Error Limitations in the Determination of Mechanical Properties of Thin Films

Abstract

This study addresses the ability to determine stiffness parameters and Poisson's ratio of ultrathin films in terms of isotropic material description. A primary concern is the precision with which such determinations can be made by means of certain continuum analyses. Starting from previously published results and drawing on energy methods for modeling the load-deflection relationship of rectangular membranes of arbitrary aspect ratio an analysis improvement reduces the error from the 40% range to 2-10% values. Further precision can only be derived from numerical analysis. By comparing the numerical data of load-versus-deflection behavior to that for the energy based approximation, Young's modulus can be determined to within 2% of the value specified, provided that Poisson's ratio, v, is known. If the latter is not the case, the error increases to 7 to 10%, if a limited range of Poisson's ratio is admitted. In addition, a method to determine Poisson's ratio is pursued by considering membranes of various aspect ratios. This method, which may also be readily applied for "exact" numerical analyses, was found to be particularly useful for materials with Poisson's ratio in the range from 0.25 to 0.5. Finally, this study is then extended to bimaterial films in two different fashions: through the use of an effective thickness defined in terms of a stretch equivalent, and through the use of effective material properties. The first method was found useful for low Poisson's ratio material whereas the second method was successful for high Poisson's ratio materials. Young's modulus of the material under test was retrieved on average within 3 %.