Electron mobility - Citizendia

In physics, electron mobility (or simply, mobility), is a quantity relating the drift velocity of electrons to the applied electric field across a material, according to the formula:

$\,v_d = \mu E$

where

$\, v_d$ is the drift velocity in m/s (SI units) or cm/s (cgs units). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. The drift velocity is the average Velocity that a particle such as an Electron, attains due to an Electric field. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units The centimetre-gram-second system ( CGS) is a system of physical units.

$\, E$ is the applied electric field in V/m (SI) or statvolt/cm (cgs). The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The statvolt is the unit of Voltage and Electrical potential used in the Cgs system of units A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth

$\, \mu$ is the mobility in m²/(V·s), in SI units, or cm²/(statvolt·s), in cgs units. M^2 redirects here For other uses see M². CM2 redirects here The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units M^2 redirects here For other uses see M². CM2 redirects here The statvolt is the unit of Voltage and Electrical potential used in the Cgs system of units The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units The centimetre-gram-second system ( CGS) is a system of physical units. A mixed mobility unit of 1 cm²/(V·s) = 0. M^2 redirects here For other uses see M². CM2 redirects here The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units 0001 m²/(V·s) is also often used. M^2 redirects here For other uses see M². CM2 redirects here The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units

It is the application for electrons of the more general phenomenon of electrical mobility of charged particles in a fluid under an applied electric field. Electrical mobility is the tendency of charged elementary particles (such as Electrons or Protons to move other than engaging in a stationary orbit (for example within

In semiconductors, mobility can also apply to holes as well as electrons. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that An electron hole is the conceptual and mathematical Opposite of an Electron, useful in the study of Physics and Chemistry.

1 Conceptual overview
2 Mobility in gas phase
3 Mobility at the silicon dioxide / silicon interface of MOSFET transistors
4 Examples
5 See also
6 References
7 External links

Conceptual overview

In a solid, electrons (and, in the case of semiconductors, both electrons and holes) will move around randomly in the absence of an applied electric field. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that An electron hole is the conceptual and mathematical Opposite of an Electron, useful in the study of Physics and Chemistry. This article is about the physical phenomenon for the stochastic process see Wiener process. Therefore, if one averages the movement over time there will be no overall motion of charge carriers in any particular direction. However upon applying an electric field, electrons will be accelerated in an opposite direction to the electric field. The summation of the time between acceleration of electrons due to electric field and deceleration of electrons due to collisions and lattice scattering events (caused by phonons, crystal defects, impurities, etc. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid Crystalline solids have a very regular atomic structure that is the local positions of atoms with respect to each other are repeated at the atomic scale ) over the mean free path between scattering events results in the electrons having an average drift velocity. In Physics the mean free path of a particle is the average distance covered by a particle ( Photon, Atom or Molecule) between subsequent impacts The drift velocity is the average Velocity that a particle such as an Electron, attains due to an Electric field. This net electron motion must be orders of magnitude less than the normally occurring random motion, otherwise the mobility equation is not valid (i. e. , typical drift speeds in copper being of the order of 10^-4 m·s⁻¹ compared to the speed of random electron motion of 10⁵ m·s⁻¹).

In a semiconductor the two charge carriers, electrons and holes, will typically have different drift velocities for the same electric field. An electron hole is the conceptual and mathematical Opposite of an Electron, useful in the study of Physics and Chemistry.

In a plasma there is analogous behavior with ions and free electrons. In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge

In a vacuum, electrons will accelerate continuously in an electric field according to Newton's second law of motion (until they reach a relativistic speed). This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the A Relativistic speed is a speed which is a significant proportion of the Speed of light. This is known as "ballistic transport". Ballistic transport is the transport of electrons in a medium with negligible Electrical resistivity due to Scattering. A steady-state drift velocity is never achieved, and thus electron mobility is undefined for electronic movement in a vacuum.

In a solid, if the electrons must move only a very short distance (distance comparable with the Brownian motion length scale), quasi-ballistic transport is possible. This article is about the physical phenomenon for the stochastic process see Wiener process. Ballistic transport is the transport of electrons in a medium with negligible Electrical resistivity due to Scattering.

Since mobility is usually a strong function of material impurities and temperature, and is determined empirically, mobility values are typically presented in table or chart form. Mobility is also different for electrons and holes in a given semiconductor. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that

An approximation of the mobility function can be written as a combination of influences from lattice vibrations (phonons) and from impurities by the Matthiessen's Rule:

$\frac{1}{\mu} = \frac{1}{\mu_{\rm lattice}}+\frac{1}{\mu_{\rm impurities}}$ . In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid

Mobility in gas phase

Mobility is defined for any species in the gas phase, encountered mostly in plasma physics and is defined as:

$\mu = \frac{q}{m\, \nu_m}$

where

$\, q$ is the charge of the species,

$\, \nu_m$ is the momentum transfer collision frequency, and

$\, m$ is the mass. In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound

Mobility is related to the species' diffusion coefficient $\, D$ through an exact (thermodynamically required) equation known as the Einstein relation:

$\mu = \frac{q}{k\, T}D$ ,

where

$\, k$ is the Boltzmann constant,

$\, T$ is the gas temperature, and

$\, D$ is a measured quantity that can be estimated. In Physics (namely in Kinetic theory) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection revealed Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics This page is about the physical properties of gas as a state of matter If one defines the mean free path in terms of momentum transfer, then one gets:

$D = \frac{\pi}{8}\lambda^2 \nu_m$ . In Physics the mean free path of a particle is the average distance covered by a particle ( Photon, Atom or Molecule) between subsequent impacts In Particle physics, Wave mechanics and Optics, momentum transfer is the amount of Momentum that one particle gives to another particle

But both the momentum transfer mean free path and the momentum transfer collision frequency are difficult to calculate. Many other mean free paths can be defined. In the gas phase, $\, \lambda$ is often defined as the diffusional mean free path, by assuming a simple approximate relation is exact:

$D = \frac{1}{2}\lambda \,v$ ,

when $\, v$ is the root mean square speed of the gas molecules:

$v = \sqrt {{3\, k\, T}\over{m}}$

where

$\, m$ is the mass of the diffusing species. In Mathematics, the root mean square (abbreviated RMS or rms) also known as the quadratic mean, is a statistical measure of the This approximate equation becomes exact when used to define the diffusional mean free path.

Mobility at the silicon dioxide / silicon interface of MOSFET transistors

For n-channel or p-channel MOSFETs, the electron or hole mobility at the silicon dioxide / silicon interface has a very strong effect on the speed of the device. The metal–oxide–semiconductor field-effect transistor ( MOSFET, MOS-FET, or MOS FET) is a device used to amplify or switch electronic signals The Chemical compound silicon dioxide, also known as silica or silox (from the Latin " Silex " is an Oxide Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 In 1997, Professor Mark Lundstrom of Purdue University pointed out for nanotransistors, quasi-ballistic transport is possible and maximum charge carrier speed is controlled by mobility (instead of by velocity saturation according to conventional theory)^[1]. Nanoelectronics refer to the use of Nanotechnology on electronic components especially Transistors. Ballistic transport is the transport of electrons in a medium with negligible Electrical resistivity due to Scattering. In Semiconductors when a strong enough electric field is applied the carrier velocity in the semiconductor reaches a maximum value Increasing the mobility of MOSFETs can have a profound benefit to digital electronics, thus all major digital semiconductor manufacturers have been exploring methods to increase mobility at the silicon dioxide / silicon interface of MOS transistors. Digital electronics are Electronics systems that use Digital signals Digital electronics are representations of Boolean algebra also see One important approach is known as strain engineering. Strain engineering refers to a general strategy employed in Semiconductor manufacturing to enhance device performance

Usually, three scattering mechanisms are present at the silicon dioxide / silicon interface of MOS transistors:

Coulombic scattering at a gate voltage slightly above the threshold voltage. In Mathematics and Physics, scattering theory is a framework for studying and understanding the Scattering of Waves and particles.
Phonon scattering at a higher gate voltage. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid
Surface roughness scattering at a higher gate voltage.

Recently, scientists have been studying the possibility of "remote Coulombic scattering", which is also known as "remote charge scattering"^[2]. Remote charge scattering can come from two sources:

Remote charge scattering due to ionized impurities in the polysilicon gate.
Remote charge scattering due to trapped charge in the high-k dielectric. The term high-κ Dielectric refers to a material with a high Dielectric constant (κ (as compared to Silicon dioxide) used in semiconductor manufacturing

In 2005, W. S. Lau pointed out as Lau's hypothesis that "remote Coulombic scattering" is only important in the subthreshold region and in the region slightly above threshold. Subthreshold leakage or subthreshold conduction or subthreshold drain current is the current that flows between the source and drain of a MOSFET ^[3].

Examples

Typical electron mobility for Si at room temperature (300 K) is 1. Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 0m²/ (V·s)

Very high mobility has been found in several low-dimensional systems, such as two-dimensional electron gases (2DEG) (3,000,000cm²/ V·s at low temperature)^[4], carbon nanotubes (100,000cm²/ V·s at room temperature) ^[5]and more recently, graphene (200,000cm²/ V·s at low temperature)^[6]. A two dimensional electron gas (2DEG is a gas of Electrons free to move in two dimensions but tightly confined in the third See also Graphene, Buckypaper Carbon nanotubes (CNTs are Allotropes of carbon with a nanostructure that can have a length-to-diameter Graphene is a one-atom-thick planar sheet of sp2-bonded Carbon atoms that are densely packed in a honeycomb crystal lattice Organic semiconductors (polymer, oligomer) developed thus far have carrier mobilities below 10cm²/(V·s), and usually much lower. A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds In Chemistry, an oligomer consists of a limited number of Monomer units (ολιγος or oligos is Greek for "a few" in contrast to a

References

^ M. The Speed of electricity refers to the relatively slow movement of free Electrons or Ions through a conductor in the presence of an Electric field S. Lundstrom, IEEE Electron Device Letters, 18, 361 (1997). doi:10.1109/55.596937
^ J. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. Koga, T. Ishihara and S. Takagi, IEEE Electron Device Letters, 24, 354, (2003).
^ Eng, C. W. ; Lau, W. S. ; Vigar, D. ; Tan, S. S. ; and Chan, L. (2005). "Effective channel length measurement of metal-oxide-semiconductor transistors with pocket implant using the subthreshold current-voltage characteristics based on remote Coulomb scattering". Applied Physics Letters 87 (15): art. no. 153510. doi:10.1063/1.2093943. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
^ Harris et al, J. Applied Physics 61, no. 3 , pp. 1219, 1987. doi:10.1063/1.338174
^ Durkop et al, Nano Letters 4, no. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. 1, pp. 35, 2004 doi:10.1021/nl034841q
^ Bolotin et al, http://arxiv.org/abs/0802.2389

External links

A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.

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Contents

Conceptual overview

Mobility in gas phase

Mobility at the silicon dioxide / silicon interface of MOSFET transistors

Examples

See also

References

External links