Fermi level is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface.

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

Fermi level is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface.

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

I define to be quite simple: Energy of latest occupied level which the states below this energy are completely occupied and above it are completely unoccupied.

Janderson has given a good definition. Another text book definition is " the energy level (if it exists) which has a 50% probability of getting occupied by an electron at any temperature.(Nicholean & Brews, Page 31). I seek a comment from other experts for this definition which I have seen somewhere else. "Fermi level is the AVERAGE ENERGY of a crystal at any temperature".

Current definition by IUPAC:

Fermi level, E_F_ - The chemical potential of electrons in a solid (metals, semiconductors or insulators) or in an electrolyte solution.

http://goldbook.iupac.org/F02341.html

This makes definitions given by Janderson and Rajeev to be consequences of the distribution law for electrons. When I was a student, we learned these two as the definition and an approximation for the distribution...

The definition of Janderson is used for the case of metalic materials,

The definition of Rajeev ( 50% probability of occupancy ) is used for semiconductor materials.

Prof Ravi,

What you said is true, but this does not represent the definition of the Fermi energy. This is the result from the definition of the Fermi energy, when you integrate the product of the density of state g(E) and the Fermi Dirac distribution f(E)=1/(1+exp(E-Ef)/kT) over energy starting from Ec to top of conduction band (or infinity) to find the concentration of electrons; similar expression is used for holes in the valence band. f(E) represents the probability of a state of energy E to be occupied, at E = Ef: f(Ef) = 1/2 (50% occupancy). The result will give n(Ef-Ec) and p(Ef-Ev) where Ec and Ev are the bottom of conduction band and top of Valence band, respectively. Then the intrinsic fermi energy Ei and the intrinsic concentration ni are defined and the concentrations are formulated using these new variables.

Thanks a lot for your answering. Thanks all

From a surface chemistry point of view it is the chemical potential of electrons.

One of the simple definitions says that the fermi level is simply that level after which occupancy is zero at zero temperature. However, for other temperatures we can say that at the fermi level the occupancy is 0.5 ...

If we go deep in the definition of Fermi level by Rajeev,( the 50% probability of occupying of electrons ) i think its also working in the matal's case how? we can visualize the top occupied state in the metal as spaced by an infinitesimal energy space with the above unfilled state in order that practically the space between is zero.. can it be a unification of the two definitions?!

regards

Fermi level is the total chemical potential for electrons which is a thermodynamic quantity (work) required to add one electron to the body. Fermi level can also be considered to be a hypothetical energy level of an electron.

The Fermi Level is defined as the highest occupied molecular orbital in the valence band at 0 K.

The Fermi level is a term derived from statistical mechanics and used to calculate the number of mobile carriers present in a solid.

In an atom there are discrete energy levels and electrons occupy the levels according to the least energy of the levels and no two electrons have the same quantum number i.e. electrons have different states in a particular energy level i.e. they have a unique quantum number, also the Fermi level is the highest energy occupied by electrons in a particular state at 0 K. Now when many atoms come together the discrete energy levels form a band of energies such as the valence band. Now, in semiconductors we have the valence band, the conduction band and the forbidden band in the band diagram, so for an intrinsic semiconductor the Fermi level lies in the forbidden gap.

 The probability of any fermion(1/2 spin) occupying any particular level at absolute temperature. This position will change  the material  to material.

The energy at which the probability of a state is occupied by an electron is 0.5.

Ashcroft

i am also not getting what exactly the fermi level are?,  how it effect the excitation of electron during light irradiation.any one pleae suggest 

 The Fermi level is defined as the energy of the highest energy electrons at zero temperature when the system is in its ground state.

http://physics.stackexchange.com/questions/30922/whats-the-difference-between-fermi-energy-and-fermi-level

the average level to which the molecular orbitals are filled with eelectrones

See this link a discussion on Fermi energy and Fermi level and the difference, chemical potential etc.

https://www.researchgate.net/post/Are_Fermi_level_and_Band_gap_same#5766ac89b0366df3944efe4a

Dear research investigators the simplest definition for the question is:

Energy corresponding to highest occupied energy state at zero Kelvin is called Fermi energy and that sate is called Fermi level.

Instead of definition how do we understand it in realistic world in the sense of device physics. For example in photovoltaics we take the Fermi level as the reference  to deal with device physics, the fermi leve which we talk about here is not the one at zero kelvin in fact its at room temperature one. So, to have an understanding of the device physics one should understand fermi level clearly at the temperature where we are using the devices in the service conditions. 

https://www.researchgate.net/post/Are_Fermi_level_and_Band_gap_same#5766ac89b0366df3944efe4a

the discussion presented in the above link addresses the issue some extent. I have put some other queries there which are yet to be addressed. Thank you all for the participation.

Sateesh Prathapani

(PhD)

The Fermi level is the total chemical potential for electrons (orelectrochemical potential for electrons) and is usually denoted by µ or EF.[1] The Fermi level of a body is athermodynamic quantity, and its significance is the thermodynamic workrequired to add one electron to the body (not counting the work required to remove the electron from wherever it came from). A precise understanding of the Fermi level—how it relates toelectronic band structure in determining electronic properties, how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics.

In a band structure picture, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. The position of the Fermi level with the relation to the band energy levels is a crucial factor in determining electrical properties. The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with avoltmeter.

The descriptions and definitions are given above are very helpful for somebody who wants to star understand the real meaning of the Fermi-Dirac energy state. For further knowledge, it is necessary to search for textbooks. Something that I did. And for that reason is my answer here. Just a tiny correction trying to help the future readers of this topic (because I searched for my self the above information) ...." Another textbook definition is " the energy level (if it exists) which has a 50% probability of getting occupied by an electron at any temperature.(Nicholean & Brews, Page 31)....." The correct names of the aforementioned textbook are E.H. Nicollian and J.R Brews with title MOS (Metal Oxide Semiconductor) Physics and Technology - Wiley 1982.

Thank you

Ioannis Kortidis

Fermi energy (FE) can be defined as the, highest electron occupied energy level of a material, whilst the material temperature level is at 0 K.

For instance in a metal, FE provides of an estimation of the velocity of the electrons in conduction, as only electrons that possess energy closer to FE can be involved in the conduction process.