## Fermi-Dirac statistics with temperature

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#### Abstract

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.

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.

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