The band theory of solids is the foundation of semiconductor physics. It explains how electrons are organized in a solid and how they conduct electricity. In a solid, electrons are arranged in energy bands. Each band represents a range of electron energy levels that electrons are allowed to occupy. There are two types of bands: valence bands and conduction bands.

The valence band is the highest energy band that is completely filled with electrons in a solid. It is the band that determines the properties of the solid, such as its conductivity and optical properties. The electrons in the valence band are tightly bound to their atoms and cannot freely move through the solid.

The conduction band is the next higher energy band that is empty or partially filled with electrons. Electrons in the conduction band are not bound to any particular atom and can move freely throughout the solid. When an electric field is applied to a solid, electrons in the conduction band move towards the positive end of the electric field and create a flow of current.

The energy gap between the valence band and the conduction band is known as the bandgap. This energy gap determines whether a solid is a conductor, an insulator, or a semiconductor. Conductors have no bandgap, while insulators have a large bandgap. Semiconductors have a small bandgap that allows them to conduct electricity under certain conditions.

For example, silicon is a semiconductor with a bandgap of 1.1 eV. At room temperature, some electrons in the valence band gain enough energy to move to the conduction band, creating free electrons and holes in the valence band. The concentration of free electrons and holes depends on the temperature and the doping of the semiconductor.

In summary, the band theory of solids explains how electrons are arranged in a solid and how they conduct electricity. The valence band is the highest energy band that is completely filled with electrons, while the conduction band is the next higher energy band that is empty or partially filled with electrons. The energy gap between the valence band and the conduction band is known as the bandgap and determines whether a solid is a conductor, an insulator, or a semiconductor.

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