Classifying Solids: Metals, Semi-Metals & Semiconductors

[aihaike]

dear all,

I don't quite get the difference between a metal, a semi metal and a semiconductor with zero gap.
So far I thought that e metal was a material with a zero gap, that does not seem to me right.
Can someone provide me a little explanation?
Thanks,

Eric.

 

[DrDu]

They differ in the density of states at the fermi energy (or in some other effective single particle property). In a metal the (quasi-) particle density is discontinuous at the Fermi Energy.

In a semi-metal like bismuth or graphite the density of states at the fermi energy is discontinuous but very small as there are only some small electron and hole pockets.

In the case of semi-conductors, the situation is more complicated, as e.g. a highly doped semiconductor can be metallic.
However, in an un-doped semiconductor, the density of states is zero at and around the Fermi energy. In a semi-conductor with zero gap, it is zero only at the Fermi energy but it is still continuous there.

 

[genneth]

By the way, all this is predicated on the assumption that electrons are non-interacting. Although this works well for many things, it is not always true. I've found graduate students who did not really understand this point.

 

[DrDu]

By the way, all this is predicated on the assumption that electrons are non-interacting. Although this works well for many things, it is not always true. I've found graduate students who did not really understand this point.

No, that's why I was talking about the DOS of quasi-particles which can be defined via the Greens function of the interacting system in a neighbourhood of the Fermi-energy. But admittedly, there are systems where even this concept breaks down. But I wouldn't speak of metals or semiconductors in the latter case.

 

[genneth]

No, that's why I was talking about the DOS of quasi-particles which can be defined via the Greens function of the interacting system in a neighbourhood of the Fermi-energy. But admittedly, there are systems where even this concept breaks down. But I wouldn't speak of metals or semiconductors in the latter case.

I know you know But the OP might not have.

 

[aihaike]

Thanks for your replies.
That's helpful.