We discussed the physical diffusion phenomena for several semiconductor materials in the previous section. The method to implement and solve these physical equations, mostly nonlinear partial differential equations (PDEs), within a numerical computer program will be given in this chapter. The numerical methods presented here are applicable for multidimensional simulations. For the sake of simplicity we explain the used methods in a two-dimensional simulation domain.
We start in Section 4.1.1 with the generation of the finite collection of points on which the diffusion problem is solved, which is also known as grid generation, and the problems involved. In Section 4.1.2 we continue with the box integration method (BM) used for the numerical discretization of the differential operators used for the diffusion simulation. Proceeding in the numerical part, we describe the solution and assembling methods of the linear and nonlinear system.
Section 4.2 gives the state-of-the-art design and architecture of PROMIS-NT which is used successfully to solve nowadays diffusion problems. A detailed description of all implemented and available diffusion models including scaling and verification is given in Section 4.3. As a novelty in process modeling we present interface models, which can be applied to the different material interfaces independently of the bulk material (segment) models. We close this chapter with a library of material interface models (Section 4.4).