# Relation between electronic band structure and Fermi energy

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1. Nov 13, 2015

### 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)?

2. Nov 16, 2015

### 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.