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.

Figure 1

The model consists of diamond with an N-$V$ center placed $5\mathrm{nm}$ below the surface and a protective layer covering the surface of the diamond. The lower black dots represent the N-$V$ center, while the upper blue dots represent the free positive charge of the protective material.

Figure 2

The charge noise spectrum: bare diamond (black); with glycerol (blue dashed); with propylene carbonate (red dashed); with dimethyl sulfoxide (black dotted); with perfluoropolyether (green dotted); with polyvinylidene fluoride (navy); and with polymethyl methacrylate (pink dashed). The N-$V$-center diamond with a liquid protective layer exhibits better noise reduction than the bare diamond and the diamond with a solid protective layer in the frequency range $<{10}^6$ Hz.

Figure 3

The (a) imaginary and (b) real permittivities as a function of frequency: bare N-$V$-center diamond (black); with glycerol (blue dashed); with propylene carbonate (red dashed); with dimethyl sulfoxide (black dotted); with perfluoropolyether (green dotted); with polyvinylidene fluoride (navy); and with polymethyl methacrylate (pink dashed). The real part of the permittivity is almost constant with frequency, except at frequencies around $1/\tau$.

Figure 4

The noise spectrum with thickness $1\mu \mathrm{m}$. Thicker surface layers have a higher noise floor. The power-law exponent changes with thickness for liquid-surface layers but remains almost the same for solid-surface layers.