Sulfur in diamond and its effect on the creation of nitrogen-vacancy defect from ab initio simulations
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2025-03-17 |
| Journal | Physical Review Research |
| Authors | Nima Ghafari Cherati, Anton Pershin, ĂdĂĄm Gali |
| Institutions | GfK (United States), HUN-REN Wigner Research Centre for Physics |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Enhanced NV Creation Yield: Sulfur (S) doping in Chemical Vapor Deposition (CVD) diamond significantly boosts the creation efficiency of negatively charged Nitrogen-Vacancy (NV-) centers, achieving yields up to 75.3% (compared to ~1% in pure diamond).
- Double Donor Mechanism: Substitutional sulfur (Ss) acts as an efficient double donor (Ss2+), which negatively charges mobile vacancies (V-) created during implantation.
- Vacancy Stabilization: Charging vacancies to V- prevents their aggregation into detrimental clusters (like V2), thereby promoting the desired combination of vacancies with implanted nitrogen (Ns) to form NV- centers.
- Dominant Competing Defect: The most stable sulfur-related defect is the Sulfur-Vacancy (SV) complex, which acts as a hyperdeep acceptor and competes with Ss for vacancies.
- Hydrogen Trapping: Both Ss and SV defects effectively trap interstitial hydrogen (Hi) present in CVD diamond, mediating its removal and preventing the formation of NV-Hydrogen (NVH) complexes, thus preserving the NV- centers.
- Improved Coherence: The dominant sulfur-related defects (SV, SVH) are found to be photostable and possess closed-shell or spin-free ground states, providing an electron spin-free environment that supports longer NV- spin coherence times.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Creation Efficiency (S-doped) | 75.3 | % | Highest reported yield (cited experimental context) |
| NV Creation Efficiency (O-doped) | 69.3 | % | Oxygen-doped diamond (cited experimental context) |
| Diamond Band Gap (Calculated) | 5.4 | eV | HSE06 functional calculation (Ec - Ev) |
| Ss Donor Level (Single) | Ec - 1.6 | eV | Substitutional Sulfur (Ss) (+ |
| Ss Donor Level (Double) | Ec - 2.9 | eV | Substitutional Sulfur (Ss) (2+ |
| SH Donor Level (Shallow) | Ec - 1.2 | eV | Sulfur-Hydrogen complex (SH) (+ |
| V(0) Diffusion Barrier (Calculated) | 2.70 to 2.8 | eV | Neutral Vacancy (V) mobility barrier |
| V(-) Diffusion Mobility Temp (Estimated) | ~800 | °C | Temperature required for V- mobility (based on 3.5 eV barrier) |
| SV Formation Binding Energy | 8.7 | eV | V(0) + Ss(2+) reaction (high stability) |
| V2 Formation Binding Energy | 4.2 | eV | V(0) + V(0) reaction (less stable than SV formation) |
| Annealing Temperature (Cited) | 1200 | °C | Temperature used post-implantation (ensures V mobility) |
| Hyperfine Constant (SV-, 33S) | 1120.7 | MHz | Calculated Axx value for the Sulfur atom in SV- defect |
Key Methodologies
Section titled âKey MethodologiesâThe study relies entirely on high-accuracy ab initio simulations using Hybrid Density Functional Theory (DFT) to model defect behavior in diamond.
- Computational Framework: Calculations were performed using the Vienna Ab initio Simulation Package (VASP) employing the Projector-Augmented-Wave (PAW) method.
- Functional Selection: The screened hybrid density functional HSE06 was used (mixing = 0.25, screening = 0.2 1/A). This functional is critical for accurately reproducing the diamond band gap and defect energy levels (accuracy typically 0.1 eV).
- Supercell Modeling: Defects were modeled within a large 4 x 4 x 4 cubic 512-atom supercell to minimize spurious defect-defect interactions. Brillouin zone sampling was restricted to the Î point.
- Structural Optimization: Geometries were relaxed until strict convergence thresholds were met: total energy (10-5 eV) and ionic forces (10-3 eV/A).
- Defect Stability Analysis: Relative stability was determined by calculating the formation energy (Ef) for various charge states (q) as a function of the Fermi level (EFermi), including necessary charge correction terms (Ecorr).
- Defect Chemistry and Binding Energy: The feasibility of complex formation (e.g., SV, SH) was assessed by calculating the binding energy (Eb) between isolated constituent defects (A and B).
- Magnetic Characterization: Hyperfine tensors (A) were calculated for paramagnetic defects (S=1/2 or S=1) to provide spectroscopic fingerprints (Fermi-contact and dipole-dipole terms) for comparison with experimental Electron Paramagnetic Resonance (EPR) data (e.g., W31 center).
Commercial Applications
Section titled âCommercial Applicationsâ- Quantum Computing and Qubits:
- Enables scalable manufacturing of high-density NV- qubit arrays by dramatically increasing the yield of functional NV centers via S-doping.
- The resulting S-doped material provides an electron spin-free environment, crucial for achieving long spin coherence times (T2) necessary for robust quantum operations.
- Quantum Sensing (Magnetometry/Thermometry):
- High-yield NV creation allows for the production of high-sensitivity quantum sensors, as sensor performance scales with the concentration of active NV centers.
- Single-Photon Emitters (Quantum Photonics):
- Facilitates the precise engineering of single-photon sources for quantum communication networks, leveraging the controlled placement and high activation rate of NV centers.
- Advanced Semiconductor Doping:
- Validates sulfur as a highly effective double donor in diamond, offering a pathway for controlled n-type doping in wide-bandgap semiconductor applications where traditional dopants are challenging.
- High-Quality CVD Diamond Production:
- The understanding of how sulfur defects interact with and trap interstitial hydrogen (Hi) is vital for optimizing the post-growth processing (annealing) of high-purity CVD diamond films used in quantum applications.
View Original Abstract
The negatively charged nitrogen-vacancy (NV) center is one of the most significant and widely studied defects in diamond that plays a prominent role in quantum technologies. The precise engineering of the location and concentration of NV centers is of great importance in quantum technology applications. To this end, irradiation techniques such as nitrogen-molecule ion implantation are applied. Recent studies have reported enhanced NV center creation and activation efficiencies introduced by nitrogen molecule ion implantation in doped diamond layers, where the maximum creation efficiency at <a:math xmlns:a=âhttp://www.w3.org/1998/Math/MathMLâ><a:mrow><a:mo>âź</a:mo><a:mn>75</a:mn><a:mo>%</a:mo></a:mrow></a:math> has been achieved in sulfur-doped layers. However, the microscopic mechanisms behind these observations and the limits of the efficiencies are far from understood. In this study, we employ hybrid density-functional-theory calculations to compute the formation energies, charge transition levels, and the magneto-optical properties of various sulfur defects in diamond where we also consider the interaction of sulfur and hydrogen in chemical vapor-deposited diamond layers. Our results imply that the competition between the donor substitutional sulfur and the hyperdeep acceptor sulfur-vacancy complex is an important limiting factor on the creation efficiency of the NV center in diamond. However, both species are able to trap interstitial hydrogen from diamond, which favorably mediates the creation of NV centers in chemical vapor-deposited diamond layers.