# What's a fermi level?

1. Oct 28, 2004

### Mk

Hey, guys, what's a fermi level?

2. Oct 28, 2004

### Galileo

It's the lowest energy level for a system of fermions.

or... that would be the fermi energy...

3. Oct 28, 2004

### Mk

Maybe the level away from fermi-energy? If zero-point energy is the lowest energy, why do fermions have a higher fermi energy?

4. Oct 28, 2004

### OldTee

Think it's the energy level where the probability of finding a fermion for a system of fermions is 50%...

5. Oct 28, 2004

### da_willem

The Fermi level is the temperature dependent 'chemical potential' of a fermionic substance. It is also the energy at wich an obital is exactly half filled. This can be seen from the Fermi-Dirac distribution:

$$f(\epsilon)=\frac{1}{e^{(\epsilon-\mu(\tau))/\tau}-1}$$

Where $\tau$ is the fundamental temperature $k_BT$, $\epsilon$ the energy of the orbital and $\mu$ the chemical potential or fermi level. This gives the probabality of finding a particle in an orbital with energy epsilon, it is also the expectation value of fermions in that orbital because there can be only 1 or 0 fermions in an orbital because of the Pauli exclusion principle. If you fill in $\epsilon=\mu$ this yields 1/2.

So for energies below the fermi level orbitals are more than half filled and above they are less than half filled. The Fermi energy is the fermi level at absolute zero temperature.

$$\epsilon_{F}=\mu(0)$$

6. Oct 28, 2004

### ZapperZ

Staff Emeritus
Er.... I think what you are describing is more appropriate for a semiconductor system.

A "fermi level" is the highest energy of the valence electronic band at T=0 K.

For a conductor, the fermi level is the highest energy of the conduction electron in the conduction band. For an intrinsic semiconductor, at T=0 K, it is technically the top of the filled valence band, since the conduction band is completely empty. However, there are many books and people who mix and match the chemical potential that is in the middle of the band gap with the Fermi level. This is where it can create confusion as to what a "fermi level" actually means.

http://edu.ioffe.ru/register/?doc=galperin/l4pdf2.tex [Broken]

Zz.

Last edited by a moderator: May 1, 2017
7. Oct 29, 2004

### da_willem

Im now studying for my thermal physics test on monday and what I wrote in my previous post can be found in "Thermal physics" by Kittel and Kroemer. They say the definition I gave of the Fermi level is "often used in the field of solid state physics". So I guess wou're right when you say the meaning of the Fermi-level depends on the field and the book you're reading...

Last edited by a moderator: May 1, 2017
8. Oct 29, 2004

### ZapperZ

Staff Emeritus
And in case you don't know, Kittel also wrote a solid state physics text. :)

Zz.