Types of energy range in a solid where no electron states can exist
In semiconductors, 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 hydrogenated 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.
Energy vs. crystal momentum for a semiconductor with an indirect band gap, showing that an electron cannot shift from the highest-energy state in the valence band (red) to the lowest-energy state in the conduction band (green) without a change in momentum. Here, almost all of the energy comes from a photon (vertical arrow), while almost all of the momentum comes from a phonon (horizontal arrow).Energy vs. crystal momentum for a semiconductor with a direct band gap, showing that an electron can shift from the highest-energy state in the valence band (red) to the lowest-energy state in the conduction band (green) without a change in crystal momentum. Depicted is a transition in which a photon excites an electron from the valence band to the conduction band.Bulk band structure for Si, Ge, GaAs and InAs generated with tight binding model. Note that Si and Ge are indirect band gap with minima at X and L, while GaAs and InAs are direct band gap materials.
