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 customgenerated 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.

Compact modeling of charge trapping processes in GaN transistors is of fundamental importance for advanced circuit design. The goal of this article is to propose a methodology for modeling the dynamic characteristics of GaN power HEMTs in the realistic case where trapping/detrapping kinetics are described by stretched exponentials, contrary to ideal pure exponentials, thus significantly improving the state of the art. The analysis is based on: 1) an accurate methodology for describing stretched-exponential transients and extracting the related parameters and 2) a novel compact modeling approach, where the stretched exponential behavior is reproduced via multiple RC networks, whose parameters are specifically tuned based on the results of 1). The developed compact model is then used to simulate the transient performance of the HEMT devices as a function of duty cycle and frequency, thus providing insight on the impact of traps during the realistic switching operation.