Group Theory to Understand Band Gap Structure of Semiconductor Oxides

[drizzle]

ehim ehim...hello,
I wonder if anyone knows about “group theory” [= approximation method] which is helpful in describing band gap structure of semiconductor oxides, my main problem is the high symmetry points i.e. gama point which occur at k=0 [the first Brillion zone], how it varies from gama 1 to gama 7 when the bands splits -under the effect of crystal field and spin-orbit splitting- and what do these numbers represent, if anyone have a brief explanation of it please do. also any articles, books or sites that you recommend will be helpful. thanks.

 

[Dr Transport]

Group Theory describes the behavior of energy bands and their symmetry properties, it won't tell you any specifics about semiconductor oxides. If you know the symmetry of the crystal, you'll be able to determine specifics, i.e. if a transition will occur, which transitions are allowed, how bands split under crystal-fields etc. One thing everyone gets confused about is that group theory determines whether or not a transition is allowed, it will not determine the strength.

Look for Tinkham's text on group theory and quantum mechanics, it is terse but if you find a couple of others to help you, it'll be worth it.