%Fig7_10b.m %Essential Electron Transport for Device Physics %Zero temperature Lindhard dielectric funtion in GaAs with optical phonons; %calculates elastic scattering rate as function of electron %injection energy (meV) 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=['\fontname{MT Extra}h\fontname{Arial}']; Emax=400; %maximum energy of injected electron (meV) 300 npoints=40; %number of points in plot ntheta=40; %number of increments dth in angular integral n1=1.e18; %electron carrier concentration (cm^-3) n=n1*1.e6; %convert to m^-3 m0=9.1095e-31; %bare electron mass mass=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 hb=1.05459e-34; %Plank constant (J s) echarge=1.60219e-19; %electron chanrge (C) a0=0.529177e-8; %Bohr radius (cm) kf=(3.0*(pi^2)*n)^(1/3); %Fermi wave vector (m^-1) Ef=((hb*kf)^2)/(2*m0*mass); %Fermi energy (eV) Ef=(Ef*1e3)/echarge; %Fermi energy (meV) Estep=(Emax-Ef)/npoints; %electron increment in energy %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ak3=(kf^3); a=einf*((wLO/wTO)^2); %zero frequency contribution from lattice const=(2.0*mass*pi*n1*3.0)/(ak3*137.036*a0*1.0e8); rs=((mass*.33172)/a0)*((3.0/(4.0*pi*n1))^0.3333333333333); ei=(Ef-Estep)/Ef; dth=pi/ntheta; % % for i=1:1:npoints+1 ei=ei+(Estep/Ef); %increment electron energy normalized to Ef ak=ei^-1.5; x1=2.*sqrt(ei); aint1=0.0; %set angular integral to zero theta=0.0; %set angular integral to zero for j=1:1:(ntheta/2) theta=theta+dth; %******************************************************** x=x1*sin(theta); b=x+(1.-((x^2)/4.))*log(abs((x+2.0)/(x-2.0))); g=(tan(theta))*(((sin(theta))*(a+(rs/(x^3))*b))^2); gchi=1./g; %******************************************************** aint1=aint1+(dth*gchi); end y2(i)=const*ak*aint1; x2(i)=Ef*ei; end figure(1); plot(x2,y2*1e12); xlabel('Energy, \itE_k\rm (meV)'); ylabel('Elastic scattering rate, 1/ \tau_{el} (ps^{-1})'); axis([0 Emax 0 15]); ttl2=['\rmFig7.10b, GaAs, \itT\rm=0 K, \itm\rm^*_e=',num2str(mass),... '\times\itm\rm_0, \itn\rm_0=',... num2str(n1/1e18),'\times10^{18} cm^{-3}, \itE\rm_F=',... num2str(Ef,'%5.1f'),' meV']; title(ttl2); return