About Fermi energy and Fermi temperature

In summary: Hi, I just learned this concept of fermi sphere a few months ago as well. What I understand from the term "fermi termperature" is that it is just another way of expressing the fermi energy. It is a purely fictional concept and it just borrows the term "temperature" because it has a linear relationship with Energy:EF = kB TFwhich is similar to the thermodynamics equationE = n kB TI don't think it has anything to do with the real physical temperature of the electron itself.Thanks. But one more thing. The Fermi energy and consequently the Fermi temperature is very large in dense systems e.g. electrons
  • #1
shabbir
5
0
In classical statistical mechanics, temperature of a system is the measure of its average kinetic energy. In quantum statistical mechanics, Fermi energy corresponds to last filled level at absolute zero and corresponding temperature is the Fermi temperature. Is the Fermi temperature also take some averages into account? What about the temperature of the particles having energy below Fermi energy? Anyone to share me in this regard will be appreciated.
 
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  • #2
All the particles are at the same temperature, regardless of their energy. Temperature is a property of a distribution of energies of particles, not a single particle.

Now, once you look at the Fermi-Dirac distribution, and study it for a while, you notice that the combination [tex]\frac{E_f}{k_B}[/tex] is important, and this has the right units to be called a temperature. It turns out that the system behaves more and more differently beyond that temperature.
 
  • #3
It means all the Fermions may be at the same temperature simultanously, as it is clear. And Fermi temperature is a purely quantum mechanical concept. So can we say that the Fermi temperature corresponds to ensemble of Fermions in many particle degerate Fermi system? I am bit confused in the sense that Pauli's principle restrict two Fermions to be in the same quantum state, and "temperature" is an average phenomenon, so how to visualize the Fermi temperature?
 
  • #4
lbrits said:
All the particles are at the same temperature, regardless of their energy. Temperature is a property of a distribution of energies of particles, not a single particle.

Now, once you look at the Fermi-Dirac distribution, and study it for a while, you notice that the combination [tex]\frac{E_f}{k_B}[/tex] is important, and this has the right units to be called a temperature. It turns out that the system behaves more and more differently beyond that temperature.
It means all the Fermions may be at the same temperature simultanously, as it is clear. And Fermi temperature is a purely quantum mechanical concept. So can we say that the Fermi temperature corresponds to ensemble of Fermions in many particle degerate Fermi system? I am bit confused in the sense that Pauli's principle restrict two Fermions to be in the same quantum state, and "temperature" is an average phenomenon, so how to visualize the Fermi temperature? Can many Fermions (e.g., electrons/positrons) in a many-particle system be at same "Fermi temperature"?
 
  • #5
Hi, I just learned this concept of fermi sphere a few months ago as well. What I understand from the term "fermi termperature" is that it is just another way of expressing the fermi energy. It is a purely fictional concept and it just borrows the term "temperature" because it has a linear relationship with Energy:

EF = kB TF

which is similar to the thermodynamics equation

E = n kB T

I don't think it has anything to do with the real physical temperature of the electron itself.
 
  • #6
Thanks. But one more thing. The Fermi energy and consequently the Fermi temperature is very large in dense systems e.g. electrons in metals. So At some temperature say 400K, the Fermi pressure is very large as compared with thermal pressure. Can this Fermi pressure drive waves/oscillations due to electronic or ionic motion?
 
  • #7
TheWye said:
Hi, I just learned this concept of fermi sphere a few months ago as well. What I understand from the term "fermi termperature" is that it is just another way of expressing the fermi energy. It is a purely fictional concept and it just borrows the term "temperature" because it has a linear relationship with Energy:

EF = kB TF

which is similar to the thermodynamics equation

E = n kB T

I don't think it has anything to do with the real physical temperature of the electron itself.

Thanks. But one more thing. The Fermi energy and consequently the Fermi temperature is very large in dense systems e.g. electrons in metals. So for some thermal energy say 0.1eV, the Fermi pressure is still very large as compared with thermal pressure. Can this Fermi pressure drive waves/oscillations due to electronic or ionic motion in a Fermi gas of electrons?
 

1. What is Fermi energy and why is it important in materials science?

Fermi energy is the energy level at which the electrons in a material have a 50% probability of being occupied at absolute zero temperature. It is an important concept in materials science because it helps to understand the electronic properties of materials, such as their electrical conductivity, thermal conductivity, and magnetic properties.

2. How is Fermi energy related to the Fermi temperature?

The Fermi temperature is the temperature at which the thermal energy of the material is equal to the Fermi energy. This means that at the Fermi temperature, all available energy states for electrons are filled, and no more can be added. It is related to the Fermi energy through the equation EF = kBTF, where kB is the Boltzmann constant and TF is the Fermi temperature.

3. How does Fermi energy change with temperature?

Fermi energy remains constant as temperature increases, but the Fermi level (the energy level at which the probability of electron occupation is 50%) shifts up or down depending on the type of material. In metals, the Fermi level increases with temperature, while in semiconductors, it decreases. This is because in metals, electrons can easily move between energy levels, while in semiconductors, there is an energy gap between the valence and conduction bands that restricts electron movement.

4. How does the Fermi energy affect the electrical properties of a material?

The Fermi energy determines the number of electrons available to participate in electrical conduction. In metals, where the Fermi level is close to the conduction band, there is a large number of electrons available for conduction, making them good conductors of electricity. In semiconductors, the Fermi level is closer to the valence band, and there are fewer electrons available for conduction, making them poorer conductors. In insulators, the Fermi level is within the energy gap, and there are no available electrons for conduction.

5. How is the Fermi energy calculated?

The Fermi energy can be calculated using the formula EF = ħ2kF2/2m, where ħ is the reduced Planck's constant, kF is the Fermi wavevector (related to the electron density), and m is the effective mass of the electrons in the material. Alternatively, it can be experimentally measured using techniques such as angle-resolved photoemission spectroscopy or scanning tunneling microscopy.

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