NMR Technique for Determining the Depth of Shallow Nitrogen-Vacancy Centers in Diamond

We demonstrate a robust experimental method for determining the depth of individual shallow Nitrogen-Vacancy (NV) centers in diamond with $\sim1$ nm uncertainty. We use a confocal microscope to observe single NV centers and detect the proton nuclear magnetic resonance (NMR) signal produced by objective immersion oil, which has well understood nuclear spin properties, on the diamond surface. We determine the NV center depth by analyzing the NV NMR data using a model that describes the interaction of a single NV center with the statistically-polarized proton spin bath. We repeat this procedure for a large number of individual, shallow NV centers and compare the resulting NV depths to the mean value expected from simulations of the ion implantation process used to create the NV centers, with reasonable agreement.