Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 16, 2023

Fermi Level Calculator allows you to quickly check fermi parameters such as fermi energy, fermi wave number, fermi temperature, and fermi velocity. It simply takes the number density of electrons and quickly and accurately calculates the output.

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Number density of electrons

What is Fermi Level Energy?

The Fermi level is the maximum energy level that an electron may achieve at absolute zero temperature. Because electrons remain in the lowest energy state at absolute zero temperature, the Fermi level is the state between the conduction and valence bands.

How is Fermi Energy Calculated?

The Equations of Fermi level that can be used to estimate:

Fermi energy: Ef = h2*kf2/(2*m)

  • Calculate the Planck's constant square and the fermi wave number.
  • To check the fermi energy, multiply the squares by twice the electron mass.

Fermi Temperature: Tf = Ef / k

  • The fermi temperature is computed by dividing the fermi energy by the Boltzmann constant.
  • Here, Ef is the Fermi energy
  • Tf is the Fermi Temperature
  • k is the Boltzmann constant k = 1.38064852*10-23m2* kg/(s2 * K).
  • E be the energy of a particle

Fermi Velocity: vf = ħ * kf / m

  • The Planck's constant is multiplied by the fermi wavenumber.
  • To check the fermi velocity, divide the value by the electron's mass.
  • Here, m be the electron mass. The value of m = 9.10938356*10-31kg

Fermi Wave Vector: kf = (3π2n)(1/3)

  • Fermi Wave vector is also known as Fermi wavenumber
  • Calculate the electron number density.
  • Multiply the density of numbers by 3π2
  • To check the fermi wave vector, find the 1/3 power of the product.
  • Here, n denoted as the number density

Fermi-Dirac Distribution

The Fermi-Dirac distribution (also known as Fermi-Dirac statistics) is the likelihood of an electron being in a certain energy state (energy level). It refers to identical, indistinguishable half-integer spin particles (fermions), particularly electrons.

The Fermi function is defined as follows in our Fermi level calculator: f(E) = 1 / (e[(E-Ef)/ (k * T)] + 1)

  • Where, f(E) denotes the probability that a particle will have energy E,
  • E is the energy of a particle
  • e be the mathematical constant, i.e., e ≈ 2.71828
  • Ef is the Fermi energy
  • T is the temperature

For more concepts check out to get quick answers by using this free tool.

Free Electron Number Densities Table

We employ this fact in electronics because most metals are good electrical conductors. The so-called free electron model can accurately describe the behaviour of their electrons.

Metal Number density (*1028 electrons/m3)
Cu (copper) 8.47
Ag (silver)td> 5.86
Au (gold) 5.90
Be (beryllium) 24.7
Mg (magnesium) 8.61
Ca (calcium) 4.61
Sr (strontium) 3.55
Ba (barium) 3.15
Nb (niobium) 5.56
Fe (iron) 17.0
Zn (zinc) 13.2
Cd (cadmium) 9.27
Al (aluminium) 18.1
Ga (gallium) 15.4
In (indium) 11.5
Sn (tin) 14.8
Pb (lead) 13.2

FAQs on Fermi Level Calculator

1. What is the Fermi Energy Level, and what does it mean?

We must first understand Pauli's exclusion principle in order to comprehend what is a fermi energy level and its existence. The existence of this energy is explained by the fact that two fermions cannot have the same quantum state.

2. What are some of the uses of Fermi Energy?

There are spme of the Fermi energy applications. They are:

  • It's employed in semiconductors and insulators.
  • Metals, insulators, and semiconductors are all described using its theory.
  • The Fermi energy is used to describe and determine a solid's thermal and electrical properties.


3. How is the Fermi Level determined?

With the following Fermi level equations, you may rapidly compute Fermi parameters using our Fermi level calculator:

  1. Fermi wavenumber(Fermi wave vector):kf = kf = (3π2n)(1/3)
  2. Fermi energy:Ef =h2*kf2/(2*m)
  3. Fermi Temperature:Tf = Ef / k
  4. Fermi velocity:vf = ħ * kf / m