Stress and deformation of thin films and patterned lines on substrates

Abstract

The thermomechanical response of thin films/lines on thicker substrates under internal loadings resulting from material mismatch is examined. As the well-known Stoney formula is limited to isotropic, blanket films that undergo only small deformations, proper interpretation of curvature-stress relationships for new film geometries and for new experimental testing techniques requires an extension of this analytical framework. Mismatch stresses in thin films/lines and consequent curvature evolution of the film/line-substrate system are investigated in realistic, complex geometries relevant to industrial trends, such as high line aspect ratio, multi-level structure, and large diameter wafers. A combined analytical and numerical method is presented to evaluate curvature and stress evolution in metal and dielectric lines in an interconnect structure on a Si substrate during fabrication steps and subsequent thermal loading. An engineering map based on a closed-form solution for volume-averaged thermal stresses in lines is developed for material selection and design optimization. Coherent gradient sensing (CGS), an optical, full-field and vibration-insensitive experimental method, is used to study large deformation behavior of thin film-substrate systems by measuring the gradient of out-of-plane displacement of deformed surfaces. Experimental results are discussed in terms of the limitation of the small deformation theory upon which the Stoney formula is predicated. In particular, this work seeks to incorporate anisotropy and non-linearity arising from geometrical changes such as directional patterning and large deformation in the range of isotropic and linear-elastic material behavior.