• vgbraymond
In summary, the fermi energy is an intrinsic value for a metal, and it is in the middle of the energy levels of a semiconductor. Adding impurities does not change the Fermi energy of a semiconductor.
vgbraymond
In metal, fermi energy is the highest energy states that electron occupied at T=0. And so, fermi energy of a particular metal is an intrinsic value, and won't be changed.

Then for a semiconductor,
What is fermi energy, is there any concrete interpretation as of metal?
Why is it just in the middle of energy of VB and CB?
Besides adding impurities, would the fermi energy of a SC changed according to, say, temperature?

vgbraymond said:
In metal, fermi energy is the highest energy states that electron occupied at T=0. And so, fermi energy of a particular metal is an intrinsic value, and won't be changed.

Then for a semiconductor,
What is fermi energy, is there any concrete interpretation as of metal?
Why is it just in the middle of energy of VB and CB?
Besides adding impurities, would the fermi energy of a SC changed according to, say, temperature?

Check out : http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html

Indeed, the Fermi Level (FL) is a "metal concept". For a SC, the FL is actually defined as the chemical potential. In the case of an intrinsic SC, the FL is in the middle of the bandgap because if you apply the FL definition (based upon the Fermi Dirac distribution theory, just like in the case of metals), you wind up in the middle of the band gap. Doping (ie adding impurities) changes the position of the FL because you are adding or removing electrons. Adding electrons (ie adding electron donor atoms like P) makes the FL go up (ie go towards the conduction band edge), while adding holes (ie removing electrons) has the opposite effect on the FL.

Yes, the FL does NOT depend on T because it is defined based upon a condition that requires T to be 0 K ! The electrondistribution, obviously, changes with T as explained by the Fermi Dirac distribution.

marlon

The definition of the fermi energy is as follows:

At T=0 (ground state) it simply states that all states with an energy $$\epsilon$$ lower than the fermi energy $$\epsilon_F$$ are occupied, and all states with a higher energy are unoccupied:

At T=0:
$$\epsilon < \epsilon_F \rightarrow$$ occupied state
$$\epsilon > \epsilon_F \rightarrow$$ unoccupied state

For higher temperatures the distribution of particles will change according to the Fermi-Dirac distribution. But the Fermi energy does not change! It is, as you correctly stated, an intrinsic quantity. For example, an ideal Fermi gas has a Fermi energy which only depends on the particle density:
$$\epsilon_F = \frac{\hbar^2}{2m}\left (6\pi^2 n\right )^{2/3}$$

## 1. What is Fermi Energy?

Fermi Energy is a concept in physics that describes the highest energy level of electrons in a solid material at absolute zero temperature. It is a measure of the energy required to remove an electron from the highest occupied energy level in a material.

## 2. How does Fermi Energy relate to the behavior of electrons in a material?

The Fermi Energy level determines the behavior of electrons in a material, as it dictates the maximum energy that an electron can have in the material. Electrons with energy levels below the Fermi Energy are considered to be in the valence band and are tightly bound to the material, while those with energy levels above the Fermi Energy are in the conduction band and are free to move within the material.

## 3. What factors affect the Fermi Energy of a material?

The Fermi Energy of a material is affected by various factors, including the number of electrons in the material, the type of material, and the temperature. As the number of electrons or the temperature increases, the Fermi Energy also increases.

## 4. How is Fermi Energy measured or calculated?

Fermi Energy can be measured experimentally using various techniques, such as photoemission spectroscopy or tunneling spectroscopy. It can also be calculated theoretically using mathematical models, such as the Fermi-Dirac distribution.

## 5. Why is Fermi Energy important in understanding the properties of materials?

Fermi Energy plays a crucial role in understanding the electronic properties of materials. It determines the electrical conductivity, thermal conductivity, and other properties of a material. It also helps in predicting the behavior of materials under different conditions, such as temperature and pressure.

• Atomic and Condensed Matter
Replies
2
Views
3K
• Atomic and Condensed Matter
Replies
4
Views
3K
• Atomic and Condensed Matter
Replies
3
Views
2K
• Atomic and Condensed Matter
Replies
21
Views
78K
• Atomic and Condensed Matter
Replies
1
Views
4K
• Quantum Physics
Replies
16
Views
1K
• Atomic and Condensed Matter
Replies
2
Views
6K
• Atomic and Condensed Matter
Replies
3
Views
17K