J. Sarvas et J. Spanier, A DIRECT APPROACH TO SOLVING THE DRIFT-DIFFUSION MODEL-EQUATIONS FOR USE IN CERTAIN MOSFET DEVICES, Mathematical and computer modelling, 22(8), 1995, pp. 17-31
The behavior of metal oxide semiconductor field effect transistors (MO
SFETs) has frequently been modeled using the drift-diffusion partial d
ifferential equations. In this paper, we show how extensions of previo
usly studied techniques may be applied to these equations to obtain bo
th current-voltage relationships and pointwise variation of the potent
ial functions arising in a number of practical cases. While our method
makes use of perturbation theory, we are able to avoid the complicate
d asymptotic matching methods that have been widely adopted by a numbe
r of authors for studying such MOSFETs. Our numerical approach can tre
at the important practical case of variable doping and gives rise to a
ccurate, and numerically stable, solutions of the model equations.