Determining lifetime in silicon blocks and wafers with accurate expressions for carrier density

In recent years, many studies of silicon minority-carrier lifetime have been performed with quasi-steady-state photoconductance measurements. The method has been used to characterize the defect levels, surface passivation, and trapping effects in wafers by using absolutely calibrated data for minority-carrier lifetime versus minority-carrier injection level. This paper generalizes the quasi-steady-state photoconductance technique for use in thick wafers or blocks of silicon where the diffusion length or light absorption depth is much less than the sample thickness. The photogeneration and carrier diffusion profiles are calculated for special cases of interest. The measured effective lifetimes can then be used to estimate the bulk lifetime in the material, and report this lifetime at an appropriate average minority-carrier density for the measurement conditions. In this way, the results and measurement methodologies previously developed for use on wafers can be applied to single- or multi-crystalline silicon ingots or thick wafers. In thick silicon samples, long-wavelength weakly absorbed light can be used to reduce the effects of surface recombination on the measurement giving important advantages compared to the case of measuring unpassivated wafers. The generalization presented here offers advantages for accurately determining the bulk lifetime of silicon material prior to sawing into wafers and without requiring surface passivation.