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 metric units, mobility is normally 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.
Typical electron mobility for GaAs at room temperature (300K) is 9200 cm2/(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}D</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 through an equation known as the Einstein relation:
<math>\mu = \frac{q}{kT}D</math>
where,
<math>D = \frac{\pi}{8}\lambda^2 \nu_m</math> is Diffusion constant,
<math>\lambda</math> is the mean free path,
k - Boltzmann constant
T - Species temperature