Mass-Action Law of Semiconductors
In an intrinsic semiconductor at thermal equilibrium, carrier generation and recombination rate will be balanced so that net carrier density is constant. Also the concentrations n and p, of the electrons and holes are equal.

For any semiconductor,

$$ np = n_i^2 $$ 

Where ni is known as intrinsic career concentration of the semiconductor. This relation is called mass action law.

When an intrinsic semiconductor is doped with a dopor impurity like Phosphorus, electron concentration will increase, due to the surplus electron provided by each of the doper atom. Hole concentration remains the same. The net effect is -> \$ np&gt; n_i^2 \$ . But mass action law has to be obeyed in the doped semiconductor too. So when it is doped, recombination rate will increase from its earlier rate to reduce the hole concentration. It drives the semiconductor back to the thermal equilibrium. i.e,\$ np = n_i^2 \$ . 

So yes, Recombination Process is the sole reason for reducing the hole concentration while doping. Recombination Processes are of different types : band to band , auger recombination etc.