Density of States for Solids

DENSITY OF STATES FOR SOLIDS

Definition

Electron density is the number of electrons per unit volume in a material. It is determined by using density of states.

Density of states

In solid, the total number of electron energy states N with energies upto E is determined based on quantum mechanics using the following equation

Here, the volume of the material is represented as a³ (a being the characteristic dimension of the solid),

E - Maximum energy level

m - mass of an electron

h - Planck's constant.

Number of energy states per unit volume

Density of states function Z (E) is obtained after taking the derivative of this expression with respect to energy (dn/dE)

This function gives the number of available electron energy states per unit volume per unit energy.

In a conductor at 0 K, the electron distribution goes from zero energy upto Fermi energy E_F.

So, the number of free electrons per unit volume, or electron density, in a bulk conductor at 0 K using eqn (2).

The minute size of the nanomaterials gives unique mb electronic properties. One of the major ways in which small-volume materials differ from bulk solids is the number of available energy states.