Energy Band Theory of Crystals!

This topic is one of the most interesting things one would be studying in the Electronic Devices subject. But sadly it is given the least priority on the list.

Hence, this creates a great anxiety in the avid reader to learn everything about the energy band theory and what it does!

As we know, the inner-shell electrons are the least effected when atoms form a crystal and the outer-most shell electrons are the easily influenced part of an atom. Thus, when the atoms in a crystal are placed close to each other, there is more possibility of electrons of two adjacent atoms to either collapse or bound to each other.

For example, lets just consider an example of two simple magnets:

More the distance between them, lesser is the attraction between them and vice-versa!

The adjacent figure depicts the energy band diagram (energy, E vs interatomic spacing, d).

From the fig., it’s clear that, more the interatomic spacing, lesser is the energy(attraction) between them.

And as the distance between them is reduced(moving from right to left), there will be a gradual increase in the interactions between the neighboring atoms. Because of this interaction, the atomic wave functions overlap and the crystal becomes an electronic system which must obey Pauli exclusion principle.

Here, there are 2N electrons completely filling the 2N possible s levels of the atom and 2N electrons filling the 6N possible p states.

Thus, when the “d” is reduced, the 2N- s states spread out to form a band of energy. And the 4N electrons remain unoccupied in the p levels.

The total spread between the minimum and the maximum energy levels becomes very large( several eV) and is known as Energy Bands. An energy gap (Eg) exists between them. this is known as forbidden energy gap (no electrons can occupy states in this gap).

When this energy gap is further reduced to make it zero, the 6N upper level and 2N lower level states merge and form 8N levels out of which 4N electrons are already occupied (2N+2N). Now these 4N electrons neither belong to the p subshell nor the s subshell but belong to the crystal as a whole.

The energy band produced due to these electrons is known as a Valence Band.

If the energy gap is further reduced, the interaction between them grows very large and finally a shape is obtained, as shown below:

The energy band diagram depends upon the orientation of the atoms relative to one another in space as well as their atomic numbers.

The above vacant band is known as Conduction Band.

Hence, the entire concept of energy band theory of crystals becomes extremely fascinating!

Thank You.