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We can distinguish semiconductors from metals by saying that metals still conduct at absolute zero whereas semiconductors don't.

Does this still apply to doped semiconductors which have an excess of electrons or holes? What happens to these charge carriers at absolute zero? Why can't they be freely moving the way electrons in metals are?

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    $\begingroup$ Because they are tied back to the dopants. No thermal energy means no way of exciting the carriers into the conduction or valence bands. $\endgroup$
    – Jon Custer
    Commented Aug 19, 2020 at 13:36

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I'll need to revisit the theory about this topic in particular to ensure I'm not saying anything wrong, but my first instinct/thaught would be that there is still a gap between the band and the dopant level. Since the dopants are tied to the dopping levels (a bit above the valence band or a bit under the conduction band), and that there is no thermal energy, they can't jump the gap to the next band, preventing them to conduct current. Hope this answer gives you a good starting point to understand the situation.

Cheers

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