Imaging crystal stress in diamond using ensembles of nitrogen-vacancy centers

We present a micrometer-scale-resolution stress imaging method with millimeter field-of-view for diamonds containing a thin surface layer of nitrogen-vacancy (NV) centers. In this method, we reconstruct stress tensor elements over a two-dimensional field of view from NV optically detected magnetic resonance (ODMR) spectra. We use this technique to study how stress inhomogeneity affects NV magnetometry performance and show how NV $M_{z,\kappa }$ imaging is a useful and direct way to assess these effects. This tool for mapping stress in diamond will aid optimization of NV-diamond sensing, with wide-ranging applications in the physical and life sciences.

Figure 1

Schematic of the combined NV stress and birefringence imager. The NV stress imager (blue labels) uses a 532-nm laser to illuminate the diamond, an applied microwave field to drive transitions between NV ground-state sublevels, and a bias magnetic field. The birefringence imager (maroon labels) uses a light-emitting diode (LED) illuminator, two linear polarizers, and a quarter-wave plate. Both imagers use the same microscope and CCD camera (black labels) to collect and image the transmitted light. The photograph on the right shows the diamond sample A studied in this work.

Figure 2

(a) NV centers in the diamond lattice, with the four N-V axes shown in green [18]. Carbon atoms are black, nitrogen atoms are red, and vacancies are gray. (b) Example ODMR spectrum with $\vec{B}=\{220,593,1520\}\mu \mathrm{T}$ in the diamond chip coordinate system (fit function plotted in red). The labels indicate the resonances from the different NV orientations. Each NV resonance is split into three lines due to hyperfine interactions with the spin-1 ${}^{14}\mathrm{N}$ nucleus.

Figure 3

Example NV $M_{z,\kappa }$ and $\{{\sigma }_{\text{diag}},{\sigma }_{XY},{\sigma }_{XZ},{\sigma }_{YZ}\}$ maps for sample A. After measuring the $M_{z,\kappa }$ maps in the top row from the NV resonance frequencies, we calculate the stress tensor element maps in the bottom row using Eqs. (9)–(12). The diamond chip has high-stress and low-stress regions, and most of the $M_{z,\kappa }$ inhomogeneity comes from ${\sigma }_{\text{diag}}$ and ${\sigma }_{XY}$ stress terms.

Figure 4

Birefringence ${sin}^{-1}|sin\delta |$ and NV stress maps for the lower-left corner region of sample A. Both techniques show similar phenomena, though the NV stress imaging maps are immune to the $\delta >\pi /2$ phase ambiguity, can resolve the petal-shaped defects localized in the NV layer, separate out strain phenomena into different stress tensor contributions, and predict how strain features affect the NV magnetic microscopy performance.

Figure 5

(a) Enlarged $M_{z,\kappa }$ map (lower left corner of Fig. 3), showing the locations of the example pixels. (b) Fitted ODMR spectra for example pixels (i), (ii), and (iii) (green, red, and blue, respectively). Each has varying $M_{z,\kappa }$ gradients and offsets. (c) Derivatives $F^{\prime }\left(f\right)$ for the ODMR line shapes plotted in panel (b). Pixel (i) has the best $C/\mathrm{\Gamma }$ slope and two-point responsivity, while pixel (ii) has a good $C/\mathrm{\Gamma }$ slope but a poor two-point responsivity since the $M_{z,\kappa }$ offset means we probe this pixel at a suboptimal microwave frequencies compared to the others. Pixel (iii) has poor $C/\mathrm{\Gamma }$ slope and two-point responsivity due to the high $M_{z,\kappa }$ inhomogeneity in this pixel.

Figure 6

Comparisons between $M_{z,\kappa }$, $C/\mathrm{\Gamma }$ slope, and two-point responsivity for common strain feature types found in sample A. The $C/\mathrm{\Gamma }$ and responsivity maps are related to the magnetic microscopy performance when using the full-sweep method and the two-point method, respectively. Note that the two-point responsivity is more susceptible to $M_{z,\kappa }$ inhomogeneity, while the full-sweep method can tolerate some range of $M_{z,\kappa }$ offsets.