Editing Electron mobility (section)

==Electric field dependence and velocity saturation==
{{Main|Velocity saturation}}

At low fields, the drift velocity ''v''<sub>''d''</sub> is proportional to the electric field ''E'', so mobility ''μ'' is constant. This value of ''μ'' is called the ''low-field mobility''.

As the electric field is increased, however, the carrier velocity increases sublinearly and asymptotically towards a maximum possible value, called the ''saturation velocity'' ''v''<sub>sat</sub>. For example, the value of ''v''<sub>sat</sub> is on the order of 1×10<sup>7</sup> cm/s for both electrons and holes in Si. It is on the order of 6×10<sup>6</sup> cm/s for Ge. This velocity is a characteristic of the material and a strong function of [[Doping (semiconductor)|doping]] or impurity levels and temperature. It is one of the key material and semiconductor device properties that determine a device such as a transistor's ultimate limit of speed of response and frequency.

This velocity saturation phenomenon results from a process called ''[[optical phonon]] scattering''. At high fields, carriers are accelerated enough to gain sufficient [[kinetic energy]] between collisions to emit an optical phonon, and they do so very quickly, before being accelerated once again. The velocity that the electron reaches before emitting a phonon is:
<math display="block">\frac{m^* v_\text{emit}^2}{2} \approx \hbar \omega_\text{phonon (opt.)}</math>
where ''ω''<sub>phonon(opt.)</sub> is the optical-phonon angular frequency and m* the carrier effective mass in the direction of the electric field. The value of ''E''<sub>phonon (opt.)</sub> is 0.063 eV for Si and 0.034 eV for GaAs and Ge. The saturation velocity is only one-half of ''v''<sub>emit</sub>, because the electron starts at zero velocity and accelerates up to ''v''<sub>emit</sub> in each cycle.<ref name=Mitin>{{cite book|author1=Vladimir Vasilʹevich Mitin|author2=Vi︠a︡cheslav Aleksandrovich Kochelap |author3=Michael A. Stroscio|title=Quantum heterostructures: microelectronics and optoelectronics| url=https://books.google.com/books?id=Wzo4IdxS48oC&pg=PA308|access-date=2 March 2011|year=1999|publisher=Cambridge University Press |isbn=978-0-521-63635-3|pages=307–9}}</ref> (This is a somewhat oversimplified description.<ref name=Mitin/>)

Velocity saturation is not the only possible high-field behavior. Another is the [[Gunn effect]], where a sufficiently high electric field can cause intervalley electron transfer, which reduces drift velocity. This is unusual; increasing the electric field almost always ''increases'' the drift velocity, or else leaves it unchanged. The result is [[negative differential resistance]].

In the regime of velocity saturation (or other high-field effects), mobility is a strong function of electric field. This means that mobility is a somewhat less useful concept, compared to simply discussing drift velocity directly.