Measuring the stress tensor in nitrogen-doped CVD diamond using solid-state quantum sensor
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2025-08-18 |
| Journal | Science and Technology of Advanced Materials |
| Authors | Takeyuki Tsuji, Shunta Harada, Tokuyuki Teraji |
| Institutions | National Institute for Materials Science, Nagoya University |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This study successfully measured the full residual stress tensor in nitrogen-doped Chemical Vapor Deposition (CVD) diamond films using Nitrogen-Vacancy (NV) centers as solid-state quantum sensors.
- Core Achievement: Direct, unique measurement of the six independent components of the residual stress tensor (σxy, σyz, σzx, and the sum of axial stresses σxx + σyy + σzz) in a CVD diamond film.
- Stress State: The film exhibited significant residual compressive axial stress, averaging 1.52 GPa.
- Volumetric Change: This compressive stress caused a calculated volumetric decrease of 0.073% in the CVD diamond film.
- Shear Dominance: The film was primarily subjected to shear stress in the z-direction (growth direction), with shear strains (εyz and εzx) being up to ten times greater than the in-plane shear strain (εxy).
- Mechanism Identified: The incorporation of nitrogen during CVD growth is considered the primary cause of the observed compressive stress and subsequent volume reduction.
- Methodology: The stress tensor was derived from the shift in the Optically Detected Magnetic Resonance (ODMR) spectra of the NV centers, mapped spatially using confocal microscopy.
- Engineering Implication: Stress evaluation is crucial for improving quantum device performance, as residual stress degrades the spin coherence time (T2) of NV centers.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Film Thickness | 20 | µm | Homoepitaxial CVD diamond |
| Substrate Type | HPHT type-Ib (100) | N/A | Diamond substrate |
| Axial Stress Sum (σxx + σyy + σzz) | 1.52 (± 0.05) | GPa | Average residual compressive stress |
| Shear Stress (σyz) | -0.39 (± 0.02) | GPa | Average residual stress component |
| Shear Stress (σzx) | -0.67 (± 0.02) | GPa | Average residual stress component |
| Volumetric Strain (εv) | -0.073 | % | Decrease due to compressive stress |
| Maximum Shear Strain (εzx) | 0.12 | % | Strain component in the [001] growth direction |
| Nitrogen Density [N] | ~13 | ppm | Estimated in the CVD film |
| NV Center Density | ~0.1 | ppm | Estimated in the CVD film |
| Spin Coherence Time (T2) | ~13 | µs | Measured in the low-defect area |
| Zero-Field Splitting (D) | 2.87 | GHz | NV electronic ground state parameter |
| Stress Susceptibility (a1) | 4.86 | MHz/GPa | Used for axial stress calculation |
| Elastic Compliance (s11) | 0.952 x 10-3 | GPa-1 | Diamond constant |
Key Methodologies
Section titled “Key Methodologies”The experiment involved the growth of nitrogen-doped CVD diamond followed by high-resolution stress mapping using quantum sensors.
- Substrate Preparation: A 500 µm-thick HPHT type-Ib (100) single crystal diamond was used as the substrate, polished along the [110] direction.
- CVD Growth Parameters: A 20 µm homoepitaxial film was grown under oxygen-adding conditions to minimize dislocation generation:
- Pressure: 110 Torr.
- Microwave Power: 1.4 kW.
- Temperature: 1020-1090 °C.
- Gas Ratios: 10% CH4, 10% N2, and 2% O2 (relative to total gas flow).
- Defect Screening: Grazing Incident Reflection Synchrotron X-ray Topography (XRT) and birefringence microscopy were used to identify and select a 260 µm x 260 µm area with low defect density for precise stress measurement.
- Quantum Sensing Setup: A continuous-wave confocal microscope was utilized, employing a 514 nm laser (3 mW) and an objective lens (NA 1.42). The detection volume was approximately 0.5 µm3.
- Magnetic Field Application: A static magnetic field (7.2 mT) was applied using a samarium-cobalt magnet to lift the degeneracy of the NV center energy states, enabling the observation of eight distinct resonance frequencies.
- Stress Tensor Extraction: Optically Detected Magnetic Resonance (ODMR) spectra were measured by scanning the sample stage. The shifts in the eight resonance frequencies (ω±i) were used to uniquely calculate the three shear stress components (σxy, σyz, σzx) and the sum of the axial stress components (σxx + σyy + σzz) based on the spin-mechanical interaction Hamiltonian.
Commercial Applications
Section titled “Commercial Applications”The ability to precisely measure and map the full stress tensor in diamond films is essential for advancing quantum technology and high-performance material engineering.
- Quantum Sensing and Metrology:
- Application: Fabrication of highly sensitive NV-diamond quantum sensors (e.g., magnetometers, electrometers, thermometers).
- Relevance: Stress inhomogeneity is a major factor limiting the spin dephasing time (T2) and sensitivity. This method provides the necessary feedback for stress mitigation during growth.
- Quantum Computing and Networks:
- Application: Development of solid-state spin quantum memories and quantum network nodes.
- Relevance: Reducing residual stress is fundamental for achieving long spin coherence times, which are necessary for reliable quantum information processing.
- Advanced Material Quality Control:
- Application: Quality assurance for high-purity, homoepitaxial CVD diamond used in optics, high-power electronics, and heat sinks.
- Relevance: Provides a non-destructive, high-resolution method superior to conventional techniques (like Raman spectroscopy or XRT) for characterizing internal mechanical integrity.
- Strain Engineering in Wide-Bandgap Semiconductors:
- Application: Optimization of CVD growth recipes, particularly for doping profiles.
- Relevance: The finding that nitrogen doping causes compressive stress suggests that grading the nitrogen density (e.g., decreasing N concentration from the substrate interface to the surface) is a viable strategy to minimize residual stress in commercial films.
View Original Abstract
We measured the residual stress tensor in a nitrogen-doped chemical vapor deposition (001) diamond film. The stress tensor was evaluated from the amount of the shift in optically detected magnetic resonance (ODMR) spectra of NV center in the diamond. A confocal microscopy setup was used to observe the spatial variation of the stress tensor in the diamond film. We found that the components of the stress tensor, σ<sub>xy</sub>, σ<sub>yz</sub>, σ<sub>zx</sub> and σ<sub>xx</sub>+ σ<sub>yy</sub>+ σ<sub>zz</sub>, of the residual stress were approximately 0.077, -0.39, -0.67 and 1.52 GPa, respectively, in the x = [100], y = [010], z = [001] coordinate system. Regarding the components of the shear stress, σ<sub>xy</sub>, σ<sub>yz</sub> and σ<sub>zx</sub>, the nitrogen-doped CVD diamond film grown in this study had mainly sheared stress in the z-direction, which was the growth direction of the CVD diamond film. In addition, regarding axial stress σ<sub>xx</sub>+ σ<sub>yy</sub>+ σ<sub>zz</sub>, the CVD diamond film was subjected to compressive stress. Due to this compressive stress, the volume of the CVD diamond film decreased by approximately 0.073%. We considered that nitrogen doping contributed to the decrease in volume of the CVD diamond film.