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Gain_interband_Main.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%% last update 11February2020, lne %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This program computes the absorption and gain of interband transition in
% semiconductor. It can computes the gain in bulk (3D) or in quantum well (2D)
% Various materials and their alloys are available in the library
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Library; % load material parameter DB from "materialDB_ZB.csv"
ExtractParameters; % extract parameter from the Library
TernaryAlloy; % compute the ternary alloy
%QuaternaryAlloy; % compute the quaternary alloy
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% input parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N3d= 5e18*1e6; % Carrier concentration [m-3]
M = InGaAs10; % Choose the material from the library
%M = GaAs; % Choose the material from the library
T = 300; % Temperature [K]
d = 3; % Dimension, bulk=3, Quantum well=2
Lqw= 10e-9; % Quantum well width (meter) if d=2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% Grabbing the parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Eg = M(idx_Eg6c) - (M(idx_alphaG)*T^2) ./ (T+M(idx_betaG)); %Eg = Eg0 - (a*T.^2)./(T + b);
EP = M(idx_EP_K); % EP Kane
me = M(idx_me); % electron mass
mhh = M(idx_mhh); % heavy hole mass
mr = me*mhh/(me+mhh); % reduced mass
nopt=sqrt(M(idx_Epsi)); % optical index
FWHM=1e-3; % homogeneous broadening (eV)
% in case we wanna have current instead of electron number
%I=10e-3; % injected current (A)
%S=pi*(10e-6)^2; % surface pumped (m-2)
%tau=1e-9; % total interband recombinason time (s)
%N3d=I/S/e/Lqw*tau % injected charge [m-3]
N2d=N3d*Lqw; % sheet density in case d=2 [m-2]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E=linspace(-0.25,2,1000);
EEx=repmat(E,length(E),1);
EEy=repmat(E',1,length(E));
%L=(FWHM/2)^2 * 1./ ( ( E-E' ).^2 + (FWHM/2).^2 ) ;
L=(FWHM/2)^2 * 1./ ( ( EEx-EEy ).^2 + (FWHM/2).^2 ) ;
%L=L./trapz(E,L,2);
L=L./repmat(trapz(E,L,2) , 1 ,length(E) );
Echv = Eg + mr/me *(E-Eg);
Evhv = - mr/mhh*(E-Eg);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if d==2
[Efc,Efv,ron,rop,FEc,FEv,FEcc,FEvv,alpha,Gain]=Gain2D_interband_f(N2d,me,mhh,E,Eg,EP,L,T,nopt,FWHM,2,Lqw);
end
if d==3
[Efc,Efv,ron,rop,FEc,FEv,FEcc,FEvv,alpha,Gain]=Gain3D_interband_f(N3d,me,mhh,E,Eg,EP,L,T,nopt,FWHM,3);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure('position',[-3500 10 1200 900])
figure('position',[100 100 1200 900])
FS=15;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,1,'fontsize',FS)
hold on;grid on; box on;
plot(E,rop ,'b.-')
plot(E,rop.*FEv,'r.-')
plot(Efv*[1 1] ,[0 1]*max(rop.*FEv)*5,'m')
xlim([-1 1]*0.25)
ylim([0 1]*max(rop.*FEv)*5)
xlabel('E (eV)')
if d==2
ylabel('2d Density of state (eV-1.m-2)')
title(strcat('2d: \color{red}Efv=', num2str(Efv*1e3,'%.1f'),'meV'))
elseif d==3
ylabel('3d Density of state (eV-1.m-3)')
title(strcat('3d: \color{red}Efv=', num2str(Efv*1e3,'%.1f'),'meV'))
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,2,'fontsize',FS)
hold on;grid on; box on;
plot(E,ron ,'b.-')
plot(E,ron .* FEc,'g.-')
plot(Efc*[1 1]+Eg,[0 1]*max(ron.*FEc)*5,'m')
xlim([0.9 1.2]*Eg)
ylim([0 1]*max(ron.*FEc)*5)
xlabel('E (eV)')
if d==2
ylabel('2d Density of state (eV-1.m-2)')
title(strcat('2d: \color{green}Efc=',num2str(Efc*1e3,'%.1f'),'meV'))
elseif d==3
ylabel('3d Density of state (eV-1.m-3)')
title(strcat('3d: \color{green}Efc=',num2str(Efc*1e3,'%.1f'),'meV'))
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,3,'fontsize',FS)
hold on; grid on;box on;
plot(E,FEcc,'g.-')
plot(E,FEvv,'r.-')
plot(E,FEcc-FEvv,'b.-')
xlabel('E (eV)')
ylabel('Losses / Gain')
xlim([0 E(end)])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,4,'fontsize',FS)
hold on; grid on;box on;
plot(E,Gain,'m.-')
xlabel('E (eV)')
ylabel('Losses / Gain (cm-1)')
xlim([0.9*Eg E(end)])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%