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Prove that the Fermi level lies exactly at the centre of the forbidden energy gap in case of an intrinsic semiconductor.
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It can be shown for intrinsic semiconductors that fermi energy level  lies midway between conduction band and valence band. The proof is as follows:

At any temperature (T>0K)

ne = number of electrons in conduction band

nv = number of electrons in valence band

We have, by definition of intrinsic …

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