Band Theory Of Solids - Practice Questions & MCQ

On the basis of conductivity-

On the basis of the relative values of electrical conductivity $(\sigma)$ or resistivity, the solids are broadly classified as:
- Conductor-

The materials which easily allow the flow of electric current through them are called conductors. Metals such as copper, silver, iron, aluminum, etc. are good conductors of electricity.

They possess very low resistivity (or high conductivity).

$
\begin{aligned}
& \text { i.e } \rho \sim 10^{-2}-10^{-8} \Omega m \\
& \sigma \sim 10^2-10^8 S^{-1}
\end{aligned}
$

- Insulator-

The materials which do not allow the flow of electric current through them are called insulators. Insulators are also called as poor conductors of electricity. Rubber, wood, diamond, plastic are some examples of insulators.

They have high resistivity (or low conductivity).

$
\begin{aligned}
& \text { i.e } \rho \sim 10^{11}-10^{19} \Omega \mathrm{~m} \\
& \sigma \sim 10^{-11}-10^{-19} \mathrm{Sm}^{-1}
\end{aligned}
$

- Semiconductors-

They have resistivity or conductivity intermediate to metals and insulators.

$
\begin{aligned}
& \text { i.e } \rho \sim 10^{-5}-10^6 \Omega \mathrm{~m} \\
& \sigma \sim 10^5-10^{-6} \mathrm{Sm}^{-1}
\end{aligned}
$

Note-At 0 K , it behaves like an insulator ( $\mathrm{Si}, \mathrm{Ge})$

Semiconductors are further divided as follows

(i) Elemental semiconductors: Si and Ge

(ii) Compound semiconductors: Examples are:

• Inorganic: CdS, GaAs, CdSe, InP, etc.

• Organic: anthracene, doped pthalocyanines, etc.

• Organic polymers: polypyrrole, polyaniline, polythiophene, etc

 

Materials are also classified on the basis of energy bands. So lets first know about the energy band.

Energy Band Theory-

 There is a number of energy bands in solids but three of them are very important which are shown in the below figure.

• Valence band-

The energy band which is formed by grouping the range of energy levels of the valence electrons or outermost orbit electrons is called a valence band. The valence band is present below the conduction band as shown in the above figure.

So Electrons in the valence band have lower energy than the electrons in the conduction band.

The electrons present in the valence band are loosely bound to the nucleus of an atom.

• Conduction band-

The energy band which is formed by grouping the range of energy levels of the free electrons is called a conduction band.

Generally, the conduction band is empty but when external energy has applied the electrons in the valence band then electrons jump into the conduction band and become free electrons.

Electrons in the conduction band have higher energy than the electrons in the valence band.

The conduction band electrons are not bound to the nucleus of the atom. 

• Forbidden band or forbidden gap-

The energy band which is present between the valence band and conduction band by separating these two energy bands is called a forbidden band.

In solids, electrons cannot stay in a forbidden band because there is no allowed energy state in this region.

The energy associated with the forbidden band is called the energy gap and it is measured in unit electron volt (eV).

The applied external energy in the form of heat or light must be equal to the forbidden gap in order to push an electron from valence band to the conduction band. 

Classification of materials based on a forbidden gap-

• Conductors-

In a conductor, the valence band and conduction band overlap each other as shown in the below figure. Therefore, there is no forbidden gap in a conductor.

A small amount of applied external energy provides enough energy for the valence band electrons to move into the conduction band.

When valence band electrons move to conduction band they become free electrons.

In conductors, a large number of electrons are present in the conduction band at room temperature and these electrons move freely by carrying the electric current from one point to another.

• Insulators

The forbidden gap between the valence band and conduction band is very large in insulators as shown in the below figure.

Note- When the energy gap between the valence band and conduction band is more than 3 eV. then the material is insulators.

Normally, in insulators, the valence band is fully occupied with electrons due to the sharing of outer most orbit electrons with the neighboring atoms. While no electrons are present in the conduction band. Free electrons density is negligible in the case of the insulator. The electrons in the valence band cannot move by themself because they are locked up between the atoms.

• Semiconductors

In semiconductors, the forbidden gap between the valence band and conduction band is very small as shown in the below figure.

Note- When the Energy gap between the valence band and conduction band is less than 3 e.v. Then the material is a semiconductor.

At low temperature, the valence band is completely occupied with electrons and the conduction band is empty because the electrons in the valence band do not have enough energy to move into the conduction band. Therefore, semiconductor behaves as an insulator at low temperature.

However, at room temperature, some of the electrons in valence band gains enough energy in the form of heat and moves into the conduction band. When the temperature increases, then the number of valence band electrons moving into the conduction band also increases. So free electron density in the conduction band increases.  This shows that the electrical conductivity of the semiconductor increases with an increase in temperature.