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Updated: Jun 30, 2025
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
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A tight-binding model for illustrating exciton confinement in semiconductor nanocrystals
1Physics and Chemistry of Nanostructures, Ghent University, 9000 Gent, Belgium.
The Journal of Chemical Physics
|March 20, 2024
Summary
This study introduces a new Hubbard model to describe electron-hole interactions in semiconductor nanocrystals. The model captures the transition from weak to strong confinement and exciton delocalization, offering insights into nanocrystal properties.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Quantum Chemistry
Background:
- The Brus equation relates electron-hole pair energy to semiconductor crystallite size.
- Existing models struggle with the transition from weak to strong confinement and associated phenomena.
Purpose of the Study:
- To develop a model that describes the transition from weak to strong confinement in semiconductor nanocrystals.
- To investigate charge-carrier delocalization and changes in transition dipole moment.
- To provide a tool for understanding and teaching confinement effects.
Main Methods:
- Utilized a one-dimensional, two-particle Hubbard model for interacting electron-hole pairs.
- Extended the tight-binding approach with a point-like electron-hole interaction.
- Introduced infinite-well boundary conditions and a dipole operator.
Main Results:
- Exciton states on infinite chains show established relations between Bohr radius, binding energy, and effective mass.
- The model successfully tracks the transition from weak to strong confinement.
- Variations in transition dipole moment were mapped across different confinement regimes.
Conclusions:
- The proposed Hubbard model offers a comprehensive approach to electron-hole interactions in semiconductor nanocrystals.
- It provides a versatile tool for researchers studying confinement effects and exciton behavior.
- The model facilitates exploration and understanding of semiconductor nanocrystal physics.
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