Home / Topics / Kinetic Theory & Statistical Physics
Fermi–Dirac statistics
Advanced
Distribution for fermions obeying Pauli exclusion.
f(E) = 1/(e^{(E−μ)/kT}+1)Identical fermions (electrons, protons) can't share a quantum state, so the occupation is f(E) = 1/(e^{(E−μ)/kT} + 1). At T = 0 states fill up to the Fermi energy.
Electrons in metals.
Never greater than one per state.
In more detail
Fermi-Dirac statistics describe particles with half-integer spin, such as electrons, which obey the Pauli exclusion principle. Each state holds at most one particle.
Real-world uses
- Electron behaviour in metals and semiconductors follows Fermi-Dirac statistics.
- Transistors and solar cells rely on the Fermi-Dirac distribution.
- Electrons in a metal follow Fermi–Dirac statistics, which explains their heat capacity and electrical conduction.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is the Pauli exclusion principle?
No two identical fermions can occupy the same quantum state.
Why do metals conduct?
Electrons near the Fermi level are free to move into empty states.
What are fermions?
Particles with half-integer spin, such as electrons and protons, which obey the Pauli exclusion principle.
Related topics in Kinetic Theory & Statistical Physics
Boltzmann distribution · Partition function · Canonical ensemble · Bose–Einstein statistics · Bose–Einstein condensate · Fermi energy