Support Options

Submit a Support Ticket

Home Animations Fermi-Dirac statistics with temperature About

Fermi-Dirac statistics with temperature

By Saumitra Raj Mehrotra1, Gerhard Klimeck1

1. Purdue University



Published on


Fermi-Dirac statistics is applied to identical particles with half-integer spin (such as electrons) in a system that is in thermal equilibrium. Since particles are assumed to have negligible mutual interactions, this allows a multi-particle system to be described in terms of single-particle energy states. Fermi-Dirac statistics are commonly used in semiconductors to find the distribution of electrons as a function of energy.

Fermi-Dirac statistics with temperature

The image shows Fermi-Dirac distribution, F(E) vs. energy (E), at a Fermi level (in which Ef=0.55 eV) for temperature range of T=50K-375K. At higher temperatures, carriers are more energetic and have higher probability to occupy energy levels above Fermi level. As temperature is reduced, Fermi-Dirac distribution tends towards a step function. At T=0 K no free carriers exist and the electronic system is said to be frozen with all the electrons bounded to atoms.


Image rendered using nanoHUB tool Carrier Statistics Lab (

Cite this work

Researchers should cite this work as follows:

  • Saumitra Raj Mehrotra; Gerhard Klimeck (2010), "Fermi-Dirac statistics with temperature,"

    BibTex | EndNote

Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.