Chapter 1

% Fig.1.1.1

clear all%Constants (all MKS, except energy which is in eV)hbar=1.055e-34;q=1.602e-19;eps0=8.854E-12;epsr=4;m=0.25*9.11e-31;%Effective massI0=q*q/hbar;%ParametersW=1e-6;L=10e-9;t=1.5e-9;%W=Width,L=Length of active region,t=oxide thicknessCg=epsr*eps0*W*L/t;Cs=0.05*Cg;Cd=0.05*Cg;CE=Cg+Cs+Cd;U0=q/CE;alphag=Cg/CE,alphad=Cd/CE%alphag=1;alphad=0.5;U0=0.25;kT=0.025;mu=0;ep=0.2;v=1e5;%Escape velocityg1=hbar*v/(q*L);g2=g1;g=g1+g2;%g1=0.005;g2=0.005;g=g1+g2;%Energy gridNE=501;E=linspace(-1,1,NE);dE=E(2)-E(1);D0=m*q*W*L/(pi*hbar*hbar);% Step Density of states per eVD=D0*[zeros(1,251) ones(1,250)];%D=(2*g/(2*pi))./((E. 2)+((g/2) 2));% Lorentzian Density of states per eV%D=D./(dE*sum(D));%Normalizing to one%Reference number of electronsf0=1./(1+exp((E+ep-mu)./kT));N0=2*dE*sum(D.*f0);ns=N0/(L*W*1e4),%/cm 2%BiasIV=61;VV=linspace(0,0.6,IV);for iV=1:IVVg=0.5;Vd=VV(iV);%Vd=0.5;Vg=VV(iV);mu1=mu;mu2=mu1-Vd;UL=-(alphag*Vg)-(alphad*Vd);U=0;%Self-consistent fielddU=1;while dU>1e-6f1=1./(1+exp((E+UL+U+ep-mu1)./kT));f2=1./(1+exp((E+UL+U+ep-mu2)./kT));N(iV)=dE*sum(D.*((f1.*g1/g)+(f2.*g2/g)));Unew=U0*(N(iV)-N0);dU=abs(U-Unew);U=U+0.1*(Unew-U);endI(iV)=dE*I0*(sum(D.*(f1-f2)))*g1*g2/g;endhold onh=plot(VV,I,'b');set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' Voltage (V) --->')ylabel(' Current (A) ---> ')grid on 

% Fig.1.1.3

clear allE=linspace(-.25,.25,501);dE=E(2)-E(1);kT=0.025;Ef=0;V=0;mu1=Ef+(V/2);mu2=Ef-(V/2);f1=1./(1+exp((E-mu1)./kT));f2=1./(1+exp((E-mu2)./kT));%dE*(sum(f1-f2))/Vhold onh=plot(f1,E,'g');set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' Fermi function --->')ylabel(' E - mu (eV) ---> ')grid on 

% Fig.1.3.3, 1.5.1

clear allE=linspace(-.5,.5,50001);dE=E(2)-E(1);gam=0.05;D=(gam/(2*pi))./((E.^2)+((gam/2)^2));%D=(gam/(2*pi))./(((E-0.25).^2)+((gam/2)^2));%Use for Fig.1.5.2%D=D+((gam/(2*pi))./(((E+0.25).^2)+((gam/2)^2)));%Use for Fig.1.5.2dE*sum(D)hold onh=plot(D,E,'g'); <a name="1099"></a><a name="IDX-345"></a>set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' D (E) --->')ylabel(' E (eV) ---> ')grid on 

% Fig.1.4.6

clear all%Constants (all MKS, except energy which is in eV)hbar=1.055e-34;q=1.602e-19;I0=q*q/hbar;%ParametersU0=0.025;kT=0.025;mu=0;ep=0.2;g1=0.005;g2=0.005;g=g1+g2;alphag=1;alphad=0.5;%Energy gridNE=501;E=linspace(-1,1,NE);dE=E(2)-E(1);D=(g/(2*pi))./((E.^2)+((g/2)^2));% Lorentzian Density of states per eVD=D./(dE*sum(D));%Normalizing to one%BiasIV=101;VV=linspace(0,1,IV);for iV=1:IVVg=0;Vd=VV(iV);%Vd=0;Vg=VV(iV);mu1=mu;mu2=mu1-Vd;UL=-(alphag*Vg)-(alphad*Vd);U=0;%Self-consistent fielddU=1;while dU>1e-6f1=1./(1+exp((E+ep+UL+U-mu1)./kT));f2=1./(1+exp((E+ep+UL+U-mu2)./kT));N(iV)=dE*sum(D.*((f1.*g1/g)+(f2.*g2/g)));Unew=U0*N(iV);dU=abs(U-Unew);U=U+0.1*(Unew-U);endI(iV)=dE*I0*(sum(D.*(f1-f2)))*(g1*g2/g);endhold onh=plot(VV,N,'b');%h=plot(VV,I,'b');set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' Voltage(V)--->')%ylabel(' Current(A)---> ')ylabel('Number of electrons ---> ')grid on 

% Fig.E.1.3

clear all%Constants (all MKS, except energy which is in eV)hbar=1.055e-34;q=1.602e-19;I0=q*q/hbar;%ParametersU0=0.025;kT1=0.026;kT2=0.025;ep=0.2;g1=0.005;g2=0.005;g=g1+g2;alphag=1;alphad=0.5;%Energy gridNE=501;E=linspace(-1,1,NE);dE=E(2)-E(1);g1=0.005*(E+abs(E))./(E+E+1e-6);% zero for negative Eg2=0.005*ones(1,NE);g1=g2;g=g1+g2;%BiasIV=101;VV=linspace(-0.25,0.25,IV);for iV=1:IVmu1=ep+VV(iV);mu2=mu1;f1=1./(1+exp((E-mu1)./kT1));f2=1./(1+exp((E-mu2)./kT2));D=(g./(2*pi))./(((E-ep).^2)+((g./2).^2));D=D./(dE*sum(D));I(iV)=dE*2*I0*(sum(D.*(f1-f2).*g1.*g2./g));endhold on%h=plot(VV,N/2,'b');%Part (a)h=plot(VV,I,'b');set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' Voltage(V)--->')ylabel(' Current (A)---> ')%ylabel(' Number of electrons ---> ')grid on 

% Fig.E.1.4

clear all%Constants (all MKS, except energy which is in eV)hbar=1.055e-34;q=1.602e-19;I0=q*q/hbar;%ParametersU0=0.025;kT=0.025;mu=0;ep=0.2;N0=0;g1=0.005;g2=0.005;g=g1+g2;alphag=1;alphad=0.5;%Energy gridNE=501;E=linspace(-1,1,NE);dE=E(2)-E(1); <a name="1101"></a><a name="IDX-347"></a>g1=0.005*(E+abs(E))./(E+E+1e-6);% zero for negative Eg2=0.005*ones(1,NE);g=g1+g2;%BiasIV=101;VV=linspace(-.6,.6,IV);for iV=1:IVVg=0;Vd=VV(iV);%Vd=0;Vg=VV(iV);mu1=mu;mu2=mu1-Vd;UL=-(alphag*Vg)-(alphad*Vd);U=0;%Self-consistent fielddU=1;while dU>1e-6f1=1./(1+exp((E-mu1)./kT));f2=1./(1+exp((E-mu2)./kT));D=(g./(2*pi))./(((E-ep-UL-U).^2)+((g./2).^2));D=D./(dE*sum(D));N(iV)=dE*2*sum(D.*((f1.*g1./g)+(f2.*g2./g)));Unew=U0*(N(iV)-N0);dU=abs(U-Unew);U=U+0.1*(Unew-U);endI(iV)=dE*2*I0*(sum(D.*(f1-f2).*g1.*g2./g));endhold on%h=plot(VV,N/2,'b');%Part (a)h=plot(VV,I,'b');set(h,'linewidth',[2.0])set(gca,'Fontsize',[25])xlabel(' Voltage (V) ---> ')ylabel(' Current (A) ---> ')%ylabel(' Number of electrons ---> ')grid on 

Chapter 2

% Fig.2.3.2a, b

clear all%Constants (all MKS, except energy which is in eV)hbar=1.055e-34;m=9.110e-31;epsil=8.854e-12;q=1.602e-19;%LatticeNp=100;a=1e-10;X=a*[1:1:Np];t0=(hbar^2)/(2*m*(a^2))/q;L=a*(Np+1);T=(2*t0*diag(ones(1,Np)))-(t0*diag(ones(1,Np-1),1))-(t0*diag(ones(1,Np-1),-1));[V,D]=eig(T);D=diag(D);[Enum,ind]=sort(D);E1=D(ind(1));psi1=abs(V(:,ind(1)));P1=psi1.*conj(psi1);E2=D(ind(25));psi2=abs(V(:,ind(25)));P2=psi2.*conj(psi2); <a name="1103"></a><a name="IDX-348"></a>%analytical eigenvaluesEan=(((hbar*pi)^2)/(2*m*(L^2))/q)*[1:Np].*[1:Np];hold on%h=plot(Enum,'bx');% Part (a)%h=plot(Ean,'b');% Part (a)h=plot(P1,'b');%...