Novel Technique to Determine Elastic Constants of Thin Films
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1139-GG03-31
Novel Technique to Determine Elastic Constants of Thin Films
K.J. Martinschitz1, R. Daniel2, Ch. Mitterer2 and J. Keckes1,* 1
Erich Schmid Institute for Materials Science, Austrian Academy of Science and Department of Materials Physics, University of Leoben, Austria
2
Department of Physical Metallurgy and Materials Testing and Christian-Doppler Laboratory for Advanced Hard Coatings, University of Leoben, Austria * [email protected]
ABSTRACT A new X-ray diffraction technique to determine elastic moduli of polycrystalline thin films deposited on monocrystalline substrates is demonstrated. The technique is based on the combination of sin2ψ and X-ray diffraction wafer curvature techniques which are used to characterize X-ray elastic strains and macroscopic stress in thin film. The strain measurements must be performed for various hkl reflections. The stresses are determined from the substrate curvature applying the Stoney’s equation. The stress and strain values are used to calculate hkl reflection dependent X-ray elastic moduli. The mechanical elastic moduli can be then extrapolated from X-ray elastic moduli considering macroscopic elastic anisotropy of the film. The derived approach shows for which reflection and corresponding value of the X-ray anisotropic factor Γ the X-ray elastic moduli are equal to their mechanical counterparts in the case of fibre-textured cubic polycrystalline aggregates. The approach is independent of the crystal elastic anisotropy and depends on the fibre texture type, the texture sharpness, the amount of randomly oriented crystallites and on the supposed grain interaction model. The new method is demonstrated on a fiber textured Cu thin film deposited on monocrystalline Si(100) substrate. The advantage of the new technique remains in the fact that moduli are determined nondestructively, using a static diffraction experiment and represent volume averaged quantities.
INTRODUCTION The reliability and the performance of thin films used e.g. in microelectronics or as protective coatings on working tools is closely related to their mechanical properties [1,2]. Advanced characterization techniques operating on very small scale have been used to assess phenomena like residual stress, yield stress, hardness, indentation modulus etc. [1]. Recently, it has been demonstrated that X-ray elastic strain and macroscopic stress in polycrystalline thin films can be rapidly determined by a simultaneous application of sin2ψ and X-ray diffraction (XRD) substrate curvature techniques [3-5]. The experimental strain and stress values were used to quantify X-ray elastic constants and stress factors [3-5]. Mechanical elastic constants can be extrapolated from X-ray elastic constants considering macroscopic elastic anisotropy of the sample. In the case of cubic polycrystalline aggregates with macroscopic elastic isotropy (quasi-isotropic materials) which obey the Hill grain interaction model [6,7], it was demonstrated that X-ray elastic constants correspond to their mechanical
counterpart
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