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?
Best Answer
There is one relevant gap in semiconductor physics: the gap between the highest fully occupied energy band (valence band) and the lowest unoccupied band (conduction band). But there are also gaps between other energy bands. The thing is just that they are not very relevant for the semiconducting effect. Between full bands they have no effect because there is no transition possible between full bands and between empty bands well ... they are empty anyways, aren't they? As to which band in the graphic corresponds to which band, this depends on the semiconductor we are talking about. Note that the energy bands (or surfaces/volumes in 3D k-space) of real materials often look a lot more complicated. Electrons can belong to the same band and have different energies, that is correct. Each band represents an intervall of possible energies that the electrons in this band can take on. But as there is an energy gap between conduction and valence band, an electron in the conduction band has at least the amount of that energy gap more energy than the electron in the valence band.