A vibrational approach to determine the elastic modulus of individual thin films in multilayers

Abstract

A vibrational approach is presented to determine the elastic modulus of individual thin films deposited over a thicker substrate in multilayered systems. The approach requires measurement of the fundamental frequency of the multilayer and a laminated beam model for data reduction. A one-dimensional model based on classical laminated beam theory is introduced to provide a simple analytical approximation of the natural frequency of thin multilayered materials deposited over a significantly thicker substrate in cantilever beam configuration. The model has the advantage of providing an easy-to-use analytical expression for the natural frequency of a multilayered beam in terms of the elastic moduli of each layer, which can be inverted to calculate the elastic modulus of any individual layer if the elastic modulus of the remaining layers is known, and the natural frequency of the multilayered beam is measured. The limits of applicability of the proposed model are investigated by comparing its predictions of the fundamental frequency to those of an existent analytical model for bilayers and finite element analysis of materials comprising two and three dissimilar layers. The proposed model is applied to obtain the elastic modulus of Al and Au thin films in an Al/Au/Kapton multilayer.