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Comparison of Slowness Profiles of Lamb Wave with Elastic Moduli and Crystal Structure in Single Crystalline Silicon Wafers

  • Min, Youngjae (Applied Acoustics Lab, Korea Science Academy of KAIST) ;
  • Yun, Gyeongwon (Applied Acoustics Lab, Korea Science Academy of KAIST) ;
  • Kim, Kyung-Min (Applied Acoustics Lab, Korea Science Academy of KAIST) ;
  • Roh, Yuji (Applied Acoustics Lab, Korea Science Academy of KAIST) ;
  • Kim, Young H. (Applied Acoustics Lab, Korea Science Academy of KAIST)
  • Received : 2015.10.28
  • Accepted : 2016.01.25
  • Published : 2016.02.28

Abstract

Single crystalline silicon wafers having (100), (110), and (111) directions are employed as specimens for obtaining slowness profiles. Leaky Lamb waves (LLW) from immersed wafers were detected by varying the incident angles of the specimens and rotating the specimens. From an analysis of LLW signals for different propagation directions and phase velocities of each specimen, slowness profiles were obtained, which showed a unique symmetry with different symmetric axes. Slowness profiles were compared with elastic moduli of each wafer. They showed the same symmetries as crystal structures. In addition, slowness profiles showed expected patterns and values that can be inferred from elastic moduli. This implies that slowness profiles can be used to examine crystal structures of anisotropic solids.

Keywords

References

  1. S. J. Song, Y. H. Kim, S. D. Kwon and Y. -M. Cheong, "Determination of phase velocity dispersion curve and group velocity of Lamb waves using backward radiation," Journal of Acoustical Society of Korea, Vol. 22, pp. 61-68 (2003)
  2. S. Sasaki, "Back reflection of ultrasonic wave obliquely incident to solid surface in water," Japanese Journal of Applied Physics, Vol. 2, pp. 198 (1963) https://doi.org/10.1143/JJAP.2.198
  3. H. L. Bertoni and T. Tamir, "Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces," Applied Physics, Vol. 2, No. 4, pp. 157-172 (1973) https://doi.org/10.1007/BF00884205
  4. Y. H. Kim, S.-J. Song, D. H. Bae and S.-D Kwon, "Assessment of material degradation due to corrosion-fatigue using a backscattered Rayleigh surface wave," Ultrasonics, Vol. 42, No. 1. pp. 545-550 (2004) https://doi.org/10.1016/j.ultras.2004.01.078
  5. M. de Billy, L. Adler and G. Quentin, "Measurements of backscattered leaky Lamb waves in plates," Journal of Acoustical Society of America, Vol. 75, pp. 998-1001 (1984) https://doi.org/10.1121/1.390567
  6. D. E. Chimenti and A. H. Nayfeh, "Leaky Lamb waves in fibrous composite laminates," Journal of Applied Physics, Vol. 58, pp. 4531-4538 (1985) https://doi.org/10.1063/1.336268
  7. M. A. Torres-Arredondo, H. Jung and C. -P. Fritzen, "A study of attenuation and acoustic energy anisotropy of Lamb waves in multilayered anisotropic media for NDT and SHM applications,'' 6th International Workshop on NDT in Progress, Prague, Czech Republic (2011)
  8. L. Adler, S. -W. Wang, K. Bolland, M. de Billy and G. Q. Jentin, "Rayleigh angle back scattering of ultrasonic beam from single crystal nickel in 111 and 110 planes," Journal of Acoustical Society of America, Vol. 77, pp. 1950-1953 (1985) https://doi.org/10.1121/1.391841
  9. Y. K. Park and Y. H. Kim, "Lamb waves in an anisotropic plate of a single crystal silicon wafer," 6th International Workshop on NDT in Progress, Prague, Czech Republic (2011)
  10. J. Kim, D. Cho and R. S. Muller, "Why is (111) silicon a better mechanical material for MEMS?," Transducers 2001, Munich, pp. 662-665 (2001)
  11. J. J. Wortman and R. A. Evans, "Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium," Journal of Applied Physics, Vol. 36, pp. 153-156 (1965) https://doi.org/10.1063/1.1713863
  12. H. F. Pollard, "Sound Waves in Solids," Pion Limited, London, pp. 9-15 (1977)
  13. J. F. Nye, "Physical Properties of Crystals: Their Representation by Tensors and Matrices," Oxford University Press, Oxford, pp. 142-145 (1957)
  14. V. Kaajakari, "Silicon as an anisotropic mechanical material - a tutorial," http://www.kaajakari.net/-ville/research/tutorials/ tutorials.shtml.
  15. M. A. Hopcroft, W. D. Nix and T. W. Kenny, "What is the Young's modulus of silicon?," Journal of Microelectromechanical Systems, Vol. 19, pp. 229-238 (2010) https://doi.org/10.1109/JMEMS.2009.2039697
  16. S. D. Kwon, M. S. Choi and S. H. Lee, "The applications of ultrasonic backward radiation from a layered substrate submerged in liquid," NDT&E International, Vol. 33, pp. 275-281 (2000) https://doi.org/10.1016/S0963-8695(99)00050-X
  17. B. Pavlakovic and M. J. S. Lowe, "Disperse Version 2.0," Imperial College NDT Lab, London (2002)

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