Nanoscale electric-field imaging based on a quantum sensor and its charge-state control under ambient condition

Nitrogen-vacancy (NV) centers in diamond can be used as quantum sensors to image the magnetic field with nanoscale resolution. However, nanoscale electric-field mapping has not been achieved so far because of the relatively weak coupling strength between NV and electric field. Here, using individual shallow NVs, we quantitatively image electric field contours from a sharp tip of a qPlus-based atomic force microscope (AFM), and achieve a spatial resolution of ~10 nm. Through such local electric fields, we demonstrated electric control of NV’s charge state with sub-5 nm precision. This work represents the first step towards nanoscale scanning electrometry based on a single quantum sensor and may open up the possibility of quantitatively mapping local charge, electric polarization, and dielectric response in a broad spectrum of functional materials at nanoscale.


Supplementary Note 1: Simulation of the scanning gradient-field images
In our system, we used NVˉ associated with N 15 isotope as probes. Instead of employing nuclear spin state mI=0 for sensing the external electric field 1,2 , we measured the field strength from the frequency shift of mI= ±1/2 states (Fig. 1d). The spin Hamiltonian of ground triplet states of NVˉ under the magnetic field, electric field and hyperfine interaction can be written as: H gs =H el +H hf (1) where (3)  Supplementary Fig. 1d.
Next, we simulated the field-gradient imaging with the same experimental parameters as in Fig. 2b. We simply modeled the conducting tip as a triangular pyramid with equal sides and a finite spherical tip apex at the end, which is consistent with FIB cutting process (see inset in Fig. 2a). Then we simulated its electric field distribution by COMSOL (Fig. 2d). The frequency shifts arising from the projected E ⊥ and E ∥ were calculated through Supplementary Eq. (3) and convolved with the experimental pulsed-ODMR spectra. We fit the pulsed-ODMR resonant peak by the Lorentz function: P= a with a=-0.11 and fFWHM=260 kHz, which were extracted from the experimental data acquired by the same NV in Fig. 2b and c. The simulated scanning field-gradient image ( Fig. 2e) agrees well with the experimental one (Fig. 2b). However, the bias voltage of the tip used in the simulation (-9.6 V) is somewhat smaller than that in experiment (-16 V). We attributed this to the screening effect resulting from the defect donors, hydration layers or induced ions by high voltage near diamond surface 4 , which is not considered in our model. It is possible to quantitatively extract the surface screening effect by modeling the dielectric response of the surface charges on the diamond.
Finally, we simulated the field distribution along the surface normal (E z , denoted as the gray arrow in Fig. 2a) of the same tip model. We could obtain the maximum field strength of 14 MV cm -1 when tip is right above a NV center with the depth of 5 nm (Fig.   2d). The positioning precision of NV center through scanning field-gradient imaging is 4 ~13.9 nm, which is limited by the field gradient of tip and the spectral broadening of pulsed-ODMR (Fig. 2f).

AFM tip
Once the tip or the sample is electrically charged, the noise induced by the oscillating AFM tip can significantly degrade the NV coherence. In order to estimate the effect of tip oscillation on the ODMR line broadening, we adopt the conditions in Fig. 2b, where the tip voltage is -16 V, the horizontal tip-NV distance is about 100 nm, and the field spatial resolution is ~10 nm. Considering the field sensitivity of our NV system (~17.6 kV cm -1 ), the estimated field gradient is ΔE=1.8 kV cm -1 nm -1 .
Next, we ignored the contribution from the parallel component of external field E ∥ to the spin energy level shift and assumed roughly that the field gradient is homogeneous. Then, we obtained the variation of frequency shift (∆ ) under an A.C. electric field induced by the oscillating tip: where A is the amplitude of tip oscillation, =17 Hz cm V -1 , and θ is the angle between [100] and [111] direction of the diamond sample with cos 0.82. This relation suggests that a tip amplitude of ~5 nm will lead to a spectral broadening of 251 kHz, which is comparable to the intrinsic FWHM of the pulsed-ODMR spectra (~300 kHz in our case). Considering that the oscillation amplitude of conventional NV-AFM is typically well above 5 nm, the induced noise will undoubtedly affect the electric-field sensing based on the NV center.

Supplementary Note 3: Highly efficient control of charge state
In order to achieve highly efficient control on the NV charge state, it is necessary to locate the AFM tip to the proximity of NV with nanoscale precision. Thanks to the weak scattered light from the AFM tip, we can roughly guide the tip close to the selected fluorescent NV spot through the confocal image ( Supplementary Fig. 2b). The tip can 5 be also positioned on the NV by simultaneously recording the AFM force signals (frequency shift) when acquiring the confocal image ( Supplementary Fig. 2a). An obvious frequency-shift change will appear at the position of tip because of the laserinduced thermal expansion under high laser powers (typically >200 μW in our experiments). In our case, the scanning speed of laser focus with a diameter of ~300 nm is typically 20~40 μm s -1 , which is faster than the PID parameter of AFM feedback  Supplementary Fig. 4), due to the large weight of its side band below 650 nm. It is known that the laser excitation can induce interconversion between NV 0 and NVˉ, with a larger recombination rate into NVˉ under high excitation powers (>50 μW) 5 . In Fig. 3, we used relatively large laser powers to ensure the sufficient signal-to-noise ratio of PL measurements (400~500 μW).
Therefore, the NV 0 /NVˉ transition is likely smeared out, leading to the absence of such a two-step structure.

Supplementary Note 5: Local contact potential difference measurements
In order to confirm the tip-induced surface polarization during the charge-state control, we performed local contact potential difference (LCPD) measurements on the sample B. To ensure good conductivity of the tip, we treated the tip on graphite first by applying bias pulses (+4~10 V in magnitude and ~200 ms in width) or directly poking into graphite surface by several tens of nanometers. After the treatment, we checked the tip conductivity through the tunneling current at low biases. Typically, a tip with good conductivity only needs a small excitation energy for maintaining preset amplitude of tuning fork (~300 pm during tip treatments). Then, we transferred the tip onto the diamond surface and focused on a single NV. The laser was turned off to avoid the change of surface polarization during the LCPD measurements. To obtain LCPD 7 signals with high signal-to-noise ratio, we need to polarize the selected region under high positive voltages (>+90 V) and large laser powers (>200 μW). The surface polarization before the LCPD measurements in Fig. 4c was induced by a tip bias of +120 V with 1-s integration time per pixel under 420 μW. We polarized a small region of 300×300 nm 2 on the diamond surface and compared the local electrostatic potential inside and outside this region. We didn't perform LCPD measurements on the sample A due to the instability of surface adsorbents on sample A.

Supplementary Note 6: Surface-chemistry dependence of charge-state transition
Since the surface polarization should be very sensitive to the chemical species adsorbed on the diamond surface, we performed a comparison experiment on acidboiled chips (sample A) and isopropanol-immersed chips (sample B) (see Methods).
The AFM images show a much cleaner surface of sample B while the sample A is covered by ~5 nm thick adsorption layers ( Supplementary Fig. 6). In this work, we have However, when we used the nanopillar with a 20-nm diameter for the simulation, the distortion effect in the measured electric field imaging is somewhat more prominent (Supplementary Fig. 8d and h). This is because that the diameter of the nanopillar is close to the size of the conical tip apex (10 nm in this simulation). In addition, we found that the screening effect marginally degrades the spatial resolution of electric-field contour imaging ( Supplementary Fig. 8e-h). However, the spatial resolution shows weak dependence on the size of the diamond pillar, which maintains the level of <10 nm.
Due to the existence of the charged defects and trapped charges on/near the diamond surface, obtaining the absolute strength of electric field is challenging for the NV in diamond. However, since the NV-based electrometry measures external signals in a quantitative manner, this shortcoming can be possibly circumvented by a precalibration procedure. For example, before measuring the target sample by the diamond 9 tip, a metal tip with well-defined tip apex produced by focused ion beams can be used for obtaining the standard electric-field imaging or providing the point-spread function, which is a general method in other NV-SPM techniques 7,8 . Such a reference image can be compared with the COMSOL simulation by the same tip model. Then, the averaged background shielding effect either from the dielectric diamond host or the surface adsorption layers in ambient conditions can be reasonably estimated through this process. An effective dielectric constant, which may have spatial dependence, can be extracted by the pre-calibration and used for calculating the absolute values of local electric fields.
Therefore, we conclude that the flat-top diamond pillar has no obvious effects on the NV-based electric-field imaging as long as the size of diamond host is far larger than the spatial resolution of NV-based electrometry. Typically, for the diamond tip generally used in scanning magnetometry 6 , shallow NVs were grown in a flat-top diamond pillar with a diameter around 200 nm, which corresponds to the optimized size for achieving high-efficiency photon collection and retaining good coherence. We believe that the diamond tip, which has already been extensively used in scanning magnetometry, is also suitable for future applications in scanning electrometry.