# Fermi level

by sandakelum
Tags: fermi
 P: 2 In a semiconductor @ 0k highest energy state lie on fermilevel(all electrons @ valence band). but @ room temperature highest energy state of covelence band lie below the fermilevel. how can i understand this? pls help me.
 Mentor P: 9,625 The fermi level can increase with temperature. More energy -> the energy level where half of the states are (or would be) occupied is higher. Where is the problem?
P: 1,632
 Quote by sandakelum In a semiconductor @ 0k highest energy state lie on fermilevel(all electrons @ valence band). but @ room temperature highest energy state of covelence band lie below the fermilevel. how can i understand this? pls help me.
What is your definition of Fermi level for semiconductors?
Note that according to the common use, the "Fermi level" in semiconductors is in the band gap. This is because what is called Fermi level in semiconductors is actually the chemical potential.
Even if you stick with the definition used for metals, Fermi level is the maximum energy level occupied at zero K. So it does not change with temperature, by definition.
The chemical potential is what changes with temperature.

Mentor
P: 9,625

## Fermi level

 The central task of basic semiconductor physics is to establish formulas for the position of the Fermi level EF relative to the energy levels EC and E [...] and causes the Fermi level EF to shift
Found here

Looks like the regular Fermi level.

Do you mean the Fermi energy? That is at T=0.
 P: 2 If fermi level is changing with temperature its ok. my quaestion was when temperature up energies of covalence band also up. so if highest energy electrons @ covalance band occupy near to fermilevel @ 0 K (fermi level is the upper ,argin of the fermi sea) when temperature up higest covelence electrone energy must exceeds fermi energy.(some of them may have enough to go to conduction band).
 PF Patron P: 220 IF I understand correctly you believe that: The fact that some of the valence band electrons managed to reach the conduction band edge at non-zero Temperature and hence exceeding the Fermi Level , means that the valence band edge now has to be considered shifted up as well exceeding the Fermi level. This is not the case. The energy of the "free" electrons do not define where the edge of the valence band resides on the energy scale. Having said that, I have a couple of comments on the ongoing discussion. 1) Heating the material generally leads to reducing the band gap , thus the valence band edge may indeed go up a bit (but not exceeding the Fermi Level). 2) Heating the material does not necessarily implies elevating the chemical potential of electrons (Fermi level). It may be the case that self doping effects can lead to lowering the Fermi level by heating up the system.
P: 25
 Quote by nasu What is your definition of Fermi level for semiconductors? Note that according to the common use, the "Fermi level" in semiconductors is in the band gap. This is because what is called Fermi level in semiconductors is actually the chemical potential. Even if you stick with the definition used for metals, Fermi level is the maximum energy level occupied at zero K. So it does not change with temperature, by definition. The chemical potential is what changes with temperature.
As I read it somewhere, Fermi level is a (the sole) parameter of Fermi-Dirac distribution function, which should apply to electron gas only(?), and FL does change with temperature. (And as I remember it, at FL the occupancy rate of state is 0.5.)

For an electron system that cannot be treated as gas, the measured chemical potential could not be viewed as Fermi level, and thus Fermi-Dirac distribution function could not apply.

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