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Hey, guys, what's a fermi level?
Galileo said:It's the lowest energy level for a system of fermions.
or... that would be the fermi energy...
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]
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
Zz.
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...
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.
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.
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.
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.
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.