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I am teaching a modern physics course and we are discussing the way in which
very similar valence electron configuration (2 electrons in a p-shell) leads
to very different conduction behaviors for carbon, silicon, germanium, etc.
My solid state is pretty rusty so I am seeking some help.
As we bring many C atoms together, the 2s and 2p bands mix together.
However, if you bring them even closer together a split occurs, creating the
valence and conduction bands for C, SI, etc.
I am having trouble finding a good sophomore-level description of what
causes the splitting to occur. That is, why don't the 2s and 2p bands just
continue to overlap, forming one huge band? What is the mechanism for the
later split.