7. Numerical Considerations

In numerical device simulation environments, the physical properties of a semiconductor device are described using models based on differential equation systems as shown in Chapters 4-6. Generally, the problems cannot be solved analytically and numerical solution techniques are required. Discretization methods are used to transform the partial differential equation system to difference equations. Meshes are required to define the spatial discretization of the simulation domain. Section 7.1 will give a short introduction to this topic. The discretization of the semiconductor equations in the context of the box discretization method is introduced in Section 7.2. The difference equation system is then solved using nonlinear solving techniques, typically Newton's iteration scheme is applied.

Special considerations are required to represent vector quantities in discretized systems. Section 7.3 will give an overview on that subject. Section 7.4 will discuss numerical consideration, which are especially important for simulations in high-voltage devices.

- 7.1 Meshing
- 7.2 Box Discretization
- 7.2.1 Derivation
- 7.2.2 Discretization of Edges
- 7.2.3 Discretization of the Right Hand Side
- 7.2.4 Limitations of the Box Discretization Method

- 7.3 Vectors in Discretized Systems
- 7.3.1 Discretization Approach by Laux
- 7.3.2 Box Discretized Vector Quantities
- 7.3.3 Comparison of the Discretization Schemes

- 7.4 Numerical Challenges Related to High-Voltage Devices
- 7.5 Summary

O. Triebl: Reliability Issues in High-Voltage Semiconductor Devices