Solid State in tight binding approximation, Brillouin zone, Fermi

Hello,

In few days, I have an examination, and I still have some dark zone in my head! If somebody could help me by giving me some advices/answers/way of reflexion/books to consult, it could be very great!

Here is my questions:
How to determine energy levels and wavefunction of the localized electronic states on
the defect for a periodic lattice?

Electrons on a two dimensional square lattice in tight-binding approximation
-how to obtain band structure?
-how to obtain E(kx; ky) in the first Brillouin zone?
-how to draw the Fermi surface with one and two electrons per site?
-how to determine if it is a metal or insulator?

Thank's a lot

(I'm sorry, but I'm not English speaker, so mistakes are possible;))
 

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