# semiconductors extrinsic and intrinsic carriers concentrations equations

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?

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