= Solution
A <direct band gap> has its <conduction band> minimum and <valence band> maximum at the same <crystal momentum>. Near-edge absorption or emission can therefore conserve momentum with the electron and photon alone, since optical photon momentum is small on the Brillouin-zone scale. An <indirect band gap> has its extrema at different wavevectors and normally needs a <phonon> or another momentum-transfer process in addition to the photon.
\b[Direct-gap materials are usually preferred for efficient light emission], because the radiative transition avoids the extra phonon-assisted process. Their stronger near-edge absorption also permits thinner photovoltaic absorbers. Indirect-gap materials can nevertheless make excellent solar cells: sufficiently thick optical paths, light trapping, long carrier lifetimes and suitable material quality can compensate for weaker absorption. The direct/indirect distinction alone does not rank every device.
This momentum distinction and the difference between bound exciton lines and the free-pair continuum are treated together in the primary effective-mass absorption theory.<Intensity of Optical Absorption by Excitons by Roger James Elliott>[Abstract, direct versus phonon-assisted indirect transitions]{ref}
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