Mean lifetimes of quasi-bound electronic states in rectangular GaAs/AlGaAs barriers

In our previous work [S.J. Vlaev, V.M. González Robles, Phys. Stat. Sol.(c) 2 (2005) 3653.] we have developed a numerical scheme to calculate the mean lifetimes of virtual energy levels. In the present study, this scheme is applied to the quasi-bound electronic states in rectangular GaAs/AlGaAs quantum barriers. We have considered rectangular barriers of different widths and heights. The numerical calculations of the energy spectrum, the line shape and the mean lifetime are performed in a semi-empirical sp3s* tight-binding model including the spin. The SGFM method is applied to treat the interface problem [S. Vlaev, V.R. Velasco, F. García-Moliner, Phys. Rev. B 49 (1994) 11222]. We found that the mean lifetime increases significantly for thin barriers reaching values of nanoseconds and even more in some cases. The strong spatial localizations of the quasi-bound states correspond to their strong energy localizations and large mean lifetimes. The relation between the de Broglie wavelength of the barrier material and the barrier width determines the characteristics of the quasi-bound states for electrons and holes. A qualitative interpretation in terms of electron wave diffraction is suggested.