bDept. of SYDE, University of Waterloo, Waterloo, Ontario, CANADA ... MEMS switches under study were fabricated as bridges over 50 ohms G/S/G Coplanar.
Procedia Chemistry Procedia Chemistry 1 (2009) 622–625
www.elsevier.com/locate/procedia
Proceedings of the Eurosensors XXIII conference
Dynamic Pull-in of Shunt Capacitive MEMS Switches Krishna Vummidia, * , M. Khaterb, E. Abdel-Rahmanb, A. Nayfehc, S. Ramana b
a Bradley Dept. of ECE, Virginia Tech, Blacksburg, Virginia, USA Dept. of SYDE, University of Waterloo, Waterloo, Ontario, CANADA c Dept. of ESM, Virginia Tech, Blacksburg, Virginia, USA
Abstract
We report experimental results for a capacitive MEMS shunt switch that employs Dynamic Pull-in (VDP = VDC + RMS vac) as an actuation method. We show that VDP is significantly less than the static pull-in voltage (VSP = VDC) traditionally used for actuation. We also show that the reduction in actuation voltage can be enhanced be operating at the nonlinear resonance frequency. Keywords: Shunt switches, Dynamic Actuation, MEMS, Reduced-order models
1. Introduction MEMS switches have many potential RF applications including signal routing, tunable impedance matching networks, antenna switches, true time-delay (TTD) phase shifters, tunable filters and other high-frequency reconfigurable circuits. MEMS switches are better suited for these applications compared to their solid-state counterparts because they offer low insertion loss, high off-state isolation and better linearity over broad frequency ranges [1]. While a number of actuation schemes have been proposed, electrostatic actuation is currently dominant due to its power efficiency, relatively high speed, fabrication simplicity and easiness of the required biasing networks. Traditionally, electrostatic MEMS switches have been “statically” actuated by applying a constant DC voltage across the switch plates. We are proposing to actuate shunt switches “dynamically” by applying a combination of DC and a vac whose frequency is close to a natural frequency of the switch. Dynamic (resonant) pull-in of electrostatic actuators has been studied experimentally and theoretically [2, 3]. They indicate that an excitation waveform ( = vac cos Ωt) has a reduced pull-in voltage VDP = VDC + RMS (vac) compared to static pull-in voltage VSP = VDC. Experimental results for dynamic actuation [3] show lower pull-in voltages with appropriate combination of AC and DC voltages. In this paper we investigate the use dynamic actuation (vac ≠ 0) in shunt capacitive switches, examine the voltage savings accrued by tuning to the nonlinear resonance frequency. . 2. Geometry and Model
1876-6196/09 © 2009 Published by Elsevier B.V. Open access under CC BY-NC-ND license. doi:10.1016/j.proche.2009.07.155
623
K. Vummidi et al. / Procedia Chemistry 1 (2009) 622–625
The Shunt Capacitive MEMS switches under study were fabricated as bridges over 50 ohms G/S/G Coplanar Waveguides (CPW) on Si substrates. The geometry of the switch is shown in Fig. 1. The switch dimensions are given in Table 1. Brief fabrication procedure is illustrated in Fig. 2. The actuation voltages (vac and VDC) are applied to the signal line (S) via a bias Tee.
NOMENCLATURE
ν
Material Properties 0.42
ρ
19320 kg/m 3
b h
1.7
N
17 MPa
d
1.8
E
80 GPa
We
45
l b
Device Dimensions (µm) l 225 20
We G
S
G
Fig. 1. SEM picture of a single-bridge MEMS switch. Multiple-bridge switches are shown in the inset. Insertion loss is reduced without increase in actuation voltage by having multiple switches in parallel. Inset Table: Switch Dimensions and Material Properties
Fig. 2: Fabrication procedure of the capacitive shunt switch. (a) CPW patterning (b) Dielectric layer - PECVD SiN deposit and patterning (c) Sacrificial layer with anchor patterning; seed layer (Ti/Au/Ti) by evaporation (d) Au Electroplating and Sacrificial layer removal followed by Critical Point Drier release.
We adapt the reduced-order modeling approach proposed by Younis et al. [4] to model the switch as a clampedclamped microbeam according to Euler-Bernoulli beam theory. The electrostatic force between the microbeam and the bottom electrode is modeled according to parallel-plate theory. The non-dimensional equation of motion governing the transverse deflection of the microbeam , can be written as
Γ,
(1)
where the non-dimensional parameters appearing in the equation are defined as follows:
̂ !
"#$
, 6 &(' ,
* !
) "#
,
+ , !
" -. / .
,0 1
2 3 - ! "#
(2)
where & is the height of unactuated beam above the bottom electrode, ν is the poisson’s ratio, ρ is the density of * is the axial force in the beam due to residual stresses, ̂ is the viscous damping coefficient, 4 is the electrical gold, permittivity of air. The parameters h, b, E and I are the beam thickness, width, modulus of elasticity, and second moment of area, respectively. The operator Γ is defined as
Γ, 56
&
(3)
K. Vummidi et al. / Procedia Chemistry 1 (2009) 622–625
624
The last term in Equation (1) represents the electrostatic force between the beam and the electrode generated by a static VDC and a dynamic v(t) voltage components. The dynamic voltage component is a harmonic function given by v(t) = vac cos (Ωt) where vac is the AC amplitude and Ω is the non-dimensional excitation frequency. The reducedorder model is generated from Equation (1) by discretizing it into a finite-degree-of-freedom system consisting of ordinary differential equations in time 3. Experimental Results A laser vibrometer, Polytec Inc. MSV-400 shown in Fig. 3, was used to measure the frequency-response of the velocity at the mid-point of the bridge. The bridge was excited with a harmonic AC signal in the vicinity of its first natural frequency. To determine the frequency range of interest, the first natural frequency was measured at various DC voltages (Fig. 4) as well as the static pull-in voltage (VSP = 68.5 V). To obtain a point on this curve, the value of the DC voltage is fixed, the amplitude of the harmonic AC is set to a small value and the frequency of the AC signal is varied while tracking the FFT of the response. The excitation frequency corresponding to the maximum spike at Ω corresponds to the natural frequency of the bridge. A parameter identification technique was developed to estimate the bridge thickness by fitting the natural frequency curve obtained using the model with that of the experimental results. The fit shown in Fig. 4 results in a beam thickness estimate of h =1.7 µm. 100
a
Frequency (KHz)
80
RMS Velocity mm/sec
160 Q= 7 VDC = 5 V vac (amp.) = 14 V
b 120
60 Model Experiment
40
80
20 40
Vsp
0 60
80
100
120
Frequency (KHz)
140
0 0
20
40
60
DC (volt)
Fig. 3: A vibrometer measured the velocity RMS of the bridge mid-point (inset a) to construct the frequency-response curve shown in inset b; Fig. 4: The fundamental natural frequency as a function of VDC obtained from the model (solid line) and experiment (x).
Two methods were used to achieve dynamic pull-in. (1) A force sweep: At a fixed VDC, the amplitude vac was swept until pull-in while holding the excitation frequency Ω equal to the natural frequency corresponding to VDC as measured in Fig. 4. (2) A frequency-sweep: At a fixed VDC, the excitation frequency Ω was swept while holding the amplitude vac constant to find the nonlinear resonance frequency (peak) at this amplitude. Because of the switch softening nonlinearity, this peak shifts to lower frequency values as vac increases (Fig. 5). The curve of nonlinear resonance frequency versus vac was tracked until (dynamic) pull-in. The last point in each of the curves in Fig. 5 is the highest realizable vac where bounded motions were observed, beyond that value dynamic pull-in occurs. Fig. 6a shows the combination of VDC and RMS (vac) needed for pull-in and Fig. 6b illustrates the percentage savings using the dynamic mode of actuation (dynamic pull-in) over VSP for procedure 1 (dashed lines) and procedure 2 (solid lines). It can be seen that both procedures produce actuation voltage savings compared to VSP. Procedure 2 is superior to procedure 1 because it guarantees the minimum actuation voltage required for dynamic pull-in at a given VDC. The voltage savings using procedure 2 is as high as 42 % when operated at around 20 Volts of VDC
K. Vummidi et al. / Procedia Chemistry 1 (2009) 622–625
625
Frequency (KHz)
100
90
80
DC=10 DC=20 DC=30 DC=50
70
v v v v
60
0
10
20
30
40
50
AC (volt)
Fig. 5: Nonlinear resonance frequency versus the amplitude of vac at various DC voltages
Fig. 6: a) Combinations of VDC and RMS vac that lead to pull-in at nonlinear resonance frequency (solid) and natural frequency (dotted). b) Percentage savings of VDP w.r.t VSP procedure 1 (dotted) and procedure 2 (solid).
4. Conclusions Capacitive shunt switches were fabricated on Si substrates. The switches were actuated both statically and dynamically. The static pull-in voltage was around 68.5 V. Dynamic pull-in ensures reduction in the effective voltage required to actuate the switch. The savings are a lot greater when the switch is operated at the correct nonlinear frequency as suggested in procedure 2. Best case percentage savings is when VDC = 20 V and RMS vac = 19.5 V and savings are close to 42 %.
Acknowledgements The authors would like to acknowledge Dr. Dev Palmer, Program Manager, Army Research Office for partially funding (W911NF-06-1-0422) this project. The authors would also like to acknowledge Mr. Riku Sudo’s valuable contributions to micro-motion measurements.
References 1. Rebeiz G, Muldavin J. RF MEMS switches and switch circuits. IEEE Microwave magazine 2001;2:59-71. 2. Nayfeh A, Younis M, Abdel-Rahman E. Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dynamics 2007;48:153 -163. 3. Farqas-Marques A, Casals-Terre J, Shkel A. Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators. J. Microelectromech. Syst 2007;16:1044-1053. 4. Younis M, Abdel-Rahman E, Nayfeh A. A reduced-order model for electrically actuated microbeam-based MEMS. J. Microelectromech. Syst 2003;12:672-680.
