A Stochastic Multi-Scale Model for Predicting MEMS Stiction Failure
Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn e
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A Stochastic Multi-Scale Model for Predicting MEMS Stiction Failure T.V. Hoang, L. Wu, S. Paquay, J.-C. Golinval, M. Arnst, and L. Noels
Abstract Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way. To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random mesoscale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of micro-beam stiction is then studied in a probabilistic way. Keywords Stiction • Adhesive contact • Random surface • Multi-scale contact • Uncertainty quantification
1.1 Introduction Stiction is the common failure in MEMS in which two micro surfaces permanently adhere together due to the adhesive forces such as capillary forces and van der Waal forces. The stiction failure of micro cantilever beams is illustrated in Fig. 1.1a, in which the cantilever beams are stuck on their substrate. In the present work, only the humid stiction failure resulting from the capillary forces is considered. In MEMS, because of the comparable length of the two scales, the surface roughness (nanometres) and the ranges of the adhesive forces (nanometres), the interaction involves only the highest asperities of the rough surfaces, see Fig. 1.1b [1]. Moreover, due to the scale separation between the ranges of the adhesive forces (nanometres) and the structural displacements (micrometres), the effective contact regions are much smaller than the structural dimensions. For instance, in the case of micro cantilever beams at failure configuration, the effective contact region locates only around the crack tips which is defined as the separating points between the unattached part, for which there is no more interaction forces, and the attached part, see Fig. 1.1a [2]. Therefore, there exist uncertainties in the adhesive behaviors of the micro structures. For instance, in the case of the micro cantilever beam failure, the crack lengths, defined as the length of the unattached part
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