Interband transition

An interband transition moves an electron between distinct energy bands. A direct optical transition approximately conserves crystal momentum because optical photon momentum is small compared with a reciprocal lattice vector. A phonon-assisted transition can supply the momentum difference needed near an indirect band gap. Transition energies alone do not fix their optical intensities, which also depend on matrix elements and occupations.

An optical interband transition that requires another momentum source, commonly a phonon, to connect initial and final electronic wavevectors. Near an indirect band gap, phonon emission gives a threshold photon energy $E_g+\hslash \Omega$, while phonon absorption gives $E_g-\hslash \Omega$ and requires an occupied phonon mode. The temperature dependence of the absorption therefore contains phonon-population information in addition to electronic occupations.

A photon-induced interband transition that approximately preserves the electron's crystal wavevector because the photon momentum is small compared with reciprocal-lattice momenta. Its strength depends on the dipole matrix element and the joint density of states. A direct band gap permits such a transition between the band-edge states, but optical selection rules can still suppress it.

A vertical direct transition at a common wavevector puts an electron above the conduction edge and leaves a hole below the valence edge. Their parabolic kinetic energies are inversely proportional to their effective masses. The excess photon energy is therefore split as $K_e/K_h=m_h^{\ast }/m_e^{\ast }$, rather than equally unless the masses match. The initial valence electron energy is $-K_h$ relative to its band maximum; the final conduction energy is $E_g+K_e$.

Absorption in which a photon excites an electron between different energy bands, requiring an occupied initial state, an available final state and a nonzero transition matrix element. Indirect band-edge transitions also need momentum transfer, commonly through a phonon. Such absorption can prevent optical transmission even above a metal's free-carrier plasma edge.