Vacancy-impurity complexes and limitations for implantation doping of diamond

Many candidates have been proposed as shallow donors in diamond, but the small lattice constant means that many substitutional impurities generate large strains and thus yield low solubilities. Strained impurities favor complex formation with other defects and, in particular, the lattice vacancy. We report the results of first-principles calculations regarding the geometry, electronic structure, and energetics of impurity-vacancy complexes in diamond and show that such complexes explain the generally low doping efficiency for implanted material.