Validity of simplified Shockley-Read-Hall statistics for modeling carrier lifetimes in crystalline silicon

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Abstract
The Shockley-Read-Hall model, in its simplest and most common form, is often used to describe both injection- and temperature-dependent carrier lifetime measurements. Such lifetime modeling has provided the basis for ultrasensitive spectroscopic techniques for the study of recombination centers in crystalline silicon. However, this approximate model is only valid when the density of recombination centers is small enough to avoid trapping effects, which cause distortions in the excess mobile carrier concentrations. In this work, the simplified Shockley-Read-Hall model is compared with a more general solution of the continuity equations that takes account of carrier trapping. This comparison leads to an expression for the upper limit on the recombination center density for which the simplified Shockley-Read-Hall model remains accurate. The limit depends not only on the dopant density, but also on the energy level and electron and hole capture cross sections for a given type of recombination center. The results allow experimental conditions that do not invalidate the use of the simplified Shockley-Read-Hall model to be determined.