User:Mitiku21/sandbox

Valence and conduction band
Electronic band structure is used to study the electrical properties of the material. By using the band gap one can identify whether the material is metal, non metal or semiconductor. Electronic band structure also helps to identify the material and make useful transition material properties for example we can change non metal to metal

The density of states function, DOSg(E), is defined as the number of electronic states per unit volume, per unit energy, for electron energies between E and E + dEnear E. and given by

DOS(E) = dNdE,

Where N= N(E) —  number of states occupied at energy E. The Fermi energy, E=EFis the highest occupied energy level, a.k.a. Fermi Energy (citation for Kittel).

The Let’s look at the derivation of DOS(E) for the Particle in 3D Box model at 0K, which can be used as an approximation for electrons in the metal. The energy of a state at n=(nx,ny,nz) is given by E=h28meL2(nx2+ny2+nz2), where h is Planck’s constant, me— mass of electron, and L— box length. Thus the number of states with EEFis given by twice the volume of a positive octant of the sphere with radius n:

N(E) = 2 1/8 43n3 = 83(2meEh2)3/2L3=83(2meEh2)3/2V,

Where V=L3— volume of the box. Now using the definition of DOS we find:

DOS(E) = dNdE=4(2meh2)3/2E1/2V=V22(2mehbar)3/2E1/2V

One can define g(E) = DOS(E) / V, or density of states per unit volume. Thus, the g(E) at 0K is proportional to E1/2 (see Fig.). At finite temperatures, g(E) is modulated by Fermi-Dirac distribution.

The density of states function is important for calculations of effects based on band theory. In Fermi's Golden Rule, a calculation for the rate of optical absorption, it provides both the number of excitable electrons and the number of final states for an electron. It appears in calculations of.