Semiconductor has electron and hole, why not conductor has hole?

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For intrinsic semiconductor, the know its conductivity=2 neμ , where his the number of electron per cubic meter, e is the charge of an electron, μ is the electron mobility.
But if I want to calculate the conductivity of a conductor= neμ.
Why not consider the hole in? Electron leaves its original place to conduction band will leave a hole behind, this is not true in conductor?

Thank you.
 
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The electrons in conductors responsible for electrical conduction are already in the conduction band even at 0K (ie the Fermi level is in the conduction band). That's why we call them "conductors" to begin with.
 
Some do

Some conductors, like tin, do support hole conduction. They are termed semimetals. The classic semimetallic elements are arsenic, antimony, bismuth, α-tin (gray tin) and graphite, an allotrope of carbon. http://en.wikipedia.org/wiki/Semimetal
 
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