Name: Energy Band Gap
Uploaded: 2019-07-19
Duration: 5 min 21 s
Description: We know that certain materials conduct electricity whereas some don’t. Has it got anything to do with their energy bandgap? Let’s find out in this video.

Question

Discuss the classification of solids as conductors, insulators and semiconductors on the basis of band theory.

Accepted Answer

The substances which contain free charge carriers are called conductors, while the substances which do not contain any free charge carrier are called insulators. Semi-conductors are intermediate to conductors and insulators.

The conductors, insulators, and semiconductors are distinguished based on band theory. The electrons revolving around the nucleus of an isolated atom possess discrete energy states $1 s$ , $2 s$ , $2 p$ ,...and they occupy the quantum states available in those energy levels. Due to the periodicity of lattice, each atom is in the electronic field of neighbouring atoms. Consequently, the energy levels of an individual atom lose their validity. If the crystal contains $N ‐$ atoms, then due to interaction between the atoms, each discrete energy level of an individual atom splits into $N ‐$ close sub $‐$ levels. As $N$ is very large the separation between sub $‐$ levels is very small so that these dense levels are almost continuous and are said to form an energy band.

According to Pauli exclusion principle, each energy level can be occupied by two electrons having opposite spins. Hence, normally only lower energy bands will be filled with electrons. The highest occupied band at $0 K$ is called the valence band which is occupied by valence electrons. The band above the valence band is known as the conduction band. The electrons in the conduction band are free electrons. The energy gap between the conduction band and valence band is known as the forbidden energy gap.

Solids can be classified into three groups on the basis of the width of the forbidden energy gap $(∆)$ of band theory as follows $:$

$(i)$ Conductors if $∆ = 0$

$(i i)$ Semiconductors if $∆ < 2 eV$

$(i i i)$ Insulators if $∆ > 2 eV$

$(i)$ Conductors $:$

A solid can be conductor under the following two circumstances $:$

$(a)$ If the conduction band is partially filled $:$

Atoms having an odd number of electrons in their valence shell exhibit band structure as shown in the figure below.

At absolute zero, half of the energy levels of the conduction band are occupied and the other half of the energy levels are completely empty. The highest occupied level of the conduction band at $0 K$ is known as the Fermi level and its energy is known as Fermi energy. When an electric field is applied, the electrons receive energy and get excited into empty energy levels just above the Fermi level in the conduction band and drift, giving rise to electrical conductivity. Sodium, potassium, lithium have this type of band structure.

$(b)$ If the conduction band is completely empty and overlap with fully filled valence band $:$

In this case, the forbidden energy gap is zero. Even a feeble electric field enables, the electrons to shift from the valence band to the conduction band and drift, constituting the electric current. Such solids conduct electricity and are good conductors. Some examples are beryllium, magnesium, zinc, etc.

$(i i)$ Semiconductors $:$

Solids having their valence bands completely filled with electrons at $0 K$ and conduction bands completely empty with a narrow forbidden band gap are called semiconductors. The band structure of semiconductors is shown below $:$

At room temperature, thermal collisions may push some electrons from the valence band to empty conduction and creating empty spaces in the valence band. These electrons move when a potential difference is applied across the semiconductor, but the concentration of conduction electrons is less hence the conductivity is quite small as compared to conductors but greater than insulators. Some examples of semiconductors are silicon with band gap of $1.17 eV$ and germanium having a band gap of $0.74 eV$ .

$(i i i)$ Insulators

Solids having their valence bands completely filled with electrons at absolute zero and the conduction bands completely empty with a very large forbidden gap are called insulators. When an electric field is applied to an insulator, electrons in the valence band cannot gain sufficient energy to reach the conduction band for conduction. Diamond is an example that has a forbidden gap of $5.4 eV$ .

Discuss the classification of solids as conductors, insulators and semiconductors on the basis of band theory.

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