# What is the solid body gang theory

## Transparency of solids using band gaps and relationship to conduction and valence bands

The following is the beginner's guide to the band structure. I've taken considerable liberties with the details to simplify this, so don't take it too literally!

This will be a strange place to start, but consider filling the atomic orbitals in an atom with electrons. If you take a noble gas, e.g. B. Xenon, each orbital is completely filled with two electrons, which is why xenon is inert. If you take potassium instead, you will find that all of the lower orbitals are filled with two electrons, but the outermost orbital contains only one electron, so the orbital is only half full. That is why potassium is very reactive.

When you group atoms into a solid, the interactions between the atoms distribute the sharp atomic orbitals into energy bands. Assuming our solid contains n xenon atoms, then each band 2 can contain n electrons. But each xenon atom contributes 2 electrons to each band, so the energy bands in solid xenon are all full. That is why solid xenon is an insulator. In the case of potassium, all of the lower energy bands with 2 are full n electrons, but the upper band contains only n electrons, meaning it is only half full because each potassium atom has only 1 electron left to get into that band. That is why solid potassium is a conductor.

The position of an electron in an energy band determines not only its energy, but also its momentum. If you want to move an electron so that it can conduct electricity, you have to change its momentum and therefore you have to change its position in the energy band. When the bands are full you cannot change the energy / momentum of an electron because there are no free spaces in the band for the electron to move into. Therefore, filled tapes isolate and partially filled tapes conduct.

Now if you imagine taking your solid matter and filling the energy bands with electrons, there will be a most highly occupied band and a lowest unoccupied band. Now the nomenclature can be a little confusing. When the most occupied band is full (like solid xenon) it tends to be called Valence band and the lowest unoccupied band as Conduction band called . The energy difference between the ligaments is that Band gap . The reason we have the lowest unoccupied band this Call conduction band, is that all electrons excited into it conduct; Electrons in the valence band do not conduct (because the valence band is full).

However, if the highest-occupied band is only partially full (like solid potassium), we call this this band Conduction band, because the electrons it contains can conduct. In fact, the highest band is both that Valence band as well as that Conduction band but convention dictates that we do it that Call the conduction band . With metals, we are usually not concerned about the lowest unoccupied band and band gap because they are not part of the power line.

Now for transparency. When a photon interacts with an electron, it transfers its momentum to the electron, that is, it changes the momentum of the electron. However, if you remember from above, you cannot change the momentum of an electron in a full band. The only way to change the electron momentum is to hit it hard enough, that is, with enough energy, to jump over the band gap into the lowest unoccupied energy band. So if you measure optical absorption as a function of energy, you will find little absorption until the photon energy matches the band gap and the absorption suddenly increases. For many materials, the band gap energy corresponds to ultraviolet light, so the solid does not absorb visible light, ie it is transparent. As you say, these solids are also insulators because the same mechanism (change in electron pulse) determines both conductivity and optical absorption.

In metals, the lowest occupied band (the conduction band) is only partially full, so the electron momentum can be changed by any amount. Therefore, metals absorb light (and radio waves, etc.) very strongly and are opaque.

By the way, you get borderline cases. Pure silicon is an insulator, but the band gap is only about 1.12 eV and this is less than the wavelength of red light. So silicon absorbs light even though it is an insulator. Well it's an insulator in the dark. As soon as you shine light on it, the electrons that excite you across the band gap conduct electricity, so when you shine light on it, silicon conducts.

I hope all of this helps. If you would like to clarify any of the above, please comment.

### Neon22

This is super useful and very clear, thanks. I notice that the transparent metals like ITO (en.wikipedia.org/wiki/Indium_tin_oxide) are right on the verge of conduction and transparency. Now I understand why. Cheers...