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

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Discussion Overview

The discussion revolves around the concept of the exciton Bohr radius, its definition, and its significance in the context of excitons, particularly in quantum dots. Participants explore the relationship between the exciton Bohr radius and the effective mass of the electron and hole, as well as implications of confinement in quantum systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the definition of the exciton Bohr radius and its relation to the paired distance of an electron and hole.
  • Another participant explains that the Bohr radius can be calculated for the Hydrogen atom and suggests replacing the effective mass with that of the electron and hole for excitons.
  • A question is raised regarding the scenario of a quantum dot being smaller than the exciton Bohr radius.
  • It is noted that the Bohr radius for a free exciton is derived from considering kinetic energy and Coulomb interaction, with the possibility of reducing the distance between electron and hole through confinement in quantum dots, leading to enhanced Coulomb interaction and discrete energy states.
  • A participant seeks clarification on the term "no center of mass notation" mentioned in the context of excitons and quantum dots.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the exciton Bohr radius and its implications, indicating that multiple competing views remain without a consensus on certain aspects, particularly concerning the effects of confinement in quantum dots.

Contextual Notes

The discussion includes assumptions about effective mass and the nature of confinement in quantum dots, which may not be fully explored or defined. The implications of these assumptions on the exciton Bohr radius and related concepts remain unresolved.

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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