Some questions about electrons and the Fermi energy

[Jeff Chen]

Hello ,evreyone.I have two questions about fermi energy.
1,Can I claim that 'fermi energy ' play the role of chemical potential?
2,I have learned from thermal physics that only electrons near fermi level can conduct in metals.How can electrons behave like this? I can't figure out why only electrons near fermi level can conduct in metals.
Thanks!​

 

[MisterX]

1) The "Fermi Level" is the same thing as chemical potential. The "Fermi energy" is the chemical potential at 0 K.
2) Only energy levels near the Fermi level participate in electrical conduction. This is because energy levels farther away from the Fermi level are either mostly full or mostly empty. Mostly full levels do not conduct much because a full energy level forces the average velocity to be 0. In a full level just as many electrons are traveling one way as the other, so there is no net current, no conduction. Mostly empty energy levels have so few electrons in them that they can't contribute much either. Only the partially filled levels near Fermi level have the freedom to reconfigure so that there is a significant net velocity in one way while still containing a significant number of electrons.

 

[BPHH85]

I just want to add some information to the already good description. In a metall at equilibrium, all states up to the Fermi level are filled and all states above it are empty. That's a conclusion of the Fermi–Dirac statistics where the occupation probability is exactly 1/2 at the Fermi energy. So at equlibrium, beside some thermal excitation fluctuation that leads to an average current of I = 0, there is no net flow of charge. One needs to bring in energy (thermal disequilibrium) to excite electrons in higher states but these electrons won't come from states close to the nucleus. Instead they are from states close to the Fermi level. However "electroncs near the Fermi level" is an elastic term as it depends a bit on the amount of excitation and disequlibrium.

 

[fluidistic]

I just want to add some information to the already good description. In a metall at equilibrium, all states up to the Fermi level are filled and all states above it are empty. That's a conclusion of the Fermi–Dirac statistics where the occupation probability is exactly 1/2 at the Fermi energy. So at equlibrium, beside some thermal excitation fluctuation that leads to an average current of I = 0, there is no net flow of charge. One needs to bring in energy (thermal disequilibrium) to excite electrons in higher states but these electrons won't come from states close to the nucleus. Instead they are from states close to the Fermi level. However "electroncs near the Fermi level" is an elastic term as it depends a bit on the amount of excitation and disequlibrium.

I find these explanations a bit misleading. In a metal at equilibrium, it isn't necessarily true that all states up to the Fermi level are filled and all states above are empty. It does not come out from the Fermi-Dirac statistics. In fact this only holds at 0K. However, any temperature for a solid metal is generally "cold" (thus, not much different from the 0K situation), so the statement holds approximately quite well, but it isn't quite exact.

Then, saying that it isn't the electrons near the nuclei that contributes to thermal excitation is completely trivial, since they aren't even considered as free electrons, they do not even enter the Fermi sphere (they are entirely ignored, they do not take part in the "sea of free electrons" which models the metal). What should be claimed instead, is that it isn't the least energetic free electrons that can get excited by a thermal gradient, it is only those having an energy near the Fermi energy. That is all due to Pauli's exclusion principle and Fermi-Dirac statistics.