In case of intrinsic semiconductors, the product of n and p is a constant for a certain semiconductor at a certain temperature and is given by
There is no condition in the expression that restricts it to intrinsic semiconductors because Eg does not change with impurity concentration and Nc and Nᵥ are constants. This product is therefore a constant equally valid for intrinsic as well as for extrinsic semiconductors.
Denoting the electron concentration in n-type semiconductor by nₙ and the hole concentration by Pₙ we can write
The law of mass action is very important relation because it in conjunction with charge neutrality condition enables us calculate minority carrier concentration.
The minority carriers decrease in number below the intrinsic value because the majority carriers increase the rate of re-combinations.
The law of mass action states that the product of majority and minority carriers remains constant in an extrinsic semiconductor and it is independent of the amount of donor and acceptor impurity concentrations.
Note that when the doping is heavy, the minority carrier concentration will be low and if doping is lighter, the minority carrier concentration will be larger.
