Additive Decomposition Applied to the Semiconductor
Drift-Diffusion Model

James M. McDonough,Marek Turowski,Elizabeth J. Brauer

doi:10.1155/1998/96170

Abstract

A new numerical method for semiconductor device simulation is presented. The additive decomposition method has been successfully applied to Burgers' and Navier-Stokes equations governing turbulent fluid flow by decomposing the equations into large-scale and small-scale parts without averaging. The additive decomposition (AD) technique is well suited to problems with a large range of time and/or space scales, for example, thermal-electrical simulation of power semiconductor devices with large physical size. Furthermore, AD adds a level of parallelization for improved computational efficiency. The new numerical technique has been tested on the 1-D drift-diffusion model of a p-i-n diode for reverse and forward biases. Distributions of φ, n and p have been calculated using the AD method on a coarse large-scale grid and then in parallel small-scale grid sections. The AD results agreed well with the results obtained with a traditional one-grid approach, while potentially reducing memory requirements with the new method.

Highlights

The numerical method, additive decomposition, has been successfully applied in mechanical and chemical engineering to Burgers’ equation and the Navier-Stokes equations governing turbulent fluid flow by decomposing governing equations into large-scale and small-scale parts without averaging, e.g., [1,2,3]
Semiconductor device simulation is a natural application of the additive decomposition numerical technique
After successful implementation for the drift-diffusion equations, we plan to apply the new approach to the hydrodynamic semiconductor model

Summary

INTRODUCTION

The numerical method, additive decomposition, has been successfully applied in mechanical and chemical engineering to Burgers’ equation and the Navier-Stokes equations governing turbulent fluid flow by decomposing governing equations into large-scale and small-scale parts without averaging, e.g., [1,2,3]. The additive decomposition (AD) technique is well suited to problems with a large range of time and/or space scales, for example, thermal-electrical simulation of power semiconductor devices with large physical size. Semiconductor device simulation is a natural application of the additive decomposition numerical technique. We decompose the simplest device equations, the drift-diffusion model, to test the method. After successful implementation for the drift-diffusion equations, we plan to apply the new approach to the hydrodynamic semiconductor model. The standard drift-diffusion model of semiconductors consists of the following equations. V2 q (p- n + Nd- Na) (1) Es and the continuity equations for electrons and holes are

On Ot

NUMERICAL EXPERIMENTS

Findings

CONCLUSION