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