Highly accurate estimation of elastic constants and thickness of thin solid films from velocity dispersion of surface acoustic waves utilizing an inverse analysis

摘要

We investigated a highly accurate estimation method of both elastic constants and thickness of thin solid films from velocity dispersion of surface acoustic waves ( SAW) by an inverse analysis. We examined the sensitivity of inverse analysis by numerical calculation with a single-film model to estimate unknown parameters simultaneously with good accuracy. We confirmed that it is essential to choose modes and frequency of propagating SAW whose velocity dispersion possesses not only large change but also change in a different manner due to a variation of individual parameters. With the results of the sensitivity analysis, we carried out a verification experiment for four kinds of boron-doped SiO{sub}2 films. The elastic constants and thickness of the films were estimated from velocity dispersion of SAW which were measured by the scanning interference fringes approach of the phase velocity scanning method. The estimated film thickness agreed well with the one measured by SEM within 1.4 % error. The boron concentration dependence of estimated Young's modulus was able to be represented by a smooth curve. Therefore, we judged that we succeeded in estimating both elastic constants and thickness of thin solid film simultaneously with high accuracy. According to the estimated elastic constants, we found that SiO{sub}2 films were almost isotropic. Estimated Young's modulus decreased with an increase of boron concentration in these films and was found to be 42.22 GPa on the sample with 6.65 wt% boron concentration, and estimated Poisson's ratio was in the range of 0.12 - 0.2.