A two dimensional electron gas (2DEG) is a gas of electrons free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantized energy levels for motion in that direction, which can then be ignored for most problems. Thus the electrons appear to be a 2D sheet embedded in a 3D world. Such a construct of holes is called a two dimensional hole gas (2DHG), and such systems have many useful and interesting properties. The electron is a fundamental subatomic particle that carries a negative electric charge. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... In solid state physics, an electron hole (usually referred to simply as a hole) is the absence of an electron from the otherwise full valence band. ...

Geometries

In MOSFETs, the 2DEG is only present when the transistor is in inversion mode, and is found directly beneath the gate oxide.

Energy Band of basic HEMT.

Most 2DEGs are found in transistor-like structures made from semiconductors. The most commonly encountered 2DEG is the layer of electrons found in MOSFET transistors. When the transistor is in inversion mode, the electrons underneath the gate oxide are tightly held against the semiconductor-oxide interface, and thus occupy well defined energy levels. Nearly always, only the lowest level is occupied, and so the motion of the electrons perpendicular to the interface can be ignored. However, the electron is free to move parallel to the interface, and so is quasi two dimensional. MOSFET cross section Figure made by mysef. ... MOSFET cross section Figure made by mysef. ... Assorted transistors A transistor is a semiconductor device that uses a small amount of voltage or electrical current to control a larger change in voltage or current. ... A semiconductor is a solid whose electrical conductivity can be controlled over a wide range, either permanently or dynamically. ... The metal-oxide-semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), is by far the most common field-effect transistor in both digital and analog circuits. ...

Other methods for creating 2DEGs are high-electron-mobility-transistors (HEMT) and quantum wells. HEMTs are similar in structure to MOSFETs, but instead use two dissimilar semiconducting materials to trap electrons against an interface, rather than a semiconductor-oxide interface. In all other respects, the two are virtually identical. Electrons confined in heterojunction of HEMTs have higher mobility than those in MOSFETs, since HEMTs use an undoped channel and MOSFETs use a doped channel. HEMT stands for High Electron Mobility Transistor, and is also called heterostructure FET (HFET). ... A quantum well is a potential well that confines particles in one dimension, forcing them to occupy a planar region. ... In physics, electron mobility (or simply, mobility), is used to describe the relation between drift velocity of electrons or holes in a solid material or electrons/ions in a gas, and an applied electric field. ...

Quantum wells are slightly different, since they use two heterojunction interfaces very close together to confine the electrons. This method, which creates a "well" like structure, offers better control of the confinement length and the density of electrons. Quantum wells are thus more versatile than MOSFETs or single heterojunctions, which confine the electrons in a triangular well, as opposed to a square one.

Sometimes electrons are confined on the surface of a material. Free electrons will float on the surface of liquid helium, and are free to move along the surface, but stick to the helium. Some of the earliest work in 2DEGs was done using this system[1]. It is also possible to attract electrons onto the surface of graphene sheets, using the field effect. This has been a topic of much research recently, due to the promise of carbon nanotubes for quantum computing and single electron transistors. Helium exists in liquid form only at very low temperatures. ... Figure 1. ... An electronic device known as a diode can be formed by joining two nanoscale carbon tubes with different electronic properties. ... Molecule of alanine used in NMR implementation of error correction. ... In physics, a Coulomb blockade, named after Charles-Augustin de Coulomb, is the increased resistance at small bias voltages of an electronic device comprising at least one low-capacitance tunnel junction. ...

Experiments

Considerable research involving 2DEGs and 2DHGs has been done, and much continues to this day. 2DEGs offer a mature system of extremely high mobility electrons, especially at low temperatures. When cooled to 10 millikelvins, systems with mobilities of 30,000,000 cm²/(V·s) are not uncommon. 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. In physics, electron mobility (or simply, mobility), is used to describe the relation between drift velocity of electrons or holes in a solid material or electrons/ions in a gas, and an applied electric field. ... To help compare different orders of magnitude this page lists temperatures between 1 millikelvin and 1 kelvin. ... In solid state physics, a particles effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. ... A micrometre (American spelling: micrometer, symbol µm) is an SI unit of length equal to one millionth of a metre, or about a tenth of the size of a droplet of mist or fog. ...

Aside from being in practically every semiconductor device in use today, two dimensional systems allow access to interesting physics. The quantum Hall effect was first observed in a 2DEG[2], which led to two Nobel Prizes, in 1985 and 1998. The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ takes on the quantized values where e is the elementary charge and h is Plancks constant. ...

Footnotes

• 1. W. T. Sommer Liquid Helium as a Barrier to Electrons Physical Review Letters 12 271-273 (1964)
• 2. K. v. Klitzing, G. Dorda, and M. Pepper New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance Physical Review Letters 45, 494-497 (1980).

References

• Quantum Semiconductor Structures by Claude Weisbach and Borge Vinter, ISBN 0-12-742680-9
• Physics of Low Dimensional Semiconductors by John H. Davies, ISBN 0-521-48148-1