Classical solutions of drift-diffusion equations for semiconductor devices: the 2d case

摘要

We regard drift-diffusion equations for semiconductor devices in Lebesguespaces. To that end we reformulate the (generalized) van Roosbroeck system asan evolution equation for the potentials to the driving forces of the currentsof electrons and holes. This evolution equation falls into a class ofquasi-linear parabolic systems which allow unique, local in time solution incertain Lebesgue spaces. In particular, it turns out that the divergence of theelectron and hole current is an integrable function. Hence, Gauss' theoremapplies, and gives the foundation for space discretization of the equations bymeans of finite volume schemes. Moreover, the strong differentiability of theelectron and hole density in time is constitutive for the implicit timediscretization scheme. Finite volume discretization of space, and implicit timediscretization are accepted custom in engineering and scientificcomputing.--This investigation puts special emphasis on non-smooth spatialdomains, mixed boundary conditions, and heterogeneous material compositions, asrequired in electronic device simulation.