# Semiconductors and energy bands

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?

The bands appear as parabolas due to the dispersion of a quasi-free electron/hole $$E(k) = \frac{\hbar^2 k^2}{2 m^{\ast}}$$