Band Gap Formation: Bragg Reflection & Standing Waves

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SUMMARY

The discussion centers on the formation of band gaps in solids, specifically how they arise due to lattice potential and Bragg reflection at the zone boundary. It is established that at the zone boundary, a traveling wave reflects and transforms into a standing wave, which is a key mechanism in band gap formation. The mathematical representation of this phenomenon involves the superposition of traveling waves, resulting in a total wave vector of zero, thereby creating a standing wave. This understanding is crucial for grasping the behavior of waves in solid-state physics.

PREREQUISITES
  • Understanding of lattice potential in solid-state physics
  • Knowledge of Bragg reflection and its role in wave behavior
  • Familiarity with wave mechanics, particularly traveling and standing waves
  • Basic mathematical skills to interpret wave equations
NEXT STEPS
  • Study the principles of Bragg's law in crystallography
  • Explore the mathematical derivation of standing waves from traveling waves
  • Investigate the implications of band gaps in semiconductor physics
  • Learn about the role of lattice structures in electronic properties of materials
USEFUL FOR

Physicists, materials scientists, and students studying solid-state physics who seek to understand the mechanisms behind band gap formation and wave behavior in crystalline structures.

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band gap arises due to lattice potential.band gap is produced at zone boundary due to bragg reflection.there it behaves like standing wave instead of traveling wave?further formation of 2 standing waves?please help
 
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i tried best to clear my question,
band gap in solids arises due to lattice potential.this lattice potential has max. effect at zone boundary.band gap is produced at zone boundary due to bragg reflection of traveling wave.after reflection it becomes standing wave instead of traveling wave?howz this possible?please help
 
I'm not an expert, but I here's my opinion:

Yes, bandgap arises from the bragg reflections at the zone boundary. the traveling wave becomes a standing wave - I agree. How is this possible? The mathematical definition of traveling wave is: Amplitude * cos( k * x - omega * t), where k is the wavevector of the wave, omega is its characteristic frequency, x and t are spatial and time coordinates. When traveling wave suffers a reflection off the zone boundary there's an equal but opposite traveling wave (reflected part). By superposition then, the total k of the wave is zero - hence standing wave.
 

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