-cell", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Planar cell", - "text": "Planar cell\nNow we define the planar cell, and options for the solver:\n\ncell_planar = tmm_structure(\n ARC + GaInP_junction + tunnel_1 + GaAs_junction + tunnel_2 + Si_junction,\n incidence=Air, transmission=Ag,\n)\n\nn_layers = cell_planar.layer_stack.num_layers\n\ncoherency_list = [\"c\"]*coh_layers + [\"i\"]*(n_layers-coh_layers)\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl,\n output_units=\"photon_flux_per_m\")\n\noptions.wavelength = wl\noptions.coherency_list = coherency_list\noptions.coherent = False\n\nRun the TMM calculation for the planar cell, and then extract the relevant layer absorptions. These are used to calculate limiting currents (100% internal quantum efficiency), which are displayed on the plot with the absorption in each layer.\n\ntmm_result = cell_planar.calculate(options=options)\n\nGaInP_A = tmm_result['A_per_layer'][:,3]\nGaAs_A = tmm_result['A_per_layer'][:,8]\nSi_A = tmm_result['A_per_layer'][:,coh_layers]\n\nJmax_GaInP = q*np.trapz(GaInP_A*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_A*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_A*AM15G.spectrum()[1], x=wl)/10\n\nR_spacer_ARC = tmm_result['R']\n\nplt.figure(figsize=(6,4))\nplt.plot(wl * 1e9, GaInP_A, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_A, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_A, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, 1 - R_spacer_ARC, '-y', label=\"1 - R\")\n\nplt.text(450, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(860, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance\")\nplt.tight_layout()\nplt.legend(loc='upper right')\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.show()\n\nWARNING: The option 'wavelengths' (plural) will be deprecated in the next version. Please use 'wavelength' (singular) instead. Currently, wavelengths (plural) will override wavelength (singular) if both are specified.\n\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded." + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#the-shockley-queisser-efficiency-limit", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#the-shockley-queisser-efficiency-limit", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "The Shockley-Queisser Efficiency limit", + "text": "The Shockley-Queisser Efficiency limit\nShockley & Queisser refined the Trivich-Flinn limit by linking the voltage a solar cell can deliver to the Fermi level separation in the conduction and valance bands, not the band-gap energy.\nTo do this, a model is required for the recombination processes between the conduction and valance bands. The most fundamental (and inescapable) recombination mechanism is the radiative process. In section 3 we will derive a limit to Shockley’s diode equation \\(J=J_0 e^{\\frac{V}{kT}}\\) for the radiative limit, that being a diode where all current flows are linked to an optical process, either absorption or recombination.\nIn the radiative limit and an abrupt band-edge at band-gap energy \\(E_g\\) it can be shown that \\(J_0\\) is approximated by \\(J_0=q \\frac{2 \\pi}{c^2 h^3} kT \\left(E_g^2+2 E_g k T+2 k^2 T^2\\right) e^{\\frac{-E_g}{k T}}\\)\nWe can now plot a chart of \\(J_0\\) as a function of band-gap energy using this expression:\n\n# Define some physical constants:\nq = 1.60217662E-19 # electronic charge [C]\nk = 1.38064852E-23/q # Boltzmann constant [eV/K]\nh = 6.62607004E-34/q # Planck constant expressed in [eV.s]\nc = 299792458 # Speed of light [m.s^-1]\n\nt = 300 # Perform the calculation for a solar cell at 300K.\n\n# Define a function to return J0 implementing the expression above\ndef getJ0(eg):\n return k*t*q*(2*np.pi/(c**2*h**3))*(eg**2+2*eg*k*t+2*k**2*t**2)*np.exp(-eg/(k*t))\n\neg = np.linspace(0.5,2.5,100)\nj0 = np.vectorize(getJ0)(eg)\n\nplt.figure()\nplt.title('The radiative limit to $J_0$ plotted as a function of band-gap energy Eg')\nplt.plot(eg,j0,label='J0') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.2, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('$J_{0}$ ($A.m^{-2}$)')\nplt.yscale(\"log\")\nplt.legend()\n\n<matplotlib.legend.Legend at 0x177f1ccd0>\n\n\n\n\n\nLet’s obtain J0 for GaAs and InGaP, two common III-V materials that are used in tandem solar cells: evaluate getJ0() for Eg=1.42 and Eg=1.88\n\ngetJ0(1.42)\n\n1.195457897843886e-17\n\n\n\ngetJ0(1.88)\n\n3.888154629395649e-25" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#cell-with-rear-grating", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#cell-with-rear-grating", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Cell with rear grating", - "text": "Cell with rear grating\nNow, for the cell with a grating on the rear, we have a multi-scale problem where we must combine the calculation of absorption in a very thick (compared to the wavelengths of light) layer of Si with the effect of a wavelength-scale (1000 nm pitch) diffraction grating. For this, we will use the Angular Redistribution Matrix Method (ARMM) which was also used in Example 8.\nThe front surface of the cell (i.e. all the layers on top of Si) are planar, and can be treated using TMM. The rear surface of the cell, which has a crossed grating consisting of silver and SU8, must be treated with RCWA to account for diffraction. The thick Si layer will be the bulk coupling layer between these two interfaces.\nFirst, we set up the rear grating surface; we must define its lattice vectors, and place the Ag rectangle in the unit cell of the grating. More details on how unit cells of different shapes can be defined for the RCWA solver can be found here.\n\nx = 1000\n\nd_vectors = ((x, 0), (0, x))\narea_fill_factor = 0.4\nhw = np.sqrt(area_fill_factor) * 500\n\nback_materials = [\n Layer(width=si(\"250nm\"), material=SU8,\n geometry=[{\"type\": \"rectangle\", \"mat\": Ag, \"center\": (x / 2, x / 2),\n \"halfwidths\": (hw, hw), \"angle\": 0}])]\n\nNow, we define the Si bulk layer, and the III-V layers which go in the front interface. Finally, we put everything together into the ARMM Structure, also giving the incidence and transmission materials.\n\nbulk_Si = BulkLayer(280e-6, Si(), name=\"Si_bulk\")\n\nIII_V_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + tunnel_2\n\nfront_surf_planar = Interface(\"TMM\", layers=III_V_layers, name=\"III_V_front\",\n coherent=True)\n\nback_surf_grating = Interface(\"RCWA\", layers=back_materials, name=\"crossed_grating_back\",\n d_vectors=d_vectors, rcwa_orders=60)\n\ncell_grating = Structure([front_surf_planar, bulk_Si, back_surf_grating],\n incidence=Air, transmission=Ag)\n\nBecause RCWA calculations are very slow compared to TMM, it makes sense to only carry out the RCWA calculation at wavelengths where the grating has any effect. Depending on the wavelength, all the incident light may be absorbed in the III-V layers or in its first pass through the Si, so it never reaches the grating. We check this by seeing which wavelengths have even a small amount of transmission into the silver back mirror, and only doing the new calculation at these wavelengths. At shorter wavelengths, the results previously calculated using TMM can be used.\n\nwl_rcwa = wl[tmm_result['T'] > 1e-4] # check where transmission fraction is bigger\n# than 1E-4\n\noptions.wavelength = wl_rcwa\noptions.project_name = \"III_V_Si_cell\"\noptions.n_theta_bins = 30\noptions.c_azimuth = 0.25\noptions.RCWA_method = \"inkstone\"\n\nprocess_structure(cell_grating, options, save_location='current')\nresults_armm = calculate_RAT(cell_grating, options, save_location='current')\nRAT = results_armm[0]" + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-iv-curve", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-iv-curve", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "Calculating the IV curve", + "text": "Calculating the IV curve\nWe are now able to calculate the limiting efficiency for a solar cell using the simple Shockley diode expression \\(J(V)=J_{s c}-J_0\\left(e^{\\frac{q V}{k T}}-1\\right)\\). Let’s plot the IV curve for a band-gap of 1.42eV\n\ndef getJ(v,eg):\n return getJsc(eg) - getJ0(eg)*(np.exp(v/(k*t)) - 1)\n\neg = 1.42\nv = np.linspace(0,1.2,100)\nj = np.vectorize(getJ)(v,eg)\n\nplt.figure(3)\nplt.title('Limiting Efficiency IV curve for Eg=1.42eV (GaAs)')\nplt.plot(v,j/10) #convert to mA.cm^-2\nplt.xlim(0.2, 1.2)\nplt.ylim(0,35)\nplt.xlabel('Voltage (V)')\nplt.ylabel('Current ($mA.cm^{-2}$)')\n\nText(0, 0.5, 'Current ($mA.cm^{-2}$)')" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#comparison-of-planar-and-grating-cell", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#comparison-of-planar-and-grating-cell", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Comparison of planar and grating cell", - "text": "Comparison of planar and grating cell\nWe extract the relevant absorption per layer, and use it to calculate the new limiting current for the Si junction. The plot compares the absorption in the Si with and without the grating.\n\nSi_A_total = np.zeros(len(wl))\nSi_A_total[tmm_result['T'] > 1e-4] = RAT['A_bulk'][0]\nSi_A_total[tmm_result['T'] <= 1e-4] = Si_A[tmm_result['T'] <= 1e-4]\n\nJmax_Si_grating = q*np.trapz(Si_A_total*AM15G.spectrum()[1], x=wl)/10\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_A, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_A, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_A, \"--r\", label=\"Si (planar)\")\nplt.plot(wl * 1e9, Si_A_total, '-r', label=\"Si (with grating)\")\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.50, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(860, 0.45, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si_grating))\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance\")\n\nplt.tight_layout()\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-electrical-power-curve-and-finding-the-maximum-power", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-electrical-power-curve-and-finding-the-maximum-power", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "Calculating the electrical power curve and finding the maximum power", + "text": "Calculating the electrical power curve and finding the maximum power\n\nplt.figure()\nplt.title('Limiting Efficiency power curve for $E_g$ = 1.42 eV (GaAs)')\nplt.plot(v,v*j)\nplt.xlim(0.2, 1.2)\nplt.ylim(0,350)\nplt.xlabel('Voltage (V)')\nplt.ylabel('Power ($W.m^{-2}$)')\n\nText(0, 0.5, 'Power ($W.m^{-2}$)')\n\n\n\n\n\nDefine a function to find the maximum power point of the curve above:\n\ndef getPmax(eg):\n v = np.linspace(0,eg-0.1,500)\n p = v*np.vectorize(getJ)(v,eg)\n return (np.amax(p)) # The amax command returns the maximum value in the array p\n\nTest it out on the curve above\n\ngetPmax(1.42)\n\n331.6412760959975\n\n\n\nPlotting the Shockley-Queisser efficiency limit graph:\nFinally we can calculate the Shockley-Queisser efficiency limit for AM1.5G\n\neg = np.linspace(0.5,2.5,100)\np = np.vectorize(getPmax)(eg)\n\nplt.figure(3)\nplt.title('Limiting Shockley-Queisser Efficiency Curve')\nplt.plot(eg, p/b, label='AM1.5G') # Remember b is the integrated power of the\n# incident sunlight\nplt.xlim(0.2, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x298214750>" }, { - "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#questions", - "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#questions", - "title": "Section 9a: Planar III-V on planar Si, with rear grating", - "section": "Questions", - "text": "Questions\n\nWhy does the grating only affect the absorption in Si at long wavelengths?\nWhat is the reason for using the angular redistribution matrix method, rather than defining an RCWA-only structure (rcwa_structure)?" + "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#an-easier-way-using-solcore", + "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#an-easier-way-using-solcore", + "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "section": "An easier way – using Solcore!", + "text": "An easier way – using Solcore!\nThe Solcore library has all the functions we have written above built into it. We worked through this example step by step, but we can calculate the same result using the code below. First let’s calculate an IV curve for a Shockley-Queisser solar cell with a band-gap of 1.42eV:\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\nfrom solcore.solar_cell import SolarCell\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.structure import Junction\n\n# Load the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 # wl contains the x-coordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl, version='AM1.5g')\n\neg = 1.42\nV = np.linspace(0, 1.3, 500)\ndb_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1) #\n# detailed-balance junction (Shockley-Queisser limit)\n\nmy_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\nsolar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True,\n 'internal_voltages': np.linspace(0, 1.3, 400), 'wavelength': wl,\n 'mpp': True, 'light_source': am15g})\n\nplt.figure()\nplt.title('Limiting Efficiency IV curve for $E_g$ = 1.42eV')\nplt.plot(V, my_solar_cell.iv.IV[1], 'k')\nplt.ylim(0, 350)\nplt.xlim(0, 1.2)\nplt.text(0.1,300,f'Jsc: {my_solar_cell.iv.Isc:.2f}')\nplt.text(0.1,280,f'Voc: {my_solar_cell.iv.Voc:.2f}')\nplt.text(0.1,260,f'Pmax: {my_solar_cell.iv.Pmpp:.2f}')\nplt.xlabel('Voltage (V)')\nplt.ylabel('Current (A/m$^2$)')\nplt.show()\n\n/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/registries.py:73: UserWarning: Optics solver 'RCWA' will not be available. An installation of S4 has not been found.\n warn(\n\n\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\n\n\n\nThe Shockley-Queisser efficiency calculation can now be performed over a range of band-gap energies. To do this, we make a function that calculates the maximum power Pmax as a function of band-gap energy.\n\n%%capture\n# A command that prevents the screen from filling up with unnecessary working\n\n# Function that returns the maximum power for a Shockley-Queisser solar cell with band-gap Eg\ndef getPmax(eg):\n V = np.linspace(0, eg-0.1, 500)\n db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)\n my_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\n solar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,\n 'mpp': True, 'light_source': am15g})\n return(my_solar_cell.iv.Pmpp)\n\n# Define the range of band-gaps to perform the calculation over\neg=np.linspace(0.5,2.5,100)\n# Perform the claculation for all values of eg\np=np.vectorize(getPmax)(eg)\n\nNow let’s plot the result:\n\nplt.figure() # Plot the results calculated above:\nplt.title('Shockley-Queisser Limiting Efficiency for Unconentrated Sunlight')\nplt.plot(eg, p/am15g.power_density,label='AM1.5G')\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x2981fe210>\n\n\n\n\n\n\nEffect of solar concentration on a Shockley-Queisser Solar Cell\nIn a Trivich-Flinn model for a solar cell, concentrated sunlight is only expected to increase the current of a solar cell, not the voltage. In that model the current would increase in proportion with the concentration so the efficiency of the solar cell would be unchanged.\nIn the Shockley-Queisser model, concentrated sunlight increased both the current and the voltage of the solar cell which, in the absence of series resistance losses, leads to an increase in the efficiency of the solar cell. Here we calculate the Shockley-Queisser efficiency at different solar concentrations under the direct solar spectrum AM1.5D:\n\n%%capture\n\n# Set up a series of AM1.5D solar spectra at different concentrations\nwl = np.linspace(300, 4000, 4000) * 1e-9 #wl contains the x-ordinate in wavelength\nam15d1x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=1)\nam15d30x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=30)\nam15d1000x = LightSource(source_type='standard', x=wl, version='AM1.5d',\n concentration=1000)\n\n#Define a function to find Pmax for a particular band-gap energy and solar spectrum\ndef getPmax(eg,spectrum):\n V = np.linspace(0, eg-0.1, 500)\n db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)\n my_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\n solar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,\n 'mpp': True, 'light_source': spectrum})\n return my_solar_cell.iv.Pmpp\n\n# Evaluate the Pmax function for band-gaps spanning 0.8 to 1.6eV and concentrations 1x,30x,1000x\neg = np.linspace(0.8,1.6,100)\np1x = np.vectorize(getPmax)(eg, am15d1x)\np30x = np.vectorize(getPmax)(eg, am15d30x)\np1000x = np.vectorize(getPmax)(eg, am15d1000x)\n\n\n# Setup a figure for dual y-axes\nfig, ax = plt.subplots(1)\n\n# Plot the SQ curves\ncolors = sns.color_palette('husl', n_colors=3)\nax.plot(eg, 100*p1x/am15d1x.power_density,label='$\\eta$ @ AM1.5d 1x', color=colors[0])\nax.axvline(eg[np.argmax(p1x)], color=colors[0])\n\nax.plot(eg, 100*p30x/am15d30x.power_density,label='$\\eta$ @ AM1.5d 30x', color=colors[1])\nax.axvline(eg[np.argmax(p30x)], color=colors[1])\n\nax.plot(eg, 100*p1000x/am15d1000x.power_density,label='$\\eta$ @ AM1.5d 1000x', color=colors[2])\nax.axvline(eg[np.argmax(p1000x)], color=colors[2])\n\n# Define the second y-axis and plot the photon flux in units of eV\nax2 = ax.twinx()\nax2.plot(eg, am15d1x.spectrum(x=eg, output_units=\"photon_flux_per_ev\")[1],\n '--', color='grey', label=\"AM1.5d\")\n\nax.set_xlim(0.8, 1.6)\nax.set_xlabel('Band Gap energy (eV)')\nax.set_ylabel('Efficiency (%)')\nax2.set_ylabel(r'Photon flux (s$^{-1}$ m$^{-2}$ eV$^{-1}$)')\nax.legend()\nax2.legend()\n\n<matplotlib.legend.Legend at 0x2bf13f050>\n\n\n\n\n\nThe maximum band-gap energy moves to lower energies with increaseing solar concentration. This arises since although the current increases with increasing solar concentration, the cell voltage also increases which means the optimal effiicency is obtained at lower band-gaps. However, the drop in band-gap energy is modest owing to a strong atmospheric absorption feature at 1.1um which serves to pin the optimum bandgap around 1.12eV.\n\n\nExercise: Concentrated AM0\nTry repeating the example above but use the AM0 extraterrestial spectrum. Observe what happens to the band-gap shift with increasing concentration. How is it different to AM1.5d?" }, { "objectID": "solcore-workshop-2/notebooks/6a-TMM_introduction.html", "href": "solcore-workshop-2/notebooks/6a-TMM_introduction.html", "title": "Section 6a: Basic cell optics", "section": "", - "text": "In this script, we will build on the TMM model from example 1(a) and look at the effects of interference.\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer\nfrom solcore.absorption_calculator import calculate_rat, OptiStack\nimport seaborn as sns" + "text": "In this script, we will build on the TMM model from example 1(a) and look at the effects of interference.\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer\nfrom solcore.absorption_calculator import calculate_rat, OptiStack\nimport seaborn as sns\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found." }, { "objectID": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#setting-up", @@ -473,21 +459,21 @@ "href": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#effect-of-si-thickness", "title": "Section 6a: Basic cell optics", "section": "Effect of Si thickness", - "text": "Effect of Si thickness\nNow we are going to loop through the different Si thicknesses generated above, and create a simple solar cell-like structure. Because we will only do an optical calculation, we don’t need to define a junction and can just make a simple stack of layers.\nWe then calculate reflection, absorption and transmission (RAT) for two different situations: 1. a fully coherent stack 2. assuming the silicon layer is incoherent. This means that light which enters the Si layer cannot interfere with itself, but light in the ARC layer can still show interference. In very thick layers (much thicker than the wavelength of light being considered) this is likely to be more physically accurate because real light does not have infinite coherence length; i.e. if you measured wavelength-dependent transmission or reflection of a Si wafer hundreds of microns thick you would not expect to see interference fringes.\nPLOT 1\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p) # silicon layer\n solar_cell = OptiStack([ARC_layer, base_layer]) # OptiStack (optical stack) to feed into calculate_rat function\n\n # Coherent calculation:\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False) # coherent calculation\n # For historical reasons, Solcore's default setting is to ignore reflection at the back of the cell (i.e. at the\n # interface between the final material in the stack and the substrate). Hence we need to tell the calculate_rat\n # function NOT to ignore this reflection (no_back_reflection=False).\n\n # Calculation assuming no interference in the silicon (\"incoherent\"):\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i']) # partially coherent: ARC is coherent, Si is not\n\n # Plot the results:\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1], label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(1) Absorption in Si with varying thickness\")\nplt.show()\n\nWe can see that the coherent calculations (solid lines) show clear interference fringes which depend on the Si thickness. The incoherent calculations do not have these fringes and seem to lie around the average of the interference fringes. For both sets of calculations, we see increasing absorption as the Si gets thicker, as expected." + "text": "Effect of Si thickness\nNow we are going to loop through the different Si thicknesses generated above, and create a simple solar cell-like structure. Because we will only do an optical calculation, we don’t need to define a junction and can just make a simple stack of layers.\nWe then calculate reflection, absorption and transmission (RAT) for two different situations: 1. a fully coherent stack 2. assuming the silicon layer is incoherent. This means that light which enters the Si layer cannot interfere with itself, but light in the ARC layer can still show interference. In very thick layers (much thicker than the wavelength of light being considered) this is likely to be more physically accurate because real light does not have infinite coherence length; i.e. if you measured wavelength-dependent transmission or reflection of a Si wafer hundreds of microns thick you would not expect to see interference fringes.\nPLOT 1\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p) # silicon layer\n solar_cell = OptiStack([ARC_layer, base_layer]) # OptiStack (optical stack) to feed into calculate_rat function\n\n # Coherent calculation:\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False) # coherent calculation\n # For historical reasons, Solcore's default setting is to ignore reflection at the back of the cell (i.e. at the\n # interface between the final material in the stack and the substrate). Hence we need to tell the calculate_rat\n # function NOT to ignore this reflection (no_back_reflection=False).\n\n # Calculation assuming no interference in the silicon (\"incoherent\"):\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i']) # partially coherent: ARC is coherent, Si is not\n\n # Plot the results:\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1], label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(1) Absorption in Si with varying thickness\")\nplt.show()\n\n\n\n\nWe can see that the coherent calculations (solid lines) show clear interference fringes which depend on the Si thickness. The incoherent calculations do not have these fringes and seem to lie around the average of the interference fringes. For both sets of calculations, we see increasing absorption as the Si gets thicker, as expected." }, { "objectID": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", "href": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", "title": "Section 6a: Basic cell optics", "section": "Effect of reflective substrate", - "text": "Effect of reflective substrate\nNow we repeat the calculation, but with an Ag substrate under the Si. Previously, we did not specify the substrate and so it was assumed by Solcore to be air (\\(n\\) = 1, \\(\\kappa\\) = 0).\nPLOT 2\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p)\n\n # As before, but now we specify the substrate to be silver:\n solar_cell = OptiStack([ARC_layer, base_layer], substrate=Ag)\n\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False)\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1],\n label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(2) Absorption in Si with varying thickness (Ag substrate)\")\nplt.show()\n\nWe see that the interference fringes get more prominent in the coherent calculation, due to higher reflection at the rear Si/Ag surface compared to Ag/Air. We also see a slightly boosted absorption at long wavelengths at all thicknesses, again due to improved reflection at the rear surface" + "text": "Effect of reflective substrate\nNow we repeat the calculation, but with an Ag substrate under the Si. Previously, we did not specify the substrate and so it was assumed by Solcore to be air (\\(n\\) = 1, \\(\\kappa\\) = 0).\nPLOT 2\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p)\n\n # As before, but now we specify the substrate to be silver:\n solar_cell = OptiStack([ARC_layer, base_layer], substrate=Ag)\n\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False)\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1],\n label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(2) Absorption in Si with varying thickness (Ag substrate)\")\nplt.show()\n\n\n\n\nWe see that the interference fringes get more prominent in the coherent calculation, due to higher reflection at the rear Si/Ag surface compared to Ag/Air. We also see a slightly boosted absorption at long wavelengths at all thicknesses, again due to improved reflection at the rear surface" }, { "objectID": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", "href": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", "title": "Section 6a: Basic cell optics", "section": "Effect of polarization and angle of incidence", - "text": "Effect of polarization and angle of incidence\nFinally, we look at the effect of incidence angle and polarization of the light hitting the cell.\nPLOT 3\n\nangles = [0, 30, 60, 70, 80, 89] # angles in degrees\n\nARC_layer = Layer(width=si('75nm'), material=SiN)\nbase_layer = Layer(width=si(\"100um\"), material=Si_p)\n\ncolors = sns.cubehelix_palette(n_colors=len(angles))\n\nplt.figure()\n\nfor i1, theta in enumerate(angles):\n\n solar_cell = OptiStack([ARC_layer, base_layer])\n\n RAT_s = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='s',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n RAT_p = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='p',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n\n plt.plot(wavelengths*1e9, RAT_s[\"A\"], color=colors[i1], label=str(round(theta)))\n plt.plot(wavelengths*1e9, RAT_p[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"$\\theta (^\\circ)$\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(3) Absorption in Si with varying angle of incidence\")\nplt.show()\n\nFor normal incidence (\\(\\theta = 0^\\circ\\)), s (solid lines) and p (dashed lines) polarization are equivalent. As the incidence angle increases, in general absorption is higher for p-polarized light (due to lower reflection). Usually, sunlight is modelled as unpolarized light, which computationally is usually done by averaging the results for s and p-polarized light." + "text": "Effect of polarization and angle of incidence\nFinally, we look at the effect of incidence angle and polarization of the light hitting the cell.\nPLOT 3\n\nangles = [0, 30, 60, 70, 80, 89] # angles in degrees\n\nARC_layer = Layer(width=si('75nm'), material=SiN)\nbase_layer = Layer(width=si(\"100um\"), material=Si_p)\n\ncolors = sns.cubehelix_palette(n_colors=len(angles))\n\nplt.figure()\n\nfor i1, theta in enumerate(angles):\n\n solar_cell = OptiStack([ARC_layer, base_layer])\n\n RAT_s = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='s',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n RAT_p = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='p',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n\n plt.plot(wavelengths*1e9, RAT_s[\"A\"], color=colors[i1], label=str(round(theta)))\n plt.plot(wavelengths*1e9, RAT_p[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"$\\theta (^\\circ)$\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(3) Absorption in Si with varying angle of incidence\")\nplt.show()\n\n\n\n\nFor normal incidence (\\(\\theta = 0^\\circ\\)), s (solid lines) and p (dashed lines) polarization are equivalent. As the incidence angle increases, in general absorption is higher for p-polarized light (due to lower reflection). Usually, sunlight is modelled as unpolarized light, which computationally is usually done by averaging the results for s and p-polarized light." }, { "objectID": "solcore-workshop-2/notebooks/6a-TMM_introduction.html#conclusions", @@ -966,312 +952,298 @@ "text": "Times & locations\nPre-workshop help sessions (OPTIONAL):\n\nMonday 20 November, 3-4 pm\nTuesday 21 November, 3-4 pm\n\nIn TETB meeting room Gnd 22 (Ground Floor, across from the main entrance). If the installation described above works for you, no need to attend either of these!\nWorkshop:\nWednesday - Friday, 22 - 24 November\n1 - 5 pm. Click here for full schedule (subject to change).\nLocation: F10 June Griffith M10 (K-F10-M10), UNSW Sydney\n(June Griffith building is next to the Law faculty, diagonally across from Tyree on the University Mall. When you enter the building from the University Mall (coming from Tyree), you need to go up the set of stairs by the main entrance, go through the fire doors, and turn left. If you are coming from the other side, the room is directly on your right when you enter)." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", "section": "", - "text": "The structure in this example is based on that of the previous example (9a), but with the planar bottom Si cell replaced by a Si cell with a pyramidal texture, bonded to the III-V top cells with a low-index epoxy/glass layer.\nWe could use the angular redistribution matrix method as in the previous example - however, because in this example we only need to use TMM and ray-tracing (RT), we can use the ray-tracing method with integrated RT directly (this is generally faster, because we do not need to calculate the behaviour of the surfaces for every angle of incidence)." + "text": "In this example, we will build two structures similar to those described in this paper. These are both triple-junction, two-terminal GaInP/GaAs/Si cells; one cell is planar, while the other has a diffraction grating deposited on the rear of the bottom Si cell to boost its current." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#setting-up", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#setting-up", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#setting-up", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#setting-up", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", "section": "Setting up", - "text": "Setting up\nWe load relevant packages and define materials, the same as in the previous example.\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.ray_tracing import rt_structure\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.textures import planar_surface, regular_pyramids\nfrom rayflare.options import default_options\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# download_db()\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nepoxy = material(\"BK7\")()\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nAlGaAs = material(\"AlGaAs\")\n\nAir = material(\"Air\")()\n\nGaAs = material(\"GaAs\")\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nWe define the layers we will need, as before. We specify the thickness of the silicon (280 \\(\\mu\\)m) and epoxy (1 mm) at the top:\n\nd_Si = 280e-6 # thickness of Si wafer\nd_epoxy = 1e-3 # thickness of epoxy\n\nARC = [\n Layer(110e-9, MgF2),\n Layer(65e-9, Ta2O5),\n]\n\nGaInP_junction = [\n Layer(17e-9, window),\n Layer(400e-9, GaInP(In=0.50)),\n Layer(100e-9, AlGaAs(Al=0.8))]\n\n# 100 nm TJ\ntunnel_1 = [\n Layer(80e-9, AlGaAs(Al=0.8)),\n Layer(20e-9, GaInP(In=0.5)),\n]\n\nGaAs_junction = [\n Layer(17e-9, GaInP(In=0.5), role=\"window\"),\n Layer(1050e-9, GaAs()),\n Layer(70e-9, AlGaAs(Al=0.8), role=\"bsf\")]\n\nspacer_ARC = [\n Layer(80e-9, Ta2O5),\n]" + "text": "Setting up\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.options import default_options\nfrom rayflare.structure import Interface, BulkLayer, Structure\nfrom rayflare.matrix_formalism import process_structure, calculate_RAT\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\nAs before, we load some materials from the refractiveindex.info database. The MgF\\(_2\\) and Ta\\(_2\\)O\\(_5\\) are the same as the ARC example; the SU8 is a negative photoresist which was used in the reference paper The optical constants for silver are also loaded from a reliable literature source. Note that the exact compositions of some semiconductor alloy layers (InGaP, AlInP and AlGaAs) are not given in the paper and are thus reasonable guesses.\n\n# download_db(confirm=True) # only needs to be run once\n# commented out because this should have already been done in a previous example. Uncomment if necessary.\n\n\n%%capture\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")(In=0.5)\nAlGaAs = material(\"AlGaAs\")(Al=0.8)\nGaAs = material(\"GaAs\")()\nSi = material(\"Si\")\n\nAir = material(\"Air\")()\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()" }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-cell-layers", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-cell-layers", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#defining-the-cell-layers", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#defining-the-cell-layers", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", "section": "Defining the cell layers", - "text": "Defining the cell layers\nThere are three interfaces in the cell which will define the structure to simulate:\n\nthe III-V/epoxy interface, where the epoxy itself will be treated as a bulk layer in the simulation\nthe epoxy/Si interface, where the Si has a pyramidal texture (the Si itself is another bulk layer in the simulation).\nthe rear surface of the cell, where the Si again has a pyramidal texture (and we assume there is a silver back mirror behind the cell)\n\nThese 3 interfaces are defined here, using the pre-defined textures for a planar surface or regular pyramids:\n\nfront_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + spacer_ARC\n\nfront_surf = planar_surface(\n interface_layers = front_layers\n)\n\nSi_front = regular_pyramids(\n elevation_angle=50,\n upright=True\n)\n\nSi_back = regular_pyramids(\n elevation_angle=50,\n upright=False\n)\n\nNow we set relevant options for the solver. We set the number of rays to trace at each wavelength (more rays will make the result less noisy, but increase computation time) and whether to calculate the absorption profile in the bulk layers (no, in this case). The randomize_surface options determines whether the ray keeps track of its positions in the unit cell while travelling between surfaces; we set this to False to mimic random pyramids.\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl,\n output_units=\"photon_flux_per_m\")\n\noptions.wavelength = wl\noptions.project_name = \"III_V_Si_cell\"\n\n# options for ray-tracing\noptions.randomize_surface = True\noptions.n_rays = 1000\noptions.bulk_profile = False\noptions.theta_in = 45*np.pi/180" + "text": "Defining the cell layers\nNow we define the layers for the III-V top junctions, and the Si wafer, grouping them together in a logical way. In this example, we will only do optical simulations, so we will not set e.g. diffusion lengths or doping levels.\n\nARC = [Layer(110e-9, MgF2), Layer(65e-9, Ta2O5)]\n\nGaInP_junction = [Layer(17e-9, window), Layer(400e-9, GaInP), Layer(100e-9, AlGaAs)]\n\ntunnel_1 = [Layer(80e-9, AlGaAs), Layer(20e-9, GaInP)]\n\nGaAs_junction = [Layer(17e-9, GaInP), Layer(1050e-9, GaAs), Layer(70e-9, AlGaAs)]\n\ntunnel_2 = [Layer(50e-9, AlGaAs), Layer(125e-9, GaAs)]\n\nSi_junction = [Layer(280e-6, Si(Nd=si(\"2e18cm-3\"), hole_diffusion_length=2e-6), role=\"emitter\")]\n\ncoh_layers = len(ARC) + len(GaInP_junction) + len(tunnel_1) + len(GaAs_junction) + len(tunnel_2)\n\nAs for Example 7, to get physically reasonable results we must treat the very thick layers in the structure incoherently. The coh_layers variable sums up how many thin layers (which must be treated coherently) must be included in the coherency_list options." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-structures", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-structures", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Defining the structures", - "text": "Defining the structures\nFinally, we define the ray-tracing structure we will use, using the interfaces, bulk materials, and options set above. Because we want to calculate the reflection/absorption/transmission probabilities at the front surface using TMM, we set the use_TMM argument to True. We also define a completely planar cell with the same layer thicknesses etc. to compare and evaluate the effect of the textures Si surfaces.\n\nsolar_cell = rt_structure(\n textures=[front_surf, Si_front, Si_back],\n materials=[epoxy, Si()],\n widths=[d_epoxy, d_Si],\n incidence=Air,\n transmission=Ag,\n options=options,\n use_TMM=True,\n save_location=\"current\", # lookup table save location\n overwrite=True, # whether to overwrite any previously existing results, if found\n)\n\n# options for TMM\noptions.coherent = False\noptions.coherency_list = len(front_layers)*['c'] + ['i']*2\n\nsolar_cell_planar = tmm_structure(\n layer_stack = front_layers + [Layer(d_epoxy, epoxy), Layer(d_Si, Si())],\n incidence=Air,\n transmission=Ag,\n)" + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#planar-cell", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#planar-cell", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", + "section": "Planar cell", + "text": "Planar cell\nNow we define the planar cell, and options for the solver:\n\ncell_planar = tmm_structure(\n ARC + GaInP_junction + tunnel_1 + GaAs_junction + tunnel_2 + Si_junction,\n incidence=Air, transmission=Ag,\n)\n\nn_layers = cell_planar.layer_stack.num_layers\n\ncoherency_list = [\"c\"]*coh_layers + [\"i\"]*(n_layers-coh_layers)\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl,\n output_units=\"photon_flux_per_m\")\n\noptions.wavelength = wl\noptions.coherency_list = coherency_list\noptions.coherent = False\n\nRun the TMM calculation for the planar cell, and then extract the relevant layer absorptions. These are used to calculate limiting currents (100% internal quantum efficiency), which are displayed on the plot with the absorption in each layer.\n\ntmm_result = cell_planar.calculate(options=options)\n\nGaInP_A = tmm_result['A_per_layer'][:,3]\nGaAs_A = tmm_result['A_per_layer'][:,8]\nSi_A = tmm_result['A_per_layer'][:,coh_layers]\n\nJmax_GaInP = q*np.trapz(GaInP_A*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_A*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_A*AM15G.spectrum()[1], x=wl)/10\n\nR_spacer_ARC = tmm_result['R']\n\nplt.figure(figsize=(6,4))\nplt.plot(wl * 1e9, GaInP_A, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_A, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_A, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, 1 - R_spacer_ARC, '-y', label=\"1 - R\")\n\nplt.text(450, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(860, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance\")\nplt.tight_layout()\nplt.legend(loc='upper right')\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.show()\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ag/Jiang.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#calculations", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#calculations", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Calculations", - "text": "Calculations\nCalculate the R/A/T for the planar reference cell:\n\ntmm_result = solar_cell_planar.calculate(options=options)\n\nGaInP_A_tmm = tmm_result['A_per_layer'][:,3]\nGaAs_A_tmm = tmm_result['A_per_layer'][:,8]\nSi_A_tmm = tmm_result['A_per_layer'][:,len(front_layers)+1]\n\nJmax_GaInP_tmm = q*np.trapz(GaInP_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs_tmm = q*np.trapz(GaAs_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_Si_tmm = q*np.trapz(Si_A_tmm*AM15G.spectrum()[1], x=wl)/10\n\nCalculate the R/A/T for the textured cell:\n\nrt_result = solar_cell.calculate(options=options)\n\nGaInP_absorption_ARC = rt_result['A_per_interface'][0][:,3]\nGaAs_absorption_ARC = rt_result['A_per_interface'][0][:,8]\nSi_absorption_ARC = rt_result['A_per_layer'][:,1]\n\nJmax_GaInP = q*np.trapz(GaInP_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_absorption_ARC*AM15G.spectrum()[1], x=wl)/10" + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#cell-with-rear-grating", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#cell-with-rear-grating", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", + "section": "Cell with rear grating", + "text": "Cell with rear grating\nNow, for the cell with a grating on the rear, we have a multi-scale problem where we must combine the calculation of absorption in a very thick (compared to the wavelengths of light) layer of Si with the effect of a wavelength-scale (1000 nm pitch) diffraction grating. For this, we will use the Angular Redistribution Matrix Method (ARMM) which was also used in Example 8.\nThe front surface of the cell (i.e. all the layers on top of Si) are planar, and can be treated using TMM. The rear surface of the cell, which has a crossed grating consisting of silver and SU8, must be treated with RCWA to account for diffraction. The thick Si layer will be the bulk coupling layer between these two interfaces.\nFirst, we set up the rear grating surface; we must define its lattice vectors, and place the Ag rectangle in the unit cell of the grating. More details on how unit cells of different shapes can be defined for the RCWA solver can be found here.\n\nx = 1000\n\nd_vectors = ((x, 0), (0, x))\narea_fill_factor = 0.4\nhw = np.sqrt(area_fill_factor) * 500\n\nback_materials = [\n Layer(width=si(\"250nm\"), material=SU8,\n geometry=[{\"type\": \"rectangle\", \"mat\": Ag, \"center\": (x / 2, x / 2),\n \"halfwidths\": (hw, hw), \"angle\": 0}])]\n\nNow, we define the Si bulk layer, and the III-V layers which go in the front interface. Finally, we put everything together into the ARMM Structure, also giving the incidence and transmission materials.\n\nbulk_Si = BulkLayer(280e-6, Si(), name=\"Si_bulk\")\n\nIII_V_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + tunnel_2\n\nfront_surf_planar = Interface(\"TMM\", layers=III_V_layers, name=\"III_V_front\",\n coherent=True)\n\nback_surf_grating = Interface(\"RCWA\", layers=back_materials, name=\"crossed_grating_back\",\n d_vectors=d_vectors, rcwa_orders=60)\n\ncell_grating = Structure([front_surf_planar, bulk_Si, back_surf_grating],\n incidence=Air, transmission=Ag)\n\nBecause RCWA calculations are very slow compared to TMM, it makes sense to only carry out the RCWA calculation at wavelengths where the grating has any effect. Depending on the wavelength, all the incident light may be absorbed in the III-V layers or in its first pass through the Si, so it never reaches the grating. We check this by seeing which wavelengths have even a small amount of transmission into the silver back mirror, and only doing the new calculation at these wavelengths. At shorter wavelengths, the results previously calculated using TMM can be used.\n\n%%capture\n\nwl_rcwa = wl[tmm_result['T'] > 1e-4] # check where transmission fraction is bigger\n# than 1E-4\n\noptions.wavelength = wl_rcwa\noptions.project_name = \"III_V_Si_cell\"\noptions.n_theta_bins = 30\noptions.c_azimuth = 0.25\noptions.RCWA_method = \"inkstone\"\n\nprocess_structure(cell_grating, options, save_location='current')\nresults_armm = calculate_RAT(cell_grating, options, save_location='current')\nRAT = results_armm[0]\n\nINFO: Making matrix for planar surface using TMM for element 0 in structure\nINFO: RCWA calculation for element 2 in structure\nINFO: RCWA calculation for wavelength = 940.0000000000001 nm\nINFO: RCWA calculation for wavelength = 990.0 nm\nINFO: RCWA calculation for wavelength = 960.0000000000001 nm\nINFO: RCWA calculation for wavelength = 1000.0000000000001 nm\nINFO: RCWA calculation for wavelength = 1010.0000000000001 nm\nINFO: RCWA calculation for wavelength = 950.0 nm\nINFO: RCWA calculation for wavelength = 1020.0 nm\nINFO: RCWA calculation for wavelength = 1030.0 nm\nINFO: RCWA calculation for wavelength = 970.0 nm\nINFO: RCWA calculation for wavelength = 980.0000000000001 nm\nINFO: RCWA calculation for wavelength = 1040.0 nm\nINFO: RCWA calculation for wavelength = 1050.0 nm\nINFO: RCWA calculation for wavelength = 1060.0 nm\nINFO: RCWA calculation for wavelength = 1070.0000000000002 nm\nINFO: RCWA calculation for wavelength = 1080.0 nm\nINFO: RCWA calculation for wavelength = 1090.0000000000002 nm\nINFO: RCWA calculation for wavelength = 1100.0 nm\nINFO: RCWA calculation for wavelength = 1110.0000000000002 nm\nINFO: RCWA calculation for wavelength = 1120.0 nm\nINFO: RCWA calculation for wavelength = 1130.0 nm\nINFO: RCWA calculation for wavelength = 1140.0 nm\nINFO: RCWA calculation for wavelength = 1150.0 nm\nINFO: RCWA calculation for wavelength = 1160.0000000000002 nm\nINFO: RCWA calculation for wavelength = 1170.0 nm\nINFO: RCWA calculation for wavelength = 1180.0000000000002 nm\nINFO: RCWA calculation for wavelength = 1190.0 nm\nINFO: RCWA calculation for wavelength = 1200.0000000000002 nm\nINFO: After iteration 1: maximum power fraction remaining = 0.6314182213481858\nINFO: After iteration 2: maximum power fraction remaining = 0.4894786243853588\nINFO: After iteration 3: maximum power fraction remaining = 0.37936409941254223\nINFO: After iteration 4: maximum power fraction remaining = 0.2923832297564508\nINFO: After iteration 5: maximum power fraction remaining = 0.22442973939149682\nINFO: After iteration 6: maximum power fraction remaining = 0.17246216581794507\nINFO: After iteration 7: maximum power fraction remaining = 0.13285217091457766\nINFO: After iteration 8: maximum power fraction remaining = 0.10234781936869419\nINFO: After iteration 9: maximum power fraction remaining = 0.07886820065679137\nINFO: After iteration 10: maximum power fraction remaining = 0.06079469712756424\nINFO: After iteration 11: maximum power fraction remaining = 0.046878313361311943\nINFO: After iteration 12: maximum power fraction remaining = 0.03615861519954806\nINFO: After iteration 13: maximum power fraction remaining = 0.027897938239687625\nINFO: After iteration 14: maximum power fraction remaining = 0.021529761625524578\nINFO: After iteration 15: maximum power fraction remaining = 0.01661882076260673\nINFO: After iteration 16: maximum power fraction remaining = 0.01283049650651593\nINFO: After iteration 17: maximum power fraction remaining = 0.009907380417311016\n\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.WARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#plotting-the-results", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#plotting-the-results", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Plotting the results", - "text": "Plotting the results\nFinally, we plot the results; the solid lines show the results for the textured Si cell (calculated using ray-tracing), the dashed lines for the planar cell (calculated using TMM). The maximum possible currents are shown in the plot, with the value in brackets for Si being for the planar cell.\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_absorption_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_absorption_ARC, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_absorption_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, GaInP_A_tmm, \"--k\")\nplt.plot(wl * 1e9, GaAs_A_tmm, \"--b\")\nplt.plot(wl * 1e9, Si_A_tmm, \"--r\")\nplt.plot(wl * 1e9, rt_result['R'], '-', color='grey', label=\"Reflected\")\nplt.plot(wl * 1e9, tmm_result['R'], '--', color='grey')\n\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(870, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.text(870, 0.45, r\"({:.1f} mA/cm$^2)$\".format(Jmax_Si_tmm))\n\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.tight_layout()\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#comparison-of-planar-and-grating-cell", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#comparison-of-planar-and-grating-cell", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", + "section": "Comparison of planar and grating cell", + "text": "Comparison of planar and grating cell\nWe extract the relevant absorption per layer, and use it to calculate the new limiting current for the Si junction. The plot compares the absorption in the Si with and without the grating.\n\nSi_A_total = np.zeros(len(wl))\nSi_A_total[tmm_result['T'] > 1e-4] = RAT['A_bulk'][0]\nSi_A_total[tmm_result['T'] <= 1e-4] = Si_A[tmm_result['T'] <= 1e-4]\n\nJmax_Si_grating = q*np.trapz(Si_A_total*AM15G.spectrum()[1], x=wl)/10\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_A, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_A, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_A, \"--r\", label=\"Si (planar)\")\nplt.plot(wl * 1e9, Si_A_total, '-r', label=\"Si (with grating)\")\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.50, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(860, 0.45, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si_grating))\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance\")\n\nplt.tight_layout()\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#questionschallenges", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#questionschallenges", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Questions/challenges", - "text": "Questions/challenges\n\nDoes it make sense to do a ray-tracing calculation for short wavelengths? For this structure, can you speed up the calculation and avoid the random noise at short wavelengths?\nHow much current is lost to parasitic absorption in e.g. tunnel junctions, window layers etc.?\nHow can we reduce reflection at the epoxy interfaces?\nIf the epoxy/glass layer is much thicker than the relevant incident wavelengths, and not absorbing, does the exact thickness matter in the simulation?\nWhat happens if only the rear surface is textured? Would a structure without the front texture have other advantages?\nWhy does the Si have lower absorption/limiting current in this structure compared to the previous example?" + "objectID": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#questions", + "href": "solcore-workshop-2/notebooks/9a-GaInP_GaAs_Si_grating.html#questions", + "title": "Section 9a: Planar III-V on planar Si, with rear grating", + "section": "Questions", + "text": "Questions\n\nWhy does the grating only affect the absorption in Si at long wavelengths?\nWhat is the reason for using the angular redistribution matrix method, rather than defining an RCWA-only structure (rcwa_structure)?" }, { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html", + "title": "Section 5b: Planar Si solar cell using PDD", "section": "", - "text": "Tuesday 1 August 2023" + "text": "In the previous example, we looked at a silicon cell using the depletion approximation. Here, we will instead use one of Solcore’s Poisson drift-diffusion (PDD) solvers, which can handle doping profiles (not just constant doping levels). Note that Solcore actually has two PDD solvers: a built-in one which was developed in Fortran specifically for cells with quantum wells, and an interface to the Sesame package, which was written in Python and developed for silicon-based cells. Here, we will use the Sesame solver.\nThe script starts of in much the same way as the DA cell in the previous example: we import relevant external packages and Solcore features, define some of the materials we will use, and set user options for solar_cell_solver.\nfrom solcore.solar_cell import SolarCell, Junction, Layer\nfrom solcore.state import State\nfrom solcore.solar_cell_solver import solar_cell_solver\nimport numpy as np\nfrom solcore.light_source import LightSource\nfrom scipy.special import erfc\n\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\n\nAir = material(\"Air\")()\nMgF2 = material(\"MgF2\")()\nAg = material(\"Ag\")()\nTCO = material('ITO2')()\n\nwavelengths = np.linspace(280, 1200, 100)*1e-9\n\noptions = State() # initialise the options\noptions.wavelength = wavelengths\noptions.optics_method = 'TMM'\noptions.light_iv = True\noptions.T = 298\noptions.light_source = LightSource(source_type=\"standard\",\n version=\"AM1.5g\", x=options.wavelength)\n\noptions.voltages = np.linspace(0, 0.8, 40)\noptions.internal_voltages = options.voltages\noptions.mpp = True\noptions.no_back_reflection = False\noptions.position = 1e-9" }, { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#trivich-flinn-efficiency-limit", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#trivich-flinn-efficiency-limit", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "Trivich-Flinn Efficiency limit", - "text": "Trivich-Flinn Efficiency limit\nIn 1955 Trivich & Flinn published a model for limiting efficiency. The limit it produces is too high, but it represents a good place to start with a computer model.\nTrivich D, Flinn PA. Maximum efficiency of solar energy conversion by quantum processes. In Solar Energy Research, Daniels F, Duffie J (eds). Thames and Hudson: London, 1955.\nTrivich & Flinn assumed that the ideal solar cell would absorb all photons with energy above the band-gap energy \\(E_g\\) and that the maximum voltage that could ever be attained in a solar cell is the band-gap energy. The latter assumption is incorrect unless the solar cell is operating at absolute zero temperature.\nTo develop a model for the Trivich & Flinn efficiency limit the first step is to calculate what the limit to the photocurrent is in a solar cell." - }, - { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#limits-to-the-short-circuit-current", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#limits-to-the-short-circuit-current", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "Limits to the short-circuit current", - "text": "Limits to the short-circuit current\n\nSolar Spectrum\nThe solar spectrum defines the ultimate current that a solar cell can produce. First we will plot the AM1.5G solar spectrum \\(b(\\lambda)\\) as a spectral irradiance, meaning that the y-axis has units of \\(W.m^{-2}.nm^{-1}\\)\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\nimport seaborn as sns\n\n# Setup the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 # wl contains the x-coordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl*1e9, version='AM1.5g',\n output_units=\"power_density_per_nm\")\n\nplt.figure()\nplt.title('Spectral Irradiance')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\nLet us now integrate the solar spectrum to provide the total irradiance in units of [\\(W.m^{-2}\\)]. The code below performs the following operation \\(b=\\int^{\\infty}_{0} b(\\lambda) d\\lambda\\)\n\n# Since .spectrum function returns a tuple (x,y) but np.trapz requires data in format (y,x) these are extracted into separate 1D np arrays.\nyval = am15g.spectrum()[1]\nxval = am15g.spectrum()[0]\nintegrated_value = np.trapz(yval,xval) # Perform integration using trapezium rule\nb = integrated_value # Save the integrated power density for the sun for later.\nprint('b = ', integrated_value)\n\nLet’s take the opportunity to learn how to format numbers nicely in Python. Here we use the command “%.0f” % to display the value to zero decimal places.\n\nprint('b = ',\"%.0f\" % integrated_value,\"W.m-2\")\n\nSolcore performs this integration for us internally. Let’s try the same exercise but for the extraterrestrial solar spectrum, AM0\n\nam0 = LightSource(source_type='standard', x=wl*1e9, version='AM0')\nprint(\"AM0 integrates to\", \"%.0f\" % am0.power_density, \"W.m-2\")\n\n\n\nSpectral Photon Flux\nTo calculate a short-circuit current it is convenient to change the units. Two changes are necessary : 1. Since we specify band-gap energies in electron volts (eV) we need to transform the x-axis from nm to eV 2. Photocurrent is proportional to the incident photon flux (number of photons per second) not the irradiance (watts) so we need to convert the y-axis from energy to photon number.\nNote: The conversion is performed internally within the software but be aware that because the transformation from wavelength is non-linear, changing the x-axis from nm to eV also changes the y-values of the data. This is known as a Jacobian transformation and discussed in more detail in an article “Getting the basics right: Jacobian Conversion of Wavelength and Energy Scales for Quantatitive Analysis of Emission Spectra”, Journal of Physical Chemistry, 4(19) 3316 (2013)\n\nev = np.linspace(0.02,4,4000)\nflux = LightSource(source_type='standard', version='AM1.5g', x=ev, output_units='photon_flux_per_ev')\n\nplt.figure()\nplt.title('Spectral Photon Flux')\nplt.plot(*flux.spectrum(), label='AM1.5G')\nplt.xlim(0.2, 4)\nplt.xlabel('Photon Energy (eV)')\nplt.ylabel('Photon flux N ($ph.s^{-1}m^{-2}eV^{-1}$)')\nplt.legend()\n\n\n\nCalculating the short-circuit current\nIntegrating the photon flux can provide an upper limit to the short-circuit current [A.m-2]. We can integrate the spectrum over the entire spectral range using \\(J_{sc}=q\\int_{0}^{\\infty}N(E)dE\\)\n\nq = 1.60217662E-19\nyval = flux.spectrum()[1]\nxval = flux.spectrum()[0]\nyint = q*np.trapz(yval,xval) # Perform integration using trapezium rule\n\nprint(\"%.0f\" % yint)\n\nA more useful calculation is to calculate the current that a solar cell would produce with a particular band-gap energy. To do this requires a bit more coding, since we now wish to integrate between limits: \\(J_{sc}=q\\int_{Eg}^{\\infty}N(E)dE\\)\nLet’s do this for a band-gap of 1.42 eV:\n\nq = 1.60217662E-19\neg = 1.42\nyval = flux.spectrum()[1]\nxval = flux.spectrum()[0]\n\nyval[xval < eg] = 0 # set photon flux to zero for photon energies below the band-gap\n\nyint = q*np.trapz(yval,xval) # Perform integration using trapezium rule\n\nprint(\"%.0f\" % yint)\n\nLet’s reproduce the \\(J_{sc}\\) vs \\(E_g\\) graph that is shown on p. 87 of Martin Green’s Solar Cells book:\n\nq = 1.60217662E-19\n\ndef getJsc(eg):\n yval = flux.spectrum()[1] # Start with the solar spectrum in yval & xval\n xval = flux.spectrum()[0]\n yval[xval < eg] = 0 # set photon flux to zero for photon energies below the band-gap\n return q*np.trapz(yval,xval) # return the integrated value\n\neg = np.linspace(0.5,2.5,100)\njsc = np.vectorize(getJsc)(eg)\n\nplt.figure()\nplt.title('Limit to the short-circuit current $J_{sc}$')\nplt.plot(eg, jsc/10, label='AM1.5G') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('$J_{sc}$ ($mA.cm^{-2}$)')\nplt.legend()\n\n\n\nCalculating the Trivich-Flinn Efficiency limit\nNow that the limit to \\(J_{sc}\\) is known, we can estimate the power of delivered by the solar cell by evaluating \\(\\frac{Eg J_{sc}}{b}\\)\n\nplt.figure()\nplt.title('Trivich-Flinn Single Junction Efficiency Limit')\nplt.plot(eg, 100*eg*jsc/b,label='AM1.5G') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()" - }, - { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#the-shockley-queisser-efficiency-limit", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#the-shockley-queisser-efficiency-limit", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "The Shockley-Queisser Efficiency limit", - "text": "The Shockley-Queisser Efficiency limit\nShockley & Queisser refined the Trivich-Flinn limit by linking the voltage a solar cell can deliver to the Fermi level separation in the conduction and valance bands, not the band-gap energy.\nTo do this, a model is required for the recombination processes between the conduction and valance bands. The most fundamental (and inescapable) recombination mechanism is the radiative process. In section 3 we will derive a limit to Shockley’s diode equation \\(J=J_0 e^{\\frac{V}{kT}}\\) for the radiative limit, that being a diode where all current flows are linked to an optical process, either absorption or recombination.\nIn the radiative limit and an abrupt band-edge at band-gap energy \\(E_g\\) it can be shown that \\(J_0\\) is approximated by \\(J_0=q \\frac{2 \\pi}{c^2 h^3} kT \\left(E_g^2+2 E_g k T+2 k^2 T^2\\right) e^{\\frac{-E_g}{k T}}\\)\nWe can now plot a chart of \\(J_0\\) as a function of band-gap energy using this expression:\n\n# Define some physical constants:\nq = 1.60217662E-19 # electronic charge [C]\nk = 1.38064852E-23/q # Boltzmann constant [eV/K]\nh = 6.62607004E-34/q # Planck constant expressed in [eV.s]\nc = 299792458 # Speed of light [m.s^-1]\n\nt = 300 # Perform the calculation for a solar cell at 300K.\n\n# Define a function to return J0 implementing the expression above\ndef getJ0(eg):\n return k*t*q*(2*np.pi/(c**2*h**3))*(eg**2+2*eg*k*t+2*k**2*t**2)*np.exp(-eg/(k*t))\n\neg = np.linspace(0.5,2.5,100)\nj0 = np.vectorize(getJ0)(eg)\n\nplt.figure()\nplt.title('The radiative limit to $J_0$ plotted as a function of band-gap energy Eg')\nplt.plot(eg,j0,label='J0') # Divide by 10 to convert from A.m^-2 to mA.cm^-2\nplt.xlim(0.2, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('$J_{0}$ ($A.m^{-2}$)')\nplt.yscale(\"log\")\nplt.legend()\n\nLet’s obtain J0 for GaAs and InGaP, two common III-V materials that are used in tandem solar cells: evaluate getJ0() for Eg=1.42 and Eg=1.88\n\ngetJ0(1.42)\n\n\ngetJ0(1.88)" + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#defining-materials-and-doping-profile", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#defining-materials-and-doping-profile", + "title": "Section 5b: Planar Si solar cell using PDD", + "section": "Defining materials and doping profile", + "text": "Defining materials and doping profile\nThe Sesame PDD solver which we will be using can accept depth-dependent doping profiles (although you can also still set constant doping, like in the previous example, for each layer). Because we are going to pass a doping profile rather than distinct p and n-type materials, we just define one Si material which will be used for the whole junction, with electron and hole mobilities and lifetimes.\nOf course, there are many other material parameters which the PDD solver must have access to, such as radiative and Auger recombination rates, electron affinity, etc.; these are stored in Solcore’s material database, but they can always be overridden by user-specified values when calling the material function.\n\nSi_pn = material(\"Si\")(electron_mobility=si(\"1e4cm2\"), hole_mobility=si(\"1e3cm2\"),\n electron_minority_lifetime=0.001, hole_minority_lifetime=0.001)\n\nNow we will define the doping profile. We will define a p-n junction, with the highly-doped region (the emitter) at the rear and an complimentary error function (‘erfc’) profile at the front and rear surfaces. Note that Solcore expects the doping to be provided in base Si units (per m3). Solcore expects the doping profile information in the form of a function which returns the doping at a given depth (in m) in the junction. Positive values are n-type doping, negative values are p-type.\n\nnD = si(\"1e20cm-3\") # maximum n-type (donor) doping\nnA = si(\"1e19cm-3\") # maximum p-type (acceptor) doping\nbulk_doping = si(\"5e15cm-3\") # n type bulk doping\n\nd_bulk = 100e-6 # Si thickness, in m\n\n# rear junction (n-type)\ndef doping_profile_func(x):\n\n L = d_bulk\n\n doping_profile = - nA * erfc(x/300e-9) # characteristic depth of 300 nm - front p-type doping\n\n doping_profile_rear = nD * erfc((L - x)/200e-9) # characteristic depth of 200 nm - rear n-type doping\n\n return doping_profile + doping_profile_rear + bulk_doping\n\nTo check it looks reasonable, let’s plot this doping profile:\n\ndepth = np.linspace(0, d_bulk, int(1e5))\n\nplt.figure()\nplt.plot(depth*1e6, doping_profile_func(depth))\nplt.xlabel(r\"Depth ($\\mu$m)\")\nplt.ylabel(r\"Doping (m$^{-3}$)\")\nplt.show()\n\n\n\n\nThat didn’t help very much, because the cell is too wide compared to the region where the doping is changing! Let’s try again but splitting the plot into two parts for the front and rear surface (since nothing interesting is happening in the middle).\n\nfig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(5, 3))\n\nax1.plot(depth*1e6, doping_profile_func(depth))\nax1.set_xlim(0, 0.5)\nax1.set_ylabel(r\"Doping (m$^{-3}$)\")\nax1.set_xlabel('x (um)')\n\nax2.plot(depth*1e6, doping_profile_func(depth))\nax2.set_xlim(d_bulk*1e6 - 0.5, d_bulk*1e6)\nax2.set_xlabel('x (um)')\nplt.tight_layout()\nplt.show()\n\n\n\n\nWe will add transparent conducting oxides (TCOs) and an anti-reflection coating. Note that a real Si cell would have a more complicated layer structure (for example, for a heterojunction cell, the amorphous Si layers); we can add as many layers as we want for Solcore to consider, but will keep it simple here. In this case, these layers will be outside the junction: this means they will have optical effects but will not be included in the drift-diffusion calculation. They can be included in the junction, but this requires setting the relevant transport-related parameters.\n\nfront_materials = [Layer(80e-9, MgF2), Layer(55e-9, TCO)]\n\nback_materials = [Layer(55e-9, TCO),\n Layer(120e-9, MgF2)]" }, { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-iv-curve", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-iv-curve", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "Calculating the IV curve", - "text": "Calculating the IV curve\nWe are now able to calculate the limiting efficiency for a solar cell using the simple Shockley diode expression \\(J(V)=J_{s c}-J_0\\left(e^{\\frac{q V}{k T}}-1\\right)\\). Let’s plot the IV curve for a band-gap of 1.42eV\n\ndef getJ(v,eg):\n return getJsc(eg) - getJ0(eg)*(np.exp(v/(k*t)) - 1)\n\neg = 1.42\nv = np.linspace(0,1.2,100)\nj = np.vectorize(getJ)(v,eg)\n\nplt.figure(3)\nplt.title('Limiting Efficiency IV curve for Eg=1.42eV (GaAs)')\nplt.plot(v,j/10) #convert to mA.cm^-2\nplt.xlim(0.2, 1.2)\nplt.ylim(0,35)\nplt.xlabel('Voltage (V)')\nplt.ylabel('Current ($mA.cm^{-2}$)')" + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#defining-the-junction-and-the-cell", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#defining-the-junction-and-the-cell", + "title": "Section 5b: Planar Si solar cell using PDD", + "section": "Defining the junction and the cell", + "text": "Defining the junction and the cell\nAnother important cell parameter, for both the depletion approximation and the drift-diffusion solvers, is the surface recombination. This is passed to Solcore as a surface recombination velocity (SRV). With the Si_pn material, the doping profile function, and the SRVs, we define the Junction. We set the kind of junction to sesame_PDD, so that Solcore knows to use the Sesame PDD solver.\n\nSi_junction = [Junction([Layer(d_bulk, Si_pn)],\n doping_profile=doping_profile_func, kind='sesame_PDD',\n sn=2, sp=1 # SRVs. Note these should be in m/s, not cm/s! sn refers to the n-type region (can be at the back or the front!), sp to the p-type.\n )]\n\nNow we combine the surface layers and the junction into a solar cell, with 2% shading and a silver back mirror.\n\nSi_cell = SolarCell(front_materials +\n Si_junction +\n back_materials,\n shading=0.02,\n substrate=Ag,\n )" }, { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-electrical-power-curve-and-finding-the-maximum-power", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#calculating-the-electrical-power-curve-and-finding-the-maximum-power", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "Calculating the electrical power curve and finding the maximum power", - "text": "Calculating the electrical power curve and finding the maximum power\n\nplt.figure()\nplt.title('Limiting Efficiency power curve for $E_g$ = 1.42 eV (GaAs)')\nplt.plot(v,v*j)\nplt.xlim(0.2, 1.2)\nplt.ylim(0,350)\nplt.xlabel('Voltage (V)')\nplt.ylabel('Power ($W.m^{-2}$)')\n\nDefine a function to find the maximum power point of the curve above:\n\ndef getPmax(eg):\n v = np.linspace(0,eg-0.1,500)\n p = v*np.vectorize(getJ)(v,eg)\n return (np.amax(p)) # The amax command returns the maximum value in the array p\n\nTest it out on the curve above\n\ngetPmax(1.42)\n\n\nPlotting the Shockley-Queisser efficiency limit graph:\nFinally we can calculate the Shockley-Queisser efficiency limit for AM1.5G\n\neg = np.linspace(0.5,2.5,100)\np = np.vectorize(getPmax)(eg)\n\nplt.figure(3)\nplt.title('Limiting Shockley-Queisser Efficiency Curve')\nplt.plot(eg, p/b, label='AM1.5G') # Remember b is the integrated power of the\n# incident sunlight\nplt.xlim(0.2, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()" + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#calculating-the-iv-and-qe", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#calculating-the-iv-and-qe", + "title": "Section 5b: Planar Si solar cell using PDD", + "section": "Calculating the IV and QE", + "text": "Calculating the IV and QE\nNow we ask Solcore to solve both the light IV and QE of the cell:\n\nsolar_cell_solver(Si_cell, 'qe', options)\nsolar_cell_solver(Si_cell, 'iv', options)\n\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving QE of the solar cell...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\nNow we plot the results. Here we have multiple layers, and the junction is actually the third element in the solar cell, so we could access its properties by typing Si_cell[2] (since Python starts counting at 0). However, Solcore has a built-in way to find only the junctions (so, the electrically active) parts of the cell: Si_cell(0) will automatically find the first junction. Similarly, Si_cell(1) would give us the second junction, etc. This avoids having to manually count layers to find out which ones are the Junctions.\n\nresult_stack = np.vstack([Si_cell.reflected, [layer.layer_absorption for layer in Si_cell], Si_cell.transmitted])\n\nfig, (ax, ax2) = plt.subplots(1, 2, figsize=(10, 3.5))\nax.stackplot(wavelengths * 1e9, 100 * result_stack[::-1], linewidth=0.5, alpha=0.5,\n labels=['Ag', 'MgF2 (rear)', 'TCO (rear)', 'Si bulk', 'TCO (front)', 'MgF2 (front)',\n 'Reflection'])\nax.plot(wavelengths * 1e9, 100 * Si_cell(0).eqe(wavelengths), '-k', linewidth=2,\n label='EQE')\n\nax.set_xlim(280, 1200)\nax.set_ylim(0, 100)\nax.set_xlabel(\"Wavelength (nm)\")\nax.set_ylabel(\"R / A / EQE (%)\")\nax.set_title('a) EQE and cell optics', loc='left')\nax.legend()\n\njsc = Si_cell.iv.Isc / 10\n\nax2.plot(Si_cell.iv['IV'][0], Si_cell.iv['IV'][1] / 10, '-', label='IV',\n linewidth=2, color='k')\n\nax2.set_ylim(0, 1.03 * jsc)\nax2.set_xlim(np.min(options.voltages), np.max(options.voltages))\nax2.set_xlabel('Voltage (V)')\nax2.set_ylabel('Current density (mA/cm$^2$)')\nax2.set_title('b) IV characteristics and power output', loc='left')\n\nax3 = ax2.twinx()\nax3.plot(options.voltages, Si_cell.iv['IV'][0] * Si_cell.iv['IV'][1],\n '-r', label='Power', linewidth=2)\nax3.set_ylabel('Power density (W m$^{-2}$)')\nax3.set_ylim(0, 1.03 * jsc * 10)\n\nax3.spines['right'].set_color('r')\nax3.yaxis.label.set_color('r')\nax3.tick_params(axis='y', colors='r')\n\nax2.set_axisbelow(True)\nax3.set_axisbelow(True)\n\nax2.text(0.02, 0.9 * jsc, r'$J_{SC}$', zorder=5)\nax2.text(0.02, 0.8 * jsc, r'$V_{OC}$')\nax2.text(0.02, 0.7 * jsc, 'FF')\nax2.text(0.02, 0.6 * jsc, r'$\\eta$')\nax2.text(0.02, 0.5 * jsc, r'$J_{MPP}$')\nax2.text(0.02, 0.4 * jsc, r'$V_{MPP}$')\n\nax2.text(0.1, 0.9 * jsc, r'= {:.2f} mA/cm$^2$'.format(jsc))\nax2.text(0.1, 0.8 * jsc, r'= {:.3f} V'.format(Si_cell.iv.Voc))\nax2.text(0.1, 0.7 * jsc, '= {:.2f} %'.format(Si_cell.iv.FF * 100))\nax2.text(0.1, 0.6 * jsc, r'= {:.2f} %'.format(Si_cell.iv.Eta * 100))\nax2.text(0.1, 0.5 * jsc, r'= {:.2f} mA/cm$^2$'.format( Si_cell.iv.Impp / 10))\nax2.text(0.1, 0.4 * jsc, r'= {:.3f} V'.format(Si_cell.iv.Vmpp))\nax2.grid(which='major', alpha=0.35)\n\nax3.grid(False)\nplt.tight_layout()\n\nplt.show()\n\n\n\n\nSince this is a planar cell (i.e. no pyramids or other textured surface to reduce reflectance and increase the path length inside the cell), we see high losses due to reflection. We also see parasitic absorption in the front and rear TCO." }, { - "objectID": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#an-easier-way-using-solcore", - "href": "solcore-workshop-2/notebooks/2-Efficiency_limits.html#an-easier-way-using-solcore", - "title": "Section 2: Integration for limiting current, limiting voltage model, efficiency limit", - "section": "An easier way – using Solcore!", - "text": "An easier way – using Solcore!\nThe Solcore library has all the functions we have written above built into it. We worked through this example step by step, but we can calculate the same result using the code below. First let’s calculate an IV curve for a Shockley-Queisser solar cell with a band-gap of 1.42eV:\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\nfrom solcore.solar_cell import SolarCell\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.structure import Junction\n\n# Load the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 # wl contains the x-coordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl, version='AM1.5g')\n\neg = 1.42\nV = np.linspace(0, 1.3, 500)\ndb_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1) #\n# detailed-balance junction (Shockley-Queisser limit)\n\nmy_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\nsolar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True,\n 'internal_voltages': np.linspace(0, 1.3, 400), 'wavelength': wl,\n 'mpp': True, 'light_source': am15g})\n\nplt.figure()\nplt.title('Limiting Efficiency IV curve for $E_g$ = 1.42eV')\nplt.plot(V, my_solar_cell.iv.IV[1], 'k')\nplt.ylim(0, 350)\nplt.xlim(0, 1.2)\nplt.text(0.1,300,f'Jsc: {my_solar_cell.iv.Isc:.2f}')\nplt.text(0.1,280,f'Voc: {my_solar_cell.iv.Voc:.2f}')\nplt.text(0.1,260,f'Pmax: {my_solar_cell.iv.Pmpp:.2f}')\nplt.xlabel('Voltage (V)')\nplt.ylabel('Current (A/m$^2$)')\nplt.show()\n\nThe Shockley-Queisser efficiency calculation can now be performed over a range of band-gap energies. To do this, we make a function that calculates the maximum power Pmax as a function of band-gap energy.\n\n%%capture\n# A command that prevents the screen from filling up with unnecessary working\n\n# Function that returns the maximum power for a Shockley-Queisser solar cell with band-gap Eg\ndef getPmax(eg):\n V = np.linspace(0, eg-0.1, 500)\n db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)\n my_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\n solar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,\n 'mpp': True, 'light_source': am15g})\n return(my_solar_cell.iv.Pmpp)\n\n# Define the range of band-gaps to perform the calculation over\neg=np.linspace(0.5,2.5,100)\n# Perform the claculation for all values of eg\np=np.vectorize(getPmax)(eg)\n\nNow let’s plot the result:\n\nplt.figure() # Plot the results calculated above:\nplt.title('Shockley-Queisser Limiting Efficiency for Unconentrated Sunlight')\nplt.plot(eg, p/am15g.power_density,label='AM1.5G')\nplt.xlim(0.5, 2.5)\nplt.xlabel('Band Gap energy (eV)')\nplt.ylabel('Efficiency (%)')\nplt.legend()\n\n\nEffect of solar concentration on a Shockley-Queisser Solar Cell\nIn a Trivich-Flinn model for a solar cell, concentrated sunlight is only expected to increase the current of a solar cell, not the voltage. In that model the current would increase in proportion with the concentration so the efficiency of the solar cell would be unchanged.\nIn the Shockley-Queisser model, concentrated sunlight increased both the current and the voltage of the solar cell which, in the absence of series resistance losses, leads to an increase in the efficiency of the solar cell. Here we calculate the Shockley-Queisser efficiency at different solar concentrations under the direct solar spectrum AM1.5D:\n\n%%capture\n\n# Set up a series of AM1.5D solar spectra at different concentrations\nwl = np.linspace(300, 4000, 4000) * 1e-9 #wl contains the x-ordinate in wavelength\nam15d1x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=1)\nam15d30x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=30)\nam15d1000x = LightSource(source_type='standard', x=wl, version='AM1.5d',\n concentration=1000)\n\n#Define a function to find Pmax for a particular band-gap energy and solar spectrum\ndef getPmax(eg,spectrum):\n V = np.linspace(0, eg-0.1, 500)\n db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)\n my_solar_cell = SolarCell([db_junction], T=300, R_series=0)\n\n solar_cell_solver(my_solar_cell, 'iv',\n user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,\n 'mpp': True, 'light_source': spectrum})\n return my_solar_cell.iv.Pmpp\n\n# Evaluate the Pmax function for band-gaps spanning 0.8 to 1.6eV and concentrations 1x,30x,1000x\neg = np.linspace(0.8,1.6,100)\np1x = np.vectorize(getPmax)(eg, am15d1x)\np30x = np.vectorize(getPmax)(eg, am15d30x)\np1000x = np.vectorize(getPmax)(eg, am15d1000x)\n\n\n# Setup a figure for dual y-axes\nfig, ax = plt.subplots(1)\n\n# Plot the SQ curves\ncolors = sns.color_palette('husl', n_colors=3)\nax.plot(eg, 100*p1x/am15d1x.power_density,label='$\\eta$ @ AM1.5d 1x', color=colors[0])\nax.axvline(eg[np.argmax(p1x)], color=colors[0])\n\nax.plot(eg, 100*p30x/am15d30x.power_density,label='$\\eta$ @ AM1.5d 30x', color=colors[1])\nax.axvline(eg[np.argmax(p30x)], color=colors[1])\n\nax.plot(eg, 100*p1000x/am15d1000x.power_density,label='$\\eta$ @ AM1.5d 1000x', color=colors[2])\nax.axvline(eg[np.argmax(p1000x)], color=colors[2])\n\n# Define the second y-axis and plot the photon flux in units of eV\nax2 = ax.twinx()\nax2.plot(eg, am15d1x.spectrum(x=eg, output_units=\"photon_flux_per_ev\")[1],\n '--', color='grey', label=\"AM1.5d\")\n\nax.set_xlim(0.8, 1.6)\nax.set_xlabel('Band Gap energy (eV)')\nax.set_ylabel('Efficiency (%)')\nax2.set_ylabel(r'Photon flux (s$^{-1}$ m$^{-2}$ eV$^{-1}$)')\nax.legend()\nax2.legend()\n\nThe maximum band-gap energy moves to lower energies with increaseing solar concentration. This arises since although the current increases with increasing solar concentration, the cell voltage also increases which means the optimal effiicency is obtained at lower band-gaps. However, the drop in band-gap energy is modest owing to a strong atmospheric absorption feature at 1.1um which serves to pin the optimum bandgap around 1.12eV.\n\n\nExercise: Concentrated AM0\nTry repeating the example above but use the AM0 extraterrestial spectrum. Observe what happens to the band-gap shift with increasing concentration. How is it different to AM1.5d?" + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#auger-limited-cell", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#auger-limited-cell", + "title": "Section 5b: Planar Si solar cell using PDD", + "section": "Auger-limited cell", + "text": "Auger-limited cell\nRecently, record-efficiency silicon cells have been optimized to such a level that Auger recombination (rather than Shockley-Read-Hall recombination) becomes the dominant recombination mechanism. SRH recombination is parameterized in the PDD solver through the minority lifetimes. Here, we will scan through different minority carrier lifetimes and look at the effect on cell parameters. Other cell parameters are assumed to stay the same.\n\nlifetime_exp = np.linspace(-4, -1.5, 6) # exponent for the lifetimes\n\nlifetimes = 10.0**lifetime_exp # lifetimes which are linearly spaced on a log scale\n\ncell_results = np.zeros(([len(lifetimes), 4])) # make an array to store the efficiency, FF, Voc, Jsc for each lifetime\n\nfor i1, lt in enumerate(lifetimes): # loop through the lifetimes\n\n options.recalculate_absorption = True\n\n Si_pn = material(\"Si\")(electron_mobility=si(\"1e4cm2\"), hole_mobility=si(\"1e3cm2\"),\n electron_minority_lifetime=lt, hole_minority_lifetime=lt)\n\n Si_junction = [Junction([Layer(d_bulk, Si_pn)],\n doping_profile=doping_profile_func, kind='sesame_PDD',\n sn=2, sp=1)]\n\n Si_cell = SolarCell(front_materials +\n Si_junction +\n back_materials,\n shading=0.02,\n substrate=Ag,\n )\n\n solar_cell_solver(Si_cell, 'iv', options)\n\n cell_results[i1] = np.array([100*Si_cell.iv.Eta, 100*Si_cell.iv.FF, Si_cell.iv.Voc, Si_cell.iv.Isc/10])\n\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\nNow we plot the results. The points are labelled with the lifetime in ms in the left-hand plot.\n\nfig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.5))\n\nax1.plot(cell_results[:, 2], cell_results[:, 1], 'ko')\n\nfor i, lt in enumerate(lifetimes):\n ax1.annotate(str(np.round(1000*lt,2)), (cell_results[i, 2] - 0.001, cell_results[i, 1]), ha='right')\n\nax1.set_xlabel(r'V$_{oc}$ (V)')\nax1.set_ylabel('FF (%)')\nax1.set_xlim(0.69, 0.75)\n\nax2.semilogx(lifetimes, cell_results[:, 0], 'o', color='k')\nax2.set_ylabel('Efficiency (%)')\nax3 = ax2.twinx()\nax3.plot(lifetimes, cell_results[:, 3], 'o', color='r', markerfacecolor='none')\nax3.set_ylim(33, 34)\nax3.set_ylabel(r'$J_{sc}$ (mA/cm$^2$)', color='r')\n\nax2.set_xlabel(r'$\\tau$ (s)')\n\nplt.tight_layout()\nplt.show()\n\n\n\n\nAs the lifetimes become very long, the fill factor shoots up rapidly, while the open-circuit voltage saturates. This increase in FF is faster than would be expected with an ideality factor of 1 (for SRH recombination) in the diode equation, and occurs because recombination becomes increasingly dominated by Auger recombination (ideality factor = 2/3). Compare the plot on the left with Figure 1b in this paper, where much the same behaviour is observed with data from real record efficiency devices." }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html", - "title": "Section 7: Planar GaInP//Si tandem cell", + "objectID": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#other-outputs-from-the-pdd-solver", + "href": "solcore-workshop-2/notebooks/5b-Si_cell_PDD.html#other-outputs-from-the-pdd-solver", + "title": "Section 5b: Planar Si solar cell using PDD", + "section": "Other outputs from the PDD solver", + "text": "Other outputs from the PDD solver\nBecause we used a PDD solver, there are additional outputs in additional to the ones provided by all the junction models (open-circuit voltage, short-circuit current, efficiency, fill factor, etc.). Since solving the PDD equations requires calculating the distribution of carriers in the cell depending on the light and voltage biasing, we can access this information. Here, we will plot the energy levels of the conduction and valence band, and the electron and hole quasi-Fermi levels.\nFirst, we find the index in the voltage array where the voltage is zero (i.e. short circuit), and the index where it is closest to the voltage at the maximum power point (Vmpp), which was calculated during the IV calculation earlier.\n\n# index where voltage is zero:\nSC_ind = np.argmin(np.abs(options.internal_voltages)) # index in voltage array where voltage is (closest to) zero: short circuit\nMPP_ind = np.argmin(np.abs(options.internal_voltages - Si_cell.iv.Vmpp)) # index in voltage array where voltage is closest to Vmpp.\n\nNow we get the conduction and valence band energy levels (Ec and Ev) and the electron and hole quasi-Fermi levels (Efe and Efh), at both of these voltages. The additional outpit from the PDD model are stored in each junction:\nEc_sc = Si_cell(0).pdd_output.Ec[SC_ind] Ev_sc = Si_cell(0).pdd_output.Ev[SC_ind]\nEfe_sc = Si_cell(0).pdd_output.Efe[SC_ind] Efh_sc = Si_cell(0).pdd_output.Efh[SC_ind]\nEc_mpp = Si_cell(0).pdd_output.Ec[MPP_ind] Ev_mpp = Si_cell(0).pdd_output.Ev[MPP_ind]\nEfe_mpp = Si_cell(0).pdd_output.Efe[MPP_ind] Efh_mpp = Si_cell(0).pdd_output.Efh[MPP_ind]\nNow we plot thesince the cell is very wide, let’s split the plot into two parts again, like we did for the doping, and plot the quantities we just extracted for at short circuit:\n\nfig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(5, 3))\nax1.plot(Si_cell(0).mesh*1e6, Ec_sc, label='CB', color='k')\nax1.plot(Si_cell(0).mesh*1e6, Ev_sc, label='VB', color='g')\nax1.plot(Si_cell(0).mesh*1e6, Efe_sc, label=r'$E_{f, e}$', color='r')\nax1.plot(Si_cell(0).mesh*1e6, Efh_sc, label=r'$E_{f, h}$', color='b')\n\nax1.set_xlim(0, 2)\nax1.set_xlabel('x (um)')\nax1.legend()\nax1.set_title(\"Short circuit\", loc='left')\n\nax2.plot(Si_cell(0).mesh*1e6, Ec_sc, label='CB', color='k')\nax2.plot(Si_cell(0).mesh*1e6, Ev_sc, label='VB', color='g')\nax2.plot(Si_cell(0).mesh*1e6, Efe_sc, label=r'$E_{f, e}$', color='r')\nax2.plot(Si_cell(0).mesh*1e6, Efh_sc, label=r'$E_{f, h}$', color='b')\n\nax2.set_xlim(d_bulk*1e6 - 2, d_bulk*1e6)\nax2.set_xlabel('x (um)')\nplt.tight_layout()\nplt.show()\n\n\n\n\nAnd at the maximum power point:\n\nfig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(5, 3))\n\nax1.plot(Si_cell(0).mesh*1e6, Ec_mpp, label='CB', color='k')\nax1.plot(Si_cell(0).mesh*1e6, Ev_mpp, label='VB', color='g')\nax1.plot(Si_cell(0).mesh*1e6, Efe_mpp, label=r'$E_{f, e}$', color='r')\nax1.plot(Si_cell(0).mesh*1e6, Efh_mpp, label=r'$E_{f, h}$', color='b')\nax1.set_xlim(0, 2)\nax1.set_xlabel('x (um)')\nax1.legend()\nax1.set_title(\"Maximum power point\", loc='left')\n\nax2.plot(Si_cell(0).mesh*1e6, Ec_mpp, label='CB', color='k')\nax2.plot(Si_cell(0).mesh*1e6, Ev_mpp, label='VB', color='g')\nax2.plot(Si_cell(0).mesh*1e6, Efe_mpp, label=r'$E_{f, e}$', color='r')\nax2.plot(Si_cell(0).mesh*1e6, Efh_mpp, label=r'$E_{f, h}$', color='b')\n\nax2.set_xlim(d_bulk*1e6 - 2, d_bulk*1e6)\nax2.set_xlabel('x (um)')\nplt.tight_layout()\nplt.show()\n\n\n\n\nAs expected, we see that at forward bias, the band-bending is reduced. We also see that at the rear, where the cell is very highly doped, the electron quasi-Fermi level is inside the conduction band." + }, + { + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", "section": "", - "text": "This example is partly based on the structure presented in this paper, but with planar interfaces instead of a textured Si surface. This is a four-terminal GaInP/Si device which uses an epoxy and glass to bond the two cells together mechanically. First, we will do optical-only calculations to look at the effect of an intermediate anti-reflection coating (on top of the epoxy/glass) on the absorption in the bottom Si cell, and then we will use the results of the optical calculation to do a device simulation and calculate external quantum efficiency and current-voltage under AM1.5G.\nNote: the paper linked above has a GaInP/AlGaInP heterojunction as the top junction. Because we do not have AlGaInP built in to Solcore’s database, this is replaced by a GaInP homojunction in this example.\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver, default_options\nfrom solcore.solar_cell import SolarCell\nfrom solcore.light_source import LightSource\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt" + "text": "SPCTRAL 2 is a clear-sky spectral irradiance model that accounts for variations in the atmospheric conditions and air-mass. Developed at NREL in 1984, it generates terrestrial spectral irradiance from 300nm to 4um with a resolution of approximately 10nm.\n“Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth’s Surface for Cloudless Atmospheres”, R. Bird, C. Riordan, December 1984\nThe Solcore implementation accomodates the following inputs (stated values are defaults):\nAll the inputs are numeric other than the aod_model whose options are: ‘rural’, ‘urban’, ‘maritime’ and ‘tropospheric’." }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#defining-materials-layers-and-junctions", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#defining-materials-layers-and-junctions", - "title": "Section 7: Planar GaInP//Si tandem cell", - "section": "Defining materials, layers and junctions", - "text": "Defining materials, layers and junctions\nThe paper referenced above uses a double-layer anti-reflection coating (ARC) made of MgF\\(_2\\) and ZnS. As in the previous example, we use the interface to the refractiveindex.info database to select optical constant data from specific sources, and define Solcore materials using this data. The III-V materials are taken from Solcore’s own material database.\nNote that for the epoxy/glass layer, we use only a single material (BK7 glass). The epoxy and glass used in the paper have the same refractive index (n = 1.56), so we can use a single material with an appropriate refractive index to represent them.\n\ndownload_db(confirm=True) # uncomment to download database\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nZnS_pageid = search_db(os.path.join(\"ZnS\", \"Querry\"))[0][0];\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nZnS = material(str(ZnS_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nBSF = material(\"AlGaAs\")(Al=0.5)\n\nepoxy = material(\"BK7\")()\n\nFor the Si cell, the front surface has both a low-index and high-index SiN\\(x\\) layer. The rear surface uses Al\\(2\\)O\\(3\\), and the cell has Al at the rear surface.\n\nSiOx = material(\"SiO\")()\nSiN_191_pageid = search_db(\"Vogt-1.91\")[0][0];\nSiN_213_pageid = search_db(\"Vogt-2.13\")[0][0];\nSiN_191 = material(str(SiN_191_pageid), nk_db=True)();\nSiN_213 = material(str(SiN_213_pageid), nk_db=True)();\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nWe now define the layers used in the top cell stack: the ARC and window layer for the top cell, and the GaInP junction itself. The ARC and window layers are not involved in the electrical calculation using the depletion approximation, so they are defined as simple layers, while the GaInP emitter and base are defined as part of a Junction object.\n\nARC_window = [\n Layer(97e-9, MgF2),\n Layer(41e-9, ZnS),\n Layer(17e-9, window, role=\"window\"),\n]\n\nGaInP_junction = Junction([\n Layer(200e-9, GaInP(In=0.50, Nd=si(\"2e18cm-3\"), hole_diffusion_length=si(\"300nm\")),\n role=\"emitter\"),\n Layer(750e-9, GaInP(In=0.50, Na=si(\"1e17cm-3\"), electron_diffusion_length=si(\n \"800nm\")),\n role=\"base\"),\n Layer(500e-9, BSF, role=\"bsf\")], kind=\"DA\", sn=1, sp=1\n)\n\nWe now define the spacer layer, with and without a ZnS anti-reflection coating, so we can compare their performance in the cell stack. Note that we set the epoxy thickness here to be 10 microns, although the real thickness is much higher - this is because the epoxy/glass is not absorbing at the wavelengths which are able to reach it (which are not absorbed in the GaInP top cell), and we will treat it incoherently (no thin-film interference), so the exact thickness does not matter.\n\nspacer = [\n Layer(82e-9, ZnS),\n Layer(10e-6, epoxy), # real thickness is much higher, but since this layer is\n # non-absorbing at the relevant wavelength (> 650 nm) and treated incoherently,\n # this does not matter\n]\n\nspacer_noARC = [\n Layer(10e-6, epoxy),\n]\n\nNow we define the layer stacks for the Si cell, including the front SiO\\(_x\\)/SiN\\(_x\\) stack, the junction itself, and the back dielectric layers.\n\nSi_front_surf = [\n Layer(100e-9, SiOx),\n Layer(70e-9, SiN_191),\n Layer(15e-9, SiN_213),\n ]\n\nSi_junction = Junction([\n Layer(1e-6, Si(Nd=si(\"2e18cm-3\"), hole_diffusion_length=2e-6), role=\"emitter\"),\n Layer(150e-6, Si(Na=si(\"2e15cm-3\"), electron_diffusion_length=150e-6), role=\"base\"),\n], kind=\"DA\", sn=0.1, sp=0.1)\n\nSi_back_surf = [\n Layer(15e-9, Al2O3),\n Layer(120e-9, SiN_191)\n]" + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#comparison-between-spctral2-with-default-parameters-and-am1.5g", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html#comparison-between-spctral2-with-default-parameters-and-am1.5g", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "section": "Comparison between SPCTRAL2 with default parameters and AM1.5G", + "text": "Comparison between SPCTRAL2 with default parameters and AM1.5G\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom solcore.light_source import LightSource\n\n# Setup the AM1.5G solar spectrum\nwl = np.linspace(300, 4000, 4000) * 1e-9 #wl contains the x-ordinate in wavelength\nam15g = LightSource(source_type='standard', x=wl*1e9, version='AM1.5g')\n\nspc2default = LightSource(source_type='SPECTRAL2', x=wl * 1e9)\n\nplt.figure()\nplt.title(\"Comparing SPCTRAL 2 vs AM1.5G\")\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\n<matplotlib.legend.Legend at 0x12ee06f50>" }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#comparing-the-optical-performance-with-and-without-intermediate-arc", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#comparing-the-optical-performance-with-and-without-intermediate-arc", - "title": "Section 7: Planar GaInP//Si tandem cell", - "section": "Comparing the optical performance with and without intermediate ARC", - "text": "Comparing the optical performance with and without intermediate ARC\nNow we will run the calculation. We will treat some of the layers (those above the epoxy) with a coherent TMM calculation, and the epoxy and the layers below it using incoherent TMM. We will discuss the difference this makes, why this is important, and when to use coherent and incoherent layers.\n\nn_coh_layers = len(ARC_window + GaInP_junction)\nn_inc_layers = 1 + len(Si_front_surf + Si_junction + Si_back_surf)\n\nwl = np.linspace(300, 1200, 600) * 1e-9\n\noptions = default_options\noptions.recalculate_absorption = True\noptions.wavelength = wl\noptions.optics_method = 'TMM'\n\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl*1e9,\n output_units=\"photon_flux_per_nm\")\n\nNow we define two versions of the cell for optical calculations, without and with the ZnS anti-reflection coating on the epoxy. Note that we also set the substrate for the calculation (aluminium) here.\n\ncell_no_ARC = SolarCell(\n ARC_window + GaInP_junction + spacer_noARC + Si_front_surf + Si_junction +\n Si_back_surf,\n substrate=Al,\n)\n\ncell_with_ARC = SolarCell(\n ARC_window + GaInP_junction + spacer + Si_front_surf + Si_junction + Si_back_surf,\n substrate=Al,\n)\n\nWe set the appropriate coherency list for the structure (a list with entry ‘c’ for a coherent layer or ‘i’ for an incoherent layer), and solve for the cell optics of the cell without the intermediate ARC. We get the total absorption in the GaInP and Si junctions.\n\noptions.coherency_list = ['c']*(n_coh_layers) + ['i']*n_inc_layers\nsolar_cell_solver(cell_no_ARC, \"optics\", options)\n\nGaInP_A = cell_no_ARC[3].layer_absorption + cell_no_ARC[4].layer_absorption\nSi_A = cell_no_ARC[10].layer_absorption + cell_no_ARC[11].layer_absorption\n\nAs above, but for the cell with an intermediate ARC:\n\noptions.coherency_list = [\"c\"]*(n_coh_layers + 1) + ['i']*n_inc_layers\nsolar_cell_solver(cell_with_ARC, \"optics\", options)\n\nGaInP_A_ARC = cell_with_ARC[3].layer_absorption + cell_with_ARC[4].layer_absorption\nSi_A_ARC = cell_with_ARC[11].layer_absorption + cell_with_ARC[12].layer_absorption\n\nNow we plot the GaInP and Si absorption, and the reflectance of the whole structure, for both cells:\n\nplt.figure()\n\nplt.plot(wl * 1e9, GaInP_A_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, Si_A_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, cell_with_ARC.reflected, '-b', label=\"R\")\n\nplt.plot(wl * 1e9, GaInP_A, \"--k\", label=\"No middle ARC\")\nplt.plot(wl * 1e9, Si_A, \"--r\")\nplt.plot(wl * 1e9, cell_no_ARC.reflected, '--b')\n\nplt.legend(loc='upper right')\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance/Reflectance\")\nplt.tight_layout()\nplt.show()\n\nWe see that the cell without an ARC on the epoxy shows much stronger interference fringes (due to the thickness of the top stack), and higher reflectance overall in the long-wavelength region (at short wavelengths, light is absorbed before it is able to reach the epoxy at all). Before doing an actual electrical calculation, we will calculate the limiting current in both of the sub-cells (assuming all the generated charge carriers can be collected):\n\nJ_GaInP = q*np.trapz(GaInP_A * AM15G.spectrum()[1], wl*1e9)\nJ_Si = q*np.trapz(Si_A * AM15G.spectrum()[1], wl*1e9)\n\nprint(\"Limiting short-circuit currents without ARC (mA/cm2): {:.1f} / {:.1f}\".format(\n J_GaInP/10, J_Si/10))\n\nJ_GaInP_ARC = q*np.trapz(GaInP_A_ARC * AM15G.spectrum()[1], wl*1e9)\nJ_Si_ARC = q*np.trapz(Si_A_ARC * AM15G.spectrum()[1], wl*1e9)\n\nprint(\"Limiting short-circuit currents with ARC (mA/cm2): {:.1f} / {:.1f}\".format(\n J_GaInP_ARC/10, J_Si_ARC/10))\n\nAs expected from the reduced reflection and increased absorption in the Si, the cell with an intermediate ARC has significantly higher maximum current in the bottom Si cell." + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#adjusting-the-precipitable-water-value", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html#adjusting-the-precipitable-water-value", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "section": "Adjusting the precipitable water value", + "text": "Adjusting the precipitable water value\nThe default SPCTRAL2 parameters results in almost no atmospheric absorption. This suggests the precipitable water column thickness is much too low, the default is 0.00142 cm. Let’s increase that value to 1cm to roughly match AM1.5G:\n\nspc2pc = LightSource(source_type='SPECTRAL2', precipwater=1.0, x=wl * 1e9)\n\nplt.figure()\nplt.title('Comparions between SPCTRAL2 defaults, 1cm precipitable water & AM1.5G')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')\nplt.plot(*spc2pc.spectrum(wl*1e9), label='PC water')\n\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x12ef7a890>" }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#eqe-and-iv-calculation", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#eqe-and-iv-calculation", - "title": "Section 7: Planar GaInP//Si tandem cell", - "section": "EQE and IV calculation", - "text": "EQE and IV calculation\nNow, just taking the structure with an intermediate ARC, we do a cell calculation using the depletion approximation.\n\noptions.mpp = True\noptions.light_iv = True\noptions.voltages = np.linspace(-1.9, 0.1, 100)\noptions.light_source = AM15G\n\nsolar_cell = SolarCell(\n ARC_window + [GaInP_junction] + spacer + Si_front_surf + [Si_junction] +\n Si_back_surf,\n substrate=Al,\n)\n\nFirst, we calculate and plot the external quantum efficiency (EQE):\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nplt.figure()\nplt.plot(wl * 1e9, GaInP_A_ARC, \"--k\", label=\"GaInP only absorption\")\nplt.plot(wl * 1e9, Si_A_ARC, \"--r\", label=\"Si only absorption\")\nplt.plot(wl*1e9, solar_cell[3].eqe(wl), '-k')\nplt.plot(wl*1e9, solar_cell[9].eqe(wl), '-r')\nplt.legend(loc='upper right')\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorptance/EQE\")\nplt.ylim(0,1)\nplt.tight_layout()\nplt.show()\n\nAnd the current-voltage under AM1.5G:\n\nsolar_cell_solver(solar_cell, 'iv', options)\n\nplt.figure()\nplt.plot(-options.voltages, -solar_cell.iv['IV'][1]/10, 'k', linewidth=3,\n label='Total (2-terminal)')\nplt.plot(-options.voltages, solar_cell[3].iv(options.voltages)/10, 'b',\n label='GaInP')\nplt.plot(-options.voltages, solar_cell[9].iv(options.voltages)/10, 'g',\n label='Si')\nplt.text(0.1, 18, r\"2-terminal $\\eta$ = {:.2f}%\".format(solar_cell.iv[\"Eta\"]*100))\nplt.legend()\nplt.ylim(0, 20)\nplt.xlim(0, 1.9)\nplt.ylabel('Current (mA/cm$^2$)')\nplt.xlabel('Voltage (V)')\nplt.tight_layout()\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#atmospheric-turbidity", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html#atmospheric-turbidity", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "section": "Atmospheric Turbidity", + "text": "Atmospheric Turbidity\nThe short wavelength is attenuated which is likely due to a high level of aerosol loading in the default spectrum. To address this atmospheric turbidity can be reduced to around 0.05.\n\nspc2high = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2, x=wl * 1e9)\nspc2med = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.1, x=wl * 1e9)\nspc2low = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.05, x=wl * 1e9)\n\nplt.figure()\nplt.title('Spectral Irradiance Plotted for Different Aersol Models')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2high.spectrum(wl*1e9), label='Turbidity = 0.2')\nplt.plot(*spc2med.spectrum(wl*1e9), label='Turbidity = 0.1')\nplt.plot(*spc2low.spectrum(wl*1e9), label='Turbidity = 0.05')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x12f727450>" }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#two-vs.-four-terminal-efficiency", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#two-vs.-four-terminal-efficiency", - "title": "Section 7: Planar GaInP//Si tandem cell", - "section": "Two vs. four-terminal efficiency", - "text": "Two vs. four-terminal efficiency\nBy default, Solcore assumes any SolarCell object is a two-terminal device, and will thus calculate the total I-V curve assuming the cells are connected in series and that the current is limited by the lowest-current sub-cell. However, it will also calculate the I-V curves of the individual cells, so we can use this information to calculate the possible power output in a 4-terminal configuration where the cells operate independently from an electrical point of view:\n\nV = np.linspace(0, 1.3, 100)\nP_GaInP = V*solar_cell[3].iv(V)\nP_Si = V*solar_cell[9].iv(V)\n\nP_MPP_GaInP = max(P_GaInP)\n\nP_MPP_Si = max(P_Si)\n\neta_4T = (P_MPP_GaInP + P_MPP_Si)/AM15G.power_density\n\nprint('4-terminal efficiency: {:.1f} %'.format(eta_4T*100))" + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#variation-with-aerosol-models", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html#variation-with-aerosol-models", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "section": "Variation with Aerosol models", + "text": "Variation with Aerosol models\nSeveral standard aerosol models are implemented in SPCTRAL 2 that were established by Shettle & Fenn.\nShettle, E. P., and R. W. Fenn, “Models of the Atmospheric Aerosol and Their Optical Properties, II Proceedings of the Advisory Group for Aerospace Reseach and Development Conference No . 183, Optical Propagation in the Atmosphere, 1975, pp. 2.1-2.16. Presented at the Electromagnetic Wave Propagation Panel Symposium, Lyngby, Denmark; 27-31 October 1975.\nHere we plot some of them with a turbidity of 0.2 to emphasise the different spectral behaviour:\n\nspc2rural = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='rural', x=wl * 1e9)\nspc2marit = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='maritime', x=wl * 1e9)\nspc2tropo = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,\n aod_model='tropospheric', x=wl * 1e9)\n\nplt.figure(1)\nplt.title('Spectral Irradiance Plotted for Different Aersol Models')\nplt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')\nplt.plot(*spc2rural.spectrum(wl*1e9), label='rural')\nplt.plot(*spc2marit.spectrum(wl*1e9), label='maritime')\nplt.plot(*spc2tropo.spectrum(wl*1e9), label='tropospheric')\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x12f7769d0>" }, { - "objectID": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#questionschallenges", - "href": "solcore-workshop-2/notebooks/7-InGaP_Si_planar.html#questionschallenges", - "title": "Section 7: Planar GaInP//Si tandem cell", - "section": "Questions/challenges", - "text": "Questions/challenges\n\nWhat causes the strange, sharp fringes in the simulation data of Fig. 1 in the reference paper? Can you reproduce them by modifying this code? Which version of the simulation do you think is more correct, and why?\nHow could you increase the current in one or both of the sub-cells (remember, unlike the paper, we assumed all the layers in the cell are planar!).\nOnce the light encounters an ‘incoherent’ (thick) layer, does it make sense to treat any layers below that as coherent?" + "objectID": "solcore-workshop-2/notebooks/4-Spectral2.html#changing-the-time-of-day", + "href": "solcore-workshop-2/notebooks/4-Spectral2.html#changing-the-time-of-day", + "title": "Section 4: Calculating Spectral Irradiance using SPCTRAL 2", + "section": "Changing the time of day", + "text": "Changing the time of day\nOne of the most common uses for a spectral irradiance model such as SPCTRAL2 is to calculate how a particular solar cell technology behaves under varying spectral conditions during the day. This is particularly important whan working with series connected tandem solar cells where the current matching condition will vary according to the incident spectrum. Here we plot the spectral irradiance at 12pm, 2pm, 3pm, 4pm, 5pm, 6pm and 7pm. Note the strong relative loss in short-wavelength light relative to the infrared as the air-mass increases throughout the afternoon.\n\nimport datetime\n\nplt.figure(1)\nplt.title('Spectral Irradiance plotted from 12pm-7pm')\nhours=[12, 14, 15, 16, 17, 18, 19]\n\nfor h in hours:\n spc2 = LightSource(source_type='SPECTRAL2', dateAndTime=datetime.datetime(2011, 6, 30, h, 00),\n precipwater=1.0, turbidity=0.05, x=wl * 1e9)\n plt.plot(*spc2.spectrum(wl*1e9), label='hour '+ str(h))\n\nplt.xlim(300, 3000)\nplt.xlabel('Wavelength (nm)')\nplt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')\nplt.legend()\n\n<matplotlib.legend.Legend at 0x12f8a5d10>" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html", - "title": "Section 8: Textured Si", + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html", + "title": "Section 5a: Planar Si solar cell using DA", "section": "", - "text": "This example is based on Figures 6, 7 and 8 from this paper. This compares three different structures, all based on a 200 micron thick slab of silicon with different surface textures:\nThe methods which will be used to calculate the redistribution matrices in each case are given in brackets. If case 1 and 2 are calculated first, then case 3 does not require the calculations of any additional matrices, since it will use the rear matrix from (1) and the front matrix from (2)." + "text": "In this first set of examples, we will look at simple planar Si solar cell.\nIn this script, we will look at the difference between Beer-Lambert absorption calculations, using the Fresnel equations for front-surface reflection, and using the transfer-matrix model.\nFirst, lets import some very commonly-used Python packages:\nimport numpy as np\nimport matplotlib.pyplot as plt\nNumpy is a Python library which adds supports for multi-dimensional data arrays and matrices, so it is very useful for storing and handling data. You will probably use it in every Solcore script you write. Here, it is imported under the alias ‘np’, which you will see used below. matplotlib is used for making plots, and is imported under the alias ‘plt’. Both the ‘np’ and ‘plt’ aliases are extremely commonly used in Python programming.\nNow, let’s import some things from Solcore (which will be explained as we use them):\nfrom solcore import material, si\nfrom solcore.solar_cell import SolarCell, Layer, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.interpolate import interp1d" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#setting-up", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#setting-up", - "title": "Section 8: Textured Si", - "section": "Setting up", - "text": "Setting up\nFirst, importing relevant packages:\n\nimport numpy as np\nimport os\n\n# solcore imports\nfrom solcore.structure import Layer\nfrom solcore import material\nfrom solcore import si\n\nfrom rayflare.structure import Interface, BulkLayer, Structure\nfrom rayflare.matrix_formalism import process_structure, calculate_RAT\nfrom rayflare.utilities import get_savepath\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.angles import theta_summary, make_angle_vector\nfrom rayflare.textures import regular_pyramids\nfrom rayflare.options import default_options\n\nimport matplotlib.pyplot as plt\nimport matplotlib as mpl\nimport seaborn as sns\nfrom sparse import load_npz\n\nSetting options (taking the default options for everything not specified explicitly):\n\nangle_degrees_in = 8 # same as in Fraunhofer paper\n\nwavelengths = np.linspace(900, 1200, 20) * 1e-9\n\nSi = material(\"Si\")()\nAir = material(\"Air\")()\n\noptions = default_options()\noptions.wavelength = wavelengths\noptions.theta_in = angle_degrees_in * np.pi / 180 # incidence angle (polar angle)\noptions.n_theta_bins = 30\noptions.c_azimuth = 0.25\noptions.n_rays = 5e4 # number of rays per wavelength in ray-tracing\noptions.project_name = \"OPTOS_comparison\"\noptions.orders = 60 # number of RCWA orders to use (more = better convergence, but slower)\noptions.pol = \"u\" # unpolarized light\noptions.only_incidence_angle = True\noptions.RCWA_method = \"Inkstone\"" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-materials", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-materials", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Defining materials", + "text": "Defining materials\nTo define our solar cell, we first want to define some materials. Then we want to organise those materials into Layers, organise those layers into a Junction (or multiple Junctions, for a multi-junction cell, as we will see later), and then finally define a SolarCell with that Junction.\nFirst, let’s define a silicon material. Silicon, along with many other semiconductors, dielectrics, and metals common in solar cells, is included in Solcore’s database:\n\nSi = material(\"Si\")\n\nThis creates an instance of the Si material. However, to use this in a solar cell we need to do specify some more information, specifically the doping level and the minority carrier diffusion length. The ‘si’ function comes in handy here to convert all quantities to base units e.g. m, m\\(^{-3}\\)…\n\nSi_p = Si(Na=si(\"1e21cm-3\"), electron_diffusion_length=si(\"4um\"))\nSi_n = Si(Nd=si(\"1e16cm-3\"), hole_diffusion_length=si(\"200um\"))" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#defining-the-structures", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#defining-the-structures", - "title": "Section 8: Textured Si", - "section": "Defining the structures", - "text": "Defining the structures\nNow, set up the grating basis vectors for the RCWA calculations and define the grating structure. These are squares, rotated by 45 degrees. The halfwidth is calculated based on the area fill factor of the etched pillars given in the paper.\n\nx = 1000\n\nd_vectors = ((x, 0), (0, x))\narea_fill_factor = 0.36\nhw = np.sqrt(area_fill_factor) * 500\n\nback_materials = [\n Layer(width=si(\"120nm\"), material=Si,\n geometry=[{\"type\": \"rectangle\", \"mat\": Air, \"center\": (x / 2, x / 2),\n \"halfwidths\": (hw, hw), \"angle\": 45}],\n )]\n\nNow we define the pyramid texture for the front surface in case (2) and (3) and make the four possible different surfaces: planar front and rear, front with pyramids, rear with grating. We specify the method to use to calculate the redistribution matrices in each case and create the bulk layer.\n\nsurf = regular_pyramids(elevation_angle=55, upright=False)\n\nfront_surf_pyramids = Interface(\n \"RT_Fresnel\",\n texture=surf,\n layers=[],\n name=\"inv_pyramids_front_\" + str(options[\"n_rays\"]),\n)\n\nfront_surf_planar = Interface(\"TMM\", layers=[], name=\"planar_front\")\n\nback_surf_grating = Interface(\n \"RCWA\",\n layers=back_materials,\n name=\"crossed_grating_back\",\n d_vectors=d_vectors,\n rcwa_orders=20,\n)\n\nback_surf_planar = Interface(\"TMM\", layers=[], name=\"planar_back\")\n\nbulk_Si = BulkLayer(200e-6, Si, name=\"Si_bulk\")\n\nNow we create the different structures and ‘process’ them (this will calculate the relevant matrices if necessary, or do nothing if it finds the matrices have previously been calculated and the files already exist). We don’t need to process the final structure because it will use matrices calculated for SC_fig6 and SC_fig7.\n\nSC_fig6 = Structure(\n [front_surf_planar, bulk_Si, back_surf_grating], incidence=Air, transmission=Air\n)\nSC_fig7 = Structure(\n [front_surf_pyramids, bulk_Si, back_surf_planar], incidence=Air, transmission=Air\n)\nSC_fig8 = Structure(\n [front_surf_pyramids, bulk_Si, back_surf_grating], incidence=Air, transmission=Air\n)\n\nprocess_structure(SC_fig6, options, save_location='current') # if you want to overwrite previous results, add overwrite=Trues\nprocess_structure(SC_fig7, options, save_location='current')\n\nINFO: Making matrix for planar surface using TMM for element 0 in structure\nINFO: RCWA calculation for element 2 in structure\nINFO: RCWA calculation for wavelength = 947.3684210526316 nm\nINFO: RCWA calculation for wavelength = 915.7894736842105 nm\nINFO: RCWA calculation for wavelength = 978.9473684210526 nm\nINFO: RCWA calculation for wavelength = 1010.5263157894736 nm\nINFO: RCWA calculation for wavelength = 994.7368421052631 nm\nINFO: RCWA calculation for wavelength = 931.578947368421 nm\nINFO: RCWA calculation for wavelength = 1026.3157894736842 nm\nINFO: RCWA calculation for wavelength = 900.0000000000001 nm\nINFO: RCWA calculation for wavelength = 1042.1052631578948 nm\nINFO: RCWA calculation for wavelength = 963.1578947368421 nm\nINFO: RCWA calculation for wavelength = 1057.8947368421054 nm\nINFO: RCWA calculation for wavelength = 1073.6842105263158 nm\nINFO: RCWA calculation for wavelength = 1089.4736842105265 nm\nINFO: RCWA calculation for wavelength = 1105.2631578947369 nm\nINFO: RCWA calculation for wavelength = 1121.0526315789475 nm\nINFO: RCWA calculation for wavelength = 1136.842105263158 nm\nINFO: RCWA calculation for wavelength = 1152.6315789473683 nm\nINFO: RCWA calculation for wavelength = 1168.421052631579 nm\nINFO: RCWA calculation for wavelength = 1184.2105263157896 nm\nINFO: RCWA calculation for wavelength = 1200.0000000000002 nm\nINFO: Ray tracing with Fresnel equations for element 0 in structure\nINFO: Calculating matrix only for incidence theta/phi\nINFO: RT calculation for wavelength = 931.578947368421 nm\nINFO: RT calculation for wavelength = 900.0000000000001 nm\nINFO: RT calculation for wavelength = 915.7894736842105 nm\nINFO: RT calculation for wavelength = 947.3684210526316 nm\nINFO: RT calculation for wavelength = 963.1578947368421 nm\nINFO: RT calculation for wavelength = 978.9473684210526 nm\nINFO: RT calculation for wavelength = 994.7368421052631 nm\nINFO: RT calculation for wavelength = 1010.5263157894736 nm\nINFO: RT calculation for wavelength = 1042.1052631578948 nm\nINFO: RT calculation for wavelength = 1026.3157894736842 nm\nINFO: RT calculation for wavelength = 1057.8947368421054 nm\nINFO: RT calculation for wavelength = 1073.6842105263158 nm\nINFO: RT calculation for wavelength = 1089.4736842105265 nm\nINFO: RT calculation for wavelength = 1105.2631578947369 nm\nINFO: RT calculation for wavelength = 1136.842105263158 nm\nINFO: RT calculation for wavelength = 1152.6315789473683 nm\nINFO: RT calculation for wavelength = 1121.0526315789475 nm\nINFO: RT calculation for wavelength = 1168.421052631579 nm\nINFO: RT calculation for wavelength = 1184.2105263157896 nm\nINFO: RT calculation for wavelength = 1200.0000000000002 nm\nINFO: RT calculation for wavelength = 900.0000000000001 nm\nINFO: RT calculation for wavelength = 915.7894736842105 nm\nINFO: RT calculation for wavelength = 931.578947368421 nm\nINFO: RT calculation for wavelength = 947.3684210526316 nm\nINFO: RT calculation for wavelength = 963.1578947368421 nm\nINFO: RT calculation for wavelength = 978.9473684210526 nm\nINFO: RT calculation for wavelength = 994.7368421052631 nm\nINFO: RT calculation for wavelength = 1010.5263157894736 nm\nINFO: RT calculation for wavelength = 1026.3157894736842 nm\nINFO: RT calculation for wavelength = 1042.1052631578948 nm\nINFO: RT calculation for wavelength = 1057.8947368421054 nm\nINFO: RT calculation for wavelength = 1073.6842105263158 nm\nINFO: RT calculation for wavelength = 1089.4736842105265 nm\nINFO: RT calculation for wavelength = 1105.2631578947369 nm\nINFO: RT calculation for wavelength = 1121.0526315789475 nm\nINFO: RT calculation for wavelength = 1136.842105263158 nm\nINFO: RT calculation for wavelength = 1152.6315789473683 nm\nINFO: RT calculation for wavelength = 1168.421052631579 nm\nINFO: RT calculation for wavelength = 1184.2105263157896 nm\nINFO: RT calculation for wavelength = 1200.0000000000002 nm\nINFO: Making matrix for planar surface using TMM for element 2 in structure\n\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.WARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found." + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-layers", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#defining-layers", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Defining layers", + "text": "Defining layers\nNow we define the emitter and base layers we will have in the solar cell; we specify their thickness, the material they are made of and the role they play within the cell (emitter or base). We create a junction which is a total of 200 \\(\\mu\\)m thick, with a 1 \\(\\mu\\)m junction depth.\n\nemitter_layer = Layer(width=si(\"1um\"), material=Si_p, role='emitter')\nbase_layer = Layer(width=si(\"199um\"), material=Si_n, role='base')\n\nNow we create the p-n junction using the layers defined above. We set kind=“DA” to tell Solcore to use the Depletion Approximation in the calculation:\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#calculating-rat", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#calculating-rat", - "title": "Section 8: Textured Si", - "section": "Calculating R/A/T", - "text": "Calculating R/A/T\nThen we ask RayFlare to calculate the reflection, transmission and absorption through matrix multiplication, and get the required result out (absorption in the bulk) for each cell. We also load the results from the reference paper to compare them to the ones calculated with RayFlare.\n\nresults_fig6 = calculate_RAT(SC_fig6, options, save_location='current')\nresults_fig7 = calculate_RAT(SC_fig7, options, save_location='current')\nresults_fig8 = calculate_RAT(SC_fig8, options, save_location='current')\n\nRAT_fig6 = results_fig6[0]\nRAT_fig7 = results_fig7[0]\nRAT_fig8 = results_fig8[0]\n\nsim_fig6 = np.loadtxt(\"data/optos_fig6_sim.csv\", delimiter=\",\")\nsim_fig7 = np.loadtxt(\"data/optos_fig7_sim.csv\", delimiter=\",\")\nsim_fig8 = np.loadtxt(\"data/optos_fig8_sim.csv\", delimiter=\",\")\n\nFinally, we use TMM to calculate the absorption in a structure with a planar front and planar rear, as a reference.\n\nstruc = tmm_structure([Layer(si(\"200um\"), Si)], incidence=Air, transmission=Air)\noptions.coherent = False\noptions.coherency_list = [\"i\"]\nRAT = tmm_structure.calculate(struc, options)" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#setting-user-options", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#setting-user-options", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Setting user options", + "text": "Setting user options\nWavelengths we want to use in the calculations; wavelengths between 300 and 1200 nm, at 200 evenly spaced intervals:\n\nwavelengths = si(np.linspace(300, 1200, 200), \"nm\")\n\nNote that here and above in defining the layers and materials we have used the “si()” function multiple times: you can use this to automatically convert quantities in other units to base SI units (e.g. nanometres to metres).\nNow we specify some options for running the calculation. Initially we will use the Beer-Lambert absorption law (\\(I(z) = I_0 e^{-\\alpha*z}\\)) to calculate the optics of the cell (“BL”). We set the wavelengths we want to use, and we set “recalculate_absorption” to True so that further down in the script when we try different optics methods, Solcore knows we want to re-calculate the optics of the cell rather than re-using previous results. We can specify the options in a Python format called a dictionary:\n\noptions = {\n \"recalculate_absorption\": True,\n \"optics_method\": \"BL\",\n \"wavelength\": wavelengths\n }" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#plotting", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#plotting", - "title": "Section 8: Textured Si", - "section": "Plotting", - "text": "Plotting\nPlot everything together, including data from the reference paper for comparison:\n\npalhf = sns.color_palette(\"hls\", 4)\n\nfig = plt.figure()\nplt.plot(sim_fig6[:, 0], sim_fig6[:, 1],\n \"--\", color=palhf[0], label=\"OPTOS - rear grating (1)\")\nplt.plot(wavelengths * 1e9, RAT_fig6[\"A_bulk\"][0],\n \"-o\", color=palhf[0], label=\"RayFlare - rear grating (1)\", fillstyle=\"none\")\nplt.plot(sim_fig7[:, 0], sim_fig7[:, 1],\n \"--\", color=palhf[1], label=\"OPTOS - front pyramids (2)\",)\nplt.plot(wavelengths * 1e9, RAT_fig7[\"A_bulk\"][0],\n \"-o\", color=palhf[1], label=\"RayFlare - front pyramids (2)\", fillstyle=\"none\")\nplt.plot(sim_fig8[:, 0], sim_fig8[:, 1],\n \"--\", color=palhf[2], label=\"OPTOS - grating + pyramids (3)\")\nplt.plot(wavelengths * 1e9, RAT_fig8[\"A_bulk\"][0],\n \"-o\", color=palhf[2],label=\"RayFlare - grating + pyramids (3)\", fillstyle=\"none\",)\nplt.plot(wavelengths * 1e9, RAT[\"A_per_layer\"][:, 0], \"-k\", label=\"Planar\")\nplt.legend(loc=\"lower left\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Absorption in Si\")\nplt.xlim([900, 1200])\nplt.ylim([0, 1])\nplt.show()\n\n\n\n\nWe can see good agreement between the reference values and our calculated values. The structure with rear grating also behaves identically to the planar TMM reference case at the short wavelengths where front surface reflection dominates the result, as expected. Clearly, the pyramids perform much better overall, giving a large boost in the absorption at long wavelengths and also reducing the reflection significantly at shorter wavelengths. Plotting reflection and transmission emphasises this:\n\nfig = plt.figure()\nplt.plot(wavelengths * 1e9,RAT_fig6[\"R\"][0],\n \"-o\", color=palhf[0], label=\"RayFlare - rear grating (1)\", fillstyle=\"none\")\nplt.plot(wavelengths * 1e9, RAT_fig7[\"R\"][0],\n \"-o\", color=palhf[1], label=\"RayFlare - front pyramids (2)\", fillstyle=\"none\")\nplt.plot(wavelengths * 1e9, RAT_fig8[\"R\"][0],\n \"-o\", color=palhf[2], label=\"RayFlare - grating + pyramids (3)\", fillstyle=\"none\")\n\nplt.plot(wavelengths * 1e9, RAT_fig6[\"T\"][0], \"--o\", color=palhf[0])\nplt.plot(wavelengths * 1e9, RAT_fig7[\"T\"][0], \"--o\", color=palhf[1])\nplt.plot(wavelengths * 1e9, RAT_fig8[\"T\"][0], \"--o\", color=palhf[2])\n\n# these are just to create the legend:\nplt.plot(-1, 0, \"k-o\", label=\"R\", fillstyle=\"none\")\nplt.plot(-1, 0, \"k--o\", label=\"T\")\n\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"Reflected/transmitted fraction\")\nplt.xlim([900, 1200])\nplt.ylim([0, 0.6])\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#running-cell-simulations", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#running-cell-simulations", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Running cell simulations", + "text": "Running cell simulations\nDefine the solar cell; in this case it is very simple and we just have a single junction:\n\nsolar_cell = SolarCell([Si_junction])\n\nNow we use solar_cell_solver to calculate the QE of the cell; we can ask solar_cell_solver to calculate ‘qe’, ‘optics’ or ‘iv’.\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nSolving QE of the solar cell...\n\n\nPLOT 1: plotting the QE in the Si junction, as well as the fraction of light absorbed in the junction and reflected. Because we are using the Beer-Lambert absorption law and we did not specify external reflectance, the reflectance = 0 over the whole wavelength range.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell[0].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell[0].layer_absorption, label='Absorptance (A)')\nplt.plot(wavelengths*1e9, 100*solar_cell.reflected, label='Reflectance (R)')\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.title(\"(1) QE of Si cell - Beer-Lambert absorption\")\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#redistribution-matrices", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#redistribution-matrices", - "title": "Section 8: Textured Si", - "section": "Redistribution matrices", - "text": "Redistribution matrices\nPlot the redistribution matrix for the rear grating (summed over azimuthal angles) at 1100 nm:\n\ntheta_intv, phi_intv, angle_vector = make_angle_vector(\n options[\"n_theta_bins\"], options[\"phi_symmetry\"], options[\"c_azimuth\"])\n\npath = get_savepath(save_location='current', project_name=options.project_name)\nsprs = load_npz(os.path.join(path, SC_fig6[2].name + \"frontRT.npz\"))\n\nwl_to_plot = 1100e-9\nwl_index = np.argmin(np.abs(wavelengths - wl_to_plot))\n\nfull = sprs[wl_index].todense()\n\nsummat = theta_summary(full, angle_vector, options[\"n_theta_bins\"], \"front\")\nsummat_r = summat[: options[\"n_theta_bins\"], :]\nsummat_r = summat_r.rename({ r\"$\\theta_{in}$\": r\"$\\sin(\\theta_{in})$\",\n r\"$\\theta_{out}$\": r\"$\\sin(\\theta_{out})$\"})\n\nsummat_r = summat_r.assign_coords({r\"$\\sin(\\theta_{in})$\": np.sin(summat_r.coords[r\"$\\sin(\\theta_{in})$\"]).data,\n r\"$\\sin(\\theta_{out})$\": np.sin(summat_r.coords[r\"$\\sin(\\theta_{out})$\"]).data})\n\npalhf = sns.cubehelix_palette(256, start=0.5, rot=-0.9)\npalhf.reverse()\nseamap = mpl.colors.ListedColormap(palhf)\n\nfig = plt.figure()\nax = plt.subplot(111)\nax = summat_r.plot.imshow(ax=ax, cmap=seamap, vmax=0.3)\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-fresnel", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-fresnel", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Adding front-surface reflection: Fresnel", + "text": "Adding front-surface reflection: Fresnel\nNow, to make this calculation a bit more realistic, there are a few things we could do. We could load some measured front surface reflectance from a file, or we could calculate the reflectance. To calculate the reflectance, there are many approaches we could take; we are going to explore two of them here.\nIf we assume the silicon is infinitely thick (or at least much thicker than the wavelengths of light we care about) then the reflectance will approach the reflectivity of a simple air/Si interface. We can calculate what this is using the Fresnel equation for reflectivity.\n\ndef calculate_R_Fresnel(incidence_n, transmission_n, wl):\n # return a function that gives the value of R (at normal incidence) at the input wavelengths\n\n Rs = np.abs((incidence_n - transmission_n)/(incidence_n + transmission_n))**2\n\n return interp1d(wl, Rs)\n\nThe transmission_n is the complex reflective index of Si at our wavelengths for the transmission medium (Si), which we can extract easily from the Si material object in Solcore. The incidence_n = 1 (air). Note that the function above is specifically for normal incidence.\n\ntrns_n = Si_n.n(wavelengths) + 1j*Si_n.k(wavelengths)\nreflectivity_fn = calculate_R_Fresnel(1, trns_n, wavelengths)\n\nWe define the solar cell again, with the same layers but now supplying the function for the externally-calculated reflectivity, and calculate the optics (reflection, absorption, transmission) again:\n\nsolar_cell_fresnel = SolarCell([Si_junction], reflectivity=reflectivity_fn)\n\nsolar_cell_solver(solar_cell_fresnel, 'optics', options)" }, { - "objectID": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#questions", - "href": "solcore-workshop-2/notebooks/8-grating_pyramids_OPTOS.html#questions", - "title": "Section 8: Textured Si", - "section": "Questions", - "text": "Questions\n\nIf you can add only one of the textures (pyramids or a grating), which one is better? Why?\nWhy do the structures with a front-surface texture have high reflection at long wavelengths? The anti-reflection properties of pyramids (treated with ray optics) are mostly independent of the wavelength, so why does apparent reflection increase near the bandgap of Si?\nCan you explain any of the features present in the angular redistribution matrix of the rear grating surface?" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-tmm", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-front-surface-reflection-tmm", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Adding front surface reflection: TMM", + "text": "Adding front surface reflection: TMM\nFinally, we do the same again but now instead of supplying the external reflectivity we ask set the optics_method to “TMM” (Transfer Matrix Method), to correctly calculate reflection at the front surface. We will learn more about the transfer matrix method later.\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")\n\nsolar_cell_TMM = SolarCell([Si_junction])\n\nSet some more options for the cell calculation:\n\noptions[\"optics_method\"] = \"TMM\"\nvoltages = np.linspace(-1.1, 1.1, 100)\noptions[\"light_iv\"] = True\noptions[\"mpp\"] = True\noptions[\"voltages\"] = voltages\noptions[\"internal_voltages\"] = voltages\n\nwe calculate the QE and the IV (we set the light_iv option to True; if we don’t do this, Solcore just calculates the dark IV). We also ask Solcore to find the maximum power point (mpp) so we can get the efficiency. Note that the sign convention used by Solcore means that an n-on-p cell with have a negative open-circuit voltage.\n\nsolar_cell_solver(solar_cell_TMM, 'iv', options)\nsolar_cell_solver(solar_cell_TMM, 'qe', options)\n\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving QE of the solar cell...\n\n\nPLOT 2: here we plot the reflection, transmission, and absorption calculated with the Fresnel equation defined above, and with the TMM solver in Solcore, showing that for this simple situation (no anti-reflection coating, thick Si junction) they are exactly equivalent.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, color='firebrick', label = \"R (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.reflected, '--', color='orangered', label = \"R (Fresnel)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.absorbed, color='dimgrey', label = \"A (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.absorbed, '--', color='lightgrey', label = \"A (Fresnel)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, color='blue', label = \"T (TMM)\")\nplt.plot(wavelengths*1e9, 100*solar_cell_fresnel.transmitted, '--', color='dodgerblue', label = \"T (Fresnel)\")\nplt.ylim(0, 100)\nplt.legend()\nplt.title(\"(2) Optics of Si cell - Fresnel/TMM\")\nplt.show()\n\n\n\n\nPLOT 3: As above for the TMM calculation, plotting the EQE as well, which will be slightly lower than the absorption because not all the carriers are collected. Comparing to plot (1), we can see we now have lower absorption due to the inclusion of front surface reflection, which is ~ 30% or more over the wavelength range of interest for a bare Si surface.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].layer_absorption, label='A')\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, label=\"R\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, label=\"T\")\nplt.title(\"(3) QE of Si cell (no ARC) - TMM\")\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.ylim(0, 100)\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html", - "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html", - "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", - "section": "", - "text": "This example shows how you can simulate a perovskite-Si tandem cell with pyramidal surface textures, where the perovskite and other surface layers are assumed to be deposited conformally (i.e., also in a pyramid shape) on top of the Si. The perovskite optical constants are from this paper, while the structure is based on this paper We will calculate total reflection, transmission and absorption per layer as well as the wavelength-dependent absorption profiles in the perovskite and Si, which can be used in e.g. device simulations. We will look at the effect of treating the layers deposited on Si (including the perovskite) coherently or incoherently.\nFirst, import relevant packages and RayFlare functions:\nimport numpy as np\nimport os\n\nfrom solcore.structure import Layer\nfrom solcore.constants import q\nfrom solcore import material\nfrom solcore.absorption_calculator import search_db, download_db\nfrom solcore.light_source import LightSource\n\nfrom rayflare.textures import regular_pyramids\nfrom rayflare.options import default_options\nfrom rayflare.ray_tracing import rt_structure\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\nfrom cycler import cycler\nNow we set some relevant options. We will scan across 20 x 20 surface points of the pyramid unit cell between 300 and 1200 nm, for unpolarized, normally-incident light. The randomize_surface option is set to True to prevent correlation between the incident position on the front and rear pyramids. The n_jobs option is set to -1, which means that all available cores will be used. If you want to use all but one core, change this to -2 etc. We also need to provide a project_name to save the lookup tables which will be calculated using TMM to use during ray-tracing.\nwavelengths = np.linspace(300, 1200, 40) * 1e-9\n\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wavelengths,\n output_units=\"photon_flux_per_m\")\n\noptions = default_options()\noptions.wavelength = wavelengths\noptions.nx = 20\noptions.ny = options.nx\noptions.n_rays = 4 * options.nx**2\noptions.depth_spacing = 1e-9\noptions.pol = \"u\"\noptions.I_thresh = 1e-3\noptions.project_name = \"perovskite_Si_rt\"\noptions.randomize_surface = True\noptions.n_jobs = -1 # use all cores; to use all but one, change to -2 etc.\nWe define our materials. Note that some of these are custom materials added to the database; we only need to do this once. We then define the front layer stack (i.e. all the materials which are on top of the Si, excluding Si itself, which will be the ‘bulk’ material) and the rear layer stack. Layer stacks are always defined starting with the layer closest to the top of the cell.\n# Can comment out this block after running once to add materials to the database\nfrom solcore.material_system import create_new_material\n\ncreate_new_material(\"Perovskite_CsBr_1p6eV\", \"data/CsBr10p_1to2_n_shifted.txt\",\n \"data/CsBr10p_1to2_k_shifted.txt\")\ncreate_new_material(\"ITO_lowdoping\", \"data/model_back_ito_n.txt\",\n \"data/model_back_ito_k.txt\")\ncreate_new_material(\"aSi_i\", \"data/model_i_a_silicon_n.txt\",\n \"data/model_i_a_silicon_k.txt\")\ncreate_new_material(\"aSi_p\", \"data/model_p_a_silicon_n.txt\",\n \"data/model_p_a_silicon_k.txt\")\ncreate_new_material(\"aSi_n\", \"data/model_n_a_silicon_n.txt\",\n \"data/model_n_a_silicon_k.txt\")\ncreate_new_material(\"C60\", \"data/C60_Ren_n.txt\",\n \"data/C60_Ren_k.txt\")\ncreate_new_material(\"IZO\", \"data/IZO_Ballif_rO2_10pcnt_n.txt\",\n \"data/IZO_Ballif_rO2_10pcnt_k.txt\")\n# Comment out until here\n# download_db()\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nSi = material(\"Si\")()\nAir = material(\"Air\")()\nMgF2 = material(str(MgF2_pageid), nk_db=True)()\nITO_back = material(\"ITO_lowdoping\")()\nPerovskite = material(\"Perovskite_CsBr_1p6eV\")()\nAg = material(str(Ag_pageid), nk_db=True)()\naSi_i = material(\"aSi_i\")()\naSi_p = material(\"aSi_p\")()\naSi_n = material(\"aSi_n\")()\nLiF = material(\"LiF\")()\nIZO = material(\"IZO\")()\nC60 = material(\"C60\")()\n\n# stack based on doi:10.1038/s41563-018-0115-4\nfront_materials = [\n Layer(100e-9, MgF2),\n Layer(110e-9, IZO),\n Layer(15e-9, C60),\n Layer(1e-9, LiF),\n Layer(440e-9, Perovskite),\n Layer(6.5e-9, aSi_n),\n Layer(6.5e-9, aSi_i),\n]\n\nback_materials = [Layer(6.5e-9, aSi_i), Layer(6.5e-9, aSi_p), Layer(240e-9, ITO_back)]\nNow we define our front and back surfaces, including interface_layers. We will use regular pyramids for both the front and back surface; these pyramids point out on both sides, but since the direction of the pyramids is defined relative to the front surface, we must set upright=True for the top surface and upright=False for the rear surface. We also gives the surfaces a name (used to save the lookup table data) and ask RayFlare to calculate the absorption profile in the 5th layer, which is the perovskite.\ntriangle_surf = regular_pyramids(\n elevation_angle=55,\n upright=True,\n size=1,\n interface_layers=front_materials,\n name=\"coh_front\",\n prof_layers=[5],\n)\n\ntriangle_surf_back = regular_pyramids(\n elevation_angle=55,\n upright=False,\n size=1,\n interface_layers=back_materials,\n name=\"Si_back\",\n coherency_list=[\"i\"] * len(back_materials),\n)\nNow we make our ray-tracing structure by combining the front and back surfaces, specifying the material in between (Si) and setting its width to 260 microns. In order to use the TMM lookuptables to calculate reflection/transmission/absorption probabilities we must also set use_TMM=True.\nrtstr_coh = rt_structure(\n textures=[triangle_surf, triangle_surf_back],\n materials=[Si],\n widths=[260e-6],\n incidence=Air,\n transmission=Ag,\n use_TMM=True,\n options=options,\n overwrite=True,\n save_location=\"current\",\n)\n\n# calculate:\nresult_coh = rtstr_coh.calculate(options)\nNow we define the same front surface and structure again, except now we will treat all the layers incoherently (i.e. no thin-film interference) in the TMM.\ntriangle_surf = regular_pyramids(\n elevation_angle=55,\n upright=True,\n size=1,\n interface_layers=front_materials,\n coherency_list=[\"i\"] * len(front_materials),\n name=\"inc_front\",\n prof_layers=[5],\n)\n\nrtstr_inc = rt_structure(\n textures=[triangle_surf, triangle_surf_back],\n materials=[Si],\n widths=[260e-6],\n incidence=Air,\n transmission=Ag,\n use_TMM=True,\n options=options,\n overwrite=True,\n save_location=\"current\",\n)\n\nresult_inc = rtstr_inc.calculate(options)\nNow we plot the results for reflection, transmission, and absorption per layer for both the coherent and incoherent cases.\npal = sns.color_palette(\"husl\", n_colors=len(front_materials) + len(back_materials) + 2)\n# create a colour palette\n\ncols = cycler(\"color\", pal)\n# set this as the default colour palette in matplotlib\n\nparams = {\n \"axes.prop_cycle\": cols,\n}\n\nplt.rcParams.update(params)\n\nfig = plt.figure(figsize=(8, 3.7))\nplt.subplot(1, 1, 1)\nplt.plot(wavelengths * 1e9, result_coh[\"R\"], \"-ko\", label=\"R\")\nplt.plot(wavelengths * 1e9, result_coh[\"T\"], mfc=\"none\", label=\"T\")\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_layer\"][:, 0], \"-o\", label='Si')\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_interface\"][0], \"-o\",\n label=[None, \"IZO\", \"C60\", None, \"Perovskite\", None, None])\nplt.plot(wavelengths * 1e9, result_coh[\"A_per_interface\"][1], \"-o\",\n label=[None, None, \"ITO\"])\n\nplt.plot(wavelengths * 1e9, result_inc[\"R\"], \"--ko\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"T\"], mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_layer\"][:, 0], \"--o\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_interface\"][0], \"--o\", mfc=\"none\")\nplt.plot(wavelengths * 1e9, result_inc[\"A_per_interface\"][1], \"--o\", mfc=\"none\")\n\nplt.plot([300, 301], [0, 0], \"-k\", label=\"coherent\")\nplt.plot([300, 301], [0, 0], \"--k\", label=\"incoherent\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"R / A / T\")\nplt.ylim(0, 1)\nplt.xlim(300, 1200)\nplt.legend(bbox_to_anchor=(1.05, 1))\nplt.tight_layout()\nplt.show()\nCalculate and print the limiting short-circuit current per junction:\nJmax_Pero_coh = q*np.trapz(result_coh[\"A_per_interface\"][0][:,4]*AM15G.spectrum()[1],\n x=wavelengths)/10\nJmax_Si_coh = q*np.trapz(result_coh[\"A_per_layer\"][:, 0]*AM15G.spectrum()[1],\n x=wavelengths)/10\n\nprint(\"Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:\"\n \".2f}\".format(Jmax_Pero_coh, Jmax_Si_coh))\n\nJmax_Pero_inc = q*np.trapz(result_inc[\"A_per_interface\"][0][:,4]*AM15G.spectrum()[1],\n x=wavelengths)/10\nJmax_Si_inc = q*np.trapz(result_inc[\"A_per_layer\"][:, 0]*AM15G.spectrum()[1],\n x=wavelengths)/10\n\nprint(\"Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:\"\n \".2f}\".format(Jmax_Pero_inc, Jmax_Si_inc))\nWe can also plot the absorption profiles, for wavelengths up to 800 nm, in the perovskite (since we asked the solver to calculate the profile in the perovskite layer above).\nwl_Eg = wavelengths < 800e-9\n\npal = sns.cubehelix_palette(sum(wl_Eg), reverse=True)\ncols = cycler(\"color\", pal)\nparams = {\n \"axes.prop_cycle\": cols,\n}\nplt.rcParams.update(params)\n\npos = np.arange(0, rtstr_coh.interface_layer_widths[0][4], options.depth_spacing*1e9)\n\nfig, (ax1, ax2) = plt.subplots(1,2)\nax1.plot(pos, result_coh[\"interface_profiles\"][0][wl_Eg].T)\nax1.set_ylim(0, 0.02)\nax1.set_xlabel(\"z (nm)\")\nax1.set_ylabel(\"a(z)\")\nax1.set_title(\"Coherent\")\nax2.plot(pos, result_inc[\"interface_profiles\"][0][wl_Eg].T)\nax2.set_ylim(0, 0.02)\nax2.yaxis.set_ticklabels([])\nax2.set_xlabel(\"z (nm)\")\nax2.set_title(\"Incoherent\")\nplt.show()\nWe see that, as expected, the coherent case shows interference fringes while the incoherent case does not. We can also plot the absorption profile in the Si (> 800 nm):\npos_bulk = pos = np.arange(0, rtstr_coh.widths[0]*1e6, options.depth_spacing_bulk*1e6)\n\nfig, (ax1, ax2) = plt.subplots(1,2)\nax1.semilogy(pos, result_coh[\"profile\"][~wl_Eg].T)\nax1.set_ylim(1e-8, 0.00015)\nax1.set_xlabel(\"z (um)\")\nax1.set_ylabel(\"a(z)\")\nax1.set_title(\"Coherent\")\nax2.semilogy(pos, result_inc[\"profile\"][~wl_Eg].T)\nax2.set_ylim(1e-8, 0.00015)\nax2.yaxis.set_ticklabels([])\nax2.set_xlabel(\"z (um)\")\nax2.set_title(\"Incoherent\")\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-an-arc", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#adding-an-arc", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Adding an ARC", + "text": "Adding an ARC\nThe reflectance of bare Si is very high. Let’s try adding a simple anti-reflection coating (ARC), a single layer of silicon nitride (Si\\(_3\\)N\\(_4\\)):\n\nSiN = material(\"Si3N4\")()\n\nSi_junction = Junction([emitter_layer, base_layer], kind=\"DA\")\n\nsolar_cell_TMM_ARC = SolarCell([Layer(width=si(75, \"nm\"), material=SiN), Si_junction])\n\nsolar_cell_solver(solar_cell_TMM_ARC, 'qe', options)\nsolar_cell_solver(solar_cell_TMM_ARC, 'iv', options)\n\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving QE of the solar cell...\nTreating layer(s) 2 incoherently\nCalculating RAT...\nCalculating absorption profile...\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\nPLOT 4: Absorption, EQE, reflection and transmission for the cell with a simple one-layer ARC. We see the reflection is significantly reduced from the previous plot leading to higher absorption/EQE.\n\nplt.figure()\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].eqe(wavelengths), 'k-', label=\"EQE\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].layer_absorption, label='A')\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.reflected, label=\"R\")\nplt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.transmitted, label=\"T\")\nplt.legend()\nplt.title(\"(4) QE of Si cell (ARC) - TMM\")\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"QE/Absorptance (%)\")\nplt.ylim(0, 100)\nplt.show()\n\n\n\n\nPLOT 5: Compare the IV curves of the cells with and without an ARC. The efficiency is also shown on the plot. Note that because we didn’t specify a light source, Solcore will assume we want to use AM1.5G; in later examples we will set the light source used for light IV simulations explicitly.\n\nplt.figure()\nplt.plot(voltages, -solar_cell_TMM[0].iv(voltages)/10, label=\"No ARC\")\nplt.plot(voltages, -solar_cell_TMM_ARC[1].iv(voltages)/10, label=\"75 nm SiN\")\nplt.text(0.5, 1.02*abs(solar_cell_TMM.iv[\"Isc\"])/10, str(round(solar_cell_TMM.iv[\"Eta\"]*100,\n 1)) + ' %')\nplt.text(0.5, 1.02*abs(solar_cell_TMM_ARC.iv[\"Isc\"])/10, str(round(solar_cell_TMM_ARC\n .iv[\"Eta\"]*100, 1)) + ' %')\nplt.ylim(0, 38)\nplt.xlim(-0.8, 0.8)\nplt.legend()\nplt.xlabel(\"V (V)\")\nplt.ylabel(r\"J (mA/cm$^2$)\")\nplt.title(\"(5) IV curve of Si cell with and without ARC\")\nplt.show()" }, { - "objectID": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#questions", - "href": "solcore-workshop-2/notebooks/10-perovskite_Si_rt.html#questions", - "title": "Section 10: Perovskite-Si tandem cell with pyramidal surfaces", + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#conclusions", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#conclusions", + "title": "Section 5a: Planar Si solar cell using DA", + "section": "Conclusions", + "text": "Conclusions\nWe see that the cell with an ARC has a significantly higher \\(J_{sc}\\), and a slightly higher \\(V_{oc}\\), than the bare Si cell. In reality, most Si cells have a textured surface rather than a planar surface with an ARC; this will be discussed later in the course.\nOverall, some things we can take away from the examples in this script:\n\nThe Beer-Lambert law is a very simple way to calculate absorption in a cell, but won’t take into account important effects such as front-surface reflection or the effects of anti-reflection coatings.\nUsing the transfer-matrix method (TMM), we can account for front surface reflection and interference effects which make e.g. ARCs effective. In the simple situation of a thick cell without any front surface layers, it is equivalent to simply calculating the reflection with the Fresnel equations and assuming Beer-Lambert absorption in the cell.\nAdding a simple, one-layer ARC can significantly reduce front-surface reflection for a single-junction cell, leading to improved short-circuit current. To correctly account for interference in this layer, which is what causes its anti-reflective properties, we most use the transfer-matrix method (TMM) optical solver." + }, + { + "objectID": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#questions", + "href": "solcore-workshop-2/notebooks/5a-simple_Si_cell.html#questions", + "title": "Section 5a: Planar Si solar cell using DA", "section": "Questions", - "text": "Questions\n\nWhy do you think the total absorption is slightly lower in the incoherent calculation?\nEven though the layers on top of the Si are not very thick compared to the wavelength, and they are the first thing encountered by the light, why might it make sense to treat them incoherently?\nCan you improve the current-matching (at least in terms of limiting currents) between the perovskite and the Si?" + "text": "Questions\n\nWhich parameters could we change which would affect the EQE and/or IV of the cell?\nWhy can’t we just use the Fresnel equations to calculate the effect of an anti-reflection coating?" }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html", + "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html", + "title": "Section 6b: Optimizing an ARC", "section": "", - "text": "The structure in this example is based on that of the previous example (9a), but with the planar bottom Si cell replaced by a Si cell with a pyramidal texture, bonded to the III-V top cells with a low-index epoxy/glass layer.\nWe could use the angular redistribution matrix method as in the previous example - however, because in this example we only need to use TMM and ray-tracing (RT), we can use the ray-tracing method with integrated RT directly (this is generally faster, because we do not need to calculate the behaviour of the surfaces for every angle of incidence)." + "text": "In the previous example, we introduced a simple one-layer anti-reflection coating (ARC); ARCs are a standard feature of all high-efficiency solar cells. But how do you find out the right thickness for the anti-reflection coating layer(s) (or the right dimensions for a light-trapping grating, or some other structure in your cell)? This is where optimization comes in. Here, we will look at a very simple ‘brute-force’ optimization for a single or double-layer ARC.\nimport numpy as np\nimport os\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer, SolarCell\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom solcore.light_source import LightSource\nfrom solcore.absorption_calculator import search_db, download_db\nfrom solcore.absorption_calculator import calculate_rat\nfrom solcore.state import State\n\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.options import default_options\nimport seaborn as sns" }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#setting-up", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#setting-up", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#setting-up", + "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#setting-up", + "title": "Section 6b: Optimizing an ARC", "section": "Setting up", - "text": "Setting up\nWe load relevant packages and define materials, the same as in the previous example.\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.ray_tracing import rt_structure\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.textures import planar_surface, regular_pyramids\nfrom rayflare.options import default_options\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# download_db()\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nepoxy = material(\"BK7\")()\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nAlGaAs = material(\"AlGaAs\")\n\nAir = material(\"Air\")()\n\nGaAs = material(\"GaAs\")\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n234 main MgF2 Rodriguez-de_Marcos main/MgF2/Rodriguez-de Marcos.yml 1 1 0.0299919 2.00146 960\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n475 main Ta2O5 Rodriguez-de_Marcos main/Ta2O5/Rodriguez-de Marcos.yml 1 1 0.0294938 1.51429 212\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n2 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2835 other negative_tone_photoresists Microchem_SU8_2000 other/resists/Microchem SU-8 2000.yml 1 0 0.32 0.8 200\n2836 other negative_tone_photoresists Microchem_SU8_3000 other/resists/Microchem SU-8 3000.yml 1 0 0.32 1.7 200\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2 main Ag Jiang main/Ag/Jiang.yml 1 1 0.3 2.0 1701\n\n\nWe define the layers we will need, as before. We specify the thickness of the silicon (280 \\(\\mu\\)m) and epoxy (1 mm) at the top:\n\nd_Si = 280e-6 # thickness of Si wafer\nd_epoxy = 1e-6 # thickness of epoxy. In reality, the epoxy is much thicker, but the exact thickness doesn't matter \n # because the material is transparent and we will treat it incoherently.\n\nGaInP_total_thickness = 350e-9\nGaAs_total_thickness = 1200e-9\n\nARC = [Layer(110e-9, MgF2), Layer(65e-9, Ta2O5)]\n\nGaInP_junction = [Layer(20e-9, window), Layer(GaInP_total_thickness, GaInP(In=0.50))]\n\n# 100 nm TJ\ntunnel_1 = [Layer(100e-9, AlGaAs(Al=0.8)), Layer(20e-9, GaInP(In=0.5))]\n\nGaAs_junction = [Layer(20e-9, GaInP(In=0.5)), Layer(GaAs_total_thickness, GaAs()), Layer(70e-9, AlGaAs(Al=0.8))]\n\nspacer_ARC = [Layer(80e-9, Ta2O5)]" - }, - { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-cell-layers", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-cell-layers", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Defining the cell layers", - "text": "Defining the cell layers\nThere are three interfaces in the cell which will define the structure to simulate:\n\nthe III-V/epoxy interface, where the epoxy itself will be treated as a bulk layer in the simulation\nthe epoxy/Si interface, where the Si has a pyramidal texture (the Si itself is another bulk layer in the simulation).\nthe rear surface of the cell, where the Si again has a pyramidal texture (and we assume there is a silver back mirror behind the cell)\n\nThese 3 interfaces are defined here, using the pre-defined textures for a planar surface or regular pyramids:\n\nfront_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + spacer_ARC\n\nfront_surf = planar_surface(interface_layers = front_layers, prof_layers=np.arange(1, len(front_layers)+1))\n\nSi_front = regular_pyramids(elevation_angle=50, upright=True)\n\nSi_back = regular_pyramids(elevation_angle=50, upright=False)\n\nNow we set relevant options for the solver. We set the number of rays to trace at each wavelength (more rays will make the result less noisy, but increase computation time) and whether to calculate the absorption profile in the bulk layers (no, in this case). The randomize_surface options determines whether the ray keeps track of its positions in the unit cell while travelling between surfaces; we set this to False to mimic random pyramids.\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl, output_units=\"photon_flux_per_m\")\n\noptions.wavelength = wl\noptions.project_name = \"III_V_Si_cell\"\n\n# options for ray-tracing\noptions.randomize_surface = True\noptions.n_rays = 1000\noptions.bulk_profile = False" - }, - { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-structures", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#defining-the-structures", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Defining the structures", - "text": "Defining the structures\nFinally, we define the ray-tracing structure we will use, using the interfaces, bulk materials, and options set above. Because we want to calculate the reflection/absorption/transmission probabilities at the front surface using TMM, we set the use_TMM argument to True. We also define a completely planar cell with the same layer thicknesses etc. to compare and evaluate the effect of the textures Si surfaces.\n\noptical_structure = rt_structure(\n textures=[front_surf, Si_front, Si_back],\n materials=[epoxy, Si()],\n widths=[d_epoxy, d_Si],\n incidence=Air,\n transmission=Ag,\n options=options,\n use_TMM=True,\n save_location=\"current\", # lookup table save location\n overwrite=True, # whether to overwrite any previously existing results, if found\n)\n\n# options for TMM\noptions.coherent = False\noptions.coherency_list = len(front_layers)*['c'] + ['i']*2\n\nplanar_optical_structure = tmm_structure(\n layer_stack = front_layers + [Layer(d_epoxy, epoxy), Layer(d_Si, Si())],\n incidence=Air,\n transmission=Ag,\n)\n\nINFO: Pre-computing TMM lookup table(s)\n\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/MgF2/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded.\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaterial main/Ta2O5/Rodriguez-de Marcos.yml loaded." + "text": "Setting up\nWe set some options, as in previous examples, setting the wavelengths and defining the incident spectrum. We are going to do a partially coherent calculation, treating the ARC as a coherent layer and the thick Si layer as incoherent (no thin-film interference).\n\nopts = State()\n\nwavelengths = np.linspace(300, 1200, 800)*1e-9\n\nAM15g = LightSource(source_type=\"standard\", version=\"AM1.5g\", output_units=\"photon_flux_per_m\")\nspectrum = AM15g.spectrum(wavelengths)[1]\nnormalised_spectrum = spectrum/np.max(spectrum)\n\nopts.wavelength = wavelengths\nopts.coherency_list = ['c', 'i']\nopts.optics_method = 'TMM'\nopts.position = 100e-6\nopts.no_back_reflection = False\n\nSi = material(\"Si\")()\nSiN = material(\"Si3N4\")()\nAg = material(\"Ag\")()\nAir = material(\"Air\")()" }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#calculations", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#calculations", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Calculations", - "text": "Calculations\nCalculate the R/A/T for the planar reference cell:\n\ntmm_result = planar_optical_structure.calculate(options=options)\n\nGaInP_A_tmm = tmm_result['A_per_layer'][:,3]\nGaAs_A_tmm = tmm_result['A_per_layer'][:,7]\nSi_A_tmm = tmm_result['A_per_layer'][:,len(front_layers)+1]\n\nJmax_GaInP_tmm = q*np.trapz(GaInP_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs_tmm = q*np.trapz(GaAs_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_Si_tmm = q*np.trapz(Si_A_tmm*AM15G.spectrum()[1], x=wl)/10\n\nCalculate the R/A/T for the textured cell:\n\nrt_result = optical_structure.calculate(options=options)\n\nGaInP_absorption_ARC = rt_result['A_per_interface'][0][:,3]\nGaAs_absorption_ARC = rt_result['A_per_interface'][0][:,7]\nSi_absorption_ARC = rt_result['A_per_layer'][:,1]\n\nJmax_GaInP = q*np.trapz(GaInP_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_absorption_ARC*AM15G.spectrum()[1], x=wl)/10" + "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#single-layer-arc", + "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#single-layer-arc", + "title": "Section 6b: Optimizing an ARC", + "section": "Single-layer ARC", + "text": "Single-layer ARC\nHere, we will calculate the behaviour of a single-layer SiN anti-reflection coating on Si while changing the ARC thickness between 0 and 200 nm. We will consider two values to optimize: the mean reflectance mean_R, and the reflectance weighted by the photon flux in an AM1.5G spectrum (weighted_R). The reason for considering the second value is that it is more useful to suppress reflection at wavelengths where there are more photons which could be absorbed by the cell (up to the cell’s bandgap).\nWe will loop through the different ARC thicknesses in d_range, build the structure for each case, and then calculate the reflectance. We then save the mean reflected and weighted mean reflectance in the corresponding arrays. We also plot the reflectance for each 15th loop (this is just so the plot does not get too crowded).\n\n%%capture\n\nd_range = np.linspace(0, 200, 200)\n\nmean_R = np.empty_like(d_range)\nweighted_R = np.empty_like(d_range)\n\ncols = sns.cubehelix_palette(np.ceil(len(d_range)/15))\n\nplt.figure()\njcol = 0\n\nfor i1, d in enumerate(d_range):\n\n struct = SolarCell([Layer(si(d, 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\n solar_cell_solver(struct, task='optics', user_options=opts)\n\n if i1 % 15 == 0:\n plt.plot(wavelengths*1e9, struct.reflected, label=str(np.round(d, 0)), color=cols[jcol])\n jcol += 1\n\n mean_R[i1] = np.mean(struct.reflected)\n weighted_R[i1] = np.mean(struct.reflected*normalised_spectrum)\n\nplt.legend()\nplt.show()\n\nWe now find at which index mean_R and weighted_R are minimised using np.argmin, and use this to print the ARC thickness at which this occurs (rounded to 1 decimal place).\n\nprint('Minimum mean reflection occurs at d = ' + str(np.round(d_range[np.argmin(mean_R)], 1)) + ' nm')\nprint('Minimum weighted reflection occurs at d = ' + str(np.round(d_range[np.argmin(weighted_R)], 1)) + ' nm')\n\nMinimum mean reflection occurs at d = 67.3 nm\nMinimum weighted reflection occurs at d = 74.4 nm\n\n\nWe see that the values of \\(d\\) for the two different ways of optimizing are very similar, but not exactly the same, as we would expect. The minimum in both cases occurs around 70 nm. We can also plot the variation of the mean and weighted \\(R\\) with ARC thickness \\(d\\):\n\nplt.figure()\nplt.plot(d_range, mean_R, label='Mean reflection')\nplt.plot(d_range[np.argmin(mean_R)], np.min(mean_R), 'ok')\nplt.plot(d_range, weighted_R, label='Weighted mean reflection')\nplt.plot(d_range[np.argmin(weighted_R)], np.min(weighted_R), 'ok')\nplt.xlabel('d$_{SiN}$')\nplt.ylabel('(Weighted) mean reflection 300-1200 nm')\nplt.legend()\nplt.show()\n\n\n\n\nNow, to see what the reflectance looks like for the optimized structure, we make new tmm_structures with the optimal values and calculate and plot the reflectance:\n\nstruct_1 = SolarCell([Layer(si(d_range[np.argmin(mean_R)], 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\nsolar_cell_solver(struct_1, task='optics', user_options=opts)\nR_1 = struct_1.reflected\n\nstruct_2 = SolarCell([Layer(si(d_range[np.argmin(weighted_R)], 'nm'), SiN), Layer(si('120um'), Si)], substrate=Ag)\nsolar_cell_solver(struct_2, task='optics', user_options=opts)\nR_2 = struct_2.reflected\n\nplt.figure()\nplt.plot(wavelengths*1e9, R_1, label='Mean R minimum')\nplt.plot(wavelengths*1e9, R_2, label='Weighted R minimum')\nplt.legend()\nplt.xlabel(\"Wavelength (nm)\")\nplt.ylabel(\"R\")\nplt.show()\n\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\nTreating layer(s) 1 incoherently\nCalculating RAT...\nCalculating absorption profile...\n\n\n\n\n\nWe see that the two reflectance curves are very similar, as expected because the layer thicknesses are very similar." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#plotting-the-results", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#plotting-the-results", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Plotting the results", - "text": "Plotting the results\nFinally, we plot the results; the solid lines show the results for the textured Si cell (calculated using ray-tracing), the dashed lines for the planar cell (calculated using TMM). The maximum possible currents are shown in the plot, with the value in brackets for Si being for the planar cell.\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_absorption_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_absorption_ARC, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_absorption_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, GaInP_A_tmm, \"--k\")\nplt.plot(wl * 1e9, GaAs_A_tmm, \"--b\")\nplt.plot(wl * 1e9, Si_A_tmm, \"--r\")\nplt.plot(wl * 1e9, rt_result['R'], '-', color='grey', label=\"Reflected\")\nplt.plot(wl * 1e9, tmm_result['R'], '--', color='grey')\n\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(870, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.text(870, 0.45, r\"({:.1f} mA/cm$^2)$\".format(Jmax_Si_tmm))\n\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.tight_layout()\nplt.show()" + "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#double-layer-arc", + "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#double-layer-arc", + "title": "Section 6b: Optimizing an ARC", + "section": "Double-layer ARC", + "text": "Double-layer ARC\nWe will now consider a similar situation, but for a double-layer MgF\\(_2\\)/Ta\\(_2\\)O\\(_5\\) ARC on GaAs.\nSolcore can directly interface with the database from www.refractiveindex.info, which contains around 3000 sets of data for a large number of different materials. Before the first use, it is necessary to download the database. This only needs to be done once, so you can comment this line out after it’s done:\n\ndownload_db(confirm=True) # only needs to be done once\n\nDatabase file found at /Users/z3533914/.solcore/nk/nk.db\nMaking request to https://refractiveindex.info/download/database/rii-database-2021-07-18.zip\nDownloaded and extracting...\nWrote /var/folders/wh/w5k56r_927j4yp3mh91bggfc0000gq/T/tmp48b25bqt/database from https://refractiveindex.info/download/database/rii-database-2021-07-18.zip\nLOG: 2746,other,PtAl2,Chen : Bad Material YAML File.\n***Wrote SQLite DB on /Users/z3533914/.solcore/nk/nk.db\n\n\nWe search for materials in the refractiveindex.info database, and use only the part of the solar spectrum relevant for absorption in GaAs (in this case, there is no benefit to reducing absorption above the GaAs bandgap around 900 nm). We will only consider the weighted mean \\(R\\) in this case. Since all the layers in the structure are relatively thin compared to the wavelengths of light, we do a coherent calculation.\n\n%%capture\n\npageid_MgF2 = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0]\npageid_Ta2O5 = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0]\n\nGaAs = material(\"GaAs\")()\nMgF2 = material(str(pageid_MgF2), nk_db=True)()\nTa2O5 = material(str(pageid_Ta2O5), nk_db=True)()\n\nMgF2_thickness = np.linspace(50, 100, 20)\nTa2O5_thickness = np.linspace(30, 80, 20)\n\nweighted_R_matrix = np.zeros((len(MgF2_thickness), len(Ta2O5_thickness)))\n\nwavelengths_GaAs = wavelengths[wavelengths < 900e-9]\nnormalised_spectrum_GaAs = normalised_spectrum[wavelengths < 900e-9]\n\nopts.coherency_list = None\nopts.wavelength = wavelengths_GaAs\nopts.position = 20e-6\n\nWe now have two thicknesses to loop through; otherwise, the procedure is similar to the single-layer ARC example.\n\n%%capture\n\nfor i1, d_MgF2 in enumerate(MgF2_thickness):\n for j1, d_Ta2O5 in enumerate(Ta2O5_thickness):\n struct = SolarCell([Layer(si(d_MgF2, 'nm'), MgF2), Layer(si(d_Ta2O5, 'nm'), Ta2O5),\n Layer(si('20um'), GaAs)],\n substrate=Ag)\n solar_cell_solver(struct, 'optics', opts)\n R = struct.reflected\n\n weighted_R_matrix[i1, j1] = np.mean(R * normalised_spectrum_GaAs)\n\n# find the row and column indices of the minimum weighted R value\nri, ci = np.unravel_index(weighted_R_matrix.argmin(), weighted_R_matrix.shape)\n\nWe plot the total absorption (\\(1-R\\)) in the structure with the optimized ARC, and print the thicknesses of MgF\\(_2\\) and Ta\\(_2\\)O\\(_5\\) at which this occurs:\n\nplt.figure()\nplt.imshow(1-weighted_R_matrix, extent=[min(Ta2O5_thickness), max(Ta2O5_thickness),\n min(MgF2_thickness), max(MgF2_thickness)],\n origin='lower', aspect='equal')\nplt.plot(Ta2O5_thickness[ci], MgF2_thickness[ri], 'xk')\nplt.colorbar()\nplt.xlabel(\"Ta$_2$O$_5$ thickness (nm)\")\nplt.ylabel(\"MgF$_2$ thickness (nm)\")\nplt.show()\n\nprint(\"Minimum reflection occurs at MgF2 / Ta2O5 thicknesses of %.1f / %.1f nm \"\n % (MgF2_thickness[ri], Ta2O5_thickness[ci]))\n\n\n\n\nMinimum reflection occurs at MgF2 / Ta2O5 thicknesses of 73.7 / 53.7 nm \n\n\nFor these two examples, where we are only trying to optimize one and two parameters respectively across a relatively small range, using a method (TMM) which executes quickly, brute force searching is possible. However, as we introduce more parameters, a wider parameter space, and slower simulation methods, it may no longer be computationally tractable; in that case, using for example differential evolution or other types of numerical optimization may be more appropriate (see this example)." }, { - "objectID": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#questionschallenges", - "href": "solcore-workshop-2/notebooks/9b-GaInP_GaAs_Si_pyramids.html#questionschallenges", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Questions/challenges", - "text": "Questions/challenges\n\nDoes it make sense to do a ray-tracing calculation for short wavelengths? For this structure, can you speed up the calculation and avoid the random noise at short wavelengths?\nHow much current is lost to parasitic absorption in e.g. tunnel junctions, window layers etc.?\nHow can we reduce reflection at the epoxy interfaces?\nIf the epoxy/glass layer is much thicker than the relevant incident wavelengths, and not absorbing, does the exact thickness matter in the simulation?\nWhat happens if only the rear surface is textured? Would a structure without the front texture have other advantages?\nWhy does the Si have lower absorption/limiting current in this structure compared to the previous example?\n\nNow we can also use RayFlare’s optical results to run an electrical simulation in Solcore. To use the depletion approximation (DA) or drift-diffusion (PDD) solvers, we need the front surface reflectivity, and a depth-dependent absorption/generation profile. While so far we have been plotting total absorption per layer, RayFlare can calculate depth-dependent profiles too.\n\nfrom solcore.solar_cell import SolarCell, Junction\nfrom solcore.solar_cell_solver import solar_cell_solver\nfrom rayflare.utilities import make_absorption_function\nfrom solcore.state import State\n\noptions = State(options) # convert to Solcore options object so Solcore will recognise it\nV = np.linspace(-3, 0, 100)\n\noptions.bulk_profile = True\noptions.depth_spacing = 1e-9\noptions.depth_spacing_bulk = 10e-9\noptions.optics_method = 'external'\noptions.voltages = V\noptions.internal_voltages = np.linspace(-4, 1, 200)\noptions.light_iv = True\noptions.mpp = True\noptions.light_source = AM15G\noptions.recalculate_absorption = True\n\nprofile_data = optical_structure.calculate_profile(options)\n\ndepths, external_optics_func = make_absorption_function(profile_data, optical_structure, options)\n\noptions.position = depths\n\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\nINFO: Calculating next wavelength...\n\n\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\nWARNING: The RCWA solver will not be available because an S4 installation has not been found.\n\n\nPreviously, we defined RayFlare rt_structure and tmm_structure objects to do the optical calculation. For the cell calculation, we need a Solcore SolarCell object, which needs different information (such as doping levels) to perform the electrical calculation.\n\nGaInP_emitter_thickness = 100e-9\nGaAs_emitter_thickness = 200e-9\nSi_emitter_thickness = 1e-6\n\nGaInP_base_thickness = GaInP_total_thickness - GaInP_emitter_thickness\nGaAs_base_thickness = GaAs_total_thickness - GaAs_emitter_thickness\nSi_base_thickness = d_Si - Si_emitter_thickness\n\nGaInP_junction = Junction([\n Layer(20e-9, material(\"AlInP\")(Al=0.52), Nd=si(\"1e18cm-3\"), role=\"window\"), # window\n Layer(GaInP_emitter_thickness, GaInP(In=0.50, Nd=si(\"1e18cm-3\"), hole_diffusion_length=si(\"200nm\")), role=\"emitter\"), # emitter\n Layer(GaInP_base_thickness, GaInP(In=0.50, Na=si(\"1e17cm-3\"), electron_diffusion_length=si(\"300nm\")), role=\"base\"), # base\n ], kind=\"DA\") # TJ\n\nGaAs_junction = Junction([\n Layer(20e-9, GaInP(In=0.5, Nd=si(\"1e18cm-3\")), role=\"window\"), # window\n Layer(GaAs_emitter_thickness, GaAs(Nd=si(\"1e18cm-3\"), hole_diffusion_length=si(\"250nm\")), role=\"emitter\"), # emitter\n Layer(GaAs_base_thickness, GaAs(Na=si(\"9e16cm-3\"), electron_diffusion_length=si(\"1000nm\")), role=\"base\"), # basee\n Layer(70e-9, AlGaAs(Al=0.8, Na=si(\"4e18cm-3\")), role=\"bsf\") # BSF\n ], kind=\"DA\")\n\nSi_junction = Junction([\n Layer(Si_emitter_thickness, Si(Nd=si(\"1e19cm-3\"), hole_diffusion_length=si(\"1000nm\")), role=\"emitter\"),\n Layer(Si_base_thickness, Si(Na=si(\"1e16cm-3\"), electron_diffusion_length=si(\"250um\")), role=\"base\")],\n kind=\"DA\")\n\nsolar_cell = SolarCell(\n ARC + [GaInP_junction] + tunnel_1 + [GaAs_junction] + spacer_ARC + [Layer(d_epoxy, epoxy)] + [Si_junction],\n external_reflected=rt_result[\"R\"],\n external_absorbed=external_optics_func)\n\n\nsolar_cell_solver(solar_cell, 'iv', options)\n\nplt.figure(2)\nplt.plot(-V, -solar_cell.iv['IV'][1]/10, 'k', linewidth=3, label='3J cell')\nplt.plot(-V, solar_cell(0).iv(V)/10, 'b', label='InGaP sub-cell')\nplt.plot(-V, solar_cell(1).iv(V)/10, 'g', label='GaAs sub-cell')\nplt.plot(-V, solar_cell(2).iv(V)/10, 'r', label='Si sub-cell')\nplt.text(1.5, 5,f'Jsc= {abs(solar_cell.iv.Isc/10):.2f} mA.cm' + r'$^{-2}$')\nplt.text(1.5, 4,f'Voc= {abs(solar_cell.iv.Voc):.2f} V')\nplt.text(1.5, 3,f'FF= {solar_cell.iv.FF*100:.2f} %')\nplt.text(1.5, 2,f'Eta= {solar_cell.iv.Eta*100:.2f} %')\n\nplt.legend()\nplt.ylim(-10, 15)\nplt.xlim(0, 3)\nplt.ylabel('Current (mA/cm$^2$)')\nplt.xlabel('Voltage (V)')\nplt.show()\n\nINFO: Solving optics of the solar cell...\n\n\nSolving IV of the junctions...\nSolving IV of the tunnel junctions...\nSolving IV of the total solar cell...\n\n\n\n\n\n\nV\n\narray([-3. , -2.96969697, -2.93939394, -2.90909091, -2.87878788,\n -2.84848485, -2.81818182, -2.78787879, -2.75757576, -2.72727273,\n -2.6969697 , -2.66666667, -2.63636364, -2.60606061, -2.57575758,\n -2.54545455, -2.51515152, -2.48484848, -2.45454545, -2.42424242,\n -2.39393939, -2.36363636, -2.33333333, -2.3030303 , -2.27272727,\n -2.24242424, -2.21212121, -2.18181818, -2.15151515, -2.12121212,\n -2.09090909, -2.06060606, -2.03030303, -2. , -1.96969697,\n -1.93939394, -1.90909091, -1.87878788, -1.84848485, -1.81818182,\n -1.78787879, -1.75757576, -1.72727273, -1.6969697 , -1.66666667,\n -1.63636364, -1.60606061, -1.57575758, -1.54545455, -1.51515152,\n -1.48484848, -1.45454545, -1.42424242, -1.39393939, -1.36363636,\n -1.33333333, -1.3030303 , -1.27272727, -1.24242424, -1.21212121,\n -1.18181818, -1.15151515, -1.12121212, -1.09090909, -1.06060606,\n -1.03030303, -1. , -0.96969697, -0.93939394, -0.90909091,\n -0.87878788, -0.84848485, -0.81818182, -0.78787879, -0.75757576,\n -0.72727273, -0.6969697 , -0.66666667, -0.63636364, -0.60606061,\n -0.57575758, -0.54545455, -0.51515152, -0.48484848, -0.45454545,\n -0.42424242, -0.39393939, -0.36363636, -0.33333333, -0.3030303 ,\n -0.27272727, -0.24242424, -0.21212121, -0.18181818, -0.15151515,\n -0.12121212, -0.09090909, -0.06060606, -0.03030303, 0. ])\n\n\n\n\nsolar_cell_solver(solar_cell, 'qe', options)\n\nplt.figure(1)\nplt.plot(wl * 1e9, solar_cell(0).eqe(wl) * 100, 'b', label='GaInP QE')\nplt.plot(wl * 1e9, solar_cell(1).eqe(wl) * 100, 'g', label='GaAs QE')\nplt.plot(wl * 1e9, solar_cell(2).eqe(wl) * 100, 'r', label='Si QE')\nplt.fill_between(wl * 1e9, GaInP_absorption_ARC * 100, 0, alpha=0.3,\n label='GaInP Abs.', color='b')\nplt.fill_between(wl * 1e9, GaAs_absorption_ARC * 100, 0, alpha=0.3,\n label='GaAs Abs.', color='g')\nplt.fill_between(wl * 1e9, Si_absorption_ARC * 100, 0, alpha=0.3,\n label='Ge Abs.', color='r')\n\nplt.plot(wl*1e9, 100*(1-solar_cell.reflected), '--k', label=\"100 - Reflectivity\")\nplt.legend()\nplt.ylim(0, 100)\nplt.ylabel('EQE (%)')\nplt.xlabel('Wavelength (nm)')\nplt.show()\n\nINFO: Solving optics of the solar cell...\n\n\nSolving QE of the solar cell..." + "objectID": "solcore-workshop-2/notebooks/6b-arc_optimization.html#questions", + "href": "solcore-workshop-2/notebooks/6b-arc_optimization.html#questions", + "title": "Section 6b: Optimizing an ARC", + "section": "Questions", + "text": "Questions\n\nApart from varying the thickness of the layers, what else could we change?\nHow do we know where to start when designing an ARC (layer thickness/material)?" }, { - "objectID": "solcore-workshop/workshop2023.html", - "href": "solcore-workshop/workshop2023.html", - "title": "Solcore Workshop 2023 (SKKU)", + "objectID": "solcore-workshop-2/schedule.html", + "href": "solcore-workshop-2/schedule.html", + "title": "Schedule", "section": "", - "text": "Click here to view all the slides.\nOutline:\nDay 1:\n\nIntroduction to Solcore & computer modelling (lecture)\nIntegration for limiting current, limiting voltage model\nShockley-Queisser efficiency limit and detailed balance (DB) junction model (lecture)\n\nDay 2:\n\nIntroduction to drift-diffusion junction model, depletion approximation (lecture) & spectral irradiance\nThe depletion approximation: Si cell and GaAs cell\nOptical modelling using the transfer-matrix model (TMM):\n\nTMM introduction\nOptimizing an anti-reflection coating\n\nPlanar III-V on Si tandem solar cell\n\nDay 3:\n\nOptical absorption in textured Si: ray-tracing for pyramid textures, rigorous coupled-wave analysis (RCWA) for nano-scale gratings\nIII-V/Si cells with light-trapping structures:\n\nPlanar III-V wafer-bonded to silicon with planar front using e.g. epoxy\nPlanar III-V bonded to textured silicon with diffraction grating on rear\n\nConformal perovskite on silicon tandem cells" + "text": "Day 1 (Wednesday 22/11)\n\nDay 2 (Thursday 23/11)\n\nDay 3 (Friday 24/11)\n\n\n\n\nThemes:\nIntroduction, efficiency limits & fitting data\n\nJunction models & planar optics\n\nAdvanced light-trapping structures\n\n\n1.00 - 1.30\nIntroduction to computer modelling & Solcore\n1.00 - 1.30\nIntroduction to different junction models\n1.00 - 1.20\nIntroduction to RayFlare & different optical methods\n\n\n1.30 - 2.15\nLimiting current & voltage models\n1.30 - 2.00\nPlanar Si cell using depletion approximation junction\n1.20 - 2.00\nEffect of diffraction grating (RCWA) and ray-tracing (RT) on a silicon wafer\n\n\n2.15 - 2.45\nBreak\n2.00 - 2.45\nIntroduction to the transfer-matrix method: interference and anti-reflection coatings\n2.00 - 2.30\nGaInP/GaAs/Si triple-junction cell with rear diffraction grating\n\n\n2.45 - 3.30\nShockley-Queisser efficiency limit\n2.45 - 3.15\nBreak\n2.30 - 3.00\nBreak\n\n\n3.30 - 4.00\nChanging irradiance spectra\n3.00 - 3.45\nPlanar Si cell using drift-diffusion junction\n3.00 - 3.45\nEpoxy-bonded GaInP/GaAs//Si triple-junction cell with pyramidally textured silicon\n\n\n4.00 - 4.15\nBreak\n3.45 - 4.15\nBreak\n3.45 - 4.30\nPerovskite on silicon tandem cell with pyramidcal texturing\n\n\n4.15 - 5.00\nTwo-diode model fits to experimental data\n4.15 - 5.00\nOptical model of a planar III-V on Si tandem cell\n4.30 - 5.00\nUsing the Katana HPC" }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html", + "title": "Section 6a: Basic cell optics", "section": "", - "text": "The structure in this example is based on that of the previous example (9a), but with the planar bottom Si cell replaced by a Si cell with a pyramidal texture, bonded to the III-V top cells with a low-index epoxy/glass layer.\nWe could use the angular redistribution matrix method as in the previous example - however, because in this example we only need to use TMM and ray-tracing (RT), we can use the ray-tracing method with integrated RT directly (this is generally faster, because we do not need to calculate the behaviour of the surfaces for every angle of incidence)." + "text": "In this script, we will build on the TMM model from example 1(a) and look at the effects of interference.\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom solcore import material, si\nfrom solcore.solar_cell import Layer\nfrom solcore.absorption_calculator import calculate_rat, OptiStack\nimport seaborn as sns" }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#setting-up", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#setting-up", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#setting-up", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#setting-up", + "title": "Section 6a: Basic cell optics", "section": "Setting up", - "text": "Setting up\nWe load relevant packages and define materials, the same as in the previous example.\n\nfrom solcore import material, si\nfrom solcore.absorption_calculator import search_db, download_db\nimport os\nfrom solcore.structure import Layer\nfrom solcore.light_source import LightSource\nfrom rayflare.ray_tracing import rt_structure\nfrom rayflare.transfer_matrix_method import tmm_structure\nfrom rayflare.textures import planar_surface, regular_pyramids\nfrom rayflare.options import default_options\nfrom solcore.constants import q\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# download_db()\n\n\nMgF2_pageid = search_db(os.path.join(\"MgF2\", \"Rodriguez-de Marcos\"))[0][0];\nTa2O5_pageid = search_db(os.path.join(\"Ta2O5\", \"Rodriguez-de Marcos\"))[0][0];\nSU8_pageid = search_db(\"SU8\")[0][0];\nAg_pageid = search_db(os.path.join(\"Ag\", \"Jiang\"))[0][0];\n\nepoxy = material(\"BK7\")()\n\nMgF2 = material(str(MgF2_pageid), nk_db=True)();\nTa2O5 = material(str(Ta2O5_pageid), nk_db=True)();\nSU8 = material(str(SU8_pageid), nk_db=True)();\nAg = material(str(Ag_pageid), nk_db=True)();\n\nwindow = material(\"AlInP\")(Al=0.52)\nGaInP = material(\"GaInP\")\nAlGaAs = material(\"AlGaAs\")\n\nAir = material(\"Air\")()\n\nGaAs = material(\"GaAs\")\n\nSi = material(\"Si\")\n\nAl2O3 = material(\"Al2O3P\")()\nAl = material(\"Al\")()\n\nDatabase file found at /Users/phoebe/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n234 main MgF2 Rodriguez-de_Marcos main/MgF2/Rodriguez-de Marcos.yml 1 1 0.0299919 2.00146 960\nDatabase file found at /Users/phoebe/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n475 main Ta2O5 Rodriguez-de_Marcos main/Ta2O5/Rodriguez-de Marcos.yml 1 1 0.0294938 1.51429 212\nDatabase file found at /Users/phoebe/.solcore/nk/nk.db\n2 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2835 other negative_tone_photoresists Microchem_SU8_2000 other/resists/Microchem SU-8 2000.yml 1 0 0.32 0.8 200\n2836 other negative_tone_photoresists Microchem_SU8_3000 other/resists/Microchem SU-8 3000.yml 1 0 0.32 1.7 200\nDatabase file found at /Users/phoebe/.solcore/nk/nk.db\n1 results found.\npageid shelf book page filepath hasrefractive hasextinction rangeMin rangeMax points\n2 main Ag Jiang main/Ag/Jiang.yml 1 1 0.3 2.0 1701\n\n\nWe define the layers we will need, as before. We specify the thickness of the silicon (280 \\(\\mu\\)m) and epoxy (1 mm) at the top:\n\nd_Si = 280e-6 # thickness of Si wafer\nd_epoxy = 1e-3 # thickness of epoxy\n\nARC = [\n Layer(110e-9, MgF2),\n Layer(65e-9, Ta2O5),\n]\n\nGaInP_junction = [\n Layer(17e-9, window),\n Layer(400e-9, GaInP(In=0.50)),\n Layer(100e-9, AlGaAs(Al=0.8))]\n\n# 100 nm TJ\ntunnel_1 = [\n Layer(80e-9, AlGaAs(Al=0.8)),\n Layer(20e-9, GaInP(In=0.5)),\n]\n\nGaAs_junction = [\n Layer(17e-9, GaInP(In=0.5), role=\"window\"),\n Layer(1050e-9, GaAs()),\n Layer(70e-9, AlGaAs(Al=0.8), role=\"bsf\")]\n\nspacer_ARC = [\n Layer(80e-9, Ta2O5),\n]" + "text": "Setting up\nFirst, let’s define some materials:\n\nSi = material(\"Si\")\nSiN = material(\"Si3N4\")()\nAg = material(\"Ag\")()\n\nNote the second set of brackets (or lack thereof). The Solcore material system essentially operates in two stages; we first call the material function with the name of the material we want to use, for example Si = material(“Si”), which creates a general Python class corresponding to that material. We then call this class to specify further details, such as the temperature, doping level, or alloy composition (where relavant). This happens below when defining Si_n and Si_p; both are use the Si class defined above, and adding further details to the material. For the definitions of SiN and Ag above, we do both steps in a single line, hence the two sets of brackets.\n\nSi_n = Si(Nd=si(\"1e21cm-3\"), hole_diffusion_length=si(\"10um\"))\nSi_p = Si(Na=si(\"1e16cm-3\"), electron_diffusion_length=si(\"400um\"))\n\nTo look at the effect of interference in the Si layer at different thicknesses, we make a list of thicknesses to test (evenly spaced on a log scale from 400 nm to 300 um):\n\nSi_thicknesses = np.linspace(np.log(0.4e-6), np.log(300e-6), 8)\nSi_thicknesses = np.exp(Si_thicknesses)\n\nwavelengths = si(np.linspace(300, 1200, 400), \"nm\")\n\noptions = {\n \"recalculate_absorption\": True,\n \"optics_method\": \"TMM\",\n \"wavelength\": wavelengths\n }\n\nMake a color palette using the seaborn package to make the plots look nicer\n\ncolors = sns.color_palette('rocket', n_colors=len(Si_thicknesses))\ncolors.reverse()\n\ncreate an ARC layer:\n\nARC_layer = Layer(width=si('75nm'), material=SiN)" }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-cell-layers", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-cell-layers", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Defining the cell layers", - "text": "Defining the cell layers\nThere are three interfaces in the cell which will define the structure to simulate:\n\nthe III-V/epoxy interface, where the epoxy itself will be treated as a bulk layer in the simulation\nthe epoxy/Si interface, where the Si has a pyramidal texture (the Si itself is another bulk layer in the simulation).\nthe rear surface of the cell, where the Si again has a pyramidal texture (and we assume there is a silver back mirror behind the cell)\n\nThese 3 interfaces are defined here, using the pre-defined textures for a planar surface or regular pyramids:\n\nfront_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + spacer_ARC\n\nfront_surf = planar_surface(\n interface_layers = front_layers\n)\n\nSi_front = regular_pyramids(\n elevation_angle=50,\n upright=True\n)\n\nSi_back = regular_pyramids(\n elevation_angle=50,\n upright=False\n)\n\nfixed h 0.5958767962971049\nfixed h 0.5958767962971049\n\n\nNow we set relevant options for the solver. We set the number of rays to trace at each wavelength (more rays will make the result less noisy, but increase computation time) and whether to calculate the absorption profile in the bulk layers (no, in this case). The randomize_surface options determines whether the ray keeps track of its positions in the unit cell while travelling between surfaces; we set this to False to mimic random pyramids.\n\noptions = default_options()\n\nwl = np.arange(300, 1201, 10) * 1e-9\nAM15G = LightSource(source_type=\"standard\", version=\"AM1.5g\", x=wl,\n output_units=\"photon_flux_per_m\")\n\noptions.wavelengths = wl\noptions.project_name = \"III_V_Si_cell\"\n\n# options for ray-tracing\noptions.randomize_surface = True\noptions.n_rays = 1000\noptions.bulk_profile = False\noptions.theta_in = 45*np.pi/180" + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-si-thickness", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-si-thickness", + "title": "Section 6a: Basic cell optics", + "section": "Effect of Si thickness", + "text": "Effect of Si thickness\nNow we are going to loop through the different Si thicknesses generated above, and create a simple solar cell-like structure. Because we will only do an optical calculation, we don’t need to define a junction and can just make a simple stack of layers.\nWe then calculate reflection, absorption and transmission (RAT) for two different situations: 1. a fully coherent stack 2. assuming the silicon layer is incoherent. This means that light which enters the Si layer cannot interfere with itself, but light in the ARC layer can still show interference. In very thick layers (much thicker than the wavelength of light being considered) this is likely to be more physically accurate because real light does not have infinite coherence length; i.e. if you measured wavelength-dependent transmission or reflection of a Si wafer hundreds of microns thick you would not expect to see interference fringes.\nPLOT 1\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p) # silicon layer\n solar_cell = OptiStack([ARC_layer, base_layer]) # OptiStack (optical stack) to feed into calculate_rat function\n\n # Coherent calculation:\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False) # coherent calculation\n # For historical reasons, Solcore's default setting is to ignore reflection at the back of the cell (i.e. at the\n # interface between the final material in the stack and the substrate). Hence we need to tell the calculate_rat\n # function NOT to ignore this reflection (no_back_reflection=False).\n\n # Calculation assuming no interference in the silicon (\"incoherent\"):\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i']) # partially coherent: ARC is coherent, Si is not\n\n # Plot the results:\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1], label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(1) Absorption in Si with varying thickness\")\nplt.show()\n\n\n\n\nWe can see that the coherent calculations (solid lines) show clear interference fringes which depend on the Si thickness. The incoherent calculations do not have these fringes and seem to lie around the average of the interference fringes. For both sets of calculations, we see increasing absorption as the Si gets thicker, as expected." }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-structures", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#defining-the-structures", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Defining the structures", - "text": "Defining the structures\nFinally, we define the ray-tracing structure we will use, using the interfaces, bulk materials, and options set above. Because we want to calculate the reflection/absorption/transmission probabilities at the front surface using TMM, we set the use_TMM argument to True. We also define a completely planar cell with the same layer thicknesses etc. to compare and evaluate the effect of the textures Si surfaces.\n\nsolar_cell = rt_structure(\n textures=[front_surf, Si_front, Si_back],\n materials=[epoxy, Si()],\n widths=[d_epoxy, d_Si],\n incidence=Air,\n transmission=Ag,\n options=options,\n use_TMM=True,\n save_location=\"current\", # lookup table save location\n overwrite=True, # whether to overwrite any previously existing results, if found\n)\n\n# options for TMM\noptions.coherent = False\noptions.coherency_list = len(front_layers)*['c'] + ['i']*2\n\nsolar_cell_planar = tmm_structure(\n layer_stack = front_layers + [Layer(d_epoxy, epoxy), Layer(d_Si, Si())],\n incidence=Air,\n transmission=Ag,\n)\n\nPre-computing TMM lookup table(s)" + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-reflective-substrate", + "title": "Section 6a: Basic cell optics", + "section": "Effect of reflective substrate", + "text": "Effect of reflective substrate\nNow we repeat the calculation, but with an Ag substrate under the Si. Previously, we did not specify the substrate and so it was assumed by Solcore to be air (\\(n\\) = 1, \\(\\kappa\\) = 0).\nPLOT 2\n\nplt.figure()\n\nfor i1, Si_t in enumerate(Si_thicknesses):\n\n base_layer = Layer(width=Si_t, material=Si_p)\n\n # As before, but now we specify the substrate to be silver:\n solar_cell = OptiStack([ARC_layer, base_layer], substrate=Ag)\n\n RAT_c = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False)\n RAT_i = calculate_rat(solar_cell, wavelengths*1e9, no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n plt.plot(wavelengths*1e9, RAT_c[\"A\"], color=colors[i1],\n label=str(round(Si_t*1e6, 1)), alpha=0.7)\n plt.plot(wavelengths*1e9, RAT_i[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"Thickness ($\\mu$m)\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(2) Absorption in Si with varying thickness (Ag substrate)\")\nplt.show()\n\n\n\n\nWe see that the interference fringes get more prominent in the coherent calculation, due to higher reflection at the rear Si/Ag surface compared to Ag/Air. We also see a slightly boosted absorption at long wavelengths at all thicknesses, again due to improved reflection at the rear surface" }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#calculations", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#calculations", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Calculations", - "text": "Calculations\nCalculate the R/A/T for the planar reference cell:\n\ntmm_result = solar_cell_planar.calculate(options=options)\n\nGaInP_A_tmm = tmm_result['A_per_layer'][:,3]\nGaAs_A_tmm = tmm_result['A_per_layer'][:,8]\nSi_A_tmm = tmm_result['A_per_layer'][:,len(front_layers)+1]\n\nJmax_GaInP_tmm = q*np.trapz(GaInP_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs_tmm = q*np.trapz(GaAs_A_tmm*AM15G.spectrum()[1], x=wl)/10\nJmax_Si_tmm = q*np.trapz(Si_A_tmm*AM15G.spectrum()[1], x=wl)/10\n\nCalculate the R/A/T for the textured cell:\n\nrt_result = solar_cell.calculate(options=options)\n\nGaInP_absorption_ARC = rt_result['A_per_interface'][0][:,3]\nGaAs_absorption_ARC = rt_result['A_per_interface'][0][:,8]\nSi_absorption_ARC = rt_result['A_per_layer'][:,1]\n\nJmax_GaInP = q*np.trapz(GaInP_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_GaAs = q*np.trapz(GaAs_absorption_ARC*AM15G.spectrum()[1], x=wl)/10\nJmax_Si = q*np.trapz(Si_absorption_ARC*AM15G.spectrum()[1], x=wl)/10" + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#effect-of-polarization-and-angle-of-incidence", + "title": "Section 6a: Basic cell optics", + "section": "Effect of polarization and angle of incidence", + "text": "Effect of polarization and angle of incidence\nFinally, we look at the effect of incidence angle and polarization of the light hitting the cell.\nPLOT 3\n\nangles = [0, 30, 60, 70, 80, 89] # angles in degrees\n\nARC_layer = Layer(width=si('75nm'), material=SiN)\nbase_layer = Layer(width=si(\"100um\"), material=Si_p)\n\ncolors = sns.cubehelix_palette(n_colors=len(angles))\n\nplt.figure()\n\nfor i1, theta in enumerate(angles):\n\n solar_cell = OptiStack([ARC_layer, base_layer])\n\n RAT_s = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='s',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n RAT_p = calculate_rat(solar_cell, wavelengths*1e9, angle=theta,\n pol='p',\n no_back_reflection=False,\n coherent=False, coherency_list=['c', 'i'])\n\n plt.plot(wavelengths*1e9, RAT_s[\"A\"], color=colors[i1], label=str(round(theta)))\n plt.plot(wavelengths*1e9, RAT_p[\"A\"], '--', color=colors[i1])\n\nplt.legend(title=r\"$\\theta (^\\circ)$\")\nplt.xlim(300, 1300)\nplt.ylim(0, 1.02)\nplt.ylabel(\"Absorption\")\nplt.title(\"(3) Absorption in Si with varying angle of incidence\")\nplt.show()\n\n\n\n\nFor normal incidence (\\(\\theta = 0^\\circ\\)), s (solid lines) and p (dashed lines) polarization are equivalent. As the incidence angle increases, in general absorption is higher for p-polarized light (due to lower reflection). Usually, sunlight is modelled as unpolarized light, which computationally is usually done by averaging the results for s and p-polarized light." }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#plotting-the-results", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#plotting-the-results", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Plotting the results", - "text": "Plotting the results\nFinally, we plot the results; the solid lines show the results for the textured Si cell (calculated using ray-tracing), the dashed lines for the planar cell (calculated using TMM). The maximum possible currents are shown in the plot, with the value in brackets for Si being for the planar cell.\n\nplt.figure(figsize=(6,3))\nplt.plot(wl * 1e9, GaInP_absorption_ARC, \"-k\", label=\"GaInP\")\nplt.plot(wl * 1e9, GaAs_absorption_ARC, \"-b\", label=\"GaAs\")\nplt.plot(wl * 1e9, Si_absorption_ARC, \"-r\", label=\"Si\")\nplt.plot(wl * 1e9, GaInP_A_tmm, \"--k\")\nplt.plot(wl * 1e9, GaAs_A_tmm, \"--b\")\nplt.plot(wl * 1e9, Si_A_tmm, \"--r\")\nplt.plot(wl * 1e9, rt_result['R'], '-', color='grey', label=\"Reflected\")\nplt.plot(wl * 1e9, tmm_result['R'], '--', color='grey')\n\nplt.text(420, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaInP))\nplt.text(670, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_GaAs))\nplt.text(870, 0.55, r\"{:.1f} mA/cm$^2$\".format(Jmax_Si))\nplt.text(870, 0.45, r\"({:.1f} mA/cm$^2)$\".format(Jmax_Si_tmm))\n\nplt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\nplt.tight_layout()\nplt.show()" + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#conclusions", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#conclusions", + "title": "Section 6a: Basic cell optics", + "section": "Conclusions", + "text": "Conclusions\nWe have now seen some effects of interference in layers of different thicknesses, and seen the effect of adding a highly reflective substrate. So we already have two strategies for light-trapping/improving the absorption in a solar cell: adding an anti-reflection coating (in example 1a), to reduce front-surface reflection and get more light into the cell, and adding a highly reflective layer at the back, to reduce loss through the back of the cell and keep light trapped in the cell." }, { - "objectID": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#questionschallenges", - "href": "solcore-workshop/notebooks/9b-GaInP_GaAs_Si_pyramids_new.html#questionschallenges", - "title": "Section 9b: Planar III-V epoxy-bonded to textured Si", - "section": "Questions/challenges", - "text": "Questions/challenges\n\nDoes it make sense to do a ray-tracing calculation for short wavelengths? For this structure, can you speed up the calculation and avoid the random noise at short wavelengths?\nHow much current is lost to parasitic absorption in e.g. tunnel junctions, window layers etc.?\nHow can we reduce reflection at the epoxy interfaces?\nIf the epoxy/glass layer is much thicker than the relevant incident wavelengths, and not absorbing, does the exact thickness matter in the simulation?\nWhat happens if only the rear surface is textured? Would a structure without the front texture have other advantages?\nWhy does the Si have lower absorption/limiting current in this structure compared to the previous example?" + "objectID": "solcore-workshop/notebooks/6a-TMM_introduction.html#questions", + "href": "solcore-workshop/notebooks/6a-TMM_introduction.html#questions", + "title": "Section 6a: Basic cell optics", + "section": "Questions", + "text": "Questions\n\nWhy are the interference fringes stronger when adding a silver back mirror, compared to having air behind the Si?\nWe modelled s and p-polarized light - how do we normally model unpolarized light?" }, { "objectID": "solcore-workshop/notebooks/2-Efficiency_limits.html", diff --git a/docs/solcore-workshop-2/notebooks/10-perovskite_Si_rt.html b/docs/solcore-workshop-2/notebooks/10-perovskite_Si_rt.html index 6cef005..408b9ed 100644 --- a/docs/solcore-workshop-2/notebooks/10-perovskite_Si_rt.html +++ b/docs/solcore-workshop-2/notebooks/10-perovskite_Si_rt.html @@ -147,7 +147,11 @@

On this page

@@ -173,7 +177,7 @@

Section 10: Perovskite-Si tandem cell with pyramidal surfaces<

This example shows how you can simulate a perovskite-Si tandem cell with pyramidal surface textures, where the perovskite and other surface layers are assumed to be deposited conformally (i.e., also in a pyramid shape) on top of the Si. The perovskite optical constants are from this paper, while the structure is based on this paper We will calculate total reflection, transmission and absorption per layer as well as the wavelength-dependent absorption profiles in the perovskite and Si, which can be used in e.g. device simulations. We will look at the effect of treating the layers deposited on Si (including the perovskite) coherently or incoherently.

First, import relevant packages and RayFlare functions:

-
+
import numpy as np
 import os
 
@@ -190,244 +194,392 @@ 
Section 10: Perovskite-Si tandem cell with pyramidal surfaces<
 import seaborn as sns
 
 from cycler import cycler
+
+
WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+

Now we set some relevant options. We will scan across 20 x 20 surface points of the pyramid unit cell between 300 and 1200 nm, for unpolarized, normally-incident light. The randomize_surface option is set to True to prevent correlation between the incident position on the front and rear pyramids. The n_jobs option is set to -1, which means that all available cores will be used. If you want to use all but one core, change this to -2 etc. We also need to provide a project_name to save the lookup tables which will be calculated using TMM to use during ray-tracing.

-
-
wavelengths = np.linspace(300, 1200, 40) * 1e-9
-
-AM15G = LightSource(source_type="standard", version="AM1.5g", x=wavelengths,
-                    output_units="photon_flux_per_m")
-
-options = default_options()
-options.wavelength = wavelengths
-options.nx = 20
-options.ny = options.nx
-options.n_rays = 4 * options.nx**2
-options.depth_spacing = 1e-9
-options.pol = "u"
-options.I_thresh = 1e-3
-options.project_name = "perovskite_Si_rt"
-options.randomize_surface = True
-options.n_jobs = -1 # use all cores; to use all but one, change to -2 etc.
+
+
wavelengths = np.linspace(300, 1200, 40) * 1e-9
+
+AM15G = LightSource(source_type="standard", version="AM1.5g", x=wavelengths,
+                    output_units="photon_flux_per_m")
+
+options = default_options()
+options.wavelength = wavelengths
+options.nx = 20
+options.ny = options.nx
+options.n_rays = 4 * options.nx**2
+options.depth_spacing = 1e-9
+options.pol = "u"
+options.I_thresh = 1e-3
+options.project_name = "perovskite_Si_rt"
+options.randomize_surface = True
+options.n_jobs = -1 # use all cores; to use all but one, change to -2 etc.
+
+

Adding custom materials

We define our materials. Note that some of these are custom materials added to the database; we only need to do this once. We then define the front layer stack (i.e. all the materials which are on top of the Si, excluding Si itself, which will be the ‘bulk’ material) and the rear layer stack. Layer stacks are always defined starting with the layer closest to the top of the cell.

-
-
# Can comment out this block after running once to add materials to the database
-from solcore.material_system import create_new_material
-
-create_new_material("Perovskite_CsBr_1p6eV", "data/CsBr10p_1to2_n_shifted.txt",
-                    "data/CsBr10p_1to2_k_shifted.txt")
-create_new_material("ITO_lowdoping", "data/model_back_ito_n.txt",
-                    "data/model_back_ito_k.txt")
-create_new_material("aSi_i", "data/model_i_a_silicon_n.txt",
-                    "data/model_i_a_silicon_k.txt")
-create_new_material("aSi_p", "data/model_p_a_silicon_n.txt",
-                    "data/model_p_a_silicon_k.txt")
-create_new_material("aSi_n", "data/model_n_a_silicon_n.txt",
-                    "data/model_n_a_silicon_k.txt")
-create_new_material("C60", "data/C60_Ren_n.txt",
-                    "data/C60_Ren_k.txt")
-create_new_material("IZO", "data/IZO_Ballif_rO2_10pcnt_n.txt",
-                    "data/IZO_Ballif_rO2_10pcnt_k.txt")
-# Comment out until here
-
-
-
# download_db()
+
+
# Can comment out this block after running once to add materials to the database
+from solcore.material_system import create_new_material
+
+create_new_material("Perovskite_CsBr_1p6eV", "data/CsBr10p_1to2_n_shifted.txt",
+                    "data/CsBr10p_1to2_k_shifted.txt")
+create_new_material("ITO_lowdoping", "data/model_back_ito_n.txt",
+                    "data/model_back_ito_k.txt")
+create_new_material("aSi_i", "data/model_i_a_silicon_n.txt",
+                    "data/model_i_a_silicon_k.txt")
+create_new_material("aSi_p", "data/model_p_a_silicon_n.txt",
+                    "data/model_p_a_silicon_k.txt")
+create_new_material("aSi_n", "data/model_n_a_silicon_n.txt",
+                    "data/model_n_a_silicon_k.txt")
+create_new_material("C60", "data/C60_Ren_n.txt",
+                    "data/C60_Ren_k.txt")
+create_new_material("IZO", "data/IZO_Ballif_rO2_10pcnt_n.txt",
+                    "data/IZO_Ballif_rO2_10pcnt_k.txt")
+# Comment out until here
-
-
MgF2_pageid = search_db(os.path.join("MgF2", "Rodriguez-de Marcos"))[0][0];
-Ag_pageid = search_db(os.path.join("Ag", "Jiang"))[0][0];
-
-Si = material("Si")()
-Air = material("Air")()
-MgF2 = material(str(MgF2_pageid), nk_db=True)()
-ITO_back = material("ITO_lowdoping")()
-Perovskite = material("Perovskite_CsBr_1p6eV")()
-Ag = material(str(Ag_pageid), nk_db=True)()
-aSi_i = material("aSi_i")()
-aSi_p = material("aSi_p")()
-aSi_n = material("aSi_n")()
-LiF = material("LiF")()
-IZO = material("IZO")()
-C60 = material("C60")()
-
-# stack based on doi:10.1038/s41563-018-0115-4
-front_materials = [
-    Layer(100e-9, MgF2),
-    Layer(110e-9, IZO),
-    Layer(15e-9, C60),
-    Layer(1e-9, LiF),
-    Layer(440e-9, Perovskite),
-    Layer(6.5e-9, aSi_n),
-    Layer(6.5e-9, aSi_i),
-]
-
-back_materials = [Layer(6.5e-9, aSi_i), Layer(6.5e-9, aSi_p), Layer(240e-9, ITO_back)]
+
+
# download_db()
-

Now we define our front and back surfaces, including interface_layers. We will use regular pyramids for both the front and back surface; these pyramids point out on both sides, but since the direction of the pyramids is defined relative to the front surface, we must set upright=True for the top surface and upright=False for the rear surface. We also gives the surfaces a name (used to save the lookup table data) and ask RayFlare to calculate the absorption profile in the 5th layer, which is the perovskite.

-
-
triangle_surf = regular_pyramids(
-    elevation_angle=55,
-    upright=True,
-    size=1,
-    interface_layers=front_materials,
-    name="coh_front",
-    prof_layers=[5],
-)
-
-triangle_surf_back = regular_pyramids(
-    elevation_angle=55,
-    upright=False,
-    size=1,
-    interface_layers=back_materials,
-    name="Si_back",
-    coherency_list=["i"] * len(back_materials),
-)
+
+
MgF2_pageid = search_db(os.path.join("MgF2", "Rodriguez-de Marcos"))[0][0];
+Ag_pageid = search_db(os.path.join("Ag", "Jiang"))[0][0];
+
+Si = material("Si")()
+Air = material("Air")()
+MgF2 = material(str(MgF2_pageid), nk_db=True)()
+ITO_back = material("ITO_lowdoping")()
+Perovskite = material("Perovskite_CsBr_1p6eV")()
+Ag = material(str(Ag_pageid), nk_db=True)()
+aSi_i = material("aSi_i")()
+aSi_p = material("aSi_p")()
+aSi_n = material("aSi_n")()
+LiF = material("LiF")()
+IZO = material("IZO")()
+C60 = material("C60")()
+
+# stack based on doi:10.1038/s41563-018-0115-4
+front_materials = [
+    Layer(100e-9, MgF2),
+    Layer(110e-9, IZO),
+    Layer(15e-9, C60),
+    Layer(1e-9, LiF),
+    Layer(440e-9, Perovskite),
+    Layer(6.5e-9, aSi_n),
+    Layer(6.5e-9, aSi_i),
+]
+
+back_materials = [Layer(6.5e-9, aSi_i), Layer(6.5e-9, aSi_p), Layer(240e-9, ITO_back)]
+
+
Database file found at /Users/z3533914/.solcore/nk/nk.db
+1 results found.
+pageid  shelf   book    page    filepath    hasrefractive   hasextinction   rangeMin    rangeMax    points
+234 main    MgF2    Rodriguez-de_Marcos main/MgF2/Rodriguez-de Marcos.yml   1   1   0.0299919   2.00146 960
+Database file found at /Users/z3533914/.solcore/nk/nk.db
+1 results found.
+pageid  shelf   book    page    filepath    hasrefractive   hasextinction   rangeMin    rangeMax    points
+2   main    Ag  Jiang   main/Ag/Jiang.yml   1   1   0.3 2.0 1701
-

Now we make our ray-tracing structure by combining the front and back surfaces, specifying the material in between (Si) and setting its width to 260 microns. In order to use the TMM lookuptables to calculate reflection/transmission/absorption probabilities we must also set use_TMM=True.

-
-
rtstr_coh = rt_structure(
-    textures=[triangle_surf, triangle_surf_back],
-    materials=[Si],
-    widths=[260e-6],
-    incidence=Air,
-    transmission=Ag,
-    use_TMM=True,
-    options=options,
-    overwrite=True,
-    save_location="current",
-)
-
-# calculate:
-result_coh = rtstr_coh.calculate(options)
-

Now we define the same front surface and structure again, except now we will treat all the layers incoherently (i.e. no thin-film interference) in the TMM.

-
+
+
+

Defining the interfaces and structure

+

Now we define our front and back surfaces, including interface_layers. We will use regular pyramids for both the front and back surface; these pyramids point out on both sides, but since the direction of the pyramids is defined relative to the front surface, we must set upright=True for the top surface and upright=False for the rear surface. We also gives the surfaces a name (used to save the lookup table data) and ask RayFlare to calculate the absorption profile in the 5th layer, which is the perovskite.

+
triangle_surf = regular_pyramids(
     elevation_angle=55,
     upright=True,
     size=1,
     interface_layers=front_materials,
-    coherency_list=["i"] * len(front_materials),
-    name="inc_front",
-    prof_layers=[5],
-)
-
-rtstr_inc = rt_structure(
-    textures=[triangle_surf, triangle_surf_back],
-    materials=[Si],
-    widths=[260e-6],
-    incidence=Air,
-    transmission=Ag,
-    use_TMM=True,
-    options=options,
-    overwrite=True,
-    save_location="current",
-)
-
-result_inc = rtstr_inc.calculate(options)
+ name="coh_front", + prof_layers=[5], +) + +triangle_surf_back = regular_pyramids( + elevation_angle=55, + upright=False, + size=1, + interface_layers=back_materials, + name="Si_back", + coherency_list=["i"] * len(back_materials), +)
+
+

Now we make our ray-tracing structure by combining the front and back surfaces, specifying the material in between (Si) and setting its width to 260 microns. In order to use the TMM lookuptables to calculate reflection/transmission/absorption probabilities we must also set use_TMM=True.

+
+
%%capture
+
+rtstr_coh = rt_structure(
+    textures=[triangle_surf, triangle_surf_back],
+    materials=[Si],
+    widths=[260e-6],
+    incidence=Air,
+    transmission=Ag,
+    use_TMM=True,
+    options=options,
+    overwrite=True,
+    save_location="current",
+)
+
+# calculate:
+result_coh = rtstr_coh.calculate(options)
+
+
INFO: Pre-computing TMM lookup table(s)
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+
+
+
Database file found at /Users/z3533914/.solcore/nk/nk.db
+Material main/MgF2/Rodriguez-de Marcos.yml loaded.
+Database file found at /Users/z3533914/.solcore/nk/nk.db
+Material main/MgF2/Rodriguez-de Marcos.yml loaded.
+Database file found at /Users/z3533914/.solcore/nk/nk.db
+Material main/Ag/Jiang.yml loaded.
+Database file found at /Users/z3533914/.solcore/nk/nk.db
+Material main/Ag/Jiang.yml loaded.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+
+
+ +
+

Incoherent calculation

+

Now we define the same front surface and structure again, except now we will treat all the layers incoherently (i.e. no thin-film interference) in the TMM.

+
+
%%capture
+
+triangle_surf = regular_pyramids(
+    elevation_angle=55,
+    upright=True,
+    size=1,
+    interface_layers=front_materials,
+    coherency_list=["i"] * len(front_materials),
+    name="inc_front",
+    prof_layers=[5],
+)
+
+rtstr_inc = rt_structure(
+    textures=[triangle_surf, triangle_surf_back],
+    materials=[Si],
+    widths=[260e-6],
+    incidence=Air,
+    transmission=Ag,
+    use_TMM=True,
+    options=options,
+    overwrite=True,
+    save_location="current",
+)
+
+result_inc = rtstr_inc.calculate(options)
+
+
INFO: Pre-computing TMM lookup table(s)
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+INFO: Calculating next wavelength...
+

Now we plot the results for reflection, transmission, and absorption per layer for both the coherent and incoherent cases.

-
-
pal = sns.color_palette("husl", n_colors=len(front_materials) + len(back_materials) + 2)
-# create a colour palette
-
-cols = cycler("color", pal)
-# set this as the default colour palette in matplotlib
-
-params = {
-    "axes.prop_cycle": cols,
-}
-
-plt.rcParams.update(params)
-
-fig = plt.figure(figsize=(8, 3.7))
-plt.subplot(1, 1, 1)
-plt.plot(wavelengths * 1e9, result_coh["R"], "-ko", label="R")
-plt.plot(wavelengths * 1e9, result_coh["T"], mfc="none", label="T")
-plt.plot(wavelengths * 1e9, result_coh["A_per_layer"][:, 0], "-o", label='Si')
-plt.plot(wavelengths * 1e9, result_coh["A_per_interface"][0], "-o",
-         label=[None, "IZO", "C60", None, "Perovskite", None, None])
-plt.plot(wavelengths * 1e9, result_coh["A_per_interface"][1], "-o",
-         label=[None, None, "ITO"])
-
-plt.plot(wavelengths * 1e9, result_inc["R"], "--ko", mfc="none")
-plt.plot(wavelengths * 1e9, result_inc["T"], mfc="none")
-plt.plot(wavelengths * 1e9, result_inc["A_per_layer"][:, 0], "--o", mfc="none")
-plt.plot(wavelengths * 1e9, result_inc["A_per_interface"][0], "--o", mfc="none")
-plt.plot(wavelengths * 1e9, result_inc["A_per_interface"][1], "--o", mfc="none")
-
-plt.plot([300, 301], [0, 0], "-k", label="coherent")
-plt.plot([300, 301], [0, 0], "--k", label="incoherent")
-plt.xlabel("Wavelength (nm)")
-plt.ylabel("R / A / T")
-plt.ylim(0, 1)
-plt.xlim(300, 1200)
-plt.legend(bbox_to_anchor=(1.05, 1))
-plt.tight_layout()
-plt.show()
+
+
pal = sns.color_palette("husl", n_colors=len(front_materials) + len(back_materials) + 2)
+# create a colour palette
+
+cols = cycler("color", pal)
+# set this as the default colour palette in matplotlib
+
+params = {
+    "axes.prop_cycle": cols,
+}
+
+plt.rcParams.update(params)
+
+fig = plt.figure(figsize=(8, 3.7))
+plt.subplot(1, 1, 1)
+plt.plot(wavelengths * 1e9, result_coh["R"], "-ko", label="R")
+plt.plot(wavelengths * 1e9, result_coh["T"], mfc="none", label="T")
+plt.plot(wavelengths * 1e9, result_coh["A_per_layer"][:, 0], "-o", label='Si')
+plt.plot(wavelengths * 1e9, result_coh["A_per_interface"][0], "-o",
+         label=[None, "IZO", "C60", None, "Perovskite", None, None])
+plt.plot(wavelengths * 1e9, result_coh["A_per_interface"][1], "-o",
+         label=[None, None, "ITO"])
+
+plt.plot(wavelengths * 1e9, result_inc["R"], "--ko", mfc="none")
+plt.plot(wavelengths * 1e9, result_inc["T"], mfc="none")
+plt.plot(wavelengths * 1e9, result_inc["A_per_layer"][:, 0], "--o", mfc="none")
+plt.plot(wavelengths * 1e9, result_inc["A_per_interface"][0], "--o", mfc="none")
+plt.plot(wavelengths * 1e9, result_inc["A_per_interface"][1], "--o", mfc="none")
+
+plt.plot([300, 301], [0, 0], "-k", label="coherent")
+plt.plot([300, 301], [0, 0], "--k", label="incoherent")
+plt.xlabel("Wavelength (nm)")
+plt.ylabel("R / A / T")
+plt.ylim(0, 1)
+plt.xlim(300, 1200)
+plt.legend(bbox_to_anchor=(1.05, 1))
+plt.tight_layout()
+plt.show()
+
+

+

Calculate and print the limiting short-circuit current per junction:

-
-
Jmax_Pero_coh = q*np.trapz(result_coh["A_per_interface"][0][:,4]*AM15G.spectrum()[1],
-                                                        x=wavelengths)/10
-Jmax_Si_coh = q*np.trapz(result_coh["A_per_layer"][:, 0]*AM15G.spectrum()[1],
-                     x=wavelengths)/10
-
-print("Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:"
-      ".2f}".format(Jmax_Pero_coh, Jmax_Si_coh))
-
-Jmax_Pero_inc = q*np.trapz(result_inc["A_per_interface"][0][:,4]*AM15G.spectrum()[1],
-                                                        x=wavelengths)/10
-Jmax_Si_inc = q*np.trapz(result_inc["A_per_layer"][:, 0]*AM15G.spectrum()[1],
-                     x=wavelengths)/10
-
-print("Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:"
-      ".2f}".format(Jmax_Pero_inc, Jmax_Si_inc))
+
+
Jmax_Pero_coh = q*np.trapz(result_coh["A_per_interface"][0][:,4]*AM15G.spectrum()[1],
+                                                        x=wavelengths)/10
+Jmax_Si_coh = q*np.trapz(result_coh["A_per_layer"][:, 0]*AM15G.spectrum()[1],
+                     x=wavelengths)/10
+
+print("Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:"
+      ".2f}".format(Jmax_Pero_coh, Jmax_Si_coh))
+
+Jmax_Pero_inc = q*np.trapz(result_inc["A_per_interface"][0][:,4]*AM15G.spectrum()[1],
+                                                        x=wavelengths)/10
+Jmax_Si_inc = q*np.trapz(result_inc["A_per_layer"][:, 0]*AM15G.spectrum()[1],
+                     x=wavelengths)/10
+
+print("Limiting short-circuit currents in coherent calculation (mA/cm2): {:.2f} / {:"
+      ".2f}".format(Jmax_Pero_inc, Jmax_Si_inc))
+
+
Limiting short-circuit currents in coherent calculation (mA/cm2): 19.27 / 21.47
+Limiting short-circuit currents in coherent calculation (mA/cm2): 18.67 / 20.98
+
+
+
+

Absorption profiles

We can also plot the absorption profiles, for wavelengths up to 800 nm, in the perovskite (since we asked the solver to calculate the profile in the perovskite layer above).

-
-
wl_Eg = wavelengths < 800e-9
-
-pal = sns.cubehelix_palette(sum(wl_Eg), reverse=True)
-cols = cycler("color", pal)
-params = {
-    "axes.prop_cycle": cols,
-}
-plt.rcParams.update(params)
-
-pos = np.arange(0, rtstr_coh.interface_layer_widths[0][4], options.depth_spacing*1e9)
-
-fig, (ax1, ax2) = plt.subplots(1,2)
-ax1.plot(pos, result_coh["interface_profiles"][0][wl_Eg].T)
-ax1.set_ylim(0, 0.02)
-ax1.set_xlabel("z (nm)")
-ax1.set_ylabel("a(z)")
-ax1.set_title("Coherent")
-ax2.plot(pos, result_inc["interface_profiles"][0][wl_Eg].T)
-ax2.set_ylim(0, 0.02)
-ax2.yaxis.set_ticklabels([])
-ax2.set_xlabel("z (nm)")
-ax2.set_title("Incoherent")
-plt.show()
+
+
wl_Eg = wavelengths < 800e-9
+
+pal = sns.cubehelix_palette(sum(wl_Eg), reverse=True)
+cols = cycler("color", pal)
+params = {
+    "axes.prop_cycle": cols,
+}
+plt.rcParams.update(params)
+
+pos = np.arange(0, rtstr_coh.interface_layer_widths[0][4], options.depth_spacing*1e9)
+
+fig, (ax1, ax2) = plt.subplots(1,2)
+ax1.plot(pos, result_coh["interface_profiles"][0][wl_Eg].T)
+ax1.set_ylim(0, 0.02)
+ax1.set_xlabel("z (nm)")
+ax1.set_ylabel("a(z)")
+ax1.set_title("Coherent")
+ax2.plot(pos, result_inc["interface_profiles"][0][wl_Eg].T)
+ax2.set_ylim(0, 0.02)
+ax2.yaxis.set_ticklabels([])
+ax2.set_xlabel("z (nm)")
+ax2.set_title("Incoherent")
+plt.show()
+
+

+

We see that, as expected, the coherent case shows interference fringes while the incoherent case does not. We can also plot the absorption profile in the Si (> 800 nm):

-
-
pos_bulk = pos = np.arange(0, rtstr_coh.widths[0]*1e6, options.depth_spacing_bulk*1e6)
-
-fig, (ax1, ax2) = plt.subplots(1,2)
-ax1.semilogy(pos, result_coh["profile"][~wl_Eg].T)
-ax1.set_ylim(1e-8, 0.00015)
-ax1.set_xlabel("z (um)")
-ax1.set_ylabel("a(z)")
-ax1.set_title("Coherent")
-ax2.semilogy(pos, result_inc["profile"][~wl_Eg].T)
-ax2.set_ylim(1e-8, 0.00015)
-ax2.yaxis.set_ticklabels([])
-ax2.set_xlabel("z (um)")
-ax2.set_title("Incoherent")
-plt.show()
+
+
pos_bulk = pos = np.arange(0, rtstr_coh.widths[0]*1e6, options.depth_spacing_bulk*1e6)
+
+fig, (ax1, ax2) = plt.subplots(1,2)
+ax1.semilogy(pos, result_coh["profile"][~wl_Eg].T)
+ax1.set_ylim(1e-8, 0.00015)
+ax1.set_xlabel("z (um)")
+ax1.set_ylabel("a(z)")
+ax1.set_title("Coherent")
+ax2.semilogy(pos, result_inc["profile"][~wl_Eg].T)
+ax2.set_ylim(1e-8, 0.00015)
+ax2.yaxis.set_ticklabels([])
+ax2.set_xlabel("z (um)")
+ax2.set_title("Incoherent")
+plt.show()
+
+

+
+

Questions

@@ -335,226 +377,283 @@

The

To do this, a model is required for the recombination processes between the conduction and valance bands. The most fundamental (and inescapable) recombination mechanism is the radiative process. In section 3 we will derive a limit to Shockley’s diode equation \(J=J_0 e^{\frac{V}{kT}}\) for the radiative limit, that being a diode where all current flows are linked to an optical process, either absorption or recombination.

In the radiative limit and an abrupt band-edge at band-gap energy \(E_g\) it can be shown that \(J_0\) is approximated by \(J_0=q \frac{2 \pi}{c^2 h^3} kT \left(E_g^2+2 E_g k T+2 k^2 T^2\right) e^{\frac{-E_g}{k T}}\)

We can now plot a chart of \(J_0\) as a function of band-gap energy using this expression:

-
-
# Define some physical constants:
-q = 1.60217662E-19  # electronic charge [C]
-k = 1.38064852E-23/q   # Boltzmann constant [eV/K]
-h = 6.62607004E-34/q  # Planck constant expressed in [eV.s]
-c = 299792458  # Speed of light [m.s^-1]
-
-t = 300  # Perform the calculation for a solar cell at 300K.
-
-# Define a function to return J0 implementing the expression above
-def getJ0(eg):
-    return k*t*q*(2*np.pi/(c**2*h**3))*(eg**2+2*eg*k*t+2*k**2*t**2)*np.exp(-eg/(k*t))
-
-eg = np.linspace(0.5,2.5,100)
-j0 = np.vectorize(getJ0)(eg)
-
-plt.figure()
-plt.title('The radiative limit to $J_0$ plotted as a function of band-gap energy Eg')
-plt.plot(eg,j0,label='J0')  # Divide by 10 to convert from A.m^-2 to mA.cm^-2
-plt.xlim(0.2, 2.5)
-plt.xlabel('Band Gap energy (eV)')
-plt.ylabel('$J_{0}$ ($A.m^{-2}$)')
-plt.yscale("log")
-plt.legend()
+
+
# Define some physical constants:
+q = 1.60217662E-19  # electronic charge [C]
+k = 1.38064852E-23/q   # Boltzmann constant [eV/K]
+h = 6.62607004E-34/q  # Planck constant expressed in [eV.s]
+c = 299792458  # Speed of light [m.s^-1]
+
+t = 300  # Perform the calculation for a solar cell at 300K.
+
+# Define a function to return J0 implementing the expression above
+def getJ0(eg):
+    return k*t*q*(2*np.pi/(c**2*h**3))*(eg**2+2*eg*k*t+2*k**2*t**2)*np.exp(-eg/(k*t))
+
+eg = np.linspace(0.5,2.5,100)
+j0 = np.vectorize(getJ0)(eg)
+
+plt.figure()
+plt.title('The radiative limit to $J_0$ plotted as a function of band-gap energy Eg')
+plt.plot(eg,j0,label='J0')  # Divide by 10 to convert from A.m^-2 to mA.cm^-2
+plt.xlim(0.2, 2.5)
+plt.xlabel('Band Gap energy (eV)')
+plt.ylabel('$J_{0}$ ($A.m^{-2}$)')
+plt.yscale("log")
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x177f1ccd0>
+
+
+

+

Let’s obtain J0 for GaAs and InGaP, two common III-V materials that are used in tandem solar cells: evaluate getJ0() for Eg=1.42 and Eg=1.88

-
-
getJ0(1.42)
+
+
getJ0(1.42)
+
+
1.195457897843886e-17
+
+
+
+
getJ0(1.88)
+
+
3.888154629395649e-25
-
-
getJ0(1.88)

Calculating the IV curve

We are now able to calculate the limiting efficiency for a solar cell using the simple Shockley diode expression \(J(V)=J_{s c}-J_0\left(e^{\frac{q V}{k T}}-1\right)\). Let’s plot the IV curve for a band-gap of 1.42eV

-
-
def getJ(v,eg):
-    return getJsc(eg) - getJ0(eg)*(np.exp(v/(k*t)) - 1)
-
-eg = 1.42
-v = np.linspace(0,1.2,100)
-j = np.vectorize(getJ)(v,eg)
-
-plt.figure(3)
-plt.title('Limiting Efficiency IV curve for Eg=1.42eV (GaAs)')
-plt.plot(v,j/10)  #convert to mA.cm^-2
-plt.xlim(0.2, 1.2)
-plt.ylim(0,35)
-plt.xlabel('Voltage (V)')
-plt.ylabel('Current ($mA.cm^{-2}$)')
+
+
def getJ(v,eg):
+    return getJsc(eg) - getJ0(eg)*(np.exp(v/(k*t)) - 1)
+
+eg = 1.42
+v = np.linspace(0,1.2,100)
+j = np.vectorize(getJ)(v,eg)
+
+plt.figure(3)
+plt.title('Limiting Efficiency IV curve for Eg=1.42eV (GaAs)')
+plt.plot(v,j/10)  #convert to mA.cm^-2
+plt.xlim(0.2, 1.2)
+plt.ylim(0,35)
+plt.xlabel('Voltage (V)')
+plt.ylabel('Current ($mA.cm^{-2}$)')
+
+
Text(0, 0.5, 'Current ($mA.cm^{-2}$)')
+
+
+

+

Calculating the electrical power curve and finding the maximum power

-
-
plt.figure()
-plt.title('Limiting Efficiency power curve for $E_g$ = 1.42 eV (GaAs)')
-plt.plot(v,v*j)
-plt.xlim(0.2, 1.2)
-plt.ylim(0,350)
-plt.xlabel('Voltage (V)')
-plt.ylabel('Power ($W.m^{-2}$)')
+
+
plt.figure()
+plt.title('Limiting Efficiency power curve for $E_g$ = 1.42 eV (GaAs)')
+plt.plot(v,v*j)
+plt.xlim(0.2, 1.2)
+plt.ylim(0,350)
+plt.xlabel('Voltage (V)')
+plt.ylabel('Power ($W.m^{-2}$)')
+
+
Text(0, 0.5, 'Power ($W.m^{-2}$)')
+
+
+

+

Define a function to find the maximum power point of the curve above:

-
-
def getPmax(eg):
-    v = np.linspace(0,eg-0.1,500)
-    p = v*np.vectorize(getJ)(v,eg)
-    return (np.amax(p))  # The amax command returns the maximum value in the array p
+
+
def getPmax(eg):
+    v = np.linspace(0,eg-0.1,500)
+    p = v*np.vectorize(getJ)(v,eg)
+    return (np.amax(p))  # The amax command returns the maximum value in the array p

Test it out on the curve above

-
-
getPmax(1.42)
+
+
getPmax(1.42)
+
+
331.6412760959975
+

Plotting the Shockley-Queisser efficiency limit graph:

Finally we can calculate the Shockley-Queisser efficiency limit for AM1.5G

-
-
eg = np.linspace(0.5,2.5,100)
-p = np.vectorize(getPmax)(eg)
-
-plt.figure(3)
-plt.title('Limiting Shockley-Queisser Efficiency Curve')
-plt.plot(eg, p/b, label='AM1.5G')  # Remember b is the integrated power of the
-# incident sunlight
-plt.xlim(0.2, 2.5)
-plt.xlabel('Band Gap energy (eV)')
-plt.ylabel('Efficiency (%)')
-plt.legend()
+
+
eg = np.linspace(0.5,2.5,100)
+p = np.vectorize(getPmax)(eg)
+
+plt.figure(3)
+plt.title('Limiting Shockley-Queisser Efficiency Curve')
+plt.plot(eg, p/b, label='AM1.5G')  # Remember b is the integrated power of the
+# incident sunlight
+plt.xlim(0.2, 2.5)
+plt.xlabel('Band Gap energy (eV)')
+plt.ylabel('Efficiency (%)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x298214750>
+
+
+

+

An easier way – using Solcore!

The Solcore library has all the functions we have written above built into it. We worked through this example step by step, but we can calculate the same result using the code below. First let’s calculate an IV curve for a Shockley-Queisser solar cell with a band-gap of 1.42eV:

-
-
import numpy as np
-import matplotlib.pyplot as plt
-from solcore.light_source import LightSource
-from solcore.solar_cell import SolarCell
-from solcore.solar_cell_solver import solar_cell_solver
-from solcore.structure import Junction
-
-# Load the AM1.5G solar spectrum
-wl = np.linspace(300, 4000, 4000) * 1e-9    # wl contains the x-coordinate in wavelength
-am15g = LightSource(source_type='standard', x=wl, version='AM1.5g')
-
-eg = 1.42
-V = np.linspace(0, 1.3, 500)
-db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1) #
-# detailed-balance junction (Shockley-Queisser limit)
-
-my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
-
-solar_cell_solver(my_solar_cell, 'iv',
-                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True,
-                                    'internal_voltages': np.linspace(0, 1.3, 400), 'wavelength': wl,
-                                    'mpp': True, 'light_source': am15g})
-
-plt.figure()
-plt.title('Limiting Efficiency IV curve for $E_g$ = 1.42eV')
-plt.plot(V, my_solar_cell.iv.IV[1], 'k')
-plt.ylim(0, 350)
-plt.xlim(0, 1.2)
-plt.text(0.1,300,f'Jsc: {my_solar_cell.iv.Isc:.2f}')
-plt.text(0.1,280,f'Voc: {my_solar_cell.iv.Voc:.2f}')
-plt.text(0.1,260,f'Pmax: {my_solar_cell.iv.Pmpp:.2f}')
-plt.xlabel('Voltage (V)')
-plt.ylabel('Current (A/m$^2$)')
-plt.show()
+
+
import numpy as np
+import matplotlib.pyplot as plt
+from solcore.light_source import LightSource
+from solcore.solar_cell import SolarCell
+from solcore.solar_cell_solver import solar_cell_solver
+from solcore.structure import Junction
+
+# Load the AM1.5G solar spectrum
+wl = np.linspace(300, 4000, 4000) * 1e-9    # wl contains the x-coordinate in wavelength
+am15g = LightSource(source_type='standard', x=wl, version='AM1.5g')
+
+eg = 1.42
+V = np.linspace(0, 1.3, 500)
+db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1) #
+# detailed-balance junction (Shockley-Queisser limit)
+
+my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
+
+solar_cell_solver(my_solar_cell, 'iv',
+                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True,
+                                    'internal_voltages': np.linspace(0, 1.3, 400), 'wavelength': wl,
+                                    'mpp': True, 'light_source': am15g})
+
+plt.figure()
+plt.title('Limiting Efficiency IV curve for $E_g$ = 1.42eV')
+plt.plot(V, my_solar_cell.iv.IV[1], 'k')
+plt.ylim(0, 350)
+plt.xlim(0, 1.2)
+plt.text(0.1,300,f'Jsc: {my_solar_cell.iv.Isc:.2f}')
+plt.text(0.1,280,f'Voc: {my_solar_cell.iv.Voc:.2f}')
+plt.text(0.1,260,f'Pmax: {my_solar_cell.iv.Pmpp:.2f}')
+plt.xlabel('Voltage (V)')
+plt.ylabel('Current (A/m$^2$)')
+plt.show()
+
+
/Users/z3533914/.pyenv/versions/3.11.5/lib/python3.11/site-packages/solcore/registries.py:73: UserWarning: Optics solver 'RCWA' will not be available. An installation of S4 has not been found.
+  warn(
+
+
+
Solving IV of the junctions...
+Solving IV of the tunnel junctions...
+Solving IV of the total solar cell...
+
+
+

+

The Shockley-Queisser efficiency calculation can now be performed over a range of band-gap energies. To do this, we make a function that calculates the maximum power Pmax as a function of band-gap energy.

-
-
%%capture
-# A command that prevents the screen from filling up with unnecessary working
-
-# Function that returns the maximum power for a Shockley-Queisser solar cell with band-gap Eg
-def getPmax(eg):
-    V = np.linspace(0, eg-0.1, 500)
-    db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)
-    my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
-
-    solar_cell_solver(my_solar_cell, 'iv',
-                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,
-                                    'mpp': True, 'light_source': am15g})
-    return(my_solar_cell.iv.Pmpp)
-
-# Define the range of band-gaps to perform the calculation over
-eg=np.linspace(0.5,2.5,100)
-# Perform the claculation for all values of eg
-p=np.vectorize(getPmax)(eg)
+
+
%%capture
+# A command that prevents the screen from filling up with unnecessary working
+
+# Function that returns the maximum power for a Shockley-Queisser solar cell with band-gap Eg
+def getPmax(eg):
+    V = np.linspace(0, eg-0.1, 500)
+    db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)
+    my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
+
+    solar_cell_solver(my_solar_cell, 'iv',
+                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,
+                                    'mpp': True, 'light_source': am15g})
+    return(my_solar_cell.iv.Pmpp)
+
+# Define the range of band-gaps to perform the calculation over
+eg=np.linspace(0.5,2.5,100)
+# Perform the claculation for all values of eg
+p=np.vectorize(getPmax)(eg)

Now let’s plot the result:

-
-
plt.figure()  # Plot the results calculated above:
-plt.title('Shockley-Queisser Limiting Efficiency for Unconentrated Sunlight')
-plt.plot(eg, p/am15g.power_density,label='AM1.5G')
-plt.xlim(0.5, 2.5)
-plt.xlabel('Band Gap energy (eV)')
-plt.ylabel('Efficiency (%)')
-plt.legend()
+
+
plt.figure()  # Plot the results calculated above:
+plt.title('Shockley-Queisser Limiting Efficiency for Unconentrated Sunlight')
+plt.plot(eg, p/am15g.power_density,label='AM1.5G')
+plt.xlim(0.5, 2.5)
+plt.xlabel('Band Gap energy (eV)')
+plt.ylabel('Efficiency (%)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x2981fe210>
+
+
+

+

Effect of solar concentration on a Shockley-Queisser Solar Cell

In a Trivich-Flinn model for a solar cell, concentrated sunlight is only expected to increase the current of a solar cell, not the voltage. In that model the current would increase in proportion with the concentration so the efficiency of the solar cell would be unchanged.

In the Shockley-Queisser model, concentrated sunlight increased both the current and the voltage of the solar cell which, in the absence of series resistance losses, leads to an increase in the efficiency of the solar cell. Here we calculate the Shockley-Queisser efficiency at different solar concentrations under the direct solar spectrum AM1.5D:

-
-
%%capture
-
-# Set up a series of AM1.5D solar spectra at different concentrations
-wl = np.linspace(300, 4000, 4000) * 1e-9    #wl contains the x-ordinate in wavelength
-am15d1x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=1)
-am15d30x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=30)
-am15d1000x = LightSource(source_type='standard', x=wl, version='AM1.5d',
-                         concentration=1000)
-
-#Define a function to find Pmax for a particular band-gap energy and solar spectrum
-def getPmax(eg,spectrum):
-    V = np.linspace(0, eg-0.1, 500)
-    db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)
-    my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
-
-    solar_cell_solver(my_solar_cell, 'iv',
-                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,
-                                    'mpp': True, 'light_source': spectrum})
-    return my_solar_cell.iv.Pmpp
-
-# Evaluate the Pmax function for band-gaps spanning 0.8 to 1.6eV and concentrations 1x,30x,1000x
-eg = np.linspace(0.8,1.6,100)
-p1x = np.vectorize(getPmax)(eg, am15d1x)
-p30x = np.vectorize(getPmax)(eg, am15d30x)
-p1000x = np.vectorize(getPmax)(eg, am15d1000x)
-
-
-
# Setup a figure for dual y-axes
-fig, ax = plt.subplots(1)
-
-# Plot the SQ curves
-colors = sns.color_palette('husl', n_colors=3)
-ax.plot(eg, 100*p1x/am15d1x.power_density,label='$\eta$ @ AM1.5d 1x', color=colors[0])
-ax.axvline(eg[np.argmax(p1x)], color=colors[0])
-
-ax.plot(eg, 100*p30x/am15d30x.power_density,label='$\eta$ @ AM1.5d 30x', color=colors[1])
-ax.axvline(eg[np.argmax(p30x)], color=colors[1])
-
-ax.plot(eg, 100*p1000x/am15d1000x.power_density,label='$\eta$ @ AM1.5d 1000x', color=colors[2])
-ax.axvline(eg[np.argmax(p1000x)], color=colors[2])
-
-# Define the second y-axis and plot the photon flux in units of eV
-ax2 = ax.twinx()
-ax2.plot(eg, am15d1x.spectrum(x=eg, output_units="photon_flux_per_ev")[1],
-         '--', color='grey', label="AM1.5d")
-
-ax.set_xlim(0.8, 1.6)
-ax.set_xlabel('Band Gap energy (eV)')
-ax.set_ylabel('Efficiency (%)')
-ax2.set_ylabel(r'Photon flux (s$^{-1}$ m$^{-2}$ eV$^{-1}$)')
-ax.legend()
-ax2.legend()
+
+
%%capture
+
+# Set up a series of AM1.5D solar spectra at different concentrations
+wl = np.linspace(300, 4000, 4000) * 1e-9    #wl contains the x-ordinate in wavelength
+am15d1x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=1)
+am15d30x = LightSource(source_type='standard', x=wl, version='AM1.5d', concentration=30)
+am15d1000x = LightSource(source_type='standard', x=wl, version='AM1.5d',
+                         concentration=1000)
+
+#Define a function to find Pmax for a particular band-gap energy and solar spectrum
+def getPmax(eg,spectrum):
+    V = np.linspace(0, eg-0.1, 500)
+    db_junction = Junction(kind='DB', T=300, Eg=eg, A=1, R_shunt=np.inf, n=1)
+    my_solar_cell = SolarCell([db_junction], T=300, R_series=0)
+
+    solar_cell_solver(my_solar_cell, 'iv',
+                      user_options={'T_ambient': 300, 'db_mode': 'top_hat', 'voltages': V, 'light_iv': True, 'wavelength': wl,
+                                    'mpp': True, 'light_source': spectrum})
+    return my_solar_cell.iv.Pmpp
+
+# Evaluate the Pmax function for band-gaps spanning 0.8 to 1.6eV and concentrations 1x,30x,1000x
+eg = np.linspace(0.8,1.6,100)
+p1x = np.vectorize(getPmax)(eg, am15d1x)
+p30x = np.vectorize(getPmax)(eg, am15d30x)
+p1000x = np.vectorize(getPmax)(eg, am15d1000x)
+
+
+
# Setup a figure for dual y-axes
+fig, ax = plt.subplots(1)
+
+# Plot the SQ curves
+colors = sns.color_palette('husl', n_colors=3)
+ax.plot(eg, 100*p1x/am15d1x.power_density,label='$\eta$ @ AM1.5d 1x', color=colors[0])
+ax.axvline(eg[np.argmax(p1x)], color=colors[0])
+
+ax.plot(eg, 100*p30x/am15d30x.power_density,label='$\eta$ @ AM1.5d 30x', color=colors[1])
+ax.axvline(eg[np.argmax(p30x)], color=colors[1])
+
+ax.plot(eg, 100*p1000x/am15d1000x.power_density,label='$\eta$ @ AM1.5d 1000x', color=colors[2])
+ax.axvline(eg[np.argmax(p1000x)], color=colors[2])
+
+# Define the second y-axis and plot the photon flux in units of eV
+ax2 = ax.twinx()
+ax2.plot(eg, am15d1x.spectrum(x=eg, output_units="photon_flux_per_ev")[1],
+         '--', color='grey', label="AM1.5d")
+
+ax.set_xlim(0.8, 1.6)
+ax.set_xlabel('Band Gap energy (eV)')
+ax.set_ylabel('Efficiency (%)')
+ax2.set_ylabel(r'Photon flux (s$^{-1}$ m$^{-2}$ eV$^{-1}$)')
+ax.legend()
+ax2.legend()
+
+
<matplotlib.legend.Legend at 0x2bf13f050>
+
+
+

+

The maximum band-gap energy moves to lower energies with increaseing solar concentration. This arises since although the current increases with increasing solar concentration, the cell voltage also increases which means the optimal effiicency is obtained at lower band-gaps. However, the drop in band-gap energy is modest owing to a strong atmospheric absorption feature at 1.1um which serves to pin the optimum bandgap around 1.12eV.

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Section 4: Calculating Spectral Irradiance using SPCTRAL 2

All the inputs are numeric other than the aod_model whose options are: ‘rural’, ‘urban’, ‘maritime’ and ‘tropospheric’.

Comparison between SPCTRAL2 with default parameters and AM1.5G

-
+
import numpy as np
 import matplotlib.pyplot as plt
 from solcore.light_source import LightSource
@@ -211,44 +211,65 @@ 
plt.xlabel('Wavelength (nm)')
 plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
 plt.legend()
+
+
WARNING: The RCWA solver will not be available because an S4 installation has not been found.
+
+
+
<matplotlib.legend.Legend at 0x12ee06f50>
+
+
+

+

Adjusting the precipitable water value

The default SPCTRAL2 parameters results in almost no atmospheric absorption. This suggests the precipitable water column thickness is much too low, the default is 0.00142 cm. Let’s increase that value to 1cm to roughly match AM1.5G:

-
-
spc2pc = LightSource(source_type='SPECTRAL2', precipwater=1.0, x=wl * 1e9)
-
-plt.figure()
-plt.title('Comparions between SPCTRAL2 defaults, 1cm precipitable water & AM1.5G')
-plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
-plt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')
-plt.plot(*spc2pc.spectrum(wl*1e9), label='PC water')
-
-plt.xlim(300, 3000)
-plt.xlabel('Wavelength (nm)')
-plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
-plt.legend()
+
+
spc2pc = LightSource(source_type='SPECTRAL2', precipwater=1.0, x=wl * 1e9)
+
+plt.figure()
+plt.title('Comparions between SPCTRAL2 defaults, 1cm precipitable water & AM1.5G')
+plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
+plt.plot(*spc2default.spectrum(wl*1e9), label='SPC-default')
+plt.plot(*spc2pc.spectrum(wl*1e9), label='PC water')
+
+plt.xlim(300, 3000)
+plt.xlabel('Wavelength (nm)')
+plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x12ef7a890>
+
+
+

+

Atmospheric Turbidity

The short wavelength is attenuated which is likely due to a high level of aerosol loading in the default spectrum. To address this atmospheric turbidity can be reduced to around 0.05.

-
-
spc2high = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2, x=wl * 1e9)
-spc2med = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.1, x=wl * 1e9)
-spc2low = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.05, x=wl * 1e9)
-
-plt.figure()
-plt.title('Spectral Irradiance Plotted for Different Aersol Models')
-plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
-plt.plot(*spc2high.spectrum(wl*1e9), label='Turbidity = 0.2')
-plt.plot(*spc2med.spectrum(wl*1e9), label='Turbidity = 0.1')
-plt.plot(*spc2low.spectrum(wl*1e9), label='Turbidity = 0.05')
-plt.xlim(300, 3000)
-plt.xlabel('Wavelength (nm)')
-plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
-plt.legend()
+
+
spc2high = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2, x=wl * 1e9)
+spc2med = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.1, x=wl * 1e9)
+spc2low = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.05, x=wl * 1e9)
+
+plt.figure()
+plt.title('Spectral Irradiance Plotted for Different Aersol Models')
+plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
+plt.plot(*spc2high.spectrum(wl*1e9), label='Turbidity = 0.2')
+plt.plot(*spc2med.spectrum(wl*1e9), label='Turbidity = 0.1')
+plt.plot(*spc2low.spectrum(wl*1e9), label='Turbidity = 0.05')
+plt.xlim(300, 3000)
+plt.xlabel('Wavelength (nm)')
+plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x12f727450>
+
+
+

+
@@ -256,45 +277,57 @@

Variation wi

Several standard aerosol models are implemented in SPCTRAL 2 that were established by Shettle & Fenn.

Shettle, E. P., and R. W. Fenn, “Models of the Atmospheric Aerosol and Their Optical Properties, II Proceedings of the Advisory Group for Aerospace Reseach and Development Conference No . 183, Optical Propagation in the Atmosphere, 1975, pp. 2.1-2.16. Presented at the Electromagnetic Wave Propagation Panel Symposium, Lyngby, Denmark; 27-31 October 1975.

Here we plot some of them with a turbidity of 0.2 to emphasise the different spectral behaviour:

-
-
spc2rural = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
-                        aod_model='rural', x=wl * 1e9)
-spc2marit = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
-                        aod_model='maritime', x=wl * 1e9)
-spc2tropo = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
-                        aod_model='tropospheric', x=wl * 1e9)
-
-plt.figure(1)
-plt.title('Spectral Irradiance Plotted for Different Aersol Models')
-plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
-plt.plot(*spc2rural.spectrum(wl*1e9), label='rural')
-plt.plot(*spc2marit.spectrum(wl*1e9), label='maritime')
-plt.plot(*spc2tropo.spectrum(wl*1e9), label='tropospheric')
-plt.xlim(300, 3000)
-plt.xlabel('Wavelength (nm)')
-plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
-plt.legend()
+
+
spc2rural = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
+                        aod_model='rural', x=wl * 1e9)
+spc2marit = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
+                        aod_model='maritime', x=wl * 1e9)
+spc2tropo = LightSource(source_type='SPECTRAL2', precipwater=1.0, turbidity=0.2,
+                        aod_model='tropospheric', x=wl * 1e9)
+
+plt.figure(1)
+plt.title('Spectral Irradiance Plotted for Different Aersol Models')
+plt.plot(*am15g.spectrum(wl*1e9), label='AM1.5G')
+plt.plot(*spc2rural.spectrum(wl*1e9), label='rural')
+plt.plot(*spc2marit.spectrum(wl*1e9), label='maritime')
+plt.plot(*spc2tropo.spectrum(wl*1e9), label='tropospheric')
+plt.xlim(300, 3000)
+plt.xlabel('Wavelength (nm)')
+plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x12f7769d0>
+
+
+

+

Changing the time of day

One of the most common uses for a spectral irradiance model such as SPCTRAL2 is to calculate how a particular solar cell technology behaves under varying spectral conditions during the day. This is particularly important whan working with series connected tandem solar cells where the current matching condition will vary according to the incident spectrum. Here we plot the spectral irradiance at 12pm, 2pm, 3pm, 4pm, 5pm, 6pm and 7pm. Note the strong relative loss in short-wavelength light relative to the infrared as the air-mass increases throughout the afternoon.

-
-
import datetime
-
-plt.figure(1)
-plt.title('Spectral Irradiance plotted from 12pm-7pm')
-hours=[12, 14, 15, 16, 17, 18, 19]
-
-for h in hours:
-    spc2 = LightSource(source_type='SPECTRAL2', dateAndTime=datetime.datetime(2011, 6, 30, h, 00),
-                       precipwater=1.0, turbidity=0.05, x=wl * 1e9)
-    plt.plot(*spc2.spectrum(wl*1e9), label='hour '+ str(h))
-
-plt.xlim(300, 3000)
-plt.xlabel('Wavelength (nm)')
-plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
-plt.legend()
+
+
import datetime
+
+plt.figure(1)
+plt.title('Spectral Irradiance plotted from 12pm-7pm')
+hours=[12, 14, 15, 16, 17, 18, 19]
+
+for h in hours:
+    spc2 = LightSource(source_type='SPECTRAL2', dateAndTime=datetime.datetime(2011, 6, 30, h, 00),
+                       precipwater=1.0, turbidity=0.05, x=wl * 1e9)
+    plt.plot(*spc2.spectrum(wl*1e9), label='hour '+ str(h))
+
+plt.xlim(300, 3000)
+plt.xlabel('Wavelength (nm)')
+plt.ylabel('Power density (Wm$^{-2}$nm$^{-1}$)')
+plt.legend()
+
+
<matplotlib.legend.Legend at 0x12f8a5d10>
+
+
+

+
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In this first set of examples, we will look at simple planar Si solar cell.

In this script, we will look at the difference between Beer-Lambert absorption calculations, using the Fresnel equations for front-surface reflection, and using the transfer-matrix model.

First, lets import some very commonly-used Python packages:

-
+
import numpy as np
 import matplotlib.pyplot as plt

Numpy is a Python library which adds supports for multi-dimensional data arrays and matrices, so it is very useful for storing and handling data. You will probably use it in every Solcore script you write. Here, it is imported under the alias ‘np’, which you will see used below. matplotlib is used for making plots, and is imported under the alias ‘plt’. Both the ‘np’ and ‘plt’ aliases are extremely commonly used in Python programming.

Now, let’s import some things from Solcore (which will be explained as we use them):

-
+
from solcore import material, si
 from solcore.solar_cell import SolarCell, Layer, Junction
 from solcore.solar_cell_solver import solar_cell_solver
@@ -200,36 +200,36 @@ 
Section 5a: Planar Si solar cell using DA

 
Defining materials

 
To define our solar cell, we first want to define some materials. Then we want to organise those materials into Layers, organise those layers into a Junction (or multiple Junctions, for a multi-junction cell, as we will see later), and then finally define a SolarCell with that Junction.

 
First, let’s define a silicon material. Silicon, along with many other semiconductors, dielectrics, and metals common in solar cells, is included in Solcore’s database:

-

+

 
Si = material("Si")

 

 
This creates an instance of the Si material. However, to use this in a solar cell we need to do specify some more information, specifically the doping level and the minority carrier diffusion length. The ‘si’ function comes in handy here to convert all quantities to base units e.g. m, m\(^{-3}\)…

-

-
Si_n = Si(Nd=si("1e21cm-3"), hole_diffusion_length=si("10um"))
-Si_p = Si(Na=si("1e16cm-3"), electron_diffusion_length=si("400um"))

+

+
Si_p = Si(Na=si("1e21cm-3"), electron_diffusion_length=si("4um"))
+Si_n = Si(Nd=si("1e16cm-3"), hole_diffusion_length=si("200um"))

 

 
 

 
Defining layers

 
Now we define the emitter and base layers we will have in the solar cell; we specify their thickness, the material they are made of and the role they play within the cell (emitter or base). We create a junction which is a total of 200 \(\mu\)m thick, with a 1 \(\mu\)m junction depth.

-

-
emitter_layer = Layer(width=si("1um"), material=Si_n, role='emitter')
-base_layer = Layer(width=si("199um"), material=Si_p, role='base')

+

+
emitter_layer = Layer(width=si("1um"), material=Si_p, role='emitter')
+base_layer = Layer(width=si("199um"), material=Si_n, role='base')

 

 
Now we create the p-n junction using the layers defined above. We set kind=“DA” to tell Solcore to use the Depletion Approximation in the calculation:

-

+

 
Si_junction = Junction([emitter_layer, base_layer], kind="DA")

 

 

 

 
Setting user options

 
Wavelengths we want to use in the calculations; wavelengths between 300 and 1200 nm, at 200 evenly spaced intervals:

-

+

 
wavelengths = si(np.linspace(300, 1200, 200), "nm")

 

 
Note that here and above in defining the layers and materials we have used the “si()” function multiple times: you can use this to automatically convert quantities in other units to base SI units (e.g. nanometres to metres).

 
Now we specify some options for running the calculation. Initially we will use the Beer-Lambert absorption law (\(I(z) = I_0 e^{-\alpha*z}\)) to calculate the optics of the cell (“BL”). We set the wavelengths we want to use, and we set “recalculate_absorption” to True so that further down in the script when we try different optics methods, Solcore knows we want to re-calculate the optics of the cell rather than re-using previous results. We can specify the options in a Python format called a dictionary:

-

+

 
options = {
     "recalculate_absorption": True,
     "optics_method": "BL",
@@ -240,144 +240,186 @@ 
Setting user options<
 

 
Running cell simulations

 
Define the solar cell; in this case it is very simple and we just have a single junction:

-

+

 
solar_cell = SolarCell([Si_junction])

 

 
Now we use solar_cell_solver to calculate the QE of the cell; we can ask solar_cell_solver to calculate ‘qe’, ‘optics’ or ‘iv’.

-

+

 
solar_cell_solver(solar_cell, 'qe', options)

+

+
Solving QE of the solar cell...

+

 

 
PLOT 1: plotting the QE in the Si junction, as well as the fraction of light absorbed in the junction and reflected. Because we are using the Beer-Lambert absorption law and we did not specify external reflectance, the reflectance = 0 over the whole wavelength range.

-

-
plt.figure()
-plt.plot(wavelengths*1e9, 100*solar_cell[0].eqe(wavelengths), 'k-', label="EQE")
-plt.plot(wavelengths*1e9, 100*solar_cell[0].layer_absorption, label='Absorptance (A)')
-plt.plot(wavelengths*1e9, 100*solar_cell.reflected, label='Reflectance (R)')
-plt.legend()
-plt.xlabel("Wavelength (nm)")
-plt.ylabel("QE/Absorptance (%)")
-plt.title("(1) QE of Si cell - Beer-Lambert absorption")
-plt.show()

+

+
plt.figure()
+plt.plot(wavelengths*1e9, 100*solar_cell[0].eqe(wavelengths), 'k-', label="EQE")
+plt.plot(wavelengths*1e9, 100*solar_cell[0].layer_absorption, label='Absorptance (A)')
+plt.plot(wavelengths*1e9, 100*solar_cell.reflected, label='Reflectance (R)')
+plt.legend()
+plt.xlabel("Wavelength (nm)")
+plt.ylabel("QE/Absorptance (%)")
+plt.title("(1) QE of Si cell - Beer-Lambert absorption")
+plt.show()

+

+

+

 

 

 

 
Adding front-surface reflection: Fresnel

 
Now, to make this calculation a bit more realistic, there are a few things we could do. We could load some measured front surface reflectance from a file, or we could calculate the reflectance. To calculate the reflectance, there are many approaches we could take; we are going to explore two of them here.

 
If we assume the silicon is infinitely thick (or at least much thicker than the wavelengths of light we care about) then the reflectance will approach the reflectivity of a simple air/Si interface. We can calculate what this is using the Fresnel equation for reflectivity.

-

-
def calculate_R_Fresnel(incidence_n, transmission_n, wl):
-    # return a function that gives the value of R (at normal incidence) at the input wavelengths
-
-    Rs = np.abs((incidence_n - transmission_n)/(incidence_n + transmission_n))**2
-
-    return interp1d(wl, Rs)

+

+
def calculate_R_Fresnel(incidence_n, transmission_n, wl):
+    # return a function that gives the value of R (at normal incidence) at the input wavelengths
+
+    Rs = np.abs((incidence_n - transmission_n)/(incidence_n + transmission_n))**2
+
+    return interp1d(wl, Rs)

 

 
The transmission_n is the complex reflective index of Si at our wavelengths for the transmission medium (Si), which we can extract easily from the Si material object in Solcore. The incidence_n = 1 (air). Note that the function above is specifically for normal incidence.

-

-
trns_n = Si_n.n(wavelengths) + 1j*Si_n.k(wavelengths)
-reflectivity_fn = calculate_R_Fresnel(1, trns_n, wavelengths)

+

+
trns_n = Si_n.n(wavelengths) + 1j*Si_n.k(wavelengths)
+reflectivity_fn = calculate_R_Fresnel(1, trns_n, wavelengths)

 

 
We define the solar cell again, with the same layers but now supplying the function for the externally-calculated reflectivity, and calculate the optics (reflection, absorption, transmission) again:

-

-
solar_cell_fresnel = SolarCell([Si_junction], reflectivity=reflectivity_fn)
-
-solar_cell_solver(solar_cell_fresnel, 'optics', options)

+

+
solar_cell_fresnel = SolarCell([Si_junction], reflectivity=reflectivity_fn)
+
+solar_cell_solver(solar_cell_fresnel, 'optics', options)

 

 

 

 
Adding front surface reflection: TMM

 
Finally, we do the same again but now instead of supplying the external reflectivity we ask set the optics_method to “TMM” (Transfer Matrix Method), to correctly calculate reflection at the front surface. We will learn more about the transfer matrix method later.

-

-
Si_junction = Junction([emitter_layer, base_layer], kind="DA")
-
-solar_cell_TMM = SolarCell([Si_junction])

+

+
Si_junction = Junction([emitter_layer, base_layer], kind="DA")
+
+solar_cell_TMM = SolarCell([Si_junction])

 

 
Set some more options for the cell calculation:

-

-
options["optics_method"] = "TMM"
-voltages = np.linspace(-1.1, 1.1, 100)
-options["light_iv"] = True
-options["mpp"] = True
-options["voltages"] = voltages
-options["internal_voltages"] = voltages

+

+
options["optics_method"] = "TMM"
+voltages = np.linspace(-1.1, 1.1, 100)
+options["light_iv"] = True
+options["mpp"] = True
+options["voltages"] = voltages
+options["internal_voltages"] = voltages

 

 
we calculate the QE and the IV (we set the light_iv option to True; if we don’t do this, Solcore just calculates the dark IV). We also ask Solcore to find the maximum power point (mpp) so we can get the efficiency. Note that the sign convention used by Solcore means that an n-on-p cell with have a negative open-circuit voltage.

-

-
solar_cell_solver(solar_cell_TMM, 'iv', options)
-solar_cell_solver(solar_cell_TMM, 'qe', options)

+

+
solar_cell_solver(solar_cell_TMM, 'iv', options)
+solar_cell_solver(solar_cell_TMM, 'qe', options)

+

+
Treating layer(s) 1 incoherently
+Calculating RAT...
+Calculating absorption profile...
+Solving IV of the junctions...
+Solving IV of the tunnel junctions...
+Solving IV of the total solar cell...
+Treating layer(s) 1 incoherently
+Calculating RAT...
+Calculating absorption profile...
+Solving QE of the solar cell...

+

 

 
PLOT 2: here we plot the reflection, transmission, and absorption calculated with the Fresnel equation defined above, and with the TMM solver in Solcore, showing that for this simple situation (no anti-reflection coating, thick Si junction) they are exactly equivalent.

-

-
plt.figure()
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, color='firebrick', label = "R (TMM)")
-plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.reflected, '--', color='orangered', label = "R (Fresnel)")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM.absorbed, color='dimgrey', label = "A (TMM)")
-plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.absorbed, '--', color='lightgrey', label = "A (Fresnel)")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, color='blue', label = "T (TMM)")
-plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.transmitted, '--', color='dodgerblue', label = "T (Fresnel)")
-plt.ylim(0, 100)
-plt.legend()
-plt.title("(2) Optics of Si cell - Fresnel/TMM")
-plt.show()

+

+
plt.figure()
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, color='firebrick', label = "R (TMM)")
+plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.reflected, '--', color='orangered', label = "R (Fresnel)")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM.absorbed, color='dimgrey', label = "A (TMM)")
+plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.absorbed, '--', color='lightgrey', label = "A (Fresnel)")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, color='blue', label = "T (TMM)")
+plt.plot(wavelengths*1e9, 100*solar_cell_fresnel.transmitted, '--', color='dodgerblue', label = "T (Fresnel)")
+plt.ylim(0, 100)
+plt.legend()
+plt.title("(2) Optics of Si cell - Fresnel/TMM")
+plt.show()

+

+

+

 

 
PLOT 3: As above for the TMM calculation, plotting the EQE as well, which will be slightly lower than the absorption because not all the carriers are collected. Comparing to plot (1), we can see we now have lower absorption due to the inclusion of front surface reflection, which is ~ 30% or more over the wavelength range of interest for a bare Si surface.

-

-
plt.figure()
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].eqe(wavelengths), 'k-', label="EQE")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].layer_absorption, label='A')
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, label="R")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, label="T")
-plt.title("(3) QE of Si cell (no ARC) - TMM")
-plt.legend()
-plt.xlabel("Wavelength (nm)")
-plt.ylabel("QE/Absorptance (%)")
-plt.ylim(0, 100)
-plt.show()

+

+
plt.figure()
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].eqe(wavelengths), 'k-', label="EQE")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM[0].layer_absorption, label='A')
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM.reflected, label="R")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM.transmitted, label="T")
+plt.title("(3) QE of Si cell (no ARC) - TMM")
+plt.legend()
+plt.xlabel("Wavelength (nm)")
+plt.ylabel("QE/Absorptance (%)")
+plt.ylim(0, 100)
+plt.show()

+

+

+

 

 

 

 
Adding an ARC

 
The reflectance of bare Si is very high. Let’s try adding a simple anti-reflection coating (ARC), a single layer of silicon nitride (Si\(_3\)N\(_4\)):

-

-
SiN = material("Si3N4")()
-
-Si_junction = Junction([emitter_layer, base_layer], kind="DA")
-
-solar_cell_TMM_ARC = SolarCell([Layer(width=si(75, "nm"), material=SiN), Si_junction])
-
-solar_cell_solver(solar_cell_TMM_ARC, 'qe', options)
-solar_cell_solver(solar_cell_TMM_ARC, 'iv', options)

+

+
SiN = material("Si3N4")()
+
+Si_junction = Junction([emitter_layer, base_layer], kind="DA")
+
+solar_cell_TMM_ARC = SolarCell([Layer(width=si(75, "nm"), material=SiN), Si_junction])
+
+solar_cell_solver(solar_cell_TMM_ARC, 'qe', options)
+solar_cell_solver(solar_cell_TMM_ARC, 'iv', options)

+

+
Treating layer(s) 2 incoherently
+Calculating RAT...
+Calculating absorption profile...
+Solving QE of the solar cell...
+Treating layer(s) 2 incoherently
+Calculating RAT...
+Calculating absorption profile...
+Solving IV of the junctions...
+Solving IV of the tunnel junctions...
+Solving IV of the total solar cell...

+

 

 
PLOT 4: Absorption, EQE, reflection and transmission for the cell with a simple one-layer ARC. We see the reflection is significantly reduced from the previous plot leading to higher absorption/EQE.

-

-
plt.figure()
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].eqe(wavelengths), 'k-', label="EQE")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].layer_absorption, label='A')
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.reflected, label="R")
-plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.transmitted, label="T")
-plt.legend()
-plt.title("(4) QE of Si cell (ARC) - TMM")
-plt.xlabel("Wavelength (nm)")
-plt.ylabel("QE/Absorptance (%)")
-plt.ylim(0, 100)
-plt.show()

+

+
plt.figure()
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].eqe(wavelengths), 'k-', label="EQE")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC[1].layer_absorption, label='A')
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.reflected, label="R")
+plt.plot(wavelengths*1e9, 100*solar_cell_TMM_ARC.transmitted, label="T")
+plt.legend()
+plt.title("(4) QE of Si cell (ARC) - TMM")
+plt.xlabel("Wavelength (nm)")
+plt.ylabel("QE/Absorptance (%)")
+plt.ylim(0, 100)
+plt.show()

+

+

+

 

 
PLOT 5: Compare the IV curves of the cells with and without an ARC. The efficiency is also shown on the plot. Note that because we didn’t specify a light source, Solcore will assume we want to use AM1.5G; in later examples we will set the light source used for light IV simulations explicitly.

-

-
plt.figure()
-plt.plot(-voltages, solar_cell_TMM[0].iv(voltages)/10, label="No ARC")
-plt.plot(-voltages, solar_cell_TMM_ARC[1].iv(voltages)/10, label="75 nm SiN")
-plt.text(0.5, 1.02*abs(solar_cell_TMM.iv["Isc"])/10, str(round(solar_cell_TMM.iv["Eta"]*100,
-                                                      1)) + ' %')
-plt.text(0.5, 1.02*abs(solar_cell_TMM_ARC.iv["Isc"])/10, str(round(solar_cell_TMM_ARC
-                                                          .iv["Eta"]*100, 1)) + ' %')
-plt.ylim(0, 38)
-plt.xlim(-0.8, 0.8)
-plt.legend()
-plt.xlabel("V (V)")
-plt.ylabel(r"J (mA/cm$^2$)")
-plt.title("(5) IV curve of Si cell with and without ARC")
-plt.show()

+

+
plt.figure()
+plt.plot(voltages, -solar_cell_TMM[0].iv(voltages)/10, label="No ARC")
+plt.plot(voltages, -solar_cell_TMM_ARC[1].iv(voltages)/10, label="75 nm SiN")
+plt.text(0.5, 1.02*abs(solar_cell_TMM.iv["Isc"])/10, str(round(solar_cell_TMM.iv["Eta"]*100,
+                                                      1)) + ' %')
+plt.text(0.5, 1.02*abs(solar_cell_TMM_ARC.iv["Isc"])/10, str(round(solar_cell_TMM_ARC
+                                                          .iv["Eta"]*100, 1)) + ' %')
+plt.ylim(0, 38)
+plt.xlim(-0.8, 0.8)
+plt.legend()
+plt.xlabel("V (V)")
+plt.ylabel(r"J (mA/cm$^2$)")
+plt.title("(5) IV curve of Si cell with and without ARC")
+plt.show()

+

+

+

 

 

 

diff --git a/docs/solcore-workshop-2/notebooks/5a-simple_Si_cell_files/figure-html/cell-12-output-1.png b/docs/solcore-workshop-2/notebooks/5a-simple_Si_cell_files/figure-html/cell-12-output-1.png
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diff --git a/docs/solcore-workshop-2/notebooks/5b-Si_cell_PDD.html b/docs/solcore-workshop-2/notebooks/5b-Si_cell_PDD.html
index 0362211..67ed7b1 100644
--- a/docs/solcore-workshop-2/notebooks/5b-Si_cell_PDD.html
+++ b/docs/solcore-workshop-2/notebooks/5b-Si_cell_PDD.html
@@ -142,11 +142,21 @@
 

 
 
-