Fig. 2: NV-based nanoscale scanning electrometry and quantitative estimation.

a Schematic graph showing the simple triangular-tip model with a spherical tip apex. \({E}_{\perp }\) and \({E}_{\parallel }\) (green lines) are projected onto a NV with a depth of d at a tip height of h. During the simulation, we set \({\varepsilon }_{{\rm{d}}}\) = 5.7 for diamond material. Inset: Scanning electron microscope (SEM) image of FIB-treated tungsten tip. Scale bar: 1 μm. b Scanning field-gradient imaging obtained at −16 V with ODMR setpoint of 700 kHz. The dashed arrows reflect the direction and magnitude of field gradient. c Scanning field-gradient imaging of the tip under different biases. AFM setpoint: \({\triangle f}_{{\rm{AFM}}}\) = +10 Hz. Pulsed-ODMR setpoint: \(\triangle f\)=400 kHz. d Simulated field distribution along the surface normal (E_z) from the triangular-tip model (a) with a side length of 220 nm, apex radius of 30 nm, h = 1 nm, d = 5 nm and bias = −150 V. A field strength as large as 14.1 MV cm⁻¹ can be experienced by the NV. e Simulated scanning-field gradient image at the bias = −10 V. The ODMR setpoint is set to be 700 kHz. The non-spherical shape arises from both the triangular tip and the fact that NV axis is not perpendicular to diamond surface. Scale bars in b, d, and e are 100 nm. f A series of simulated scanning gradient-field images under the same geometric parameters as in (e), demonstrating a precision of 13.9 nm for positioning the NV underneath.