Tunneling dynamics in stationary field emission



Stationary three-dimensional field emission out of an ultrathin quantum well is analyzed in terms of the semiclassical Hamilton-Jacobi theory. We compare the spatial quantum distribution of the tunneling electrons with the corresponding results obtained from real-time tunneling trajectories. The classical-limit trajectory method reproduces the exact quantum distribution for weak external fields. The Büttiker-Landauer expression for the barrier crossing velocity is confirmed.