Understanding Energy Bands in Solids: A Quick Question on Band Theory

[tomz]

Hello everyone, I have finished high school not long ago, and haven't start my uni. So I take this time to read some physics. I have no one teachs me, the only book I have is 'Giancoli's PHYSICS'. Its a good book (discriptive but not mathematical, which suits me as I haven't done much sophisticate math).

Here is my question, are energy bands for every atoms in a solid (every single atom have energy band). Or the whole solid posses energy band (with each atom still have discrete energy level)? Or should I say the solid posses energy band with atom indistinguishable?

I have searched for a while, but cannot have a clear answer

Thank you for any help

 

[mfb]

Energy bands are a property of the whole solid object. While the individual states within these bands can be local (valence band), the "band" comes from the fact that you have a large amount of atoms in the material.

 

[bcbwilla]

Yeah, energy bands are a property of the solid. I've found images like this one helpful:

http://www4.nau.edu/meteorite/Meteorite/Images/Band.jpg

When you bring together a bunch of atoms to form a material, you suddenly have a bunch of similar energy levels from different atoms all overlapping. The energy levels don't like to sit directly on top of each other, so they kind of shift around, resulting in a bunch of very closely spaced energy levels, or bands.

 

[tomz]

Energy bands are a property of the whole solid object. While the individual states within these bands can be local (valence band), the "band" comes from the fact that you have a large amount of atoms in the material.

Yeah, energy bands are a property of the solid. I've found images like this one helpful:

When you bring together a bunch of atoms to form a material, you suddenly have a bunch of similar energy levels from different atoms all overlapping. The energy levels don't like to sit directly on top of each other, so they kind of shift around, resulting in a bunch of very closely spaced energy levels, or bands.

Thank you very much. I think I may get it.

 

[dlgoff]

... So I take this time to read some physics ... are energy bands for every atoms in a solid (every single atom have energy band). Or the whole solid posses energy band (with each atom still have discrete energy level)? Or should I say the solid posses energy band with atom indistinguishable?

These questions are answered in detail by studying Condensed Matter (Physics of the Solid State). And in particular, the Band Theory of Solids.

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.

 

[tomz]

These questions are answered in detail by studying Condensed Matter (Physics of the Solid State). And in particular, the Band Theory of Solids.

Thank you!

 

[M Quack]

Bands are properties of the whole solid - in principle.

There can be localized electrons "belonging" to a single atom even in a solid. In general, these are the core level electrons that are buried deep inside the atom so that their wave functions don't overlap much with the neighbors. For example the Uranium or Lead 1s electrons in a lead or uranium compound or alloy will remain very localized.

As a rule of thumb, when you look at the "spaghetti diagram" of energy vs. wave vector of the bands, the localized bands will be flat, and the delocalized (with contributions from many atoms) will have a strong dispersion (energy varies a lot).