Indirect and direct band gaps in silicon

[Aun-shi]

Hi

This semester my group and I are calculating the band structure of silicone (bulk and nano crystals).
In bulk silicon a indirect band gap occurs, where the highest occupied valence band and the lowest unoccupied conduction band are situated at different k-values.

Does anyone know why this actually happens? If you have some literature that gives a valid explanation I would appreciate it.

Another interesting thing is when quantum confining silicon structure the indirect band gap becomes direct. Does anyone know why reducing the size of silicon result in a more direct band gap? Also here if anyone has some literature that explains it I would appreciate it.


Thanks!

 

[TeethWhitener]

There isn’t a single reason for why some materials have a direct band gap and others have an indirect band gap. The lattice parameters, crystal symmetry, and nature of the orbitals involved will all play a role in determining the band structure of the material, and I doubt there’s an easy way to tell whether the gap will be direct or indirect without explicitly solving the electronic structure.

That said, you are correct that geometry and particle size can play a role in band structure. A very famous recent example is MoS₂, which has a layered structure. A single layer has a direct band gap whereas 2 or more layers stacked in their native rhombohedral state have an indirect gap.