Semiconductor Ballistic Electron Reflection, Refraction, Interference, and Diffraction Effects: Modeling and Quantum Device Applications

Semiconductor growth techniques such as molecular beam epitaxy have been refined so that nanostructures can be grown with precise monolayer and compositional control [1]. This has produced semiconductor materials in which ballistic (collisionless) electron transport lengths of over a micron have been observed [2-4]. That is, the electrons traverse the sample as quantum mechanical plane waves experiencing no elastic or inelastic scattering events. Ballistic electrons can account for more than half of the current in small devices [3]. Since ballistic electrons are quantum mechanical deBroglie waves, they can be reflected, refracted, interfered, and diffracted [5] in a manner analogous to electromagnetic optical waves [6]. Recently, it has been shown that these electron wave optical effects are exactly analogous to electromagnetic waves in general dielectrics (lossless materials with arbitrary permittivity ϵ and permeability µ) [7]. Electron wave interference effects have been observed experimentally for electron energies below the barriers in double-barrier and multi-barrier resonant tunneling devices and for electron energies above the conduction band edges in Ga1-xAlxAs heterostructures [5]. In addition, by combining growth techniques with nanolithography, electron wave refraction has been experimentally demonstrated through the fabrication of electron lenses and prisms [8,9] in a two-dimensional GaAs electron gas.