Consistent treatment of carrier emission and capture kinetics in electrothermal and energy transport models

The traditional approach to semiconductor device modelling relies on balance equations for particle and energy flow, which include various source and sink terms accounting for all the involved generation and loss processes governing the reaction kinetics of electrons, holes and impurities during the device operation. Usually the so-called quasi-static approximation is employed to model the reaction kinetics. In this work, this approximation is critically re-examined, showing that in the case of high trap concentrations, compensated doping distributions, hot carriers, low temperature operating conditions or wide-gap devices, the commonly used balance equations must be supplemented by additional terms in order to correctly include the emission and capture kinetics of the free carriers.