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In the case of semiconductors the intrinsic charge carrier concentration N, always remains constant. This explains the decrease in number of holes when donor impurities are added to an intrinsic semiconductor and the decrease in number of free electrons when acceptor impurities are added. Is there any explanation for the constancy of this intrinsic charge carrier concentration?

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Assuming a pure semiconductor, the intrinsic carrier concentration is due to thermal excitation of electrons from the valence band to the conduction band. This depends on properties of the semiconductor that are constants, e.g. the band gap, so for a particular material at a particular temperature the intrinsic charge carrier concentration is a constant. However the carrier concentration depends on temperature. See for example this paper by Misiakos and Tsamakis.

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