Fowler Nordheim Plot Simulations (F-N Plot)

Last few days I was trying to do a simulation on Fowler Nordheim tunneling. It has different name. Mostly it is known as F-N plot or J/E^2 vs. 1/E plot. Here is the matlab coding for this simulation.



%% Electric Field
% $$ V_t=V_{fb}+2(\psi_b)+ $$
Ub=.42;
Vfb=4.1-(4.05+.56+Ub);        %Flate band voltage   4.1-(4.05+1.12/2+.6)        
Vg=0:0.1:10;                %For positive gate voltage
%Vg(202:402)=0:-0.1:-20;
%Vgneg=-20:0.1:0;              %For negative gate voltage
Vsub=-1;                     %For positive sunstrate voltage
%Vsub(202:402)=-1;
                 %Vsubng=-1;                    %For negative sunstrate voltage
doxfs=7.8e-7;                 % Dielectric thickness
E=(Vg-Vfb-Vsub)./doxfs;
%% Current Density J
%A constant
mo=9.1093e-31;
mox=0.5*mo;
%moxmo=mox/mo
q=1.602e-19; %C
Si_SiO=3.2; %eV
h=4.135e-15;   %eV.s
%A=1.54e-6;
%B=6.87e7;
%A=(mo/mox)*(q^3)/((8*pi*h*Si_SiO)*q^2)
%B Constant
%B=(8*pi*(sqrt(2*mox))*Si_SiO^(1.5))*q/(3*q*h)  %V/m
%Alternative A and B calculation          
% Ref: On tunneling in metal-oxide-silicon structures by z. A.  Weinberg
%IBM Thomas J.  Watson Research Center,  Yorktown Heights,  New York 10598
A=(mo/mox)*(1/Si_SiO)*1.54e-6         %A/{V}^2
B=sqrt(mox/mo)*(Si_SiO^(3/2))*6.83e7  %V/cm
% Current Density Finial Calculation
y=(A.*exp(-B./(E)));
J=y.*(E.^2);
I=J*1.05e-7;
%J=(A*E.^2).*exp(-B./E);
%y=log(J./E.^2);
%x=(1e-7.*E).^-1;
x=1./(E);
%y=log(A)-(B./E);
%y=abs(yy);
xx=transpose(x);
yy=transpose(y);
plot(x,y)
ylabel('J/{E}^2,(Amp/V)')
xlabel('1/{E},({10}^{-7}cm/MV)')
title('FN Plot')

Panorama Photography

Last weekend it was a amazing day after a long winter and annoying weekend rain. It was like bad weather was waiting for every weekend. Depressingly temperature was still below zero for some days even in the end of May. However at last things start to change and start to feel like Spring. And this week end sun start to feel bad for Winnipeg people and start to glow with its glory. Still there were some cloud in the sky, but its was kind of blessing. Full summer in Winnipeg is as bad as full Winter. Usually wind is very strong on the prairie but this weekend it was perfect. It was hard to site inside home in a day like this. In the afternoon I Grab my bike and went to see King's park. I am living here almost for 2 years. But unfortunately I didn't get time to see this beautiful place. Here is one panorama of king's park