Numerical Simulation of the Carrier Transport in Semiconductor Devices on the Base of an Energy Model

Abstract

The energy model is one of the phenomenological models which allow the simulation of carrier transport in semiconductor devices. It can be considered as an extension of the widely accepted drift-diffusion model which consists in the van Roosbroeck system of partial differential equations for the electrostatic potential and for the densities of electrons and holes in a semiconductor device. Solving this system under some prescribed boundary conditions and in the transient case under some initial conditions enables one to simulate the function or to analyse the operating schema of this element. In the driftdiffusion model the temperature is a constant parameter. An electric current, however, transforms electric energy into heat. In many applications the amount of this energy is negligible small, but in some situations it may be desirable to consider the temperature as an dynamic variable too. Thermoelectric effects, in particular, can not be described by means of the drift-diffusion model. H. Gajewski and co-workers [8] implemented a two-dimensional version of the drift-diffusion model in the program package TOSCA. This package has been successfully applied (cf. [4], [10],[15]) such that we have decided to extend it by including an energy model too.