Parameterisation of injection-dependent lifetime measurements in semiconductors in terms of Shockley-Read-Hall statistics: An application to oxide precipitates in silicon

Abstract

Injection-dependent minority carrier lifetime measurements are a valuable characterisation method for semiconductor materials, particularly those for photovoltaic applications. For a sample containing defects which obey Shockley-Read-Hall statistics, it is possible to use such measurements to determine (i) the location of energy levels within the band-gap and (ii) the ratios of the capture coefficients for electrons and holes. In this paper, we discuss a convenient methodology for determining these parameters from lifetime data. Minority carrier lifetime is expressed as a linear function of the ratio of the total electron concentration to the total hole concentration for p-type (or vice versa for n-type) material. When this is plotted on linear scales, a single-level Shockley-Read-Hall centre manifests itself as a straight line. The gradient and intercepts of such a plot can be used to determine recombination parameters. The formulation is particularly instructive when multiple states are recombination-active in a sample. To illustrate this, we consider oxide precipitates in silicon as a case study and analyse lifetime data for a wide variety of p-type and n-type samples as a function of temperature. We fit the data using both a single two-level defect and two independent single-level defects and find the latter can fit the lifetime curves in all cases studied. The first defect is at EV + 0.22 eV and has a capture coefficient for electrons ∼157 times greater than that for holes at room temperature. The second defect is at EC − 0.08 eV and has a capture coefficient for holes ∼1200 times greater than that for electrons at room temperature. We find that the presence of dislocations and stacking faults around the precipitates acts to increase the density of both states without introducing new levels. Using the analysis method described, we present a parameterisation of the minority carrier lifetime in silicon containing oxide precipitates.