-
Notifications
You must be signed in to change notification settings - Fork 1
/
kp_8bands_Luttinger_DKK_strain_f.m
156 lines (111 loc) · 4.67 KB
/
kp_8bands_Luttinger_DKK_strain_f.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
function[E]=kp_8bands_Luttinger_DKK_strain_f(k_list, Eg, EP, Dso, F, g123, ac, av, bv, dv, exx, ezz)
% DKK model: Dresselhaus, Kip and Kittel
% Calin Galeriu
% PhD thesis: "k.p Theory of semiconductor nanostructures" (2005)
% Chapter 3, page 26
% Download:
% https://web.wpi.edu/Pubs/ETD/Available/etd-120905-095359/unrestricted/cgaleriu.pdf
% Stefan Birner (Nextnano)
% PhD thesis: "Modeling of semiconductor nanostructures and semiconductor-electrolyte interfaces" (2011)
% Chapter3, page 36: "Multi-band k.p envelope function approximation"
% Download:
% https://mediatum.ub.tum.de/doc/1084806/1084806.pdf
% https://www.nextnano.com/downloads/publications/PhD_thesis_Stefan_Birner_TUM_2011_WSIBook.pdf
% Thomas B. Bahder,
% "Eight-band k.p model of strained zinc-blende crystals", PRB 41, 11992 (1990)
% https://journals.aps.org/prb/abstract/10.1103/PhysRevB.41.11992
% https://www.researchgate.net/publication/235532200_Eight-band_k_p_model_of_strained_zinc-blende_crystals
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Constants %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
h=6.62606896E-34; %% Planck constant [J.s]
hbar=h/(2*pi);
e=1.602176487E-19; %% electron charge [Coulomb]
m0=9.10938188E-31; %% electron mass [kg]
H0=hbar^2/(2*m0) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Dso = Dso*e;
Eg = Eg*e;
EP = EP*e;
P = sqrt(EP*hbar^2/(2*m0)) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
eyy = exx;
exy = 0; eyx=0;
ezx = 0; exz=0;
eyz = 0; ezy=0;
ee = exx+eyy+ezz;
ac = -abs(ac)*e;
av = +abs(av)*e;
bv = +abs(bv)*e;
dv = +abs(dv)*e;
l = av-2*bv;
m = av+bv;
bb = 0;
n = sqrt(3)*dv;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% gc= 1+2*F + EP*(Eg+2*Dso/3) / (Eg*(Eg+Dso)) ; % =1/mc electron in CB eff mass
% renormalization of the paramter from 6x6kp to 8x8kp
% gc=gc-EP/3*( 2/Eg + 1/(Eg+Dso) );
gc = 1+2*F;
g1 = g123(1)-EP/(3*Eg);
g2 = g123(2)-EP/(6*Eg);
g3 = g123(3)-EP/(6*Eg);
L = H0*(-1-g1-4*g2);
M = H0*(-1-g1+2*g2);
N = -H0*6*g3;
B = H0*0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% Building of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:length(k_list(:,1))
kx = k_list(i,1);
ky = k_list(i,2);
kz = k_list(i,3);
k=sqrt(kx.^2 + ky.^2 + kz.^2);
Hdiag = H0*k^2*[gc 1 1 1] + [Eg -Dso/3 -Dso/3 -Dso/3 ];
H4=[
0 1i*P*kx 1i*P*ky 1i*P*kz
0 0 0 0
0 0 0 0
0 0 0 0
];
HH4 = H4' + H4 + diag(Hdiag);
HR=[
0 B*ky*kz B*kx*kz B*kx*ky
B*ky*kz L*kx^2+M*(ky^2+kz^2) N*kx*ky N*kx*kz
B*kx*kz N*kx*ky L*ky^2+M*(kx^2+kz^2) N*ky*kz
B*kx*ky N*kx*kz N*ky*kz L*kz^2+M*(kx^2+ky^2)
];
Hso=[
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1i
0 -1 0 0 0 0 0 1
0 0 0 0 0 -1i -1 0
0 0 0 0 0 0 0 0
0 0 0 -1i 0 0 -1 0
0 0 0 1 0 1 0 0
0 1i -1 0 0 0 0 0
];
Hs1=[
ac*ee bb*eyz bb*exz bb*exy
bb*eyz l*exx+m*(eyy+ezz) n*exy n*exz
bb*exz n*exy l*eyy+m*(exx+ezz) n*eyz
bb*exy n*exz n*eyz l*ezz+m*(exx+eyy)
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Here are the terms that make it slightly different from Pistl-1 and Fishman Hamiltonian
%% Removing those terms gives exactly the same results
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Hs2=[
0 -1i*P*(exx*kx+exy*ky+exz*kz) -1i*P*(eyx*kx+eyy*ky+eyz*kz) -1i*P*(ezx*kx+ezy*ky+ezz*kz)
0 0 0 0
0 0 0 0
0 0 0 0
];
Hs=Hs1;%+Hs2+Hs2';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H=[HH4 zeros(4,4) ; zeros(4,4) HH4] + Hso*Dso/(3i) + [HR zeros(4,4) ; zeros(4,4) HR] + [Hs zeros(4,4) ; zeros(4,4) Hs];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e ;
end
end