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. M

    To calculate Fermi energy from arbitrary dispersion relation

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  2. G

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  3. bayan

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  4. C

    Suppose there is a semiconductor with Fermi energy

    Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form \bar n(T)={N\over \exp\beta(\mu-E_f)+1} where \mu is the chemical potential. ____ I can see that the Fermi...
  5. G

    Fermi energy of nucleus

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  6. N

    Density of States at the Fermi Energy

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  7. E

    A couple questions about energy bands and Fermi energy

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  8. S

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  9. S

    How to Calculate Fermi Energy for a 1D Lattice with 2 Electrons per K-State

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  10. P

    Fermi Energy and Fermi Level in Semiconductors

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  11. R

    Calculating Fermi Energy for Gold Atoms

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  12. B

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  13. fluidistic

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  14. G

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  15. A

    What is the Fermi energy of Liquid He3 at absolute zero?

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  16. H

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  17. L

    Question: # of particles within an energy range below Fermi Energy.

    Homework Statement Here's what the question says. "Consider a cube of gold 1 mm on an edge. calculate the approximate number of conduction electrons in this cube whose energies lie in the range from 4.000 to 4.025 at 300k. Assume Ef(300K) = Ef(0)." Homework Equations Well, I know...
  18. itaischles

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  19. M

    Fermi Energy level with respect to band gap energy

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  20. T

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  21. R

    Fermi energy (density of electron)

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  22. M

    Quick Fermi Energy QuestionFree electrons?

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  23. B

    Fermi Energy of Non-Interacting Identical Li Atoms in a 3D Harmonic Potential Well

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  24. M

    Find Fermi Level Pos. of Si w/ 6x1015 Donors & 2x1015 Acceptors @ 300K

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  25. H

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  26. P

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  27. A

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  28. S

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  29. I

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  30. B

    What is the relationship between Fermi Energy and Electron Density of States?

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  31. D

    Fraction of electrons within kT of fermi energy?

    I was reading this website, and I don't understand this last statement. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html It reads: "Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat...
  32. K

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  33. C

    Effect of Doping on Fermi Energy

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  34. C

    Effect of Compression on Fermi Energy.

    I know that when a metal is compressed its fermi energy is increased. I would attempt to explain this by saying, "as the volume has been decreased, so has the allowed number of particle in a 3D box states, thus as we have the same number of electrons and fewer allowed states, and the pauli...
  35. S

    How Does the Fermi Energy of Bare Protons Influence Chemical Reactions?

    As I know chemical potential of two reacting substances strongly depends on difference in Fermi energy between them. Fermi energy is inversely proportional to the mass of particles. Does that mean that Fermi energy of bare proton will be 2000 time smaller than that of electron? Usually...
  36. B

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  37. C

    Chemical Potential & Fermi Energy

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  38. J

    What is the Fermi energy of metallic potassium at 0K?

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  39. V

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  40. V

    Calculating Fermi Energy for Neutrons Confined to a Nucleus

    I am wondering about something: Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m. the formula of the fermi Energy is EF= ((h-bar)^2*(3*pi^2*n)^(2/3))/2m m:mass of electron, n = number...
  41. H

    Fermi Energy in 2D: Find Relation w/ 3D E=h(cut square)k(square)/2m

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  42. C

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  43. C

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  44. C

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  45. S

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  46. P

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  47. T

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  48. S

    Solving the Fermi Energy of Copper: Momentum, Wavelength, Velocity

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  49. N

    Doping of semiconductors and fermi energy.

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  50. V

    Please share with me about your thinking on Fermi Energy

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