Unit-I

Density of States

General Objective

To derive an expression for the density of states

Specific Objectives

You will be able to

1. Define Fermi energy

2. Derive an expression for the density of states in metals

Fermi Energy level (EF)

Fermi energy level is the maximum energy level

up to which the electrons can be filled at 0 K.

Importance of Fermi energy level

It act as a reference level which separates the vacant and filled states at 0K.

It gives the information about the filled electrons states and the empty states.

At 0K, below Fermi energy level electrons are filled, whereas at above Fermi energy level it will be empty.

When the temperature is increased, few electron gains the thermal energy and it goes to higher energy levels.

Example: Energy levels in the shells

DENSITY OF STATES

n+dn is

Case (ii) At T>0 K

Average energy of an electron at 0K

• Average of an electron =total energy of the electrons at 0K / number of energy states at 0K

• Avg. Energy of an electron (Eave) = 3/5 EF0

Thank you