In electronics and semiconductor physics, the law of mass action relates the concentrations of free electrons and electron holes under thermal equilibrium. It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration . The intrinsic carrier concentration is a function of temperature.
The equation for the mass action law for semiconductors is:
In semiconductors, free electrons and holes are the carriers that provide conduction. For cases where the number of carriers are much less than the number of band states, the carrier concentrations can be approximated by using Boltzmann statistics, giving the results below.
The free-electron concentration n can be approximated by
where
The free-hole concentration p is given by a similar formula
where
Using the carrier concentration equations given above, the mass action law can be stated as
where E<sub>g</sub> is the band gap energy given by E<sub>g</sub> = E<sub>c</sub> â E<sub>v</sub>. The above equation holds true even for lightly doped extrinsic semiconductors as the product is independent of doping concentration.