Editing Fermi level (section)

==Out of equilibrium==
{{See also|Quasi-Fermi level}}
The Fermi level, ''μ'', and temperature, ''T'', are well defined constants for a solid-state device in thermodynamic equilibrium situation, such as when it is sitting on the shelf doing nothing. When the device is brought out of equilibrium and put into use, then strictly speaking the Fermi level and temperature are no longer well defined. Fortunately, it is often possible to define a quasi-Fermi level and quasi-temperature for a given location, that accurately describe the occupation of states in terms of a thermal distribution. The device is said to be in ''quasi-equilibrium'' when and where such a description is possible.

[[File:Diode quasi-fermi levels.svg|thumb|Quasi-fermi levels (dashed) of electrons and holes in a [[p-n junction]] under forward bias, corresponding to out-of-equilibrium charge carrier densities (filled curves).]]

The quasi-equilibrium approach allows one to build a simple picture of some non-equilibrium effects as the [[electrical conductivity]] of a piece of metal (as resulting from a gradient of ''μ'') or its [[thermal conductivity]] (as resulting from a gradient in ''T''). The quasi-''μ'' and quasi-''T'' can vary (or not exist at all) in any non-equilibrium situation, such as:
*If the system contains a chemical imbalance (as in a [[Battery (electricity)|battery]]).
*If the system is exposed to changing electromagnetic fields (as in [[capacitor]]s, [[inductor]]s, and [[transformer]]s).
*Under illumination from a light-source with a different temperature, such as the sun (as in [[solar cell]]s),
*When the temperature is not constant within the device (as in [[thermocouple]]s),
*When the device has been altered, but has not had enough time to re-equilibrate (as in [[piezoelectricity|piezoelectric]] or [[pyroelectricity|pyroelectric]] substances).

In some situations, such as immediately after a material experiences a high-energy laser pulse, the electron distribution cannot be described by any thermal distribution.
One cannot define the quasi-Fermi level or quasi-temperature in this case; the electrons are simply said to be ''non-thermalized''. In less dramatic situations, such as in a solar cell under constant illumination, a quasi-equilibrium description may be possible but requiring the assignment of distinct values of ''μ'' and ''T'' to different bands (conduction band vs. valence band). Even then, the values of ''μ'' and ''T'' may jump discontinuously across a material interface (e.g., [[p–n junction]]) when a current is being driven, and be ill-defined at the interface itself.