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Fermi energy is often defined as the highest occupied energy level of a material at absolute zero temperature. In other words, all electrons in a body occupy energy states at or below that body's Fermi energy at 0K. 

The fermi energy is the difference in energy, mostly kinetic. In metals this means that it gives us the velecity of the electrons during conduction. So during the conduction process, only electrons that have an energy that is close to that of the fermi energy can be involved in the process.

This concept of Fermi energy is useful for describing and comparing the behaviour of different semiconductors. For example: an n-type semiconductor will have a Fermi energy close to the conduction band, whereas a p-type semiconductor will have a Fermi energy close to the valence band.

Fermi energies of different material types. Source: http://commons.wikimedia.org/wiki/File:Band_filling_diagram.svg

As a material's temperature rises above absolute zero, the probability of electrons existing in an energy state greater than the Fermi energy increases, and there is no longer any constant highest occupied level, so while the material's Fermi energy may be useful as a reference, it is not very useful at real temperatures.

Instead, we can approximate the average energy level at which an electron is present is with the Fermi-Dirac distribution: 

where E is the energy level, k is the Boltzmann constant, T is the (absolute) temperature, and E_F is the Fermi level. The Fermi level is defined as the chemical potential of electrons, as well as the (hypothetical) energy level where the probability of an electron being present is 50%.

You can calculate the fermi energy state using:

N - number of possible quantum states
V - volume
m - mass of electron
h - planc's constant

Sources:

http://en.wikipedia.org/wiki/Fermi_level

http://en.wikipedia.org/wiki/Fermi_energy

http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html

http://www.eng.umd.edu/~dilli/courses/enee313_spr09/files/supplement1_carrierconc.pdf

http://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics

http://web.ift.uib.no/AMOS/PHYS208/larsP-N/p-n-slide-lars.pdf

http://courses.washington.edu/overney/FermiEnergy.pdf

http://faculty.kfupm.edu.sa/COE/elrabaa/rich%20text/coe360/Week2/Lec4%20SEP16.pdf

 

 

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