Band Gap in a Square Quantum Well

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SUMMARY

The discussion focuses on the variation of the direct band gap in Gallium Arsenide (GaAs) as it relates to the width of a square quantum well. It is established that the energy difference between the first bound state levels of electrons and holes decreases with increasing well width. The conversation highlights the challenge of determining the valence band in comparison to the conduction band, emphasizing the need for band structure calculations in semiconductors. The importance of computational methods and knowledge of coordination numbers for accurate band structure analysis is also noted.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically square and infinite well problems.
  • Familiarity with semiconductor physics, particularly direct band gaps in materials like GaAs.
  • Knowledge of band structure calculations and their significance in semiconductor analysis.
  • Experience with computational methods for material science, including effective mass considerations.
NEXT STEPS
  • Research band structure calculations for semiconductors using tools like Quantum ESPRESSO.
  • Explore the effective mass approximation in semiconductor physics.
  • Study the coordination number's role in determining electronic properties of materials.
  • Investigate the differences between conduction and valence band calculations in semiconductor materials.
USEFUL FOR

Researchers, physicists, and engineers in the fields of semiconductor technology and quantum mechanics, particularly those focused on band gap analysis and quantum well structures.

John.Blair571
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How does a direct band gap (like that in GaAs) vary with its well width?
 
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Different semiconducting material have different band gaps, that is the
reason why electrons and holes can be trapped into the wells.
I think your problem is the same as the examples from the elementary
quantum mechanics: square well or infinite well problems
Usually, the gap (the energy difference between the first bound state level for
the electron and the first bound state level for
the hole) will shrink with the increase of the well width.
 
It has been easy to find literature for the calculation of the conduction band, but how does one determine the valence band? Is it by the same means, only with a different effective mass?
 
Not sure if I've understood your question here. Aren't you really looking for the band structure calculations for a straightforward band semiconductor (as opposed to the more exotic Mott insulators, for example)? If you are, then (i) it really isn't this trivial and (ii) it should give you both the valence and conduction bands. So I'm not sure how you are able to find literature on the conduction band, but not on the valence band. I would imagine various computational methods once one knows the coordination number of various elements within the unit cell would be able to produce such band structures.

Zz.
 

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