Direct Band Gap

Implications for 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. The involvement of the phonon makes this process much less likely to occur in a given span of time, which is why radiative recombination is far slower in indirect band gap materials than direct band gap ones. This is why light-emitting and laser diodes are almost always made of direct band gap materials, and not indirect band gap ones like silicon.