DIFFERENTIAL ELECTRODE DESIGN FOR ELECTROSTATIC ACTUATOR IN CONDUCTING MEDIA Vikram Mukundan and Beth Pruitt Department of Mechanical Engineering, Stanford University, Stanford, USA (Tel : +1-650-725-0307; E-mail:
[email protected]) Abstract: We present the design, modeling and experimental validation of a novel differential actuation scheme to enhance the performance of comb-drive electrostatic actuators in aqueous media. The new design mitigates the losses in parasitic impedance and extends the actuation of the devices into frequency ranges suitable for biological samples, achieving a displacement of 3.5 µm in 100mM KCl. The frequency dependence of the electrostatic force has been tested by operating the devices in media of different ionic concentrations. Circuit models for the electric double layer phenomena are used to analyze the device behavior. Keywords: comb-drive electrostatic actuator, ionic solutions, electric double layer, circuit model 1. INTRODUCTION Electrostatic actuation is a popular means of actuation in silicon Microelectromechanical systems (MEMS)[1, 2]. Fast actuation, large displacements and low power consumption being some of the advantages. Operation of electrostatic devices in conducting, liquid media requires high frequency signals to overcome ionic screening and electrochemical interactions[3-5]. The frequency of the signal must be chosen such that the polarity of the field changes at a rate faster than that the ionic response time. Earlier, we presented the characterization of electrostatic actuators in ionic media[5]. While higher frequencies are required for operation in more conducting media, the attenuation is also higher and this limited operation to solutions of less than 1 mM. Since these actuators are designed as a part of controllable on-chip system for mechanical stimulation of live cells, they have to be operated in solutions of 150 mM ionic strength. In this paper, we present a differential electrode design (Figure 1) for electrostatic actuation in highly conducting media. To the best of our knowledge our design enables the first substantial actuation in biological media, by extending the frequency range of actuation. We adapted the scheme from Bhave et al’s demonstration of a fully differential Lame mode SiC resonator with improved quality factor by minimizing substrate losses[6]. We present the design and characterization of the first differential electrode
design and operation for electrostatic actuators operated in conducting media.
Figure 1. Scanning Electron Micrograph of differential electrode electrostatic comb-drive actuator, indicating drive electrodes 1 and 2, beam suspension and cell binding site. 2. THEORY A comb-drive actuator comprises interdigitated pairs of electrodes, with one suspended and free to move. When a voltage V is applied across the electrodes, the electrostatic force is balanced by the stiffness in the suspension. The force displacement relation in a dielectric medium is given by N εb 2 F = kx = V , (1) d where k is the suspension stiffness, ε is the permittivity of the medium. N is the number of
fingers, d is the gap length and b is the thickness of the device. In conducting media, the mobile ions migrate towards electrodes of opposite polarity. When a solid surface is immersed in an electrolyte, there is spontaneous accumulation of ions near the electrodes due to surface potential at the interface, called the electric double layer. The same occurs when an external potential is applied at the electrode. The linearized expression for the double layer capacitance per unit area is given by[7] ε (2) C EDL = , λD where λD is the Debye length of the double layer and ε the permittivity of the solvent(water). We consider a circuit model shown in Figure 2. Rw, the resistance of the medium between the electrodes is derived from the electrolyte conductivity (σ). The Stern layer (thickness λs) formed by adsorption of ions at the surface also contributes to the interface capacitance. Additionally, the electrodes have parasitic capacitance to ground and other electrodes which are not considered here for the estimation of frequency response. The shielding time constant is determined by the effective series capacitance and resistance to be , λ λ s D + + εs ε w ε ox
τ c = RW CEff
εd = 0 2σ t
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where εox, εS and εw refer to the relative permittivity of the oxide, Stern layer and water respectively. The actuating frequency must be greater than the inverse of the shielding time constant. Silicon Electrode
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Figure 2. (a) Silicon electrode schematic indicating gap dimension d and native oxide thickness t~2nm. (b) Circuit model of electrode indicating Cox, CINT and CW to estimate operating frequency in conducting media.
3. FABRICATION The devices are fabricated on Silicon-OnInsulator (SOI) wafers as shown in. The wafers are P-type silicon with resistivity of between 0.005 and 0.02 ohm-cm. The silicon electrodes and suspension beams are etched into the device layer by a Deep Reactive Ion Etching (DRIE) process. Metal lines (Cr-250 Å/Pt-500 Å/Au-3000 Å) are deposited by e-beam evaporation and patterned by a lift-off process. A wafer saw is used to dice devices before the sacrificial layer release etch. The devices are released by a timed wet-etch of the underlying oxide. The devices are then dried in a liquid CO2 critical point dryer (CPD) to avoid stiction. 4. EXPERIMENTAL RESULTS The device was packaged on a ceramic Dual Inline Package (DIP) and immersed in test solution. The actuation signal was applied between the electrodes, with the substrate grounded. DC voltages were used to actuate the device in air, while AC voltages were used in solutions. The frequencies of AC signals were predicted using the modeling approach described above. The displacement was measured by an image processing code written in MATLAB. Pixel resolution of the camera enables a measurement with an accuracy of about 200 nm in displacement (for a 50x objective lens). We present data from single electrode actuation to compare the results with the new design. 4.1 Single electrode actuation The device was characterized in terms of its displacement in KCl solutions (Figure 3) by applying constant amplitude of 3.5V while varying the frequency. While higher frequency is required for increasing concentrations as expected, the displacement falls off after 1 MHz. Moreover, the maximum observed displacement also decreases for higher concentration solutions. Displacement was below measurement resolution in solutions of concentration greater than 1mM. These shortcomings are attributed to the parasitic impedance losses, which were larger than initially expected.
Figure 3. Frequency response of actuator in KCl solutions, operated in single electrode mode. While higher frequencies are required to actuate in higher concentrations the maximum displacement is reduced due to parasitic losses. 4.2 Differential electrode actuation To minimize the attenuation, a two design improvements are presented. First, the resistivity of the device layer is reduced to minimize the voltage drop across the suspension. Figure 4 shows a comparison of displacements obtained from devices of resistivities 0.02 and 0.005 ohmcm. We observed that the displacement plateau is broader for the device of lower resistivity, as the roll-off sets in at higher frequencies. However, the roll-off remains unaffected. As mentioned earlier, this is believed to be the result of distributed parasitic resistors and capacitors between the electrode and substrate.
The second improvement is to minimize or eliminate the current flow through the substrate. This is accomplished by the schematic shown in Figure 5(a) and (b). By using two electrodes excited by signals of opposite polarity, zero current is injected into the substrate, assuming the impedances are symmetric. Since the electrostatic actuator responds to the RMS voltage, we get nonzero displacement. A comparison of the frequency responses of the same device operated with in-phase and out-ofphase signals, in DI water, is shown in Figure 5(c). The displacement in the out-of-phase excitation shows a relatively flatter response curve, indicating reduced effects of parasitic impedance. R
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Figure 5.(a) Schematic of differential electrode design indicating current flow. (b) Circuit model of electrode (c) Comparison of same phase (dashed) and out-of-phase (continuous) signal operations indicating flatter response due to reduced parasitic losses in latter case.
Figure 4. Effect of varying resistivity (dashed: 0.02 ohm-cm, continuous: 0.005 ohm-cm) on the frequency response. The maximum displacement plateau is broader due to reduced voltage drop.
To test the performance of this actuation scheme in solution of increasing ionic concentrations, the frequency response is measured in KCl solution. Figure 6(a) indicates that both the roll-off and the attenuation of maximum displacement are significantly reduced.
This response is relatively flat up to a frequency of 5 MHz. For 5V (peak-to-peak) applied signal, the maximum displacement (5µm) is maintained in 10 mM KCl, and 70% maximum displacement (3.5µm) in the case of 100 mM solution. The present drive electronics limit the actuation to 5 MHz and signal distortions are observed beyond this. Moreover, unbalanced impedances may also cause some attenuation and the nature of attenuation is under investigation. Nevertheless, the design modifications have largely minimized the high frequency losses thus allowing actuation in highly concentrated ionic media. This renders the device suitable for on-chip mechanical stimulation of cells.
Figure 6. Frequency response of differentially actuated device in KCl solutions up to 100 mM, operated at a constant amplitude of 5V (peak-topeak). 5. CONCLUSION The differential electrode design for electrostatic actuators minimizes the effect of parasitic impedance and enables actuation up to 5 MHz. This allows actuation in solutions up to 100 mM, while earlier designs were limited to 1 mM. This design has allowed operation of electrostatic devices in ionic solutions suitable for sustaining cells. Future work will include increasing the maximum displacement by extending the frequency and voltage range of driving electronics and testing with cells. 6. ACKNOWLEDGMENTS VM was supported by the Stanford Graduate Fellowship (2003-06). Fabrication work was
performed in part at the Stanford Nanofabrication Facility (a member of the National Nanotechnology Infrastructure Network) which is supported by the National Science Foundation under Grant ECS-9731293, its lab members, and the industrial members of the Stanford Center for Integrated Systems. This work was supported by NSF CAREER Award ECS-0449400. REFERENCES [1] W. C. Tang, T.-C. H. Nguyen, M. W. Judy, and R. T. Howe, "Electrostatic-comb drive of lateral polysilicon resonators," Sensors and Actuators A: Physical, vol. 21, pp. 328-331, 1990. [2] W. C. Tang, M. G. Lin, and R. T. Howe, "Electrostatic Comb Drive Levitation and Control Method," Journal of Microelectromechanical Sytems, vol. 1, 1992. [3] T. L. Sounart, T. A. Michalske, and K. R. Zavadil, "Frequency-Dependent Electrostatic Actuation in Microfluidic MEMS," Journal of Microelectromechanical Sytems, vol. 14, pp. 125-133, 2005. [4] H. V. Panchawagh, D. Serrell, D. S. Finch, T. Oreskovic, and R. L. Mahajan, "Design and Characterization of a BioMEMS device for invitro mechanical simulation of single adherent cells," presented at ASME International Mechanical Engineering Congress and Expedition, Orlando, 2005. [5] V. Mukundan and B. L. Pruitt, "Experimental Characterization of Frequency Dependent Electrostatic Actuator for Aqueous Media," presented at Solid State Sensors and Actuators, Hilton Head Island, 2006. [6] S. A. Bhave, D. Gao, R. Maboudian, and R. T. Howe, "Fully-Differential Poly-SiC Lamemode Resonator and Checkerboard Filter," presented at Solid State Sensors and Acuators conference, 2005. [7] M. Z. Bazant, K. Thornton, and A. Ajdari, "Diffuse-charge Dynamics in Electrochemical Systems," Physical Review E, vol. 70, pp. 021506-1-23, 2004.
