Introduction to Nanomaterials and Devices

Appendix F

Transmission Coefficient in Superlattices

The following is a Matlab program for the calculation of the transmission coefficient in short-period superlattices, which is based on the propagation matrix method. This program is adapted from Levi's “Applied quantum mechanics,” (Cambridge University Press, Cambridge, England, 2003).

 %Superlattices.m %resonant tunneling through 4 barriers of short period superlattices clear clf; nbarrier=4; %number of potential barriers bx=2.5e-9; %barrier width (m) wx=2.e-9; %well width (m) V0=0.68; %barrier energy (eV) N=(2*nbarrier)+1; %number of samples of potential for j=1:2:(2*nbarrier) %set up distance 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=1.0; %maximum particle energy (eV) npoints=2000; %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=0.22; %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)); ...