Time-dependent resonant tunneling of wave packets in the tight-binding model

We consider the dynamics of resonant tunneling through a double barrier within a simple one-dimensional tight-binding model. High-frequency experiments on double-barrier semiconductor structures have motivated theoretical studies of the various time scales that exist in a resonant-tunneling process. Numerical results involving wave packets have shown that the transient process of building up a resonant state in a double-barrier well is qualitatively different from the exponential decay out of the well. These results are confirmed in the present paper. We investigate how the transient buildup depends on barrier and initial-state parameters, and find the perhaps surprising result that, for opaque barriers, the particle density inside the well evolves in time essentially independently from barrier width and height. In our opinion, this shows that one cannot use the concept of a classical velocity for particles moving through classically forbidden regions of space. Also, we find that the buildup time mainly reflects the spatial extent of the incoming wave packet. Our conclusion is, therefore, that the limiting factor for a maximum operating frequency is either due to properties of the incoming electrons, in particular, their spatial extent, or due to inelastic-scattering or external-circuit effects, not incorporated in our simple model.