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Before i start, i should say that i have been working in the field of quantam mechanics for just 6 months now. I have a problem where i have to draw numerically the IV curve of Si in MATLAB under forward bias condition. I have the electric field and potential calculated the following way, respectively -

Efield(jj) = q*dx*( -1*sum(drho(1:jj)) + sum(drho(jj:end)) )/(2*KS*8.85e-12);

U(jj) = U(jj-1)-Efield(jj)*dx;

where the drho is the total charge(n+p+nuclear charge). and U is the electrostatic potential.

So far this equations were used for the equilibrium conditions from which current (J) is calculated in the form of derivative of electron/hole density with respect to time (dn/dt or dp/dt); (J = sum(dn/dt)*dx). To plot the IV curves now i have to use the forward bias values (VA) so the potential on the n-side will change. But i couldnt figure out how i can introduce that into my MATLAB script. How can i relate the applied voltage with the resultant current (dn/dt or J)? Can anyone please give me some suggestions.

Thanks in advance.