Help Understanding Energy Band Diagram

In summary: The red line is supposed to represent the total energy of the system, but it only goes up to +4 on the x-axis which is supposed to represent the nucleaus of the atom. Beyond that, the line just disappears. Additionally, the y-axis is labeled "energy", but it's not clear what it is supposed to represent.
  • #1
es
70
0
I come across the attached diagram in electrical engineering books quite often and, not being a physics text, they often fail to explain it. I tried to do my homework by spending a couple of hours on google trying to figure out the answer to my question myself, but all I can find online are summaries lacking any real meat or explanations practically identical to my text's.

Some help with my diagram:
I am copying a "diagram of a cross section of the total energy surface" of an SI atom. The red lines are total energy. The +4 on the x-axis is supposed to be the nucleaus of the SI atom plus 10 inner electrons. I left out the 3s2 layer purposely to keep the diagram cleaner.

My questions are:
I get the y-axis but what is the x-axis susposed to be? Is it the radius of the orbital circumference, the diameter of the orbital circumference, or something else entirely? My guess is the later because I cannot figure out how either can pass through zero on the x-axis for an outer shell. I guess what I really want to know is, how was the cut made through the total energy surface? Are all the electrons in the same surface, but occuping different points on that surface. Or do they actually have a unique surface? I think the "unique energy level" criteria (Pauli Exclusion Principle) could be satisfied either way. I dunno, perhaps my real problem is with visualizing the energy surface...

This diagram is supposed to provide "deep insight" into the operation of semiconductor devices so I really would like to understand it.

Thanks for your time,
es
 

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  • #2
es said:
I come across the attached diagram in electrical engineering books quite often and, not being a physics text, they often fail to explain it. I tried to do my homework by spending a couple of hours on google trying to figure out the answer to my question myself, but all I can find online are summaries lacking any real meat or explanations practically identical to my text's.

Some help with my diagram:
I am copying a "diagram of a cross section of the total energy surface" of an SI atom. The red lines are total energy. The +4 on the x-axis is supposed to be the nucleaus of the SI atom plus 10 inner electrons. I left out the 3s2 layer purposely to keep the diagram cleaner.

My questions are:
I get the y-axis but what is the x-axis susposed to be? Is it the radius of the orbital circumference, the diameter of the orbital circumference, or something else entirely? My guess is the later because I cannot figure out how either can pass through zero on the x-axis for an outer shell. I guess what I really want to know is, how was the cut made through the total energy surface? Are all the electrons in the same surface, but occuping different points on that surface. Or do they actually have a unique surface? I think the "unique energy level" criteria (Pauli Exclusion Principle) could be satisfied either way. I dunno, perhaps my real problem is with visualizing the energy surface...

This diagram is supposed to provide "deep insight" into the operation of semiconductor devices so I really would like to understand it.

Thanks for your time,
es

First of all, you need to be "less sloppy" on your notation. I spent several minutes trying to figure out what is "SI atom". Please note that atomic symbols are often case-sensitive. So silicon is "Si", not "SI".

Secondly, a "band diagram" is not about the atom itself. The atom has lost its individuality when it forms a solid. So the bands are really the "hybridization" of all the orbitals that have overlapped and form a continuum of states for the solid.

Thirdly, in a crystal structure, the ions that make up the solid form a regular pattern or location in space. So where these ions are located are usually the potential energy well. The red line is trying to show that, but doing it very poorly, because it (i) ignores that there are other repeated potential well and (ii) it seems to show that a charge carrier in that semiconductor as always confined unless it is above the vacuum state.

It is a poorly drawn sketch.

Zz.

P.S. The y-axis is energy, sometime called binding energy.
 
  • #3
es said:
This diagram is supposed to provide "deep insight" into the operation of semiconductor devices so I really would like to understand it.
Looking at that picture, I can not disagree more. I strongly recommend you abandon that diagram and get a fundamental understanding of semiconductor physics from a regular solid-state physics textbook.
 
  • #4
Wow, I had no idea things were so badly depicted. Perhaps that's why I was so confused.

I did know that as atoms are added to a crystal, electrons states split due to the Pauli exclusion principle and that in a real solid, due to the large number of atoms, the bands become a continuum. So I previously assumed the diagram was just trying to show the simplified case where the number of atoms in the solid was one. I guess this is an invalid case for a band diagram.

Also, sorry about the notation confusion.

I was looking to understand the physics that underlies the operation of a MOSFET but perhaps it would be better to just study solid-state physics first. Can you recommend a textbook suitable for self study? I do have a good working knowledge of linear algebra, calculus and differential equations.

Thanks for the help.
 
  • #5
Kittel's Introduction to solid state physics is a fairly standard introductory text. Your mathematical skills should be enough but you should also know a bit of quantum mechanics.
 

1. What is an energy band diagram?

An energy band diagram is a graphical representation of the energy levels of electrons in a material. It shows the different energy levels available to electrons and how they are filled according to the material's properties.

2. How is an energy band diagram used in materials science?

An energy band diagram is used to understand the electrical and optical properties of materials. It helps scientists predict how materials will behave in different conditions and how they can be used in various applications.

3. What do the different energy bands in a diagram represent?

The different energy bands in a diagram represent the energy levels available to electrons in a material. The valence band is the highest energy level that is fully occupied by electrons, while the conduction band is the lowest energy level that is partially occupied by electrons. The band gap is the energy difference between the two bands.

4. How does temperature affect the energy band diagram of a material?

As temperature increases, the energy bands in a material become broader due to thermal energy. This results in more available energy levels for electrons to occupy, which can affect the material's electrical and optical properties.

5. Can energy band diagrams be used to explain the behavior of semiconductors?

Yes, energy band diagrams are commonly used to explain the properties of semiconductors. They show how the band gap in a semiconductor material can be manipulated to control the flow of electrons, making them useful for electronic devices like transistors and diodes.

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