The electrical conductivity of semi-conductors involving inclusions of another phase

Inclusions of metal or a metal oxide of a higher valence state in a base metal oxide may provide clouds of excess electrons or holes, respectively, surrounding the individual inclusions as space charge layers without charge compensation by other defects in the base metal oxide. The electrical potential and furthermore the concentration of electrons and holes as a function of radial distance from an included particle of the second phase is calculated and the resulting overall electrical conductivity of the two-phase sample is estimated.