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Schroedinger3D_Main_GaN.m
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Schroedinger3D_Main_GaN.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% last update 11Jan2018, lne %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% model activation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0 for turn off
% 1 for turn on
FE_Method=0; % Diagonalization of the Hamiltonian (FEM)
PWE_Method=1; % Plane Wave Expansion (PWE)
saveXYZ=0;
saveV=0;
savePSI=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n=12; %% number of solution asked
Fx=0;%5e7; %% Electric field [V/m] in the x-direction
Fy=0;%5e6; %% Electric field [V/m] in the y-direction
Fz=0;%5e7; %% Electric field [V/m] in the z-direction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% Potential definition %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Three vectors (x, y and z) and one 3D-matrix V0 must be defined with homogeneous grid
% x, y and z [meter]
% V0 [eV]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nx=64; %% Meshing point in x-direction
Ny=64; %% Meshing point in y-direction
Nz=64; %% Meshing point in z-direction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Choose your between the next 3 potentials or build your own!
%Pot_InAs_GaAs
%Pot_InAs_AlInAs
Pot_GaN_AlN
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%% NOTHING TO CHANGE ANYMORE!!! %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% Selection of the model %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E1=[];E2=[];
display('=======================================')
if FE_Method==1
tic
if length(x)*length(y)*length(z)>1e4
N=length(x)*length(y)*length(z);
display(strcat('Warning: Take care, H=',num2str(N),'x',num2str(N),'elements'))
end
[E1,psi1] = Schroed3D_FEM_f(x,y,z,V0,Mass,n); % m=cste
display(strcat('-> Finite Elements method =',num2str(toc),'sec'))
end
if PWE_Method==1
Nx = 64 ; % number of points on the x grid % has to be a power of 2 (32,64,128,256,512,...) (smaller => faster)
Ny = 64 ; % number of points on the y grid % has to be a power of 2 (32,64,128,256,512,...) (smaller => faster)
Nz = 64 ; % number of points on the y grid % has to be a power of 2 (32,64,128,256,512,...) (smaller => faster)
NGx = 13;%Nx/2-1 ; % number of harmonics % must be at least 2 times -1 smaller than Nz (smaller => faster)
NGy = 15;%Ny/2-1 ; % number of harmonics % must be at least 2 times -1 smaller than Nz (smaller => faster)
NGz = 17;%Ny/2-1 ; % number of harmonics % must be at least 2 times -1 smaller than Nz (smaller => faster)
tic
[E2,psi2] = Schroed3D_PWE_f(x,y,z,V0,Mass,n,Nx,Ny,Nz,NGx,NGy,NGz);
display(strcat('-> PWE method =',num2str(toc),'sec'))
if Fx~=0 || Fy~=0 || Fz~=0
display('Warning: The PWE method is not the best for non-periodic potential')
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Display Results %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E=nan(n,2);
E(1:length(E1),1)=E1;
E(1:length(E2),2)=E2;
display('=======================================')
display('Results:')
display('=======================================')
display(strcat('E(eV)='))
display(strcat(num2str(E)))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if FE_Method==1
c=0;
ii=0;
for i=1:n
if i>18
break
end
if i==1 || i==7 || i==13
figure('Name','FEM method','position',[100 100 1600 800])
c=c+1;
ii=0;
end
ii=ii+1;
subplot(2,3,ii,'fontsize',10)
hold on;grid on;view (-38, 20);
idz=find(z>0);idz=idz(1);
pcolor(x*1e9,y*1e9,squeeze(V0(:,:,idz)))
colormap(cool)
%shading flat
PSI=abs(psi1(:,:,:,i)).^2;
p = patch(isosurface(x*1e9,y*1e9,z*1e9,PSI,max(PSI(:))/6));
isonormals(x*1e9,y*1e9,z*1e9,PSI, p)
set(p, 'FaceColor', 'red', 'EdgeColor', 'none', 'FaceLighting', 'gouraud')
daspect([1,1,1])
light ('Position', [1 1 5]);
M=max([Mx My]);
xlim([-1 1]*M/3*1e9)
ylim([-1 1]*M/3*1e9)
zlim([-1 1]*M/3*1e9)
xlabel('x (nm)')
ylabel('y (nm)')
zlabel('z (nm)')
title(strcat('E',num2str(i),'-E1=',num2str((E(i,1)-E(1,1))*1000,'%.1f'),'meV'))
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if PWE_Method==1
c=0;
ii=0;
for i=1:n
if i>18
break
end
if i==1 || i==7 || i==13
figure('Name','PWE method','position',[-1900 50 1850 1050])
c=c+1;
ii=0;
end
ii=ii+1;
% subplot(2,3,ii,'fontsize',10)
x0=0;y0=0;
ww=0.35;
hh=0.35;
if i<4
subplot('position',[x0+(i-1)*0.35 y0+0.6 ww hh])
elseif i<7
subplot('position',[x0+(i-4)*0.35 y0+0.05 ww hh])
elseif i<10
subplot('position',[x0+(i-7)*0.35 y0+0.6 ww hh])
elseif i<13
subplot('position',[x0+(i-10)*0.35 y0+0.05 ww hh])
end
hold on;%grid on;
%axis off
view (-38, 30);
aa=[
-sqrt(3)/2*a -a/2 0
-sqrt(3)/2*a +a/2 0
0 +a 0
+sqrt(3)/2*a +a/2 0
+sqrt(3)/2*a -a/2 0
0 -a 0
-sqrt(3)/2*a -a/2 0
]*1e9;
plot3(aa(:,1),aa(:,2),aa(:,3),'k','linewidth',2)
bb=[
+(QDh-h)/h*sqrt(3)/2*a -(h-QDh)*a/h/2 QDh
+(QDh-h)/h*sqrt(3)/2*a +(h-QDh)*a/h/2 QDh
0 +(h-QDh)*a/h QDh
-(QDh-h)/h*sqrt(3)/2*a +(h-QDh)*a/h/2 QDh
-(QDh-h)/h*sqrt(3)/2*a -(h-QDh)*a/h/2 QDh
0 -(h-QDh)*a/h QDh
+(QDh-h)/h*sqrt(3)/2*a -(h-QDh)*a/h/2 QDh
]*1e9;
plot3(bb(:,1),bb(:,2),bb(:,3),'k','linewidth',2)
for j=1:length(aa(:,1))
plot3([aa(j,1) bb(j,1)],[aa(j,2) bb(j,2)],[aa(j,3) bb(j,3)],'k','linewidth',2)
end
%contour(x*1e9,y*1e9,squeeze(V0(:,:,idz)),1,'linewidth',3,'linecolor','k')
%idz=find(z>QDh);idz=idz(1)-1;
%contour(x*1e9,y*1e9,squeeze(V0(:,:,idz)),1,'linewidth',3,'linecolor','k')
%shading flat
PSI=abs(psi2(:,:,:,i)).^2;
p = patch(isosurface(x*1e9,y*1e9,z*1e9,PSI,max(PSI(:))/6));
isonormals(x*1e9,y*1e9,z*1e9,PSI, p)
set(p, 'FaceColor', 'red', 'EdgeColor', 'none', 'FaceLighting', 'gouraud')
daspect([1,1,1])
light ('Position', [1 1 5]);
M=max([Mx My]);
xlim([-1 1]*M/3*1e9)
ylim([-1 1]*M/3*1e9)
zlim([-1 1]*M/3*1e9)
xlabel('x (nm)')
ylabel('y (nm)')
zlabel('z (nm)')
title(strcat('E',num2str(i),'-E1=',num2str((E(i,2)-E(1,2))*1000,'%.1f'),'meV'))
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Data save %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if saveXYZ==1;
x=x';y=y';z=z';
save('data_x.txt','x','-ascii')
save('data_y.txt','y','-ascii')
save('data_z.txt','z','-ascii')
end
if saveV==1;
save('data_V.txt','V0','-ascii')
end
if savePSI==1;
if FE_Method==1
for i=1:n
M1 = psi1(:,:,:,i);
save(strcat('data_psi',num2str(i),'_FEM.txt'),'M1','-ascii')
end
end
if PWE_Method==1
for i=1:n
M2 = real(psi2(:,:,:,i));
save(strcat('data_psi',num2str(i),'_PWE.txt'),'M2','-ascii')
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%