On the implication of spatial carrier density non-uniformity on lifetime determination in silicon

Measuring the excess charge carrier density is a widespread approach to accessing the charge carrier lifetime in silicon using an equation of continuity. In this paper, we investigate the scenario of a spatially non-uniform pulsed or modulated optical excitation and a measurement of the emitted photoluminescence intensity. In order to ascertain how to obtain the charge carrier lifetime in this scenario, a rigorous theoretical analysis of the induced charge carrier dynamics is elaborated. Emanating from a photoluminescence intensity-weighted average of charge carrier density, we obtain a macroscopic equation of continuity which accounts for the spatial non-uniformity of charge carrier density. An iterative solution to this equation is given. A numerical simulation reveals distortions to the measured charge carrier lifetime, which occur if the commonly used arithmetic average of the equation of continuity is used instead. We show that the transient measurement of low lifetimes below 10 μs regime is strongly affected and, in particular, that our approach renders necessary for an accurate lifetime determination if using focused excitation as for micro-photoluminescence spectroscopy