The valence and conduction band of a semi-conductor are often drawn as here click.
This plot has essentially two features and I would like to understand them.
The peak and the valley of the two bands coincide, in what sense is this a characteristic feature for a semiconductor. I mean, I could have that they don't agree at all, would this necessarily mean that my material is not a semiconductor. I don't think so, as this should mostly depend on the energy gap. So why is this important in these drawings?
Both bands are drawn as parabolas ( with opposite curvatures), where does this come from?