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X射线衍射法测量碳化硅单晶的残余应力

邓亚 张宇民 周玉锋

邓亚, 张宇民, 周玉锋. X射线衍射法测量碳化硅单晶的残余应力. 力学学报, 2022, 54(1): 1-7 doi: 10.6052/0459-1879-21-426
引用本文: 邓亚, 张宇民, 周玉锋. X射线衍射法测量碳化硅单晶的残余应力. 力学学报, 2022, 54(1): 1-7 doi: 10.6052/0459-1879-21-426
Deng Ya, Zhang Yumin, Zhou Yufeng. Measurement of residual stress in single-crystal sic by x-ray diffraction method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-7 doi: 10.6052/0459-1879-21-426
Citation: Deng Ya, Zhang Yumin, Zhou Yufeng. Measurement of residual stress in single-crystal sic by x-ray diffraction method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-7 doi: 10.6052/0459-1879-21-426

X射线衍射法测量碳化硅单晶的残余应力

doi: 10.6052/0459-1879-21-426
详细信息
    作者简介:

    周玉锋, 副教授, 主要研究方向: 材料无损应力检测. E-mail: zhouyf@hit.edu.cn

  • 中图分类号: O721

MEASUREMENT OF RESIDUAL STRESS IN SINGLE-CRYSTAL SIC BY X-RAY DIFFRACTION METHOD

  • 摘要: 为了准确评估晶体的质量、提高器件的使用性能, 本文围绕单晶碳化硅材料残余应力方面开展了相关研究工作. 首先通过对原有的多重线性回归分析方法加以改进, 推导出适用于求解六方晶系单晶碳化硅试样所处应力状态的相关理论. 其次, 采用该方法对沿着$[10\overline 1 0]$取向生长的6H-SiC单晶片进行了残余应力检测, 同时选用{214}晶面族作为测量衍射面. 最后, 探究了来源于不同晶面组数的数据进行计算时对残余应力测量结果的影响. 结果显示: 采用多重线性回归分析方法可以实现单晶6H-SiC的面内残余应力的测定; 当给定无应力晶面间距d0的精确值时, 该应力结果的误差高于选用5组以上(hkl)晶面数计算得到的残余应力结果的误差; 如果d0未知, 则随着参与应力计算的晶面组数的增加, 平面残余应力的误差结果会逐渐降低并趋于平稳. 这表明实验测定的残余应力结果具有较高的精度. 另外, 为了保证实验测得的应力结果的可靠性, 应该选用六组及以上衍射面数通过多元回归分析方法来求解单晶碳化硅试样所处的残余应力状态.

     

  • 图  1  坐标系示意图

    Figure  1.  Schematic diagram of coordinate systems

    图  2  转换矩阵示意图

    Figure  2.  Schematic diagram of transformation matrixes

    图  3  6 H-SiC晶体的X射线摇摆曲线

    Figure  3.  X-ray rocking curve of 6 H-SiC single crystal

    图  4  6 H-SiC{214}晶面族的极图

    Figure  4.  Pole figure of 6 H-SiC{214} crystal plane family

    图  5  不同晶面的衍射峰

    Figure  5.  Diffraction peaks from different crystal planes

    图  6  6 H-SiC单晶片应力分量的误差分析

    Figure  6.  Error analysis of stress components of 6 H-SiC

    表  1  {214}晶面族的φ角和ψ

    Table  1.   φ- and ψ-angle of {214} crystal plane family

    CalculatedMeasured
    PlanePhiPsiPhiPsi
    (214)−89.9640.00−89.9640.00
    (421)−0.0320.01−0.0320.01
    (412)−25.0037.98−25.0037.98
    下载: 导出CSV

    表  2  实验测定的ππ−1结果

    Table  2.   Results of π and π−1 measured by experiment

    Tr Matrix πInv Tr Matrix π−1
    0.6570.1430.6901.053−1.211−0.223
    −0.2410.3180.5520.0350.350−0.841
    −0.072−1.0500.2580.4391.0820.388
    下载: 导出CSV

    表  3  应力系数计算所需数据

    Table  3.   Data required for stress coefficient calculation

    Planeγ31γ32γ33cosφsinψsinφsinψcosψ
    (214)0.43640.21820.87290.000449−0.6427900.766044
    (421)0.87290.43640.21820.342184−0.0001800.939633
    (412)0.87290.21820.43640.557729−0.2600700.788226
    下载: 导出CSV

    表  4  平面应力计算所需数据

    Table  4.   Data required for plane stress calculation

    PlanePhiPsiAi( × 10−6)Bi( × 10−6)Ci( × 10−6)d’
    (142) −171.63 41.57 0.4592 0.5213 −0.3080 0.786324
    (124) −133.69 35.76 0.1503 0.6400 −0.1740 0.786159
    (214) −89.96 41.43 −0.2227 −0.2368 0.4586 0.787399
    (412) −24.00 33.64 0.1383 −0.5957 −0.1738 0.786953
    (421) −1.03 20.01 −0.1134 0.0012 −0.2292 0.786223
    $(\overline 4\; \overline 2 \;1)$ 39.85 43.69 0.2828 1.1443 0.2435 0.786648
    $(\overline 1 \;\overline 4 \;2)$ 134.01 50.98 0.1224 −1.2405 0.4230 0.788337
    $(\overline 2 \;\overline 4 \;1)$ 132.41 35.32 −0.1098 −0.5835 0.1831 0.787284
    (241) 166.03 26.96 −0.0095 −0.0126 −0.2278 0.786337
    下载: 导出CSV

    表  5  6 H-SiC$[10\overline 1 0]$晶向的应力结果

    Table  5.   Stress results of 6 H-SiC$[10\overline 1 0]$ growth orientation

    Number of diffraction planes$\sigma _{11}^{S}$/MPa$\sigma _{12}^{S}$/MPa$\sigma _{22}^{S}$/MPad0
    4 985.2635 −656.5240 1654.5609 0.787094
    5 988.5134 −656.1808 1659.6881 0.787005
    6 988.0712 −654.9843 1657.1123 0.786987
    7 988.0777 −654.8199 1656.8464 0.786999
    8 988.2805 −654.7312 1656.0486 0.786980
    9 988.0522 −653.7244 1654.7442 0.786883
    下载: 导出CSV
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  • 录用日期:  2021-11-23
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