Why Can't Electrons Occupy the Band Gap in a Material?

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Discussion Overview

The discussion revolves around the question of why electrons cannot occupy the band gap in a material. Participants explore the theoretical underpinnings of this phenomenon, referencing concepts from quantum mechanics and solid-state physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether it is impossible for electrons to occupy the band gap at any energy level.
  • Another participant draws an analogy with the energy levels of an isolated Hydrogen atom, suggesting that similar principles apply to the band gap in materials.
  • A further participant seeks clarification on the reasons preventing electrons from occupying the band gap.
  • One participant explains Bloch's theorem, stating that in a periodic potential, certain energy levels do not have valid solutions to Schrödinger's Equation, leading to the existence of band gaps where electrons cannot reside.
  • Another participant asserts that the absence of energy levels for electrons in the band gap is the reason they cannot occupy those states.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding regarding the reasons for the existence of band gaps, with some providing analogies and others focusing on theoretical explanations. The discussion does not reach a consensus on the fundamental reasons behind the phenomenon.

Contextual Notes

Participants reference Schrödinger's Equation and Bloch's theorem, but the discussion does not resolve the underlying assumptions or implications of these concepts in relation to the band gap.

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Hello, do you know why no electron can stay in the band gap? Is it impossible at every energy?

Thank you!
 
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Do you know no electron can stay between -13.6eV and -3.4eV energy levels in an isolated Hydrogen atom? Now, apply the analogy.
 
Yes but why they cannot stay there?
What does impede them to stay in that levels^
 
Bloch's theorem says that anytime you have a periodic potential (like in a lattice of a metal or semiconductor where the atoms are equally spaced apart), then the solutions to Schrödinger's Equation will be plane waves, i.e. \psi ~ e^{i kx} where k is the wave number. When you actually solve a particular problem, you will find certain restrictions on k, that is, you will find for certain values of k, no such plane wave solutions exist. Since k is related to the energy, then you also get restrictions on the energy. That is, for certain values of the energy, there will be no valid solutions to Shrodinger's Equation. These energy levels where no solution exists are referred to as Energy gaps, or Band gaps. The reason the electron can't be on one of these gaps is because there is no solution to Shrodinger's equation in these regions, hence they are forbidden.
 
Because there are no energy levels for them to sit in.

Energy levels are time-independent solutions to the Schrödinger equation.

Claude.
 

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