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Has anyone tried getting the voltage distribution of a biased solar cell with the poisson equation ( (d"V/dx") = (q/e)*(p-n) ) and electron and hole densities equation

( n = Nc*exp(-(Ec-qV-F)/kT) , p = Nv*(exp(Ev-qV-F)/kT) ) where Nc and Nv are the effective density of states, Ec and Ev are the transport level, F is the fermi level, e is the electric constant and V is the voltage?

I've tried make some guesses on the initial V distribution, and put them in the e-/h+ density equations, then putting the n and p into the poisson equations, and solve V using finite difference method. The voltage I got was in the order of 1x10^3x and the numbers gets bigger and bigger after each itteration. I need to reduce the grid size to 1e-40 in order to get some reasonable voltage. But that means that I can either have an extreamly thin layer or have a grid number that is too big for matlab to handle.

I've also found that the bigger my voltage gets at the Boundary, the smaller the grid size need to be.

Has anyone came across problem as such before?

Thanks!

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# Problem with modeling solar cell voltage distribution

Can you offer guidance or do you also need help?

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