An interpretation of the Scharfetter-Gummel finite difference scheme

Abstract

We give an interpretation of the Scharfetter-Gummel (SG) scheme in the theory of semiconductor devices. The key fact is that the SG scheme is based on a harmonic relation between the Green function and the Green matrix for a two-point boundary value problem. An a consequence of our interpretation, we obtain error estimates in $L^r$, $r\in[2,\infty]$, where the coefficient functions may be discontinuous.