Contactless defects detection using modulated photoluminescence technique: model for a single Shockley-Read-Hall trap in a semiconductor thin layer

Studying defects in semiconductors is, in practice, a very important topic for opto-electronic applications. It involves advanced characterization tools able to quantify and qualify the defect densities present in the materials. In the present article we focus on the use of a contactless frequency domain technique: modulated photoluminescence (MPL), and show its potential to detect defects. MPL has been used for the measurement of differential lifetime for several decades in silicon wafers. By extending it to low lifetime/highly defective materials we discovered its potential to become a defect spectroscopy method, measuring time constants close to the ones governing impedance spectroscopy measurements. Proofs of concept and an analytical model for doped materials have been presented already. Here, we reformulate the analytical model more explicitly and check its applicability by extensive numerical simulations for the case of a low illumination for a thin layer with a single defect. We present a parametric numerical study simulating the response of a single Shockley-Read-Hall center, showing the appearance of so-called V-Shapes in the MPL phase patterns as predicted by the analytical model, and valid beyond small-signal approximation. We discuss the difference between these two approaches and extend the analytical model and numerical investigations to intrinsic materials.