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Decoupling analysis of stress components on monocrystalline silicon using angle-resolved oblique backscattering Raman spectroscopy

基于角度分辨倾斜背散射拉曼光谱的单晶硅应力分量解耦分析

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Abstract

Stress is a key to controlling the electro-optical properties of semiconductor devices based on strain engineering. Micro-Raman spectroscopy is regarded as an effective technique of non-destructive measurement for the stress in semiconductor material. What the results using traditional Raman methods, however, are usually the sum of in-plane principal stress, or some form of equivalent stress, on a specific crystal plane. It is regarded far from possible to detect any stress components using Raman on a random crystal plane. This work presented a method of stress analysis based on angle-resolved oblique backscattering micro-Raman spectroscopy. A general physical-mechanical model was proposed by solving the equation of lattice dynamics in the sample coordinate system and then performing Raman selection in the eigenvector coordinate system. Using this model and considering the factors including refraction, polarization diversion, and numerical aperture (NA), this work established the analytic relationship between the increment of polarized Raman shift and all the stress components on a random crystal plane (taking {100} plane of monocrystalline silicon as an example) under any stress state. The stress component results of verification experiments quite agreed with their corresponding theoretical resolutions. It proved that the proposed method based on angle-resolved oblique backscattering micro-Raman spectroscopy, including both the model and the device, solved the widely recognized problem that the stress components of monocrystalline silicon, especially on {100} crystal plane, could not be decoupled by Raman.

摘要

对于应变工程而言, 应力是控制半导体器件光电性能的关键. 显微拉曼光谱是一种有效的半导体材料应力无损分析技术. 然而, 使用传统拉曼方法得到的结果通常是特定晶体/特定晶面的面内等效应力或主应力和. 本文提出了一种基于角度分辨倾斜背散射显微 拉曼光谱的应力分析方法. 通过在样品坐标系中求解晶格动力学方程, 在特征向量坐标系中进行拉曼选择, 提出了一种通用的物理力 学模型. 利用该模型, 考虑折射率、转偏和数值孔径影响等因素, 建立了任意应力状态下任意晶面(以单晶硅{100}面为例)上偏振拉曼 频移与各应力分量的解析关系. 验证实验表明, 应力分量的分析结果与施加的应力状态非常吻合. 证明了基于角度分辨倾斜背散射显 微拉曼光谱的方法、模型和仪器, 能够解决单晶硅特别是{100}晶面上的应力分量不能通过拉曼测量解耦的普遍问题.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12125203, 12021002, and 11890680).

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Authors and Affiliations

  1. Tianjin Key Laboratory of Modern Engineering Mechanics, Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Ying Chang  (常颖), Saisai He  (何赛赛), Mingyuan Sun  (孙铭媛), Yuqi Zhao  (赵宇琦), Lulu Ma  (马路路) & Wei Qiu  (仇巍)

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  1. Ying Chang  (常颖)
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  6. Wei Qiu  (仇巍)
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Contributions

Author contributions Ying Chang designed the research. Ying Chang wrote the first draft of the manuscript. Ying Chang, Saisai He, Mingyuan Sun, and Yuqi Zhao set up the experiment. Ying Chang and Saisai He set up and processed the experiment data. Wei Qiu and Lulu Ma helped organize the manuscript. Ying Chang and Wei Qiu revised and edited the final version

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Correspondence to Wei Qiu  (仇巍).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Chang, Y., He, S., Sun, M. et al. Decoupling analysis of stress components on monocrystalline silicon using angle-resolved oblique backscattering Raman spectroscopy. Acta Mech. Sin. 40, 423418 (2024). https://doi.org/10.1007/s10409-023-23418-x

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