Because the product of the electron and hole concentrations is a constant
independent of impurity concentration at a given temperature, the introduction
of a small proportion of a suitable impurity to increase n, say, must decrease p.
This result is important in practice—we can reduce the total carrier concentration
n p in an impure crystal, sometimes enormously, by the controlled introduction
of suitable impurities. Such a reduction is called compensation.
In an intrinsic semiconductor the number of electrons is equal to the
number of holes, because the thermal excitation of an electron leaves behind a
hole in the valence band. Thus from (43) we have, letting the subscript i denote
intrinsic and