Exciton Bohr Radius: What is It & Why Does it Matter?

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SUMMARY

The exciton Bohr radius is defined as the distance between an electron and a hole in an exciton, calculated using the effective mass of both particles. In quantum dots, the exciton Bohr radius can be smaller than the nanoparticle size due to confinement effects, which enhance Coulomb interactions and create discrete energy states. The Bohr radius is derived from considering kinetic energy and Coulomb interaction, and the absence of center-of-mass motion further influences the behavior of excitons in confined systems.

PREREQUISITES
  • Understanding of excitons and their properties
  • Knowledge of the Bohr model and its application to quantum mechanics
  • Familiarity with quantum dots and their confinement effects
  • Basic principles of Coulomb interaction in particle physics
NEXT STEPS
  • Study the effective mass concept in semiconductor physics
  • Explore the mathematical derivation of the Bohr radius for excitons
  • Investigate the role of confinement in quantum dots and its impact on exciton behavior
  • Learn about discrete energy states in quantum mechanical systems
USEFUL FOR

Physicists, materials scientists, and engineers working with semiconductor technologies, particularly those focused on exciton dynamics and quantum dot applications.

bluejay27
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What is the exciton Bohr radius? I understand that the exciton is the paired distance of an electron and hole. How does the Bohr radius play a role in this?
 
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The Bohr radius can be calculated for the Hydrogen atom. To make the translation to an exciton, replace the effective mass by the effective mass of the electron and hole.
 
So for a quantum dot, how can the nanoparticle be smaller than the exciton Bohr radius?
 
The Bohr radius is the radius you get for a free exciton just by considering kinetic energy and the Coulomb interaction. Of course you can reduce the distance between electron and holes by means of confinement as it is done in quantum dots. This results in enhanced Coulomb interaction and discrete energy states as there is no center-of-mass motion.
 
Cthugha said:
The Bohr radius is the radius you get for a free exciton just by considering kinetic energy and the Coulomb interaction. Of course you can reduce the distance between electron and holes by means of confinement as it is done in quantum dots. This results in enhanced Coulomb interaction and discrete energy states as there is no center-of-mass motion.

what do you mean by no center of mass notation?
 

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