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kp_6bands_WZ_strain_f.m
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kp_6bands_WZ_strain_f.m
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function[E]=kp_6bands_WZ_strain_f(k_list, Dcr, Dso, AA, DD, exx, ezz)
% 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
% S. L. Chuang et al. PRB, 54, 2491 (1996)
% "k.p method for strained wurtzite semiconductors"
% M. Kumagai, S. L. Chuang et al. PRB, 57, 15304 (1998)
% "Analytical solutions of the block-diagonalized Hamiltonian for strained wurtzite semiconductors"
% Seoung-Hwan Park and S. L. Chuang, PRB, 59, 4726 (1999)
% "Crystal-orientation effects on the piezoelectric field and electronic properties of strained wurtzite semiconductors"
% D. J. Dugdale, S. Brand, and R. A. Abram, PRB, 61, 12934 (2000)
% "Direct calculation of k"p parameters for wurtzite AlN, GaN, and InN"
% W. J. Fan et al. J. Crystal Growth, 287, 28 (2006)
% "Electronic structures of wurtzite ZnO and ZnO/MgZnO quantum well"
% P. Rinke, PRB, 77, 075202 (2008)
% "Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN"
% http://cmt.dur.ac.uk/ssterratum/paper/node4.html
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Dcr = Dcr*e;
Dso = Dso*e;
A1=AA(1);A2=AA(2);A3=AA(3);A4=AA(4);A5=AA(5);A6=AA(6);A7=AA(7)*e*1e-10;
D1=DD(1)*e;D2=DD(2)*e;D3=DD(3)*e;D4=DD(4)*e;D5=DD(5)*e;D6=DD(6)*e;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
eyy = exx;
exy = 0; eyx=0;
ezx = 0; exz=0;
eyz = 0; ezy=0;
ee = exx+eyy+ezz;
%l1 = D2+D4+D5;
%l2 = D1;
%m1 = D2+D4-D5;
%m2 = D1+D3;
%m3 = D2;
%n1 = 2*D5;
%n2 = sqrt(2)*D6;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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);
% keep in mind
% Delta1=Dcr
% Delta2=Delta3=Dso/3
lambda = H0*( A1*kz^2 + A2*(kx^2+ky^2) ) + D1*ezz + D2*(exx+eyy);
theta = H0*( A3*kz^2 + A4*(kx^2+ky^2) ) + D3*ezz + D4*(exx+eyy);
F = Dcr + Dso/3 + lambda + theta ;
G = Dcr - Dso/3 + lambda + theta ;
K = H0*A5*( kx + 1i*ky )^2 + D5*( exx-eyy + 2i*exy);
H = H0*A6*( kx + 1i*ky ) * kz + D6*( ezx + 1i*eyz );
Delta = sqrt(2)*Dso/3 ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hamiltonian WZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
HH=[
F -K' -H' 0 0 0
-K G H 0 0 Delta
-H H' lambda 0 Delta 0
0 0 0 F -K H
0 0 Delta -K' G -H'
0 Delta 0 H' -H lambda
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(HH)/e ;
end
end