Relation between electronic band structure and Fermi energy

[cytochrome]

I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level).

1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ?

2) I assume something with density of states is involved (is it?). If it is, what is the relation between density of states, electronic dispersion, and Fermi energy (or level)?

 

[DrDu]

From a band structrure calculation you also get the DOS as a function of energy. If the electronic density is n, then $\int_{-\infty}^E DOS(E')dE'=n$ fixes the Fermi level E. The DOS is proportional to the inverse slope of E vs k, i.e. dispersion.