Indirect bandgap

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. The k-vector difference represents a difference in momentum.

Semiconductors that have an indirect bandgap are inefficient at emitting light. This is because any electrons present in the conduction band quickly settle into the energy minimum of that band. Electrons in this minimum require some source of momentum allowing them to overcome the offset and fall into the valence band. Photons have very little momentum compared to this energy offset. 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. Silicon is an indirect bandgap semiconductor, and hence is not generally useful for light-emitting diodes or laser diodes.

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. This can be done by creating a dislocation loop in the silicon. 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. 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. 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. 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.

External links

* [http://ece-www.colorado.edu/~bart/book/book/chapter4/ch4_6.htm B. Van Zeghbroeck's Principles of Semiconductor Devices] at Electrical and Computer Engineering Department of University of Colorado at Boulder
* [http://britneyspears.ac/physics/indirect/indirect.htm Tongue in cheek, but accurate guide to Semiconductor physics]