Calculation of absorptivity/emissivity of a silicon heterojunction cell with pyramid textures¶

This example calculates the absorption (and thus emissivity) in all the individual layers of a silicon heterojunction (HIT) solar cell. This paper gives more details.

Start with relevant imports:

[13]:

import numpy as np
import os

from solcore.structure import Layer
from solcore import material
from solcore.light_source import LightSource
from solcore.constants import q

from rayflare.textures import regular_pyramids
from rayflare.structure import Interface, BulkLayer, Structure
from rayflare.matrix_formalism import calculate_RAT
from rayflare.matrix_formalism import process_structure
from rayflare.options import default_options

import matplotlib.pyplot as plt
import seaborn as sns

from cycler import cycler

We then generate the wavelengths (equally spaced between 300 nm and 16 microns on a log scale) at which to calculate, and set some options. Note that for this example, we are using relatively few rays and angular bins so the example runs in a reasonable amount of time, but this means the results will have a lot of noise due to the stochastic nature of the ray-tracing.

[14]:

wavelengths = np.linspace(np.log(300), np.log(16*1000), 104)
wavelengths = np.round(np.floor(np.exp(wavelengths))*1e-9, 12)

options = default_options()
options.wavelength = wavelengths
options.project_name = 'HIT_notebook'
options.n_rays = 10000
options.n_theta_bins = 20
options.nx = 5
options.ny = 5

Define the materials and the front and back material stacks. These are the layers which are deposited on the surface texture of the Si on each side. Note that these are custom materials (run the non-notebook version of this example in the examples folder to add them to your database).

[15]:

Si = material('Si_UVtoMIR')()
Air = material('Air')()
ITO_front = material('ITO_front')()
ITO_back = material('ITO_back')()
Ag = material('Ag_Jiang')()
aSi_i = material('aSi_i')()
aSi_p = material('aSi_p')()
aSi_n = material('aSi_n')()


# stack based on doi:10.1038/s41563-018-0115-4
front_materials = [Layer(80e-9, ITO_front), Layer(6.5e-9, aSi_p), 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)]

Define the surface textures for the front and back surface. These are pyramids in both cases, but because the pyramids are achieved using a chemical etch and are thus ‘pointing out’ of the surface in both cases. RayFlare defines ‘upright’ relative to the direction from which light is coming in, so the pyramids on the front surface are upright while those on the back surface are inverted (upright=False). The surface textures are used in combination with the layer stacks defined above to define the Interfaces of the cell, which are to be treated with the ‘RT_TMM’ method (ray-tracing + transfer-matrix method to correctly treat the surface layers). Then, finally, the bulk of the cell (Si) and thus the overall structure (front surface, bulk, back surface) is defined, also specifying the incidence medium above the cell (air) and the semi-infinite transmission medium behind the cell (silver).

[16]:

surf = regular_pyramids(elevation_angle=55, upright=True)
surf_back = regular_pyramids(elevation_angle=55, upright=False)

front_surf = Interface('RT_TMM', texture=surf, layers=front_materials, name='HIT_front',
                       coherent=True)
back_surf = Interface('RT_TMM', texture=surf_back, layers=back_materials, name='HIT_back',
                      coherent=True)


bulk_Si = BulkLayer(170e-6, Si, name = 'Si_bulk') # bulk thickness in m

SC = Structure([front_surf, bulk_Si, back_surf], incidence=Air, transmission=Ag)

Now we are finished setting up, we run the calculation. process_structure calculates all the relevant matrices for the front and back surfaces (this can take a while). Then calculate_RAT does the matrix multiplication (this is fast). We then extract relevant results and use them to calculate the predicted photogenerated current in the cell.

[17]:

process_structure(SC, options)

results = calculate_RAT(SC, options)

RAT = results[0]
results_per_pass = results[1]


R_per_pass = np.sum(results_per_pass['r'][0], 2)
R_0 = R_per_pass[0]
R_escape = np.sum(R_per_pass[1:, :], 0)

# only select absorbing layers, sum over passes
results_per_layer_front = np.sum(results_per_pass['a'][0], 0)

results_per_layer_back = np.sum(results_per_pass['a'][1], 0)


allres = np.flip(np.stack((results_per_layer_front[:,0],
                        results_per_layer_front[:,1]+results_per_layer_front[:,2],
                        RAT['A_bulk'][0, :],
                        results_per_layer_back[:,0] + results_per_layer_back[:,1],
                        results_per_layer_back[:,2], RAT['T'][0, :])), 0)

# calculated photogenerated current (Jsc with 100% EQE)

spectr_flux = LightSource(source_type='standard', version='AM1.5g',
                          x=wavelengths, output_units='photon_flux_per_m',
                          concentration=1).spectrum(wavelengths)[1]

Jph_Si = q * np.trapz(RAT['A_bulk'][0] * spectr_flux, wavelengths)/10 # mA/cm2

INFO: Making RT/TMM lookuptable for element 0 in structure
INFO: Making RT/TMM lookuptable for element 2 in structure
INFO: Ray tracing with TMM lookup table for element 0 in structure
INFO: Calculating matrix only for incidence theta/phi
INFO: RT calculation for wavelength = 299.0 nm
INFO: RT calculation for wavelength = 311.0 nm
INFO: RT calculation for wavelength = 324.0 nm
INFO: RT calculation for wavelength = 336.0 nm
INFO: RT calculation for wavelength = 350.0 nm
INFO: RT calculation for wavelength = 363.0 nm
INFO: RT calculation for wavelength = 378.0 nm
INFO: RT calculation for wavelength = 393.0 nm
INFO: RT calculation for wavelength = 408.0 nm
INFO: RT calculation for wavelength = 424.0 nm
INFO: RT calculation for wavelength = 441.0 nm
INFO: RT calculation for wavelength = 458.0 nm
INFO: RT calculation for wavelength = 476.0 nm
INFO: RT calculation for wavelength = 495.0 nm
INFO: RT calculation for wavelength = 515.0 nm
INFO: RT calculation for wavelength = 535.0 nm
INFO: RT calculation for wavelength = 556.0 nm
INFO: RT calculation for wavelength = 578.0 nm
INFO: RT calculation for wavelength = 601.0 nm
INFO: RT calculation for wavelength = 624.0 nm
INFO: RT calculation for wavelength = 701.0 nm
INFO: RT calculation for wavelength = 649.0 nm
INFO: RT calculation for wavelength = 818.0 nm
INFO: RT calculation for wavelength = 757.0 nm
INFO: RT calculation for wavelength = 884.0 nm
INFO: RT calculation for wavelength = 955.0 nm
INFO: RT calculation for wavelength = 1031.0 nm
INFO: RT calculation for wavelength = 1114.0 nm
INFO: RT calculation for wavelength = 1204.0 nm
INFO: RT calculation for wavelength = 850.0 nm
INFO: RT calculation for wavelength = 674.0 nm
INFO: RT calculation for wavelength = 919.0 nm
INFO: RT calculation for wavelength = 1300.0 nm
INFO: RT calculation for wavelength = 1072.0 nm
INFO: RT calculation for wavelength = 729.0 nm
INFO: RT calculation for wavelength = 787.0 nm
INFO: RT calculation for wavelength = 1251.0 nm
INFO: RT calculation for wavelength = 992.0 nm
INFO: RT calculation for wavelength = 1158.0 nm
INFO: RT calculation for wavelength = 1405.0 nm
INFO: RT calculation for wavelength = 1518.0 nm
INFO: RT calculation for wavelength = 1640.0 nm
INFO: RT calculation for wavelength = 1771.0 nm
INFO: RT calculation for wavelength = 1913.0000000000002 nm
INFO: RT calculation for wavelength = 1352.0 nm
INFO: RT calculation for wavelength = 2067.0 nm
INFO: RT calculation for wavelength = 2233.0 nm
INFO: RT calculation for wavelength = 2412.0 nm
INFO: RT calculation for wavelength = 1704.0 nm
INFO: RT calculation for wavelength = 1577.0 nm
INFO: RT calculation for wavelength = 2815.0 nm
INFO: RT calculation for wavelength = 1989.0 nm
INFO: RT calculation for wavelength = 2606.0 nm
INFO: RT calculation for wavelength = 1460.0 nm
INFO: RT calculation for wavelength = 2149.0 nm
INFO: RT calculation for wavelength = 1841.0 nm
INFO: RT calculation for wavelength = 2321.0 nm
INFO: RT calculation for wavelength = 2507.0 nm
INFO: RT calculation for wavelength = 3041.0 nm
INFO: RT calculation for wavelength = 3286.0 nm
INFO: RT calculation for wavelength = 2926.0 nm
INFO: RT calculation for wavelength = 3549.0 nm
INFO: RT calculation for wavelength = 3834.0 nm
INFO: RT calculation for wavelength = 4142.0 nm
INFO: RT calculation for wavelength = 4475.0 nm
INFO: RT calculation for wavelength = 4834.0 nm
INFO: RT calculation for wavelength = 2709.0 nm
INFO: RT calculation for wavelength = 5222.0 nm
INFO: RT calculation for wavelength = 3161.0 nm
INFO: RT calculation for wavelength = 5641.0 nm
INFO: RT calculation for wavelength = 4305.0 nm
INFO: RT calculation for wavelength = 4651.0 nm
INFO: RT calculation for wavelength = 3415.0 nm
INFO: RT calculation for wavelength = 3689.0 nm
INFO: RT calculation for wavelength = 5428.0 nm
INFO: RT calculation for wavelength = 6094.0 nm
INFO: RT calculation for wavelength = 5024.0 nm
INFO: RT calculation for wavelength = 6583.0 nm
INFO: RT calculation for wavelength = 6842.0 nm
INFO: RT calculation for wavelength = 7112.0 nm
INFO: RT calculation for wavelength = 7392.0 nm
INFO: RT calculation for wavelength = 6334.0 nm
INFO: RT calculation for wavelength = 5863.0 nm
INFO: RT calculation for wavelength = 7683.000000000001 nm
INFO: RT calculation for wavelength = 7985.000000000001 nm
INFO: RT calculation for wavelength = 8300.0 nm
INFO: RT calculation for wavelength = 3985.0 nm
INFO: RT calculation for wavelength = 8626.0 nm
INFO: RT calculation for wavelength = 8966.0 nm
INFO: RT calculation for wavelength = 9319.0 nm
INFO: RT calculation for wavelength = 9686.0 nm
INFO: RT calculation for wavelength = 10067.0 nm
INFO: RT calculation for wavelength = 11303.0 nm
INFO: RT calculation for wavelength = 10875.0 nm
INFO: RT calculation for wavelength = 10463.0 nm
INFO: RT calculation for wavelength = 11748.0 nm
INFO: RT calculation for wavelength = 12210.0 nm
INFO: RT calculation for wavelength = 12691.0 nm
INFO: RT calculation for wavelength = 13191.0 nm
INFO: RT calculation for wavelength = 13710.0 nm
INFO: RT calculation for wavelength = 14250.0 nm
INFO: RT calculation for wavelength = 14811.0 nm
INFO: RT calculation for wavelength = 16000.0 nm
INFO: RT calculation for wavelength = 15393.999999999998 nm
INFO: RT calculation for wavelength = 299.0 nm
INFO: RT calculation for wavelength = 311.0 nm
INFO: RT calculation for wavelength = 324.0 nm
INFO: RT calculation for wavelength = 336.0 nm
INFO: RT calculation for wavelength = 350.0 nm
INFO: RT calculation for wavelength = 363.0 nm
INFO: RT calculation for wavelength = 378.0 nm
INFO: RT calculation for wavelength = 393.0 nm
INFO: RT calculation for wavelength = 408.0 nm
INFO: RT calculation for wavelength = 424.0 nm
INFO: RT calculation for wavelength = 441.0 nm
INFO: RT calculation for wavelength = 476.0 nm
INFO: RT calculation for wavelength = 458.0 nm
INFO: RT calculation for wavelength = 495.0 nm
INFO: RT calculation for wavelength = 515.0 nm
INFO: RT calculation for wavelength = 535.0 nm
INFO: RT calculation for wavelength = 556.0 nm
INFO: RT calculation for wavelength = 578.0 nm
INFO: RT calculation for wavelength = 601.0 nm
INFO: RT calculation for wavelength = 624.0 nm
INFO: RT calculation for wavelength = 649.0 nm
INFO: RT calculation for wavelength = 674.0 nm
INFO: RT calculation for wavelength = 701.0 nm
INFO: RT calculation for wavelength = 729.0 nm
INFO: RT calculation for wavelength = 757.0 nm
INFO: RT calculation for wavelength = 787.0 nm
INFO: RT calculation for wavelength = 818.0 nm
INFO: RT calculation for wavelength = 850.0 nm
INFO: RT calculation for wavelength = 884.0 nm
INFO: RT calculation for wavelength = 919.0 nm
INFO: RT calculation for wavelength = 955.0 nm
INFO: RT calculation for wavelength = 992.0 nm
INFO: RT calculation for wavelength = 1031.0 nm
INFO: RT calculation for wavelength = 1072.0 nm
INFO: RT calculation for wavelength = 1114.0 nm
INFO: RT calculation for wavelength = 1158.0 nm
INFO: RT calculation for wavelength = 1204.0 nm
INFO: RT calculation for wavelength = 1251.0 nm
INFO: RT calculation for wavelength = 1300.0 nm
INFO: RT calculation for wavelength = 1352.0 nm
INFO: RT calculation for wavelength = 1405.0 nm
INFO: RT calculation for wavelength = 1460.0 nm
INFO: RT calculation for wavelength = 1518.0 nm
INFO: RT calculation for wavelength = 1577.0 nm
INFO: RT calculation for wavelength = 1640.0 nm
INFO: RT calculation for wavelength = 1704.0 nm
INFO: RT calculation for wavelength = 1771.0 nm
INFO: RT calculation for wavelength = 1841.0 nm
INFO: RT calculation for wavelength = 1913.0000000000002 nm
INFO: RT calculation for wavelength = 1989.0 nm
INFO: RT calculation for wavelength = 2067.0 nm
INFO: RT calculation for wavelength = 2149.0 nm
INFO: RT calculation for wavelength = 2233.0 nm
INFO: RT calculation for wavelength = 2321.0 nm
INFO: RT calculation for wavelength = 2412.0 nm
INFO: RT calculation for wavelength = 2507.0 nm
INFO: RT calculation for wavelength = 2606.0 nm
INFO: RT calculation for wavelength = 2709.0 nm
INFO: RT calculation for wavelength = 2815.0 nm
INFO: RT calculation for wavelength = 2926.0 nm
INFO: RT calculation for wavelength = 3041.0 nm
INFO: RT calculation for wavelength = 3161.0 nm
INFO: RT calculation for wavelength = 3286.0 nm
INFO: RT calculation for wavelength = 3415.0 nm
INFO: RT calculation for wavelength = 3549.0 nm
INFO: RT calculation for wavelength = 3689.0 nm
INFO: RT calculation for wavelength = 3834.0 nm
INFO: RT calculation for wavelength = 3985.0 nm
INFO: RT calculation for wavelength = 4142.0 nm
INFO: RT calculation for wavelength = 4305.0 nm
INFO: RT calculation for wavelength = 4475.0 nm
INFO: RT calculation for wavelength = 4651.0 nm
INFO: RT calculation for wavelength = 4834.0 nm
INFO: RT calculation for wavelength = 5024.0 nm
INFO: RT calculation for wavelength = 5222.0 nm
INFO: RT calculation for wavelength = 5428.0 nm
INFO: RT calculation for wavelength = 5641.0 nm
INFO: RT calculation for wavelength = 5863.0 nm
INFO: RT calculation for wavelength = 6094.0 nm
INFO: RT calculation for wavelength = 6334.0 nm
INFO: RT calculation for wavelength = 6583.0 nm
INFO: RT calculation for wavelength = 6842.0 nm
INFO: RT calculation for wavelength = 7112.0 nm
INFO: RT calculation for wavelength = 7392.0 nm
INFO: RT calculation for wavelength = 7683.000000000001 nm
INFO: RT calculation for wavelength = 7985.000000000001 nm
INFO: RT calculation for wavelength = 8300.0 nm
INFO: RT calculation for wavelength = 8626.0 nm
INFO: RT calculation for wavelength = 8966.0 nm
INFO: RT calculation for wavelength = 9319.0 nm
INFO: RT calculation for wavelength = 9686.0 nm
INFO: RT calculation for wavelength = 10067.0 nm
INFO: RT calculation for wavelength = 10463.0 nm
INFO: RT calculation for wavelength = 10875.0 nm
INFO: RT calculation for wavelength = 11303.0 nm
INFO: RT calculation for wavelength = 11748.0 nm
INFO: RT calculation for wavelength = 12210.0 nm
INFO: RT calculation for wavelength = 12691.0 nm
INFO: RT calculation for wavelength = 13191.0 nm
INFO: RT calculation for wavelength = 13710.0 nm
INFO: RT calculation for wavelength = 14250.0 nm
INFO: RT calculation for wavelength = 14811.0 nm
INFO: RT calculation for wavelength = 15393.999999999998 nm
INFO: RT calculation for wavelength = 16000.0 nm
INFO: Ray tracing with TMM lookup table for element 2 in structure
INFO: RT calculation for wavelength = 299.0 nm
INFO: RT calculation for wavelength = 311.0 nm
INFO: RT calculation for wavelength = 324.0 nm
INFO: RT calculation for wavelength = 336.0 nm
INFO: RT calculation for wavelength = 350.0 nm
INFO: RT calculation for wavelength = 363.0 nm
INFO: RT calculation for wavelength = 378.0 nm
INFO: RT calculation for wavelength = 424.0 nm
INFO: RT calculation for wavelength = 393.0 nm
INFO: RT calculation for wavelength = 408.0 nm
INFO: RT calculation for wavelength = 441.0 nm
INFO: RT calculation for wavelength = 458.0 nm
INFO: RT calculation for wavelength = 476.0 nm
INFO: RT calculation for wavelength = 495.0 nm
INFO: RT calculation for wavelength = 515.0 nm
INFO: RT calculation for wavelength = 535.0 nm
INFO: RT calculation for wavelength = 556.0 nm
INFO: RT calculation for wavelength = 578.0 nm
INFO: RT calculation for wavelength = 601.0 nm
INFO: RT calculation for wavelength = 624.0 nm
INFO: RT calculation for wavelength = 649.0 nm
INFO: RT calculation for wavelength = 674.0 nm
INFO: RT calculation for wavelength = 701.0 nm
INFO: RT calculation for wavelength = 729.0 nm
INFO: RT calculation for wavelength = 757.0 nm
INFO: RT calculation for wavelength = 787.0 nm
INFO: RT calculation for wavelength = 818.0 nm
INFO: RT calculation for wavelength = 850.0 nm
INFO: RT calculation for wavelength = 884.0 nm
INFO: RT calculation for wavelength = 919.0 nm
INFO: RT calculation for wavelength = 955.0 nm
INFO: RT calculation for wavelength = 992.0 nm
INFO: RT calculation for wavelength = 1031.0 nm
INFO: RT calculation for wavelength = 1072.0 nm
INFO: RT calculation for wavelength = 1114.0 nm
INFO: RT calculation for wavelength = 1158.0 nm
INFO: RT calculation for wavelength = 1204.0 nm
INFO: RT calculation for wavelength = 1251.0 nm
INFO: RT calculation for wavelength = 1300.0 nm
INFO: RT calculation for wavelength = 1352.0 nm
INFO: RT calculation for wavelength = 1405.0 nm
INFO: RT calculation for wavelength = 1460.0 nm
INFO: RT calculation for wavelength = 1518.0 nm
INFO: RT calculation for wavelength = 1577.0 nm
INFO: RT calculation for wavelength = 1640.0 nm
INFO: RT calculation for wavelength = 1704.0 nm
INFO: RT calculation for wavelength = 1771.0 nm
INFO: RT calculation for wavelength = 1841.0 nm
INFO: RT calculation for wavelength = 1913.0000000000002 nm
INFO: RT calculation for wavelength = 1989.0 nm
INFO: RT calculation for wavelength = 2067.0 nm
INFO: RT calculation for wavelength = 2149.0 nm
INFO: RT calculation for wavelength = 2233.0 nm
INFO: RT calculation for wavelength = 2321.0 nm
INFO: RT calculation for wavelength = 2412.0 nm
INFO: RT calculation for wavelength = 2507.0 nm
INFO: RT calculation for wavelength = 2606.0 nm
INFO: RT calculation for wavelength = 2709.0 nm
INFO: RT calculation for wavelength = 2815.0 nm
INFO: RT calculation for wavelength = 2926.0 nm
INFO: RT calculation for wavelength = 3161.0 nm
INFO: RT calculation for wavelength = 3041.0 nm
INFO: RT calculation for wavelength = 3286.0 nm
INFO: RT calculation for wavelength = 3415.0 nm
INFO: RT calculation for wavelength = 3549.0 nm
INFO: RT calculation for wavelength = 3689.0 nm
INFO: RT calculation for wavelength = 3834.0 nm
INFO: RT calculation for wavelength = 3985.0 nm
INFO: RT calculation for wavelength = 4142.0 nm
INFO: RT calculation for wavelength = 4305.0 nm
INFO: RT calculation for wavelength = 4475.0 nm
INFO: RT calculation for wavelength = 4651.0 nm
INFO: RT calculation for wavelength = 4834.0 nm
INFO: RT calculation for wavelength = 5024.0 nm
INFO: RT calculation for wavelength = 5222.0 nm
INFO: RT calculation for wavelength = 5428.0 nm
INFO: RT calculation for wavelength = 5641.0 nm
INFO: RT calculation for wavelength = 5863.0 nm
INFO: RT calculation for wavelength = 6094.0 nm
INFO: RT calculation for wavelength = 6334.0 nm
INFO: RT calculation for wavelength = 6583.0 nm
INFO: RT calculation for wavelength = 6842.0 nm
INFO: RT calculation for wavelength = 7112.0 nm
INFO: RT calculation for wavelength = 7392.0 nm
INFO: RT calculation for wavelength = 7985.000000000001 nm
INFO: RT calculation for wavelength = 7683.000000000001 nm
INFO: RT calculation for wavelength = 8300.0 nm
INFO: RT calculation for wavelength = 8626.0 nm
INFO: RT calculation for wavelength = 8966.0 nm
INFO: RT calculation for wavelength = 9319.0 nm
INFO: RT calculation for wavelength = 9686.0 nm
INFO: RT calculation for wavelength = 10067.0 nm
INFO: RT calculation for wavelength = 10463.0 nm
INFO: RT calculation for wavelength = 10875.0 nm
INFO: RT calculation for wavelength = 11303.0 nm
INFO: RT calculation for wavelength = 11748.0 nm
INFO: RT calculation for wavelength = 12210.0 nm
INFO: RT calculation for wavelength = 12691.0 nm
INFO: RT calculation for wavelength = 13191.0 nm
INFO: RT calculation for wavelength = 13710.0 nm
INFO: RT calculation for wavelength = 14250.0 nm
INFO: RT calculation for wavelength = 14811.0 nm
INFO: RT calculation for wavelength = 15393.999999999998 nm
INFO: RT calculation for wavelength = 16000.0 nm
INFO: After iteration 1: maximum power fraction remaining = 0.6263919217313435
INFO: After iteration 2: maximum power fraction remaining = 0.38956713166279705
INFO: After iteration 3: maximum power fraction remaining = 0.24515482469704067
INFO: After iteration 4: maximum power fraction remaining = 0.15418570734748918
INFO: After iteration 5: maximum power fraction remaining = 0.09678801368316606
INFO: After iteration 6: maximum power fraction remaining = 0.06066147968810933
INFO: After iteration 7: maximum power fraction remaining = 0.03797784796825294
INFO: After iteration 8: maximum power fraction remaining = 0.023759689844090878
INFO: After iteration 9: maximum power fraction remaining = 0.014857958555146896
INFO: After iteration 10: maximum power fraction remaining = 0.009367916110272037

Finally, plot the results:

[18]:

pal = sns.cubehelix_palette(allres.shape[0], start=.5, rot=-.9)
pal.reverse()
cols = cycler('color', pal)

params = {'legend.fontsize': 'small',
          'axes.labelsize': 'small',
          'axes.titlesize': 'small',
          'xtick.labelsize': 'small',
          'ytick.labelsize': 'small',
          'axes.prop_cycle': cols}

plt.rcParams.update(params)

# plot total R, A, T
fig = plt.figure(figsize=(5,4))
ax = plt.subplot(111)
ax.semilogx(options['wavelength']*1e6, R_escape + R_0, '--k', label=r'$R_{total}$')
ax.semilogx(options['wavelength']*1e6, R_0, '-.k', label=r'$R_0$')
ax.stackplot(options['wavelength']*1e6, allres,
             labels=['Ag', 'Back ITO', 'a-Si (back)', 'Bulk Si', 'a-Si (front)', 'Front ITO'])
ax.set_xlabel(r'Wavelength ($\mu$m)')
ax.set_ylabel('Absorption/Emissivity')
ax.set_xlim(min(options['wavelength']*1e6), max(options['wavelength']*1e6))
ax.set_ylim(0, 1)
plt.legend()
plt.show()

../_images/Examples_HIT_emissivity_11_0.png