%Chapt4Exercise3a.m
%resonant tunneling through 12 barriers

clear
clf;
nbarrier=12;				%number of potential barriers
bx=0.1;					%barrier width (m)
wx=0.4;					%well width (m)
V0=10;						%barrier energy (eV)
v0=5;

N=(2*nbarrier)+1;			%number of samples of potential
for j=1:4:(2*nbarrier)		%set up distance and potential array
   dL(j)=wx*10^-9;   V(j)=0;
   dL(j+1)=bx*10^-9; V(j+1)=V0;
   dL(j+2)=wx*10^-9; V(j+2)=0;
   dL(j+3)=bx*10^-9; V(j+3)=v0;
end
   dL(N)=wx;   V(N)=0;
   
Emin=0;				%add (pi*1.0e-5) energy to avoid divide by zero
Emax=15;					%maximum particle energy (eV)
npoints=1500;				%number of points in energy plot
dE=Emax/npoints;			%energy increment (eV)
hbar=1.0545715e-34;			%Planck's constant (J s)
eye=complex(0.,1.);			%square root of -1
m0=9.109382e-31;			%bare electron mass (kg)
meff=1.0;					%effective electron mass / m0
m=meff*m0;					%effective electron mass (kg)
echarge=1.6021764e-19;		%electron charge (C)

   for j=1:npoints
      E(j)=dE*j+Emin;
      bigP=[1,0;0,1];		%default value of matrix bigP
      	for i=1:N
         k(i)=sqrt(2*echarge*m*(E(j)-V(i)))/hbar;%wave vector at energy E
      	end
      for n=1:(N-1)			%multiply out propagation matrix
         p(1,1)=0.5*(1+k(n+1)/k(n))*exp(-eye*k(n)*dL(n));
         p(1,2)=0.5*(1-k(n+1)/k(n))*exp(-eye*k(n)*dL(n));
         p(2,1)=0.5*(1-k(n+1)/k(n))*exp(eye*k(n)*dL(n));
         p(2,2)=0.5*(1+k(n+1)/k(n))*exp(eye*k(n)*dL(n));
         bigP=bigP*p;
      end
      Trans(j)=(abs(1/bigP(1,1)))^2;%transmission coefficient
   end
   
figure(1);					%plot potential and transmission coefficient
Vp=[V;V];Vp=Vp(:);
xcell=bx+wx;x0=[wx,wx,xcell,xcell];x=x0;
for j=1:(N-3)/2
    x=[x,x0+j*xcell];
end
x=[0,x,(nbarrier+1)*xcell];
subplot(1,2,1),plot(x,Vp),axis([0,(nbarrier+1)*xcell,0,11]);
xlabel('Position, x (nm)'),ylabel('Potential energy, V (eV)');
subplot(1,2,2),plot(Trans,E),axis([0,1,0,Emax]),...
    xlabel('Transmission coefficient'),ylabel('Energy, E (eV)');
  
figure(2);
subplot(1,2,1),plot(x,Vp);axis([0,(nbarrier+1)*xcell,0,11]);
xlabel('Position, x (nm)');ylabel('Potential energy, V (eV)');
subplot(1,2,2);plot(-log(Trans),E);axis([0,70,0,Emax]);
xlabel('-ln trans. coeff.');ylabel('Energy, E (eV)');