Solution of the semiconductor-device equations by the numerov process

The one-dimensional form of some types of differential equations that appear in the modeling of solid-state devices, like, e.g., the Poisson and Schrödinger equations, can be solved numerically using the Numerov Process (NP). The accuracy of NP is superior by at least two orders of magnitude to that of commonly-used solution methods like, e.g., the finite-difference one. Another advantage of NP is that the increase in computational cost is modest. This paper investigates the possibility of extending the applicability of NP to the whole set of equations that constitute the mathematical model of semiconductor devices. It shows that the charge-continuity and charge-transport equations can be recast in a form suitable for NP. The performance of the method is tested on an n+-n-n+ device, and the extension of the approach to the two-dimensional transport problem is worked out.