% Equilibrium Energy Band Diagram Generator

%(Si, 300K, nondegenerately doped step junction)



%Constants

T=300;        % Temperature in Kelvin

k=8.617e-5;   % Boltzmann constant (eV/K)

e0=8.85e-14;  % permittivity of free space (F/cm)

q=1.602e-19;  % charge on an electron (coul)

KS=11.8;      % Dielectric constant of Si at 300K

ni=1.0e10;    % intrinsic carrier conc. in Silicon at 300K (cm^-3)

EG=1.12;      % Silicon band gap (eV)



%Control constants

xleft = -3.5e-4;   % Leftmost x position

xright = -xleft;   % Rightmost x position

NA=input ('Please enter p-side doping (cm^-3), NA = ');

ND=input ('Please enter n-side doping (cm^-3), ND = ');



%Computations

Vbi=k*T*log((NA*ND)/ni^2);

xN=sqrt(2*KS*e0/q*NA*Vbi/(ND*(NA+ND)));    % Depletion width n-side

xP=sqrt(2*KS*e0/q*ND*Vbi/(NA*(NA+ND)));    % Depletion width p-side

x = linspace(xleft, xright, 200);

Vx1=(Vbi-q*ND.*(xN-x).^2/(2*KS*e0).*(x<=xN)).*(x>=0); 

Vx2=0.5*q*NA.*(xP+x).^2/(KS*e0).*( x>=-xP & x<0 );

Vx=Vx1+Vx2;     % V as a function of x

VMAX = 3;                        % Maximium Plot Voltage

EF=Vx(1)+VMAX/2-k*T*log(NA/ni);  % Fermi level



%Plot Diagram

close

plot ( x, -Vx+EG/2+VMAX/2);

axis ([xleft xright 0 VMAX]);

axis ('off');  hold on

plot ( x, -Vx-EG/2+VMAX/2);

plot ( x, -Vx+VMAX/2,'w:');

plot ( [xleft xright], [ EF EF ], 'w' );

plot ( [ 0 0 ], [ 0.15 VMAX-0.5 ], 'w--' );

text(xleft*1.08,(-Vx(1)+EG/2+VMAX/2-.05),'Ec');

text(xright*1.02,(-Vx(200)+EG/2+VMAX/2-.05),'Ec');

text(xleft*1.08,(-Vx(1)-EG/2+VMAX/2-.05),'Ev');

text(xright*1.02,(-Vx(200)-EG/2+VMAX/2-.05),'Ev');

text(xleft*1.08,(-Vx(1)+VMAX/2-.05),'Ei');

text(xright*1.02, EF-.05,'EF');

set(gca,'DefaultTextUnits','normalized')

text(.18, 0,'p-side');

text ( .47, 0, 'x=0');

text(.75, 0,'n-side');

set(gca,'DefaultTextUnits','data')

hold off