Determination of proof stress and strain-hardening exponent for thin film with biaxial residual stresses by in-situ XRD stress analysis combined with tensile test M. Qin a, * , V. Ji b , Y.N. Wu c , C.R. Chen a , J.B. Li a a Shenyang National Laboratory for Materials Science (SYNL), Institute of Metal Research, Chinese Academy of Sciences, 110016 Shenyang, China b LM3 ESA CNRS 8006, ENSAM, 151 Bld. de l’Ho ˆpital, 75013 Paris, France c Department of Surface Engineering of Materials, Institute of Metal Research, Chinese Academy of Sciences, 110016 Shenyang, China Received 5 August 2003; accepted in revised form 25 May 2004 Available online 26 November 2004 Abstract A new method is put forward to measure the proof stress and strain-hardening exponent of polycrystalline films (Cu, TiN) under a biaxial residual stresses state on the substrates. The Cu and TiN films were deposited on the steel substrates by ion beam-assisted magnetron sputtering and plasma-assisted chemical vapor deposition (PACVD), respectively. During the tensile test, the longitudinal stress (r 1 ) and transverse stress (r 2 ) of the films were determined by in-situ X-ray diffraction, and the applied strain (e a ) of the films were measured by a strain gauge. Based on the experimental results, the equivalent stresses ¯ r and equivalent uniaxial strains e t can be obtained. From the ¯ r – e t curves, the proof stresses r 0.1 of the Cu and TiN films have been calculated. The results indicate that the values of r 0.1 of the Cu and TiN films are 328 MPa and 4.2 GPa, respectively, and the values of the strain-hardening exponents for them are 0.62 and 0.36, respectively. In addition, evidence that the plastic flow of TiN film occurred under the tensile load is also obtained. D 2004 Published by Elsevier B.V. Keywords: Proof stress; Strain-hardening exponent; Biaxial stresses; Cu film; TiN film; Tensile test; In-situ X-ray diffraction 1. Introduction Thin films are widely used in the microelectronic devices and structural components to prevent wear and corrosion. Previous work has indicated that the mechanical behaviors of thin films are very important to the design and reliability of such devices and components [1–3]. Especially, because the yield strength has an obvious effect on the function and lifetime of thin films, it has become a key parameter of the mechanical properties of thin films. Therefore, many meth- ods such as indentation method [4,5], uniaxial tensile test of free standing films [6,7], biaxial bulge testing [8] and beam bending method [9] have been developed to study the yield strength of thin films. However, because of the difficulties in the preparation of specimens, the interpretation of exper- imental results and the sensitivity to edge effects, these methods cannot be easily used to obtain the stress–strain relationship and yield strength of the films, which are under the biaxial residual stresses state on the substrates. In order to avoid the above-mentioned disadvantages, in- situ X-ray stress/strain analysis method has been put for- ward and applied extensively in the last decade [10–13]. According to this method, the film is deposited onto the compliant substrate, which is mechanically strained by a tensile tester. During the tensile test, the stress of the film on the substrate is in-situ measured by X-ray diffraction and the applied strain is determined by the strain gage technique. Thus, the stress–strain relationship of the film is obtained. From the stress–strain curve, the yield strength of the film can be determined. However, in the previous work, only the stress in the loading direction was taken into account. In fact, the residual stresses of thin films are often biaxial and the stress state keeps biaxial under the uniaxial load. For example, Hommel et al. [14] indicate that the residual stress of Cu film is equibiaxial and the transverse stress increases under the uniaxial load, due to the difference of Poisson’s ratio m between the film and the substrate. According to the 0257-8972/$ - see front matter D 2004 Published by Elsevier B.V. doi:10.1016/j.surfcoat.2004.05.026 * Corresponding author. Advanced Science Institute, Saitama Institute of Technology, Fusaiji 1690, Okabe, Saitama 369-0293, Japan. Tel.: +81- 90-18438483; fax: +81-48-5856826. E-mail address: mqin@sit.ac.jp (M. Qin). www.elsevier.com/locate/surfcoat Surface & Coatings Technology 192 (2005) 139– 144