Different semiconducting material have different band gaps, that is the
reason why electrons and holes can be trapped into the wells.
I think your problem is the same as the examples from the elementary
quantum mechanics: square well or infinite well problems
Usually, the gap (the energy difference between the first bound state level for
the electron and the first bound state level for
the hole) will shrink with the increase of the well width.
Not sure if I've understood your question here. Aren't you really looking for the band structure calculations for a straightforward band semiconductor (as opposed to the more exotic Mott insulators, for example)? If you are, then (i) it really isn't this trivial and (ii) it should give you both the valence and conduction bands. So I'm not sure how you are able to find literature on the conduction band, but not on the valence band. I would imagine various computational methods once one knows the coordination number of various elements within the unit cell would be able to produce such band structures.