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 coll ection by a semiconductor surface with finite collection velocity. The theorem leads to a boundary-value problem for the charge collection p robability phi. This problem is solved by the eigenfunctions expansion method for the normal collector geometry, where the collecting surfac e corresponds to the edge of a nonideal junction or to a charge-collec ting grain boundary. The solution thus obtained is equivalent to that found earlier by the method of images but has a much simpler form. Thi s solution, its asymptotic approximations and low-order moments, as we ll as the boundary conditions for phi can find use in the determinatio n of the surface collection/recombination velocity and minority-carrie r diffusion length in a semiconductor from experimental induced curren t scans. The new expression for phi is used to calculate the collectio n efficiency profile of a charge-collecting grain boundary for a gener ation with finite lateral extent.