Electron mobility
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In physics, electron mobility (or simply, mobility), is used to describe the relation between drift velocity of electrons or holes in a solid material or electrons/ions in a gas, and an applied electric field. The drift velocity is directly related to the electric field as follows,
- <math>v_d = \mu E</math>,
where μ is the mobility.
In SI units, mobility is normally measured in m2/(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.
Typical electron mobility for GaAs at room temperature (300 K) is 0.92 m2/(V·s).
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):
- <math>\mu = \frac{1}{\frac{1}{\mu_{\rm lattice}}+\frac{1}{\mu_{\rm impurities}}}</math>.
Mobility in gas phase
Mobility is defined for any species in the gas phase, encountered mostly in plasma physics and is defined as :
<math>\mu = \frac{q}{m\nu_m}</math> where,
q - charge of the species,
<math>\nu_m</math> - 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:
<math>\mu = \frac{q}{kT}D</math>
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:
<math>D = \frac{\pi}{8}\lambda^2 \nu_m</math>
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:
<math>D = \frac{1}{2}\lambda \vee</math>
where v is the root mean square speed of the gas molecules:
<math>v = \sqrt {{3kT}\over{m}}</math>
where m is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path.
