Microelectronic Engineering 15 (1991) 53-56 53 Elsevier Monte-Carlo - Poisson Coupling Using Transport Coefficients H. Kosina, Ph. Lindorfer and S. Selberherr Institute for Microelectronics, Technical University of Vienna, Gutlhausstralle 27-29, A-1040 Vienna Abstract A coupling scheme between Poisson's equation and a combined Monte Carlo - Drift Diffu- sion transport model is presented. In an iterative procedure the mobility- and temperature profiles are updated. The method which exhibits a very good convergence rate is applied to study non-equilibrium transport in a one-dimensional semiconductor structure. 1 Introduction For the simulation of submicron devices a hybrid approach to the modeling of carrier transport has several benefits [1][2]. The Drift Diffusion (DD) model provides an accurate description in the low field areas of a device. Since the Monte Carlo (MC) method is computationMly expensive, it is desirable to restrict its application to areas were the DD- model becomes inaccurate, which is the case when the electric field is high an its spatial variation is large. One difficulty in this kind of regional MC analysis is the accurate handling of boundary conditions at the interface between the various regions. Furthermore in very small devices the hybrid transport model and the Poisson equation must be solved selfconsistently. In the standard iteration technique the updated MC-carrier concentrations are substi- tuted in the Poisson equation [3]. However stability problems can arise in areas with high carrier concentrations. In more recent work [4] the quasi fermi level has been proposed to be taken as MC-output and to serve as input for the Poisson equation. This algorithm solves the above mentioned stability problems and shows a better convergence rate [4]. In the following we describe a new selfconsistent iteration scheme which takes into account the hybrid nature of the transport model. During each MC-step the coefficients mobility and thermal voltage are updated. Their new vMues are then substituted in a set of equa- tions consisting of Poisson-, the continuity equation and a generalized current relation. This procedure allows in low regions the required coefficients to be related analytically to the electric field. The current relation then simplifies to the DD-relation. Just in device regions far off equilibrium the coefficients have to be calculated by MC. The area in which MC-calculation is performed is larger then the area where the coefficients are recorded. This leads to an overlap of the MC-domain with the DD-areas, which makes the boundary condition problem less stringent. 2 Iteration Technique The basis of our method is the following set of equations, which is assumed to be valid both near equilibrium and in the hot carrier regime. Neglecting pair generation and 0167-9317/91/$3.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.