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n.p = (n_i)^2

always holds, where n_i is the intrinsic carrier concentration. This makes sense to me for an un doped semiconductor (sc.). However, for a doped sc., I'm a tad confused.

For an n-doped material say, the electron conc. is approximately (a very good approx. at normal temperatures) the donor concentration, since almost all of them are ionised. This conc. is usually of order say 10^17 cm^3, where as the intrinsic conc. for silicon is about 10^10 cm^3.

How is it that this still holds now for a doped sc?

We have n as the donor conc., and p as the hole conc. (incidentally, this is the hole conc. from hols left when the donor is ionized right?). Yet how is this still equal to the tiny in comparison intrinsic conc., as in the equation?

Cheers for any input!