Classifying Solids: Metals, Semi-Metals & Semiconductors

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    Classification Solids
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Discussion Overview

The discussion centers on the classification of solids into metals, semi-metals, and semiconductors, particularly focusing on their electronic properties and the density of states at the Fermi energy. Participants explore theoretical distinctions and assumptions underlying these classifications.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Eric questions the difference between metals, semi-metals, and semiconductors, particularly regarding the concept of a zero gap.
  • One participant explains that metals have a discontinuous density of states at the Fermi energy, while semi-metals have a small density of states with limited electron and hole pockets.
  • It is noted that highly doped semiconductors can exhibit metallic properties, while un-doped semiconductors have a zero density of states at the Fermi energy.
  • Another participant emphasizes that the discussion assumes non-interacting electrons, which may not always hold true.
  • There is a mention of the density of states of quasi-particles being defined via the Green's function in interacting systems, with acknowledgment that this concept may not apply universally.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding electron interactions and the applicability of certain concepts to metals and semiconductors. The discussion remains unresolved regarding the implications of these assumptions on the classifications.

Contextual Notes

The discussion highlights limitations related to the assumptions of non-interacting electrons and the complexities involved in defining the density of states in various materials.

aihaike
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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.
 
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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.
 
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.
 
genneth said:
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.
 
DrDu said:
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 :wink: But the OP might not have.
 
Thanks for your replies.
That's helpful.
 

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