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 Δσf∕ΔT was obtained by substrate curvature measurements; in the direction perpendicular to the film, the temperature gradient of the whole thermal expansion strain Δd∕dΔT 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 Δσf∕ΔT, Δd∕dΔT, reduced modulus Er of the film, and from the thermal expansion coefficient αs of the substrate.