Band Theory

Band theory can help characterize different insulators, semi-conductors, and conductors. It provides a way to visualize how electrons behave in a material and why certain materials have specific electrical and thermal properties.

Principles

Electrons around an atom are organized into orbitals according to their discrete energy levels. These energy levels are quantized, and orbitals are filled starting from the lowest to the highest. However, in solid materials, these energy levels overlap causing energy bands to form. The spacing and size of these bands depend on the nature of the material and its atomic structure. Since there are effectively an infinite energy levels in an atom, there are an infinite number of potential bands. Among these, two important bands surrounding a band gap are given specific names:

1. Valence band: The valence band is the highest band that is fully occupied by electrons at 0 degrees kelvin. This band is composed of the valence orbitals of the atom.
2. Conduction band: The conduction band is the lowest unoccupied band above the valence band. Electrons in this band are free to move and contribute to electrical conductivity.

The band gap is the separation of the bands. The properties of this gap determine whether a material behaves as an insulator, semi-conductor, or conductor.

1. Insulator: An insulator's band gap is relatively "large", and is typically greater than 4eV. The large gap prevents electrons from gaining enough energy to "jump" to the conduction band from the valence band, making the material a poor conductor.

1. Semi-conductor: A semi-conductor's band gap is "small", ranging from 0.1eV to 4eV. This gap allows electrons that gain sufficient energy (thermally or optically) to jump to the conduction band and allowing conductivity. Semi-conductors can be doped to shift the band gap up or down.

1. Conductors: Conductors have no significant band gap and electrons can freely move between the valence and conduction band.

Band Theory and Material Properties

In addition to electrical conductivity, the behavior of electrons within bands also determines a material's properties such as its thermal conductivity and optical properties.

1. Thermal Conductivity: Free electrons within conductors contribute to heat transfer.

1. Optical Properties: The absorption and emission of light in semiconductors are tied to transitions between valence and electron bands. For example: materials with large energy band gaps that are insulators (such as glass) appear transparent, since the minimum energy required for the photoelectric effect is great, and absorbed light is simply remitted.