Tunneling time of electronic wave packet through a parabolic quantum well with double barrier

The tunneling time of electrons through a parabolic quantum well structure has been investigated. A time-dependent Schrodinger equation has been numerically solved using the transfer-matrix method and wave packet dynamic theory. The results show that the probability density of the electron inside the parabolic well first builds up to a maximum and then decays exponentially with time. Furthermore, the dependence of the build-up time on the structure parameters of the system is weak, but the resonant tunneling lifetime decreases rapidly with the increase of the well width and barrier thickness. It can also be seen from our results that the build-up time may be longer than the resonant tunneling lifetime for a narrow well. By comparing the parabolic well with a rectangular well, it is also found that the resonant tunneling lifetime through the parabolic quantum well is longer than that through the rectangular one in the case of a wide well with thin barriers. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.