Fermi Level Explained: What is It?

In summary, the Fermi level is the lowest energy level for a system of fermions, also known as the Fermi energy. It is the temperature-dependent chemical potential of a fermionic substance and the energy at which an orbital is exactly half-filled. This can be seen from the Fermi-Dirac distribution and is also the expectation value of fermions in that orbital due to the Pauli exclusion principle. The Fermi energy is the Fermi level at absolute zero temperature. However, the definition of the Fermi level can vary depending on the field and the source, causing confusion. Some sources define it as the highest energy of the valence electronic band at T=0 K, while others consider it to be the top of the
  • #1
Mk
2,043
4
Hey, guys, what's a fermi level?
 
Physics news on Phys.org
  • #2
It's the lowest energy level for a system of fermions.

or... that would be the fermi energy...
 
  • #3
Galileo said:
It's the lowest energy level for a system of fermions.

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

Maybe the level away from fermi-energy? If zero-point energy is the lowest energy, why do fermions have a higher fermi energy?
 
  • #4
Think it's the energy level where the probability of finding a fermion for a system of fermions is 50%...
 
  • #5
The Fermi level is the temperature dependent 'chemical potential' of a fermionic substance. It is also the energy at which an obital is exactly half filled. This can be seen from the Fermi-Dirac distribution:

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

Where [itex]\tau[/itex] is the fundamental temperature [itex]k_BT[/itex], [itex]\epsilon[/itex] the energy of the orbital and [itex]\mu[/itex] 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 [itex]\epsilon=\mu[/itex] 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.

[tex]\epsilon_{F}=\mu(0)[/tex]
 
  • #6
da_willem said:
The Fermi level is the temperature dependent 'chemical potential' of a fermionic substance. It is also the energy at which an obital is exactly half filled. This can be seen from the Fermi-Dirac distribution:

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

Where [itex]\tau[/itex] is the fundamental temperature [itex]k_BT[/itex], [itex]\epsilon[/itex] the energy of the orbital and [itex]\mu[/itex] 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 [itex]\epsilon=\mu[/itex] 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.

[tex]\epsilon_{F}=\mu(0)[/tex]

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:
  • #7
ZapperZ said:
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.

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:
  • #8
da_willem said:
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...

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

Zz.
 

What is Fermi Level?

Fermi level refers to the energy level at which the probability of finding an electron is equal to 0.5 in a given material at a given temperature. It is also known as the chemical potential or the electrochemical potential.

What is the significance of Fermi Level?

The Fermi level plays a crucial role in determining the electrical and thermal properties of a material. It also determines the energy distribution of electrons in a material, which is essential for understanding its electronic properties.

How is Fermi Level affected by temperature?

In a material, as the temperature increases, the Fermi level also increases. This is because with increasing temperature, more electrons are excited to higher energy levels, leading to an increase in the average energy of electrons in the material.

What is the difference between Fermi Level in metals and semiconductors?

In metals, the Fermi level lies within the conduction band, meaning that there are free electrons available for conduction. In semiconductors, the Fermi level lies within the band gap, meaning that there are no free electrons available for conduction unless they are excited to the conduction band.

How is Fermi Level affected by impurities or dopants in a material?

Impurities or dopants can alter the Fermi level in a material by either introducing extra electrons or creating electron holes. This changes the number of available electrons in the material and can shift the Fermi level up or down, depending on the type of dopant.

Similar threads

  • Atomic and Condensed Matter
Replies
3
Views
2K
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
2
Views
1K
Replies
0
Views
328
Replies
1
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
3
Views
2K
  • Atomic and Condensed Matter
Replies
4
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
2
Views
4K
Back
Top