Solids ( Modern Physics ) notes 

    SOLIDS

·     Energy Band Theory

       According to Bohr’s, every element is an isolated atom that has well-defined energy. But in crystal, no atoms come close to each other. As a result, every electron of each atom will involve in two types of interaction with the neighbouring atom i.e. each electron will interact with the electrons of the neighbouring atom which is repulsive in nature and the nucleus which is attractive in nature.

   Due to this interaction, the energy of each electron changed. In another word, the energy level of an isolated atom split during crystal formation. The number of possible fine energy will be equal to the number of interacting atoms. Therefore, the energy level diagram appears as a closely spaced continuous band. In another word, as the electron in an isolated atom has only one energy value but in a crystal, each electron has a wide range of possible energy values.
The energy range passed by electrons in a solid is called the energy band. If we consider the interaction of outermost electrons among the interacting atom, then there are three energy bands.

1)  Valence band
        The range of energy possed by valence electrons in solids is called the valence band. It is either partially filled or completely filled but it can never be empty. It means there is some probability of finding the electrons at any temperature. 

2) Conduction band
       The range of energy possed by free electrons in a solid is called the conduction band. It is either partially filled or completely empty but it can never be completely filled. 

3)  Forbidden gap
           The energy difference between of conduction band and the top of the valence band is called the forbidden gap. There is no permitted energy level found within this gap. So, the probability of finding the electrons within the forbidden gap is zero.
   It means how tightly the electron is bound with the valence band. The greater the bandgap energy, the more tightly is the electron bound in the valence bond and more energy is required to make the electron jump from the valence band to the conduction band.

 

Classification of solid

1)conductor
 - The material in which the valence band and conduction band are     overlapping

- The forbidden gap is zero

-  It is ready to conduct at any temperature

-  Charge carriers are free electrons

-  On the increasing temperature, its conductivity decreases

-  Temperature coefficient of resistance is +ve

-  Conduction band and valence band are both filled

2) Semi-conductor

      The material in which there exists a small bandgap

·      Semi-conductivity  nature,
 -  conductivity can be controlled

  - It can make current uni-direction

Properties

    At 0 K, its valence band is filled but its conduction band is completely empty which means at 0 K, no free electrons are present and hence it behaves as an insulator.

    At room temperature, its valence band is filled and the conduction band is also partially filled. At room temperature, electrons gain thermal energy to jump parent atoms and hence move on the crystal.

   Charge carriers are free electrons in the conduction band and holes in the valence band

Holes:   when an electron jumps from a covalent bond, it takes a vacancy there. An electron from a neighbouring atom can move into this vacancy,   leaving the neighbours with a new vacancy. This vacancy is called a hole that can travel through the material and server as an additional current carrier.

      The electric conduction in a semi-conductor is caused by the motion of electrons and holes. The effective current in the semi-conductor is given by I= I_e + I_n

     -  Increasing temperature, its conductivity increases

     -  Temperature coefficient of resistance is -ve
 

·Types of semi-conductor

a) Intrinsic conductor
 - extremely pure semi-conductor
 - example: Si, Ge
 - no free electrons in the conduction band=no holes in the valence band
- density and probability of free electrons=density and probability of holes
- concentration of the charge carrier is small, so a very small current is obtained in semi-conductor
- Fermi  level lies midway between conduction and valence band
- resistivity is the reciprocal of  electrical conductivity

 

b) Extrinsic semiconductors
    - impure semiconductors formed by doping a small number of impurity atoms to the pure semi-conductors
    - example: Si and Ge crystals with impurity atoms of arsenic or antimony indium
    -  no of free electrons is not equal to no of holes
   -   electrical conductivity depends upon the temperature as well as the number of impurity atoms doped in the structure
   -  electrical conductivity is high