# Discretisation of the Stationary Device Problem

• Peter A. Markowich
Part of the Computational Microelectronics book series (COMPUTATIONAL)

## Abstract

The numerical solution of boundary value problems for nonlinear systems of elliptic partial differential equations in general and the static simulation of semiconductor devices in particular usually proceeds in the following steps:
1. (i)

The ‘continuous’ problem is replaced by a suitable approximating ‘discrete’ nonlinear system of algebraic equations, whose solutions are intrinsically related to point-values of approximate solutions. This procedure is called discretisation of the boundary value problem.

2. (ii)

Since, usually, the nonlinear system of equations generated by the discretisation cannot be solved exactly, an iteration scheme based on (quasi-) linearisation is set up in order to obtain an approximate discrete solution.

3. (iii)

In each iteration step a usually large and sparse system of linear equations has to be solved.

## Keywords

Finite Difference Scheme Schottky Contact Discrete Solution Finite Element Solution Finite Element Discretisations

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