# Bands in semiconductors: $E$ vs. $k$ diagram

I always thought that in a semiconductor there was one gap, one conduction band and one valence band. However, reading a book I came across this picture

And now I'm very confused. Apparently there aris an infinite number of gaps (i.e. forbidden energy bands). Is this so? And what about the conduction and valence bands? Which of all the bands in the graphic corresponds to them?

Also, do all the electrons in the conduction or valence band have the same energy? Or can they differ? Because from this graphic, it appears that electrons with different $k$ can belong to the same band but have different amounts of energy $E$. Is this correct or not?

• In the case of silicon, I understand that its energy levels 1 and 2 are fully occupied, so the energy level 3 would be the valence one, right? Does this mean that the first two allowed bands are full and the third one (corresponding to $2\pi /a < |k|<3\pi /a$) would be the valence band? If this is right, then I believe the next band will be the conduction band. And what about the next bands? Can electrons go up there? Do they exist or what? – Tendero Jun 15 '16 at 22:22