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

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SUMMARY

The discussion focuses on the application of the Bohr model to calculate exciton binding energies in semiconductors, specifically highlighting its effectiveness in direct gap semiconductors compared to its significant underestimation in indirect gap semiconductors like silicon (Si) and germanium (Ge). The underestimation factor is approximately three, raising questions about the model's limitations in these materials. The conversation suggests that the discrepancies may relate to the effective mass of holes and electrons used in the Bohr formula, particularly how these masses are averaged in relation to the semiconductor's band gap type.

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  • Understanding of the Bohr model of excitons
  • Knowledge of semiconductor physics, particularly direct and indirect band gaps
  • Familiarity with effective mass theory in solid-state physics
  • Basic principles of exciton binding energy calculations
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  • Research the effective mass of charge carriers in silicon and germanium
  • Explore the differences between direct and indirect band gap semiconductors
  • Study advanced models for exciton binding energy in indirect gap semiconductors
  • Examine the implications of anisotropic effective masses on semiconductor properties
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Physicists, materials scientists, and semiconductor researchers interested in exciton behavior and binding energy calculations in various semiconductor materials.

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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
 
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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.
 

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