Silicon is a semiconductor with a band gap. I am curious about how exactly it forms these bands. I am bit confused if it goes to SP3 hybridization giving 4 SP3 hybrid orbitals or does the 3P levels splits into bonding and antibonding orbitals? Which theory is more appropriate?
The first proposition is the correct one, although the actual picture is somewhat more complicated, in that there is also some contribution from the d orbitals, and more (crystal field breaks the rotational symmetry of the individual atoms whereby one has in principle a mixture of all possible atomic orbitals consistent with the symmetry of the problem). The attached pictures may help. You could appreciate these pictures by imagining the forms of the atomic orbitals and consider the atomic distances in Si crystal. By doing so, you will notice substantial overlap between the s and p orbitals in the bond regions. Ideally, you should carry out a tight-binding calculation based on the construction of a Bloch sum on the basis of the atomic s and p orbitals, along the lines described in Chapter 10 of the book by Ashcroft and Mermin (Solid State Physics).
https://www.flickr.com/photos/mitopencourseware/3362461639/in/set-72157615387820466/
http://inac.cea.fr/L_Sim/TB_Sim/
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