- 2DEG
A two dimensional electron gas (2DEG) is a gas of
electron s free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantizedenergy level s 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.Geometries
Most 2DEGs are found in
transistor -like structures made fromsemiconductor s. The most commonly encountered 2DEG is the layer of electrons found inMOSFET s. When the transistor is ininversion mode , the electrons underneath thegate oxide are confined to 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.Other methods for engineering 2DEGs are high-electron-mobility-transistors (HEMTs) and rectangular
quantum well s.HEMT s arefield-effect transistors that utilize theheterojunction between two semiconducting materials to confine electrons to a triangularquantum well . Electrons confined to theheterojunction of HEMTs exhibit higher mobilities than those in MOSFETs, since the former device utilizes an unintentionally doped channel thereby mitigating the deleterious effect ofionized impurity scattering . Two closely-spacedheterojunction interfaces may be used to confine electrons to a rectangularquantum well . Careful choice of the materials and alloy compositions allow control of the carrier densities within the 2DEG.Electrons may also be confined to the surface of a material. For example, 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 [#Footnotes| [1] . It is also possible to attract electrons onto the surface ofgraphene sheets, using thefield effect . This has been a topic of current research, due to the applications ofcarbon nanotubes toquantum computing andsingle electron transistor s.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 4 K, systems with mobilities of order 1,000,000 cm^2/Vs are possible. Specially grown, state of the art heterostructures with mobilities of 30,000,000 cm²/(V·s) have been made. 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.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 [#Footnotes| [2] , which led to two Nobel Prizes, in [http://nobelprize.org/physics/laureates/1985/index.html 1985] and [http://nobelprize.org/physics/laureates/1998/ 1998] ...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 Weisbuch and Borge Vinter, ISBN 0-12-742680-9
* "Physics of Low Dimensional Semiconductors" by John H. Davies, ISBN 0-521-48148-1
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