As I understand them fermi energy is the fermi level at 0 k. That is to say fermi energy is the potential energy while fermi level is potential and kinetic energy.

As I know in simple words, Fermi level is the energy level below which all levels are occupied and above which there are unoccupied levels. The corresponding energy of Fermi level is know as Fermi energy.

The Fermi level is the occupied state of highest energy. It plays a preeminent role in the determination of conduction properties in metals.

Fermi energy is the maximum energy of an electron in the ground state of the system. At absolute zero, all individual states of energy less than Fermi energy are occupied, while those with energy greater than Fermi energy are empty.

For a free electron gas, the Fermi level at absolute zero coincides with the Fermi energy.

The explanation by M. Nassik is most accurate; what D. Szczesniak described as Fermi energy is in fact the band gap.

The highest energy level in the conduction band filled up with electrons at absolute zero is called FERMI LEVEL ad the energy corresponding to the Fermi level is called FERMI ENERGY.

Many electrons after gaining a slight amount of energy from any source get excited to the empty energy levels lying immediately above the Fermi level and become free to conduct electricity .The energy possessed by these electrons when they are at the energy level just above the Fermi level is termed as Fermi energy.

Fermi Level-Highest energy level occupied by the electrons at 0K temperature.

Fermi Energy-Total energy required by an electron to overcome the band gap.

Dear @b.Ravindran:

I don't know whether others will agree with me or not..

But I believe the definitions you gave me are the general missunderstanding or at least misnomers involving the distinction between the concepts of Fermi Energy and Fermi Level,

The Fermi Energy is a quantum mechanical concept which describes quantum systems only, thus, is only applied to systems such atoms, atomic nuclei, molecules, etc.

Its definition is the following: "is defined as the difference between the highest and the lowest occupied Energy State in a quantum system, at 0 K".

So, it's an Energy difference, and not an absolute magnitude, and it's an ideal concept, not a real Energy. normally it represents a Kinetic Energy.

On the other hand, the concept of Fermi Level is a very real Energy (not an Energy Difference), it is defined for any temperature, this is the reason we find it in real crystals and real solid systems at temperatures above 0 K.

It is defined (as you stated) as: "The Energy of the highest occupied Energy level in a system" (normally Energy States occupied by electrons),

Kind regards sir! Thank you !

Dear Franklin Uriel Parás Hernández In the quasiclassical theory of normal metals the definitions are as follows:

1. The Fermi level in a metal is a surface determined by the condition E(p) = chemical potential-mu which in momentum space gives the Fermi surface.

2. The Fermi energy in a metal is a number (for silver-Ag the Fermi energy value is 5.52 eV, Ashcroft and Mermin, pg. 38) and it is the energy difference between the Fermi level and lowest unoccupied single-particle state, at zero-temperature. Regards.

Dear P. Contreras :

Can you tell me what is E(p) in your equation, I could n't get to know what does the "(p)" stands for. Also, what does mu represent in this equation ?

On the other hand, I don't really agree that the Fermi Level represents a surface. I don't know whether the surface you mean is the "Fermi Surface" ? If so, this surface is formed by all the Fermi Velocity's vectors of the system, represented in a phase space. Surely each of these velocities has an associated kinetic energy, which in fact corresponds to the Fermi Energy.

Regards !

Yes Dear Franklin Uriel Parás Hernández I explain:

1. I am using the notation for the quasiclassical approach as used in quantum solid state theory for normal metals in the 80´s and before.

2. E(p) is the dispersion law in p-momentum space for the quasi-free electron model of a normal metal, something which nowdays we use slightly differently (now is common the tight binding aproximation E(k)).

3. mu is the greek letter that stands for the chemical potencial. In normal metals it is used P_0 = P_F and mu = P_F^2/ 2 m_eff.

4. E(p) = mu is the definition of a Fermi level and a Fermi surface in normal metals.

5, Yes, we could say so, that the this surface is formed by all the Fermi Velocity's vectors of the system, represented but in a momentum space. (phase space is used in stat. mechanics)

6. you can find my explanation in the book by Academician A. Abrikosov:

Fundamentals of the Theory of Metals A. A. Abrikosov. Dover Publications, 2017 chapter II the electron Fermi liquid: pag 19 - 28 Regards. I attached a capture from another book in Russian, where there are nice examples with contours of different mu values. Lifshitz, I.M., M.Ya Asbeland M.I. Kaganov, 1973, Electron Theory of Metals .

https://books.google.co.ve/books/about/Fundamentals_of_the_Theory_of_Metals.html?id=tTo2DwAAQBAJ&redir_esc=y