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Fermi energy
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Highest filled energy at absolute zero.
The energy of the highest filled state at T = 0: E_F = (ħ²/2m)(3π²n)^{2/3}. For copper ≈ 7 eV, so electrons move at 10⁶ m/s even at 0 K.
Only electrons near E_F take part in conduction and heat capacity.
Much larger than kT at room temperature.
In more detail
The Fermi energy is the highest occupied energy level of a fermion system at absolute zero. For electrons in metals it is typically a few electron volts.
Real-world uses
- Understanding conductivity and heat capacity of metals.
- Designing semiconductor devices around the Fermi level.
- Metal electronics designers use the Fermi energy to explain why only electrons near the top of the distribution can conduct.
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Frequently asked questions
What is the Fermi level?
The energy at which the occupation probability is one half at finite temperature.
Why do electrons not all fall to the lowest state?
The exclusion principle forces them to fill successively higher states.
Is the Fermi energy the same in all metals?
No. Each metal has its own Fermi energy, which depends on how many free electrons it has per unit volume.
Related topics in Kinetic Theory & Statistical Physics
Fermi–Dirac statistics · Bose–Einstein statistics · Bose–Einstein condensate · Specific heat of solids · Debye model · Photon gas