Physics Help Forum Why does the Fermi level of an insulator fall within the band gap?

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May 14th 2013, 11:07 PM   #1
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Why does the Fermi level of an insulator fall within the band gap?

"Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. Why does the Fermi level of an insulator fall within the band gap? There is no energy level in the band gap. See also here
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Last edited by ghk; May 14th 2013 at 11:09 PM.

May 15th 2013, 11:44 AM   #2
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 Originally Posted by ghk "Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. Why does the Fermi level of an insulator fall within the band gap? There is no energy level in the band gap. See also here
At non-zero temperatures, there are generally thermal excitations that allow electrons to move between levels easily, thus conducting heat and electricity. However, if the Fermi level is in a band gap, then there are no available levels and hence there are no conduction electrons, and the material is an insulator.
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May 15th 2013, 09:23 PM   #3
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 Originally Posted by DrPhil At non-zero temperatures, there are generally thermal excitations that allow electrons to move between levels easily, thus conducting heat and electricity. However, if the Fermi level is in a band gap, then there are no available levels and hence there are no conduction electrons, and the material is an insulator.
Do you mean that Fermi level is not an energy level of electron? No energy level is in the gap.

May 16th 2013, 10:31 AM   #4
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 Originally Posted by ghk Do you mean that Fermi level is not an energy level of electron? No energy level is in the gap.
Yes, that is what I am saying. The Fermi level is a statistical mechanics concept. It is where the upper electrons would be if the electron energies were a continuum instead of discrete levels. Thus we can say the Fermi level is in the gap, where there are no quantum levels.
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May 16th 2013, 11:01 AM   #5
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 Originally Posted by DrPhil Yes, that is what I am saying. The Fermi level is a statistical mechanics concept. It is where the upper electrons would be if the electron energies were a continuum instead of discrete levels. Thus we can say the Fermi level is in the gap, where there are no quantum levels.
How to define the exact position of the Fermi level in the gap?

May 16th 2013, 12:06 PM   #6
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 Originally Posted by ghk How to define the exact position of the Fermi level in the gap?
"In a band structure picture, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it even require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in µ can be measured simply with a voltmeter."
http://en.wikipedia.org/wiki/Fermi_level

That is a rather extensive article, with more than you probably want to know! Scanning the article, I think I haven't lied to you too much.
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 Apr 2nd 2014, 06:45 AM #7 Junior Member   Join Date: Apr 2014 Posts: 2 because there is no free electrons in the surface of insulator and even at t#0 its stay down Ev...

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