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SchrodingerPoisson1D_CB_Kane_Main.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%% last update 20December2021, lne %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This program solves the Schrodinger-Poisson equation in the conduction band
% for any heterostructures in the Zinc-Blend material.
% The program solves the Schrodinger equation with m(E,z) using different algorithms:
% -> FDM (Finite Difference Method)
% and / or
% -> Scaning/Shooting method
% The non-parabolicity is implemented via the kp model using the Kane model
% A strain model is included. It basically shifts the conduction band edge
% The strain is mainly interesting for InGaAs/GaAs heterostructures
% The non-parabolicity is also included into the density of states for the Poisson solver.
% It follows the book of Paul Harrison and actually makes the 2d density of states not constant
% -> Additionnal material can be added in the "materialDB_ZB.csv" file
% -> II-VI and cubic nitride material parameters are available but should
% be grabt in the "Library.m" file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% If the code doesn t converge:
% -> decrease the doping
% -> increase the resolution dz
% -> increase the temperature (T=0K is very bad while T=10K is already much better)
% -> increase the amount of loops, Nloops
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Constants %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
h = 6.62606896E-34; %% Planck constant [J.s]
hbar = h/(2*pi);
e = 1.602176487E-19; %% electron charge [C]
m0 = 9.10938188E-31; %% electron mass [kg]
Epsi0= 8.854187817620E-12; %% Vaccum dielectric constant [F/m]
kB = 1.3806488E-23; %% Boltzmann's constant [J/K]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nloops = 5; % number of loops
model = 2; % 1=shooting; 2=Kane
StrainModel = 0; % Activate Strain model
n = 3; % number of solution asked per model
ScF = 0.1; % scaling factor to plot the wave function [Without Dimension]
dz = 1e-10; % resolution of the grid [m]
T = 300; % Temperature [Kelvin]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DisplayResults = 1; % Switch to print or not the ISB dipoles on the shell
plot_density = 1; % Activate the plot 0 or 1
plot_convergence = 0; % Activate the plot 0 or 1
plot_field = 0; % Activate the plot 0 or 1
plot_Vbending = 0; % Activate the plot 0 or 1
plot_mass = 0; % Activate the plot 0 or 1
plot_ro = 0; % Activate the plot 0 or 1
plot_Epsi = 0; % Activate the plot 0 or 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Library; % load material parameter DB from "materialDB_ZB.csv"
ExtractParameters; % extract parameter from the Library
TernaryAlloy; % compute the ternary alloy
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%% import the layer structure file %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% first column is the material used from the "library"
% second column is the length of the layer in nm
% third column is the n doping volumique of that layer in 1e18 cm-3
% You have to put a resonable amount of doping! Otherwise, it will diverge
% and you will have to damp it more by increasing the number of loops !
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
input_file;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% NOTHING TO CHANGE ANYMORE !!! %%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% Grabbing the parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
zt = M(:,end-1)*1e-9; % conversion of the length from nm to meter
Dopt = M(:,end)*1e18*1e6; % n doping conversion from cm-3 to m-3
Egt = M(:,idx_Eg6c) - (M(:,idx_alphaG)*T^2) ./ (T+M(:,idx_betaG)); %Eg = Eg0 - (a*T.^2)./(T + b);
CBOt = Egt+M(:,idx_VBO); % CBO form band gap difference and temperature
Dsot = M(:,idx_Dso); % Spin-Orbit shift band parameter
EPt_K= M(:,idx_EP_K); % EP Kane
Epsit= M(:,idx_Epsi); % Epsilon; dielectric constant
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Strain Model %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
at = M(:,idx_a); % lattice parameter
act = M(:,idx_ac); % Conduction band strain offset parameter
avt = M(:,idx_av); % Valence band strain offset parameter
bvt = M(:,idx_bv); % Valence band strain offset parameter
c11t = M(:,idx_c11); % strain parameter
c12t = M(:,idx_c12); % strain parameter
a0 = substrate(idx_a);
if StrainModel == 1
exxt = (a0-at)/a0; % eyyt = exxt;
ezzt = -2*c12t./c11t.*exxt;
else
exxt = (a0-at)/a0 * 0; % eyyt = exxt;
ezzt = -2*c12t./c11t.*exxt;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Discretisation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% here, I descretize the grid z, the potential V0 and that values that are needed
z=0; V0=CBOt(1); Eg=Egt(1); Dso=Dsot(1); EP_K=EPt_K(1);
Dop=Dopt(1); Epsi=Epsit(1);
ac=act(1); av=avt(1); bv=bvt(1); exx=exxt(1); ezz=ezzt(1);
for i=1:length(zt)
t=zt(i);
zv= (z(end)+dz): dz : (z(end)+dz)+t;
z=[z zv];
V0 = [ V0 ones(size(zv)) * CBOt(i) ];
Eg = [ Eg ones(size(zv)) * Egt(i) ];
Dop = [ Dop ones(size(zv)) * Dopt(i) ];
Epsi= [ Epsi ones(size(zv)) * Epsit(i) ];
EP_K= [ EP_K ones(size(zv)) * EPt_K(i) ];
Dso = [ Dso ones(size(zv)) * Dsot(i) ];
ac = [ ac ones(size(zv)) * act(i) ];
av = [ av ones(size(zv)) * avt(i) ];
bv = [ bv ones(size(zv)) * bvt(i) ];
exx = [ exx ones(size(zv)) * exxt(i) ];
ezz = [ ezz ones(size(zv)) * ezzt(i) ];
end
V0=V0-min(V0); % Shift the band in order to get the bottom of the well at zero
V0=(F0*z)+V0; % adding the electric field to the potential
Ltot=z(end)-z(1);
eyy = exx;
DCBO = -abs(ac).*(exx+eyy+ezz) ; % shift of the CB due to strain
Ntott= Dopt.*zt;
Ntot = sum(Ntott); % total number of charges
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dE1=1e-3;
dE2=1e-2;
if StrainModel == 0
E1 = min(V0):dE1:min(V0)+0.2 ;
E2 = E1(end):dE2:max(V0);
En = sort([E1 E2]);
else
E1 = min(V0+DCBO):dE1:min(V0+DCBO)+0.2 ;
E2 = E1(end):dE2:max(V0+DCBO);
En = sort([E1 E2]);
end
if model==1
EEn = repmat(En', [1 length(z)]);
V0mat = repmat(V0 , [length(En) 1]);
Egmat = repmat(Eg , [length(En) 1]);
Dsomat = repmat(Dso, [length(En) 1]);
EPmat = repmat(EP_K ,[length(En) 1]);
meK2 = 1 ./ ( 1 + EPmat ./ (EEn + Egmat-V0mat+1/3*Dsomat) ); % m(z,E) in the 2 bands Kane s model
% here, I linearize the mass versus the energy
meff0 = 1 ./ ( 1 + EPmat ./ (Egmat-V0mat+1/3*Dsomat) );
alpha = ( meK2(end,:)./meff0(end,:) - 1 ) ./ EEn(end,:);
alphamat= repmat(alpha , [length(En) 1] );
meK2lin = meff0.*(1+alphamat.*EEn); % => linearized mass
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%% Starting of the Poisson s loop %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Vs=zeros(size(z)); Vsold=Vs;
ntot=0; nloop=1;
ErrVec=1; sumVtotVec=1;
while nloop<Nloops
nloop
x = 0.5;
Vbending=Vs*x + Vsold*(1-x);
Vtot=V0+Vbending;
%%%%%%%%%%%%%%%%%%%%%%%%%%%% schrodinger solver %%%%%%%%%%%%%%%%%%%%%%%%%%%%
if model==1
dE=0.002;
precision=1e-7;
Vtotmat = repmat(Vtot, [length(En) 1]);
meK2 = 1 ./ ( 1 + EPmat ./ (EEn + Egmat-Vtotmat+1/3*Dsomat) ); % m(z,E) in the 2 bands Kane s model
[Ec,psic] = Schrod_Nbands_shoot_f(z,Vtot+DCBO,meK2,n,En,dE,precision);
elseif model==2
[Ec,psic] = Schrod_2bands_Kane_f(z,Vtot,Eg,EP_K,Dso,n,ac,av,bv,exx,ezz);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Here, I re-define the energy grid in order optimize the meshing
dE1=1e-4;
dE2=1e-2;
if StrainModel == 0
E1 = Ec(1):dE1:Ec(1)+0.1 ;
E2 = E1(end):dE2:max(Vtot);
En=sort([E1 E2]);
else
E1 = Ec(1):dE1:Ec(1)+0.1 ;
E2 = E1(end):dE2:max(Vtot+DCBO);
En=sort([E1 E2]);
end
EEn = repmat(En' , [1 length(z) ]);
V0mat = repmat(V0 , [length(En) 1]);
Vtotmat = repmat(Vtot, [length(En) 1]);
Egmat = repmat(Eg , [length(En) 1]);
Dsomat = repmat(Dso , [length(En) 1]);
EPmat = repmat(EP_K, [length(En) 1]);
meK2 = 1 ./ ( 1 + EPmat ./ (EEn + Egmat-Vtotmat+1/3*Dsomat) ); % m(z,E) in the 2 bands Kane s model
% here, I linearize the mass versus the energy
meff0 = 1 ./ ( 1 + EPmat ./ (Egmat-Vtotmat+1/3*Dsomat) );
alpha = ( meK2(end,:)./meff0(end,:) - 1 ) ./ EEn(end,:);
alphamat= repmat(alpha , [length(En) 1] );
meK2lin = meff0.*(1+alphamat.*EEn); % => linearized mass
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Paul Harrisson
% Quantum Wells, Wires and Dots.
% 4th edition (2016),
% chap 2 : "Solutions to Schrodinger's equation"
% 2.42: "Two-dimensional systems" page 31
meffro = meff0.*(1+2*alphamat.*EEn); % => linearized mass
ro=[];
for i=1:length(Ec)
%ro( En>Ec(i),:,i) = e* meK2(En>Ec(i),:) * m0/(pi*hbar^2);
%ro( En>Ec(i),:,i) = e*meK2lin(En>Ec(i),:) * m0/(pi*hbar^2);
ro( En>Ec(i),:,i) = e*meffro(En>Ec(i),:) * m0/(pi*hbar^2);
ro( En<Ec(i),:,i) = 0;
end
% here is what make the code very slow
if Ntot==0
idx=find(min(CBOt)==CBOt);
Ef=-Egt(idx(1))/2;
NN=0*Ec';
roEf=ro*0;
else
[Ef,NN,roEf]=find_Ef_f(z,Ec,psic,En,ro,Ntot,T);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ntot2 = repmat(NN,[length(z) 1]).*abs(psic).^2 ;
ntot = sum(ntot2,2)' - Dop; % remove the charge positives (ions)
%%%%%%%%%%%%%%%%%%%%%%%%%% Electrical Field %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
F = e*cumtrapz(z,ntot)./(Epsi0*Epsi);
MF = trapz(z,F)/(z(end)-z(1)); % MF=mean(F) on a nonlinear grid z
F = F-MF;
%%%%%%%%%%%%%%%%%%%%%%%%%%% New Potential %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Vsold = Vs;
Vs = -cumsum(F)*dz;
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Convergence %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Err = abs( 1 - sumVtotVec(end)/sum(Vs) );
sumVtotVec(nloop) = sum(Vs);
ErrVec = [ErrVec Err];
nloop=nloop+1;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Display Results %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
scale_PSI;
computesISBdipoles;
if DisplayResults == 1
PrintResults;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%figure('position',[-3500 100 1000 700],'color','w');
figure('position',[10 100 1000 700],'color','w');
subplot(1,1,1,'fontsize',15)
hold on; grid on; box on;
col=colormap(jet);
if plot_density==1
grid off
pcolor(z*1e9,En,sum(ROEf,3)*1e-6 )
set(gca,'color',col(1,:))
shading flat
hcb=colorbar;
caxis([0 max(max(sum(ROEf,3)*1e-6))+1])
title(hcb,'\fontsize{8}cm-3')
if StrainModel == 0
plot(z*1e9,V0, 'w--','linewidth',1)
plot(z*1e9,Vtot,'w-' ,'linewidth',1)
else
plot(z*1e9,V0+DCBO, 'k--','linewidth',1)
plot(z*1e9,Vtot+DCBO,'k-' ,'linewidth',1)
end
elseif plot_density==0
if StrainModel == 0
plot(z*1e9,V0, 'b--','linewidth',1)
plot(z*1e9,Vtot,'b-' ,'linewidth',1)
else
plot(z*1e9,V0+DCBO, 'k--','linewidth',1)
plot(z*1e9,Vtot+DCBO,'k-' ,'linewidth',1)
end
end
for i=1:length(Ec)
plot(z*1e9,PSIc(:,i),'color','r','linewidth',1)
end
plot([z(1) z(end)]*1e9,[1 1]*Ef,'g','linewidth',1)
text(z(end)*1e9*0.95,Ef+0.01,'\color{green}Fermi')
xlabel('z (nm)')
ylabel('Energy (eV)')
xlim([0 z(end)*1e9])
if StrainModel == 1
title(strcat('T=',num2str(T),'K ; dz=',num2str(dz*1e9),'nm; Ntot=',num2str(Ntot*1e-4,'%.1e'),'cm-2; with STRAIN'))
else
title(strcat('T=',num2str(T),'K ; dz=',num2str(dz*1e9),'nm; Ntot=',num2str(Ntot*1e-4,'%.1e'),'cm-2; without STRAIN'))
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_convergence==1
figure('color','w')
semilogy(1:nloop,ErrVec,'bo-')
hold on; grid on; box on;
xlabel('Cycles')
ylabel('Convergence (norm. units)')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_field==1
figure('color','w')
hold on; grid on; box on;
[AX,H1,H2]=plotyy(z*1e9,F*1e-2*1e-3,z*1e9,Dop*1e-18*1e-6);
set(H1,'color','r')
set(H2,'color','b')
xlabel('z (nm)')
ylabel(AX(1),'E- field (kV/cm)','color','red')
ylabel(AX(2),'Doping (1e18 cm-3)','color','blue')
set(AX(1),'ycolor','red')
set(AX(2),'ycolor','blue')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_Vbending==1
figure('color','w')
hold on; grid on; box on;
[AX,H1,H2]=plotyy(z*1e9,Vbending,z*1e9,ntot*1e-18*1e-6);
set(H1,'color','r')
set(H2,'color','b')
xlabel('z (nm)')
ylabel(AX(1),'Vbending (eV)','color','red')
ylabel(AX(2),'ntot (1e18 cm-3)','color','blue')
set(AX(1),'ycolor','red')
set(AX(2),'ycolor','blue')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_mass==1
figure('color','w')
subplot(1,2,1)
hold on; grid on; box on;
pcolor(z*1e9,En,meK2)
colormap(jet)
hcb=colorbar;
title(hcb,'\fontsize{8}meff')
shading flat
xlabel('z (nm)')
ylabel('Energy (eV)')
title('meK2')
xlim([0 z(end)*1e9])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(1,2,2)
hold on; grid on; box on;
pcolor(z*1e9,En,meK2lin)
colormap(jet)
hcb=colorbar;
title(hcb,'\fontsize{8}meff')
shading flat
xlabel('z (nm)')
ylabel('Energy (eV)')
title('meK2-lin')
xlim([0 z(end)*1e9])
% figure
% hold on;grid on;
% idx=250;
% plot(En,meK2(:,idx),'b')
% plot(En,meK2lin(:,idx),'r')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_ro==1
figure('color','w')
hold on; grid on; box on;
surf(z*1e9,En,sum(ro,3))
view(45,30)
colormap(jet)
hcb=colorbar;
title(hcb,'\fontsize{8}ro')
shading flat
xlabel('z (nm)')
ylabel('Energy (eV)')
xlim([0 z(end)*1e9])
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if plot_Epsi==1
figure('color','w')
hold on; grid on; box on;
plot(z*1e9,Epsi,'.-')
xlabel('z (nm)')
ylabel('Epsilon')
xlim([0 z(end)*1e9])
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%