from math import pi
import numpy as np
from simudo.physics import Material
[docs]class SiliconMaterial(Material):
"""Silicon material data based on Palankovski.
V. Palankovski and R. Quay, "Analysis and Simulation of Heterostructure Devices",
Springer-Verlag (2004).
"""
name = "Silicon"
[docs] def get_dict(self):
d = super().get_dict()
U = self.unit_registry
d.update(
{
# Static dielectric constant, Palankovski Table 3.3
"poisson/permittivity": U("11.9 vacuum_permittivity"),
# Table 3.9
"CB/EgX_0K": U("1.1695 eV"),
"CB/ChiX_0K": U("4.0045 eV") - U("4 eV"),
"CB/varshni_alphaX": U("4.73e-4 eV/K"),
"CB/varshni_betaX": U("636 K"),
# Table 3.21
"CB/MCX": U("6"),
# Table 3.18
"CB/mX": U("0.328"),
"CB/m1n": U("0.009"),
# Table 3.19
"VB/m0p": U("0.55"),
"VB/m1p": U("0.6"),
"VB/m2p": U("-0.1"),
# TODO - update these mobilities from Palankovski
"CB/mobility": U("1400 cm^2/V/s"),
"VB/mobility": U(" 450 cm^2/V/s"),
# SRH recombination lifetimes
"SRH/CB/tau": U("1e-9 s"),
"SRH/VB/tau": U("1e-9 s"),
# Properties for band-to-band tunneling
"CB/eff_mass_tunnel": U("0.05"),
"VB/eff_mass_tunnel": U("0.1"),
"CB/tunnel_offset_energy": U("0 eV"),
"VB/tunnel_offset_energy": U("0 eV"),
}
)
T = self.temperature
Eg = d["CB/EgX_0K"] - d["CB/varshni_alphaX"] * T ** 2 / (
d["CB/varshni_betaX"] + T
)
Chi = d["CB/ChiX_0K"] + d["CB/varshni_alphaX"] * T ** 2 / (
d["CB/varshni_betaX"] + T
)
mn = d["CB/mX"] + d["CB/m1n"] * (T / U("300 K"))
mp = (
d["VB/m0p"]
+ d["VB/m1p"] * (T / U("300 K"))
+ d["VB/m2p"] * (T / U("300 K")) ** 2
)
m_e = U.electron_mass
k_B = U.boltzmann_constant
h = U.planck_constant
NC = 2 * d["CB/MCX"] * (2 * pi * mn * m_e * k_B * T / h ** 2) ** (3 / 2)
NV = 2 * (2 * pi * mp * m_e * k_B * T / h ** 2) ** (3 / 2)
# Effective masses and thermal velocity from Green (1990)
# mtc actually has a small temperature dependence acording to Green
mtc = U("0.28")
vth_c = (
8 * U.boltzmann_constant * T / (pi * mtc * U.electron_mass)
) ** 0.5
mtv = (
0.3676
+ U("1.98738e-5 /K^2") * T ** 2
- U("2.588144e-7 /K^3") * T ** 3
+ U("1.415372e-9 /K^4") * T ** 4
- U("3.919169e-12 /K^5") * T ** 5
+ U("5.410849e-15 /K^6") * T ** 6
- U("2.959797e-18 /K^7") * T ** 7
)
vth_v = (
8 * U.boltzmann_constant * T / (pi * mtv * U.electron_mass)
) ** 0.5
d.update(
{
"CB/mDOS": mn,
"VB/mDOS": mp,
"CB/energy_level": -Chi,
"VB/energy_level": -Chi - Eg,
"CB/effective_density_of_states": NC,
"VB/effective_density_of_states": NV,
"CB/vth": vth_c,
# "CB/vth": 7e5*U("cm/s"),
"VB/vth": vth_v,
"SRH/energy_level": -Chi - Eg / 2,
}
)
return d
[docs] def optical_properties_table(self):
"""
Optical properties from M.A. Green,
"Self-consistent optical parameters of intrinsic silicon at 300 K
including temperature coefficients", Sol. Ener. Mat. and Sol. Cells.,
https://doi.org/10.1016/j.solmat.2008.06.009
"""
# TODO: The reference includes data on temperature dependence.
# Incorporate it here.
# wavelength (nm), alpha (/cm), n, k
np.array(
[
[250, 1.84e06, 1.694, 3.66056369111359],
[260, 1.97e06, 1.8, 4.07595809258344],
[270, 2.18e06, 2.129, 4.68392997519448],
[280, 2.36e06, 3.052, 5.25847931975622],
[290, 2.24e06, 4.426, 5.16935255162476],
[300, 1.73e06, 5.055, 4.13007077323468],
[310, 1.44e06, 5.074, 3.5523383298111],
[320, 1.28e06, 5.102, 3.25949323452202],
[330, 1.17e06, 5.179, 3.07248617638904],
[340, 1.09e06, 5.293, 2.94914109549282],
[350, 1.04e06, 5.483, 2.89661996427249],
[360, 1.02e06, 6.014, 2.9220847551672],
[370, 6.97e05, 6.863, 2.05222341369844],
[380, 2.93e05, 6.548, 0.886015568192581],
[390, 1.50e05, 5.976, 0.465528208543794],
[400, 9.52e04, 5.587, 0.303031011646969],
[410, 6.74e04, 5.305, 0.219904384870072],
[420, 5.00e04, 5.091, 0.16711269024649],
[430, 3.92e04, 4.925, 0.134135786037849],
[440, 3.11e04, 4.793, 0.108893812063475],
[450, 2.55e04, 4.676, 0.091315148598975],
[460, 2.10e04, 4.577, 0.076871837513386],
[470, 1.72e04, 4.491, 0.064330427997744],
[480, 1.48e04, 4.416, 0.056531835786241],
[490, 1.27e04, 4.348, 0.049521060543043],
[500, 1.11e04, 4.293, 0.044165496708001],
[510, 9.70e03, 4.239, 0.03936697517378],
[520, 8.80e03, 4.192, 0.036414650979426],
[530, 7.85e03, 4.15, 0.033108207036692],
[540, 7.05e03, 4.11, 0.030295143417542],
[550, 6.39e03, 4.077, 0.027967502374823],
[560, 5.78e03, 4.044, 0.025757635989992],
[570, 5.32e03, 4.015, 0.024131072471593],
[580, 4.88e03, 3.986, 0.022523607546365],
[590, 4.49e03, 3.962, 0.021080867987237],
[600, 4.14e03, 3.939, 0.019767043932013],
[610, 3.81e03, 3.916, 0.018494600161994],
[620, 3.52e03, 3.895, 0.017366987390188],
[630, 3.27e03, 3.879, 0.016393754913181],
[640, 3.04e03, 3.861, 0.01548259286398],
[650, 2.81e03, 3.844, 0.014534825177867],
[660, 2.58e03, 3.83, 0.013550451854844],
[670, 2.38e03, 3.815, 0.012689423612717],
[680, 2.21e03, 3.8, 0.011958902423925],
[690, 2.05e03, 3.787, 0.011256233350174],
[700, 1.90e03, 3.774, 0.010583803715611],
[710, 1.77e03, 3.762, 0.010000500849179],
[720, 1.66e03, 3.751, 0.009511099399172],
[730, 1.54e03, 3.741, 0.008946099351195],
[740, 1.42e03, 3.732, 0.008362000710048],
[750, 1.30e03, 3.723, 0.00775880347573],
[760, 1.19e03, 3.714, 0.007196986526616],
[770, 1.10e03, 3.705, 0.006740211839942],
[780, 1.01e03, 3.696, 0.00626911320839],
[790, 9.28e02, 3.688, 0.005833983593977],
[800, 8.50e02, 3.681, 0.005411268065124],
[810, 7.75e02, 3.674, 0.004995475776297],
[820, 7.07e02, 3.668, 0.004613424335405],
[830, 6.47e02, 3.662, 0.004273389799489],
[840, 5.91e02, 3.656, 0.003950543997427],
[850, 5.35e02, 3.65, 0.003618785518552],
[860, 4.80e02, 3.644, 0.003284958025417],
[870, 4.32e02, 3.638, 0.002990839690583],
[880, 3.83e02, 3.632, 0.002682079100985],
[890, 3.43e02, 3.626, 0.002429261473883],
[900, 3.06e02, 3.62, 0.002191563566375],
[910, 2.72e02, 3.614, 0.001969701575705],
[920, 2.40e02, 3.608, 0.001757070571735],
[930, 2.10e02, 3.602, 0.001554148019292],
[940, 1.83e02, 3.597, 0.001368891665533],
[950, 1.57e02, 3.592, 0.001186897988108],
[960, 1.34e02, 3.587, 0.001023684593967],
[970, 1.14e02, 3.582, 0.000879967680355],
[980, 9.59e01, 3.578, 0.000747884993083],
[990, 7.92e01, 3.574, 0.000623951038897],
[1000, 6.40e01, 3.57, 0.000509295817894],
[1010, 5.11e01, 3.566, 0.000410707288396],
[1020, 3.99e01, 3.563, 0.000323864393698],
[1030, 3.02e01, 3.56, 0.000247533682991],
[1040, 2.26e01, 3.557, 0.000187038889122],
[1050, 1.63e01, 3.554, 0.000136196842551],
[1060, 1.11e01, 3.551, 9.3630853020962e-05],
[1070, 8.00e00, 3.548, 6.81183156433312e-05],
[1080, 6.20e00, 3.546, 5.32850749471666e-05],
[1090, 4.70e00, 3.544, 4.0767538672989e-05],
[1100, 3.50e00, 3.541, 3.06373265451899e-05],
[1110, 2.70e00, 3.539, 2.38493682223205e-05],
[1120, 2.00e00, 3.537, 1.78253536262923e-05],
[1130, 1.50e00, 3.534, 1.34883814270381e-05],
[1140, 1.00e00, 3.532, 9.07183175623803e-06],
[1150, 6.80e-01, 3.53, 6.22295827489311e-06],
[1160, 4.20e-01, 3.528, 3.87701441371857e-06],
[1170, 2.20e-01, 3.526, 2.04832411759269e-06],
[1180, 6.50e-02, 3.524, 6.10359206757419e-07],
[1190, 3.60e-02, 3.522, 3.4090988810284e-07],
[1200, 2.20e-02, 3.52, 2.10084524881302e-07],
[1210, 1.30e-02, 3.528, 1.25175362741776e-07],
[1220, 8.20e-03, 3.516, 7.9609302534566e-08],
[1230, 4.70e-03, 3.515, 4.60037363007123e-08],
[1240, 2.40e-03, 3.513, 2.3682255532074e-08],
[1250, 1.00e-03, 3.511, 9.94718394324346e-09],
[1260, 3.60e-04, 3.51, 3.60963410932419e-09],
[1270, 2.00e-04, 3.508, 2.02126777726707e-09],
[1280, 1.20e-04, 3.507, 1.22230996294576e-09],
[1290, 7.10e-05, 3.506, 7.28850061889335e-10],
[1300, 4.50e-05, 3.504, 4.65528208543794e-10],
[1310, 2.70e-05, 3.503, 2.81465516858017e-10],
[1320, 1.60e-05, 3.501, 1.68067619905041e-10],
[1330, 8.00e-06, 3.5, 8.46704297248883e-11],
[1340, 3.50e-06, 3.498, 3.73218341550495e-11],
[1350, 1.70e-06, 3.497, 1.8263029719795e-11],
[1360, 1.00e-06, 3.496, 1.08225361302489e-11],
[1370, 6.70e-07, 3.495, 7.30441611320254e-12],
[1380, 4.50e-07, 3.493, 4.94176098300335e-12],
[1390, 2.50e-07, 3.492, 2.76531713622168e-12],
[1400, 2.00e-07, 3.491, 2.22816920328653e-12],
[1410, 1.50e-07, 3.49, 1.68306352319679e-12],
[1420, 8.50e-08, 3.489, 9.60500081559588e-13],
[1430, 7.70e-08, 3.488, 8.7622753919243e-13],
[1440, 4.20e-08, 3.487, 4.81284547909892e-13],
[1450, 3.20e-08, 3.486, 3.69239467973197e-13],
]
)