Measurement of lifetime of nonequilibrium charge carriers in single-crystal silicon

Abstract

An equation of continuity describing decay of nonequilibrium charge carriers after illumination of semiconducting silicon by a long duration pulse of light with wavelength of 1.06 µm is solved by numerical methods in a one-dimensional approximation. It is shown that, when the volume recombination lifetime of minority carriers is 500 µs and higher, the known formula for “thin” samples 1/τeff = 1/τV + 2s/d cannot be used to evaluate the effective lifetime of thin plates (10 µm or above). Estimations of the range of variation of excess density in which the instantaneous lifetime achieves saturation are carried out; this takes place in the second part of the relaxation curve if the wafer thickness does not exceed three diffusion lengths of minority carriers. It is demonstrated that the formula scaled to an infinite recombination rate is applicable for thicknesses of the sample within the range from one to five diffusion lengths. For higher thicknesses, it is necessary to apply corrections taking into account the dependence of instantaneous lifetime on the excess density of nonequilibrium charge carriers.