Answer to Question #283158 in Material Science Engineering for MD HUMAYAN KABIR

Question

Describe about density of states function

Answer 1

The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy. Bulk properties such as specific heat, paramagnetic susceptibility, and other transport phenomena of conductive solids depend on this function. DOS calculations allow one to determine the general distribution of states as a function of energy and can also determine the spacing between energy bands in semi-conductors

Before we get involved in the derivation of the DOS of electrons in a material, it may be easier to first consider just an elastic wave propagating through a solid. Elastic waves are in reference to the lattice vibrations of a solid comprised of discrete atoms. Though, when the wavelength is very long, the atomic nature of the solid can be ignored and we can treat the material as a continuous mediu.

We begin with the 1-D wave equation

To begin, we must apply some type of boundary conditions to the system. The easiest way to do this is to consider a periodic boundary condition. With a periodic boundary condition we can imagine our system having two ends, one being the origin, 0, and the other, L

L. We now say that the origin end is constrained in a way that it is always at the same state of oscillation as end L.