MATLAB: Modeling surface potential of SOI MOSFET

soimossurface

The below code is compiling successfully but no graph is being displayed in the plot window. The corresponding values are also coming in the workspace. Can anybody help out ?
% Defining physical constants
epsilon_si=11.68*8.854e-14;
epsilon_ox=4*8.854e-14;
N_d=2e20;
N_a=1e17;
L=0:50:200;
t_f=2;
t_b=100;
q=1.6e-19;
phi_m=4.35;
Vds=0.05;
Vgs=4.71;
Vsub=0;
Vt=0.026;
ea_si=4.05;
Eg_si=1.12;
n_i=1.5e10;
t_si=input('Enter channel thickness in nm');
%Calculating capacitances
c_f=epsilon_ox/(t_f*1e-7);
c_si=(epsilon_si/t_si)*1e-7;
c_b=epsilon_ox/t_b;
%Calculating potentials
phi_f=Vt*log(N_a/n_i);
Vbi=Eg_si/2+phi_f;
phi_si=ea_si + Eg_si/2+ phi_f;
V_fbf=phi_m-phi_si;
Vgs1=Vgs-V_fbf;
V_fbb= -phi_si;
Vsub1=Vsub-V_fbb;
%Analysis
for x=1:length(L)
    
a=2*(1+c_f/c_b+c_f/c_si)/(t_si*t_si*1e-14*(1+(2*c_si/c_b)));
b=(q*N_a/epsilon_si)-(2*Vgs1*(c_f/c_b+c_f/c_si))/(t_si*t_si*1e-14*(1+(2*c_si/c_b)))-(2*Vsub1)/(t_si*t_si*1e-14*(1+(2*c_si/c_b)));
lambda=sqrt(a);
c=b/a;
a1=(((Vbi+c+Vds)-(Vbi+c)*exp(-lambda*L(x)))/(1-exp(-2*lambda*L(x))))*exp(-lambda*L(x));
b1=((Vbi+c)-(Vbi+c+Vds)*exp(-lambda*L(x)))/(1-exp(-2*lambda*L(x)));
phi_s(1,x)=a1*exp(lambda*L(x))+b1*exp(-lambda*L(x))-c;
end
plot(L,phi_s(1,5));

Best Answer

The below code is compiling successfully but no graph is being displayed in the plot window?
Because your phi_s is shown all values as NaN. Please reverify the phi_s calculation. Please note in each iteration a1 reflects as zero, a1 is multilcative factor with phi_s
Also note you are ploting single array element phi_s(1,5). In addition keep a,b,lamda and c outside of the loop, as they are independent with x
Note on phi_s line:
lambda =
   1.0684e+13
>> L=50; %Just Example
>> exp(-lambda*L)
ans =
     0
Still unsolved, provide the details of MOS equations.
Good Luck!
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