Optimization models for semiconductor dopant profiling

Abstract

The design of semiconductor devices is an important and challenging task in modern microelectronics, which is increasingly being carried out via mathematical optimization with models for the device behavior. The design variable (and correspondingly the unknown in the associated optimization problems) is the device doping profile, which describes the (charge) density of ion impurities in the device and is therefore modeled as a spatially inhomogeneous function. The optimization goals are usually related to the device characteristics, in particular to outflow currents on some contacts. This is also the typical setup we shall confine ourselves to in this chapter, namely to (approximately) achieve a certain goal related to the outflow current on a contact (e.g., a maximization or just an increase of the current), ideally with minimal change of the doping profile to some given reference state.