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

In summary, the speaker has calculated exciton binding energies using the Bohr model for different semiconductors. While it is accurate for direct gap semiconductors, it underestimates by a factor of 3 for indirect gap semiconductors such as silicon and germanium. They are puzzled by this and wonder if it is related to the effective mass used in the Bohr formula. They mention that silicon and germanium have anisotropic effective masses and provide a resource for further information.
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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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  • #2
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.
 

1. What is Bohr's model and how does it apply to Wannier excitons in indirect gap semiconductors?

Bohr's model is a simplified representation of the structure of atoms, proposed by Niels Bohr in 1913. It states that electrons orbit the nucleus in discrete energy levels, and can jump between levels by absorbing or emitting energy. This model can be applied to Wannier excitons in indirect gap semiconductors, where an electron is excited from the valence band to the conduction band, leaving behind a positively charged hole. The electron and hole are then bound together by the Coulomb force, forming an exciton.

2. What is an indirect gap semiconductor and how does it relate to the Wannier exciton?

An indirect gap semiconductor is a type of material where the minimum energy point of the conduction band does not align with the maximum energy point of the valence band. This means that for an electron to transition from the valence band to the conduction band, it must also change its momentum. In this type of material, Wannier excitons are formed when an electron and hole are bound together by the Coulomb force, as described by Bohr's model.

3. How does the Bohr model help us understand the properties of Wannier excitons in indirect gap semiconductors?

The Bohr model allows us to calculate the energy levels of the exciton, as well as the binding energy between the electron and hole. This information is crucial for understanding the stability and behavior of Wannier excitons in indirect gap semiconductors. It also helps us understand the exciton's interaction with light and other external factors.

4. What are the limitations of using Bohr's model to describe Wannier excitons in indirect gap semiconductors?

Bohr's model is a simplified representation of the complex behavior of electrons in atoms and can only be applied to a limited range of materials. It does not take into account the effects of quantum mechanics, such as electron spin, which play a crucial role in the behavior of Wannier excitons in indirect gap semiconductors. Therefore, while the Bohr model can provide a basic understanding of exciton properties, it cannot fully explain their behavior in these materials.

5. How does the study of Wannier excitons in indirect gap semiconductors contribute to advancements in technology?

Wannier excitons have unique properties that make them useful for various applications, such as optoelectronic devices, solar cells, and quantum computing. By studying their behavior in indirect gap semiconductors, scientists can gain a deeper understanding of how to control and manipulate them for specific purposes. This knowledge can lead to the development of new and improved technologies in various fields.

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