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The microscopic origin of the doping limits in semiconductors and wide-gap materials and recent developments in overcoming these limits: a review

This paper reviews the recent developments in first-principles total energy studies of the phenomenological equilibrium ‘doping limit rule’ that governs the maximum electrical conductivity of semiconductors via extrinsic or intrinsic doping. The rule relates the maximum equilibrium carrier concentrations (electrons or holes) of a wide range of materials to their respective band alignments. The microscopic origin of the mysterious ‘doping limit rule’ is the spontaneous formation of intrinsic defects: e.g., in n-type semiconductors, the formation of cation vacancies. Recent developments in overcoming the equilibrium doping limits are also discussed: it appears that a common route to significantly increase carrier concentrations is to expand the physically accessible range of the dopant atomic chemical potential by non-equilibrium doping processes, which not only suppresses the formation of the intrinsic defects but also lowers the formation energy of the impurities, thereby significantly increasing their solubility.