5.1 Physics of Resonant Tunneling

A quantum well, in the general use of this term, is a potential structure which spatially confines the electron. According to quantum mechanics, an electron subjected to potential confinement has its energy quantized and a discrete energy spectrum would be expected for the electron system. However, the electron remains free to move in the perpendicular direction. This results in the creation of a two-dimensional electron gas of quasi-bound states.

Resonant tunneling refers to tunneling in which the electron transmission coefficient through a structure is sharply peaked about certain energies. The emergence of these peaks can be qualitatively explained by introducing infinite walls as boundary conditions. It is usually possible to do this far from the quantum well itself. Then the calculation of the quantized energy levels in a quantum well of arbitrary shape is the solution of an eigenvalue problem. For electrons with an energy corresponding approximately to the virtual resonant energy level of the quantum well, the transmission coefficient is close to unity. That is, an electron with this resonant energy can cross the double barrier without being reflected. This resonance phenomenon is similar to that taking place in the optical Fabry-Perot resonator or in a microwave capacitively-coupled transmission-line resonator.

The outlined physics gives a simple theory of quantum transport through quantum wells from elementary quantum mechanics. However, for simulation, we model resonant tunneling using open systems theory.