Three-dimensional tunneling in quantum ballistic motion

Abstract

We provide an elementary case study of field-induced quantum tunneling in a realistic three-dimensional environment which exhibits both tunneling and classically allowed motion. An analytic description is presented for ballistic motion in a uniform electric field. From there we derive simple expressions concerning the wave function for field emission from an ultrathin quantum well in the tunneling limit. At the same time a wave-packet description of the tunneling process is obtained. The tunneling time can be read off from the lateral spread of the tunneling current distribution.