Formation of Energy Bands in Solids (Energy Level Approach)

In atomic physics, we learn that electrons in an atom can occupy only certain definite energy levels. These energy levels are discrete, meaning that electrons are not allowed to have energies in between. This description works perfectly well for an isolated atom.

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However, when a very large number of atoms come together to form a solid, the situation changes. In a solid, atoms are closely packed, and their outer electrons begin to interact with those of neighbouring atoms. As a result of this interaction, the discrete energy levels of individual atoms no longer remain isolated. Instead, they spread out and form energy bands.

The concept of energy bands is extremely important because it helps us understand why some materials behave as conductors, some as semiconductors, and others as insulators.

Energy Levels in an Isolated Atom

In an isolated atom:

Electrons revolve around the nucleus in well-defined energy states
Each energy state has a fixed value of energy
The allowed energies are separated by forbidden regions

According to Pauli’s exclusion principle, no two electrons in an atom can have the same set of quantum numbers. Because atoms are well separated in space, there is no interaction between the energy levels of different atoms.

Thus, isolated atoms possess sharp and discrete energy levels.

Effect of Interatomic Spacing

When atoms are brought closer together, as in the formation of a solid:

The outer electron clouds of neighbouring atoms begin to overlap.
Electrostatic interaction occurs between electrons and nearby nuclei.
Due to Pauli’s exclusion principle, electrons cannot remain in the same energy state.

As a result, each atomic energy level splits into slightly different energy levels.
The closer the atoms are, the greater is this splitting.

This interaction is negligible when atoms are far apart but becomes very strong at the equilibrium spacing found in solids.

Formation of Energy Bands: Energy Level Approach

Let us now consider a solid consisting of N identical atoms, where N is of the order of 10^23.

Each isolated atom has discrete energy levels.
When N atoms come together, each atomic energy level splits into N closely spaced levels.
Since N is extremely large, the separation between these levels becomes very small.

Because the spacing is so small, the individual energy levels appear to merge into a continuous range of energies, known as an energy band.

Thus:

Allowed energy levels form energy bands
Regions where no energy levels exist are called forbidden energy gaps

Important Energy Bands in Solids Valence Band

Valence Band

The valence band is formed from the outermost occupied energy levels of atoms.

It contains valence electrons
Electrons in this band are generally bound to atoms
These electrons take part in bonding

The valence band plays a major role in determining the electrical properties of a solid.

Conduction Band

The conduction band is formed from higher unoccupied atomic energy levels.

Electrons in this band are free to move throughout the solid
These free electrons are responsible for electrical conduction

The ease with which electrons can enter this band determines how well a material conducts electricity.

Forbidden Energy Gap

The energy region between the valence band and the conduction band, in which no electron states are permitted, is called the forbidden energy gap or band gap.

The magnitude of this band gap decides whether a material behaves as a conductor, semiconductor, or insulator.

Step-by-Step Summary of Band Formation

Isolated atoms:
Discrete energy levels exist.
Atoms approach each other:
Interaction causes splitting of energy levels.
Large number of atoms:
Closely spaced levels form continuous bands.
Final structure:
- Lower band → Valence band
- Upper band → Conduction band
- Between them → Forbidden energy gap

This explanation clearly shows how atomic-level interactions lead to the bulk electrical properties of solids.

Energy Band Diagrams

Importance of Energy Band Theory

Energy band theory:

Explains electrical behaviour of solids
Forms the basis of semiconductor physics
Helps in understanding electronic devices
Explains temperature dependence of conductivity

Without energy band theory, the electrical properties of materials cannot be properly explained.

Atomic Energy Levels vs Energy Bands

Atomic Energy Levels	Energy Bands
Discrete	Nearly continuous
Found in isolated atoms	Found in solids
Large energy separation	Very small separation
No band gap concept	Band gap present

Important Examination Questions

Short Answer

What is an energy band?
Define forbidden energy gap.
What is meant by valence band?

Long Answer

Explain the formation of energy bands in solids using energy level approach with neat diagrams.
Describe valence band, conduction band, and forbidden energy gap.

Conceptual Questions

Why do discrete energy levels merge into bands in solids?
What is the role of Pauli’s exclusion principle in band formation?