Law of Mass Action

If n is the mass concentration of free electrons and p is the concentration of holes then the law of mass action states that the product of concentrations of electrons and holes is always constant, at a fixed temperature.
Mathematically it is expressed as,
nP = ni2                                              ................(1)
where ni is intrinsic concentration.
Important Observations
1. The law can be applied to both intrinsic and extrinsic semicoductors.
2. As ni depends on temperature, the law is applicable at a fixed temperature.
3. In case of extrinsic semiconductors, ni is the intrinsic concentration of the basic semiconductor material used.
Note : The law can be used to find the electron and hole densities in intrinsic semiconductors.
1.1 Law of Mass Action for Extrinsic Semiconductors
In extrinsic materials,
1. In case of extrinsic semiconductors, ni is the intrinsic concentration of the basic semiconductor material used.
2. For n-type material n = nn while P = pn  hence law can be stated as,
nn pn = ni2                                        ..............(2)
3. For p-type material n = np while P =  pp hence law can be stated as,
np pp = ni2                                            ..............(3)
4. The law is applicable irrespective of amount of doping.
5. The law can be used both majority and minority carrier concentrations in an extrinsic semiconductor.