本研究之目的在於利用X光平均應變量測法結合奈米壓印法來準確量測氮化鋯薄膜之殘餘應力，並探討本方法所能應用的厚度極限為何，本研究目標在於藉由取得足夠的取樣體積證明本方法能夠克服非等向性的問題。

從X光平均應變的公式(σ = (AXS) E/(1+ν))可以知道說:殘餘應力可以藉由將彈性係數及柏松比帶入平均應變公式取得，本次實驗使用奈米壓印法來量測氮化鋯薄膜之彈性係數，並藉由使用多個φ角以取得足夠的取樣體積來量測X光平均應變(AXS)，X光所量得的殘餘應力的準確性可以藉由跟光學應力進行比較以驗證。實驗結果證明X光所量得的應力數值相當接近光學的結果，且利用最厚試片的彈性係數代入薄的試片所量得的X光應力數值跟光學應力的結果相差最大只有4％左右。由實驗的結果可以發現到奈米壓印法所能準確量測薄膜彈性係數的極限為500奈米左右，而AXS量測的準確性則可以達到200奈米。從應變對φ角分布圖可以注意到各試片φ角所量測到的應變數值隨著試片厚度減少而震盪漸趨劇烈，因此對於厚度小於500奈米的試片，φ角建議需要取7個或是更多以進行X光繞射量測才能量得準確的整體平均應變數值。對於AXS方法，結果顯示氮化鋯薄膜所能量測的極限厚度為200奈米。最後304不鏽鋼基材的氮化鋯薄膜的殘餘應力也成功地被量測出來，且發現到比矽基材的試片的應力大上4 GPa 左右。

The purpose of this study is to utilize average X-ray strain (AXS) method combined with nano-indentation to accurately measure the residual stress of ZrN thin film and to find out the limit thickness of our method. The goal is to verify that AXS method could overcome the problem of anisotropy by increasing the sampling volume.
Based on the equation of AXS (σ = (AXS) E/(1+ν)), it is known that stress value can be obtained by incorporating the elastic constant and strain value AXS. The elastic constant incorporated into the AXS equation to obtain the X-ray stress of the samples was measured by nano-indentation. In order to have sufficient sampling volume, multiple φ angles were chosen to carry out the X-ray diffraction measurement, and the accuracy of the X-ray stress was confirmed by comparing with the optical stress. By incorporating reliable elastic constant and accurate AXS value, the stress value of X-ray diffraction method turns out to be very close to the optical residual stress. The largest deviation was about 4％ for the X-ray stress obtained by incorporated the elastic constant of the thickest sample. It is found that the limit for nano-indentation to accurately measure the elastic constant of ZrN thin film is 500 nm, and the accuracy of AXS can reach to 200 nm with enough sampling volume. It is found that the fluctuation of the strain values measured by the φ angles increases as film thickness decreases from the distribution of strain value in respect of φ angles. It is thus recommended to utilize 7 or more φ angles to carry out the X-ray diffraction measurement to obtain accurate AXS value for the film thinner than 500 nm. The limit thickness of ZrN thin film for AXS method to carry out turns out to be 200 nm. The X-ray stress of ZrN thin film of 304SS substrate was also successfully measured, and it is about 4 GPa larger than the one of Si substrate.

Abstract i
摘要 ii
致謝 iii
Contents v
List of Figures viii
List of Tables xi
Chapter 1 Introduction 1
Chapter 2 Literature review 3
2.1 Deposition method 3
2.2 Characteristics of ZrN film 6
2.3 Optical curvature technique 8
2.4 〖sin〗^2 Ψ method 8
2.4.1 Traditional sin^2 Ψ method 8
2.4.2 Modified sin^2 Ψ method 11
2.5 〖cos〗^2 α〖sin〗^2 Ψ method 12
2.5.1 Grazing incidence cos^2 αsin^2 Ψ method 12
2.5.2 Derivation of cos^2 αsin^2 Ψ method 15
2.6 Theoretical basis of average X-ray strain (AXS) 22
2.7 X-ray studies of our group 25
Chapter 3 Experimental details 27
3.1 Specimen preparation and deposition process for ZrN film 27
3.2 Experimental procedure 28
3.3 Characterization methods 32
3.3.1 XRD 32
3.3.2 GIXRD 33
3.3.3 SEM 33
3.3.4 AFM 33
3.3.5 XPS 34
3.4 Properties measurements 36
3.4.1 Four-point probe 36
3.4.2 Nano-indentation (NIP) 38
3.4.3 Laser optical curvature 39
Chapter 4 Results 42
4.1 Characterization 45
4.1.1 XRD 45
4.1.2 GIXRD 47
4.1.3 SEM 49
4.1.4 Chemical composition (XPS) 51
4.1.5 Roughness 51
4.2 Properties 52
4.2.1 Hardness and elastic constant 52
4.2.2 Optical residual stress 54
4.2.3 X-ray residual stress 56
4.2.4 Resistivity 58
Chapter 5 Discussion 59
5.1 Comparison between the results of X-ray diffraction and laser curvature technique 59
5.2 The distribution of strain value in respect of φ angles 62
5.3 The value of elastic constant measured by nano-indentation 63
5.4 Residual stress state of ZrN film of stainless steel substrate 64
5.5 The limit of film thickness 66
5.6 The merits and drawbacks of our method comparing to other techniques. 68
Chapter 6 Conclusion 70
Chapter 7 References 71
Appendix 79
Appendix A. The SEM image of the samples 79
Appendix B. Deconvolution XPS spectra of samples 81
Appendix C. AXS regression line 93
Appendix D. Brief guide of using 〖cos〗^2 α〖sin〗^2 Ψ method to measure AXS and stress 102

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