Band Theory of Solids

Band Theory of Solids
The band theory of solids is different from the others because the atoms
are arranged very close to each other such that the energy levels of the
outermost orbital electrons are affected. But the energy level of the
innermost electrons is not affected by the neighboring atoms.
In-band theory of solid, there are many energy bands but the following are
the three most important energy bands in solids:
1. Valence band
2. Conduction band
3. Forbidden band
Valence band: The energy band that consists of valence electrons energy

levels, is known as the valence band. The valence band is present below
the conduction band and the electrons of this band are loosely bound to the
nucleus of the atom.
Conduction band: The energy band that consists of free electrons energy
levels, is known as the conduction band. For electrons to be free, external
energy must be applied such that the valence electrons get pushed to the
conduction band and become free.
Forbidden band: The energy gap between the valence band and the
conduction band is known as the forbidden band which is also known as
the forbidden gap. The electrical conductivity of a solid is determined from
the forbidden gap and also the classification of the materials as conductors,
semiconductors, and insulators.
What is Band Theory of Solids?

This theory explains the quantum state that an electron takes inside metal
solid. Every molecule comprises various discrete energy levels. The way
electrons behave inside a molecule is well explained through this theory.
 In atoms, electrons are filled in respective energy orbits following

Pauli’s exclusion principle.
 In molecules, Two atomic orbitals combine to form a molecular orbit
with two distinct energy levels.
 In solids, 1023 stacked up lines confined in a tiny space would look
like a band. Thereby forming an energy continuum called energy
bands.
 This theory helps to visualize the difference between
conductor, semiconductor, and an insulator by plotting available
energies for an electron in a material.
Consider a Sodium atom. It comprises 11 electrons. They fill up the energy

level following Pauli’s exclusion principle. Refer Figure(1).
What happens when two sodium atoms very close to each other almost
forming a molecule? Now each atom cannot have the configuration as it
followed as an individual atom If they do they will be violating Pauli’s
exclusion principle and end up with a lot of electrons of the same energy
levels.
When two atoms come very close to each other, What is going to happen
to this system? The answer is, their respective energy bands are going to
overlap on each other and transform into what we call as Molecular orbit.
That is the 1s orbit of individual Sodium atom combines to form 1s
molecular orbital. As two atomic orbital are overlapping, the molecular orbit
ends up having two discrete energy levels. Where the Lower energy level is
called bonding orbital and higher energy level is called an anti-bonding
orbital. This will repeat for all orbits.
Energy levels inside a molecule made up of three atoms

Now try to picture, what is going to happen if we add a third sodium atom to
the mix? Well, according to the theory we learned just now. Here three
atomic orbital will be overlapping forming single molecular orbital with three
discrete energy levels. Each molecular orbital here will inherit three energy
levels. In general, the more we add atoms, the more energy levels the
molecular orbit going to have. Refer figure (3)
Energy levels inside a solid made up of n-number of atoms
In general, If there are n-number of atoms, then there will be n discrete
energy levels in each energy band. In such a system of n number of atoms,
the molecular orbitals are called energy bands. The gaps between them will
be tiny such that, no longer we can notice individual energy levels. As a
result, It is convenient to think of it as continuous energy or energy
continuum. When we think in this way, we can call them an energy band
instead of a molecular orbit.
Energy levels inside material of different states of matter

If you have a single atom or if you have gas. In gas, atoms are
apart/infinitely apart; we can assume them as single atoms. Here every
atom has a discrete energy level, if electron wants to go from one level to
another, it really has to jump as no continuous energy is available (It is
similar to steps).
As atoms come close to each other and eventually form a solid, They end
up forming energy continuum, and we name that continuum as bands.
Within the bands, energy levels that are available are continuous. Thus, the
name of this theory without any surprise is, “The band theory of solids”
Using this theory, we can understand how free electrons are generated and
why certain material readily has free-electron available making them a
conductor and why some others don’t.

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Band Theory of Solids

Valence band: The energy band that consists of valence electrons energy

What is Band Theory of Solids?

 In atoms, electrons are filled in respective energy orbits following

Consider a Sodium atom. It comprises 11 electrons. They fill up the energy

Energy levels inside a molecule made up of three atoms

Energy levels inside material of different states of matter

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