Question about level splitting in band theory

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Discussion Overview

The discussion revolves around the concept of level splitting in band theory, particularly in the context of semiconductor devices. Participants explore the behavior of atomic energy levels as atoms come closer together and how this relates to the formation of energy bands.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that when atoms are far apart, they can be treated as individual systems, while closer proximity necessitates considering them collectively.
  • There is a discussion about the terminology of "splitting," with some arguing it is a matter of choice in language rather than a physical phenomenon.
  • Participants note that energy levels do not remain the same across the band, attributing differences in energy to factors such as orbital overlap and Pauli's exclusion principle.
  • One participant provides a conceptual analogy involving discrete energy levels and how they converge into a continuous band as more atoms are added.

Areas of Agreement / Disagreement

While some points, such as the treatment of atoms at varying distances, receive agreement, there are competing views on the terminology and implications of "splitting" and the nature of energy levels in the band. The discussion remains unresolved on several aspects.

Contextual Notes

Participants express varying levels of familiarity with the underlying physics, indicating that some foundational concepts may not be fully addressed or understood, particularly in relation to semiconductor devices.

Who May Find This Useful

This discussion may be useful for individuals studying band theory, semiconductor physics, or those seeking clarification on the behavior of atomic energy levels in condensed matter systems.

ahmeeeeeeeeee
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Hello ,

about the band theory I was confused some how

seeing the attached image I ask :-

1- when the atoms are far away we take a single atom alone as a system , but when atoms get closer we identify them all as the system , right ?!

2- why do we use the word " splitting" , why don't we say that every atom contributes with its _ for example_ 2s level and so the overall 2s can carry more electrons ?!

3- does the whole band have the same energy ?! if so why do we represent the increase of electron's energy by farther " rising" in conduction band ?! and if not why is there difference in energy ?!

4- I have to say that I'm studying this as an introduction to semi-conductor devices not physics course .
 

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1. yes.

2. Its just a choice of word. When describing the graph it seems as if the line is split into two.

3. No. The difference in energy is due to orbital overlap integral.

4. Hahaha. If you want to dig deeper into semiconductor you better learn the physics anyway.
 
To give an informative but non-exact picture, you can first imagine a charge q that has a lot of discrete energy levels around. If you increase the amount of the charge, these levels would get closer to each other (and when you make two atoms close together, it is like that you have a bigger system with larger amount of charges and closer energy levels) so that in the limit you gather a lot of atoms, the levels get very close and make a continuous energy band.
 
Last edited:
1 far away enough that they do not affect each other, that is why we regard them as two alone systems.
2 "splitting" is referring to the energy,
3 of course different as the picture implies due to Pauli's exclusion principle,
 

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