On iterative schemes for a stationary problem to a quantum drift diffusion model

Abstract

In this paper, we propose a new iterative scheme to obtain a stationary solution to a quantum drift diffusion (QDD) model for semiconductors in a multi-dimensional space. The model consists of two fourth order nonlinear elliptic equations for the carrier densities and the nonlinear Poisson equation for the electrostatic potential. The present scheme adopts the Gummel method to decouple the system. For the computational efficiency, this scheme also employs an exponential transformation of variables to preserve positivity of the carrier densities and an inner iteration to couple the quantum potentials with the electrostatic potential. The present scheme is constructed to improve the other schemes developed by Ancona, de Falco and Odanaka. We show the advantage of the present scheme on computational costs in comparison to the other schemes for simulations of current-voltage characteristics for a double-gate MOSFET.