Creation of Depth-Confined, Shallow Nitrogen-Vacancy Centers in Diamond With Tunable Density

Technical Summary: Creation of Depth-Confined, Shallow Nitrogen-Vacancy Centers in Diamond with Tunable Density

Problem Statement
Engineering shallow nitrogen-vacancy (NV) centers in diamond is critical for nanoscale quantum sensing, particularly for detecting highly localized fields that decay steeply with distance. Current fabrication methods predominantly rely on low-energy ion implantation. However, this approach suffers from significant variability in NV depth and properties, leading to low yields of usable sensors. For single NVs, this variability necessitates time-consuming post-selection to target specific depths. For ensembles, high implantation dosages required to achieve sufficient density often degrade coherence and contrast due to lattice damage and uncontrolled defect creation. Furthermore, existing shallow NV samples often exhibit poor depth confinement, limiting their sensitivity to surface-proximal targets. While nitrogen delta doping during plasma-enhanced chemical vapor deposition (PECVD) has shown promise for deeper NVs ($\gtrsim 100$ nm), its application to the near-surface regime ($\lesssim 10$ nm) with controlled density and depth confinement has not been thoroughly characterized.

Methodology
The authors prepared diamond samples using nitrogen delta doping during PECVD growth to create shallow NV centers with tunable density and depth. Two primary samples were fabricated:

• Sample A: Grown to contain single, individually resolvable NV centers with a target depth of 5 nm.
• Sample B: Grown to have a 10 nm-deep, densely populated NV layer. The density in this sample was further tuned via subsequent 200 keV electron irradiation and annealing.
• Sample C (Reference): A control sample created via 4 keV nitrogen ion implantation with a target depth of 7 nm.

To characterize the samples, the authors employed:

1. $^1$H NMR Depth Measurement: NV depths were measured by detecting the nuclear magnetic resonance signal from a layer of oil deposited on the diamond surface. This technique allowed for the statistical determination of NV depth distributions for single NVs in Sample A and Sample C.
2. Coherence Measurements: $T_2$ coherence times were measured using Hahn echo and XY8 pulse sequences for single NVs. For the ensemble in Sample B, coherence was evaluated using both XY8 and DROID (dynamical decoupling) pulse sequences to distinguish between surface noise and NV-NV dipolar interactions.
3. Magnetometry Demonstration: The utility of the shallow ensembles was demonstrated by imaging the stray magnetic fields of few-layer CrSBr (a 2D van der Waals magnet) placed atop the diamond surface.

Key Results

• Depth Confinement: The delta-doped Sample A exhibited a mean NV depth of $5.8 \pm 1.6$ nm. In contrast, the ion-implanted reference Sample C showed a mean depth of $8.7 \pm 3.5$ nm. The standard deviation for the delta-doped sample was more than half that of the implanted sample, demonstrating a twofold improvement in depth confinement.
• Single NV Coherence and Sensitivity: Single NVs in Sample A displayed coherence times ($T_2$) that were longer than most literature reports for shallow NVs and comparable to the best implanted samples. While surface proximity induces decoherence, the improved depth confinement allowed for high dipole sensitivity. The calculated dipole sensitivity for the shallowest NV (3 nm deep) suggested the ability to detect a single electron spin on the surface with a unity signal-to-noise ratio in approximately 100 $\mu$s.
• Ensemble Coherence and Interactions: In the high-density Sample B, the coherence time ($T_2$) increased from $27.6 \pm 0.4$ $\mu$s under XY8 sequences to $75.9 \pm 1.2$ $\mu$s under DROID sequences. This 2.7-fold extension indicates that the coherence is limited by NV-NV dipolar interactions rather than surface noise, signifying a low-disorder lattice and surface environment achieved via delta doping.
• Imaging CrSBr: The shallow NV ensemble successfully imaged the magnetic stray fields of few-layer CrSBr at 80 K. The measurements revealed non-zero magnetic fields under odd-numbered layers and vanishing fields under even-numbered layers, consistent with the material's antiferromagnetic interlayer coupling. The magnitude of the detected fields was quantitatively consistent with simulations and larger than prior measurements using deeper NV ensembles.

Significance and Claims
The paper claims that nitrogen delta doping during PECVD growth enables the reliable engineering of highly coherent single and ensemble-based NV sensors near the diamond surface with $\sim 1.6$ nm depth confinement (standard deviation). This technique overcomes the yield and variability issues associated with ion implantation.

The authors assert that this level of control over NV depth and density facilitates:

1. High-Sensitivity Single NVs: Capable of detecting external spins with strong distance-dependent fields.
2. Interaction-Limited Ensembles: Dense ensembles where coherence is limited by NV-NV interactions rather than surface disorder, potentially saturating fundamental bounds on AC sensitivity and serving as a testbed for entanglement-enhanced metrology.
3. Nanoscale Imaging: The ability to image magnetic textures and interfacial physics with high spatial resolution, as demonstrated by the CrSBr imaging.

The work positions shallow, tunably dense delta-doped NV centers as a critical advancement for applications ranging from nanoscale NMR and reporter spin sensing to entanglement-assisted metrology, offering a path toward routine nanometer-scale magnetic field imaging and strong dipole coupling to surface spins.