The requirement of stress analysis and measurement is increasing with the great development of heterogeneous structures and strain engineering in the field of semiconductors.Micro-Raman spectroscopy is an effective me...The requirement of stress analysis and measurement is increasing with the great development of heterogeneous structures and strain engineering in the field of semiconductors.Micro-Raman spectroscopy is an effective method for the measurement of intrinsic stress in semiconductor structures.However,most existing applications of Raman-stress measurement use the classical model established on the (001) crystal plane.A non-negligible error may be introduced when the Raman data are detected on surfaces/cross-sections of different crystal planes.Owing to crystal symmetry,the mechanical,physical and optical parameters of different crystal planes show obvious anisotropy,leading to the Raman-mechanical relationship dissimilarity on the different crystal planes.In this work,a general model of stress measurement on crystalline silicon with an arbitrary crystal plane was presented based on the elastic mechanics,the lattice dynamics and the Raman selection rule.The wavenumberstress factor that is determined by the proposed method is suitable for the measured crystal plane.Detailed examples for some specific crystal planes were provided and the theoretical results were verified by experiments.展开更多
基金This work is financially supported by the National Natural Science Foundation of China(Grants 11772223,11772227,and 61727810).
文摘The requirement of stress analysis and measurement is increasing with the great development of heterogeneous structures and strain engineering in the field of semiconductors.Micro-Raman spectroscopy is an effective method for the measurement of intrinsic stress in semiconductor structures.However,most existing applications of Raman-stress measurement use the classical model established on the (001) crystal plane.A non-negligible error may be introduced when the Raman data are detected on surfaces/cross-sections of different crystal planes.Owing to crystal symmetry,the mechanical,physical and optical parameters of different crystal planes show obvious anisotropy,leading to the Raman-mechanical relationship dissimilarity on the different crystal planes.In this work,a general model of stress measurement on crystalline silicon with an arbitrary crystal plane was presented based on the elastic mechanics,the lattice dynamics and the Raman selection rule.The wavenumberstress factor that is determined by the proposed method is suitable for the measured crystal plane.Detailed examples for some specific crystal planes were provided and the theoretical results were verified by experiments.
