  Noise is a detrimental issue for nitrogen-vacancy (NV) centers in diamond,
causing line broadening and decreasing the coherence time (T2). Following our
previous electric and magnetic field noise work, 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 combine the results from various noise sources to perform
comprehensive analyses on T2 and how it varies with NV depth. At a given NV
depth of 5 nm below a hydrogen- or fluorine-terminated surface, we find that
these magnetic nuclei reduce the NV coherence time the most, followed by the
surface electric field noise sources. The photon scattering and bulk magnetic
field noise effects on T2 are weak compared to the varying charge density,
electric dipole, and surface impurity noise. However, with oxygen surface
termination, the surface electric field noise becomes comparable to the surface
magnetic field noise. Our calculated values of T2,Hahn (few microseconds to ten
microseconds) 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,
where some depth-dependent parameters (e.g. NV conversion efficiency) are held
constant, we find that shallower NV layers should yield the best SNR, which is
consistent with experimental findings.
