Section 9b: Planar III-V epoxy-bonded to textured Si

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.

We 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).

Setting up

We load relevant packages and define materials, the same as in the previous example.

from solcore import material, si
from solcore.absorption_calculator import search_db, download_db
import os
from solcore.structure import Layer
from solcore.light_source import LightSource
from rayflare.ray_tracing import rt_structure
from rayflare.transfer_matrix_method import tmm_structure
from rayflare.textures import planar_surface, regular_pyramids
from rayflare.options import default_options
from solcore.constants import q
import numpy as np
import matplotlib.pyplot as plt

# download_db()

MgF2_pageid = search_db(os.path.join("MgF2", "Rodriguez-de Marcos"))[0][0];
Ta2O5_pageid = search_db(os.path.join("Ta2O5", "Rodriguez-de Marcos"))[0][0];
SU8_pageid = search_db("SU8")[0][0];
Ag_pageid = search_db(os.path.join("Ag", "Jiang"))[0][0];

epoxy = material("BK7")()

MgF2 = material(str(MgF2_pageid), nk_db=True)();
Ta2O5 = material(str(Ta2O5_pageid), nk_db=True)();
SU8 = material(str(SU8_pageid), nk_db=True)();
Ag = material(str(Ag_pageid), nk_db=True)();

window = material("AlInP")(Al=0.52)
GaInP = material("GaInP")
AlGaAs = material("AlGaAs")

Air = material("Air")()

GaAs = material("GaAs")

Si = material("Si")

Al2O3 = material("Al2O3P")()
Al = material("Al")()

We 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:

d_Si = 280e-6 # thickness of Si wafer
d_epoxy = 1e-3 # thickness of epoxy

ARC = [
    Layer(110e-9, MgF2),
    Layer(65e-9, Ta2O5),
]

GaInP_junction = [
    Layer(17e-9, window),
    Layer(400e-9, GaInP(In=0.50)),
    Layer(100e-9, AlGaAs(Al=0.8))]

# 100 nm TJ
tunnel_1 = [
    Layer(80e-9, AlGaAs(Al=0.8)),
    Layer(20e-9, GaInP(In=0.5)),
]

GaAs_junction = [
    Layer(17e-9, GaInP(In=0.5), role="window"),
    Layer(1050e-9, GaAs()),
    Layer(70e-9, AlGaAs(Al=0.8), role="bsf")]

spacer_ARC = [
    Layer(80e-9, Ta2O5),
]

Defining the cell layers

There are three interfaces in the cell which will define the structure to simulate:

1. the III-V/epoxy interface, where the epoxy itself will be treated as a bulk layer in the simulation
2. the epoxy/Si interface, where the Si has a pyramidal texture (the Si itself is another bulk layer in the simulation).
3. the 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)

These 3 interfaces are defined here, using the pre-defined textures for a planar surface or regular pyramids:

front_layers = ARC + GaInP_junction + tunnel_1 + GaAs_junction + spacer_ARC

front_surf = planar_surface(
    interface_layers = front_layers
)

Si_front = regular_pyramids(
    elevation_angle=50,
    upright=True,
)

Si_back = regular_pyramids(
    elevation_angle=50,
    upright=False,
)

Now 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.

options = default_options()

wl = np.arange(300, 1201, 10) * 1e-9
AM15G = LightSource(source_type="standard", version="AM1.5g", x=wl,
                    output_units="photon_flux_per_m")

options.wavelengths = wl
options.project_name = "III_V_Si_cell"

# options for ray-tracing
options.randomize_surface = True
options.n_rays = 1000
options.bulk_profile = False

Defining the structures

Finally, 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.

solar_cell = rt_structure(
    textures=[front_surf, Si_front, Si_back],
    materials=[epoxy, Si()],
    widths=[d_epoxy, d_Si],
    incidence=Air,
    transmission=Ag,
    options=options,
    use_TMM=True,
    save_location="current", # lookup table save location
    overwrite=True, # whether to overwrite any previously existing results, if found
)

# options for TMM
options.coherent = False
options.coherency_list = len(front_layers)*['c'] + ['i']*2

solar_cell_planar = tmm_structure(
    layer_stack = front_layers + [Layer(d_epoxy, epoxy), Layer(d_Si, Si())],
    incidence=Air,
    transmission=Ag,
)

Pre-computing TMM lookup table(s)
Database file found at /Users/phoebe/.solcore/nk/nk.db
Material main/MgF2/Rodriguez-de Marcos.yml loaded.
Database file found at /Users/phoebe/.solcore/nk/nk.db
Material main/MgF2/Rodriguez-de Marcos.yml loaded.
Database file found at /Users/phoebe/.solcore/nk/nk.db
Material main/Ta2O5/Rodriguez-de Marcos.yml loaded.
Database file found at /Users/phoebe/.solcore/nk/nk.db
Material main/Ta2O5/Rodriguez-de Marcos.yml loaded.

Calculations

Calculate the R/A/T for the planar reference cell:

tmm_result = solar_cell_planar.calculate(options=options)

GaInP_A_tmm = tmm_result['A_per_layer'][:,3]
GaAs_A_tmm = tmm_result['A_per_layer'][:,8]
Si_A_tmm = tmm_result['A_per_layer'][:,len(front_layers)+1]

Jmax_GaInP_tmm = q*np.trapz(GaInP_A_tmm*AM15G.spectrum()[1], x=wl)/10
Jmax_GaAs_tmm = q*np.trapz(GaAs_A_tmm*AM15G.spectrum()[1], x=wl)/10
Jmax_Si_tmm = q*np.trapz(Si_A_tmm*AM15G.spectrum()[1], x=wl)/10

Calculate the R/A/T for the textured cell:

rt_result = solar_cell.calculate(options=options)

GaInP_absorption_ARC = rt_result['A_per_interface'][0][:,3]
GaAs_absorption_ARC = rt_result['A_per_interface'][0][:,8]
Si_absorption_ARC = rt_result['A_per_layer'][:,1]

Jmax_GaInP = q*np.trapz(GaInP_absorption_ARC*AM15G.spectrum()[1], x=wl)/10
Jmax_GaAs = q*np.trapz(GaAs_absorption_ARC*AM15G.spectrum()[1], x=wl)/10
Jmax_Si = q*np.trapz(Si_absorption_ARC*AM15G.spectrum()[1], x=wl)/10

Plotting the results

Finally, 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.

plt.figure(figsize=(6,3))
plt.plot(wl * 1e9, GaInP_absorption_ARC, "-k", label="GaInP")
plt.plot(wl * 1e9, GaAs_absorption_ARC, "-b", label="GaAs")
plt.plot(wl * 1e9, Si_absorption_ARC, "-r", label="Si")
plt.plot(wl * 1e9, GaInP_A_tmm, "--k")
plt.plot(wl * 1e9, GaAs_A_tmm, "--b")
plt.plot(wl * 1e9, Si_A_tmm, "--r")
plt.plot(wl * 1e9, rt_result['R'], '-', color='grey', label="Reflected")
plt.plot(wl * 1e9, tmm_result['R'], '--', color='grey')

plt.text(420, 0.55, r"{:.1f} mA/cm$^2$".format(Jmax_GaInP))
plt.text(670, 0.55, r"{:.1f} mA/cm$^2$".format(Jmax_GaAs))
plt.text(870, 0.55, r"{:.1f} mA/cm$^2$".format(Jmax_Si))
plt.text(870, 0.45, r"({:.1f} mA/cm$^2)$".format(Jmax_Si_tmm))

plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.tight_layout()
plt.show()

Questions/challenges

• Does 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?
• How much current is lost to parasitic absorption in e.g. tunnel junctions, window layers etc.?
• How can we reduce reflection at the epoxy interfaces?
• If the epoxy/glass layer is much thicker than the relevant incident wavelengths, and not absorbing, does the exact thickness matter in the simulation?
• What happens if only the rear surface is textured? Would a structure without the front texture have other advantages?
• Why does the Si have lower absorption/limiting current in this structure compared to the previous example?