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Hay Jennifer - Micro and Nanomechanics, Volume 5: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics

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Hay Jennifer Micro and Nanomechanics, Volume 5: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics
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The Society for Experimental Mechanics, Inc. 2017
La Vern Starman , Jennifer Hay and Nikhil Karanjgaokar (eds.) Micro and Nanomechanics, Volume 5 Conference Proceedings of the Society for Experimental Mechanics Series 10.1007/978-3-319-42228-2_1
1. A Stochastic Multi-Scale Model for Predicting MEMS Stiction Failure
T. V. Hoang 1, L. Wu 1, S. Paquay 2, J.-C. Golinval 1, M. Arnst 1 and L. Noels 1
(1)
Department of Aerospace and Mechanical Engineering, University of Lige, Alle de la Dcouverte 9, Quartier Polytech 1, B-4000 Lige, Belgium
(2)
Open Engineering SA, Rue Bois Saint-Jean 15/1, B-4102 Seraing, Belgium
L. Noels
Email:
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 meso-scale 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.a, 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.
Fig 11 The humid stiction failure of micro cantilever beam a the S-shape - photo 1
Fig. 1.1
The humid stiction failure of micro cantilever beam: ( a ) the S-shape failure configuration, ( b ) the water condensing between the two contacting rough surfaces
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. ].
In order to predict the probabilistic behavior of micro structures involving adhesion, the stochastic model-based multi-scale method developed in []. Once the distribution of the meso-scale apparent contact forces has been obtained, the uncertainties have to be propagated upto the upper scale. The usual method is the direct Monte-Carlo simulation (MCS) which consists in explicitly evaluating for each structural realization a large number of apparent contact forces and in integrating them into the upper scale FE model in order to determine a set of structural behaviors, from which their probabilistic properties are identified. As the evaluation of the apparent contact forces is computationally expensive, the direct MCS method is not efficient. To avoid this disadvantage, the stochastic model-based method constructs a generator for these forces which is built using a relatively small number of explicitly evaluated apparent contact forces. Thanks to the combination of the multi-scale contact model with the apparent contact forces stochastic model, the probabilistic behavior of the adhesion can be determined with an acceptable computational cost.
The structure of this paper is developed as follows. In Sect., is the conclusion.
1.2 Humid Stiction of Rough Surfaces
In humid conditions, between the two hydrophilic contacting surfaces, there exists condensing water which results into a negative pressure, named Laplace pressure, and pulls the two contacting surfaces together. The Laplace pressure is evaluated by
11 where LG is the liquid vapor energy V m is the liquid molar volume is - photo 2
(1.1)
where LG is the liquid vapor energy, V m is the liquid molar volume, Picture 3 is the universal gas constant, and T is the absolute temperature, and RH is the relative humidity. There are two parameters characterizing the geometry of the menisci: the contact angles {1,2}, depending on the surfaces properties, and the Kelvin radius r K given by Cai and Bhushan []
Micro and Nanomechanics Volume 5 Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics - image 4
(1.2)
For nano rough surfaces, because the radius of a contacting asperity is much bigger than the Kelvin radius, see Fig.a, the maximum contact distance at which water can condense between two bodies, defined as the capillary range, is evaluated by
13 Figure b illustrates the evaluation of the Laplace pressures and of the - photo 5
(1.3)
Figure b illustrates the evaluation of the Laplace pressures and of the condensing water heights with humidity levels for contact angles 1=2=0.
Fig 12 The geometry of a meniscus a and the evolution of meniscus height - photo 6
Fig. 1.2
The geometry of a meniscus ( a ), and the evolution of meniscus height and Laplace pressure in terms of humidity levels ( b )
It can be observed that the Laplace pressure is much smaller than the Youngs modulus of hard materials such as polysilicon. As a result, at the equilibrium, the physical contact area is much smaller than the apparent area, the typical area ratio being Picture 7 . Moreover, the condensing water heights are comparable with the roughness of the typical MEMS surfaces []. Therefore, there exist uncertainties on the contact problem between two rough surfaces.
1.3 Modelling Method
In the following the stochastic model-based multi-scale methodology, developed by the authors in [].
In that method, the multi-scale technique is used and consists in replacing the random rough contact surface Picture 8 by its mean surface and associating it with the contact laws which are the apparent adhesive - photo 9
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