In physics, electron mobility (or simply, mobility), is a quantity relating the drift velocity of charge carriers to the applied electric field across a material. It also describes the related concept of the net flow of charge carriers. Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the fundamental laws of the universe and their precise formulation in a mathematical framework. ... The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. ... Charge carrier denotes in physics a free (mobile, unbound) particle carrying an electric charge. ... It has been suggested that optical field be merged into this article or section. ...

In a solid, electrons (and in the case of semiconductors, electron holes) will move around randomly in the absence of an applied current. Therefore if one averages the movement over time there will be no overall motion of charge carriers in any particular direction. However on applying an electric field charge carriers will on average move in a direction aligned with the electric field, with positive charge carriers such as electron holes moving in the direction of field, and negative charge carriers moving in the opposite direction. This net flow will be a lot slower than the normal random motion, with drift speeds in copper being of the order of 10^-4 ms^-1 compared a speed of 10⁵ ms^-1 for the random motion. Also different types of charge carriers will have different drift velocities for the same electric field. In a gas there is analagous behaviour with ions and free electrons. Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ... For the following two reasons the electron hole was introduced into calculations. ... ...

The drift velocity is directly related to the electric field by,

v_d = μE,

where μ is the mobility.

In SI units, mobility is normally measured in m²/(V·s). In USA, mobility is quite frequently measured in cm²/(V·s).Since mobility is a strong function of impurities as well as temperature, it is difficult to provide any values of mobility here for common materials. Mobility is also different for electrons and holes in a semiconductor. When one charge carrier is dominant the conductivity of a semiconductor is directly proportional to the mobility of the dominant carrier. Cover of brochure The International System of Units. ... The metre, or meter (U.S.), is a measure of length. ... Josephson junction array chip developed by NIST as a standard volt. ... Look up second in Wiktionary, the free dictionary. ... A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ... Josephson junction array chip developed by NIST as a standard volt. ... Look up second in Wiktionary, the free dictionary. ... A semiconductor is a solid whose electrical conductivity can be controlled over a wide range, either permanently or dynamically. ... Electrical conductivity is a measure of a materials ability to conduct an electric current. ...

Typical electron mobility for GaAs at room temperature (300 K) is 0.92 m²/(V·s) or 9200 cm²/(V·s). Gallium arsenide (GaAs) is a chemical compound composed of gallium and arsenic. ...

In approximation the mobility can be written as a combination of influences from lattice vibrations (phonons) and from impurities by the following equation (Matthiessen's Rule): Normals modes of vibration progression through a crystal. ...

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(Note: Matthiessen's rule probably originated from Ludwig Matthiessen (1830-1906), who studied electrical conduction in metals. In his days, people might not even know the existence of semiconductors. Ludwig Matthiessen pointed out when the temperature decreases, the metal resistance decreases and then becomes constant with further decrease in temperature. Ludwig Matthiessen lived in the days before superconductivity was discovered by Heike Kamerlingh Onnes.) Heike Kamerlingh Onnes (September 21, 1853 – February 21, 1926) was a Dutch physicist. ...

Mobility in gas phase

Mobility is defined for any species in the gas phase, encountered mostly in plasma physics and is defined as : A plasma lamp, illustrating some of the more complex phenomena of a plasma, including filamentation. ...

where,

q - charge of the species,

ν_m - momentum transfer collision frequency,

m - mass,

Mobility is related to the species' diffusion coefficient D through an exact (thermodynamically required) equation known as the Einstein relation: In physics, in kinetic theory the Einstein relation is a previously unexpected connection revealed by Einstein in his 1905 paper on Brownian motion: linking D, the Diffusion constant, and μ, the mobility of the particles; where k is Boltzmanns constant, and T is the absolute temperature. ...

where k the Boltzmann constant, T the gas temperature, and D is a measured quantity, that can be estimated. If one defines the mean free path in terms of momentum transfer, then one gets:

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, λ is often defined as the diffusional mean free path, by assuming a simple approximate relation is exact:

where v is the root mean square speed of the gas molecules:

where m is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path.

Mobility at the silicon dioxide / silicon interface of MOS transistors

For n-channel MOS transistors, the electron mobility at the silicon dioxide / silicon interface has a very strong effect on the speed of the device. Similarly, for p-channel MOS transistors, the hole mobility at the silicon dioxide / silicon interface has a very strong effect on the speed of the device. In 1997, Professor Mark Lundstrom (Purdue University) pointed out for nanotransistors, speed is controlled by mobility instead of by saturation velocity according to conventional theory [1]. Thus, all the major semiconductor players (Intel, IBM, etc.) have been exploring all sorts of methods to increase mobility at the silicon dioxide / silicon interface of MOS transistors. One important approach is know as strain engineering. Intel Corporation (NASDAQ: INTC, SEHK: 4335), founded in 1968 as Integrated Electronics Corporation, is an American multinational corporation that is best known for designing and manufacturing microprocessors and specialized integrated circuits. ... International Business Machines Corporation (known as IBM or Big Blue; NYSE: IBM) is a multinational computer technology corporation headquartered in Armonk, New York, USA. The company is one of the few information technology companies with a continuous history dating back to the 19th century. ... Strain engineering refers to a general strategy employed in semiconductor manufacturing to enhance device performance. ...

Usually, 3 scattering mechanisms are present:

1. Coulombic scattering at a gate voltage slightly above the threshold voltage.

2. Phonon scattering at a higher gate voltage.

3. Surface roughness scattering a a higher gate voltage.

Recently, scientists have been studying the possibility of "remote Coulombic scattering", which is also known as "remote charge scattering" [2]. In 2005, W.S. Lau pointed out that "remote Coulombic scattering" is only important in the subthreshold region and in the region slightly above threshold [3]. This is mentioned as Lau's hypothesis in reference [3].

References

[1] M.S. Lundstrom, IEEE Electron Device Lett., 18, 361 (1997).

[2] J. Koga, T. Ishihara and S. Takagi, IEEE Electron Dev. Lett, 24, 354, (2003).

[3] C. W. Eng, W. S. Lau, D. Vigar, S. S. Tan and L. Chan, Appl. Phys. Lett., 87, article number 153510 (2005).

External links

• semiconductor glossary
• Bart Van Zeghbroeck's Online Book Principles of Semiconductor Devices