DENSITY OF STATES:

The number of states per unit volume of the crystal which are contained in the energy interval between E and E+dE defines a density of states Z(E).


The Fermi function does not gives us the number of electrons which have certain energy. It gives us only the probability of occupation of an energy state by a single electron. In a small energy interval dE there are many discrete energy levels. So the concept of density of state is introduced to calculate the number of electrons with a given energy. By multiplying the number of states by probability occupation we get the actual number of electrons.

If N(E) is the number of electrons in a system that have energy E and Z(E) is the number of states at that energy, then

N(E) dE = Z(E) p(E) (48)

The number of energy states, with a particular value of E, depends on how many combinations of the quantum number results in the same value of n. Since we are dealing with almost a continuum of energy levels, we may construct a space of points represented by the values of nx, ny and nz and let each point with integer values of the coordinate represent an energy state.