On the basis of band structure, there are two types of semiconductor: direct gap and indirect gap. The difference is that in direct gap semiconductors, the top and bottom of the valance and conduction bands are directly above each other (hence the name). In an indirect gap semiconductor however, the bottom of the conduction band is not directly above the top of the valence band.
This leads to a difference in the process to bring an electron from the valence band to the conduction band. A direct gap semiconductor only requires the transfer of energy (from say a photon) to reach the conduction band while an indirect gap semiconductor requires a change in both energy (from a photon) and momentum (from a phonon) to reach the conduction band.
when there is the highest energy in the valance band at different k-space than the lowest point in the conduction band it is indirect semiconductor i.e bad photon emitter/absorber. The group theory which is dependent on the lattice structure determines how and where band can split, corss and bend(or not) to differentiate the direct and indirect semiconductors.
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