Velocity Saturation
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Saturation velocity is the maximum velocity a charge carrier in a
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...
, generally an
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...
, attains in the presence of very high electric fields. When this happens, the semiconductor is said to be in a state of velocity saturation.
Charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is u ...
s normally move at an average
drift speed In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an ...
proportional to the electric
field strength In physics, field strength means the '' magnitude'' of a vector-valued field (e.g., in volts per meter, V/m, for an electric field ''E''). For example, an electromagnetic field results in both electric field strength and magnetic field strength. ...
they experience temporally. The proportionality constant is known as
mobility Mobility may refer to: Social sciences and humanities * Economic mobility, ability of individuals or families to improve their economic status * Geographic mobility, the measure of how populations and goods move over time * Mobilities, a conte ...
of the carrier, which is a material property. A good
conductor Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble, such as an orchestra. * ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of structured free improvisation ...
would have a high mobility value for its charge carrier, which means higher velocity, and consequently higher current values for a given electric field strength. There is a limit though to this process and at some high field value, a charge carrier can not move any faster, having reached its saturation velocity, due to mechanisms that eventually limit the movement of the carriers in the material. As the applied electric field increases from that point, the carrier velocity no longer increases because the carriers lose energy through increased levels of interaction with the lattice, by emitting
phonons In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechan ...
and even
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
s as soon as the carrier energy is large enough to do so.


Field effect transistors

Saturation velocity is a very important parameter in the design of semiconductor devices, especially
field effect transistors The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs cont ...
, which are basic building blocks of almost all modern
integrated circuits An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Transistor count, Large ...
. Typical values of saturation velocity may vary greatly for different materials, for example for Si it is in the order of 1×107 cm/s, for
GaAs Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated ...
1.2×107 cm/s, while for 6H-SiC, it is near 2×107 cm/s. Typical electric field strengths at which carrier velocity saturates is usually on the order of 10-100 kV/cm. Both saturation field and the saturation velocity of a semiconductor material are typically strong function of impurities, crystal defects and temperature.


Small scale devices

For extremely small scale devices, where the high-field regions may be comparable or smaller than the average
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
of the charge carrier, one can observe velocity overshoot, or hot electron effects which has become more important as the transistor geometries continually decrease to enable design of faster, larger and more dense integrated circuits.High Field Hole Velocity and Velocity Overshoot in Silicon Inversion Layers, D. Sinitsky, F. Assaderaghi, C. Hu, and J. Bokor, IEEE Electron Device Letters, vol. 18, no. 2, February 1997 The regime where the two terminals between which the electron moves is much smaller than the mean free path, is sometimes referred as ballistic transport. There have been numerous attempts in the past to build
transistors upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
based on this principle without much success. Nevertheless, developing field of
nanotechnology Nanotechnology, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal o ...
, and new materials such as
Carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon makes ...
nanotube A nanotube is a nanometer-scale hollow tube-like structure. Kinds of nanotubes * BCN nanotube, composed of comparable amounts of boron, carbon, and nitrogen atoms * Boron nitride nanotube, a polymorph of boron nitride * Carbon nanotube, includes ...
s and
graphene Graphene () is an allotrope of carbon consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice nanostructure.
, offers new hope.


Negative differential resistivity

Though in a semiconductor such as Si saturation velocity of a carrier is same as the peak velocity of the carrier, for some other materials with more complex energy band structures, this is not true. In
GaAs Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monolithic microwave integrated ...
or InP for example the carrier drift velocity reaches to a maximum as a function of field and then it begins to actually decrease as the electric field applied is increased further. Carriers which have gained enough energy are kicked up to a different
conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...
which presents a lower drift velocity and eventually a lower saturation velocity in these materials. This results in an overall decrease of current for higher voltage until all electrons are in the "slow" band and this is the principle behind operation of a
Gunn diode A Gunn diode, also known as a transferred electron device (TED), is a form of diode, a two-terminal semiconductor electronic component, with negative resistance, used in high-frequency electronics. It is based on the "Gunn effect" discovered in ...
, which can display negative differential resistivity. Due to the transfer of electrons to a different conduction band involved, such devices, usually single terminal, are referred to as
Transferred electron device A Gunn diode, also known as a transferred electron device (TED), is a form of diode, a two-terminal semiconductor electronic component, with negative resistance, used in high-frequency electronics. It is based on the "Gunn effect" discovered in ...
s, or TEDs.


Design considerations

When designing
semiconductor device A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material (primarily silicon, germanium, and gallium arsenide, as well as organic semiconductors) for its function. Its conductivit ...
s, especially on a sub-micrometre scale as used in modern
microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circu ...
s, velocity saturation is an important design characteristic. Velocity saturation greatly affects the voltage transfer characteristics of a
field-effect transistor The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs con ...
, which is the basic device used in most
integrated circuits An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Transistor count, Large ...
. If a semiconductor device enters velocity saturation, an increase in voltage applied to the device will not cause a linear increase in current as would be expected by
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equatio ...
. Instead, the current may only increase by a small amount, or not at all. It is possible to take advantage of this result when trying to design a device that will pass a constant current regardless of the voltage applied, a current limiter in effect.


References

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Transistors upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
Charge carriers Physical quantities Semiconductors