A sheet of electrons free to move in two directions but trapped in the third, so tightly that across it they have only one way to sit. It need not be a thin material: most electron gases live at the boundary between two thick crystals, or under the gate of a silicon , with ordinary bulk material all around. A layer of graphene is the extreme case, where the crystal itself is as thin as its sheet of electrons. Electron gases like these are where the was discovered.
As the site uses it
In Ca2N the space between the calcium–nitrogen layers contains no atoms, just a two-dimensional electron gas that is part of the chemical formula.
The effect was found in a two-dimensional electron gas inside a silicon transistor, and it was the first demonstration that confining electrons to a plane produces something a bulk crystal cannot do at all.
Pressed against an interface, electrons fill only the lowest level of a narrow well and move freely along the interface alone. Usually that sheet is buried between thick crystals – under the oxide of a silicon transistor, or where LaAlO3 meets SrTiO3. In graphene the crystal is as thin as its sheet of electrons.
Trapped in one direction
Electrons pressed against an interface by an electric field sit in a potential well a few nanometres wide. Across the well their motion is quantised into levels, called subbands; if only the lowest is occupied, every electron is in the same state across the well and can move only along the plane. That is what makes the gas two-dimensional – the electrons, not necessarily the material around them.
The first such gases were the inversion layers of silicon transistors: a draws electrons to the silicon’s interface with its oxide and sets how many there are. Their energy levels, transport and optics were mapped in detail by the early 1980s (Ando, Fowler and Stern, 1982). In two dimensions the number of available states per energy interval does not change with energy, unlike in a bulk crystal – one of several ways in which the physics of a sheet differs from that of a solid.
Clean gases and the quantum Hall effect
In 1980 von Klitzing, Dorda and Pepper measured the of the electron gas in a silicon transistor in a strong magnetic field and found that, at particular electron densities, the Hall resistance took fixed values set only by fundamental constants and independent of the device’s shape – the quantum Hall effect, now the basis of the resistance standard.
What limits such a gas is how often its electrons scatter, and the ionised donors that supply them are among the worst offenders. Modulation moves them out of the way: in GaAs–AlGaAs structures the donors sit in the AlGaAs, and the electrons they release gather in the neighbouring GaAs, away from the ions left behind. rose above those of comparably doped bulk GaAs (Dingle and colleagues, 1978).
Gases at oxide interfaces, and sheets one atom thick
Electron gases also form at the interface of two oxides. When LaAlO3 grown on SrTiO3 reaches four , the interface starts to conduct, with 3.5 to 6.3 × 1013 electrons per square centimetre in films four to ten cells thick and no steady rise as the film grows (Lee and colleagues, 2016). In the layered Ca2N, electrons fill the space between the calcium–nitrogen layers.
A and a 2D electron gas are easily confused. In GaAs or LaAlO3/SrTiO3 the crystals are thick and only the electrons are two-dimensional, buried at an interface that a gate reaches only through the material on top. In graphene the crystal is as thin as the electron sheet and lies open on its surface – so its electrons can be reached by any gate, probe or neighbouring layer, and also feel every impurity on the .
For specialists
Electrons confined in one direction to the lowest subband of a potential well – an inversion layer at the Si/SiO2 interface, a GaAs/AlGaAs heterojunction, an oxide interface such as LaAlO3/SrTiO3 – and free in the other two, with a that does not depend on energy and a density set by gates or doping. Modulation doping, which places the donors away from the electrons, gave GaAs electron gases mobilities above those of comparable bulk GaAs; the quantized Hall resistance was first measured in the electron gas of a silicon MOSFET. Atomically thin crystals such as graphene host two-dimensional electron systems of their own, with no buried interface.
A two-dimensional electron gas in a uniform neutralizing background forms a triangular at low density. In a strongly mass-asymmetric , localized heavy holes instead provide a nonuniform positive background that supports an electron crystal at densities two orders of magnitude higher…
effect (FQAHE) has been discovered in twisted MoTe2 and graphene/hBN . Such feature a tuning knob of gate displacement field D, which is absent from the conventional fractional quantum Hall systems in two-dimensional…
The conventional generates spin currents through interfacial thermal conduction. In this Letter, we establish a -mediated spin Seebeck effect driven by thermal radiation. Using a monolayer separated from a thermal emitter by a vacuum gap, we…