Interaction of hydrogen with boron, phosphorus, and sulfur in diamond

The production of $n$-type doped diamond has proved very difficult. Phosphorus, and possibly sulfur, when in substitutional sites in the lattice, forms a donor which could be used in electronic devices. Boron, which is a relatively shallow acceptor, can be passivated by hydrogen, and it is possible that some of the difficulties in producing electrically active donors could be due to their passivation by the hydrogen which is present during the chemical vapor deposition growth of diamond. We report ab initio modeling of these dopants and their complexes with hydrogen in diamond and show that it is energetically favorable for hydrogen to be trapped and to passivate boron and phosphorus. We predict that sulfur with one hydrogen atom produces shallow donor levels in the band gap of diamond with a previously unconsidered configuration being the most stable and producing the shallowest level. We show that the S-H pair is stable under conditions of limited H availability. Further, we show that it is energetically favorable for both P-H and $\mathrm{P}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ to dissociate forming $\mathrm{H}_{2}{}^{*}$. H diffusion in $n$-type P-doped diamond is inhibited by this formation of immobile $\mathrm{H}_{2}{}^{*}$. This is in contrast to B-doped diamond, where we predict that $\mathrm{H}_{2}{}^{*}$ will dissociate in the presence of substitutional B atoms, forming B-H complexes. We demonstrate that the recently observed shallow $n$-type conductivity is unlikely to arise from $\mathrm{B}\text{\ensuremath{-}}{\mathrm{D}}_{2}$ complexes, because these complexes would dissociate into B-D plus a distant deuterium interstitial. We also predict that they would induce deep levels in the band gap.