I have learned from a text book of electronics that the free electron density, n (which is equal to that of hole, p) of intrinsic semiconductor due to thermal excitation is a function of temperature and the relation is given by
ni = B T3/2 e-Eg/2kT
Since, both p and n are equal, we can write, np = ni2
Now, when some doping materials are added with doping concentration ND >> ni, it is assumed that now free electron density n = ND
In the book, it says that though impure atoms are now added in the intrinsic semiconductor but we still can write, np = ni2
My question is, since we have added impurity which provides more free electrons in the semiconductor, shouldn't the value of np > ni2?