Microscopic origin of the phenomenological equilibrium "Doping limit Rule" in n-type III-V semiconductors

The highest equilibrium free-carrier doping concentration possible in a given material is limited by the "pinning energy" which shows a remarkable universal alignment in each class of semiconductors. Our first-principles total energy calculations reveal that equilibrium n-type doping is ultimately limited by the spontaneous formation of close-shell acceptor defects: the (3-)-charged cation vacancy in AlN, GaN, InP, and GaAs and the (1-)-charged DX center in AlAs, AlP, and GaP. This explains the alignment of the pinning energies and predicts the maximum equilibrium doping levels in different materials.