Patricio Farrell acquires Junior Group in Leibniz competition

Leibniz Association funds research project on Numerics for innovative semiconductor devices over a period of 5 years (2020-2024)

Today's ecological, economical and scientific challenges demand accurate simulations of innovative and complex semiconductor devices. Solar cells, for example, are central to the energy transition from carbon to renewable energies. Hence, it is imperative to improve the fundamental design of standard solar cells with respect to cost and efficiency. Two promising ideas are to replace the bulk silicon with low-cost perovskites or resource-efficient nanowires (usually studied at temperatures close to absolute zero). However, in perovskites and very cold nanowires -- unlike for silicon at room temperature -- physics dictates that electrons and holes diffuse nonlinearly, namely several orders faster when highly concentrated. This nonlinearity severely complicates simulations since classic numerical methods violate basic physical principles, e.g. producing negative densities or unphysical electric currents. Similar mathematical difficulties arise for laser, battery, OLED and even biosensor devices. Recently, substantial progress by successfully introducing and analyzing physics preserving numerics for nonlinear diffusion could be made. To this end, the drift-diffusion models for charge transport have been discrtized with specialized finite volume methods. Apart from preserving the physics, these discretizations are also stable -- even when drift dominates diffusion.

The aim of this junior research group is threefold: (i) Develop and analyze physics preserving numerical techniques which can handle stiffness as well as incorporate additional physical laws (e.g. heat and light) and charge carriers (e.g. ions for perovskites); (ii) optimize these techniques by developing novel preconditioners and anisotropic meshing strategies; (iii) use them to simulate realistic and innovative multidimensional devices. This will lead to a unique user-friendly, multiphysics, multidimensional open-source device simulation tool.