Density of States
The density of states (DOS) corresponds to electrons with a spherically-symmetric parabolic dispersion
- ,
with two electrons (one of each spin) per each "quantum" of the phase space, . In 3D, this corresponds to
- ,
where is the total volume.
Combining the expressions for the Fermi energy and the DOS, one can show that the following relationship holds at the Fermi level:
where Z is the charge of each of the N metal ions in the crystal.
Read more about this topic: Free Electron Model
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