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