Electron Mobility

Electron mobility - Wikipedia, the free encyclopedia
Typical electron mobility for Si at room temperature (300 K) is 1.0m2/ (V·s) ... semiconductor glossary entry for electron mobility ...
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electron mobility: Definition from Answers.com
electron mobility ( i?lek?trän m??bil?d? ) ( solid-state physics ) The drift mobility of electrons in a semiconductor, being the electron velocity
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Electron Mobility 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 \, E is the applied electric field \, \mu is the mobility

In semiconductors, mobility can also apply to Electron hole as well as electrons.

Conceptual overview In a solid, electrons (and in the case of semiconductors, electron hole) will Brownian motion in the absence of an applied electric field. 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.) over the mean free path between scattering events results in the electrons having an average drift velocity. 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, electron and Electron hole, will typically have different drift velocities for the same electric field.

In a Plasma (physics) there is analogous behavior with ions and free electrons.

In a vacuum, electrons will accelerate non-stop in an electric field according to Newton's second Newton's laws of motion. This is known as "ballistic transport". 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), quasi-ballistic transport is possible.

In SI units, mobility is normally measured in metre2/(volt·second). 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 semiconductor.

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:

\mu = \frac{1}{\frac{1}{\mu_{\rm lattice-->+\frac{1}{\mu_{\rm impurities-->}.

(Note: Matthiessen's rule originated from Augustus MatthiessenA. Matthiessen, Rep. Brit. Ass. 32, 144 (1862)A. Matthiessen, Progg. Anallen, 122, 47 (1864), who studied electrical conduction in metals. In his days, people might not even know the existence of semiconductors, as Augustus Matthiessen (1831-1870) lived in the days before superconductivity was discovered by Heike Kamerlingh Onnes in about 1911.)

Mobility in gas phase Mobility is defined for any species in the gas phase, encountered mostly in Plasma (physics) 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.

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. If one defines the mean free path in terms of momentum transfer, then one gets:

D = \frac{\pi}{8}\lambda^2 \nu_m.

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 \vee.

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. 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. In 1997, Professor Mark Lundstrom of Purdue University pointed out for Nanoelectronics, quasi-ballistic transport is possible and maximum charge carrier speed is controlled by mobility (instead of by velocity saturation according to conventional theory)M.S. Lundstrom, IEEE Electron Device Letters, 18, 361 (1997).. 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. One important approach is known as strain engineering.

Usually, three Scattering theory are present at the silicon dioxide / silicon interface of MOS transistors:

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

Phonon scattering at a higher gate voltage.

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"J. Koga, T. Ishihara and S. Takagi, IEEE Electron Device Letters, 24, 354, (2003).. Remote charge scattering can come from two sources:

Remote charge scattering due to ionized impurities in the Polycrystalline silicon gate.

Remote charge scattering due to trapped charge in the high-k dielectric.

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.C. W. Eng, W. S. Lau, D. Vigar, S. S. Tan and L. Chan, Applied Physics Letters, 87, article number 153510 (2005)..

Examples Typical electron mobility for Si at room temperature (300 K) is 0.92 m2/(V·s)

References

External links

semiconductor glossary entry for electron mobility
Bart Van Zeghbroeck's Online Book, Principles of Semiconductor Devices

Electron mobility - Wikipedia, the free encyclopedia
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 ...

Electron mobility 4.4.2
4.4.2 Electron mobility. Free electrons have a velocity which depends upon their energy. In the absence of an electric or magnetic field the electron energy approaches that of ...

Strathprints - Electron scattering in atomic liquids: application to ...
The phenomenon of the maximum of the electron mobility in liquids with a high atomic polarizability at the density Nm is explained by the suggestion of weakness of the s-wave ...

The electron mobility transition in n-GaAs heavily doped channel - ECS ...
Ohkura, Y., Mizuta, H., Ohbu, I., Kagaya, O., Katayama, K. and Ihara, S. (1994) The electron mobility transition in n-GaAs heavily doped channel. Semiconductor Science and ...

Electron mobility - Appropedia: The sustainability wiki
This page has been accessed 274 times. This page was last modified 14:39, 9 April 2008 by Benjamin W. Sturtz. Content is available under GNU FDL. Privacy policy; About Appropedia ...

Glasgow ePrints Service - Molecular-beam epitaxy growth of InGaAs ...
The electron densities in the channel of Si delta -doped InGaAs-InAlAs high electron mobility transistors grown on InP by molecular-beam epitaxy have been investigated by 1.4 K ...

Glasgow ePrints Service - Fabrication of 30nm T-gate high electron ...
This work reports on the development and fabrication of High Electron Mobility Transistors with a gate length of less than 30nm. The T-shaped gates were realized using a two ...

Electron Mobility Enhancement in Heavily Doped GaAs:C HBTs
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Amazon.co.uk: Microwave Metal Semiconductor Field Effect Transistors ...
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