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I understand why $n \cdot p = n_i^2$ holds for intrinsic semiconductors, but why is that the equation also holds true in the case of an extrinsic semiconductor?

Here, $n$ is the charge density of the negatively charged particles, $p$ is the density of the positively charged particles and $n_i$ is the carrier concentration.

How is it proved mathematically?

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  • $\begingroup$ Detailed balance still holds. $\endgroup$ – Jon Custer Sep 30 '15 at 21:26
  • $\begingroup$ This relation is valid only when the semiconductor is in thermal equilibrium with the surrounding. $\endgroup$ – user600016 Sep 23 at 14:06

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