On the CET-Map Ill-Posed Inversion Problem: Theory and Application to GaN HEMTs

Ideally, de-trapping transients in semiconductors originate from discrete energy levels, and the emission profile follows a pure exponential decay; however, it has been widely shown that this rarely happens in real devices, for which capture and emission processes have a strongly stretched exponential shape. Conventional methodologies for capture/emission time constants mapping (CET maps) are based on the double derivative (DD) or bivariate Gaussian (BG) approximation, which may lead to inaccuracies in the presence of complex defect distributions. In this article, we introduce a new methodology, based on the double inverse Laplace transform, to extract the accurate capture-emission time (CET) map of these defects. The proposed approach is compared with the conventional approximated solutions, thus giving insight into whether the error introduced by the simplified approaches can be considered negligible or not. First, to ensure full control of the input parameters, the analysis is carried out on custom-generated functions with different stretching parameters. Then, the developed methodology is used to extract, for the first time, the full capture/emission time map from a power GaN high-electron mobility transistor (HEMT) subjected to positive bias instability (PBI) test. The proposed approach is universal and can be adopted by a wide variety of electronic devices in the presence of charge-trapping processes.