Experimental Characterization of the static behaviour of microcatntilevers electrostatically actuated

EXPERIMENTAL CHARACTERIZATION OF THE STATIC BEHAVIOUR OF
MICROCANTILEVERS ELECTROSTATICALLY ACTUATED

Alberto Ballestra1, Eugenio Brusa2, Mircea Georghe Munteanu2, Aurelio Somà1 1 Laboratory of Microsystems, Department of Mechanics, Politecnico di Torino,
C.so Duca degli Abruzzi, 24 – 10129 Torino, Italy; alberto.ballestra@polito.it, aurelio.soma@polito.it
2 Department of Electrical, Management and Mechanical Engineering, Università di Udine,
via delle Scienze, 208 – 33100 Udine, Italy; eugenio.brusa@uniud.it, munteanu@uniud.it

ABSTRACT

This paper concerns the experimental validation of some mathematical models previously developed by the authors, to predict the static behaviour of microelectrostatic actuators, basically free-clamped microbeams. This layout is currently used in RF-MEMS design operation or even in material testing at microscale. The analysis investigates preliminarily the static behaviour of a set of microcantilevers bending in-plane. This investigation is aimed to distinguish the geometrical linear behaviour, exhibited under small displacement assumption, from the geometrical nonlinearity, caused by large deflection. The applied electromechanical force, which nonlinearly depends on displacement, charge and voltage, is predicted by a coupled-field approach, based on numerical methods and herewith experimentally validated, by means of a Fogale Zoomsurf 3D. Model performance is evaluated on pull-in prediction and on the curve displacement vs. voltage. In fact, FEM nonlinear solution performed by a coupled-field approach, available on commercial codes, and by a FEM non-incremental approach are compared with linear solution, for different values of the design parameters.

1. INTRODUCTION

In microsystem mechanical design cantilever beams are currently widely used, as basic components in
microsensors, microswitches and RF-MEMS as well as in experimental micromechanics, whose goal is characterizing the materials mechanical properties and strength, at microscale [1,2,3,4]. The latter aspects motivate the implementation of efficient numerical models to predict the electromechanical behaviours of such microdevices, under the actuation of the electric field, as stand-alone systems or better as structural components of assembled parts, as recent DTIP Conferences showed during the last years, like in [5-8]. Model validation is currently performed not only to verify the effectiveness of proposed analytical, numerical and even compact approaches [9, 10], but to define the model sensitivity on the uncertainties about the actual values of the design parameters and of materials properties, whose measurement is often fairly difficult. A couple of targets appear currently challenging for structural micromechatronics. An assessment of accurate coupled- field models and numerical solutions shall allow a coherent interpretation of the specimen response in all the experimental procedures, currently performed and aimed to characterize both the materials and the MEMS layouts [3, 4, 11, 12, 13]. Moreover, to build effective numerical simulators, able to predict the coupled behaviour of MEMS within the whole electronic circuit, only a validation of each single model included in a hierarchical approach will allow satisfying the requirement [9]. This paper contributes to the above mentioned tasks, by investigating the effectiveness and the computational performance of the numerical models proposed in [1, 14- 18], dealing with the static behaviour of microcantilevers. Moreover, the above mentioned models have to be even used in dynamic analysis algorithms, when geometrical nonlinearity has to be added to the effects of nonlinear electromechanical [16-18].

2. THE EXPERIMENTAL SET-UP

2.1. Microcantilevers with in-plane bending

A first group of specimens including free-clamped microcantilevers was designed and built, according to the design rules and the process constraints imposed by microfabrication, followed by STMicroelectronics (Cornaredo, Italy). Process “Thelma” allows a gradual growth of thick polysilicon layers, being suitable to fabricate cantilever beams, for which the bending deflection occurs in-plane, with respect to the reference plane of the wafer (Fig.1). This approach was followed to validate the developed models, by means of the experimental measures performed by Fogale Zoomsurf 3D [19]. All microspecimens consist of a massive electrode ©EDA Publishing/DTIP 2007 ISBN: 978-2-35500-000-3

A.Ballestra, E.Brusa, M.Gh. Munteanu, A.Somà Experimental characterization of the static behavior of microcantilevers electrostatically actuated

where is clamped a thin microbeam, bending across the gap towards a massive counter-electrode.

Microbeam Supporting frame Counter- electrode Microbeam Supporting frame Counter- electrode

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