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In understanding the behavior of semiconductors, I'm coming across a description of the Fermi Energy here and at Wikipedia's page (Fermi Energy, Fermi Level). If I understand correctly, the Fermi Level refers to the energy state at which there's a 50% chance of finding an electron. This varies with temperature. The Fermi Energy is the highest occupied energy state of fermions at absolute zero.

I'm a little confused as to the relation of the two terms. Additionally, in a semiconductor, the Fermi Energy falls between the valence band and the conduction band. However, my understanding is that electrons cannot exist between the two bands -- so why isn't the Fermi Energy the top of the valence band?

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The reason for this apparent contradiction is that you have two "separate" quantum effects.

  1. Fermi-Dirac distribution describes the energies of single particles in a system comprising many identical particles that obey the Pauli exclusion principle. Distribution is calculated for potential-free space and is temperature dependant.

  2. You put electrons into the material, and in the material they feel potential of atomic cores. This potential restrict possible energetic states that are available for electrons, that is it makes bands, where electrons can behave almost freely (according to Fermi-Dirac distribution), but makes energetic states between the bands forbidden.

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I hope this isn't a completely silly question, but with regards to #1, what is a particle's "energy" if there is no potential? That is to say, how can an electron have energy in the absence of the electric potential energy from an atomic core? – Perrako May 15 '12 at 7:25
If your question would be about classical mechanics, this would be trivial, as particles can have also kinetic energy. However, for quantum mechanics this is no longer trivial. If the density of electrons/fermions is too large, particles cannot just have any energy, they are bound by quantum effects. Moreover since by Pauli exclusion principe two fermions cannot be in the exacty the same quantum state (in classical physics it would be possible to have two particles with say the same kinetic energy) you get Fermi-Dirac distribution of energies. – Pygmalion May 15 '12 at 7:55

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