Microscopic Origin of the Phenomenological Equilibrium “Doping Limit Rule” inn-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 $\left(3-\right)$-charged cation vacancy in AlN, GaN, InP, and GaAs and the $\left(1-\right)$-charged $\mathrm{DX}$ center in AlAs, AlP, and GaP. This explains the alignment of the pinning energies and predicts the maximum equilibrium doping levels in different materials.