A hybrid central difference scheme for solid-state device simulation

Abstract
The differences between the Scharfetter-Gummel and central difference schemes, applied to the drift and diffusion equations, are examined. It is shown that the differences between the two approximations lie essentially in numerical, or artificial diffusion that is introduced implicitly by the Scharfetter-Gummel scheme when the potential difference between grid points becomes excessive. Based on this observation, a hybrid central difference-artificial diffusion scheme is developed. It is shown that both the Scharfetter-Gummel and the present hybrid scheme have the same limiting forms at high and low fields, and it is demonstrated that both schemes yield similar results.