Band gap - violation of principle of least energy?

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Discussion Overview

The discussion revolves around the concept of the band gap in solid-state physics and its relationship to the principle of least energy. Participants explore whether the existence of a band gap contradicts the idea that systems tend to occupy the lowest available energy states.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question how the existence of a band gap can be reconciled with the principle of least energy, suggesting that the most favorable states should correspond to minimum energy.
  • Others argue that even in the absence of a band gap, electrons occupy energy states that are not the lowest due to the filling of those states, referencing the concept of the Fermi level.
  • A participant clarifies that the states within the band gap are not filled, emphasizing that the definition of a band gap implies the absence of states in that energy range.

Areas of Agreement / Disagreement

Participants express differing views on whether the band gap violates the principle of least energy, and the discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

There are limitations in the discussion regarding the definitions of energy states and the implications of the Fermi level, which are not fully explored or agreed upon.

motoroller
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How does the band gap not violate the principle of least energy? Surely the most favourable states are those with minimum available energy - but there is a gap!
 
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motoroller said:
How does the band gap not violate the principle of least energy? Surely the most favourable states are those with minimum available energy - but there is a gap!

This is a bit puzzling. Why would the existence of a band gap violate principle of least energy? Even if there's no band gap, there are still electrons not in the "lowest" energy state, because those states are filled. That's why you have a Fermi level. So why would there be any problem when there's a band gap?

Zz.
 
ZapperZ said:
This is a bit puzzling. Why would the existence of a band gap violate principle of least energy? Even if there's no band gap, there are still electrons not in the "lowest" energy state, because those states are filled. That's why you have a Fermi level. So why would there be any problem when there's a band gap?

Zz.

But the states in the band gap aren't filled?
 
motoroller said:
But the states in the band gap aren't filled?

There are NO states in the gap!. That, by definition, is what is meant as a "band gap"! There are no states in the single-particle density of states there!

Zz.
 

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