Surface roughness noise and comprehensive depth-dependent noise effects on coherence time of NV centers in diamond

Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond, causing line broadening and decreasing the coherence time (T₂). We investigate noise caused by the diamond surface roughness, which is a source for charge density fluctuations and incoherent photon scattering. We find that the varying surface charge density noise source is prevalent throughout the entire NV dynamical decoupling frequency range, while the photon scattering noise is almost negligible. Next, we perform comprehensive analyses on T₂ and how it varies with NV depth. At a depth of 5 nm below a hydrogen- or fluorine-terminated surface, these magnetic nuclei reduce the NV coherence time the most, followed by the surface electric field noise sources. The photon scattering, bulk magnetic field noise, and oxygen surface termination effects on T₂ are weak compared to the varying charge density, electric dipole, and surface impurity noise. Our calculated values of T_2,Hahn (μs range) are in good agreement with the experimental values reported elsewhere. Finally, we calculate an anticipated signal-to-noise ratio (SNR) for NV AC magnetometry of external nuclear spins. In our simplified assessment (e.g. some depth dependent parameters are held constant), we find that shallower NV layers should yield the best SNR, which is consistent with experimental findings.