Difference Between Fermi Energy and Fermi Level

The key difference between Fermi energy and Fermi level is that Fermi energy is the energy of fermi level, whereas Fermi level is a measure of least tightly bound electrons within a solid.

The terms fermi energy and Fermi level are named after the physicist Enrico Fermi. Fermi energy is the value of energy for a Fermi level at absolute zero temperature (at 0 K) while the Fermi level is the chemical potential of electrons.

1. Overview and Key Difference
2. What is Fermi Energy
3. What is Fermi Level
4. Side by Side Comparison –Fermi Energy vs Fermi Level in Tabular Form
5. Summary

What is Fermi Energy?

Fermi energy is the value of energy for a Fermi level at absolute zero temperature (at 0 K). It is the maximum kinetic energy an electron can have at this temperature. Moreover, the value of Fermi energy is constant for a particular solid. We can define the term Fermi energy as the highest occupied energy level of a material at absolute zero temperature. In other words, all the electrons of a solid tend to occupy energy states at or below the solid’s Fermi energy at 0 K temperature.

In metals, Fermi energy gives the velocity of electrons during conduction. Therefore, during the conduction of metals, only electrons having energy close to the Fermi energy will contribute to the process.

Difference Between Fermi Energy and Fermi Level

Figure 01: Comparing Band Gaps of Metal, Semiconductor and Insulator

Furthermore, the concept of Fermi energy is important in describing the behaviour of semiconductors. For instance, n-type semiconductors have their fermi energy close to the conduction band. In contrast, p-type semiconductors have their fermi energy close to the valence band.

What is Fermi Level?

Fermi level is the chemical potential of electrons. It is an energy level in which the probability of finding an electron is 50%. Itis the highest occupied molecular orbital in the valence band at 0 K. Therefore, there are many vacant states to accept electrons. The Fermi level is located at the bandgap, between the conduction band and valence band.

What is the Difference Between Fermi Energy and Fermi Level?

Fermi energy is the value of energy for a Fermi level at absolute zero temperature (at 0 K) while the Fermi level is the chemical potential of electrons. So, we can say that the key difference between fermi energy and Fermi level is that Fermi energy is the energy of Fermi level whereas Fermi level is a measure of least tightly bound electrons within a solid.

Below infographic provides additional details on the difference between fermi energy and Fermi level.

Summary – Fermi Energy vs Fermi Level

Fermi energy is the value of energy for a Fermi level at absolute zero temperature (at 0 K) while the Fermi level is the chemical potential of electrons. Therefore, the key difference between fermi energy and Fermi level is that Fermi energy is the energy of Fermi level, whereas Fermi level is a measure of least tightly bound electrons within a solid.

Reference:

1. “What Is Fermi Energy? – Physics.” Metropolia Confluence, Available here.

Image Courtesy:

1. “BandGap-Comparison-withfermi-E” – No machine-readable author provided. S-kei assumed (based on copyright claims). – No machine-readable source provided. Own work assumed (based on copyright claims) (CC BY-SA 2.5) via Commons Wikimedia