Quantum ESPRESSO (第一原理計算) で予測された変形ポテンシャル係数を用いたラマン分光法によるSiの応力評価

抄録

It is important to determine to local strain/stress fields in power devices in order to improve their performance and reliability. Micro Raman spectroscopy is of the excellent methods to analyze local strain/stress fields in very small area. When the strain/stress tensors are identified via micro Raman spectroscopy, the phonon deformation potential constants and the elastic stiffness of measured materials are used. These parameters are determined by numerous mechanical loading tests of several single crystal specimens with different crystallographic orientations under various loading conditions, which is labor- and time-consuming. Moreover, it is very difficult to prepare several single-crystal specimens of the newly developed materials with dimensions that are capable of performing several loading tests. This study aims to predict ab-initio the phonon deformation potential constants and anisotropic elastic stiffness of a single crystal Si through first-principles calculation to determine the local strain/stress tensors using micro-Raman spectroscopy. First, the triply degenerate Raman peak with F_2g vibration mode for unstrained single-crystal Si was accurately computed by Quantum ESPRESSO based on density functional theory, plane wave and pseudo-potentials. Second, on the basis of first-principles calculation of two types strained single-crystal Si, degenerate single Raman peak of Si was split into singlet and doublet peaks or three independent singlet peaks for each loading condition. The relations between the wave number shift of Raman shift and applied strain become linear with different slopes. The values of the phonon deformation potential constants calculated from them were in good agreement with experimental values obtained by plate bending tests of Si wafer. Finally, to illustrate the application of these predicted parameters to micro-Raman stress measurements, the stress distribution from an indentation-induced crack tip in Si wafer was estimated from an experimentally measured wave number shift of Raman shift during plate bending of the cracked Si wafer.The measured stress components were in good agreement with the experiment values. Therefore, the proposed estimation method of phonon deformation potential constants and elastic constants that utilizes first-principles calculation is very effective as a simple technique without performing numerous loading tests on several single-crystal specimens.