Bohr's model applied to Wannier exciton in indirect gap semiconductors

[Tipi]

Hi all,

I've calculated the exciton binding energies for different semiconductors using the Bohr model. It works remarkably well for direct gap semiconductors, but it is not good for indirect gap semiconductors (in Si and Ge, there is an underestimation by a factor of 3, approximatively).

I'm a little puzzled by this fact. Is anyone have any idea that could explain why the Bohr model doesn't describe well the binding energy of excitons in indirect band gaps semiconductors?

Maybe it's linked to the effective mass of holes and electron used in the Bohr formula? It is not very clear for me how the concept of effective mass is affected by the fact that the gap is direct or not...

Thanks,

TP

 

[TeethWhitener]

Silicon and germanium both have anisotropic effective masses, and they’re averaged differently depending on what property you want to look at. These notes:
https://ecee.colorado.edu/~bart/book/effmass.htm#silicon
are of some relevance to the problem.