The physical behavior of semiconductor devices may be described using partial differential equation systems which can be solved using numerical methods. Discretization in space and time allows the transformation of the differential equations into difference equations which may be solved using Newton's method. Depending on the physical models used, different difficulties have to be overcome.
Power semiconductor devices are of primary interest in this work. Simulation of break-down conditions requires the consideration of impact ionization rates, which leads to numerical issues. There are convergence problems resulting from the exponential dependence in the impact ionization rate model used in the drift-diffusion equations. Additionally, this model requires not only scalar values on the mesh nodes but also vector quantities. The vectors can be calculated on different geometric entities, which means that vectors can be calculated for each box, for each element, or for a part of each element. There are also different approaches to how the vectors can be approximated on each geometric entity. The influence of the different vector discretization methods on the simulation results and on the convergence behavior are investigated by performing simulations on high-voltage devices. Another challenge arises from the fact that break-down simulations need to trace non-bijective I/V curves, which makes curve-tracing algorithms necessary. The implementation of the different schemes was added to the device simulation tool Minimos-NT, which allows the investigation of different schemes and models.