Numerical simulation of microstructured semiconductor devices, transducers, and systems

The numerical simulation of microstructured semiconductor devices, transducers, and systems aiming at an optimal layout and design often has to take into account that the operating behaviour is based on the interaction of various physical phenomena. This requires on one hand the simulation to be based on a consistent, tailored modeling of the underlying physical processes and on the other hand the use of modern methods in the numerical solution of PDEs and systems thereof such as efficient iterative solvers and adaptive grid refinement and coarsening. In this contribution, the development and implementation of such techniques will be outlined for three industrially relevant case studies. The first one is concerned with the minimization of parasitic effects in converter modules used in high power electronics which amounts to the solution of a shape and topology optimization problem. Here, we consider the efficient computation of electromagnetic potentials related to Maxwell's equations based on a discretization in terms of curl-conforming edge elements. The second problem deals with electrostatically driven micromembrane pumps that are intended to be used in medical sciences to control metabolism or in the chemical analysis of freshwater bodies. In particular, we will address the simulation of the electromechanical coupling that characterizes the operating behaviour of the electrostatic drive and the fluid-structure interaction between the fluid flow and the deformation of the passive valves. Finally, we consider the computation of the temperature and heat flow distribution in micromachined deformable mirrors that can be used for the positioning of laser beams in optical eye surgery. Emphasis will be laid on a combined time-step selection and adaptivity in space for a primal mixed discretization of the underlying heat equation.