# Band Gap Theory

Just theory, not a problem.

Is what differentiates a conductor from a semiconductor that the Fermi level has empty orbitals very close in energy to it so that electrons can be mobile in the conduction band?

So what is the largest band gap you can have before you call the material a metal?

Antimony and Tellurium would be the 2 most metallic "metal/non-metal hybrids," and I found that: "Antimony telluride (Sb2Te3) is a small bandgap semiconductor with a gap of 0.28 eV"

So how much smaller before some compound would be considered a metal? And the focus of the differentiation between semiconductor/metal is the band gap right?

## Answers and Replies

Simon Bridge
Homework Helper
In the band theory of solids:
... the atomic energy levels smear out to become energy bands... the concept of "orbitals" no longer makes sense.

But you are correct - in that model, a solid is an insulator or a semi-conductor depending on the size of the band-gap. To be a conductor, the band gap must be zero or less ... the valence and conduction bands overlap.

note: The definition of "a metal" predates band theory.

I feel like I'm still not getting something:

Out of my Atkins textbook:
"Thus, the conventional distinction between an insulator and a semiconductor is related to the band gap and is not an absolute distinction like that between a metal (incomplete bands at T= 0) and a semiconductor (full bands at T=0)."

Does he mean complete/incomplete as in this picture:
http://en.wikipedia.org/wiki/File:MalloryBrendanTom1.jpg

where the metal has its CB and VB bands merged, so that you can't say that its VB is complete, while an intrinsic elemental semiconductor like Silicon would necessarily have a complete VB? If so, is this the statement that justifies that there cannot be a positive energy difference between the CB and VB of a metal?

p.s. where can I find the original definition of "metal"? Is it just something that's lustrous?

Simon Bridge
Homework Helper
In those pictures, then bands are, for some reason, represented as parabolas.
The shaded part represents the energy levels that are occupied.

The pic for the metal just shows the conduction band... you can see that there are electrons in it, but the band is not completely full. In the others, the bands are either full or empty.

Definition of metal:
http://en.wikipedia.org/wiki/Metal
... depends on which discipline you want.
Chemically metals are covalent crystals with high conductivity etc.

Ah, so metals automatically don't even have a valence band! just one sloshed together conduction band!

Thank you!

Simon Bridge