Poisson's equation in semiconductors: impact of charge depletion on Hall effect measurements

Abstract

Space-charge effects are familiar to students of solid state physics, semiconductor devices, and surface science. They are usually estimated under the strong depletion or space-charge layer approximation (SCLA), whose limitations are rarely fully discussed. A formal description of these effects is presented, followed by numerical solutions to a one-dimensional Poisson's equation. This equation is valid in cases of charge depletion and of mild accumulation near surfaces and interfaces. Poisson's equation as it applies to a film/substrate interface is analyzed to obtain the boundary condition for the potential at the metallurgical junction. A practical applied example discusses the impact of depletion effects on the determination of the charge carrier concentration by Hall effect measurement in homoepitaxial semiconductor thin films. Examples are highlighted where the SCLA is not an accurate approximation.