A numerical method to calculate dwell time for electron in semiconductor nanostructure

Abstract

To some extent, the operational quickness of semiconductor devices depends on the transmission time of electron through semiconductor nanostructures. However, the calculation of transmission time is very difficult, thanks to both contentious definition of the time in quantum mechanics and complicated effective potential functions experienced by electron in semiconductor devices. Here, based on improved transfer matrix method to numerically solve Schrödinger equation and H.G. Winful’s (HGW) relationship to calculate the dwell time, we develop a numerical approach to evaluate the transmission time of electron in semiconductor devices. Compared to exactly resolvable case of rectangular potential barrier, the established numerical approach possesses high precision and small error, which may be employed to explore dynamic response and operating speed of semiconductor devices. This proposed numerical method is successfully applied to the calculation of dwell time for electron in double rectangular potential barriers and the dependence of transmission time on the number of potential barriers is revealed.