Abstract

Drift diffusion systems serve as a mathematical model for a wide range of phe- nomena in physics and biology. Classical examples include semiconductor device simulations, newer ones ion channels or synthetic channels. In this talk we discuss different forward and inverse problems that arise in drift diffusion systems. In particular we present an efficient optimization procedure for optimal design problems in semiconductor device applications. The objec- tives are to increase the on-state current while keeping the off-state current as small as possible. We illustrate the behavior of the scheme by 2D simulations of a MOSFET . In addition we discuss the Poisson-Nernst-Planck (PNP) equations, modeling the movement of charged particles in ionic or synthetic channels. The classical PNP equations do not include finite size effects; in recent years different gen- eralizations of the PNP equations have been proposed to include these finite size effects. We discuss numerical schemes for the PNP equations and present numerical results for 2D simulations of ion channels and synthetic channels.