It has long been known empirically that the electric resistance of a semiconductor gas sensor under exposure to a target gas (partial pressure P) is proportional to Pn where n is a constant fairly specific to the kind of target gas (power law).

This paper aims at providing a theoretical basis to such power laws. It is shown that the laws can be derived by combining a depletion theory of semiconductor, which deals with the distribution of electrons between surface state (surface charge) and bulk, with the dynamics of adsorption and/or reactions of gases on the surface, which is responsible for accumulation or reduction of surface charges.

The resulting laws describe well sensor response behavior to oxygen, reducing gases and oxidizing gases.