Energy vs. momentum for a semiconductor with an indirect band gap, showing that an electron cannot shift from the lowest potential in the conduction band (green) to the highest potential in the valence band (red) without a change in momentum, possibly assisted by a phonon. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid

In semiconductor physics, an indirect bandgap is a bandgap in which the minimum energy in the conduction band is shifted by a k-vector relative to the valence band. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Solid state physics and related applied fields a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states In the Physics field of Semiconductors and insulators the conduction band is the range of Electron Energy, higher than that of the A wave vector is a vector representation of a Wave. The wave vector has magnitude indicating Wavenumber (reciprocal of Wavelength) and the The k-vector difference represents a difference in momentum. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product

Semiconductors that have an indirect bandgap are inefficient at emitting light. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 This is because any electrons present in the conduction band quickly settle into the energy minimum of that band. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Electrons in this minimum require some source of momentum allowing them to overcome the offset and fall into the valence band. In Solids the valence band is the highest range of Electron energies where electrons are normally present at Absolute zero. Photons have very little momentum compared to this energy offset. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The momentum "kick" of a photon being emitted or absorbed is negligible and direct transitions are essentially 'vertical' in k-space.

Since the electron cannot rejoin the valence band by radiative recombination, conduction band electrons typically last quite some time before recombining through less efficient means. Spontaneous emission is the process by which a light source such as an Atom, Molecule, Nanocrystal or nucleus in an Excited state Silicon is an indirect bandgap semiconductor, and hence is not generally useful for light-emitting diodes or laser diodes. Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 A laser diode is a Laser where the active medium is a Semiconductor similar to that found in a Light-emitting diode.

However, the indirect (non-radiative) recombination takes place at point defects or at grain boundaries (surface) in Si. If the excited electrons are prevented from reaching these recombination places, they have no choice but to fall back into the valence band by radiative recombination. In Solids the valence band is the highest range of Electron energies where electrons are normally present at Absolute zero. Spontaneous emission is the process by which a light source such as an Atom, Molecule, Nanocrystal or nucleus in an Excited state This can be done by creating a dislocation loop in the silicon. Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 At the edge of the loop, the planes above and beneath the "dislocation disk" are pulled apart, creating a negative pressure, which raises the energy of the conduction band substantially, with the result that the electrons cannot pass this edge. In the Physics field of Semiconductors and insulators the conduction band is the range of Electron Energy, higher than that of the Provided that the area directly above the dislocation loop is defect-free (no non-radiative recombination possible), the electrons will fall back into the valence shell by radiative recombination and thus emitting light. Spontaneous emission is the process by which a light source such as an Atom, Molecule, Nanocrystal or nucleus in an Excited state This is the principle on which "DELEDs" (Dislocation Engineered LEDs) are based.

Likewise the absorption of light at an indirect gap is much weaker than at a direct one. As in the emission process both the laws of conservation of energy and of momentum must be observed, the only way to promote an electron from the top of the valence band to the bottom of the conduction band is to simultaneously emit (or absorb) a phonon that compensates for the missing momentum vector. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid However, such a combined transition has a much lower probability. This means, for example, that silicon is at a disadvantage as a potential solar material compared to a direct gap material like CuInSe₂.

The absorption (read: color) of an indirect bandgap material usually depends more on temperature than that of a direct material, because at low temperatures (e. g. 4K) phonons are not available for a combined (vibronic) process. Silicon e. g. starts to transmit red light at these temperatures, because red photons do not have sufficient energy for a direct process.

In some materials with an indirect gap the value of the gap is negative, i. e. the top of the valence band is higher than the bottom of the conduction band in energy. Such materials are known as semimetals. A semimetal is a material with a small overlap in the energy of the conduction band and Valence bands However the bottom of the conduction band is

External links

• B. Van Zeghbroeck's Principles of Semiconductor Devices at Electrical and Computer Engineering Department of University of Colorado at Boulder
• Tongue in cheek, but accurate guide to Semiconductor physics