  The need of near-surface color centers in diamond for quantum technologies
motivates the controlled doping of specific extrinsic impurities into the
crystal lattice. Recent experiments have shown that this can be achieved by
momentum transfer from a surface precursor via ion implantation, an approach
known as ``recoil implantation.'' Here, we extend this technique to incorporate
dielectric precursors for creating nitrogen-vacancy (NV) and silicon-vacancy
(SiV) centers in diamond. Specifically, we demonstrate that gallium
focused-ion-beam exposure to a thin layer of silicon nitride or silicon dioxide
on the diamond surface results in the introduction of both extrinsic impurities
and carbon vacancies. These defects subsequently give rise to near-surface NV
and SiV centers with desirable optical properties after annealing.
