# Gummel method solving the n-type semiconductor(Poisson equation)

1. Sep 9, 2011

### rokisr

Hello,

I am trying to simulate n-type Silicon using the Gummel method (decoupled method). Here is the link where I stuck http://courses.engr.illinois.edu/ece539/Notes/ch2.pdf . There is (37) formula in the text and I cannot figure out where I need to get V(i-1) and V(i+1) terms on the right equations side.

Help!

2. Sep 28, 2011

### baldagor

In this case the potential is a function of x, so you need an array to express V(x), as an example V[x1], V[x2], V[x3],....,V[xn], where is suposed you are using n points for the simulation. You need to define an initial guess for the values of the array, as an example V[any x]=0. So, to calculate the value in the point i, (V[xi]) you will be using the values of the last iteration. In this case the first iteration will be V[xi-1]=0, V[xi+1]=0, but in the next iterations, the values will be actualized and you will have new values different of zero for V[xi-1], V[xi+1].

I'm also trying to implement this method, I found this article useful for me, maybe it can guide you a little:

Device model for the operation of polymer/fullerene bulk heterojunction solar cells, L. J. A. Koster, E. C. P. Smits, V. D. Mihailetchi, and P. W. M. Blom, PHYSICAL REVIEW B 72, 085205 (2005)

This is the original article of Gummel:
A Self -Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculations, H. K. GUMMEL, IEEE TRANSACTIONS ON ELECTRON DEVICES, 455, 1964

3. Oct 25, 2011