Carrier profiles and collection efficiency in Gaussian p-n junctions under electron beam bombardment

Gaussian-doped semiconductor junctions have a built-in electrostatic field E which usually varies linearly with distance from the surface. A series of solutions of the one-dimensional continuity equation for linear E field are given in terms of the confluent hypergeometric function and its limiting forms. These solutions are directly applicable to the collection of hole-electron pairs generated between the surface and the junction, and can be extended readily to cover generation at greater depths. The effects of bulk recombination and spatial variation of diffusion constant on the theoretical collection efficiency are also calculated. Using a generation function appropriate to a kilovolt electron beam, the minority carrier density versus distance and the collection efficiency of the junction are evaluated for zero and infinite surface recombination velocity.