Ambipolar Carrier Transport and Surface Recombination Velocity in Semiconductor Surface Layers

In discussing charge-carrier recombination at a semiconductor surface it is natural to characterize the recombination properties of the surface itself by a true surface-reflection coefficient which expresses the non-recombination probability for an excess carrier in a single collision with the surface. It is also possible to arrive at an effective surface-reflection coefficient from experimental data by ignoring any effects which might be associated with the presence of a surface space-charge layer. The latter quantity is simply an effective value which involves effects contributed not only by the actual surface, but also by the space-charge layer which is present in the neighborhood of the surface. For a sample with a given photoconductive response, by equating expressions involving the reflectance calculated for a sample having the actual space-charge layer and for one in which space-charge effects are ignored, one may arrive at a relation between the true and effective surface-reflection coefficients. By this procedure one can define in an operational way an effective surface recombination velocity. The combined effects of a space-charge layer and an actual physical surface can then be studied as a function of the space-charge parameters and sample thickness. Results relating true and effective recombination velocities are presented, using an ambipolar-transport formulation, for both depletion-inversion and accumulation layers. Previously developed methods for relating true and effective surface recombination velocities are reviewed and compared to the operational method used herein. Certain advantages connected with the definition adopted here are pointed out. The calculations are based upon known diffusion and mobility parameters for $p$-type silicon.