Advanced Resonant-Ultrasound Spectroscopy for Studying Anisotropic Elastic Constants of Thin Films
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Advanced Resonant-Ultrasound Spectroscopy for Studying Anisotropic Elastic Constants of Thin Films Hirotsugu Ogi, Nobutomo Nakamura, Hiroshi Tanei, and Masahiko Hirao Graduate School of Engineering Science, Osaka University Toyonaka, Osaka 560-8531, Japan ABSTRACT This paper presents two advanced acoustic methods for the determination of anisotropic elastic constants of deposited thin films. They are resonant-ultrasound spectroscopy with laser-Doppler interferometry (RUS/Laser method) and picosecond-laser ultrasound method. Deposited thin films usually exhibit elastic anisotropy between the film-growth direction and an in-plane direction, and they show five independent elastic constants denoted by C11, C33, C44, C66 and C13 when the x3 axis is set along the film-thickness direction. The former method determines four moduli except C44, the out-of-plane shear modulus, through free-vibration resonance frequencies of the film/substrate specimen. This method is applicable to thin films thicker than about 200 nm. The latter determines C33, the out-of-plane modulus, accurately by measuring the round-trip time of the longitudinal wave traveling along the film-thickness direction. This method is applicable to thin films thicker than about 20 nm. Thus, combination of these two methods allows us to discuss the elastic anisotropy of thin films. The results for Co/Pt superlattice thin film and copper thin film are presented. INTRODUCTION Elastic constants of thin films are required primarily for three reasons. First, they are indispensable to calculation of internal stresses in a multiphase composite caused by lattice misfit and different thermal-expansion coefficients among constituents. Second, they are needed to calculate elastic strain energy to find a minimum of the free energy for the estimation of possible microstructure. Third, they are capable of evaluating defects because defects such as voids, dislocations, and microcrackings affect the elastic constants through elastic softening. However, measurement of the elastic constants of thin films has never been straightforward due to elastic anisotropy: Thin films, even polycrystalline thin films, show different elastic properties between along the film-growth direction and along an in-plane direction. Such anisotropy originates from texture, columnar structure, oriented microcracks or precipitates, and internal stresses. The thin films then show transverse isotropy or hexagonal symmetry and possess five independent elastic constants Cij:
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C11 [Cij ] =
C12 C11
C13 C13
0 0
0 0
C33
0
0
C44 sym.
0 C44
0 0 0 0 0 C66
when the x3 axis is taken along the film-growth direction, where C66=(C11-C12)/2. Most existing methods, however, assumed thin films to be isotropic materials and deduced only one or two moduli among five. They failed to detect elastic anisotropy. The acoustic methods we present in this paper determine four components of Cij among five. They are resonant-ultrasound spectroscopy coupled with laser-Doppler
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