Question about level splitting in band theory

In summary, the conversation is about the band theory and clarifying some confusion about its concepts. The first question addresses the identification of the system when atoms are far away versus when they are closer. The second question is about the use of the word "splitting" in relation to the energy levels of atoms. The third question discusses the energy levels in a band and the representation of electron energy. The fourth question mentions the purpose of studying the band theory and the need to understand its concepts in relation to semiconductor devices.
  • #1
ahmeeeeeeeeee
21
0
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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  • #2
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.
 
  • #3
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.
 
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  • #4
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,
 

Related to Question about level splitting in band theory

1. What is band theory?

Band theory is a concept in condensed matter physics that explains the behavior of electrons in solids. It describes how electrons in a solid can occupy a range of energy levels, known as bands, rather than just discrete energy levels like in isolated atoms.

2. What is level splitting in band theory?

Level splitting in band theory occurs when the energy levels of electrons in a solid split into multiple bands due to interactions between the electrons and the surrounding atoms or molecules. This splitting can lead to the formation of energy gaps, which determine the conductivity and other properties of the solid.

3. How does level splitting affect the properties of a material?

The level splitting in band theory can significantly impact the properties of a material. For example, the size of the energy gaps can determine whether a material is an insulator, semiconductor, or conductor. Additionally, the shape and position of the bands can affect the material's optical, magnetic, and thermal properties.

4. What factors influence level splitting in band theory?

The level splitting in band theory is influenced by several factors, including the type of atoms or molecules in the solid, the arrangement of these atoms, and the strength of the interactions between the electrons and the atoms. Temperature, pressure, and external electric or magnetic fields can also affect the level splitting in band theory.

5. Can level splitting be observed experimentally?

Yes, level splitting in band theory can be observed experimentally using various techniques such as spectroscopy and photoemission. These experiments provide information about the band structure of a material, including the size and shape of the energy bands and the position of the energy gaps.

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