= Joint density of states
{title2=$J(\Omega)=\sum_{v,c}\int\frac{d^dk}{(2\pi)^d}\,\delta(E_c(\mathbf k)-E_v(\mathbf k)-\Omega)$}
For filled valence and empty conduction <energy bands>, the joint <density of states> counts pairs of states at a prescribed interband energy difference. In a direct optical transition the photon momentum is usually negligible compared with a <Brillouin zone> dimension, so initial and final states have nearly the same <crystal momentum>. The absorption spectrum weights this count by transition <matrix elements>; its onset and structure can constrain the <band gap> and <electronic band structure>. Indirect transitions additionally involve <phonons> to supply crystal momentum.
Back to article page
