Wondering about law of mass action

[jinyong]

I am wondering why the law of mass action in semiconductors is this relation: n*p=ni^2. Any proof of this why is it not n*p=ni^3 or something...Also why doesn't dopants affect this relationship since doesn't dopants increase the overall number of carriers?

 

[Gokul43201]

Does it even make dimensional sense to write n*p=ni^3? You need to learn how the law is derived - you will find it in any solid state electronics text.

And yes, dopant concentrations are considered in arriving at that final result.