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The conductivity depends on the passage of charged particles especially electrons. In metals electrons are easily available in conduction band and so its conductivity is high. As we increase the temperature then core of atoms vibrate largely. So with positive charge it could easily minimize the electrons in the conduction band and hence fall in conductivity

In case of semiconductor there will be usually forbidden gap between valence band and conduction band. So conduction is poor at ordinary temperature. But as we increase temperature that would allow electrons to reach conduction band as covalent bonds get broken. Hence higher conductivity

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Q: Why does the electrical conductivity of pure metal decrease with temperature while that of semiconductors increases?
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