Band theory

Band Theory of Solids

Band theory describes how electrons behave in solid materials, particularly in terms of their ability to conduct electricity. It builds upon molecular orbital theory but extends its application to a vast number of atoms within a solid structure. As atoms assemble to form a solid, their outer orbitals interact and merge, creating continuous energy bands instead of distinct energy levels.

Formation of Energy Bands

Electrons in individual atoms are confined to well-defined energy levels. However, when a large number of atoms are closely packed in a solid, their energy levels split and merge into bands due to orbital interactions. Two major bands arise:

• Valence Band: The highest range of electron energies where electrons are usually present at absolute zero temperature.
• Conduction Band: The energy range above the valence band where electrons are free to move and conduct electricity.

Band Gap

The gap between the valence band and the conduction band is known as the band gap, which plays a key role in defining a material’s electrical conductivity.

Classification Based on Band Theory

• Conductors: In metals, the conduction band overlaps with the valence band or is partially filled. This allows electrons to move freely, making metals good conductors of electricity.
• Insulators: In insulators, a large band gap (typically > 3 eV) exists between the valence and conduction bands, preventing electron flow under normal conditions.
• Semiconductors: These have a moderate band gap (around 1 eV). At higher temperatures or with doping, electrons can jump the gap, allowing limited conductivity. Silicon and germanium are common examples.

Effect of Temperature

With rising temperature, semiconductors exhibit increased conductivity as more electrons acquire sufficient energy to cross the band gap. On the other hand, in metals, conductivity slightly drops due to intensified vibrations of the lattice.

Significance of Band Theory

Band theory is crucial for understanding and designing electronic devices such as diodes, transistors, and photovoltaic cells. It helps classify materials and predict their behavior in electrical and optical applications.