Temporal characteristics of electron tunneling in double-barrier stepped-quantum-well structures

The temporal development of an electron wave packet tunneling through a double-barrier stepped-quantum-well structure has been numerically investigated with the use of the transfer-matrix approach. We examine the time dependence of the probability density ${\mathit{P}}_{\mathit{w}}$(t) of finding an electron inside the stepped quantum well and find that there exist two different patterns for electron transport through the system from the analysis of the temporal behavior of the ${\mathit{P}}_{\mathit{w}}$(t). The shape of the ${\mathit{P}}_{\mathit{w}}$(t) depends on the parameters of the wave packet and the structure of the quantum wells. One pattern is that after an initial buildup time ${\mathit{P}}_{\mathit{w}}$(t) reaches its maximum and then decays exponentially with time. The other is that the decay of the ${\mathit{P}}_{\mathit{w}}$(t) deviates substantially from exponential, and two peaks appear in the ${\mathit{P}}_{\mathit{w}}$(t) curves. A possible electron-transport process corresponding to the second pattern has also been suggested.