%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;

