Electric Noise Spectra of a Near-Surface Nitrogen-Vacancy Center in Diamond with a Protective Layer

Surface noise is a detrimental issue for sensing devices based on shallow nitrogen-vacancy (N-V) color-center diamonds. A recent experiment indicates that electric-field noise is significant compared to magnetic-field noise. They also found that the electric-field noise can be reduced with a protective surface layer, although the mechanism of noise reduction is not well understood. We examine the effect of a protective surface layer on the noise spectrum, which is caused by surface-charge fluctuations. We use the fluctuation-dissipation theorem to calculate and analyze the noise spectrum for six different surface-layer materials typically used for N-V-center diamond devices. We find that four parameters largely affect the noise spectrum: the effective relaxation time, the effective loss tangent, the power-law exponent of the noise spectrum, and the layer thickness. Our results suggest that a surface-covering layer is indeed useful for decreasing surface noise, but which material is most suitable depends on the device operational frequency range.