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Re: [Phys-l] Band splitting in Carbon (diamond)...



Hi John,

Sorry if my question was ill-posed.

On Mon, Mar 1, 2010 at 2:11 PM, John Denker <jsd@av8n.com> wrote:

On 03/01/2010 01:14 PM, Jeff Loats wrote:

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.

I don't understand this question about "similar" and
"different". Different relative to what? Relative
to metals? To a sophomore-level approximation, and
even better than that, band-structure-wise, diamond
is a carbon copy of silicon.


Their bands are indeed carbon copies (nice pun!) but because of their atomic
separations diamond ends up being an insulator while silicon is a
semiconductor. That is what I mean by similar configurations (same band
structure) but different conduction behaviors.


But let's move on from that issue; the following
questions don't seem to depend on it.

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.

That seems kinda backwards. In the hypothetical lattice
where the atoms are far apart, i.e. zero overlap, the
bands are split. They start out split. This is just the
atomic s-p splitting.

So the question of "continuing to overlap" doesn't arise.


When I say "continuing to overlap" I mean as we bring them closer together.
I didn't state this well at all in my original question. Sorry about that!

As you bring the atoms closer and closer (starting from a large distance)
you first have no overlap between 3s and 3p, then the bonding and
antibonding states from the huge number of atoms create bands which spread
out and overlap, making a huge (as in many states as well as wide energy
range) band that makes lead a conductor, for example. As you continue to
reduce the separation this "huge" band splits again into two equal parts,
which gives us band gaps for Ge, Si and C. It is that final split that I am
fuzzy on.

Jeff