%Chapt4Exercise3b.m
%resonant tunneling through 3 barriers

clear
clf;
nbarrier=3;						%number of potential barriers
bx=0.1e-9;						%barrier width (m)
wx=0.4e-9;						%well width (m)
V0=10;							%barrier energy (eV)

N=(2*nbarrier)+1;				%number of samples of potential
for j=1:2:(2*nbarrier)          %set up position and potential array
   dL(j)=wx;   V(j)=0;
   dL(j+1)=bx; V(j+1)=V0;
end
   dL(N)=wx;   V(N)=0;
   
Emin=pi*1e-5;					%add (pi*1.0e-5) to 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=1.05457159e-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;deltax=xcell/1000;x0=[wx-deltax,wx,xcell-deltax,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,Emax]),xlabel('Position, x (m)'),ylabel('Potential energy, V (eV)');
ttl=['Chapt4Exercise3b (',num2str(nbarrier),'-barriers), m_{eff} = ',num2str(meff),' x m_0'];
title(ttl);
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,Emax]),xlabel('Position, x (m)');ylabel('Potential energy, V (eV)');
title(ttl);
subplot(1,2,2);plot(-log(Trans),E);axis([0,20,0,Emax]);xlabel('-ln trans. coeff.');ylabel('Energy, E (eV)');