How does band bending occur in condensed matter physics?

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SUMMARY

Band bending in condensed matter physics refers to the variation of energy band edges due to external electric fields, affecting the behavior of Bloch states. The discussion highlights the delocalization of Bloch states across the crystal and the fixed eigenvalues associated with them. It emphasizes the need for a rigorous theoretical framework to understand how eigenvalues can change along the crystal length, particularly in relation to the mean free path of electrons. The inquiry seeks clarification on the theoretical underpinnings of band bending, indicating a gap in understanding that requires further exploration.

PREREQUISITES
  • Understanding of Bloch states and their delocalization in crystals
  • Familiarity with eigenvalues and their significance in quantum mechanics
  • Basic knowledge of electric fields and their effects on semiconductor materials
  • Concept of mean free path in the context of electron transport
NEXT STEPS
  • Research the rigorous theoretical models for band bending in semiconductors
  • Study the impact of electric fields on energy band structures in materials
  • Explore the relationship between mean free path and electron mobility in solids
  • Investigate advanced topics in condensed matter physics, such as quantum transport theory
USEFUL FOR

Students and researchers in condensed matter physics, electrical engineers, and anyone interested in the theoretical aspects of band bending and its implications in semiconductor technology.

Optics_Man
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I'm trained in Condensed Matter Physics, and I'm trying to learn EE. The concept of band bending always baffled me a bit. Here's why: The band edge bloch states are delocalized over the whole of the crystal, and have fixed given eigenvalues. How can this eigenvalue change over the length of the crystal? I have heard some hand waving arguments, that we must conceptually cut up the crystal into chunks which are the size of the mean free path of the bloch electrons, and at each chunk we can consider the eigenvalue to change slightly according to the applied field. My question is: What is the rigorous theory which describes band bending?
I look forward to responses!
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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