本研究目的在探討金屬介層厚度對於硬膜應力釋放的影響。我們提出能量平衡模式用以探究金屬介層釋放應力之機制，其核心概念是以金屬介層的塑性變形功平衡硬膜中的彈性儲存能與矽基板的彎曲能。此模型並提出有效變形厚度來探討介層釋放應力之機制，此厚度可分為兩部分，有效變形厚度(硬膜)為金屬介層因釋放上層硬膜應力而塑性變形之厚度；而有效變形厚度(矽)則表示金屬介層因緩解基材彎曲而塑性變形之厚度。本研究選擇具有鈦介層的氮化鈦硬膜作為模型系統，並使用非平衡磁控濺鍍鍍製於矽基板上。實驗設計介層厚度介於50至300奈米，而上層薄膜應力則介於-2.39至-3.93GPa之間。試片的整體應力由光學曲率法量測，而氮化鈦層與鈦介層的應力則利用平均X光應變結合奈米壓印法分別量測。實驗結果顯示，介層塑性變形僅發生於靠近氮化鈦和鈦介層間的介面附近；因此可用於釋放氮化鈦層應力之鈦介層變形厚度有上限值，亦即增加介層厚度並不能降低更多應力。另一方面，厚度不足的鈦介層(低於50奈米)會因氮化鈦層與矽基板包夾之塑性限制，使其塑性變形能力降低，導致介層受到壓應力，使得介層無法有效地釋放薄膜應力；由於應力狀態改變，能量平衡模式不適用於此條件下的金屬介層。因此，金屬介層中之應力狀態可作為介層有效性的參考指標。具有拉伸應力狀態的介層可釋放鍍層之應力，然而當介層已受到壓應力時，即失去釋放應力的能力。

The purpose of this study was to investigate the effect of metal interlayer thickness on relief of residual stress in bilayer coatings. An energy balance model was proposed to facilitate the understanding the stress relief mechanism of the metal interlayer. The model is based on a concept that stored elastic energy in the coating and the bending energy in the substrate are balanced by the plastic work done by the metal interlayer. The effective deformation thickness (EDT) in the Ti interlayer was proposed to understand the stress relief mechanism. EDT includes the deformed interlayer thickness contributed to stress relief of the TiN coating (EDTf), and the deformed interlayer thickness contributed to bending curvature relaxation of the Si substrate (EDTSi). TiN/Ti bilayer thin films were selected as the model system. TiN/Ti specimens with different interlayer thicknesses ranging from 50 to 300 nm and with designed stresses of TiN film ranging from -2.39 to -3.93 GPa were prepared using unbalanced magnetron sputtering. The overall stress of the bilayer specimen was determined by laser curvature method, and the stress in each layer was measured by average X-ray strain method. The experimental results showed that there is an upper limit of Ti interlayer thickness for effectively relieving stress in the TiN thin film. Further increasing the interlayer thickness cannot increase the extent of stress relief. The plastic deformation due to the energy relief in the TiN film only occurs within a specific distance near the TiN/Ti interface. For the specimen with insufficient Ti interlayer thickness ( ≤ 50 nm), the stress of the TiN film was not effectively relieved. The thin interlayer is under plastic constraint by the TiN film and Si substrate, and hence the capacity of plastic deformation of the interlayer is limited, leading to the compressive stress in Ti interlayer. The proposed energy balance model is not valid in this case. The residual stress state of the Ti interlayer can be used as an index to evaluate the effectiveness in relieving film stress by the interlayer. The interlayer is operative by sustaining tensile stress, whereas it is ineffective if the interlayer is subjected to compressive stress.

摘要 i
Abstract ii
致謝 iii
Content v
List of Figures vii
List of Tables ix
Chapter 1 Introduction 1
Chapter 2 Literature Review 3
2.1 Residual stress in thin films 3
2.2 The effect of metal interlayer 4
2.3 Characteristics of TiN 6
2.4 Measurement methods for thin film residual stress 7
2.4.1 Wafer curvature measurement 7
2.4.2 Grazing incident XRD cos2αsin2ψ method 8
2.4.3 Average X-ray strain (AXS) method 10
Chapter 3 Theoretical basis 12
3.1 Stored elastic energy 12
3.2 Stored energy relief in the film and the substrate 12
3.3 The work done by plastic deformation of the interlayer 13
Chapter 4 Experimental details 18
4.1 Substrate preparation and film deposition 18
4.2 Characterization of structure and chemical compositions 22
4.2.1 Chemical compositions 22
4.2.2 Crystal structure 23
4.2.3 Surface morphology and cross-sectional observation 24
4.2.4 Surface roughness 24
4.3 Characterization of properties 25
4.3.1 Hardness and Young’s modulus 25
4.3.2 Residual stress 25
4.3.3 Electrical Resistivity 28
Chapter 5 Results 31
5.1 Characterization of T-series specimens 31
5.1.1 Chemical compositions 33
5.1.2 Crystal structure 33
5.1.3 Microstructure 36
5.1.4 Surface roughness 38
5.1.5 Hardness, Young’s modulus and electrical resistivity 39
5.1.6 Residual stress 39
5.2 Characterization of B- and TB-series specimens 43
5.2.1 Chemical compositions and crystal structure 45
5.2.2 Microstructure 48
5.2.3 Surface roughness 50
5.2.4 Hardness, Young’s modulus and electrical resistivity 51
5.2.5 Residual stress 51
5.3 Energy balance model 54
5.3.1 Energy relief in the coating (Gf) and the bending relaxation of the substrate (GSi) 54
5.3.2 Maximum plastic work of the interlayer and the total energy relief efficiency(ξtot) 59
Chapter 6 Discussion 61
6.1 Effect of Ti interlayer thickness 61
6.2 Effect of stress variation in the TiN top layer 68
6.3 Applications on the interlayer design 70
Chapter 7 Conclusions 71
Reference 72
Appendix A XPS Spectra 78
Appendix B AFM images of the Ti film 90
Appendix C AXS Linear Regression Fitting 91

[1] W.-J. Chou, G.-P. Yu, J.-H. Huang, Mechanical properties of TiN thin film coatings on 304 stainless steel substrates, Surf. Coat. Technol. 149 (2002) 7-13.
[2] L. Hultman, Thermal stability of nitride thin films, Vacuum 57 (2000) 1-30.
[3] W.-J. Chou, G.-P. Yu, J.-H. Huang, Corrosion behavior of TiN-coated 304 stainless steel, Corros. Sci. 43 (2001) 2023-2035.
[4] G.S. Kim, S.Y. Lee, J.H. Hahn, B.Y. Lee, J.G. Han, J.H. Lee, S.Y. Lee, Effects of the thickness of Ti buffer layer on the mechanical properties of TiN coatings, Surf. Coat. Technol. 171 (2003) 83-90.
[5] W.-L. Pan, G.-P. Yu, J.-H. Huang, Mechanical properties of ion-plated TiN films on AISI D2 steel, Surf. Coat. Technol. 110 (1998) 111-119.
[6] F. S. Shieu, L. H. Cheng, M. H. Shiao, S. H. Lin, Effects of Ti interlayer on the microstructure of ion-plated TiN coatings on AISI 304 stainless steel, Thin Solid Films 311 (1997) 138-145.
[7] A.-N. Wang, J.-H. Huang, H.-W. Hsiao, G.-P. Yu, H. Chen, Residual stress measurement on TiN thin films by combining nanoindentation and average X-ray strain (AXS) method, Surf. Coat. Technol. 280 (2015) 43-49.
[8] S. Lei, J.-H. Huang, H. Chen, Measurement of residual stress on TiN/Ti bilayer thin films using average X-ray strain combined with laser curvature and nanoindentation methods, Mater. Chem. Phys. 199 (2017) 185-192.
[9] J.A. Thornton, D.W. Hoffman, Stress-related effects in thin films, Thin Solid Films 171 (1989) 5-31.
[10] I.C. Noyan, J.B. Cohen, Residual stress: measurement by diffraction and interpretation, Springer, 1987.
[11] O. Knotek, R. Elsing, G. Krämer, F. Jungblut, On the origin of compressive stress in PVD coatings - an explicative model, Surf. Coat. Technol. 46 (1991) 265-274.
[12] H. Oettel, R. Wiedemann, S. Preißler, Residual stresses in nitride hard coatings prepared by magnetron sputtering and arc evaporation, Surf. Coat. Technol. 74-75 (1995) 273-278.
[13] Y.-W. Lin, P.-C. Chih, J.-H. Huang, Effect of Ti interlayer thickness on mechanical properties and wear resistance of TiZrN coatings on AISI D2 steel, Surf. Coat. Technol. 394 (2020) 125690.
[14] J.-H. Huang, Y.-F. Chen, G.-P. Yu, Evaluation of the fracture toughness of Ti1-xZrxN hard coatings: Effect of compositions, Surf. Coat. Technol. 358 (2019) 487-496.
[15] H. Ljungcrantz, L. Hultman, J.-E. Sandgren, S. Johansson, N. Kristensen, J.-Å. Schweitz, C. J. Shute, Residual stresses and fracture properties of magnetron sputtered Ti films on Si microelements, J. Vac. Sci. Technol. A 11 (1993) 543.
[16] J.-H. Huang, Y.-H. Chen, A.-N. Wang, G.-P. Yu, H. Chen, Evaluation of fracture toughness of ZrN hard coatings by internal energy induced cracking method, Surf. Coat. Technol. 258 (2014) 211-218.
[17] T.-W. Zheng, Effect of Ti Interlayer on Stress Relief of ZrN/Ti Bilayer Thin Films on Silicon Substrate, National Tsing Hua university, Master thesis, 2018.
[18] J. Tang, L. Feng, J. S. Zabinski, The effect of metal interlayer insertion on the friction wear and adhesion of TiC hard coatings, Surf. Coat. Technol. 99 (1998) 242-247.
[19] J. Gerth, U. Wiklund, The influence of metallic interlayers on the adhesion of PVD TiN coatings on high-speed steel, Wear 264 (2008) 885-892.
[20] S. J. Bull, P. R. Chalker, C. F. Ayres, D. S. Rickerby, The influence of titanium interlayers on the adhesion of titanium nitride coatings obtained by plasma-assisted chemical vapour deposition, Mater. Sci. Eng. A 139 (1991) 71-78.
[21] R. Ali, M. Sebastiani, E. Bemporad, Influence of Ti-TiN multilayer PVD-coatings design on residual stresses and adhesion, Mater. Des. 75 (2015) 47-56.
[22] J.-H. Huang, F.-Y. Ouyang, G.-P. Yu, Effect of film thickness and Ti interlayer on the structure and properties of nanocrystalline TiN thin films on AISI D2 steel, Surf. Coat. Technol. 201 (2007) 7043-7053.
[23] J.-H. Huang, C.-H. Ma, H. Chen, Effect of Ti interlayer on the residual stress and texture development of TiN thin film deposited by unbalanced magnetron sputtering, Surf. Coat. Technol. 201 (2006) 3199-3204.
[24] J.-H. Huang, C.-H. Ma, H. Chen, Effect of Ti interlayer on the residual stress and texture development of TiN thin films, Surf. Coat. Technol. 200 (2006) 5937-5945.
[25] R. Elo, S. Jacobson, T. Kubart, Tailoring residual stress in CrNx films on alumina and silicon deposited by high-power impulse magnetron sputtering, Surf. Coat. Technol. 397 (2020) 125990.
[26] Y.-W. Lin, J.-H. Huang, W.-J. Cheng, G.-P. Yu, Effect of Ti interlayer on mechanical properties of TiZrN coatings on D2 steel, Surf. Coat. Technol. 350 (2018) 745-754.
[27] J.-H. Huang, K.-W. Lau, G.-P. Yu, Effect of nitrogen flow rate on structure and properties of nanocrystalline TiN thin film produced by unbalanced magnetron sputtering, Surf. Coat. Technol. 191 (2005) 17-24.
[28] C.S. Shin, S. Rudenja, D. Gall, N. Hellgren, T.Y. Lee, I. Petrov, J.E. Greene, Growth, surface morphology, and electrical resistivity of fully strained substoichiometric epitaxial TiNx (0.67≤x<1.0) layers on MgO(001), J. Appl. Phys. 95 (2004) 356-362.
[29] B. O. Johansson, J. E. Sundgren, J. E. Greene. Rockett, S. A. Barnett, Growth and properties of single crystal TiN films deposited by reactive magnetron sputtering, J. Vac. Sci. Technol. A 3 (1985) 303-307.
[30] M. Stoiber, E. Badisch, C. Lugmair, C. Mitterer, Low- friction TiN coatings deposited by PACVD, Surf. Coat. Technol. 163-164 (2003) 451-456.
[31] H.O. Pierson, Handbook of refractory carbides and nitrides, Noyes publications, New Jersey, 1996.
[32] E. Budke, K. Krempel-Hesse, H. Maidhof, H. Schussler, Decorative hard coatings with improved corrosion resistance, Surf. Coat. Technol. 112 (1999) 108-113.
[33] J. Müller, E. Yurchuk, T. Schlӧsser, J. Paul, R. Hoffmann, S. Muller, D. Martin, S. Slesazeck, P. Polakowski, J. Sundqvist, M. Czernohorsky, K. Seidel, P. Kücher, R. Boschke, M. Trentzsch, K. Gebauer, U. Schrӧder, T. Mikolajick, Ferroelectricity in HfO2 enables nonvolatile data storage in 28 nm HKMG, Symp. VLSI Technol. (2012) 6242443.
[34] ICDD Kabekkodu, International Centre for Diffraction Data, (1995) PDF # 03-65-0970.
[35] H.A. Wriedt, J.L. Murray, The N-Ti (nitrogen-titanium) system, Bull. Alloy Phase Diagr. 8 (1987) 378-388.
[36] J. A. Sue, X-ray elastic constants and residual stress of textured titanium nitride coating, Surf. Coat. Technol. 54/55 (1992) 154-159.
[37] A.-N. Wang, G.-P. Yu, J.-H. Huang, Fracture toughness measurement on TiN hard coatings using internal energy induced cracking, Surf. Coat. Technol. 239 (2014) 20-27.
[38] G.G. Stoney, C.A. Parsons, The Tension of Metallic Films deposited by Electrolysis, Proc. R. Soc. Lond. A 82 (1909) 172.
[39] C. A. Klein, How accurate are Stoney’s equation and recent modifications, J. Appl. Phys. 88 (2000) 5487-5489.
[40] C.-H. Ma, J.-H. Huang, H. Chen, Residual stress measurement in textured thin film by grazing-incidence X-ray diffraction, Thin Solid Films 418 (2002) 73-78.
[41] V. Hauk, Structure and residual stress analysis by nondestructive methods, 1st ed., Elsevier Science, Aachen Germany, 10 Nov. 1997.
[42] A.-N. Wang, C.-P. Chuang, G.-P. Yu, J.-H. Huang, Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method. Surf. Coat. Technol. 262 (2015) 40-47.
[43] W.F. Hosford, R.M. Caddell, Metal Forming: Mechanics and Metallurgy, 3rd ed., Cambridge, 2007.
[44] G.E. Dieter, Mechanical Metallurgy 3rd ed, SI Metric ed., McGraw-Hill, 1986.
[45] G.A. Shirley, High-resolution X-ray photoemission spectrum of the valence bands of gold, Phys. Rev. B 5 (1972) 4709-4714.
[46] N.C. Saha, H.G. Tompkins, Titanium nitride oxidation chemistry: An x-ray photoelectron spectroscopy study, J. Appl. Phys. 72 (1992) 3072-3079.
[47] M. J. Vasile, A. B. Emerson, F. A. Baiocchi, The characterization of titanium nitride by x-ray photoelectron spectroscopy and Rutherford backscattering, J. Vac. Sci. Technol. A 8 (1990) 99-105.
[48] W. Dianis, J. E. Lester, A study of nitric oxide adsorbed on Nickel oxide, Cobalt oxide, and graphite by x-ray photoelectron spectroscopy, Surf. Sci. 43 (1974) 602-616.
[49] J. Halbritter, H. Leiste, H. J. Mathes, P. Walk, ARXPS – Studies of nucleation and make-up of sputtered TiN-layers, J. Anal. Chem. 341 (1991) 320-324.
[50] P. Scherrer, Bestimmung der inneren Struktur und der Größe von Kolloidteilchen mittels Röntgenstrahlen, Gött. Nachr. 1918 (1918) 98-100.
[51] L.V. Azaroff, M.J. Buerger, The powder method in X-ray crystallography, MaGraw-Hill, New York, USA, 1958.
[52] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992) 1564-1583.
[53] J. J. Wortman, R. A. Evans, Young’s modulus, shear modulus, and Poisson’s ratio in silicon and germanium, J. Appl. Phys. 36 (1956) 153-156.
[54] ICDD Kabekkodu, International Centre for Diffraction Data, (1952) PDF # 01-89-5009.
[55] F. M. Smits, Measurement of sheet resistivities with the four-point probe, Bell Syst. Tech. 37 (1958) 711-718.
[56] M.-L. Tsai, Depositing Thick TiN Film by Adjusting Processing Parameters of Unbalanced Magnetron Sputtering, National Tsing Hua university, Master thesis, 2013.
[57] B.D. Cullity, S.R. Stock, Elements of X-ray Diffraction 3rd ed., Prentice Hall, New Jersey, 2001.