Discretization of the Semiconductor Equations
The equations together with eqs. (1.1) and (1.3), or (1.6) and (1.7) form a system of coupled elliptical partial differential equations. This system is defined in three-dimensional space under steady state and in four-dimensional space under transient conditions. An analytical solution in accordance with the models described in chapter two is in general not possible. Therefore, we will have to solve the system by numerical methods. It is the target of this chapter to describe how the continuous space connected with the three spatial and the time coordinates is replaced by a finite subspace with discrete coordinates, to be represented on digital computers. Therefore, we will carry out the analysis of our semiconductor device on a discrete mesh in space and time, with difference equations derived from the system of partial differential equations.
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