Band gap

Lore & Background

The band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is closely related to the HOMO–LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, electrons cannot move within the solid because there are no available states, and no current can flow. However, if some electrons transfer from the valence band to the conduction band, current can flow via carrier generation and recombination. Every solid has its own characteristic energy-band structure, and this variation is responsible for the wide range of electrical characteristics observed in various materials. Depending on the dimension (one, two, or three dimensions), the band structure and spectroscopy can vary. Band gaps can be either direct or indirect, depending on the electronic band structure of the material. For a direct band gap, the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band have the same value; for an indirect band gap, they are not the same, and electronic transitions must undergo momentum transfer. Band-gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular-beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors, laser diodes, and solar cells. The band-gap energy of semiconductors tends to decrease with increasing temperature, as described by Varshni's empirical expression.

Reader's Guide

The band gap is a fundamental concept in solid-state physics and chemistry, serving as the key parameter that distinguishes insulators, semiconductors, and conductors. Its significance lies in its direct influence on electrical conductivity: materials with large band gaps are insulators, those with small band gaps are semiconductors, and conductors have very small or no band gaps due to overlapping valence and conduction bands. The band gap determines the energy required to excite electrons from the valence to the conduction band, enabling charge carrier mobility and current flow. In semiconductor physics, the band gap is central to understanding intrinsic conductivity, which is strongly dependent on the band gap and thermal excitation of electrons. The concept enables band-gap engineering, a critical technique for designing semiconductor alloys and layered materials used in heterojunction bipolar transistors, laser diodes, and solar cells. The distinction between direct and indirect band gaps affects the efficiency of electronic transitions, with direct band gaps allowing direct excitation of valence electrons. The band gap also varies with temperature and external pressure, and in quantum dot crystals, the effective band gap grows with decreasing dot size due to quantum confinement. Laser-induced insulator-metal transitions have been experimentally observed in systems like thin films of C60, doped manganites, and vanadium sesquioxide V2O3, representing special cases of metal-to-nonmetal transitions. The band gap remains a cornerstone for understanding and engineering electronic properties of materials.

Did You Know?

• The band gap is closely related to the HOMO–LUMO gap in chemistry.
• Substances with large band gaps are generally insulators, while those with small band gaps are semiconductors.
• Laser-induced insulator-metal transitions have been experimentally observed in thin films of C60, doped manganites, and vanadium sesquioxide V2O3.
• The band-gap energy of semiconductors tends to decrease with increasing temperature, as described by Varshni's empirical expression.