Measuring the stress tensor in nitrogen-doped CVD diamond using solid-state quantum sensor

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

Technical Documentation & Analysis: Stress Tensor Measurement in Nitrogen-Doped CVD Diamond

Reference: T. Tsuji, S. Harada & T. Teraji (2025) Measuring the stress tensor in nitrogen-doped CVD diamond using solid-state quantum sensor, Science and Technology of Advanced Materials, 26:1, 2546779.

Executive Summary

This research validates the use of Nitrogen-Vacancy (NV) centers in CVD diamond as highly sensitive, solid-state quantum sensors for non-destructive stress tensor mapping, a critical requirement for advanced quantum applications.

Quantum Sensing Validation: Demonstrated the unique capability of NV centers and ODMR spectroscopy to directly extract all six independent components of the residual stress tensor in a CVD diamond film.
Quantified Compressive Stress: The nitrogen-doped (001) CVD film exhibited a significant average axial compressive stress sum ($\sigma_{xx} + \sigma_{yy} + \sigma_{zz}$) of 1.52 GPa.
Shear Strain Identification: The largest shear strain component ($\epsilon_{zx}$) was measured at 0.12%, confirming that the film was primarily subjected to shear stress in the z-direction (growth direction).
Doping-Stress Correlation: Nitrogen doping (estimated at 13 ppm) was identified as the primary contributor to the compressive stress, resulting in a 0.073% decrease in the film’s volume.
Material Requirement: The study highlights that reducing residual stress—essential for improving NV center spin coherence time ($T_2$)—requires minimizing the nitrogen density mismatch between the SCD substrate and the homoepitaxial layer.
6CCVD Value Proposition: 6CCVD provides the necessary ultra-low stress, high-purity SCD substrates and custom doping profiles required to replicate and advance this critical quantum material research.

Technical Specifications

The following hard data points were extracted from the experimental results and methodology:

Parameter	Value	Unit	Context
CVD Film Thickness	20	µm	Homoepitaxial layer on HPHT substrate
Substrate Thickness	500	µm	HPHT Type-Ib (100) single crystal
Growth Temperature Range	1020 - 1090	°C	MPCVD process
Reaction Pressure	110	Torr	MPCVD process
Microwave Power	1.4	kW	MPCVD process
Methane Concentration (CH$_{4}$)	10	%	Flow rate ratio to total gas
Nitrogen Concentration (N$_{2}$)	10	%	Flow rate ratio to total gas
Oxygen Concentration (O$_{2}$)	2	%	Flow rate ratio to total gas (for dislocation reduction)
Average Axial Stress Sum ($\sigma_{xx} + \sigma_{yy} + \sigma_{zz}$)	1.52 (± 0.05)	GPa	Compressive residual stress
Average Shear Stress ($\sigma_{zx}$)	-0.67 (± 0.02)	GPa	Largest shear component
Volumetric Strain ($\epsilon_{v}$)	-0.073	%	Volume decrease due to compressive stress
Nitrogen Density ([N]) in CVD Film	~13	ppm	Estimated from $T_2$ measurement
Spin Coherence Time ($T_2$)	~13	µs	Measured in the low-defect area
Stress Susceptibility Parameter ($a_1$)	4.86	MHz/GPa	Used for stress tensor calculation
Stress Susceptibility Parameter ($a_2$)	-3.7	MHz/GPa	Used for stress tensor calculation

Key Methodologies

The residual stress tensor was evaluated using a combination of advanced CVD growth and quantum sensing techniques:

Substrate Preparation: A 500 µm thick HPHT Type-Ib (100) single crystal diamond was mechanically polished along the [110] direction.
MPCVD Growth Recipe: A 20 µm thick homoepitaxial nitrogen-doped film was grown using high gas concentrations (10% CH${4}$, 10% N${2}$) and 2% O$_{2}$ addition to minimize dislocation generation.
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 of the CVD film with low defect density for measurement.
ODMR Setup: A continuous-wave Optically Detected Magnetic Resonance (ODMR) scheme was employed using a confocal microscope setup (514 nm laser, NA 1.42 objective) to detect fluorescence from NV centers.
Stress Tensor Extraction: A static magnetic field was applied to remove the degeneracy of the NV center energy states. By measuring the eight resulting resonance frequencies ($\omega_{\pm i}$) for the four NV center directions, the six independent components of the stress tensor ($\sigma_{xy}, \sigma_{yz}, \sigma_{zx}, \sigma_{xx} + \sigma_{yy} + \sigma_{zz}$) were uniquely calculated using established spin-stress interaction equations.
Spatial Mapping: The sample stage was scanned to map the stress tensor components across a 25 µm line segment (P-Q) within the selected low-defect area.

6CCVD Solutions & Capabilities

This research confirms that residual stress is a critical limiting factor for NV center performance, directly impacting the resonance frequency and $T_2$ coherence time. 6CCVD specializes in providing the high-purity, low-stress SCD materials and custom engineering required to overcome these limitations and advance solid-state quantum sensor development.

Research Requirement	6CCVD Solution & Capability	Technical Advantage for Quantum Applications
Ultra-Low Stress Substrates	Optical Grade SCD Wafers (up to 500 µm thick) with extremely low nitrogen content (< 1 ppb).	Provides a near-perfect lattice match for homoepitaxial growth, minimizing the residual stress (1.52 GPa compressive) caused by the N-density mismatch identified in the paper.
Precise Doping Control	Custom SCD films with controlled, uniform nitrogen doping (N$_{2}$ flow ratios) from sub-ppm to high-ppm levels.	Enables researchers to systematically tune the NV center density (measured at 0.1 ppm) and optimize the trade-off between $T_2$ coherence time and residual stress.
Custom Dimensions & Orientation	SCD plates/wafers available in (001) orientation, with custom dimensions and thicknesses (0.1 µm to 500 µm film; substrates up to 10 mm).	Supports direct replication of the 20 µm film on 500 µm substrate geometry, or scaling up to larger inch-size PCD wafers (up to 125 mm) for commercial sensor arrays.
Advanced Surface Preparation	SCD polishing achieving ultra-low surface roughness (Ra < 1 nm).	Crucial for high-resolution confocal microscopy and maintaining the high-quality interface necessary for stable NV center operation.
Integrated Metalization	Internal capability for custom metalization layers (Au, Pt, Ti, W, Cu, Pd).	Facilitates the integration of microwave delivery structures (like the 20 µm copper wire used in the ODMR setup) directly onto the diamond surface for optimized quantum control.
Stress Mitigation Strategy	Engineering consultation on implementing graded nitrogen doping profiles in the CVD film.	Addresses the paper’s conclusion that gradually decreasing nitrogen density from the substrate interface to the film surface is an effective strategy for residual stress reduction.

Engineering Support

6CCVD’s in-house PhD team offers expert consultation on material selection and CVD recipe optimization for similar NV Center Quantum Sensor projects. We specialize in tailoring doping profiles and managing growth parameters to achieve the lowest possible residual stress, thereby maximizing the spin coherence time ($T_2$) essential for high-sensitivity magnetometry and electrometry.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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, σxy, σyz, σzx and σxx+ σyy+ σzz, 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, σxy, σyz and σzx, 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 σxx+ σyy+ σzz, 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.

Tech Support

Original Source

DOI: https://doi.org/10.1080/14686996.2025.2546779