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//define problem parameters
Nd=1e16*1e6;
d=0.75e-6;
W=10e-6;
L=2e-6;
eps_r=12;
Vd=0.8;
mu_n=8500e-4;
Vgs=0:-0.01:-4;
//define physical constants
q=1.60218e-19;// electron charge
eps0=8.85e-12;// permittivity of free space
eps=eps_r*eps0;
//pinch-off voltage
Vp=q*Nd*d^2/(2*eps)
//threshold voltage
Vt0=Vd-Vp
//conductivity of the channel
sigma=q*mu_n*Nd
//Channel conductance
G0=q*sigma*Nd*W*d/L
//saturation current using the exact formula
Id_sat=G0*(Vp/3-(Vd-Vgs)+2/(3*sqrt(Vp))*(Vd-Vgs).^(3/2)).*(1-(Vgs<Vt0));
Idss=Id_sat(1)
//saturation current using the quadratic law approximation
Id_sat_square=Idss*(1-Vgs/Vt0)^2;
plot(Vgs,Id_sat,Vgs,Id_sat_square);
legend('exact formula', 'quadratic approximation',2);
title('FET saturation current as a function of the gate-source voltage');
xlabel('Gate-source voltage V_{GS}, V');
ylabel('Drain saturation current I_{DSat}, A');
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