Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. Remember that the energy of free electron is changing continuously.

Energy Band Theory

According to Bohr’s theory, each and every shell and subshell of atoms contain a discrete amount of energy. An atom has different energy levels. When atoms are brought closer to each other, electrons at outermost shell interact with each other. This bonding force between electrons is called as an inter-atomic interaction.

This interaction causes the change in energy levels of electrons at the outermost shell. This change will give rise to energy band theory, and hence electrons will not be at the same level, the levels of the electrons are changed to a value which is higher or lower than that of the original level.

Each substance consists different amount of electron energy present in the energy bands, based on these different energy levels. Energy band are then further classified as:

• Valence band
• Forbidden Energy Gap
• Conduction Band

Valence Band

At absolute zero temperature, there are the different range of energies present in the solid and the band which is formed by the highest range of energy is called valence band this band is filled with valence electrons.

Valence band can also be explained as, When atoms are brought closer together to form a solid, the discrete energy levels are disturbed because of quantum mechanical effects, and many electrons in the group of the individual atom occupy a band of levels in the solid, this band of levels called as valence band. This band is formed by the electrons at an outermost shell.

It is located below the Fermi level. Electrons in the valence band have lower energy than the electrons in the conduction band. In atoms, the electrons present in the valence band is loosely bound to the nucleus. The electrical conductivity of a solid depends on the capability to move the electrons from the valence band to the conduction band.

Forbidden Energy Gap

Forbidden energy gap is also known as Fermi energy level. It is the electronic energy band where there is no electron state exists due to quantization energy. The band obtained by separating conduction band and valence band is called as forbidden energy band or forbidden gap.

In solids, the electrons do not stay in forbidden gap as there is no energy state in this region. With the help of forbidden gap, we can determine the major factor, i.e., the electrical conductivity of the solid.

Conduction Band

The energy band formed by the energy levels of the free electrons is called conduction band. The conduction band is an empty band or partially filled band, but when the external field is applied to the electrons in the valence band, the electrons jump from the valence band to the conduction band and becomes free electron.

Electrons in the conduction band have higher energy than the electrons in the valence band. In the conduction band electrons are not bound to the nucleus of the atom.

Conduction band can also be defined as empty states which are broadened into a band of levels. This band is placed above the Fermi level. It is the lowest range of vacant electronic state.

The band model of the Materials

The below figure shows the Band model of conductors, semiconductors, and Insulators.

Conductors

In conductors, the valence band is either not fully occupied with electrons, or the filled valence band overlaps with the empty conduction band. In general, both states occure at the same time, the electrons can therefore move inside the partially filled valence band or inside the two overlapping bands. In conductors there is no band gap between the valence band and conduction band.

Insulators

In insulators the valence band is fully occupied with electrons due to the covalent bonds. The electrons can not move because they're "locked up" between the atoms. To achieve a conductivity, electrons from the valence band have to move into the conduction band. This prevents the band gap, which lies in-between the valence band and conduction band.

Only with considerable energy expenditure (if at all possible) the band gap can be overcome; thus leading to a negligible conductivity.

Semiconductors

Even in semiconductors, there is a band gap, but compared to insulators it is so small that even at room temperature electrons from the valence band can be lifted into the conduction band. The electrons can move freely and act as charge carriers. In addition, each electron also leaves a hole in the valence band behind, which can be filled by other electrons in the valence band. Thus one gets wandering holes in the valence band, which can be viewed as positive charge carriers.

There are always pairs of electrons and holes, so that there are as many negative as positive charges, the semiconductor crystal as a whole is neutral. A pure undoped semiconductor is known as intrinsic semiconductor. Per cubic centimeter there are about 10¹⁰ free electrons and holes (at room temperature).

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