1%% Copyright (C) 2004-2012 Carlo de Falco 2%% 3%% This file is part of 4%% SECS1D - A 1-D Drift--Diffusion Semiconductor Device Simulator 5%% 6%% SECS1D is free software; you can redistribute it and/or modify 7%% it under the terms of the GNU General Public License as published by 8%% the Free Software Foundation; either version 3 of the License, or 9%% (at your option) any later version. 10%% 11%% SECS1D is distributed in the hope that it will be useful, 12%% but WITHOUT ANY WARRANTY; without even the implied warranty of 13%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14%% GNU General Public License for more details. 15%% 16%% You should have received a copy of the GNU General Public License 17%% along with SECS1D; If not, see <http://www.gnu.org/licenses/>. 18 19%% material properties for silicon and silicon dioxide 20%% 21%% esir = relative electric permittivity of silicon 22%% esio2r = relative electric permittivity of silicon dioxide 23%% esi = electric permittivity of silicon 24%% esio2 = electric permittivity of silicon dioxide 25%% mn = effective mass of electrons in silicon 26%% mh = effective mass of holes in silicon 27%% 28%% u0n = low field electron mobility 29%% u0p = low field hole mobility 30%% uminn = parameter for doping-dependent electron mobility 31%% betan = idem 32%% Nrefn = idem 33%% uminp = parameter for doping-dependent hole mobility 34%% betap = idem 35%% Nrefp = idem 36%% vsatn = electron saturation velocity 37%% vsatp = hole saturation velocity 38%% tp = electron lifetime 39%% tn = hole lifetime 40%% Cn = electron Auger coefficient 41%% Cp = hole Auger coefficient 42%% an = impact ionization rate for electrons 43%% ap = impact ionization rate for holes 44%% Ecritn = critical field for impact ionization of electrons 45%% Ecritp = critical field for impact ionization of holes 46%% Nc = effective density of states in the conduction band 47%% Nv = effective density of states in the valence band 48%% Egap = bandgap in silicon 49%% EgapSio2 = bandgap in silicon dioxide 50%% 51%% ni = intrinsic carrier density 52%% Phims = metal to semiconductor potential barrier 53 54esir = 11.7; 55esio2r = 3.9; 56esi = e0 * esir; 57esio2 = e0 * esio2r; 58mn = 0.26*mn0; 59mh = 0.18*mn0; 60 61qsue = q / esi; 62 63u0n = 1417e-4; 64u0p = 480e-4; 65uminn = u0n; % ref. value: 65e-4; 66uminp = u0p; % ref. value: 47.7e-4; 67betan = 0.72; 68betap = 0.76; 69Nrefn = 8.5e22; 70Nrefp = 6.3e22; 71vsatn = inf; % ref. value: 1.1e5; 72vsatp = inf; % ref. value: 9.5e4; 73 74tp = inf; % ref. value: 1e-6; 75tn = inf; % ref. value: 1e-6; 76 77Cn = 0; % ref. value: 2.8e-31*1e-12; 78Cp = 0; % ref. value: 9.9e-32*1e-12; 79an = 0; % ref. value: 7.03e7; 80ap = 0; % ref. value: 6.71e7; 81Ecritn = 1.231e8; 82Ecritp = 1.693e8; 83 84mnl = 0.98*mn0; 85mnt = 0.19*mn0; 86mndos = (mnl*mnt*mnt)^(1/3); 87 88mhh = 0.49*mn0; 89mlh = 0.16*mn0; 90mhdos = (mhh^(3/2)+mlh^(3/2))^(2/3); 91 92Nc = (6/4)*(2*mndos*Kb*T0/(hbar^2*pi))^(3/2); 93Nv = (1/4)*(2*mhdos*Kb*T0/(hbar^2*pi))^(3/2); 94Eg0 = 1.16964*q; 95alfaEg = 4.73e-4*q; 96betaEg = 6.36e2; 97Egap = Eg0-alfaEg*((T0^2)/(T0+betaEg)); 98Ei = Egap/2+Kb*T0/2*log(Nv/Nc); 99EgapSio2 = 9*q; 100deltaEcSio2 = 3.1*q; 101deltaEvSio2 = EgapSio2-Egap-deltaEcSio2; 102 103ni = sqrt(Nc*Nv)*exp(-Egap/(2*(Kb * T0))); 104Phims = - Egap /(2*q); 105