Mass action law (electronics)


In electronics and semiconductor physics, the law of mass action is a relation about 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:

Carrier concentrations

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
where

Hole concentration

The free-hole concentration p is given by a similar formula
where

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.