Fermi Level Calculation

Fermi Energy

Fermi energy is the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at a temperature of absolute zero. For a Fermi gas at absolute zero, we may define Fermi energy as the highest energy level of the Fermion. However, for ametal, it is the difference between the highest energy level of an electron and the energy at the bottom of the conduction band. This is because the lowest occupied state in a Fermi gas has zero kinetic energy. However, the bottom of the conduction band is the lowest occupied state in metals. We must note here that Fermi energy is defined for non-interacting systems only. The systems that have a well-defined, static potential are called non-interacting systems.

Fermi Level Explained

According to the Pauli exclusion principle, two fermions cannot occupy the same energy state. Therefore, even at absolute zero, the electrons (which are fermions) will constitute a sea of electron energy states. The state with the highest energy or the top of this sea is the Fermi level.

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Steps to Calculate Fermi Energy:

These are the steps required to calculate Fermi energy:

1.Get the value for the rest mass of the Fermion.

2.Get the number density N/V or N and V separately for the system under consideration.

3.Get the value of the constants involved. The reduced Planck's constant in this case.

4.Evluation.

Fermi Energy Values For Different Elements

 Fermi energy of Copper 7.0 ev Fermi energy of Magnesium 7.08 ev Fermi energy of Aluminum 11.8 ev Fermi energy of Silver 5.5 ev Fermi Energy of Gold 5.53 ev Fermi Energy of Potassium 1.9 ev Fermi energy of Sodium 3.2 ev

Systems Available

CD ComputaBio can calculate systems including but not limited to: crystalline, amorphous, 2D materials, surfaces, interfaces, solids, etc.

Algorithms and Software

USPEX, Materials Studio, VASP, Gaussian.

Application of Fermi Energy

Fermi energy is an essential concept that arises out of Fermi-Dirac statistics. It is used to study various phenomena indifferent areas of physics. Some applications of Fermi energy are listed below:

• The Fermi energy proves helpful while studying the conduction properties of different materials. This is usually done by using the electron number density we used in the earlier example.
• ln astrophysics, it is also used to study the stability of cosmic bodies like white dwarf stars, whose Fermi energy is close to 0.3 MeV.
• In nuclear physics, the Fermi energy is significant to studying a nucleus's stability and other properties, as the nucleons form a non-interacting system of fermions.
• Fermi energy is also used in quantum mechanics to study various systems of fermions.

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