結合X光繞射與光學曲率技術量測薄膜材料之彈性係數

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研究生：	張捷茵 Jeh-Yin Chang
論文名稱：	結合X光繞射與光學曲率技術量測薄膜材料之彈性係數 Measuring Elastic Constants of Thin Films by Combining X-ray Diffraction and Laser Curvature Techniques
指導教授：	黃嘉宏 Jia-Hong Huang 喻冀平 Ge-Ping Yu
口試委員:
學位類別：	碩士 Master
系所名稱：	原子科學院 - 工程與系統科學系 Department of Engineering and System Science
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	102
中文關鍵詞：	彈性係數、楊氏系數、浦松比
外文關鍵詞：	elastic constant, Young's modulus, Poisson's ratio
相關次數：	點閱：1 下載：0
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In this study, we have proposed a non-destructive method to simultaneously determine the Young’s modulus (E) and Poisson’s ratio (ν) of polycrystalline thin film materials. The method involved independent stress measurement by laser curvature technique and strain components determination by sin2□ X-ray diffraction (XRD) method, and afterward, elasticity theory was employed to calculate E and ν. The proposed method has several advantages including (1) Both XRD and optical curvature techniques are non-destructive; (2) Both measurements are well-developed techniques supported by established theoretical bases and therefore good reliability can be expected in the measurement. The accuracy of the obtained values of E and ν were further verified. The cos2αsin2□ method, associated with asymmetrical grazing incident X-ray geometry, was performed on the same film and the previously determined E and ν were used to calculate the stress which was compared with that from optical curvature method. Sine sin2y method and cos2αsin2y method explore distinct groups of crystals lying in different depth of the film, the diffraction information of these two methods does not extract from identical diffraction planes. Provided the two stress values are close enough to be within the measurement error, the accuracy of the measured E and ν can be confirmed. Furthermore, if the elastic constants of the film can be precisely determined, the depth profile of residual stress can be assessed using cos2αsin2y method by appropriately adjusting the incident angle. The experimental results also demonstrated that the elastic constants in two TiN films may have significant difference. This may be due to the variation in compositions and film structure, which results in different interatomic force and thus divergent E values. In addition, one should be cautious when employing the NIP-determined E in sin2y or cos2αsin2y method to calculate the residual stress because the modulus may not give correct stress value all the time. However, the trend of the residual stress may not be significantly affected due to the uncertainty in E value.

誌謝 …………………………………………………………………………………………..i
摘要 …………………………………………………………………………………………iii
Abstract ………………………………………………………………………………………iv
Content ………………………………………………………………………………………..v
Figure Caption ……………………………………………………………………………...viii
Table Caption …………………………………………………………………………………x
Chapter 1 Introduction ………………………………………………………………………..1
Chapter 2 Literature Review ………………………………………………………………….2
    2.1 E and ν Measurement of the Thin Film ……………………………………………..2
        2.1.1 Tensile Test …………………………………………………………………..3
        2.1.2 Bulge Test ……………………………………………………………………4
        2.1.3 Substrate Curvature Technique ………………………………………………4
        2.1.4 Microbeam Bending Test …………………………………………………….5
        2.1.5 Resonant Frequency Technique ……………………………………………...5
        2.1.6 Nanoindentation ……………………………………………………………...6
        2.1.7 X-Ray Diffraction Technique …………………………….…………………..7
Chapter 3 Theoretical Basis …………………………………………………………………11
    3.1 sin2y Diffraction Method: Determination of the Six Strain Components …………12
    3.2 cos2αsin2y Diffraction Method: Determination of Residual Stress ………………..14
Chapter 4 Experimental Details ……………………………………………………………..17
    4.1 Specimen Preparation and Deposition Process …………………………………….17
    4.2 Characterization Methods for Structure and Compositions ………………………..19
        4.2.1 Field-Emission Gun Scanning Electron Microscopy (FEG-SEM) …....……19
        4.2.2 X-Ray Diffraction (XRD) …………………………………………………..19
        4.2.3 Grazing Incidence X-Ray Diffraction (GIXRD) ………..……………….....20
        4.2.4 Pole Figure ………………………………………………………………….20
        4.2.5 Rutherford Backscattering Spectroscopy (RBS) …………………………...21
        4.2.6 X-ray Photoelectron Spectroscopy (XPS) ………………………………….22
    4.3 Characterization Methods for Properties …………………………………………..23
        4.3.1 Roughness …………………………………………………………………..23
        4.3.2 Electrical Resistivity ………………………………………………………..23
        4.3.3 Hardness and Young’s Modulus …………………………………………….24
    4.4 Measurement of Residual Stress and Strain ………………………………………..25
        4.4.1 Optical Curvature Method ………………………………………………….26
        4.4.2 sin2y and cos2αsin2y X-Ray Diffraction Methods …………………………29
Chapter 5 Results ……………………………………………………………………………32
    5.1 SEM ………………………………………………………………………………..32
    5.2 AFM ………………………………………………………………………………..36
    5.3 RBS and XPS ………………………………………………………………………36
    5.4 XRD and GIXRD …………………………………………………………………..38
    5.5 Pole Figure …………………………………………………………………………46
    5.6 Electrical Resistivity ……………………………………………………………….48
    5.7 Nanoindentation ……………………………………………………………………48
    5.8 Residual Stress, Strain and Elastic Constants ……………………………………...48
        5.8.1 Computed Strain Components and Elastic Constants ………………………49
        5.8.2 Young’s Modulus and Residual Stress ……………………………………..49
Chapter 6 Discussion ………………………………………………………………………..60
    6.1 Computation of E and ν ……………………………………………………………60
    6.2 Verification of the Computed E and ν ……………………………………………..63
    6.3 Depth Profile of Residual Stress …………………………………………………...64
    6.4 Elastic Constants of TiN Films …………………………………………………….65
    6.5 Young’s Modulus Measured from Nanoindentation ………………………………66
    6.6 Important Issues about the Proposed Method ……………………………………...69
        6.6.1 sin2y and cos2αsin2y Methods ……………………………………………...69
        6.6.2 Influence of Beam Quality on Measuring the Six Strain Components ...…..71
        6.6.3 Advantages and Limitations of the Proposed Method ……………………...72
Chapter 7 Conclusions ………………………………………………………………………74
Reference ……………………………………………………………………………………76
Appendix A ………………………………………………………………………………….84
    A.1 Tensor Notation and Coordinate Transformation …………………………………84
    A.2 Strain Formula for sin2y Diffraction Method ……………………………………..86
    A.3 Strain Formula for cos2αsin2y Diffraction Method ……………………………….88
Appendix B ………………………………………………………………………………….91
    B.1 AFM Images ……………………………………………………………………….91
Appendix C ………………………………………………………………………………….93
    C.1 Diagrams of sin2y and cos2αsin2y Methods …………….…...……………………93
Appendix D ………………………………………………………………………………….99
    D.1 Indentation Depth Test …………………………………………………………….99

                                

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