Multi-scale numerical-experimental method to determine the size dependent elastic properties of bilayer silicon copper nanocantilevers using an electrostatic pull in experiment

Abstract

Thin metal films are widely used in modern electro mechanical systems. The need for more integrated functionality and minimization of material and energy consumption leads to miniaturization of these systems. As a consequence, materials are processed on the micro- and nanometer scale. On this scale, material properties become a function of size. To predict performance and reliability, knowledge on the size dependence of material properties is imperative. In this work the unknown size dependence of the copper Young's modulus is determined by electrostatic pull-in experiments performed on bilayer copper-silicon nanocantilevers. The size effect is also predicted with a multi-scale (MS) method. In this method atomistic simulations predict the bulk elastic and surface properties of mono-crystalline silicon (Si) and poly-crystalline copper (Cu). These results are combined to represent the bilayer nanocantilevers of the experiment in a continuum model. The model is verified by comparison with a well documented size effect of the effective Si Young's modulus. It is shown that the experimental method can be used for determining the Young's modulus of thin Cu films in the 10 to 50 nm range. Both the experimental results and the MS simulation results show that there is a strong size effect present in Si and Cu.