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Asked in GSEB Board July 2021 · Doping and carrier concentration
Idea: in a pure (intrinsic) crystal the only way to get a free carrier is to break a covalent bond, and thermal energy is what breaks it.
Breaking one bond frees one electron and leaves behind exactly one hole, so carriers are always created in pairs.
There is no impurity adding carriers of one sign only, and recombination also removes them in pairs.
So the two densities stay equal at every temperature: nₑ = nₕ = nᵢ, the intrinsic carrier concentration.
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