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kp_8bands_Luttinger_DKK_f.m
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kp_8bands_Luttinger_DKK_f.m
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function[E]=kp_8bands_Luttinger_DKK_f(k_list, Eg, EP, Dso, F, g1, g2, g3)
% 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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)) ;
% 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=g1-EP/(3*Eg);
g2=g2-EP/(6*Eg);
g3=g3-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
];
H=[HH4 zeros(4,4) ; zeros(4,4) HH4] + Hso*Dso/(3i) + [HR zeros(4,4) ; zeros(4,4) HR];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e ;
end
end