quantum mechanics - What information can we extract from the electronic band structure?

I have some difficulty in understanding the electronic band structure.I want know that for a 3D crystal,what information can I extract from its complicated band structure,for example the band structure of the SiC(I downloaded this figure from google).And what intuition that I can build for such a complicated band structure?

Answer

The most useful information you can extract from the band structure for an insulator like SiC involves: (1) the value of the bandgap (the energy difference between the highest occupied band--the valence band--and the lowest unoccupied band--the conduction band); (2) the direct or indirect nature of the band gap (direct if the valence band max occurs at the same k point as the conduction band minimum, and indirect otherwise); and (3) the band dispersion or the slope of the bands involved in the band gap--steeper slopes indicate stronger orbital interactions and faster carrier mobility, on the other hand an ionic crystal will have very flat bands.