%Fig3_9.m %Essential Electron Transport for Device Physics %resonant tunneling through 3 barriers clear clf; FS = 12; %label fontsize 18 FSN = 12; %number fontsize 16 LW = 1; %linewidth % Change default axes fonts. set(0,'DefaultAxesFontName', 'Times'); set(0,'DefaultAxesFontSize', FSN); % Change default text fonts. set(0,'DefaultTextFontname', 'Times'); set(0,'DefaultTextFontSize', FSN); hbar_txt=['\fontname{MT Extra}h\fontname{Arial}']; nbarrier=3; %number of potential barriers bx=0.4e-9; %barrier thickness (m) wx=0.6e-9; %well width (m) V0=0.5; %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=0.1+(pi*1e-5); %add (pi*1.0e-5) to energy to avoid divide by zero Emax=0.5; %maximum particle energy (eV) npoints=500; %number of points in energy plot dE=(Emax-Emin)/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) bxmin=0.1e-9; %minimum central barrier thickness bxmax=1.5e-9; %maximum central barrier thickness mpoints=500; %number of samples dbx=(bxmax-bxmin)/mpoints; for mcount=1:mpoints %loop for barrier thickness dL(4)=bxmin+(mcount*dbx); %central barrier thickness xp(mcount)=dL(4); %central barrier thickness vector used in plot for j=1:npoints %loop for energy values 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,mcount)=(abs(1/bigP(1,1)))^2; %transmission coefficient end end ttl=(['\rmFig3.9 (',num2str(nbarrier),'-barriers), \itm\rm^*_e='... ,num2str(meff),'\times\itm\rm_0']); figure(1); surfl(xp,E,Trans); axis square; axis([bxmin bxmax Emin Emax 0 1]); colormap(copper); shading interp; title(ttl); xlabel('Central barrier thickness (m)'); ylabel('Energy, \itE\rm (eV)') zlabel('Transmission')