Determination of Young's modulus and Poisson's ratio of thin films by X-ray methods

摘要

Accurate determination of Young's modulus and Poisson's ratio is critical when characterizing the mechanical properties of ultra-thin films. In this work, a method to simultaneously measure the Young's modulus and Poisson's ratio of thin films by X-ray techniques combined with a four-point bending fixture is presented. The four-point bending fixture was carried out to purposely induce stresses on the thin film and cause a curvature of the film/wafer system. The induced stresses were measured by the modified conventional X-ray diffraction for film measurements. At the same time, the curvature of the film/wafer system was measured by the X-ray rocking curve. With the film stress derived from the curvature according to the Stoney formula, both the Poisson's ratio and the Young's modulus were evaluated from the plot of lattice d-spacing changes (strain) versus cos~2αsin~2Ψ. The method was applied to determine thin copper films (～180 nm). The estimated Poisson's ratios ranged from 0.18 to 0.24. Compared to the 0.34 for bulk Cu, the deviation between the bulk and the film properties was above ～30%. The Young's modulus of the films is 116.7 ± 2.9 GPa, which was comparable to those reported in the literature for -128 GPa.