Density of States.

Here is a video that shows our derivation of density of states as a function of energy within one particular band. Note that density of states has units of states/eV.

Looking further ahead, at we will use this density of states with the Fermi function to calculate the number of electrons in the conduction band. Note that F(E) has units of electrons per state, so when you multiply F(E) and D(E) together you get units of: electrons per eV. Then when you integrate that as a function of energy (over the band) you get the number of electrons. Thus, integrating f(E)*D(E) gives you the total number of filled states in the band, that is, the number of electrons in the band.