Effects of doping-density gradients on band-gap narrowing in silicon and GaAs devices

Abstract
The limitations of the theory for band-gap narrowing, which is based on uniform material, are considered in devices that have steep doping gradients. Validity criteria are derived that place upper bounds on the dopant and carrier density gradients for the application of the results from uniform theory. The existence of wave-function tailing beyond the potential barriers that occur in devices is studied. At room temperature the effects due to these tails are usually small, but at low temperatures they can become very significant.