Advanced Solid State Physics

Figure 25: Dispersion relationship for a simple cubic lattice for the empty lattice approximation

If you make a calculation you get nearly the same band structure like in the empty lattice approxi-
mation and additionally you get the gaps at the Brillouin zone boundaries like expected. So this is a
good first approximation for the real band structure.

If you compare two materials, for example the group 4 elements, you see that the structures are al-
ways repeating in various crystals. You just look at the valence electrons (C, Si, Ge all have 4 valence
electrons), the other, inner electrons do not contribute to most of the material properties.