Very simple semiconductor simulation

Topics: 4.3b, Physics, Solving

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Kristian Storm

Kristian Storm

May 9, 2011 7:50am UTC

Very simple semiconductor simulation

Hi! I'm trying to learn Comsol, but it seems have run into a wall. I've looked thoroughly through the semiconductor_diode model as well as the MOSFET model (in the showroom). However, as I implement these models myself, following the instructions point by point, the model diverges.

In general, I've noticed that I can get good convergence in a single Poisson simulation of a piece of semiconductor, with a given doping profile. As soon as I add transport of dilute species coupled with Poisson, it diverges.

In order to find my errors, I've created a very simple semiconductor model. It's basically a 1umX10um piece of silicon with a homogeneous doping concentration (but engineered such that it can be changed later). I provide an analytic initial value to an electrostatics module, which works fine and it solves the poisson equation. I then feed this solution to an electrostatic module coupled with two 'transport of dilute species' module, one for electrons and one for holes. As soon as this runs however, the model diverges.

I've attached the model (Comsol v. 4.1) and would be very grateful if someone with experience could point me in the right direction. I must be missing something fairly simple. If 'step 1' is solved, you see the potential for the first poisson solver (constant due to constant doping density). Step 2 then tries to solve poisson coupled with diffusion using the first solution as initial value, but diverges.

The essential variables are:
n0,p0,phi_init: analytic initial values fed to the first poisson solver.
phi0: potential solved by first poisson
phi,cn,cp: potential, electron and hole concentrations for second solver step.

I've been staring at this for a few days now and if I don't find the problem soon, I will have to give up using Comsol.

Thanks!

Attachments:   prototype_model.mph  

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Kristian Storm

Kristian Storm

May 11, 2011 8:05am UTC in response to Kristian Storm

Re: Very simple semiconductor simulation

I think I solved the problem. For future reference:
In the model builder, there is a menu if you click on the down arrow (v). There you can enable 'show more options'. In transport of diluted species I had to use the following settings:
- disable everything in 'consistent stabilization
- disable isotropic diffusion (this was already disabled)
- change convective term to conservative
- Change concentration discretization to quadratic

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Gilles Scheen

Gilles Scheen

June 6, 2011 9:02am UTC in response to Kristian Storm

Re: Very simple semiconductor simulation

Hello,
I am very interested in your problem. Did you find a solution?
My problem is mainly when I put a potential difference between the sides of the silicon bar.

If you are successful, thank you for your explanations.

Sincerely,

Gilles

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Carsten Madler

Carsten Madler

December 6, 2012 10:40pm UTC in response to Kristian Storm

Re: Very simple semiconductor simulation

I have a question about solving for the transport of holes and electrons using the Transport of Diluted Species Model. I am using Comsol 4.3 and in that model the species concentration has units of mol/cm^3 but the hole and electron concentration is obviously 1/m^3. Is there a way around that or was it different in previous versions of Comsol?

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Samuele Lilliu

Samuele Lilliu

December 10, 2012 9:03am UTC in response to Carsten Madler

Re: Very simple semiconductor simulation

Hi,

Try to redefine nc as nc/(1 [mol]).

By the way I have similar convergence problems. I am trying to build a model for a pn solar cell. When I change the R and G terms in Transport of Diluted Species the simulation does not converge anymore. Switching from linear to quadratic does not help.

Please have a look at the attached file.

Cheers

Attachments:   solarcellmodel4p3a_R14.mph  

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Ali Khalatpour

Ali Khalatpour

August 19, 2013 10:44pm UTC in response to Samuele Lilliu

Re: Very simple semiconductor simulation

Hi,
I believe I have the same problem in the semiconductor module. In simulation of Gunn effect we need to define field dependent mobility for electrons. This will bring serious convergence issues. I hope some one have done this before or have good suggestion for me.


Regards,
Al

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