Size-effects in time-dependent mechanics in metallic MEMS

¹ Eindhoven University of Technology, Dep. of Mechanical Engineering, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
² Foundation for Fundamental Research on Matter, P.O. Box 3021, 3502 GA, Utrecht, The Netherlands
³ Materials Innovation Institute, P.O. Box 5008, 2600 GA, Delft, The Netherlands

^a e-mail: l.i.j.c.bergers@tue.nl

Abstract

Reliability of microelectromechanical systems (MEMS) depends a.o. on time-dependent deformation such as creep and fatigue [1]. It is known from literature that this behavior is affected by size-effects: the interaction between microstructural length scales and dimensional length scales [2,3]. Not much research has focused on characterizing size-effects in time-dependent material behavior, specifically for free-standing thin films [3]. This study investigates size-effects caused by grain statistics in timedependent deformation in µm-sized free-standing aluminum cantilever beams.

A numeric-experimental method is used to determine material parameters. The experiment entails applying a constant deflection to the micro-beams for a prolonged period. The deflection is achieved with 50 nm resolution via a micro-clamp. The beams are then released. Immediately the deformation evolution is recorded by acquiring surface height profiles with a confocal optical profiler. Image correlation of the full-field beam profiles is applied to correct for specimen drift and tilt. The experiment yields the tip deflection as function of time with ~3 nm precision. In the numerical part, this data is combined with a finite element model based on a standard-solid material model. In this way material parameters describing time-dependent behavior are extracted. The time constant for the deflection evolution is determined within 20%, as verified by predicting a different experiment. Figure 1 shows the model and the numeric prediction of an experiment.