Basic question about valence/conduction bands

Question

In most introductions to solid state physics that I've read, they explain the origin, basically, of the band gap as follows: By doing a superposition of the standing waves inside a BZ, one can find two wave equations with different energy bands, with a possible gap between them (the band gap).

However, I have a difficulty relating this to the conduction/valence bands. Is the "lower energy" band always the valence band and the higher one always the conduction band? Or asked in a different way: How do we know that the electrons fill up to the top of the valence band at zero degrees K (which overlaps with the conduction band in metals)? There does not seem to be some inherent mathematical property in the theory which guarantees this?

I hope I am making sense, otherwise I will be happy to clarify my question.
Thanks.

Whit3rd · Answer

In insulators, the valence band and lower bands comprise just enough 
quantum states for the number of electrons in uncharged material.
If there's no thermal energy to promote electrons into higher
bands, the valence band will, at equilibrium, be full.   And since it is
an insulator, there's no electrons in the next higher (conduction) band.

If the material is a metal, some (but not all) the states
in the conduction band are also occupied.

Semiconductors, at absolute zero temperature, turn to insulators.

Basic question about valence/conduction bands

One Answer

Add your own answers!

Ask a Question