Two-dimensional electron gas

When the transistor is in inversion mode, the electrons underneath the gate oxide are confined to the semiconductor-oxide interface, and thus occupy well defined energy levels.

For thin-enough potential wells and temperatures not too high, only the lowest level is occupied (see the figure caption), and so the motion of the electrons perpendicular to the interface can be ignored.

HEMTs are field-effect transistors that utilize the heterojunction between two semiconducting materials to confine electrons to a triangular quantum well.

Electrons confined to the heterojunction of HEMTs exhibit higher mobilities than those in MOSFETs, since the former device utilizes an intentionally undoped channel thereby mitigating the deleterious effect of ionized impurity scattering.

Recently, atomically thin solid materials have been developed (graphene, as well as metal dichalcogenide such as molybdenum disulfide) where the electrons are confined to an extreme degree.

The two-dimensional electron system in graphene can be tuned to either a 2DEG or 2DHG (2-D hole gas) by gating or chemical doping.

[3] More examples can be found in a recent review[4] including a notable discovery of 2004, a 2DEG at the LaAlO3/SrTiO3 interface[5] which becomes superconducting at low temperatures.

The origin of this 2DEG is still unknown, but it may be similar to modulation doping in semiconductors, with electric-field-induced oxygen vacancies acting as the dopants.

[6] These enormous mobilities offer a test bed for exploring fundamental physics, since besides confinement and effective mass, the electrons do not interact with the semiconductor very often, sometimes traveling several micrometers before colliding; this so-called mean free path

The quantum Hall effect was first observed in a 2DEG,[9] which led to two Nobel Prizes in physics, of Klaus von Klitzing in 1985,[10] and of Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui in 1998.

[11] Spectrum of a laterally modulated 2DEG (a two-dimensional superlattice) subject to magnetic field B can be represented as the Hofstadter's butterfly, a fractal structure in the energy vs B plot, signatures of which were observed in transport experiments.