Quantum mechanical equivalent of electromagnetic band gap and perfect tunneling in multilayer semiconductor hetero-structures

In this article, we have applied Maxwell-Schrodinger analogy to introduce the idea of electromagnetic metamaterial based band gap in semiconductor regime. We have found a new type of band gap in semiconductor hetero-structures, which is analogous to the spatial average single negative (SASN) band gap in multi-layer photonic crystal. Interestingly, width of such bandgaps is controllable according to designers´ will. Perfect tunneling of the propagating stationary states and strong spatial delocalization of bounded electronic states have also been observed, which is electronic analogue of the enhancement of evanescent waves in Pendry´s lens. Finally, a multilayer structure has been proposed, which supports band-gap at some energy bands and perfect tunneling at target energy value. As the on-off ratio (step transition from low transmission to high transmission) is very high even if the applied energy is very low, this kind of multi-layer structures can be very useful as future low power electronic device and logic transistor.