#!/usr/bin/env python # coding: utf-8 # In[ ]: from solcore import si from solcore import material from solcore.solar_cell import SolarCell, Layer, Junction from solcore.solar_cell_solver import solar_cell_solver, default_options import numpy as np from scipy.interpolate import interp1d import matplotlib.pyplot as plt # In[ ]: T = 300 wavelengths_optics = np.linspace(300, 1200, 800)*1e-9 # Define some materials and layer widths: # In[ ]: Si = material("Si") SiO2 = material("SiO2")() # In[ ]: n_material = Si(T=T, Nd=si(1e21, "cm-3"), hole_diffusion_length=si("50um"), electron_mobility=50e-4, relative_permittivity = 11.68) p_material = Si(T=T, Na=si(1e16, "cm-3"), electron_diffusion_length=si("150um"), hole_mobility=400e-4, relative_permittivity = 11.68) # In[ ]: ARC_width = si("100nm") n_material_width = si("500nm") p_material_width = si("50um") # We are first going to get some optics data which we can then use to illustrate how to provide # the relevant quantities to the external optics solver. Obviously, this is a bit circular, since we # are first going to use Solcore to calculate reflection and absorption and then feed that information # back into solar_cell_solver in a different format, but this way we can show how the data should be # provided when using external optics and that everything is working consistently. # In[ ]: solar_cell = SolarCell( [ Layer(width=ARC_width, material=SiO2), Junction([Layer(width=n_material_width, material=n_material, role='emitter'), Layer(width=p_material_width, material=p_material, role='base'), ], sn=1, sp=1, kind='DA'), ]) # In[ ]: total_width = ARC_width + n_material_width + p_material_width # options: we are going to use TMM to calculate the optics of a silicon cell with a 100 nm SiO2 anti-reflection coating
# This will not be very realistic
# compared to a standard Si cell, which will usually have some textured surface (usually pyramids) and not just a planar
# surface with an anti-reflection coating, but it gives some physically reasonable data to use. # In[ ]: options = default_options options.optics_method = "TMM" options.wavelength = wavelengths_optics # options.position = np.linspace(0, total_width, 100000) options.light_iv = True V = np.linspace(0, 1.2, 200) # In[ ]: solar_cell_solver(solar_cell, 'iv', options) # Now we are going to get the relevant data to see how we might construct # appropriate functions to provide external optics data to Solcore. If you are # using experimental data, this could be loaded from a file, here we will take it # from the TMM calculations done above. We get the fraction of light reflected, # and the fraction of light absorbed in the Si layer. # In[ ]: reflected = solar_cell.reflected absorbed_in_Si = solar_cell[1].layer_absorption # We need to provide two attributes when defining the cell to give all the required # information for external optics: external_reflected and external_absorbed. external_reflected< # is a list of the fraction of incident light reflected at each wavelength that is specified in the user options. # external_absorbed is a function which takes as input an array of positions (depths) # in the cell in m and returns the differential absorption at each wavelength and depth; this is # a 2D numpy array where the first dimension is over the wavelengths and the second dimension # is over the positions in the cell. # We could take the diff_absorption method from solar_cell, which was constructed during the TMM # calculation done above, but in order to show how the absorption profile can be calculated from # total absorption in a layer (assuming Beer-Lambert law absorption, i.e. no interference in the layer) # we will define a function which calculates the differential absorption from just the total absorption # and the absorption coefficient of the junction material. # To illustrate how you can use data from e.g. an experiment to perform calculations at different wavelength, # we're going to take the data we calculated above but use slightly different wavelength points. # Interpolate reflection and total absorption in Si to the new wavelengths: # In[ ]: interp_ref = interp1d(options.wavelength, reflected) interp_totalA = interp1d(options.wavelength, solar_cell[1].layer_absorption) # In[ ]: wavelengths_external = np.linspace(301, 1199, 800)*1e-9 # In[ ]: alpha = n_material.alpha(wavelengths_external) A_layer = interp_totalA(wavelengths_external) # Make function which returns the absorption profile. The functional form can be found by differentiating the
# Beer-Lambert law, and making sure it is normalized correctly to give the expected total absorption # In[ ]: junction_width = n_material_width + p_material_width # In[ ]: def make_absorb_fn(alpha, A_layer, junction_width): norm = A_layer * alpha / (1 - np.exp(-alpha * junction_width)) def profile(z): xy = norm[None, :] * np.exp(-alpha * z[:, None]) return xy.T return profile # In[ ]: diff_absorb_fn = make_absorb_fn(alpha, A_layer, junction_width) # We now define a solar cell for the external optics calculation. It's the same as solar_cell, # but without the ARC layer; this does not do anything in the electrical calculation, and we must # omit it so that the diff_absorb_fn defined above works correctly. This function should describe the # differential absorption profile in the WHOLE cell, including any surface layers, # but to avoid complexity in make_absorb_fn it just calculates # Beer-Lambert absorption in the Si and ignores the ARC. So for the absorption profile to match the actual # cell, we need the front surface to be the Si emitter. # In[ ]: solar_cell_external = SolarCell( [ Junction([Layer(width=n_material_width, material=n_material, role='emitter'), Layer(width=p_material_width, material=p_material, role='base'), ], sn=1, sp=1, kind='DA'), ], external_reflected=interp_ref(wavelengths_external), external_absorbed=diff_absorb_fn) # In[ ]: options.optics_method = "external" options.wavelength = wavelengths_external # In[ ]: solar_cell_solver(solar_cell_external, 'iv', options) # Check that the total absorption and reflection are the same. The total reflection will be the same
# as it is directly supplied by the user, but the total reflection is calculated by integrating the
# differential absorption, so this is a good check: # In[ ]: plt.figure() plt.plot(wavelengths_external*1e9, solar_cell_external.reflected, label='Reflected - external') plt.plot(wavelengths_external*1e9, solar_cell_external.absorbed, label='Absorbed - external') plt.plot(wavelengths_optics*1e9, reflected, 'k--', label='Reflected - TMM') plt.plot(wavelengths_optics*1e9, absorbed_in_Si, '--', label='Absorbed - TMM') plt.legend() plt.xlabel('Wavelength (nm)') plt.ylabel('R/A') plt.show() # Compare the light-IV curves: # In[ ]: plt.figure(1) plt.plot(V, -solar_cell[1].iv(V), 'b', label='TMM calculation') plt.plot(V, -solar_cell_external[0].iv(V), 'k--', label='External optics') plt.legend() plt.ylim(-20, 350) plt.xlim(0, 1) plt.ylabel('Current (A/m$^2$)') plt.xlabel('Voltage (V)') #The expected values of Isc and Voc are 372 A/m^2 and 0.63 V respectively # In[ ]: plt.show() # Finally, compare the absorption profiles (diff_absorption). These will not be exactly identical, # because the profile for the TMM cell also contains the absorption profile in the ARC (= 0 everywhere), # so is shifted over by 100 nm. # In[ ]: position_plot = np.linspace(0, 200, 100)*1e-9 # In[ ]: absorption_profile_TMM = solar_cell[0].diff_absorption(position_plot) absorption_profile_constructed = solar_cell_external[0].diff_absorption(position_plot) # In[ ]: plt.figure(figsize=(10, 4)) plt.subplot(121) plt.imshow(absorption_profile_TMM, aspect='auto', extent=[0, 400, 1200, 300]) plt.colorbar() plt.xlabel('Depth (nm)') plt.ylabel('Wavelength (nm)') plt.title(r'Differential absorption (m$^{-1}$) in front surface of cell') # In[ ]: plt.subplot(122) plt.imshow(absorption_profile_constructed, aspect='auto', extent=[0, 400, 1200, 300]) plt.xlabel('Depth (nm)') plt.ylabel('Wavelength (nm)') # In[ ]: plt.show()