Fermi Energy and Fermi Level

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May 16, 2023

Why in news?

More research in quantum physics in recent times have shown that the fermi energy are significant and produce high energy.

What is fermi energy?

  • Fermi energy is defined as the highest occupied energy level of a material at absolute zero temperature (-273º C or 0K).
  • In other words, all electrons in a body occupy energy states at or below that body's Fermi energy at 0K.
  • It is an energy difference of the kinetic energy of a system containing fermions.
  • Fermi energy is constant for each solid.

What are fermions?

  • Fermion is any member of a group of subatomic particles having odd half-integral angular momentum (spin 1/2, 3/2).
  • Fermions mainly include quarks and leptons along with electrons, protons, and neutrons.
  • Fermions obey Fermi-Dirac statistics, which means that when one swaps two fermions, the wave function of the system changes sign.
  • Fermions obey the Pauli exclusion principle - no two fermions can exist in the same quantum state at the same time.


What is fermi level?

  • Fermi level is the measure of the energy of the least tightly held electrons within a solid.
  • It is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface.
  • The fermi energy levels enable us to
    • Calculate the density of electrons
    • Number of holes in the material
    • Relative proportion of holes and density with respect to temperature


What are the applications of fermi energy?

  • Fermi energy is
    • Applied to Determine the electrical and thermal characteristics of solids
    • Important in nuclear physics to understand the stability of white dwarfs
    • Used in semiconductors and insulators
    • Used to describe insulators, metals, and semiconductors



  1. The Hindu│Electrons And Fermi Energy
  2. Britannica│About Fermi Energy And Fermi Level
  3. Hyperphysics | Fermi levels
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