%Fig7_6b.m %Essential Electron Transport for Device Physics %Plot Thomas Fermi scattering rate as function of angle and compare with RPA 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); n=1e14; %electron carrier density (cm-3) n=n*1e6; %convert to (m-3) m0=9.10956e-31; %bare electron mass (kg) echarge=1.602192e-19; %electron charge (C) epsilon0=8.85419e-12; %Permittivity of free space (F m-1) hbar=1.054592e-34; %Planck's constant (J s) hbar3=hbar^3; m=0.07*m0; %effective electron mass epsilonr0=13.2; %relative low frequency dielectric constant epsilon=epsilon0*epsilonr0; kF=(3*(pi^2)*n)^(1/3) %Fermi wave vector (m-1) E=-0.1*echarge; for j=1:1:2 E=E+0.2*echarge; %Electron energy (eV) k=sqrt(2*m*E)/hbar; %Electron wave vector (m-1) k3=k^3; %RPA model constants rs0=((3/(4*pi*n))^(1/3))*(m*(echarge^2)/(4*pi*epsilon0*(hbar^2))); xi=((32*(pi^2)/9)^(1/3))/(pi^2); %Thomas-Fermi model constants qTF=sqrt(kF*m*echarge^2/(epsilon*(pi^2)*(hbar^2))); %plot scattering rate as function of scattered angle theta=[pi/1800:pi/1800:pi]; q=2*k*sin(theta/2); %scattered wave vector (m-1) eta=sin(theta/2); %eta calculated using theta in radians deta=pi*cos(theta/2)./2/180; %differential value of eta in degrees eta3=eta.^3; %RPA model x=q/kF; absx=abs(x+2)./abs(x-2); RPAepsilonr=epsilonr0+((rs0./x.^3)*xi.*(x+((1-((x.^2)/4)).*log(absx)))); %Thomas-Fermi model TFepsilon=epsilon*(1+qTF^2./q.^2); RPArate=2*pi*m/hbar3/k3*n*(echarge^2/4/pi/epsilon0)^2.*deta./RPAepsilonr.^2./eta3; TFrate =2*pi*m/hbar3/k3*n*(echarge^2/4/pi)^2.*deta./TFepsilon.^2./eta3; % plot(theta*180/pi, RPArate); figure(1); plot(theta*180/pi, TFrate,'r'); axis([0,35,0,9e9]); xlabel('angle, \theta (degree)'); ylabel(['scattering rate, 1/\tau_{el} (s^{-1} degree^{-1})']); hold on; plot(theta*180/pi, RPArate,'b'); end ttl=(['\rmFig7.6b, \itn\rm_0=',num2str(n/1e6,'%4.1e'),' cm^{-3}, \itm\rm^*_e=',... num2str(m/m0,'%5.2f'),'\times\itm\rm_0, \epsilon_{r0}=',... num2str(epsilonr0,'%5.1f')]); title(ttl); hold off;