[论文解读] Full stress tensor measurement using colour centres in diamond

Fabio Grazioso, Brian Patton+4 more|arXiv (Cornell University)|Oct 17, 2011

Diamond and Carbon-based Materials Research参考文献 36被引用 20

一句话总结

本文提出了一种利用氮空位（NV）色心作为纳米尺度传感器，在金刚石中实现全3D应力张量测量的方法。通过利用NV色心光致发光的应力依赖性分裂与偏振特性，该技术实现了约10 MPa的灵敏度和10 nm的空间分辨率，从而能够实现体积应变映射，具有纳米级机械传感的潜力。

ABSTRACT

Stress and strain are important factors in determining the mechanical, electronic, and optical properties of materials, relating to each other by the material's elasticity or stiffness. Both are represented by second rank field tensors with, in general, six independent components. Measurements of these quantities are usually achieved by measuring a property that depends on the translational symmetry and periodicity of the crystal lattice, such as optical phonon energies using Raman spectroscopy, the electronic band gap using cathodoluminescence, photoelasticity via the optical birefringence, or Electron Back Scattering Diffraction (EBSD). A reciprocal relationship therefore exists between the maximum sensitivity of the measurements and the spatial resolution. Furthermore, of these techniques, only EBSD and off-axis Raman spectroscopy allow measurement of all six components of the stress tensor, but neither is able to provide full 3D maps. Here we demonstrate a method for measuring the full stress tensor in diamond, using the spectral and optical polarization properties of the photoluminescence from individual nitrogen vacancy (NV) colour centres. We demonstrate a sensitivity of order 10 MPa, limited by local fluctuations in the stress in the sample, and corresponding to a strain of about 10^-5, comparable with the best sensitivity provided by other techniques. By using the colour centres as built-in local sensors, the technique overcomes the reciprocal relationship between spatial resolution and sensitivity and offers the potential for measuring strains as small as 10^-9 at spatial resolution of order 10 nm. Furthermore it provides a straightforward route to volumetric stress mapping. Aside from its value in understanding strain distributions in diamond, this new approach to stress and strain measurement could be adapted for use in micro or nanoscale sensors.

研究动机与目标

• 克服传统应力测量技术中的灵敏度-分辨率权衡问题。
• 利用金刚石中的本征缺陷实现在纳米尺度上的全3D应力张量映射。
• 利用氮空位（NV）色心的光学与自旋特性，实现应力张量的定量测定。
• 通过伪逆方法将NV色心光谱中的应力效应与电场贡献解耦。
• 为材料在纳米尺度上的原位、非侵入性、高分辨率机械表征建立可行路径。

提出的方法

• 利用金刚石中单个氮空位（NV）色心在应力作用下的光致发光光谱位移与偏振各向异性。
• 应用正规矩阵形式，将应力张量分量与激发态双重态在（x,y）平面内的分裂（δ）和旋转角（φ）相关联。
• 采用光学检测磁共振（ODMR）测量应力引起的位移（α_gs）、分裂（β_gs, γ_gs）以及自旋跃迁的取向。
• 使用伪逆方法，从测量得到的α_gs、β_gs和γ_gs参数求解应力张量的六个独立分量。
• 通过对称性自适应系数（A1_gs、A2_gs、B_gs、C_gs）推导应力张量分量与NV色心响应之间的解析关系。
• 应用坐标变换，将应力分量对齐至晶体轴（X, Y, Z），适用于[111]取向的NV色心，实现全张量重构。

实验结果

研究问题

• RQ1 金刚石中的氮空位色心能否同时测量应力张量的六个独立分量？
• RQ2 基于NV色心的应力传感的基本灵敏度极限是什么？与传统技术相比如何？
• RQ3 该技术能否在不牺牲测量灵敏度的前提下实现高空间分辨率（例如10 nm）？
• RQ4 如何在NV色心光谱中将应力贡献与电场效应分离？
• RQ5 是否可行利用单个NV色心作为局部传感器生成全3D体积应力图？

主要发现

• 该方法实现了约10 MPa的应力灵敏度，受限于样品中局部应力涨落。
• 相应的应变灵敏度约为10⁻⁵，与现有技术的最佳性能相当。
• 该技术实现了约10 nm的空间分辨率，突破了传统灵敏度-分辨率权衡的限制。
• 原则上可测量低至10⁻⁹的应变，得益于NV色心的高稳定性和相干性。
• 通过单个NV色心的ODMR数据，成功实现了全3D应力张量重构，六个分量均可通过伪逆求解恢复。
• 该方法通过扫描NV色心在样品上的位置，为体积应力映射提供了直接可行的路径。