Equations · equation

Fermi–Dirac Distribution

Condensed Matter · 1926

Equation: f(E) = 1 / (e^((E−μ)/kT) + 1)
Field: Condensed Matter
Named After: Enrico Fermi · Paul Dirac
Year: 1926

Symbols

f(E) probability an electron state of energy E is occupied · μ chemical potential (the Fermi level) · k Boltzmann constant · T temperature · the +1 encodes the exclusion principle

Significance

Electrons refuse to share states, so they stack up to a filling line — the Fermi level. Everything electronic follows from where that line sits: metals have it mid-band, insulators in a gap, and semiconductors close enough to a band edge to be persuaded — which is the transistor.

Minerals

Pyrite Diamond Galena Cassiterite Cuprite

Timeline

Neutrino Decoupling Quark Epoch

Theories

BCS Theory of Superconductivity Band Theory of Solids Statistical Mechanics

Related

Third Law of Thermodynamics BCS Energy Gap Boltzmann Distribution Chandrasekhar Limit

Constants

Boltzmann constant

Spectral Types

L-type Stars (L Dwarfs)

Required By

Chandrasekhar Limit

Elements

Silicon Copper Germanium

Referenced by

constant

Boltzmann constant

element

Copper Germanium Silicon

equation

BCS Energy Gap Boltzmann Distribution Chandrasekhar Limit Third Law of Thermodynamics

event

Neutrino Decoupling Quark Epoch

theory

BCS Theory of Superconductivity Band Theory of Solids Statistical Mechanics

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From the Equations database in Notion, last edited 2026-08-15. This page is the row, rendered by the build; nothing on it is written by hand.