%Fig5_15 %Essential Electron Transport for Device Physics %Plot Thomas Fermi scattering rate as function of angle clear; clf; n=1e18; %electron carrier density (cm-3) n=n*1e6; %convert to (m-3) m0=9.109382e-31; %bare electron mass (kg) eharge=1.6021764e-19; %electron charge (C) epsilon0=8.8541878e-12; %Permittivity of free space (F m-1) hbar=1.05457159e-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*eharge; for j=1:1:2 E=E+0.2*eharge %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*(eharge^2)/(4*pi*epsilon0*(hbar^2))); xi=((32*(pi^2)/9)^(1/3))/(pi^2); %Thomas-Fermi model constants qTF=sqrt(kF*m*eharge^2/(epsilon*(pi^2)*(hbar^2))); %plot scattering rate as function of scattered angle theta=[pi/180:pi/180: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; %Thomas-Fermi model TFepsilon=epsilon*(1+qTF^2./q.^2); NoScreenRate=2*pi*m/hbar3/k3*n*(eharge^2/4/pi)^2.*deta./epsilon.^2./eta3; TFrate =2*pi*m/hbar3/k3*n*(eharge^2/4/pi)^2.*deta./TFepsilon.^2./eta3; %plot(theta*180/pi, RPArate); %hold on; hold on; figure(1); plot(theta*180/pi, TFrate*10^-12,'b'); axis([0 100 0 0.3]);%only plot angle to 100 degrees %plot(theta*180/pi, NoScreenRate); hold on; plot(theta*180/pi, NoScreenRate*10^-12,'r'); xlabel('Angle, \theta (degree)'); ylabel('Elastic scattering rate, 1/\tau_{el} (ps^{-1} degree^{-1})'); end ttl=['\rmFig5.15, \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); grid on hold off;