Enter the number of electrons per unit volume into the calculator to determine the Fermi Energy. 

Fermi Energy Formula

The following equation is used to calculate the Fermi Energy. 

Ef = (h^2/2me) * (3*pi^2*n)^2/3

Variables:

  • Where Ef is the Fermi Energy (Joules)
  • n is the number of electrons per unit volume 
  • h is Planck’s Constant 6.62606957e-34
  • me is the electron mass 9.10938188e-31

How to Calculate Fermi Energy?

The following two example problems outline the steps and information needed in order to calculate Fermi Energy.

Example Problem #1:

  1. First, determine the number of electrons per unit volume. In this example, the number of electrons per unit volume is measured to be 9.
  2. Finally, calculate the Fermi Energy using the formula above: 

Ef = (h^2/2me) * (3*pi^2*n)^2/3 =

Inserting the values from above and solving the equation with the imputed values gives: 

Ef = (6.62606957e-34^2/(2*9.10938188e-31)) * (3*3.14159^2*9)^2/3 = 5.704e-33 joules

FAQ

What is Fermi Energy?

Fermi Energy is a concept in quantum mechanics that describes the highest energy level that electrons occupy at absolute zero temperature. It’s a crucial property in understanding the behavior of electrons in solids, particularly metals and semiconductors.

Why is the Fermi Energy important in physics and engineering?

The Fermi Energy level plays a vital role in determining the electrical, thermal, and optical properties of materials. It helps in understanding how materials conduct electricity, their electron distribution, and overall behavior under various conditions, making it essential for designing electronic devices.

How does temperature affect Fermi Energy?

While the Fermi Energy is defined at absolute zero temperature, temperature increases can excite electrons to higher energy levels. However, the Fermi Energy itself remains relatively constant with temperature changes. The distribution of electrons around the Fermi level, described by the Fermi-Dirac distribution, changes with temperature, affecting the material’s conductivity and other properties.