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Concept
Direct and indirect band gaps
Summary
In semiconductor physics, the band gap of a semiconductor can be of two basic types, a direct band gap or an indirect band gap. The minimal-energy state in the conduction band and the maximal-energy state in the valence band are each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are different, the material has an "indirect gap". The band gap is called "direct" if the crystal momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
Examples of direct bandgap materials include amorphous silicon and some III-V materials such as InAs and GaAs. Indirect bandgap materials include crystalline silicon and Ge. Some III-V materials are indirect bandgap as well, for example AlSb.
Radiative recombination
Interactions among electrons, holes, phonons, photons, and other particles are required to satisfy conservation of energy and crystal momentum (i.e., conservation of total k-vector). A photon with an energy near a semiconductor band gap has almost zero momentum. One important process is called radiative recombination, where an electron in the conduction band annihilates a hole in the valence band, releasing the excess energy as a photon. This is possible in a direct band gap semiconductor if the electron has a k-vector near the conduction band minimum (the hole will share the same k-vector), but not possible in an indirect band gap semiconductor, as photons cannot carry crystal momentum, and thus conservation of crystal momentum would be violated. For radiative recombination to occur in an indirect band gap material, the process must also involve the absorption or emission of a phonon, where the phonon momentum equals the difference between the electron and hole momentum. It can also, instead, involve a crystallographic defect, which performs essentially the same role.
Official source
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