Journal of Computational Physics 159, 197–212 (2000) doi:10.1006/jcph.2000.6428, available online at http://www.idealibrary.com on A Discretization Scheme for an Extended Drift-Diffusion Model Including Trap-Assisted Phenomena F. Bosisio, S. Micheletti, and R. Sacco Dipartimento di Matematica, “F. Brioschi,” Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy E-mail: ricsac@mate.polimi.it Received July 6, 1998; revised August 3, 1999 An extended drift-diffusion model is considered to account for the kinetics of electrons trapped in defect states within a semiconductor material. A discretization scheme based on Newton–Krylov iterations and mixed finite volumes is then pro- posed and applied to the model, even in the presence of Schottky contacts (i.e., Robin- type boundary conditions). Numerical results concerning the simulation of an electro- optical device in several working conditions are presented last. c  2000 Academic Press Key Words: semiconductors; mixed finite elements; Newton–Krylov methods. 1. INTRODUCTION This article deals with the numerical simulation of the dynamics of a CdTe resistor subject to a very high bias. Such a device is employed as a fast switch in state-of-the-art optical communication systems [34, 24, 21]. The mathematical model consists of the classical drift-diffusion equations [15, 31, 12] (henceforth denoted by DD) plus a set of ordinary differential equations (ODEs) describing the kinetics of the carriers trapped in defect states that are present within the semiconductor energy gap (henceforth referred to as traps) [10]. The spatial integration domain is assumed to be one-dimensional, L being the device length. This is due to the nature of the physical problem at hand, although the methodologies that we are going to introduce are by no means restricted to one-dimensional geometries. Suitable initial and boundary conditions (of Dirichlet and Robin type) must be provided for the unknowns of the problem, namely electric potential ψ , free electron and hole concentrations n and p, and trap concentrations n T i (i = 1,..., n D ) and p T j ( j = 1,..., n A ), where n D and n A denote the number of donor- type and acceptor-type trapping states, respectively. Despite its apparent simplicity, the CdTe resistor simulation is a heavily stiff problem, mainly due to the fact that this kind of device is quite “long” in real-life applications. This 197 0021-9991/00 $35.00 Copyright c  2000 by Academic Press All rights of reproduction in any form reserved.