Bidirectional thermal expansion measurement for evaluating Poisson's ratio of thin films

An original and practical method is demonstrated for determining Poisson's ratio of thin films by detecting thermal expansion in two directions perpendicular to each other. In the direction within the film, the temperature gradient of the biaxial thermal stress Delta sigma(f)/Delta T was obtained by substrate curvature measurements; in the direction perpendicular to the film, the temperature gradient of the whole thermal expansion strain Delta d/d Delta T along the film thickness d was measured by x-ray reflectivity. It was found that Poisson's ratio of thin films with a thickness of several hundred nanometers can be determined from Delta sigma(f)/Delta T, Delta d/d Delta T, reduced modulus E-r of the film, and from the thermal expansion coefficient alpha(s) of the substrate. (c) 2006 American Institute of Physics.