RECIPROCITY THEOREM FOR CHARGE COLLETION BY A SURFACE WITH FINITE COLLECTION VELOCITY - APPLICATION TO GRAIN-BOUNDARIES

A proof is given of a reciprocity theorem which applies to charge collection by a semiconductor surface with finite collection velocity. The theorem leads to a boundary-value problem for the charge collection probability phi. This problem is solved by the eigenfunctions expansion method for the normal collector geometry, where the collecting surface corresponds to the edge of a nonideal junction or to a charge-collecting grain boundary. The solution thus obtained is equivalent to that found earlier by the method of images but has a much simpler form. This solution, its asymptotic approximations and low-order moments, as well as the boundary conditions for phi can find use in the determination of the surface collection/recombination velocity and minority-carrier diffusion length in a semiconductor from experimental induced current scans. The new expression for phi is used to calculate the collection efficiency profile of a charge-collecting grain boundary for a generation with finite lateral extent.