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why does conductivity is calculated as:

conductivity = e.n.Un

e : electron charge n : electron concentration Un : electron mobility

but in intrinsic semiconductors

conductivity = e.n.(Un+Up)

Why does conductivity depend only on electrons in conductors but in semiconductors depends on holes and electrons?

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When the valence electron breaks the covalent bond in the semiconductor it becomes free and contributes to the conductivity. When the electron breaks the covalent bond and becomes free, it leaves a hole at the lattice place from where it got free. The valence electrons which are bound to the covalent bond will see this hole and hop to it. This hopping of electrons that are still bound to the lattice will contribute additionally to the conductivity of the semiconductor. Therefore the total conductivity of the semiconductor depends on free electrons (after breaking the covalent bond) and lattice electrons which are hopping between holes created by electrons that got free.

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