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STUDY OF AN ELECTRO-MECHANIC MECHANISM EXPLOITING IN-PLANE ROTATION FOR THE REALIZATION OF TUNEABLE CAPACITORS

Parisa Ture Savadkoohi, Benno Margesin, Dan Vasilache, Flavio Giacomozzi

FBK-irst Trento, Via Sommarive 18, 38123 Povo Trento, Italy E-mail: savadkoohi@fbk.eu

Abstract–In the last years MEMS Switches and related MEM components have encountered a great interest in the technology community for their outstanding intrinsic characteristics. MEMS Switches in particular offer low insertion loss, higher isolation, almost zero power consumption, small size and weight at very low inter-modulation distortion, which makes them suitable for many applications. The MEMS technology has demonstrated also to be able to provide potentially high quality components for other passive RF and microwave devices such as capacitors and inductors. In this paper we extend our research activities on MEM technology to the design of tuneable capacitors based with in-plane movement. Keywords: RF MEMS, Varactor, Electromechanic

1. INTRODUCTION

In order to exploit the rotational effect in a practical device and specially in a tuneable capacitor, a butterfly shaped mobile electrode, obtained from two circle segments joined in the centre and suspended with a very flexible spring has been adopted [1][2]. The device has in addition two fixed electrodes, partially overlapping the butterfly shaped mobile electrode. One is intended for actuation, i.e. for slightly rotating the structure under polarization, while the second one is the fixed electrode of the variable capacitance; more details can be found in [2].

Fig. 1. Summary of the fabrication process.

The fabrication of the device has been done at the FBK-IRST, Trento, Italy by employing a well establish process for RF MEMS switches based on the surface micromachining technique combine to standard CMOS-technology, Fig. 1 summarizes the fabrication [2].

Eight design variants illustrated in Fig. 2 have been investigated experimentally. The 8 designs differ mainly for the shape of the meander spring or the thickness of the meander. For the sake of simplicity, the devices are numbered from 1 to 8. Figure 3 shows the actuating and sensing electrodes of devices in polysilicon and metal.

.

Fig. 2. General layout of the 8 different designs.

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As suspended structures with minimal mechanical constraints are extremely sensitive to internal stress gradients after the fabrication phase, the actual shape of the mobile electrode has been measured by means of an optical profilometery in order to establish the planarity of the electrodes. The 3-D view and the height of the profile of one of devices (device 6) are depicted in Figs. 4a and 4b, respectively.

Fig. 3. a,b,c)The actuation and sensing electrode of device 1-6, device7 and device 8 in poly and metal respectively. These profiles revealed a minor out of plane

deformation of the mobile electrode of about 3 µm between the outer rim of the mobile electrode and the centre point.

a)

b)

Fig. 4. a) 3-D view and b) height profile of one the devices obtained by optical profilometry.

To evaluate the performance of the mechanism quasi static Capacitance-Voltage measurements have been carried out on all devices. All devices show in primis a switch like behavior. Four of them show in addition an unusual behavior in the CV curve, i.e. an additional capacitance change after pull-in, which is compatible with a slight in plane rotation after pull-in of the structure. Table 1 summarizes the experimental data in terms of the pull in voltage, pull out voltage, off and on capacitance and the angle of rotation corresponding to the additional capacitance change. The degree of rotation corresponding to the capacitance change immediately after pull-in or prior pull-out (C1) and the capacitance value of the plateau (C2), has been estimated by simple geometrical calculations. As an example of the obtained CV curves, Fig. 5 and 6 show the CV characteristic of device 1 and 2.

Fig. 5. CV characteristics of device 1: additional capacitance changing after actuation and due to in-plane

rotation is highlighted. Fig. 6. CV characteristics of device 2: additional capacitance changing after reaching pull-in voltage and attributed to in-

plane rotation is highlighted.

2. ANALYTICAL MODEL

In order to model the in plane movement of the devices a simple analytical model based on

C1

C2

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elementary mechanics has been set up and is reported next. More details can be found in [3].

Considering a small angle of rotation, the area of the overlap between the mobile electrode and the fixed electrode can be approximated by twice the area of the small triangle formed by the radius of the outer circular border of the butterfly structure and the small arch segment due to the rotation:

θθ2a=Α (1)

where a is the outer radius of the butterfly wing and θ is the angle of rotation. The corresponding capacitance difference is :

eff

ox

dA

C θεε 0=Δ (2)

where oε is the permittivity of the vacuum, oxε is the dielectric constant of oxide and deff the effective oxide thickness.

Three moments govern the problem and balance each other: the moment generated by the lateral electrostatic force Mel, the opposing torsion moment of the suspension springs Mt and the antagonistic moment generated by the friction between the two electrodes Mf.

ftel MMM += (3)

The lateral electrostatic force Fel developed between the two electrodes is independent from the overlap and depends only on the voltage applied and can be expressed as:

eff

oxel d

VF

20εε

= (4)

while the friction force Ff is:

effxff d

VaAF 2

22

000 )( θεεμ += (5)

The torque moment Mt generated by the suspension springs is expressed as:

θtt KM = (6)

where tK is the torque constant of the suspension springs.

Finally the rotation θ in terms of the applied voltage can be expressed as :

2

23

0

20

2

)(

effoxft

efff

effoxo

dVaK

Vd

aAda

εεμ

μεεθ

+

−= (7)

Once the dependence of the rotation on the applied voltage is known one can easily express the capacitance curve in terms of the rotation:

effox d

aCC θεε2

00 += (8)

The dependence of the rotation angle on the applied voltage has the general expression:

2

2

1)(

VVVC+

= (9)

In Fig. 7 the graph of this generic curve is shown. The distinctive features of the curve are the parabolic part near the zero and the saturation. These can also be found in all curves analysed above which show an additional change in capacitance after pull-in.

Table 1. Summary of the experimental data including the estimated values of rotation.

Device

type

Vin

Vout

C1in

C1out

C2

Estimated rotation

Analytical/ simulation

[V] [V] [pF] [pF] [pF] [°] 1 40 20 0.553 0.278 0.688 1,76 , 1,4 2 41 20 0.404 0.289 0.577 1,15 , 2 3 9.5 2 0.404 0.206 0.457 1 ,23 4 61 57.5 0.452 0.373 0.518 0,7 5 44.5 42.5 0.753 0.827 - - 6 53 24 0.604 0.324 - - 7 64 - 0.456 - - - 8 21 13 0.346 0.218 - -

All of them have a first part that is similar to a

parabola, i.e. after the pull-in the capacitance increases more than linearly with the applied voltage. Depending on the stiffness of the suspension springs this feature can be more evident like for device 2 and 4 or less evident as for device 1 and 3 [3].

Fig. 7. Generic shape of the curve of the expression of the rotation angle vs the applied voltage.

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In addition on the devices 1 and 2 numerical simulatons with ANSYS have been performed. In general the numerical calculations are in fair to good agreement with the analytical calculations. In the case of device 2 featuring stiff suspension springs the rotation found by numerical simulation is larger than the calculated one. Acknowledgement–The authors would like to acknowledge the MEMS unit group at FBK-Irst Trento-Italy for supporting the work; moreover they thank dr. Alvise Bagolini for his useful helps and comments.

References [1] M. Elwenspock, R. Wiegerink, Mechanical

Microsensors,©Springer–Verlag Berlin Heidelberg 2001.

[2] P.T. Savadkoohi, B. Margesin, S. Colpo, “Novel design of the RF MEMS Switches based on the electrostatically induced torsion”, The Journal of Microsyst Technol, 2, pp. 10.1007/s00542-009-0946-7, 2009.

[3] P.T. Savadkoohi, “Study of the electromechanic aspects of RF MEM devices with particular emphasis on the dynamic behaviour for the case of RF MEM switches and tuneable capacitors”, Ph. D thesis, April, 2010.