Fermi-dirac distribution

In summary, a Fermi-Dirac distribution is a probability distribution that describes the distribution of particles with half-integer spin, such as electrons, in a system at thermal equilibrium. It is significant because it accurately describes the behavior of electrons in metals and semiconductors and plays a crucial role in understanding the behavior of matter in extreme conditions. The Fermi-Dirac distribution differs from the Maxwell-Boltzmann distribution by taking into account the quantum mechanical effects of particles with half-integer spin. The Fermi energy, which is the energy level at which a particle has a 50% probability of being occupied according to the Fermi-Dirac distribution, is a measure of the highest energy level occupied by electrons at absolute zero
  • #1
magnifik
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An electron state has energy 0.14 eV above the Fermi energy. What is the probability that the electron state will be occupied at T = 200K?

do i just use the following formula?
disfd2.gif


the part that throws me off is the "above the Fermi energy" bit. would i just plug that number in for E - Ef??
 
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  • #2
Yep, it means that E = EF + 0.14 eV, so E - EF = 0.14 eV.
 

What is a Fermi-Dirac distribution?

A Fermi-Dirac distribution is a probability distribution that describes the distribution of particles with half-integer spin, such as electrons, in a system at thermal equilibrium. It is named after Enrico Fermi and Paul Dirac, who first proposed the concept.

What is the significance of the Fermi-Dirac distribution?

The Fermi-Dirac distribution is significant because it accurately describes the behavior of electrons in metals and semiconductors, which are essential materials for modern electronics. It also plays a crucial role in understanding the behavior of matter in extreme conditions, such as in neutron stars.

How is the Fermi-Dirac distribution different from the Maxwell-Boltzmann distribution?

The Fermi-Dirac distribution differs from the Maxwell-Boltzmann distribution in that it takes into account the quantum mechanical effects of particles with half-integer spin. This results in a sharper peak at the distribution's maximum and a harder cutoff at high energies, which is known as the Pauli exclusion principle.

What is the Fermi energy in relation to the Fermi-Dirac distribution?

The Fermi energy is the energy level at which a particle has a 50% probability of being occupied according to the Fermi-Dirac distribution. It is a measure of the highest energy level occupied by electrons at absolute zero temperature and is an important quantity in solid-state physics.

How is the Fermi-Dirac distribution used in statistical mechanics?

The Fermi-Dirac distribution is used in statistical mechanics to calculate the thermodynamic properties of a system containing a large number of particles with half-integer spin, such as electrons. It is also used in the study of topics such as electronic band structure, thermal conductivity, and electrical conductivity in materials.

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