高应变硅中拉曼应变位移的测量与第一性原理预测
Raman Strain-Shift Measurements and Prediction from First-Principles in Highly-Strained Silicon
摘要：
这项工作介绍了如何通过实验测量验证的第一性原理模拟导致一个新的准确预测的预期拉曼位移作为硅应变的函数。首先进行应变原始单元的结构弛豫，以解决每个应变水平的硅原子的相对位移。然后利用密度泛函微扰理论计算了高应变硅中光学声子模的能量，并反演了应变位移趋势。模拟验证实验表征，使用扫描电子显微镜（SEM）加上背散射拉曼光谱，硅微梁制造使用自上而下的方法。梁应变高达2 $\%$由于氮化硅致动器的内部拉伸应力，允许在高应变条件下的扰动理论的验证。将结果与声子变形势（PDP）理论进行了比较，并讨论了文献中发现的各种参数引起的不确定性。模拟的-175.77 cm $^{-1}$的应变位移系数（分别为1.000和1.000）。-400.85 cm $^{-1}$）和-160.99 cm $^{-1}$的实验值（分别为-414.97 cm $^{-1}$）的纵向光学LO（resp.横向光学TO $_1$）模式，显示出良好的一致性。
英文摘要：
This work presents how first-principles simulations validated through experimental measurements lead to a new accurate prediction of the expected Raman shift as a function of strain in silicon. Structural relaxation of a strained primitive cell is first performed to tackle the relative displacement of the silicon atoms for each strain level. Density Functional Perturbation Theory (DFPT) is then used to compute the energy of the optical phonon modes in highly-strained silicon and retrieve the strain-shift trend. The simulations are validated by experimental characterization, using scanning electron microscopy (SEM) coupled with backscattering Raman spectroscopy, of silicon microbeams fabricated using a top-down approach. The beams are strained up to 2$\%$ thanks to the internal tensile stress of silicon nitride actuators, allowing a validation of the perturbation theory in high-strain conditions. The results are compared with the phonon deformation potentials (PDP) theory and the uncertainty caused by the various parameters found in the literature is discussed. The simulated strain-shift coefficients of -175.77 cm$^{-1}$ (resp. -400.85 cm$^{-1}$) and the experimental one of -160.99 cm$^{-1}$ (resp. -414.97 cm$^{-1}$) are found for the longitudinal optical LO (resp. transverse optical TO$_1$) mode, showing good agreement.
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