What is Fermi energy: Definition and 104 Discussions

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.
In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.
The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).
There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature.
The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy.
The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi level remains well defined even in complex interacting systems, at thermodynamic equilibrium.Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state,
then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature.

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  1. phos19

    I Fermi energy for a Fermion gas with a multiplicity function ##g_n##

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  2. Dario56

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  3. B

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  4. chikchok

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  5. chikchok

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  6. B

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  7. M

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  8. J

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  9. M

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  10. S

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  11. N

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  12. Pushoam

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  13. DeathbyGreen

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  14. M

    B What is the cause of the mistake in calculating Fermi energy?

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  15. L

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  16. B

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  17. tommowg

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  18. G

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  19. sa1988

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  20. R

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  21. Y

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  22. M

    I Position of Fermi Energy for Semi-Conductors

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  23. Dimani4

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  24. C

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  25. U

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  26. O

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  27. O

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  28. R

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  29. U

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  30. August

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  31. S

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  32. A

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  33. 1

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  34. C

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  35. N

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  36. S

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  37. S

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  38. A

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  39. E

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  40. I

    What is the Fermi energy of (undoped) graphene?

    All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy )...
  41. H

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  42. M

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  43. I

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  44. N

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  45. H

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  46. H

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