在本研究，我們提出一個標準流程用平均X光應變方法去測量多晶氮化鈦鋯薄膜的殘餘應力。本研究目的是降低應力量測誤差到十百分比，並找出X光繞射及奈米壓印法的厚度限制。此外，成分對氮化鈦鋯薄膜之殘餘應力的影響也會被探討。八組不同成分及厚度的氮化鈦鋯藉由非平衡磁控濺鍍系統鍍在矽基材(100)上。薄膜的應變被cos2αsin2ψ X光繞射在眾多旋轉角中量測。奈米壓印法測量氮化鈦鋯薄膜的楊氏係數。從應變和cos2αsin2ψ作圖得到的斜率，我們可以得到平均X光應變。為了驗證測量的應力，合併平均X光應變及奈米壓印法得到的應力和光學曲率應力比較並算出誤差。實驗結果顯示壓縮應力範圍在2.69到5.10GPa，在鋯/(鋯+鈦)為0.75到達最大值。在鋯/(鋯+鈦)=0.5的壓縮應力可能會因為晶格缺陷減少隨厚度增加而下降。不同的成分在氮化鈦鋯中會導致殘餘應力的不對稱變化。殘餘應力的不對稱行為可能是因為鈦在氮化鋯晶格以及鋯在氮化鈦晶格的原子大小差異所造成。在本研究，X光繞射應力量測誤差成功地降低到九點二百分比。氮化鈦鋯(鈦:鋯:氮=1:1:2)平均X光應變厚度限制在兩百奈米以下，而奈米壓印法的厚度限制在六百奈米左右。合併平均X光應變及光學曲率應力可以決定膜厚在兩百奈米以上的平均有效X光彈性係數(AEXEC)。

In this study, we proposed a standard procedure to measure the stress of polycrystalline Ti1-xZrxN thin films by using average X-ray strain (AXS) method. The objective was to narrow down the deviation of stress measurement to 10%, and to find the thickness limit in X-ray diffraction (XRD) and nanoindentation measurement. In addition, the effect of composition on the residual stress of Ti1-xZrxN thin films was also investigated. Eight Ti1-xZrxN thin film specimens with different compositions (x=0.25, 0.50, 0.75) and thicknesses were deposited on Si(100) by unbalanced magnetron sputtering. The strain of the thin films was measured by cos2αsin2ψ XRD method at multiple rotational angles (). The Young’s modulus of Ti1-xZrxN thin films was determined by nanoindentation. The AXS can be obtained from the slope of strain vs. cos2αsin2ψ plot. To verify stress of the thin films, the stress measured by combining AXS and nanoindentation was compared with the stress measured by laser curvature method and the deviation was assessed. The results showed that the compressive stress ranged from 2.69 to 5.10 GPa, and reached a maximum for Ti0.25Zr0.75N. The compressive stress of the Ti0.5Zr0.5N specimens decreased with increasing thickness probably due to the decrease of lattice defects. The different compositions in Ti1-xZrxN induce the asymmetrical variation of residual stress. The asymmetrical behavior in residual stress may be due to the difference in atomic size between Ti atoms in ZrN lattice and Zr atoms in TiN lattice. In this study, the deviation of XRD stress measurement was successfully decreased to 9.2%. The thickness limit of AXS measurement in Ti0.5Zr0.5N thin films was smaller than 200 nm, and the thickness limit of nanoindentation was about 600nm. By combining AXS and stress obtained by laser curvature method, the average effective X-ray elastic constant (AEXEC) could be determined for film thickness down to 200 nm.

[1] Y.-F. Chen, Effect of composition on the fracture toughness of Ti1-xZrxN hard coatings, Master Thesis, National Tsing Hua University, R.O.C, 2014.
[2] B.D. Cullity, S.R. Stock, Elements of X-ray diffraction, Prentice Hall, New Jersey, 2001.
[3] M.B. Takeyama, T. Itoi, E. Aoyagi, A. Noya, Diffusion barrier properties of nano-crystalline TiZrN films in Cu/Si contact systems, Applied Surface Science, 216 (2003) 181-186.
[4] J.S. Chun, I. Petrov, J.E. Greene, Dense fully 111-textured TiN diffusion barriers: Enhanced lifetime through microstructure control during layer growth, Journal of Applied Physics, 86 (1999) 3633.
[5] M.B. Takeyama, A. Noya, K. Sakanishi, Diffusion barrier properties of ZrN films in the Cu/Si contact systems, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, 18 (2000) 1333.
[6] N. Prssall, R.E. Gold, H.A. Johansen, A study of superconductivity in interstitial compounds, Journal of Physics and Chemistry of Solids, 29 (1968) 19-38.
[7] J.-H. Huang, C.-H. Ho, G.-P. Yu, Effect of nitrogen flow rate on the structure and mechanical properties of ZrN thin films on Si(100) and stainless steel substrates, Materials Chemistry and Physics, 102 (2007) 31-38.
[8] H.A. Wriedt, J.L. Murray, The N-Ti (Nitrogen-Titanium) System, Bulletin of Alloy Phase Diagrams, 8 (1987) 378-388.
[9] H. Okamoto, N-Zr (Nitrogen-Zirconium), Journal of Phase Equilibria & Diffusion, 27 (2006) 551-551.
[10] H. Ljungcrantz, M. Oden, L. Hultman, J.E. Greene, J.E. Sundgren, Nanoindentation studies of single-crystal (001)-, (011)-, and (111)-oriented TiN layers on MgO, Journal of Applied Physics, 80 (1996) 6725-6733
[11] H.-M. Tung, J.-H. Huang, D.-G. Tsai, C.-F. Ai, G.-P. Yu, Hardness and residual stress in nanocrystalline ZrN films: Effect of bias voltage and heat treatment, Materials Science and Engineering: A, 500 (2009) 104-108.
[12] G. Abadias, V.I. Ivashchenko, L. Belliard, P. Djemia, Structure, phase stability and elastic properties in the Ti1–xZrxN thin-film system: Experimental and computational studies, Acta Materialia, 60 (2012) 5601-5614.
[13] M.L. Cai, Depositing thick TiN film by adjusting processing parameters of unbalanced magnetron sputtering, Master Thesis, National Tsing Hua University, R.O.C, 2013.
[14] P. Jin, S. Maruno, Evaluation of internal stress in reactively sputter-deposited ZrN thin films, Japanese journal of applied physics, 30 (1991).
[15] V.V. Uglov, V.M. Anishchik, V.V. Khodasevich, Z.L. Prikhodko, S.V. Zlotski, G. Abadias, S.N. Dub, Structural characterization and mechanical properties of Ti–Zr–N coatings, deposited by vacuum arc, Surface and Coatings Technology, 180-181 (2004) 519-525.
[16] O. Knotek, M. Bohmer, T. Leyendecker, F. Jungblut, The structure and composition of Ti-Zr-N, Ti-AI-Zr-N and Ti-AI-V-N coatings, Materials Science and Engineering, A 105/106 (1988) 481-488.
[17] Y.-W. Lin, J.-H. Huang, G.-P. Yu, Effect of nitrogen flow rate on properties of nanostructured TiZrN thin films produced by radio frequency magnetron sputtering, Thin Solid Films, 518 (2010) 7308-7311.
[18] H.-A. Chen, Effect of bias on the structure and properties of TiZrN thin films deposited by unbalanced magnetron sputtering, Master Thesis, National Tsing Hua University, 2014.
[19] C.-W. Lu, Characterization of Structure and Mechanical Properties of TiZrN Thin Films Deposited by DC Unbalanced Magnetron Sputtering:
Effect of Nitrogen Flow Rate, Master Thesis, National Tsing Hua University, R.O.C, 2012.
[20] A.B. O. Knotek, On spinodal decomposition in magnetron sputtered (Ti,Zr) nitride and carbide thin films, Thin Solid Films, 174 (1989) 51-56.
[21] G. Abadias, L.E. Koutsokeras, A. Siozios, P. Patsalas, Stress, phase stability and oxidation resistance of ternary Ti–Me–N (Me=Zr, Ta) hard coatings, Thin Solid Films, 538 (2013) 56-70.
[22] G. Abadias, L.E. Koutsokeras, S.N. Dub, G.N. Tolmachova, A. Debelle, T. Sauvage, P. Villechaise, Reactive magnetron cosputtering of hard and conductive ternary nitride thin films: Ti–Zr–N and Ti–Ta–N, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 28 (2010) 541.
[23] Y.-W. Lin, J.-H. Huang, G.-P. Yu, Microstructure and corrosion resistance of nanocrystalline TiZrN films on AISI 304 stainless steel substrate, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 28 (2010) 774.
[24] J. Kourtev, R. Pascova, Reactively magnetron sputtered Ti-Al-N thin films with enhanced mechanical properties, Journal of Vacuum Science & Technology 47 (1996) 1197-1201.
[25] H.-M. Tung, P.-H. Wu, G.-P. Yu, J.-H. Huang, Microstructures, mechanical properties and oxidation behavior of vacuum annealed TiZrN thin films, Vacuum, 115 (2015) 12-18.
[26] A. Hoerling, J. Sjölén, H. Willmann, T. Larsson, M. Odén, L. Hultman, Thermal stability, microstructure and mechanical properties of Ti1−xZrxN thin films, Thin Solid Films, 516 (2008) 6421-6431.
[27] 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, Surface and Coatings Technology, 258 (2014) 211-218.
[28] A.-N. Wang, G.-P. Yu, J.-H. Huang, Fracture toughness measurement on TiN hard coatings using internal energy induced cracking, Surface and Coatings Technology, 239 (2014) 20-27.
[29] D. Faurie, P.O. Renault, E. Le Bourhis, P. Villain, P. Goudeau, F. Badawi, Measurement of thin film elastic constants by X-ray diffraction, Thin Solid Films, 469-470 (2004) 201-205.
[30] R.D. Emery, G.L. Povirk, Tensile behavior of free-standing gold films. Part I. Coarse-grained films, Acta Materialia, 51 (2003) 2067-2078.
[31] C.K. Huang, W.M. Lou, C.J. Tsai, T.-C. Wu, H.-Y. Lin, Mechanical properties of polymer thin film measured by the bulge test, Thin Solid Films, 515 (2007) 7222-7226.
[32] A.J. Kalkman, A.H. Verbruggen, G.C.A.M. Janssen, High-temperature bulge-test setup for mechanical testing of free-standing thin films, Review of Scientific Instruments, 74 (2003) 1383.
[33] Y.H. Yu, M.O. Lai, L. Lu, G.Y. Zheng, Measurement of in-plane elastic constants of crystalline solid films by X-ray diffraction coupled with four-point bending, Surface and Coatings Technology, 200 (2006) 4006-4010.
[34] Y. Tomioka, N. Yuki, Bend stiffness of copper and copper alloy foils, Journal of Materials Processing Technology, 146 (2004) 228-233.
[35] S. Liu, Q.J. Wang, Determination of Young's modulus and Poisson's ratio for coatings, Surface and Coatings Technology, 201 (2007) 6470-6477.
[36] J.-Y. Chang, G.-P. Yu, J.-H. Huang, Determination of Young's modulus and Poisson's ratio of thin films by combining sin2ψ X-ray diffraction and laser curvature methods, Thin Solid Films, 517 (2009) 6759-6766.
[37] F. Richter, M. Herrmann, F. Molnar, T. Chudoba, N. Schwarzer, M. Keunecke, K. Bewilogua, X.W. Zhang, H.G. Boyen, P. Ziemann, Substrate influence in Young's modulus determination of thin films by indentation methods: Cubic boron nitride as an example, Surface and Coatings Technology, 201 (2006) 3577-3587.
[38] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, Journal of Materials Reasearch, 7 (1992) 1564-1583.
[39] R. Saha, W. D. Nix, Effects of the substrate on the determination of thin film mechanical properties by nanoindentation, Acta Materialia, 50 (2002) 23-28.
[40] A.A. Pelegri, X. Huang, Nanoindentation on soft film/hard substrate and hard film/soft substrate material systems with finite element analysis, Composites Science and Technology, 68 (2008) 147-155.
[41] P. Djemia, C. Dugautier, T. Chauveau, E. Dogheche, M.I. De Barros, L. Vandenbulcke, Mechanical properties of diamond films: A comparative study of polycrystalline and smooth fine-grained diamonds by Brillouin light scattering, Journal of Applied Physics, 90 (2001) 3771.
[42] A.G. Every, Measurement of the near-surface elastic properties of solids and thin supported films, Measurement Science and Technology, 13 (2002) R21–R39.
[43] G.G. Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 82 (1909) 172-175.
[44] K. Bouamama, P. Djemia, D. Faurie, G. Abadias, Structural and elastic properties of single-crystal and polycrystalline Ti1−xZrxN alloys: A computational study, Journal of Alloys and Compounds, 536 (2012) S138-S142.
[45] G. Abadias, L.E. Koutsokeras, P. Guerin, P. Patsalas, Stress evolution in magnetron sputtered Ti–Zr–N and Ti–Ta–N films studied by in situ wafer curvature: Role of energetic particles, Thin Solid Films, 518 (2009) 1532-1537.
[46] V.V. Uglov, V.M. Anishchik, S.V. Zlotski, G. Abadias, The phase composition and stress development in ternary Ti–Zr–N coatings grown by vacuum arc with combining of plasma flows, Surface and Coatings Technology, 200 (2006) 6389-6394.
[47] L.E. Koutsokeras, G. Abadias, Intrinsic stress in ZrN thin films: Evaluation of grain boundary contribution from in situ wafer curvature and ex situ x-ray diffraction techniques, Journal of Applied Physics, 111 (2012) 093509.
[48] A.J. Perry, V. Valvoda, D. Rafaja, X-ray residual stress measurement in TiN, ZrN and HfN films using the Seemann-Bohlin method, Thin Solid Films, 214 (1992) 169-174.
[49] E.L. Haase, The Determination of lattice parameters and strains in stressed thin films using X-ray diffraction with Seemann-Bohlin focusing, Thin Solid Films, 124 (1985) 283-291.
[50] 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.
[51] 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, Surface and Coatings Technology, 262 (2015) 40-47.
[52] B.B. He, Two-dimensional X-ray diffraction, Wiley, New Jersey, 2009.
[53] V. Hauk, Structural and residual stress analysis by nondestructive methods, Elsevier, Amsterdam, 1997.
[54] P. Scherrer, Gött Nachr, 2 (1918) 98.
[55] L.V. Azoroff, M.J. Buerger, The powder method in X-ray crystallography, New York, 1958.
[56] D. Briggs, M.P. Seah, Practical surface analysis by AES and XPS, Wiley, New York, 1983.
[57] http:/www.cem.msu.edu/~cem924sg/XPSASFs.html.
[58] J. Dean, J.M. Wheeler, T.W. Clyne, Use of quasi-static nanoindentation data to obtain stress–strain characteristics for metallic materials, Acta Materialia, 58 (2010) 3613-3623.
[59] W.D. Nix, Mechanical Properties of Thin Films, METALLURGICAL TRANSACTIONS A 20A (1989) 2217-2245.
[60] A.-N. Wang, Fracture toughness measurement on TiN hard coating, Master Thesis, National Tsing Hua University, R.O.C, 2012.
[61] Y.-H. Chen, Residual stress measurement of ZrN thin film by using average X-ray strain method combining with nano-indentation, Master Thesis, National Tsing Hua University, R.O.C, 2015.
[62] N.N. Greenwood, A. Earnshaw, Chemistry of the elements, Elsevier,1997.
[63] P.-Y. Hsiao, Z.-H. Tsai, J.-H. Huang, G.-P. Yu, Strong asymmetric effect of lattice mismatch on epilayer structure in thin-film deposition, Physical Review B, 79 (2009).
[64] Y. Lu, M. Przybylski, O. Trushin, W.H. Wang, J. Barthel, E. Granato, S.C. Ying, T. Ala-Nissila, Strain Relief in Cu-Pd Heteroepitaxy, Physical Review Letters, 94 (2005).
[65] G.C.A.M. Janssen, M.M. Abdalla, F.v. Keulen, B.R. Pujada, B.v. Venrooy, Celebrating the 100th anniversary of the Stoney equation
for film stress: developments from polycrystalline steel
strips to single crystal silicon wafers., Thin Solid Films, 517 (2009) 1858.