def equilibrium_pdd(junction, options):
""" Solves the PDD equations under equilibrium: in the dark with no external current and zero applied voltage.
:param junction: A junction object
:param options: Options to be passed to the solver
:return: None
"""
T = options.T
wl = options.wavelength
output_info = options.output_equilibrium
SetConvergenceParameters(options)
SetMeshParameters(options)
SetRecombinationParameters(options)
device = CreateDeviceStructure('Junction', T=T, layers=junction)
print('Solving equilibrium...')
output = ProcessStructure(device, options.meshpoints, wavelengths=wl)
dd.gen = 0
dd.equilibrium(output_info)
print('...done!\n')
output['Bandstructure'] = DumpBandStructure()
junction.equilibrium_data = State(**output)
def equilibrium_pdd(junction, options):
""" Solves the Poisson-DD equations under equilibrium: in the dark with no external current and zero applied voltage. Internally, it calls *ProcessStructure*. Absorption coeficients are not calculated unless *wavelengths* is given as input.
:param device: A dictionary containing the device structure. See PDD.DeviceStructure
:param output_info: Indicates how much information must be printed by the fortran solver (1=less, 2=more)
:param wavelengths: (Optional) Wavelengths at which to calculate the optical properties.
:return: Dictionary containing the device properties as a function of the position at equilibrium.
"""
T = options.T
wl = options.wavelength
output_info = options.output_equilibrium
SetConvergenceParameters(options)
SetMeshParameters(options)
SetRecombinationParameters(options)
device = CreateDeviceStructure('Junction', T=T, layers=junction)
print('Solving equilibrium...')
output = ProcessStructure(device, options.meshpoints, wavelengths=wl)
dd.gen = 0
dd.equilibrium(output_info)
print('...done!\n')
output['Bandstructure'] = DumpBandStructure()
junction.equilibrium_data = State(**output)
def test_BL_correction():
wl = np.linspace(800, 950, 4) * 1e-9
GaAs = material("GaAs")()
thick_cell = SolarCell([Layer(material=GaAs, width=si("20um"))])
opts = State()
opts.position = None
prepare_solar_cell(thick_cell, opts)
position = np.arange(0, thick_cell.width, 1e-9)
opts.position = position
opts.recalculate_absorption = True
opts.no_back_reflexion = False
opts.BL_correction = False
opts.wavelength = wl
solve_tmm(thick_cell, opts)
no_corr = thick_cell.absorbed
opts.BL_correction = True
solve_tmm(thick_cell, opts)
with_corr = thick_cell.absorbed
assert with_corr == approx(
np.array([6.71457872e-01, 6.75496354e-01, 2.09738887e-01, 0]))
assert no_corr == approx(
np.array([6.71457872e-01, 6.75496071e-01, 2.82306407e-01, 0]))
def short_circuit_pdd(junction, options):
""" Solves the devices electronic properties at short circuit. Internally, it calls Equilibrium.
:param junction: A junction object
:param options: Options to be passed to the solver
:return: None
"""
# We run equilibrium
equilibrium_pdd(junction, options)
wl = options.wavelength
wl, ph = options.light_source.spectrum(x=wl,
output_units='photon_flux_per_m')
z = junction.equilibrium_data['Bandstructure']['x']
absorption = junction.absorbed if hasattr(junction,
'absorbed') else lambda x: 0
abs_profile = CalculateAbsorptionProfile(z, wl, absorption)
dd.set_generation(abs_profile)
dd.gen = 1
dd.illumination(ph)
dd.lightsc(options.output_sc, 1)
print('...done!\n')
output = {'Bandstructure': DumpBandStructure()}
junction.short_circuit_data = State(**output)
def qe_pdd(junction, options):
""" Calculates the quantum efficiency of the device at short circuit. Internally it calls ShortCircuit
:param device: A dictionary containing the device structure. See PDD.DeviceStructure
:param wavelengths: Array with the wavelengths (in m)
:param photon_flux: Array with the photon_flux (in photons/m2/m) corresponding to the above wavelengths
:param output_info: Indicates how much information must be printed by the fortran solver (0=min, 2=max)
:param rs: Series resistance. Default=0
:return: The internal and external quantum efficiencies, in adition to the output of ShortCircuit.
"""
print('Solving quantum efficiency...')
output_info = options.output_qe
short_circuit_pdd(junction, options)
dd.runiqe(output_info)
print('...done!\n')
output = {}
output['QE'] = DumpQE()
output['QE']['wavelengths'] = options.wavelength
junction.qe_data = State(**output)
# The EQE is actually the IQE inside the fortran solver due to an error in the naming --> to be changed
junction.eqe = interp1d(options.wavelength,
output['QE']['IQE'],
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(output['QE']['IQE'][0],
output['QE']['IQE'][-1]))
def qe_pdd(junction, options):
""" Calculates the quantum efficiency of the device at short circuit. Internally it calls ShortCircuit
:param junction: A junction object
:param options: Options to be passed to the solver
:return: None
"""
print('Solving quantum efficiency...')
output_info = options.output_qe
short_circuit_pdd(junction, options)
dd.runiqe(output_info)
print('...done!\n')
output = {}
output['QE'] = DumpQE()
output['QE']['WL'] = options.wavelength
z = junction.short_circuit_data['Bandstructure']['x']
absorbed_per_wl = np.trapz(junction.absorbed(z), z, axis=0)
# This is redundant but useful to keep the same format than the other solvers
junction.qe = State(**output['QE'])
junction.qe['IQE'] = junction.qe['EQE'] / np.maximum(
absorbed_per_wl, 0.00001)
# The EQE is actually the IQE inside the fortran solver due to an error in the naming --> to be changed
junction.eqe = interp1d(options.wavelength,
output['QE']['EQE'],
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(output['QE']['EQE'][0],
output['QE']['EQE'][-1]))
def qe_detailed_balance(junction, wl):
""" Calculates the EQE and the IQE in the detailed balanced limit... which is equal to the absorptance and the absorbed fraction of the light since, by definition of detailed balanced, the carrier collection is perfect.
:param junction: Junction object of kind "DB"
:param wl: wavelength in m
:return: None
"""
absorptance_detailed_balance(junction)
# This is true just in the detailed balance limit
junction.iqe = junction.absorptance
try:
z = np.linspace(0, junction.width, 1001)
all_abs = junction.absorbed(z)
abs_vs_wl = np.trapz(all_abs, z, axis=0)
junction.eqe = interp1d(wl,
abs_vs_wl,
bounds_error=False,
fill_value=(0, 0))
except AttributeError:
junction.eqe = junction.absorptance
junction.qe = State({
'WL': wl,
'IQE': junction.iqe(wl),
'EQE': junction.eqe(wl)
})
def test_process_junction_pn():
from solcore.analytic_solar_cells.depletion_approximation import identify_layers, identify_parameters
from solcore import material
from solcore.structure import Layer, Junction
from solcore.state import State
Na = np.power(10, np.random.uniform(22, 25))
Nd = np.power(10, np.random.uniform(23, 26))
options = State()
options.T = np.random.uniform(250, 350)
Lp = np.power(10, np.random.uniform(-9, -6)) # Diffusion length
Ln = np.power(10, np.random.uniform(-9, -6)) # Diffusion length
GaAs_n = material("GaAs")(Nd=Nd, hole_diffusion_length=Ln)
GaAs_p = material("GaAs")(Na=Na, electron_diffusion_length=Lp)
p_width = np.random.uniform(500, 1000)*1e-9
n_width = np.random.uniform(3000, 5000)*1e-9
test_junc = Junction([Layer(p_width, GaAs_p, role="emitter"), Layer(n_width, GaAs_n, role="base")])
id_top, id_bottom, pRegion, nRegion, iRegion, pn_or_np = identify_layers(test_junc)
xn, xp, xi, sn, sp, ln, lp, dn, dp, Nd_c, Na_c, ni, es = identify_parameters(test_junc, options.T, pRegion, nRegion, iRegion)
ni_expect = GaAs_n.ni
assert [id_top, id_bottom] == approx([0, 1])
assert pn_or_np == 'pn'
assert [xn, xp, xi, sn, sp, ln, lp, dn, dp, Nd_c, Na_c, ni, es] == approx([n_width, p_width, 0, 0, 0, Lp, Ln, GaAs_n.hole_mobility * kb * options.T / q,
GaAs_p.electron_mobility * kb * options.T / q, Nd, Na, ni_expect, GaAs_n.permittivity])
def qe_pdd(junction, options):
""" Calculates the quantum efficiency of the device at short circuit. Internally it calls ShortCircuit
:param junction: A junction object
:param options: Options to be passed to the solver
:return: None
"""
print('Solving quantum efficiency...')
output_info = options.output_qe
short_circuit_pdd(junction, options)
dd.runiqe(output_info)
print('...done!\n')
output = {}
output['QE'] = DumpQE()
output['QE']['wavelengths'] = options.wavelength
junction.qe_data = State(**output['QE'])
# The EQE is actually the IQE inside the fortran solver due to an error in the naming --> to be changed
junction.eqe = interp1d(options.wavelength,
output['QE']['EQE'],
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(output['QE']['EQE'][0],
output['QE']['EQE'][-1]))
def short_circuit_pdd(junction, options):
""" Solves the devices electronic properties at short circuit. Internally, it calls Equilibrium.
:param device: A dictionary containing the device structure. See PDD.DeviceStructure
:param output_info: Indicates how much information must be printed by the fortran solver (0=min, 2=max)
:param rs: Series resistance. Default=0
:param wavelengths: Array with the wavelengths (in m)
:param photon_flux: Array with the photon_flux (in photons/m2/m) corresponding to the above wavelengths
:return: A dictionary containing the device properties as a function of the position at short circuit.
"""
# We run equilibrium
equilibrium_pdd(junction, options)
wl = options.wavelength
wl, ph = options.light_source.spectrum(x=wl,
output_units='photon_flux_per_m')
z = junction.equilibrium_data['Bandstructure']['x']
absorption = junction.absorbed if hasattr(junction,
'absorbed') else lambda x: 0
abs_profile = CalculateAbsorptionProfile(z, wl, absorption)
dd.set_generation(abs_profile)
dd.gen = 1
dd.illumination(ph)
dd.lightsc(options.output_sc, 1)
print('...done!\n')
output = {'Bandstructure': DumpBandStructure()}
junction.short_circuit_data = State(**output)
def test_process_junction_set_in_junction():
from solcore.analytic_solar_cells.depletion_approximation import identify_layers, identify_parameters
from solcore import material
from solcore.structure import Layer, Junction
from solcore.state import State
options = State()
options.T = np.random.uniform(250, 350)
Lp = np.power(10, np.random.uniform(-9, -6)) # Diffusion length
Ln = np.power(10, np.random.uniform(-9, -6)) # Diffusion length
sn = np.power(10, np.random.uniform(0, 3))
sp = np.power(10, np.random.uniform(0, 3))
se = np.random.uniform(1, 20) * vacuum_permittivity
GaAs_n = material("GaAs")()
GaAs_p = material("GaAs")()
GaAs_i = material("GaAs")()
p_width = np.random.uniform(500, 1000)
n_width = np.random.uniform(3000, 5000)
i_width = np.random.uniform(100, 300) * 1e-9
mun = np.power(10, np.random.uniform(-5, 0))
mup = np.power(10, np.random.uniform(-5, 0))
Vbi = np.random.uniform(0, 3)
test_junc = Junction([
Layer(p_width, GaAs_p, role="emitter"),
Layer(i_width, GaAs_i, role="intrinsic"),
Layer(n_width, GaAs_n, role="base")
],
sn=sn,
sp=sp,
permittivity=se,
ln=Ln,
lp=Lp,
mup=mup,
mun=mun,
Vbi=Vbi)
id_top, id_bottom, pRegion, nRegion, iRegion, pn_or_np = identify_layers(
test_junc)
xn, xp, xi, sn_c, sp_c, ln, lp, dn, dp, Nd_c, Na_c, ni, es = identify_parameters(
test_junc, options.T, pRegion, nRegion, iRegion)
ni_expect = GaAs_n.ni
assert [id_top, id_bottom] == approx([0, 2])
assert pn_or_np == 'pn'
assert [xn, xp, xi, sn_c, sp_c, ln, lp, dn, dp, Nd_c, Na_c, ni,
es] == approx([
n_width, p_width, i_width, sn, sp, Ln, Lp,
mun * kb * options.T / q, mup * kb * options.T / q, 1, 1,
ni_expect, se
])
def merge_dicts(*dict_args):
"""
Given any number of dicts, shallow copy and merge into a new dict,
precedence goes to key value pairs in latter dicts.
"""
result = State()
for dictionary in dict_args:
result.update(dictionary)
return result
def da_options():
from solcore.state import State
options = State()
wl = np.linspace(290, 700, 150) * 1e-9
options.T = np.random.uniform(250, 350)
options.wavelength = wl
options.light_source = da_light_source()
options.position = None
options.internal_voltages = np.linspace(-6, 4, 20)
return options
def test_state():
array1 = np.array([1, 2, 3])
array2 = np.array([2, 3, 4])
state1 = State()
state1.a = 1
state1.b = True
state1.c = array1
assert state1.__len__() == 3
assert state1.a == 1
assert state1.b == True
assert all([input == output for input, output in zip(array1, state1.c)])
state2 = State()
state2.b = False
state2.d = array2
state1.update(state2)
assert state1.__len__() == 4
assert state1.a == 1
assert state2.b == False
assert all([input == output for input, output in zip(array1, state1.c)])
assert all([input == output for input, output in zip(array2, state1.d)])
def test_inc_coh_tmm():
GaInP = material("GaInP")(In=0.5)
GaAs = material("GaAs")()
Ge = material("Ge")()
optical_struct = SolarCell([
Layer(material=GaInP, width=si("5000nm")),
Layer(material=GaAs, width=si("200nm")),
Layer(material=GaAs, width=si("5um")),
Layer(material=Ge, width=si("50um")),
])
wl = np.linspace(400, 1200, 5) * 1e-9
options = State()
options.wavelength = wl
options.optics_method = "TMM"
options.no_back_reflection = False
options.BL_correction = True
options.recalculate_absorption = True
c_list = [
["c", "c", "c", "c"],
["c", "c", "c", "i"],
["c", "i", "i", "c"],
["i", "i", "i", "i"],
]
results = []
for i1, cl in enumerate(c_list):
options.coherency_list = cl
solar_cell_solver(optical_struct, "optics", options)
results.append(optical_struct.absorbed)
A_calc = np.stack(results)
A_data = np.array(
[[0.5742503, 0.67956899, 0.73481184, 0.725372, 0.76792856],
[0.5742503, 0.67956899, 0.73481184, 0.725372, 0.76792856],
[0.5742503, 0.67956899, 0.73474943, 0.70493469, 0.70361194],
[0.5742503, 0.67956899, 0.70927724, 0.71509221, 0.71592772]])
assert A_calc == approx(A_data)
import math
from scipy.interpolate import interp1d
import numpy as np
from solcore.constants import kb, q, c, h
from solcore import si
from solcore.state import State
db_options = State()
db_options.db_mode = 'boltzmann'
def iv_detailed_balance(junction, options):
""" Calculates the IV curve of a junction of kind "DB". This is a detailed balanced calculation of the IV curve of a PN junction characterized by a certain eqe, temperature and chemical potential (voltage). Normally, the eqe will be calculated based on a a given absorption edge and absorptance level resulting in a "top hat" type of eqe, but it can also be provided externally. By default, the solver uses the Boltzmann aproximation, although the full Planck equation might be used, also.
:param junction: A Junction object of kind "DB"
:param options: Other arguments for the calculation of the IV.
:return:
"""
T = options.T
light = options.light_iv
mode = options.db_mode
Ta = options.T_ambient
wl = options.wavelength
try:
Eg = junction.Eg
n = junction.n
if not hasattr(junction, 'eqe'):
qe_detailed_balance(junction, wl)
def iv_pdd(junction, options):
""" Calculates the IV curve of the device between 0 V and a given voltage. Depending on the options, the IV will be calculated in the dark (calling the equilibrium_pdd function) or under illumination (calling the short_circuit_pdd function). If the voltage range has possitive and negative values, the problem is solved twice: from 0 V to the maximu positive and from 0 V to the maximum negative, concatenating the results afterwards.
:param junction: A junction object
:param options: Options to be passed to the solver
:return: None
"""
print('Solving IV...')
light = options.light_iv
output_info = options.output_iv
T = options.T
junction.voltage = options.internal_voltages
Eg = 10
for layer in junction:
Eg = min([Eg, layer.material.band_gap / q])
s = True if junction[0].material.Na >= junction[0].material.Nd else False
if s:
vmax = min(Eg + 3 * kb * T / q, max(junction.voltage))
vmin = min(junction.voltage)
else:
vmax = max(junction.voltage)
vmin = max(-Eg - 3 * kb * T / q, min(junction.voltage))
vstep = junction.voltage[1] - junction.voltage[0]
# POSITIVE RANGE
output_pos = None
if vmax > 0:
if light:
short_circuit_pdd(junction, options)
else:
equilibrium_pdd(junction, options)
dd.runiv(vmax, vstep, output_info, 0)
output_pos = {'Bandstructure': DumpBandStructure(), 'IV': DumpIV()}
# NEGATIVE RANGE
output_neg = None
if vmin < 0:
if light:
short_circuit_pdd(junction, options)
else:
equilibrium_pdd(junction, options)
dd.runiv(vmin, (-1 * vstep), output_info, 0)
output_neg = {'Bandstructure': DumpBandStructure(), 'IV': DumpIV()}
print('...done!\n')
# Now we need to put together the data for the possitive and negative regions.
junction.pdd_data = State({
'possitive_V': output_pos,
'negative_V': output_neg
})
if output_pos is None:
V = output_neg['IV']['V']
J = output_neg['IV']['J']
Jrad = output_neg['IV']['Jrad']
Jsrh = output_neg['IV']['Jsrh']
Jaug = output_neg['IV']['Jaug']
Jsur = output_neg['IV']['Jsur']
elif output_neg is None:
V = output_pos['IV']['V']
J = output_pos['IV']['J']
Jrad = output_pos['IV']['Jrad']
Jsrh = output_pos['IV']['Jsrh']
Jaug = output_pos['IV']['Jaug']
Jsur = output_pos['IV']['Jsur']
else:
V = np.concatenate(
(output_neg['IV']['V'][:0:-1], output_pos['IV']['V']))
J = np.concatenate(
(output_neg['IV']['J'][:0:-1], output_pos['IV']['J']))
Jrad = np.concatenate(
(output_neg['IV']['Jrad'][:0:-1], output_pos['IV']['Jrad']))
Jsrh = np.concatenate(
(output_neg['IV']['Jsrh'][:0:-1], output_pos['IV']['Jsrh']))
Jaug = np.concatenate(
(output_neg['IV']['Jaug'][:0:-1], output_pos['IV']['Jaug']))
Jsur = np.concatenate(
(output_neg['IV']['Jsur'][:0:-1], output_pos['IV']['Jsur']))
# Finally, we calculate the currents at the desired voltages
R_shunt = min(junction.R_shunt, 1e14) if hasattr(junction,
'R_shunt') else 1e14
junction.current = np.interp(junction.voltage, V,
J) + junction.voltage / R_shunt
Jrad = np.interp(junction.voltage, V, Jrad)
Jsrh = np.interp(junction.voltage, V, Jsrh)
Jaug = np.interp(junction.voltage, V, Jaug)
Jsur = np.interp(junction.voltage, V, Jsur)
junction.iv = interp1d(junction.voltage,
junction.current,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(junction.current[0],
junction.current[-1]))
junction.recombination_currents = State({
"Jrad": Jrad,
"Jsrh": Jsrh,
"Jaug": Jaug,
"Jsur": Jsur
})
def iv_depletion(junction, options):
""" Calculates the IV curve of a junction object using the depletion approximation as described in J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003). The junction is then updated with an "iv" function that calculates the IV curve at any voltage.
:param junction: A junction object.
:param options: Solver options.
:return: None.
"""
science_reference(
'Depletion approximation',
'J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003).'
)
junction.voltage = options.internal_voltages
T = options.T
# First we have to figure out if we are talking about a PN, NP, PIN or NIP junction
sn = 0 if not hasattr(junction, "sn") else junction.sn
sp = 0 if not hasattr(junction, "sp") else junction.sp
# We search for the emitter and check if it is n-type or p-type
idx = 0
pn_or_np = 'pn'
for layer in junction:
if layer.role is not 'emitter':
idx += 1
else:
Na = 0
Nd = 0
if hasattr(layer.material, 'Na'): Na = layer.material.Na
if hasattr(layer.material, 'Nd'): Nd = layer.material.Nd
if Na < Nd:
pn_or_np = "np"
nRegion = junction[idx]
else:
pRegion = junction[idx]
id_top = idx
break
# Now we check for an intrinsic region and, if there is, for the base.
if junction[idx + 1].role is 'intrinsic':
iRegion = junction[idx + 1]
if junction[idx + 2].role is 'base':
if pn_or_np == "pn":
nRegion = junction[idx + 2]
nidx = idx + 2
else:
pRegion = junction[idx + 2]
pidx = idx + 2
id_bottom = idx + 2
else:
raise RuntimeError(
'ERROR processing junctions: A layer following the "intrinsic" layer must be defined as '
'"base".')
# If there is no intrinsic region, we check directly the base
elif junction[idx + 1].role is 'base':
if pn_or_np == "pn":
nRegion = junction[idx + 1]
nidx = idx + 1
else:
pRegion = junction[idx + 1]
pidx = idx + 1
iRegion = None
id_bottom = idx + 1
else:
raise RuntimeError(
'ERROR processing junctions: A layer following the "emitter" must be defined as "intrinsic"'
'or "base".')
# With all regions identified, it's time to start doing calculations
kbT = kb * T
Egap = nRegion.material.band_gap
R_shunt = min(junction.R_shunt, 1e14) if hasattr(junction,
'R_shunt') else 1e14
xp = pRegion.width
xn = nRegion.width
xi = 0 if iRegion is None else iRegion.width
# Now we have to get all the material parameters needed for the calculation
if hasattr(junction, "dielectric_constant"):
es = junction.dielectric_constant
else:
es = nRegion.material.permittivity * vacuum_permittivity # equal for n and p. I hope.
# For the diffusion lenght, subscript n and p refer to the carriers, electrons and holes
if hasattr(junction, "ln"):
ln = junction.ln
else:
ln = pRegion.material.electron_diffusion_length
if hasattr(junction, "lp"):
lp = junction.lp
else:
lp = nRegion.material.hole_diffusion_length
# For the diffusion coefficient, n and p refer to the regions, n side and p side. Yeah, it's confusing...
if hasattr(junction, "mup"):
dp = junction.mup * kbT / q
else:
dp = pRegion.material.electron_mobility * kbT / q
if hasattr(junction, "mun"):
dn = junction.mun * kbT / q
else:
dn = nRegion.material.hole_mobility * kbT / q
# Effective masses and effective density of states
mEff_h = nRegion.material.eff_mass_hh_z * electron_mass
mEff_e = pRegion.material.eff_mass_electron * electron_mass
Nv = 2 * (mEff_h * kb * T / (2 * pi * hbar**2))**1.5 # Jenny p58
Nc = 2 * (mEff_e * kb * T / (2 * pi * hbar**2))**1.5
niSquared = Nc * Nv * np.exp(-Egap / (kb * T))
ni = np.sqrt(niSquared)
Na = pRegion.material.Na
Nd = nRegion.material.Nd
Vbi = (kbT / q) * np.log(Nd * Na / niSquared) if not hasattr(
junction, "Vbi") else junction.Vbi # Jenny p146
# And now we account for the possible applied voltage, which can be, at most, equal to Vbi
V = np.where(junction.voltage < Vbi - 0.001, junction.voltage, Vbi - 0.001)
# It's time to calculate the depletion widths
if not hasattr(junction, "wp") or not hasattr(junction, "wn"):
if hasattr(
junction, "depletion_approximation"
) and junction.depletion_approximation == "one-sided abrupt":
print(
"using one-sided abrupt junction approximation for depletion width"
)
science_reference(
"Sze abrupt junction approximation",
"Sze: The Physics of Semiconductor Devices, 2nd edition, John Wiley & Sons, Inc (2007)"
)
wp = np.sqrt(2 * es * (Vbi - V) / (q * Na))
wn = np.sqrt(2 * es * (Vbi - V) / (q * Nd))
else:
wn = (-xi + np.sqrt(xi**2 + 2. * es * (Vbi - V) / q *
(1 / Na + 1 / Nd))) / (1 + Nd / Na)
wp = (-xi + np.sqrt(xi**2 + 2. * es * (Vbi - V) / q *
(1 / Na + 1 / Nd))) / (1 + Na / Nd)
wn = wn if not hasattr(junction, "wn") else junction.wn
wp = wp if not hasattr(junction, "wp") else junction.wp
w = wn + wp + xi
# Now it is time to calculate currents
if pn_or_np == "pn":
l_top, l_bottom = ln, lp
x_top, x_bottom = xp, xn
w_top, w_bottom = wp, wn
s_top, s_bottom = sp, sn
d_top, d_bottom = dp, dn
min_top, min_bot = niSquared / Na, niSquared / Nd
else:
l_bottom, l_top = ln, lp
x_bottom, x_top = xp, xn
w_bottom, w_top = wp, wn
s_bottom, s_top = sp, sn
d_bottom, d_top = dp, dn
min_bot, min_top = niSquared / Na, niSquared / Nd
JtopDark = get_j_top(x_top, w_top, l_top, s_top, d_top, V, min_top, T)
JbotDark = get_j_bot(x_bottom, w_bottom, l_bottom, s_bottom, d_bottom, V,
min_bot, T)
# hereby we define the subscripts to refer to the layer in which the current is generated:
if pn_or_np == "pn":
JnDark, JpDark = JbotDark, JtopDark
else:
JpDark, JnDark = JbotDark, JtopDark
# These might not be the right lifetimes. Actually, they are not as they include all recombination processes, not
# just SRH recombination, which is what the equation in Jenny, p159 refers to. Let´ leave them, for now.
lifetime_n = ln**2 / dn
lifetime_p = lp**2 / dp # Jenny p163
# Here we use the full version of the SRH recombination term as calculated by Sah et al. Works for positive bias
# and moderately negative ones.
science_reference(
'SRH current term.',
'C. T. Sah, R. N. Noyce, and W. Shockley, “Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics,” presented at the Proceedings of the IRE, 1957, vol. 45, no. 9, pp. 1228–1243.'
)
Jrec = get_Jsrh(ni, V, Vbi, lifetime_p, lifetime_n, w, kbT)
J_sc_top = 0
J_sc_bot = 0
J_sc_scr = 0
if options.light_iv:
widths = []
for layer in junction:
widths.append(layer.width)
cum_widths = np.cumsum([0] + widths)
g = junction.absorbed
wl = options.wavelength
wl_sp, ph = options.light_source.spectrum(
output_units='photon_flux_per_m', x=wl)
id_v0 = np.argmin(abs(V))
# The contribution from the Emitter (top side).
xa = cum_widths[id_top]
xb = cum_widths[id_top + 1] - w_top[id_v0]
deriv = get_J_sc_diffusion(xa,
xb,
g,
d_top,
l_top,
min_top,
s_top,
wl,
ph,
side='top')
J_sc_top = q * d_top * abs(deriv)
# The contribution from the Base (bottom side).
xa = cum_widths[id_bottom] + w_bottom[id_v0]
xb = cum_widths[id_bottom + 1]
deriv = get_J_sc_diffusion(xa,
xb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
wl,
ph,
side='bottom')
J_sc_bot = q * d_bottom * abs(deriv)
# The contribution from the SCR (includes the intrinsic region, if present).
xa = cum_widths[id_top + 1] - w_top[id_v0]
xb = cum_widths[id_bottom] + w_bottom[id_v0]
J_sc_scr = q * get_J_sc_SCR(xa, xb, g, wl, ph)
# And, finally, we output the currents
junction.current = Jrec + JnDark + JpDark + V / R_shunt - J_sc_top - J_sc_bot - J_sc_scr
junction.iv = interp1d(junction.voltage,
junction.current,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(junction.current[0],
junction.current[-1]))
junction.region_currents = State({
"Jn_dif": JnDark,
"Jp_dif": JpDark,
"Jscr_srh": Jrec,
"J_sc_top": J_sc_top,
"J_sc_bot": J_sc_bot,
"J_sc_scr": J_sc_scr
})
from solcore import asUnit, constants from solcore.state import State from .ddModel import driftdiffusion as dd from .DeviceStructure import LoadAbsorption, CreateDeviceStructure, CalculateAbsorptionProfile Epsi0 = constants.vacuum_permittivity q = constants.q pi = constants.pi h = constants.h kb = constants.kb m0 = constants.electron_mass log = dd.log_file pdd_options = State() # Mesh control pdd_options.meshpoints = -400 pdd_options.growth_rate = 0.7 pdd_options.coarse = 20e-9 pdd_options.fine = 1e-9 pdd_options.ultrafine = 0.2e-9 # Convergence control pdd_options.clamp = 20 pdd_options.nitermax = 100 pdd_options.ATol = 1e-14 pdd_options.RTol = 1e-6 # Recombination control
def strain_calculation_parameters(substrate_material,
layer_material,
should_print=False,
SO=False):
"""Will extract materials parameters and perform a bit of conditioning to the values.
Returns a solcore State object with the following keys:
-- ac, the conduction band deformation potential
-- av, the valence band deformation potential
-- b, the valence band splitting deformation potential
-- C11, element of the elastic stiffness tensor
-- C12, element of the elastic stiffness tensor
-- a0, the unstrained substrate lattice constant
-- a, the unstrained layer lattice constant
-- epsilon, in-plain strain
-- epsilon_perp, out-plain strain
-- e_xx, in-plain strain (e_xx = epsilon)
-- e_yy, in-plain strain (e_yy = epsilon)
-- e_zz, out-plain strain (e_zz = epsilon_perp)
-- Tre, element of come matrix (Tre = e_xx + e_yy + e_zz)
-- Pe, parameter use by Chuang
-- Qe, parameter use by Chuang
-- cb_hydrostatic_shift, CB moved by this amount
-- vb_hydrostatic_shift, VB moved by this amount
-- vb_shear_splitting, VB split by this amount (i.e. HH/LH separation)
-- delta_Ec, final conduction band shift
-- delta_Elh, final light hole band shift
-- delta_Ehh, final heavy hole band shift
Care has to be taken when calculating the energy shifts because different
sign conversion are used by different authors. Here we use the approach of
S. L. Chuang, 'Physics of optoelectronic devices'.
Note that this requires that the 'a_v' deformation potential to be
positive, where as Vurgaftman defines this a negative!
"""
sub = substrate_material
mat = layer_material
k = State()
# deformation potentials
k.av = abs(mat.a_v) # make sure that av is positive for this calculation
k.ac = mat.a_c # Vurgaftman uses the convention that this is negative
k.b = mat.b
# Matrix elements from elastic stiffness tensor
k.C11 = mat.c11
k.C12 = mat.c12
if should_print: print(sub, mat)
# Strain fractions
k.a0 = sub.lattice_constant
k.a = mat.lattice_constant
k.epsilon = (k.a0 - k.a) / k.a # in-plain strain
k.epsilon_perp = -2 * k.C12 / k.C11 * k.epsilon # out-plain
k.e_xx = k.epsilon
k.e_yy = k.epsilon
k.e_zz = k.epsilon_perp
k.Tre = (k.e_xx + k.e_yy + k.e_zz)
k.Pe = -k.av * k.Tre
k.Qe = -k.b / 2 * (k.e_xx + k.e_yy - 2 * k.e_zz)
k.cb_hydrostatic_shift = k.ac * k.Tre
k.vb_hydrostatic_shift = k.av * k.Tre
k.vb_shear_splitting = 2 * k.b * (1 + 2 * k.C12 / k.C11) * k.epsilon
# Shifts and splittings
k.delta_Ec = k.ac * k.Tre
if should_print: print(k.ac, k.Tre)
k.delta_Ehh = -k.Pe - k.Qe
k.delta_Elh = -k.Pe + k.Qe
k.delta_Eso = 0.0
if SO:
k.delta = mat.spin_orbit_splitting
shift = k.delta**2 + 2 * k.delta * k.Qe + 9 * k.Qe**2
k.delta_Elh = -k.Pe + 0.5 * (k.Qe - k.delta + np.sqrt(shift))
k.delta_Eso = -k.Pe + 0.5 * (k.Qe - k.delta - np.sqrt(shift))
strain_calculation_asserts(k, should_print=should_print)
if should_print:
print()
print("Lattice:")
print("a0", k.a0)
print("a", k.a)
print()
print("Deformation potentials:")
print("ac = ", solcore.asUnit(k.ac, 'eV'))
print("av = ", solcore.asUnit(k.av, 'eV'))
print("ac - av = ", solcore.asUnit(k.ac - k.av, 'eV'))
print("b = ", solcore.asUnit(k.b, 'eV'))
print()
print("Matrix elements from elastic stiffness tensor:")
print("C_11 = ", solcore.asUnit(k.C11, "GPa"))
print("C_12 = ", solcore.asUnit(k.C12, "GPa"))
print()
print("Strain fractions:")
print("e_xx = e_yy = epsilon = ", k.epsilon)
print("e_zz = epsilon_perp = ", k.epsilon_perp)
print("e_xx + e_yy + e_zz = Tre = ", k.Tre)
print()
print("Shifts and splittings:")
print("Pe = -av * Tre = ", solcore.asUnit(k.Pe, 'eV'))
print("Qe = -b/2*(e_xx + e_yy - 2*e_zz) = ",
solcore.asUnit(k.Qe, 'eV'))
print("dEc = ac * Tre = ", solcore.asUnit(k.delta_Ec, 'eV'))
print("dEhh = av * Tre + b[1 + 2*C_11/C_12]*epsilon = -Pe - Qe = ",
solcore.asUnit(k.delta_Ehh, 'eV'))
print("dElh = av * Tre - b[1 + 2*C_11/C_12]*epsilon = -Pe + Qe = ",
solcore.asUnit(k.delta_Elh, 'eV'))
print()
return k
from solcore.structure import Layer, Junction, TunnelJunction
from solcore.absorption_calculator import calculate_rat_rcwa, calculate_absorption_profile_rcwa
import numpy as np
import types
from solcore.state import State
rcwa_options = State()
rcwa_options.size = [500, 500]
rcwa_options.orders = 4
rcwa_options.theta = 0
rcwa_options.phi = 0
rcwa_options.pol = 'u'
def solve_rcwa(solar_cell, options):
""" Calculates the reflection, transmission and absorption of a solar cell object using the transfer matrix method
:param solar_cell:
:param options:
:return:
"""
wl = options.wavelength
# We include the shadowing losses
initial = (1 - solar_cell.shading) if hasattr(solar_cell, 'shading') else 1
# Now we calculate the absorbed and transmitted light. We first get all the relevant parameters from the objects
widths = []
offset = 0
all_layers = []
Layer(si("200nm"), material=bot_cell_n_material, role='emitter'),
Layer(si("29800nm"), material=bot_cell_p_material, role='base')
],
sn=1,
sp=1,
kind='DA')
]
# And, finally, we put everything together, adding also the surface recombination velocities sn and sp.
# setting kind = 'DA' in the Junction definition tells the electrical solver later to use the depletion approximation
optical_struct = SolarCell(ARC + top_junction + middle_junction + DBRa + DBRb +
DBRc + bottom_junction,
shading=0.05)
wl = np.linspace(250, 1700, 400) * 1e-9
options = State()
options.wavelength = wl
options.optics_method = 'TMM'
options.no_back_reflection = False
options.pol = 'p'
options.BL_correction = True
options.coherency_list = 111 * ['c']
options.theta = 30
solar_cell_solver(optical_struct, 'qe', options)
plt.figure()
plt.plot(
wl * 1e9,
optical_struct[0].layer_absorption + optical_struct[1].layer_absorption)
plt.plot(wl * 1e9, optical_struct[2].layer_absorption)
plt.plot(wl * 1e9, optical_struct[3].layer_absorption)
def iv_depletion(junction, options):
""" Calculates the IV curve of a junction object using the depletion approximation as described in J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003). The junction is then updated with an "iv" function that calculates the IV curve at any voltage.
:param junction: A junction object.
:param options: Solver options.
:return: None.
"""
science_reference(
'Depletion approximation',
'J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003).'
)
junction.voltage = options.internal_voltages
T = options.T
kbT = kb * T
id_top, id_bottom, pRegion, nRegion, iRegion, pn_or_np = identify_layers(
junction)
xn, xp, xi, sn, sp, ln, lp, dn, dp, Nd, Na, ni, es = identify_parameters(
junction, T, pRegion, nRegion, iRegion)
niSquared = ni**2
Vbi = (kbT / q) * np.log(Nd * Na / niSquared) if not hasattr(
junction, "Vbi") else junction.Vbi # Jenny p146
#Na, Nd, ni, niSquared, xi, ln, lp, xn, xp, sn, sp, dn, dp, es, id_top, id_bottom, Vbi, pn_or_np = process_junction(junction, options)
R_shunt = min(junction.R_shunt, 1e14) if hasattr(junction,
'R_shunt') else 1e14
# And now we account for the possible applied voltage, which can be, at most, equal to Vbi
V = np.where(junction.voltage < Vbi - 0.001, junction.voltage, Vbi - 0.001)
wn, wp = get_depletion_widths(junction, es, Vbi, V, Na, Nd, xi)
w = wn + wp + xi
# Now it is time to calculate currents
if pn_or_np == "pn":
l_top, l_bottom = ln, lp
x_top, x_bottom = xp, xn
w_top, w_bottom = wp, wn
s_top, s_bottom = sp, sn
d_top, d_bottom = dp, dn
min_top, min_bot = niSquared / Na, niSquared / Nd
else:
l_bottom, l_top = ln, lp
x_bottom, x_top = xp, xn
w_bottom, w_top = wp, wn
s_bottom, s_top = sp, sn
d_bottom, d_top = dp, dn
min_bot, min_top = niSquared / Na, niSquared / Nd
JtopDark = get_j_dark(x_top, w_top, l_top, s_top, d_top, V, min_top, T)
JbotDark = get_j_dark(x_bottom, w_bottom, l_bottom, s_bottom, d_bottom, V,
min_bot, T)
# hereby we define the subscripts to refer to the layer in which the current is generated:
if pn_or_np == "pn":
JnDark, JpDark = JbotDark, JtopDark
else:
JpDark, JnDark = JbotDark, JtopDark
# These might not be the right lifetimes. Actually, they are not as they include all recombination processes, not
# just SRH recombination, which is what the equation in Jenny, p159 refers to. Let´ leave them, for now.
lifetime_n = ln**2 / dn
lifetime_p = lp**2 / dp # Jenny p163
# Here we use the full version of the SRH recombination term as calculated by Sah et al. Works for positive bias
# and moderately negative ones.
science_reference(
'SRH current term.',
'C. T. Sah, R. N. Noyce, and W. Shockley, “Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics,” presented at the Proceedings of the IRE, 1957, vol. 45, no. 9, pp. 1228–1243.'
)
Jrec = get_Jsrh(ni, V, Vbi, lifetime_p, lifetime_n, w, kbT)
J_sc_top = 0
J_sc_bot = 0
J_sc_scr = 0
if options.light_iv:
widths = []
for layer in junction:
widths.append(layer.width)
cum_widths = np.cumsum([0] + widths)
g = junction.absorbed
wl = options.wavelength
wl_sp, ph = options.light_source.spectrum(
output_units='photon_flux_per_m', x=wl)
id_v0 = np.argmin(abs(V))
# The contribution from the Emitter (top side).
xa = cum_widths[id_top]
xb = cum_widths[id_top + 1] - w_top[id_v0]
if options.da_mode == 'bvp':
deriv = get_J_sc_diffusion(xa,
xb,
g,
d_top,
l_top,
min_top,
s_top,
wl,
ph,
side='top')
else:
xbb = xb - (xb - xa) / 1001.
deriv = get_J_sc_diffusion_green(xa,
xbb,
g,
d_top,
l_top,
min_top,
s_top,
ph,
side='top')
deriv = np.trapz(deriv, wl)
J_sc_top = q * d_top * abs(deriv)
# The contribution from the Base (bottom side).
xa = cum_widths[id_bottom] + w_bottom[id_v0]
xb = cum_widths[id_bottom + 1]
if options.da_mode == 'bvp':
deriv = get_J_sc_diffusion(xa,
xb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
wl,
ph,
side='bottom')
else:
xbb = xb - (xb - xa) / 1001.
deriv = get_J_sc_diffusion_green(xa,
xbb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
ph,
side='bottom')
deriv = np.trapz(deriv, wl)
J_sc_bot = q * d_bottom * abs(deriv)
# The contribution from the SCR (includes the intrinsic region, if present).
xa = cum_widths[id_top + 1] - w_top[id_v0]
xb = cum_widths[id_bottom] + w_bottom[id_v0]
J_sc_scr = q * get_J_sc_SCR(xa, xb, g, wl, ph)
# And, finally, we output the currents
junction.current = Jrec + JnDark + JpDark + V / R_shunt - J_sc_top - J_sc_bot - J_sc_scr
junction.iv = interp1d(junction.voltage,
junction.current,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(junction.current[0],
junction.current[-1]))
junction.region_currents = State({
"Jn_dif": JnDark,
"Jp_dif": JpDark,
"Jscr_srh": Jrec,
"J_sc_top": J_sc_top,
"J_sc_bot": J_sc_bot,
"J_sc_scr": J_sc_scr
})
def qe_depletion(junction, options):
""" Calculates the QE curve of a junction object using the depletion approximation as described in J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003). The junction is then updated with an "iqe" and several "eqe" functions that calculates the QE curve at any wavelength.
:param junction: A junction object.
:param options: Solver options.
:return: None.
"""
science_reference(
'Depletion approximation',
'J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003).'
)
# First we have to figure out if we are talking about a PN, NP, PIN or NIP junction
T = options.T
kbT = kb * T
id_top, id_bottom, pRegion, nRegion, iRegion, pn_or_np = identify_layers(
junction)
xn, xp, xi, sn, sp, ln, lp, dn, dp, Nd, Na, ni, es = identify_parameters(
junction, T, pRegion, nRegion, iRegion)
niSquared = ni**2
Vbi = (kbT / q) * np.log(Nd * Na / niSquared) if not hasattr(
junction, "Vbi") else junction.Vbi # Jenny p146
wn, wp = get_depletion_widths(junction, es, Vbi, 0, Na, Nd, xi)
# Now it is time to calculate currents
if pn_or_np == "pn":
l_top, l_bottom = ln, lp
w_top, w_bottom = wp, wn
s_top, s_bottom = sp, sn
d_top, d_bottom = dp, dn
min_top, min_bot = niSquared / Na, niSquared / Nd
else:
l_bottom, l_top = ln, lp
w_bottom, w_top = wp, wn
s_bottom, s_top = sp, sn
d_bottom, d_top = dp, dn
min_bot, min_top = niSquared / Na, niSquared / Nd
widths = []
for layer in junction:
widths.append(layer.width)
cum_widths = np.cumsum([0] + widths)
g = junction.absorbed
wl = options.wavelength
wl_sp, ph = LightSource(source_type='black body', x=wl,
T=6000).spectrum(output_units='photon_flux_per_m',
x=wl)
# The contribution from the Emitter (top side).
xa = cum_widths[id_top]
xb = cum_widths[id_top + 1] - w_top
if options.da_mode == 'bvp':
deriv = get_J_sc_diffusion_vs_WL(xa,
xb,
g,
d_top,
l_top,
min_top,
s_top,
wl,
ph,
side='top')
else:
xbb = xb - (xb - xa) / 1001.
deriv = get_J_sc_diffusion_green(xa,
xbb,
g,
d_top,
l_top,
min_top,
s_top,
ph,
side='top')
j_sc_top = d_top * abs(deriv)
# The contribution from the Base (bottom side).
xa = cum_widths[id_bottom] + w_bottom
xb = cum_widths[id_bottom + 1]
if options.da_mode == 'bvp':
deriv = get_J_sc_diffusion_vs_WL(xa,
xb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
wl,
ph,
side='bottom')
else:
xbb = xb - (xb - xa) / 1001.
deriv = get_J_sc_diffusion_green(xa,
xbb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
ph,
side='bottom')
j_sc_bot = d_bottom * abs(deriv)
# The contribution from the SCR (includes the intrinsic region, if present).
xa = cum_widths[id_top + 1] - w_top
xb = cum_widths[id_bottom] + w_bottom
j_sc_scr = get_J_sc_SCR_vs_WL(xa, xb, g, wl, ph)
# The total light absorbed, but not necessarily collected, is:
xa = cum_widths[id_top]
xb = cum_widths[id_bottom + 1]
zz = np.linspace(xa, xb, 10001)
gg = g(zz) * ph
current_absorbed = np.trapz(gg, zz, axis=0)
# Now, we put everything together
j_sc = j_sc_top + j_sc_bot + j_sc_scr
eqe = j_sc / ph
eqe_emitter = j_sc_top / ph
eqe_base = j_sc_bot / ph
eqe_scr = j_sc_scr / ph
iqe = j_sc / current_absorbed
iqe[np.isnan(
iqe
)] = 0 # if zero current_absorbed, get NaN in previous line; want 0 IQE
junction.iqe = interp1d(wl, iqe)
junction.eqe = interp1d(wl,
eqe,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe[0], eqe[-1]))
junction.eqe_emitter = interp1d(wl,
eqe_emitter,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_emitter[0],
eqe_emitter[-1]))
junction.eqe_base = interp1d(wl,
eqe_base,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_base[0], eqe_base[-1]))
junction.eqe_scr = interp1d(wl,
eqe_scr,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_scr[0], eqe_scr[-1]))
junction.qe = State({
'WL': wl,
'IQE': junction.iqe(wl),
'EQE': junction.eqe(wl),
'EQE_emitter': junction.eqe_emitter(wl),
'EQE_base': junction.eqe_base(wl),
'EQE_scr': junction.eqe_scr(wl)
})
def iv_multijunction(solar_cell, options):
""" Calculates the overall IV characteristics of any number of junctions numerically at the requested voltage
points. If photocurrent is not provided, the resultant IV characteristics are purely recombination currents,
otherwise light IVs are returned.
In the end, the soalr_cell object is updated with an "iv" attribute containing a dictionary with:
"IV": (V, I) Calculated IV characteristics
"junction IV": [(V junc 1, I junc 1), (V junc 2, I junc 2), ...]
"Rseries IV": (V, I) Calculated IV characteristics of the series resistance
"coupled IV": For each junction but for the first one, a list with the coupled current coming form the upper junctions.
"Isc", Voc", "P", "FF" and "Eta": In case of mpp = True and light IV.
The sign convention is:
- Photocurrents: Positive.
- Dark Currents: Negative
:param solar_cell: A solar cell object with one or more junctions. The IV of the individual junctions must have been calculated already.
:param kwargs: A dictionary containing, at least, the following elements:
- mpp: (Boolean) If Isc, Voc, FF, Vmpp, Impp and Pmpp must be calculated.
- voltages: Array of voltages in which to calculate the data
- light_iv: (Boolean) if light IV is being calculated
:return: None
"""
output_V = options.voltages
mpp_parameters = options.mpp
radiative_coupling = options.radiative_coupling
light_iv = options.light_iv
Rs = max(solar_cell.R_series, 1e-14)
# The current and junction voltage arrays
num_jun = solar_cell.junctions
tunnel_jun = solar_cell.tunnel_indices
V_junction_array = np.zeros((len(output_V), num_jun))
# The following assumes that all junctions have the currents defined at the same voltages
minimum_J = solar_cell(0).current
for j in range(1, num_jun):
minimum_J = np.where(
np.absolute(minimum_J) < np.absolute(solar_cell(j).current),
minimum_J,
solar_cell(j).current)
minimum_J = np.sort(minimum_J)
# For each junction, we find the voltage corresponding to each of these currents
temp_V_junction_array = np.zeros((len(minimum_J), num_jun))
for j in range(num_jun):
temp_V_junction_array[:, j] = np.interp(minimum_J,
solar_cell(j).current,
solar_cell(j).voltage)
# We calculate the total voltage related to the...
# ... series resistance
temp_V_total = Rs * minimum_J
# ... tunnel junctions
for j in tunnel_jun:
temp_V_total -= solar_cell[j].vi(-minimum_J)
# ... and the normal junctions
for j in range(num_jun):
temp_V_total += temp_V_junction_array[:, j]
# Finally, we calculate the current at the requested voltages and the voltages for each junction
output_J = np.interp(output_V, temp_V_total, minimum_J)
for j in range(num_jun):
V_junction_array[:, j] = np.interp(output_V, temp_V_total,
temp_V_junction_array[:, j])
coupled_J = []
if radiative_coupling:
# First of all, we check if all the junctions are DB or 2D
ok = True
for i in range(num_jun):
ok = ok and solar_cell(i).kind in ['DB', '2D']
if ok:
output_J, V_junction_array, coupled_J = solve_radiative_coupling(
solar_cell, options, V_junction_array)
else:
print(
'WARNING: Only "DB" and "2D" junctions (using the DB solver) can use radiative coupling.\nSkipping calculation...'
)
# Finally, we calculate the solar cell parameters
Isc = None
Voc = None
Pmpp = None
Vmpp = None
Impp = None
FF = None
Eta = None
# If we are calculating the light IV, we also calculate the main parameters: Jsc, Voc, FF, MPP...
if mpp_parameters and light_iv:
VV = output_V
II = -output_J
PP = VV * II
power = options.light_source.power_density
try:
Isc = np.interp([0], VV, II)[0]
Voc = np.interp([0], -II, VV)[0]
Pmpp = np.max(PP)
idx = np.argmax(PP)
Vmpp = VV[idx]
Impp = II[idx]
FF = Pmpp / (Isc * Voc)
Eta = Pmpp / power
except Exception as err:
print('Error calculating the MPP parameters: {}'.format(err))
solar_cell.iv = State({
"IV": (output_V, -output_J),
"junction IV":
[(V_junction_array[:, i], -output_J) for i in range(num_jun)],
"coupled IV":
coupled_J,
"Rseries IV": (output_J * Rs, -output_J),
"Isc":
Isc,
"Voc":
Voc,
"FF":
FF,
"Pmpp":
Pmpp,
"Vmpp":
Vmpp,
"Impp":
Impp,
"Eta":
Eta
})
def qe_depletion(junction, options):
""" Calculates the QE curve of a junction object using the depletion approximation as described in J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003). The junction is then updated with an "iqe" and several "eqe" functions that calculates the QE curve at any wavelength.
:param junction: A junction object.
:param options: Solver options.
:return: None.
"""
science_reference(
'Depletion approximation',
'J. Nelson, “The Physics of Solar Cells”, Imperial College Press (2003).'
)
T = options.T
# First we have to figure out if we are talking about a PN, NP, PIN or NIP junction
sn = 0 if not hasattr(junction, "sn") else junction.sn
sp = 0 if not hasattr(junction, "sp") else junction.sp
# We search for the emitter and check if it is n-type or p-type
idx = 0
pn_or_np = 'pn'
homojunction = True
for layer in junction:
if layer.role.lower() != 'emitter':
idx += 1
else:
Na = 0
Nd = 0
if hasattr(layer.material, 'Na'): Na = layer.material.Na
if hasattr(layer.material, 'Nd'): Nd = layer.material.Nd
if Na < Nd:
pn_or_np = "np"
nRegion = junction[idx]
else:
pRegion = junction[idx]
id_top = idx
break
# Now we check for an intrinsic region and, if there is, for the base.
if junction[idx + 1].role.lower() == 'intrinsic':
iRegion = junction[idx + 1]
if junction[idx + 2].role.lower() == 'base':
if pn_or_np == "pn":
nRegion = junction[idx + 2]
nidx = idx + 2
else:
pRegion = junction[idx + 2]
pidx = idx + 2
id_bottom = idx + 2
homojunction = homojunction and nRegion.material.material_string == pRegion.material.material_string
homojunction = homojunction and nRegion.material.material_string == iRegion.material.material_string
else:
raise RuntimeError(
'ERROR processing junctions: A layer following the "intrinsic" layer must be defined as '
'"base".')
# If there is no intrinsic region, we check directly the base
elif junction[idx + 1].role.lower() == 'base':
if pn_or_np == "pn":
nRegion = junction[idx + 1]
nidx = idx + 1
else:
pRegion = junction[idx + 1]
pidx = idx + 1
iRegion = None
id_bottom = idx + 1
homojunction = homojunction and nRegion.material.material_string == pRegion.material.material_string
else:
raise RuntimeError(
'ERROR processing junctions: A layer following the "emitter" must be defined as "intrinsic"'
'or "base".')
# We assert that we are really working with an homojunction
assert homojunction, 'ERROR: The DA solver only works with homojunctions, for now.'
# With all regions identified, it's time to start doing calculations
kbT = kb * T
Egap = nRegion.material.band_gap
R_shunt = min(junction.R_shunt, 1e14) if hasattr(junction,
'R_shunt') else 1e14
xp = pRegion.width
xn = nRegion.width
xi = 0 if iRegion is None else iRegion.width
# Now we have to get all the material parameters needed for the calculation
if hasattr(junction, "dielectric_constant"):
es = junction.dielectric_constant
else:
es = nRegion.material.permittivity # equal for n and p. I hope.
# For the diffusion lenght, subscript n and p refer to the carriers, electrons and holes
if hasattr(junction, "ln"):
ln = junction.ln
else:
ln = pRegion.material.electron_diffusion_length
if hasattr(junction, "lp"):
lp = junction.lp
else:
lp = nRegion.material.hole_diffusion_length
# For the diffusion coefficient, n and p refer to the regions, n side and p side. Yeah, it's confusing...
if hasattr(junction, "mup"):
dp = junction.mup * kbT / q
else:
dp = pRegion.material.electron_mobility * kbT / q
if hasattr(junction, "mun"):
dn = junction.mun * kbT / q
else:
dn = nRegion.material.hole_mobility * kbT / q
# Effective masses and effective density of states
# mEff_h = nRegion.material.eff_mass_hh_z * electron_mass
# mEff_e = pRegion.material.eff_mass_electron * electron_mass
#
# Nv = 2 * (mEff_h * kb * T / (2 * pi * hbar ** 2)) ** 1.5 # Jenny p58
# Nc = 2 * (mEff_e * kb * T / (2 * pi * hbar ** 2)) ** 1.5
# niSquared = Nc * Nv * np.exp(-Egap / (kb * T))
# ni = np.sqrt(niSquared)
ni = nRegion.material.ni
niSquared = ni**2
Na = pRegion.material.Na
Nd = nRegion.material.Nd
Vbi = (kbT / q) * np.log(Nd * Na / niSquared) if not hasattr(
junction, "Vbi") else junction.Vbi # Jenny p146
# It's time to calculate the depletion widths
if not hasattr(junction, "wp") or not hasattr(junction, "wn"):
if hasattr(
junction, "depletion_approximation"
) and junction.depletion_approximation == "one-sided abrupt":
print(
"using one-sided abrupt junction approximation for depletion width"
)
science_reference(
"Sze abrupt junction approximation",
"Sze: The Physics of Semiconductor Devices, 2nd edition, John Wiley & Sons, Inc (2007)"
)
wp = np.sqrt(2 * es * Vbi / (q * Na))
wn = np.sqrt(2 * es * Vbi / (q * Nd))
else:
wn = (-xi + np.sqrt(xi**2 + 2. * es * Vbi / q *
(1 / Na + 1 / Nd))) / (1 + Nd / Na)
wp = (-xi + np.sqrt(xi**2 + 2. * es * Vbi / q *
(1 / Na + 1 / Nd))) / (1 + Na / Nd)
wn = wn if not hasattr(junction, "wn") else junction.wn
wp = wp if not hasattr(junction, "wp") else junction.wp
w = wn + wp + xi
# Now it is time to calculate currents
if pn_or_np == "pn":
l_top, l_bottom = ln, lp
x_top, x_bottom = xp, xn
w_top, w_bottom = wp, wn
s_top, s_bottom = sp, sn
d_top, d_bottom = dp, dn
min_top, min_bot = niSquared / Na, niSquared / Nd
else:
l_bottom, l_top = ln, lp
x_bottom, x_top = xp, xn
w_bottom, w_top = wp, wn
s_bottom, s_top = sp, sn
d_bottom, d_top = dp, dn
min_bot, min_top = niSquared / Na, niSquared / Nd
widths = []
for layer in junction:
widths.append(layer.width)
cum_widths = np.cumsum([0] + widths)
g = junction.absorbed
wl = options.wavelength
wl_sp, ph = options.light_source.spectrum(output_units='photon_flux_per_m',
x=wl)
# The contribution from the Emitter (top side).
xa = cum_widths[id_top]
xb = cum_widths[id_top + 1] - w_top
deriv = get_J_sc_diffusion_vs_WL(xa,
xb,
g,
d_top,
l_top,
min_top,
s_top,
wl,
ph,
side='top')
j_sc_top = d_top * abs(deriv)
# The contribution from the Base (bottom side).
xa = cum_widths[id_bottom] + w_bottom
xb = cum_widths[id_bottom + 1]
deriv = get_J_sc_diffusion_vs_WL(xa,
xb,
g,
d_bottom,
l_bottom,
min_bot,
s_bottom,
wl,
ph,
side='bottom')
j_sc_bot = d_bottom * abs(deriv)
# The contribution from the SCR (includes the intrinsic region, if present).
xa = cum_widths[id_top + 1] - w_top
xb = cum_widths[id_bottom] + w_bottom
j_sc_scr = get_J_sc_SCR_vs_WL(xa, xb, g, wl, ph)
# The total light absorbed, but not necessarily collected, is:
xa = cum_widths[id_top]
xb = cum_widths[id_bottom + 1]
zz = np.linspace(xa, xb, 10001)
gg = g(zz) * ph
current_absorbed = np.trapz(gg, zz, axis=0)
# Now, we put everything together
j_sc = j_sc_top + j_sc_bot + j_sc_scr
eqe = j_sc / ph
eqe_emitter = j_sc_top / ph
eqe_base = j_sc_bot / ph
eqe_scr = j_sc_scr / ph
junction.iqe = interp1d(wl, j_sc / current_absorbed)
junction.eqe = interp1d(wl,
eqe,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe[0], eqe[-1]))
junction.eqe_emitter = interp1d(wl,
eqe_emitter,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_emitter[0],
eqe_emitter[-1]))
junction.eqe_base = interp1d(wl,
eqe_base,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_base[0], eqe_base[-1]))
junction.eqe_scr = interp1d(wl,
eqe_scr,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(eqe_scr[0], eqe_scr[-1]))
junction.qe = State({
'WL': wl,
'IQE': junction.iqe(wl),
'EQE': junction.eqe(wl),
'EQE_emitter': junction.eqe_emitter(wl),
'EQE_base': junction.eqe_base(wl),
'EQE_scr': junction.eqe_scr(wl)
})
import solcore.analytic_solar_cells as ASC
from solcore.light_source import LightSource
from solcore.state import State
from solcore.optics import solve_beer_lambert, solve_tmm, solve_rcwa, rcwa_options, solve_external_optics
from solcore.absorption_calculator import RCWASolverError
from solcore.structure import Layer, Junction, TunnelJunction
try:
import solcore.poisson_drift_diffusion as PDD
a = PDD.pdd_options
except AttributeError:
PDD.pdd_options = {}
default_options = State()
pdd_options = PDD.pdd_options
asc_options = ASC.db_options
def merge_dicts(*dict_args):
"""
Given any number of dicts, shallow copy and merge into a new dict,
precedence goes to key value pairs in latter dicts.
"""
result = State()
for dictionary in dict_args:
result.update(dictionary)
return result
def iv_pdd(junction, options):
""" Calculates the IV curve of the device between 0 V and a given voltage. Depending if the "sol" parameter is set
or not, the IV will be calculated in the dark (calling the Equilibrium function) or under illumination (calling
the ShortCircuit function).
:param device: A dictionary containing the device structure. See PDD.DeviceStructure
:param vfin: Final voltage. If it is negative, vstep must also be negative.
:param vstep: Maximum step size for the IV curve. This is adapted dynamically to ensure that the shape is reproduced correctly.
:param output_info: Indicates how much information must be printed by the fortran solver (0=min, 2=max)
:param IV_info: If information about the Voc, Isc and FF should be provided after the calculation. Default=True
:param rs: Series resistance. Default=0
:param escape: Indicates if the calculation should stop when Voc is reached (0=False, 1=True). Default=1
:param light: Indicates if the light IV curve should be calculated
:param wavelengths: Array with the wavelengths (in m)
:param photon_flux: Array with the photon_flux (in photons/m2/m) corresponding to the above wavelengths
:return: A dictionary containing the IV curves, the different components and also the output of Equilibrium or ShortCircuit.
"""
print('Solving IV...')
light = options.light_iv
output_info = options.output_iv
T = options.T
junction.voltage = options.internal_voltages
Eg = 10
for layer in junction:
Eg = min([Eg, layer.material.band_gap / q])
s = True if junction[0].material.Na >= junction[-1].material.Nd else False
if s:
vmax = min(Eg - 3 * kb * T / q, max(junction.voltage))
vmin = min(junction.voltage)
else:
vmax = max(junction.voltage)
vmin = max(-Eg + 3 * kb * T / q, min(junction.voltage))
vstep = junction.voltage[1] - junction.voltage[0]
# POSITIVE RANGE
output_pos = None
if vmax > 0:
if light:
short_circuit_pdd(junction, options)
else:
equilibrium_pdd(junction, options)
dd.runiv(vmax, vstep, output_info, 0)
output_pos = {'Bandstructure': DumpBandStructure(), 'IV': DumpIV()}
# NEGATIVE RANGE
output_neg = None
if vmin < 0:
if light:
short_circuit_pdd(junction, options)
else:
equilibrium_pdd(junction, options)
dd.runiv(vmin, (-1 * vstep), output_info, 0)
output_neg = {'Bandstructure': DumpBandStructure(), 'IV': DumpIV()}
print('...done!\n')
# Now we need to put together the data for the possitive and negative regions.
junction.pdd_data = State({
'possitive_V': output_pos,
'negative_V': output_neg
})
if output_pos is None:
V = output_neg['IV']['V']
J = output_neg['IV']['J']
Jrad = output_neg['IV']['Jrad']
Jsrh = output_neg['IV']['Jsrh']
Jaug = output_neg['IV']['Jaug']
Jsur = output_neg['IV']['Jsur']
elif output_neg is None:
V = output_pos['IV']['V']
J = output_pos['IV']['J']
Jrad = output_pos['IV']['Jrad']
Jsrh = output_pos['IV']['Jsrh']
Jaug = output_pos['IV']['Jaug']
Jsur = output_pos['IV']['Jsur']
else:
V = np.concatenate(
(output_neg['IV']['V'][:0:-1], output_pos['IV']['V']))
J = np.concatenate(
(output_neg['IV']['J'][:0:-1], output_pos['IV']['J']))
Jrad = np.concatenate(
(output_neg['IV']['Jrad'][:0:-1], output_pos['IV']['Jrad']))
Jsrh = np.concatenate(
(output_neg['IV']['Jsrh'][:0:-1], output_pos['IV']['Jsrh']))
Jaug = np.concatenate(
(output_neg['IV']['Jaug'][:0:-1], output_pos['IV']['Jaug']))
Jsur = np.concatenate(
(output_neg['IV']['Jsur'][:0:-1], output_pos['IV']['Jsur']))
# Finally, we calculate the currents at the desired voltages
R_shunt = min(junction.R_shunt, 1e14) if hasattr(junction,
'R_shunt') else 1e14
junction.current = np.interp(junction.voltage, V,
J) + junction.voltage / R_shunt
Jrad = np.interp(junction.voltage, V, Jrad)
Jsrh = np.interp(junction.voltage, V, Jsrh)
Jaug = np.interp(junction.voltage, V, Jaug)
Jsur = np.interp(junction.voltage, V, Jsur)
junction.iv = interp1d(junction.voltage,
junction.current,
kind='linear',
bounds_error=False,
assume_sorted=True,
fill_value=(junction.current[0],
junction.current[-1]))
junction.recombination_currents = State({
"Jrad": Jrad,
"Jsrh": Jsrh,
"Jaug": Jaug,
"Jsur": Jsur
})