Theoretical study of electron tunneling time through a single/double barrier(s), and the effect of wave packet spread

Simulated single-barrier tunneling time for various wave packet spread in momentum space is compared with the theoretical phase time. The effect of the shift of the electron momentum peak after the tunneling is discussed. A simple physical formula of the phase time for resonant tunneling structures is given. Simulation results show that the phase time is of the order of decay time in the well between the two barriers. But, the resonant tunneling time is of the order of excitation time of the trapped wave functions and shorter than the phase or decay time.