Evaluation of length-scale effects for mechanical behaviour of micro- and nanocantilevers: I. Experimental determination of length-scale factors

Abstract

When the thickness of micro- and nanocantilevers, which are the building blocks of micro- and nanoelectromechanical systems, are below 10 µm, the natural frequency and quasi-static deflection of the cantilevers cannot be estimated accurately using the conventional natural frequency and quasi-static-deflection models. The effect of the thickness is summed into what is known as the length-scale factor, which is incorporated into the models in order to improve the accuracy of the models. With this in mind, this paper, which is the first of two parts, reports on the experimental determination of length-scale factors for micro- and nano-sized silicon cantilevers, the micro- and nano-sized length-scale factors are estimated using experimental data collected from nanoindentation and microindentation experiments. The same experimental data are used to cross-validate the empirical length-scale factors in the literature. The experimentally estimated length-scale factors are then incorporated into the natural frequency and static-deflection models. The experimental results presented suggest that the length-scale factors have a great influence on the natural frequency and quasi-static deflection of micro- and nano-sized silicon cantilevers, compared with the natural frequency and deflection calculated using the conventional models not incorporating the length-scale factor.