In a doped semiconductor the total number of conduction electrons
ne is due to the electrons contributed by donors and those generated
intrinsically, while the total number of holes nh is only due to the holes
from the intrinsic source But the rate of recombination of holes would
increase due to the increase in the number of electrons As a result, the
number of holes would get reduced further Thus, with proper level of doping the number of conduction electrons
can be made much larger than the number of holes