Difference Between Fermi Energy and Fermi Level

Key Difference – Fermi Energy vs Fermi Level
 

Fermi energy and Fermi level are two distinct terms that are often used interchangeably. The Fermi energy is an energy difference of the kinetic energy of a system containing fermions whereas Fermi level is a collection of kinetic and potential energies of a system containing fermions. The key difference between Fermi energy and Fermi level is that Fermi energy is defined only for absolute zero temperature whereas Fermi level is defined for any temperature.

CONTENTS

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 energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. The single-particle state of a quantum system refers to the state of a single particle being isolated. Fermions are particles that follow Fermi-Dirac statistics. Fermions mainly include quarks and leptons along with electrons, protons, and neutrons. Absolute zero temperature is the lower limit of a thermodynamic temperature scale.

A Fermi gas is a group of fermion particles having no interactions between those fermions. Hence, it is a phase of matter. The lowest occupied state of a Fermi gas is known to have a zero kinetic energy. But the lowest occupied state of a metal is the bottom of its conduction band (the bands closest to the Fermi levels, thus determine the electrical conductivity of the metal).

The fermions obey the Pauli Exclusion Principle (A principle that states two identical fermions cannot occupy the same quantum state). Therefore, the Fermi gases can be analyzed in its single-particle state. There are different single-particle states having different energies. The ground state of the whole system can be found by adding one particle into the system at a time. These added fermions will then occupy the lowest unoccupied states of that system. The Fermi energy can be determined when all the unoccupied states have been occupied by fermions. This means, even if all the energy is extracted from a Fermi gas, the fermions will still be in movement at high speeds.

What is Fermi Level?

Fermi level is a term used to describe the collection of electron energy levels at absolute zero temperature. It is a concept of Fermi-Dirac statistics. The Fermi level is denoted by µ or E_F. It is a thermodynamic quantity of a physical body.

The Fermi level is defined for any temperature. The Fermi level refers to the total of kinetic energy and potential energy of a thermodynamic system containing fermions. Therefore, the Fermi level can also be named as the electrochemical potential of a Fermion. The Fermi level can be defined even for fermions that are in complex interacting systems when the thermodynamic equilibrium state of that system is considered.

What is the Difference Between Fermi Energy and Fermi Level?

Summary – Fermi Energy vs Fermi Level

Fermi energy and Fermi level are confusing terms since they closely related, but are different from each other. The difference between Fermi energy and Fermi level is that Fermi energy is defined only for absolute zero temperature whereas Fermi level is defined for any temperature.

Reference:

1.“Fermi energy.” Wikipedia, Wikimedia Foundation, 14 Mar. 2018. Available here 
2.“Fermi level.” Wikipedia, Wikimedia Foundation, 3 Mar. 2018. Available here
3.“Fermi Level.” Fermi level and Fermi function. Available here 

Image Courtesy:

1.’Band gap comparison’By inductiveload  (CC BY-SA 2.5) via Commons Wikimedia