Scharfetter Gummel: V_diff term

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:
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


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

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:

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.

Best of luck.

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