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.
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.
Electron concentration
The free-electron concentration n can be approximated by
Nv is the effective density of states at the valence band edge given by , with m*h being the hole
effective mass and hPlanck's constant.
Mass action law
Using the carrier concentration equations given above, the mass action law can be stated as
where Eg is the
band gap energy given by Eg = Ec − Ev. The above equation holds true even for lightly doped
extrinsic semiconductors as the product is independent of
doping concentration.