Novel displacement in transmission through a two-dimensional semiconductor barrier

The lateral displacement of electron beams transmitting through a two-dimensional semiconductor barrier is quite different from the prediction from Snell's law for electron waves. It is shown that the displacement can be greatly enhanced by transmission resonance when the incidence angle is less than but close to the critical angle for total reflection. The displacement depends not only on the barrier's thickness but also on the incidence angle and the incidence energy. The influence of electron's effective mass is also discussed. Theoretical results of the stationary-phase approach are confirmed by numerical simulations for a Gaussian-shaped incident beam. These phenomena may lead to novel applications in quantum electronic devices.