Resistance fluctuations in ohmic contacts due to discreteness of dopants

The role of fluctuations in the potential due to randomly distributed dopants in the depletion layer of a metal-semiconductor junction is explored. To be specific, the case of n-GaAs is considered. Monte Carlo simulation techniques are used to calculate the potential in the junction. By using the WKB approximation and the two-band model, the small-signal resistance at zero bias is found to be lowered by up to half an order of magnitude from the result assuming a continuum distribution of dopant charge. The resistance is found to vary by an order of magnitude in the plane of the interface resulting in a very nonuniform distribution of the current.