Resonance Ultrasound Spectroscopy for Evaluating Elastic Constants and Incohesive Bonds of Thin Films

Free-vibration-resonance frequencies of a film/substrate layered specimen depend on the dimensions, densities, and elastic constants both of the film and substrate. Then, the elastic constants of thin films are inversely determined by measuring the resonance frequencies and the other parameters. Because contributions of the film elastic constants to the resonance frequencies are small, high accurate measurement of resonance frequencies is indispensable. In this study, we develop a piezoelectric tripod transducer, which enables one to measure the resonance frequencies with an accuracy better than 10. In the inverse calculation, mode identification for measured resonance frequencies is the key issue. We achieve this by measuring the surfacedisplacement distributions using laser-Doppler interferometory. We applied the proposed method to a thin film of chemical-vapor-deposition diamond. Measured elastic constants are smaller than those of bulk diamond. We attribute the compliant diamond thin film to local incohesive bonds at grain boundaries. Introduction: Accurate elastic constants of thin films are indispensable to designing and stress analysis of devices. Many studies have clarified elastic properties of bulk materials. However, those of thin films are not well known because of the difficulty of measurements. Thin films are supposed to be elastically different from the bulk and to show elastic anisotropy between the inplane and out-of-plane directions, even if they are polycrystalline. Anisotropy can be induced by residual stress, texture, columnar structure, and incohesive bonds at grain boundaries. The thin films usually show transverse isotropy and have five independent elastic constants denoted by C11, C33, C12, C13, and C44, where the x1 and x2 axes lie in the film plane and x3 is along the out-ofplane direction. Previous studies measured the thin-film elastic constants using vibrating reed method [1], nanoindentation [2], and Brillouin-scattering method [3]. Most of them assumed thin films to be elastically isotropic and involved ambiguity caused by the mechanical contact needed for gripping the specimen and for the acoustic transduction. In this study we developed an advanced resonance-ultrasound-spectroscopy (RUS) method for measuring the anisotropic thinfilm elastic constants. RUS determines elastic constants from dimensions, density, and freevibration-resonance frequencies of a solid specimen. This method has been applied to many bulk materials [4-7]. In order to apply the RUS method to thin films, high accurate measurement of resonance frequencies and correct mode identification of individual resonance are required. We overcame these difficulties by developing a piezoelectric tripod and measuring surfacedisplacement distributions of the specimen vibrating at a resonance frequency with a laserDoppler interferometer. We call this RUS/laser method. Reliability of the RUS/laser method is demonstrated by measuring elastic constants of monocrystal silicon. We then measure chemicalvapor-deposition (CVD) diamond thin films. RUS/laser method: Resonance frequencies of free vibrations of a film/substrate layered specimen depend on densities, dimensions, and elastic constants of both film and substrate. Thin film’s elastic constants are inversely determined by measuring the resonance frequencies and other measurable parameters. For the film/substrate layered specimen, an algorithm using the Rayleigh-Ritz method was established by Heyliger [8]. Rayleigh-Ritz method considers minimization of Lagrangian L;