RF-MEMS beam components : FEM modelling and experimental identification of pull-in in presence of residual stress

📝 Abstract

In this paper an experimental validation of numerical approaches aimed to predict the coupled behaviour of microbeams for out-of-plane bending tests is performed. This work completes a previous investigation concerning in plane microbeams bending. Often out-of-plane microcantilevers and clamped-clamped microbeams suffer the presence of residual strain and stress, which affect the value of pull-in voltage. In case of microcantilever an accurate modelling includes the effect of the initial curvature due to microfabrication. In double clamped microbeams a preloading applied by tensile stress is considered. Geometrical onlinearity caused by mechanical coupling between axial and flexural behaviour is detected and modelled. Experimental results demonstrate a good agreement between FEM approaches proposed and tests. A fairly fast and accurate prediction of pull-in condition is performed, thus numerical models can be used to identify residual stress in microbridges by reverse analysis from the measured value of pull-in voltage.

💡 Analysis

In this paper an experimental validation of numerical approaches aimed to predict the coupled behaviour of microbeams for out-of-plane bending tests is performed. This work completes a previous investigation concerning in plane microbeams bending. Often out-of-plane microcantilevers and clamped-clamped microbeams suffer the presence of residual strain and stress, which affect the value of pull-in voltage. In case of microcantilever an accurate modelling includes the effect of the initial curvature due to microfabrication. In double clamped microbeams a preloading applied by tensile stress is considered. Geometrical onlinearity caused by mechanical coupling between axial and flexural behaviour is detected and modelled. Experimental results demonstrate a good agreement between FEM approaches proposed and tests. A fairly fast and accurate prediction of pull-in condition is performed, thus numerical models can be used to identify residual stress in microbridges by reverse analysis from the measured value of pull-in voltage.

📄 Content

9-11 April 2008 ©EDA Publishing/DTIP 2008

ISBN: 978-2-35500-006-5

RF-MEMS beam components: FEM modelling and experimental identification
of pull-in in presence of residual stress

Alberto Ballestra1, Eugenio Brusa2, Giorgio De Pasquale1, Mircea Gh. Munteanu3, Aurelio Somà1 1 Politecnico di Torino, Mechanical Department,
c.so Duca degli Abruzzi, 24 – 10129 Torino, Italy;
alberto.ballestra@polito.it, giorgio.depasquale@polito.it, aurelio.soma@polito.it, phone ++39 011 5646951; fax ++39 011 5646999

2,3 Università degli Studi di Udine, Dept. Electrical, Management and Mechanical Engineering via delle Scienze 208 – 33100 Udine, Italy; 2 eugenio.brusa@uniud.it, 3 munteanu@uniud.it phone 2++39 0432 558299, 3++39 0432 558243, fax ++39 0432 558251

Abstract-In this paper an experimental validation of numerical approaches aimed to predict the coupled behaviour of microbeams for out-of-plane bending tests is performed. This work completes a previous investigation concerning in plane microbeams bending.
Often out-of-plane microcantilevers and clamped-clamped microbeams suffer the presence of residual strain and stress, which affect the value of pull-in voltage. In case of microcantilever an accurate modelling includes the effect of the initial curvature due to microfabrication. In double clamped microbeams a pre- loading applied by tensile stress is considered. Geometrical nonlinearity caused by mechanical coupling between axial and flexural behaviour is detected and modelled. Experimental results demonstrate a good agreement between FEM approaches proposed and tests. A fairly fast and accurate prediction of pull-in condition is performed, thus numerical models can be used to identify residual stress in microbridges by reverse analysis from the measured value of pull-in voltage. I. INTRODUCTION Microcantilevers and microbridges are currently widely used in RF applications as microswitches and microresonators [1], [2] and in experimental micromechanics, where materials mechanical properties and strength are measured. Therefore, it is required implementing efficient numerical models to predict the electromechanical performance of microstructures actuated by electric field [2], [3], [4], [5]. A wide variety of approaches has been proposed in literature to predict static and dynamic behaviour of microbeams [1], [6], [7], [8]. Experimental validation is therefore aimed to verify their effectiveness in predicting pull-in condition and frequency response. Usually model sensitivity on the uncertainties of numerical values of design parameters and material properties is investigated. Very often is rather difficult to know precisely material properties and microspecimen dimensions. FEM original approaches developed by the authors were proposed in [9], [10], [11], [12] and were already validated in [13]. A preliminary experimental investigation was aimed to predict the static behaviour of planar microcantilevers, for in- plane bending test. Present research is devoted to complete previous investigation activity focusing on out-of-plane bending microbeams.
Fully coupled electromechanical problem has electrical and mechanical coordinates, which are linked by the electromechanical coupling effect. Pull-in condition is responsible of a snap down of microbeam on the counter- electrode. In present case pull-in may be affected by some initial stress or strain present on the microsystem before the application of electric field. Moreover, it is well known that the problem is nonlinear because of the dependence of electromechanical force on displacement and voltage and, sometimes, of the so-called geometrical nonlinearity [10], [11], [12], [13]. To include these effects, models of microcantilever have to introduce the approximated analytical description of the initial curvature. It is usually sufficient to predict with enough accuracy the pull-in voltage and displacement, with an error of 2-3% maximum. For microbridges with double clamps axial stress is required to perform a coherent simulation of the actual system. II. SPECIMEN CHARACTERIZATION A. Fabrication process and measurement methods Specimens used for this work were realized by ITC-IRST Research Center (Trento, Italy), by means of the so-called RF Switch (RFS) Surface Micromachining process. Gold is used for the suspended structures; material is deposited through electroplating by means of a chromium-gold PVD adhesion layer [14], [15]. Profilometric measures and pull-in tests were performed by Fogale Zoomsurf 3D optical profiling system, based on non-contact optical interferometry [16]. The lateral resolution is ±0.3 µm, while the vertical resolution reaches ±0.5·10-4 µm [17].Tables 1 and 2 show the dimensions of microbeams used as specimens in testing, all measures are
9-11 April 2008 ©EDA Publishing/DTIP 2008

ISBN: 978-2-35500-006-5

Fig. 1-Geometry 4 seri

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