Scharfetter Gummel: V_diff term

models
1

Hey Everyone,
I’m new here. I have started looking into writing my own modified drift-diffusion transport simulation (for 2D material devices). Doing so I have stumbled across the simple physics drift-diffusion example.

Jn = “ElectronChargemu_nEdgeInverseLengthV_tkahan3(Electrons@n1Bern01, Electrons@n1vdiff, -Electrons@n0*Bern01)”

To understand the expression for the electron current I searched the literature a bit on the scharfetter gummel discretization. I found the following article: http://mx.nthu.edu.tw/~jlliu/proj/Device/SGMethod.pdf
From the article I am able to understand the use of the Bernoulli expression in the expression for the electrone (and hole) current. It is however unclear to me where the term

Electrons@n1*vdiff

comes from, as it is not present in the given article.
Would you mind helping me out here?
Regards JD

2

Hi @Jan_David_Fischbach

Thanks for posting. Please note that there are many useful relations that can reduce the number of evaluations of the Bernoulli function. For example:

B(-x)=B(x) + x

which is equation 3.5 in this document:
https://github.com/devsim/devsim_misc/blob/main/devsim_docs/TCADdocs.pdf

Please let me know if you have any questions. An interesting manuscript related to the use of quasi Fermi level based SG is here:

Stanojevic, Zlatan; Gonzalez Medina, Jose Maria; Schanovsky, Franz; Karner, Markus (2022): Quasi-Fermi-Based Charge Transport Scheme for Device Simulation in Cryogenic, Wide-Band-Gap, and High-Voltage Applications. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.21132637.v2

Best of luck.

3

Ah thanks, that makes sense. I must have overseen the missing minus sign :slight_smile: