%Fig6_1.m %Essential Electron Transport for Device Physics %GaAs with LO phonons; %plotting parameters + fontsizes clear all; clf; FS = 12; %label fontsize 18 FSN = 12; %number fontsize 16 LW = 1; %linewidth % Change default axes fonts. set(0,'DefaultAxesFontName', 'Times New Roman') set(0,'DefaultAxesFontSize', FSN) % Change default text fonts. set(0,'DefaultTextFontname', 'Times New Roman') set(0,'DefaultTextFontSize', FSN) hbar=('\fontname{MT Extra}h\fontname{Times New Roman}'); %************************************************************************** n1=1.e18 %electron carrier concentration (cm^-3) n=n1*1.e6; %convert to m^-3 m0=9.1095e-31; %bare electron mass ms=0.07; %effective electron mass in conduction band wLO=36.3; %longitudinal optic phonon energy (meV) wTO=33.3; %transverse optic phonon energy (meV) einf=11.1; %high frequency dielectric constant e0=einf*(wLO/wTO)^2; %low frequency dielectric constant hb=1.05459e-34; %Plank constant (J s) e=1.60219e-19; %electron chanrge (C) a0=0.529177e-10; %Bohr radius (m) kf=(3*(pi^2)*n)^(1/3); %Fermi wave vector (m^-1) kf1=kf*1e-2; %Fermi wave vector (cm^-1) Ef=((hb*kf)^2)/(2*m0*ms); %Fermi energy (eV) Ef=(Ef*1e3)/e; %Fermi energy (meV) wLO2=(wLO/Ef)^2; wTO2=(wTO/Ef)^2; zeta=ms/(pi*kf*a0); gamma=.035; %Energy broadening (GAMMA / Ef) 0.01 x=0.2; %Wave vector (k/kf) 0.1 zeta=zeta/x^3; a4=2*x; %[ start:increment:stop]; y=[0:.001:1.1]; %energy loss OMEGA/Ef ygamma=y+(i*gamma); %energy loss OMEGA/Ef with small broadening % a1=(1-1/4*(x-y/x).^2).*log((y-x*(x+2))./(y-x*(x-2))); % a2=(1-1/4*(x+y/x).^2).*log((-y-x*(x+2))./(-y-x*(x-2))); % a3=zeta*(a4+a1+a2); % epsi=((y./(y-i*gamma)).*a3)+(einf*((y.^2-wLO2)./(y.^2-wTO2)));%with LO phonons %epsi=((y./(y-i*gamma)).*a3)+einf; %without phonons epsi=(einf*(((y.*ygamma)-wLO2)./((y.*ygamma)-wTO2))); %with LO phonons only %************************************************************************** ttl=['\rmFig6.1, \itm\rm^*_e = ',num2str(ms),... '\times\itm\rm_0, \gamma = ',num2str(gamma*Ef,'%3.1f'),' meV']; figure(1); %plot real and imaginary epsilon plot(y*Ef,real(epsi),'b','LineWidth',LW); hold on; plot(y*Ef,imag(epsi),'r','LineWidth',LW); grid on title(ttl); x1=wLO/10; yscale=ylim; y1=yscale(2)/2; y2=y1*1.2; y3=y1*1.4; y4=y1*1.6; text(x1,y1,[hbar,'\omega_{LO} = ',num2str(wLO),' meV ']); text(x1,y2,[hbar,'\omega_{TO} = ',num2str(wTO),' meV']); text(x1,y3,['\epsilon_{\infty} = ',num2str(e0,'%3.1f')]); text(x1,y4,['\epsilon_{\infty} = ',num2str(einf,'%3.1f')]); xttl=['Energy loss, ',hbar,'\omega (meV)']; xlabel(xttl); ylabel('Dielectric function, \epsilon(\omega)'); axis([0 max(y*Ef) 1.1*min(real(epsi)) 1.1*max(imag(epsi))]); hold off; figure(2); %plot loss function plot(y*Ef,-imag(1./epsi),'r','LineWidth',LW); grid on title(ttl); xlabel(xttl); ylabel('Loss function, Im(-1/\epsilon(\omega))'); x1=wLO/10; yscale=ylim; y1=yscale(2)/2; y2=y1*1.2; y3=y1*1.4; y4=y1*1.6; text(x1,y1,[hbar,'\omega_{LO} = ',num2str(wLO),' meV ']); text(x1,y2,[hbar,'\omega_{TO} = ',num2str(wTO),' meV']); text(x1,y3,['\epsilon_{\infty} = ',num2str(e0,'%3.1f')]); text(x1,y4,['\epsilon_{\infty} = ',num2str(einf,'%3.1f')]); y1=yscale(2)/2; axis([0 max(y*Ef) 0 1.1*max(-imag(1./epsi))]); hold off;