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Least-squares refinement of biaxial stress components and unit-cell parameter in a 〈111〉 textured cubic TiN polycrystalline thin film by X-ray diffraction

Published online by Cambridge University Press:  29 February 2012

Ryouichi Yokoyama ,
Jimpei Harada  and
Yoshiaki Akiniwa
Ryouichi Yokoyama*
Affiliation:
Rigaku Corporation, 3-9-12 Akishima, Tokyo 196-8666, Japan
Jimpei Harada
Affiliation:
Rigaku Corporation, 3-9-12 Akishima, Tokyo 196-8666, Japan
Yoshiaki Akiniwa
Affiliation:
Department of Mechanical Engineering and Materials Science, Yokohama National University, 79-1 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
*
a)Author to whom correspondence should be addressed. Electronic mail: yoko@rigaku.co.jp
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Abstract

Biaxial residual stress in a 〈111〉 textured cubic TiN polycrystalline thin film was analyzed by linear least-squares refinement using the method proposed by Yokoyama and Harada [J. Appl. Crystallogr. 42, 185–191 (2009)]. Values of the unstressed (or stress-free) unit-cell parameter a0=4.2332±0.0006 Å and the stress components of σ11=397(88), σ22=401(88), and σ12=−110(100) were obtained. The values of the in-plane stresses σ11 and σ22 presented in the TiN film are practically the same, while σ12 is relatively small. The results obtained in this study confirm that the above theoretical prediction by Yokoyama and Harada can be used to obtain reliable values of stress-free unit-cell parameter and three biaxial stress components of a textured cubic thin film.

Keywords

residual stresstexturestress-free unit-cell parameterleast-squares refinement
Type
Technical Articles
Information
Powder Diffraction , Volume 25 , Issue 1 , March 2010 , pp. 25 - 30
Copyright
Copyright © Cambridge University Press 2010

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References

Aigner, K., Lengauer, W., Rafaja, D., and Ettmayer, P. (1994). “Lattice parameters and thermal expansion of Ti(CxN1-x), Zr(CxN1-x), Hf(CxN1-x) and TiN1-x from 298 to 1473 K as investigated by high-temperature X-ray diffraction,” J. Alloys Compd. JALCEU 215, 121–126. 10.1016/0925-8388(94)90828-1CrossRefGoogle Scholar
Burns, G. and Glazer, A. M. (1978). Space Group for Solid State Scientists (Academic Press, London).Google Scholar
Clemens, B. M. and Bain, J. A. (1992). “Stress determination in textured thin films using X-ray diffraction,” Mater. Res. Bull. MRBUAC 17, 46–51.Google Scholar
Hanabusa, T. (1999). “X-ray measurement of stresses in deposited thin film fiber texture,” Mater. Sci. Res. Int. MSRIFY 5, 63–73.Google Scholar
Kumar, A., Welzel, U., and Mittemeijer, I. J. (2006). “Diffraction stress analysis of strongly fibre-textured gold layers,” Z. Kristallogr. Suppl. 23, 55–60.CrossRefGoogle Scholar
Mura, T. (1991). Micromechanics of Defects in Solids (Kluwer Academic Publishers, Dordrecht), p. 426.Google Scholar
Noyan, I. C. (1985). “Determination of the unstressed lattice parameter “ a0” for (triaxial) residual stress determination of X-rays,” Adv. X-Ray Anal. AXRAAA 28, 281–288.Google Scholar
Noyan, I. C. and Cohen, J. B. (1987). Residual Stress (Springer-Verlag, New York).Google Scholar
Nye, J. F. (1957). Physical Properties of Crystals (University Press, Oxford).Google Scholar
Perry, A. J. (1989). “The relation between residual stress, X-ray elastic constants and lattice parameters in TiN films made by physical vapour deposition,” Thin Solid Films THSFAP 170, 63–70. 10.1016/0040-6090(89)90622-6CrossRefGoogle Scholar
Prince, E. (2004). International Tables for X-ray Crystallography (Springer, Chester), Vol. C, p. 203.Google Scholar
Rachinger, W. A. (1948). “A correction for the α1 α2 doublet in the measurement of widths of X-ray diffraction lines,” J. Sci. Instrum. JSINAY 25, 254–255. 10.1088/0950-7671/25/7/125CrossRefGoogle Scholar
Reuss, A. (1929). “Berechnung der fliessgrenze von mischkristallen auf grund der plastizitatsbedingung fur. einkristalle,” Z. Angew. Math. Mech. ZAMMAX 9, 49–58. 10.1002/zamm.19290090104CrossRefGoogle Scholar
Taguchi, T. (2008). “Next generation X-ray detectors for in-house XRD,” Powder Diffr. PODIE2 23, 101–105. 10.1154/1.2912455Google Scholar
Tanaka, K. and Akiniwa, Y. (1998). “X-ray stress measurement of hexagonal polycrystals with [001] fiber texture,” Trans. Jpn. Soc. Mech. Eng., Ser. A NKGADA 41, 287–289.Google Scholar
Tanaka, K., Akiniwa, Y., Ito, T., and Inoue, K. (1999). “Elastic constants and X-ray stress measurement of cubic thin films with fiber texture,” Trans. Jpn. Soc. Mech. Eng., Ser. A NKGADA 42, 224–234.Google Scholar
Welzel, U., Ligot, J., Lamparter, P., Vermeulen, A. C., and Mittemeijer, E. J. (2005). “Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction,” J. Appl. Crystallogr. JACGAR 38, 1–29. 10.1107/S0021889804029516CrossRefGoogle Scholar
Winholtz, R. A. and Cohen, J. B. (1988). “Generalized least-squares determination of triaxial stress states by X-ray diffraction and the associated errors,” Aust. J. Phys. AUJPAS 41, 189–199.CrossRefGoogle Scholar
Yen, C. M., Toth, L. E., and Shy, Y. M. (1967). “Superconducting Hc-Jc and Tc measurement in the Nb-Ti-N, Nb-Hf-N, and Nb-V-N ternary systems,” J. Appl. Crystallogr. JACGAR 38, 2268–2271.Google Scholar
Yokoyama, R. and Harada, J. (2009). “Re-evaluation of formulae for X-ray stress analysis in polycrystalline specimens with fibre texture,” J. Appl. Crystallogr. JACGAR 42, 185–191. 10.1107/S0021889809003409CrossRefGoogle Scholar
Yokoyama, R., Harada, J., and Akiniwa, Y. (2009). “Re-evaluation of formulae for X-ray stress analysis in polycrystalline specimens with fibre texture: Experimental confirmation,” J. Appl. Crystallogr. JACGAR 42, 776–782. 10.1107/S0021889809026636CrossRefGoogle Scholar