Time resolution of tunnelling effect

Abstract

The double barrier is used by way of example for obtaining the charge transfer, as it evolves in time, across the barrier under the influence of an applied field. A charge carrier is initially considered in a state described by a wavepacket lying on the barrier’s l.h.s. The semiclassical propagator is then employed for deriving the wavefunction on the other side. Charge and current density evolutions are then obtained. The tunnelling current (carrier’s energy below barrier’s height) rises initially and then drops essentially to zero. For barrier heights of a few tenths of eV the typical time over which tunnelling takes place is of the order of 10⁻¹³ s. However, both duration and magnitude of the current density are greatly dependent on the initial wavepacket extent.