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

  1. Sep 9, 2011 #1
    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. jcsd
  3. Sep 28, 2011 #2
    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
     
  4. Oct 25, 2011 #3
    Thanks for your reply and sorry for my late answer :).
    I would like to ask about which device you are writing a model. Because I am writing about pn junction (time-independent dn/dt=dp/dt=0) and my programme shows just a little convergence when bias voltage is applied. I need an advice.

    Thanks!
     
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