Hydrogen atom pairs in diamond bulk and at the surface: Hybrid density functional theory and cluster models

Abstract

Hydrogen pair defects in bulk diamond and on the (111) surface have been investigated using hybrid density functional theory and cluster models, including relaxation of defect atoms. The ${\mathrm{H}}_{2}^{*}$ defect, consisting of one hydrogen atom in a bond inserted (BI) site and the other in an adjacent ``antibonding'' site, is calculated to be 2.65 eV more stable than two isolated BI hydrogen atoms, and 3.97 eV less stable than two gas phase hydrogen atoms. This is in general agreement with results calculated by other methods that have been reported in the literature. However, when the ``antibonding'' hydrogen atom is on the surface and the BI hydrogen is just beneath it, the energy with respect to two gas phase hydrogen atoms (hydrogen atoms are present in the reactor and are necessary for growth) is stable by 0.95 eV and it is stable by 7.57 eV relative to two bulk BI hydrogens. The hydrogen atom bond to the surface has a strength of 3.89 eV. Such structures have not been reported previously and they may contribute to the excess hydrogen found at diamond surfaces and may provide a route to ${\mathrm{H}}_{2}^{*}$ formation in the bulk.