548 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL…katsuokurabayashi.com/wp-content/uploads/2010/06/EOS-Actuator... · 548 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14,

548 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 3, JUNE 2005

A Single-Layer PDMS-on-Silicon HybridMicroactuator With Multi-Axis Out-of-Plane Motion

Capabilities—Part I: Design and AnalysisYi-Chung Tung, Student Member, IEEE, and Katsuo Kurabayashi, Member, IEEE

Abstract—This paper proposes a new single-layer electrostaticmicroactuator design that generates three-axis motion resultingin vertical translation and out-of-plane tilting. The new actuatordesign combines a micrometer-scale three-dimensional (3-D)polydimethylsiloxane (PDMS) structure fabricated using softlithography with comb drives processed using a single mask on asilicon-on-insulator (SOI) wafer. The multi-axis actuation capa-bility of the proposed actuator is enabled by coupling the in-planeactuation motion of the comb drives with the elastic bending ofPDMS flexural microjoints. To predict the static and dynamic per-formance of the actuator, this paper develops a four-bar-linkagemodel and applies Lagrangian dynamics theory. The developedanalytical model is validated using finite element analysis (FEA)and allows us to perform parametric design of the actuator. Theanalysis indicates that the proposed PDMS-on-silicon hybridactuator can yield the desired multi-axis actuation capability witha dynamic bandwidth as large as 5 kHz. [1378]

Index Terms—Comb-drive actuator, finite element analysis(FEA), multi-axis microactuator, parametric design, PDMS-on-sil-icon microsystems.

I. INTRODUCTION

M ICROMETER-SCALE actuation with multiple degreesof freedom plays an essential role in many micro-

electromechanical systems (MEMS) applications, includingmicrorobotics [1], micromanipulation [2], [3], and microop-tics systems [4]–[10]. Significant research efforts have beenmade to develop electrostatic MEMS actuators capable ofmulti-axis in-plane/out-of-plane motions [3], [4], [9]–[12].However, the fabrication of these actuators is often challengingand time-consuming, requiring multilayer structures [4], [6]or relatively complex mechanisms [12]. Furthermore, theirassembly requires precise alignment and bonding of multiplesilicon substrates, adding more complexity to the laboriousfabrication processes.

Comb-drive actuators are commonly adapted in electrostaticMEMS actuation devices as they can be fabricated usingCMOS-compatible standard silicon surface micromachiningand yield a large dynamic bandwidth [13]. The comb-drivestructure simply consists of interdigitated electrodes of a

Manuscript received July 8, 2004; revised August 27, 2004. This work wassupported by the National Science Foundation CAREER Award. Subject EditorC. Hierold.

The authors are with the Department of Mechanical Engineering, Univer-sity of Michigan, Ann Arbor, MI 48109 USA (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/JMEMS.2005.844761

rectangular finger shape that are engaged with each other andmechanically compliant spring beams that suspend one ofthe electrodes. Electrostatic force resulting from bias voltagebetween the engaging electrodes drives their lateral motion.Despite their common use in MEMS technology, the short-coming of comb drives is that they predominately generateone-dimensional (1-D) motion, which usually lies parallel tothe substrate plane [10], [11], [13]–[15]. This leads to the needfor the aforementioned complex fabrication processes.

For example, Kwon et al. [6] have recently presented anasymmetric comb drive on a silicon-on-insulator (SOI) wafer.It was fabricated by a three-step back and front side deepreactive ion etch (DRIE) process, and it achieved out-of-planepiston motion. Using both surface [Multiuser MEMS Processes(MUMPS)] and bulk micromachining (DRIE), Piyawat-tanametha et al. [16] developed an angular vertical comb driveto generate out-of-plane tilting motion with one degree offreedom. Moreover, they integrated two sets of the actuatorsto generate out-of-plane tilting motion in two orthogonal axes.Xie et al. [17] also exploited curled hinges, which resultedfrom residual stress between different materials, to constructa similar vertically angled offset comb drive that yields tiltingmotion. Walraven and Jokiel [12] constructed a spatial mi-crostage that yields three degree-of-freedom motion [eitherXYZ translation or piston-tip-tilt (PTT)] using the Sandia Ul-traplanar MEMS Multilevel Technology (SUMMiT-V) siliconsurface micromachining process. With the same process, Hahet al. [18] developed a comb-drive actuated micromirror arraythat generates single degree-of-freedom motion (out-of-planetilting).

This paper proposes a novel polymer/silicon hybrid actuatorthat allows multi-axis, out-of-plane vertical and tilting actuationmotions, only requiring a single silicon layer with comb drives.The actuator design incorporates a 3-D polydimethylsiloxane(PDMS) microstructure placed on a silicon device layer. Withthis new actuator design, we theoretically demonstrate how theintegration of a 3-D PDMS microstructure can allow us to de-velop a new type of MEMS actuator. The performance of theactuator can be substantially enhanced by the flexibility of thepolymer. This paper focuses on the design and analysis of theproposed PDMS-on-Silicon hybrid microactuator.

II. HYBRID ACTUATOR DESIGN

Fig. 1 illustrates the actuator proposed in this paper. Theactuator is designed to translate the in-plane 1-D motion of

1057-7157/$20.00 © 2005 IEEE

Authorized licensed use limited to: University of Michigan Library. Downloaded on November 12, 2009 at 23:42 from IEEE Xplore. Restrictions apply.

TUNG AND KURABAYASHI: A SINGLE-LAYER PDMS-ON-SILICON HYBRID MICROACTUATOR—PART I 549

Fig. 1. Schematic drawing of the PDMS-on-silicon hybrid actuator.

comb drives to the out-of-plane motion of a PDMS microstruc-ture with multiple degrees of freedom. The actuator structureconsists of two major components: (1) multiple comb drivesfabricated on a SOI wafer; and (2) a PDMS micromotion trans-lator connected to the comb drives. The PDMS micromotiontranslator is composed of a micrometer-scale platform and fourconnectors. Each of the PDMS microconnectors provides amechanical connection between the platform and a comb-driverotor beam via two thin flexural microjoints.

We assume that the PDMS micromotion translator is fab-ricated using soft lithography here [19]. PDMS is an organicelastomer material widely used in a number of BioMEMS andmicrofluidic applications [20]–[23] due to its excellent opticalproperties ( 92% transmission for visible light [24]) and largemaximum strain limit near 40% [25], [26] (for silicon material,it is 1%.) With its high optical transparency and mechanicalrobustness, the PDMS micromotion translator can be an excel-lent structural component in optical MEMS applications.

Fig. 2 shows the details of the PDMS micro-connector withits end attached to a comb drive rotor beam. This connectorplays a primary role in converting the in-plane motion of thecomb drive to the out-of-plane motion of the mechanically rigidPDMS microplatform. The PDMS microconnector attached tothe electrically controllable comb drives is designed to achieveprecise nanopositioning and displacement multiplication. Sys-tematically coupling the motion of each comb drive allows theactuator to switch its modes in a programmable manner. For in-stance, simultaneously pulling the PDMS-silicon connectionsby activating either all of the four comb drives (#1 to #4) or twoof them facing each other (e.g., comb drives #1 and #3 or #2and #4) would cause vertical motion of the PDMS microplat-form in Fig. 3(a). On the other hand, the PDMS microplatformwill generate out-of-plane tilting motion with only two orthog-onal comb drives activated (#1 and #4). In addition, the oppositetilting motion with respect to the same axis can be achieved bycombining the motions of another pair of comb drives (#2 and

Fig. 2. Simplified four-bar linkage model of the PDMS microconnectorattached to a comb-drive actuator rotor.

#3), which doubles the tilting angle range for each axis as shownin Fig. 3(b). Similarly, the tilting around the other axis can beachieved using other combinations of moving comb drives [e.g.,comb drives #1 and #2; #3 and #4 as shown in Fig. 3(c)].



Fig. 3. Actuation modes resulting in (a) vertical motion, (b) tilting motion 1,and (c) tilting motion 2 of the hybrid actuator.

III. HYBRID ACTUATOR MODELING AND FEA VALIDATION

In this section, we develop an analytical model based on afour-bar-linkage mechanism to theoretically study the actuatorperformance and compare calculations using this model to nu-merical results from finite element analysis (FEA). The devel-oped analytical model allows for subsequent parametric designwith less computational time and expense than FEA.

A. Modeling of Hybrid Actuator

We model each of the four PDMS microconnectors as afour-bar linkage with two rotational springs as shown in Fig. 2.Each of the two flexural microjoints has thickness andlength , which are smaller than the other dimensions of themicromotion translator. This design leads to the deformation ofthese flexural microjoints caused by bending motion about the

-axis. As a result, we treat each of them as a pin joint locatedat its middle position with a rotational spring constant . Arigid-body boundary condition is applied for both ends of theflexural microjoint as they are connected to either a stiff siliconcomb-drive rotor beam or a thicker PDMS layer.

Now, we use simple beam theory to evaluate the rotationalspring constant of the flexural microjoints. When subjected toa bending moment , the microjoint attached to a rigid bodyyields a slope at its end, given by

(1)

where is the Young’s Modulus of the beam material(PDMS), and is the moment of inertia of the beam representingthe microjoint. Thus

(2)

Furthermore, the geometrical relations of the equivalentfour-bar linkage are given by

(3a)

(3b)

(3c)

(3d)

where and are the initial lengths of the linkage in the- and -directions, respectively, is the initial length of the

linkage, and is the initial angle of the linkage, is the lengthof the flexural microjoint, is the length of the microconnector,

is the thickness of the flexural microjoint, and is the thick-ness of the microconnector. When the microconnector rotates byan angle , the mathematical expressions for the input in-planedisplacement of the comb drive and the output vertical dis-placement of the PDMS platform are given by

(4a)

(4b)

where and are the positions of the comb drive and thePDMS microplatform in the coordinate system shown in Fig. 2.Equations (4a) and (4b) allow us to evaluate how much the inputdisplacement is multiplied through its translation to the ver-tical output displacement . Here, we define a displacementmultiplication ratio as , which can be given by

(5)

For a small rotational angle (i.e., ), the multiplicationratio can be simplified as

(6)

which can provide us an approximate value of multiplicationratio for selected device design parameters in the simple



Fig. 4. FEA simulation results. (a) Vertical displacement of the PDMS micromotion translator. (b) von Mises stress distribution in the PDMS micromotiontranslator.



TABLE IMATERIAL PROPERTIES USED FOR ANALYSIS

analytical form. With an input force applied to the PDMSmicroconnector from the comb drive, the resulting rotationalangle against the two rotational springs in series is givenby

(7)From (7), the vertical position of the PDMS microplatform isalso the function of . By knowing the rotational angle of themicroconnector for a given applied force , the dis-placements of the PDMS micromotion translator in the hori-zontal and vertical directions and can be calculatedfrom (4). Since the relation between and is nonlinear,the analysis requires iterative calculations.

B. Model Validation Using FEA

To validate the developed four-bar linkage model, we per-formed FEA using the commercial software ANSYS Release7.0 (ANSYS Inc., PA.) The symmetry of the PDMS micromo-tion translator allows us to analyze its mechanical behavior bysimply taking the quarter part, as shown in Fig. 4. In the simu-lation, we used the 3-D brick element SOLID45, each node ofwhich has three degrees of freedom. Also, a nonlinear finite el-ement simulation option was employed to account for large de-formations of the structure. There are two boundary conditionswe utilized to validate the developed model: (a) the displace-ment boundary condition, where a given displacement input isapplied to the end of the PDMS flexural linkage; and (b) theforce boundary condition, where the displacement input in (a)is replaced with a given force input.

Table I shows the material properties used for both of thefour-bar linkage model and the FEA simulation. The results ofthe FEA are shown in Fig. 4. The simulation indicates that thethin joints of the PDMS microconnector yield much larger de-formation than the thicker platform part. This allows us to safelyassume that the PDMS microplatform is a perfectly rigid body inthe model. In addition, local stresses are mainly concentrated inthe thin joints of the microconnector, which proves that they canact as flexural joints during the actuator operation as assumedin the analytical model. Fig. 5 compares the results obtainedfrom the analytical calculation and the FEA simulation under(a) the displacement and (b) the force boundary conditions. It isshown that the calculation based on the four-bar linkage modelis in a good agreement with the FEA simulation with an errorless than 5% at input displacement up to 5 . Fig. 5(c) showsthe simulated displacement multiplication ratio for theinput displacement up to 5 . Both analytical calculation andFEA simulation yield the multiplication ratio approximate 2 forthe selected device design parameters. The slight increase of

the multiplication ratio indicates the minor nonlinearity of thePDMS micromotion translator performance. The results provethat the PDMS micromotion translator not only translates thein-plane displacement to the out-of-plane direction but also am-plifies the magnitude of the input displacement from the combdrive. The analytical model is shown to predict the device per-formance reasonably well for typical comb-drive actuation in-puts.

IV. STATIC AND DYNAMIC PERFORMANCE ANALYSIS

We use a simplified parallel-plate capacitor model [14] to pre-dict the actuation behavior of the comb drives. Combing thefour-bar linkage model with the parallel plate capacitor modelallows us to model the performance of the entire hybrid actuator.In this paper, the whole device structure is modeled as a dis-crete mass-spring system subjected to external load as shown inFig. 6. This model allows us to predict the relationship betweenthe in-plane electrostatic actuation force of the comb drive andthe vertical displacement of the PDMS microplatform. Here, theexternal load generated by each comb drive is given by

(8)

where is the gap between the adjacent comb fingers, is thethickness of the comb fingers, is the total number of the combfingers, is the voltage applied across the engaging comb elec-trodes, and is the vacuum permittivity. There are two springconstant sources in the model: (1) one from the folded beams ofthe comb drive, whose spring constant is assumed to be invariantwith the rotor deflection; and (2) another from the elasticityof the PDMS flexural microjoints, which has a spring constantvarying with the deflection. The spring constant of the foldedsuspension beam of the comb drive is given by [14]

(9)

where is Young’s Modulus of silicon, is the thickness ofthe silicon structure, and and are the width and length ofthe suspension beams, respectively. By calculating the displace-ment of the rotor (i.e., the in-plane displacement input tothe PDMS microconnector), the vertical output displacement ofthe PDMS microplatform is calculated for a given inputvoltage .

Fig. 7 shows the calculated static performance of the actu-ator with the dimensions shown in Table II. Fig. 7(a) shows theactuation force generated by each comb drive as a function of

given by (8). Fig. 7(b) shows the calculated and asfunctions of when two facing comb drives are activated. Fol-lowing the same approach, the tilting angle of the PDMS mi-croplatform generated by two orthogonally activated combdrives can be calculated by

(10)

where is the distance between the two parallel lines connectinga pair of orthogonal comb drives as shown in Fig. 3(b). Thecalculated as a function of is shown in Fig. 7(c).



Fig. 5. Comparison of four-bar linkage analysis and FEA simulation of the PDMS micromotion translator performance using (a) displacement boundary condition,and (b) force boundary condition. (c) Displacement multiplication ratio calculated from (a) and (b).

Fig. 6. Discrete mass-spring system model for the entire device structure.

To study the dynamic performance of the hybrid actuator, wehave applied Lagrange’s equations to the developed analyticalmodel. The Lagrangian is defined as

(11)

where and are kinetic energy and potential energy, respec-tively. By definition, and of the designed system can begiven by

(12a)

(12b)

Thus, the Lagrangian can be written as

(13)

where is the mass of the comb drive rotor, is themass of the PDMS microplatform, is the spring constantof the silicon suspension beam, and is the rotationalspring constant of the PDMS flexural microjoint. The springconstant of the folded suspension beam of the comb drive isgiven by (9), and the rotational spring constant of PDMS flexuralmicrojoint is equal to given by (2). Therefore, theLagrange’s equation of motion of the system can be written inthe form

(14)Substituting , and given by (13), (8), and (4a) yieldsan expression for each term of (14) as

(15a)

(15b)

(15c)

(15d)



Fig. 7. Theoretical static performance of the hybrid actuator as a function of applied actuation voltage. (a) Electrostatic force generated at each comb drive.(b) In-plane displacement of comb-drive rotor�X and vertical displacement of the PDMS microplatform�Z . (c) Tilting angle of the PDMS micro-platform��.

TABLE IINOMINAL VALUES OF THE ACTUATOR DESIGN PARAMETERS USED FOR

THEORETICAL ANALYSIS

The equations derived above shows the nonlinearity of thesystem, which would be complex to analyze. For simplicity, thefirst-order linearization is applied by assuming

(16)

Then each term in the equation of motion can be simplified as

(17a)

(17b)

(17c)

Consequently, the resulting equation of motion for the systemwithout damping can be expressed as

(18)

Moreover, the viscous damping term is added to the equationof motion for evaluating the performance of the damped systemas

(19)

where is the rotational damping coefficient. For a sinusoidalvoltage excitation at an angular frequency , the applied voltagecan be written as

(20)

where is the dc offset voltage. Fig. 8 shows the calculatedtime-domain vertical velocity and displacement of the hybridactuator with two facing comb drives activated at 1 kHz when

. The calculation assumes a low damping systemwith the damping ratio , where can be calculated by(21) shown at the bottom of the next page.

Fig. 8(c) shows little distortion in the displacement profilewith respect to the sinusoidal actuation signal, indicating a goodlinearity of the actuation motion. Fig. 9 shows the calculated



Fig. 8. Predicted time-domain dynamic performance of the actuator using the developed model. (a) Input actuation voltage signal. (b) Vertical velocity of thePDMS microplatform. (c) Vertical displacement of the PDMS microplatform.

Fig. 9. Calculated amplitude spectrum of vertical displacement of the hybridactuator.

vertical displacement spectrum of the hybrid actuator at actua-tion frequencies between 500 Hz and 10 kHz with various valuesof the damping ratio. All the calculations presented here havebeen performed with the device dimensions shown in Table II.The calculation predicts that the resonant frequency of the actu-ator is about 4.86 kHz.

V. PARAMETRIC ANALYSIS

The actuator capable of multi-axis out-of-plane motion mayfind broad applications. The performance requirement is dif-ferent depending on each application. For example, fast out-of-plane actuation capability with wide bandwidth ( 1 kHz) is re-quired for a confocal scanning microscope to observe biolog-ical phenomena occurring on the microsecond timescale [27].For dense wavelength-division-multiplexed (DWDM) compo-nents, actuation of a mirror with a large static scan angle (e.g.,

at 40 V) is needed [28]. To observe how the proposed ac-tuator can be designed to fulfill the different requirements, westudy the sensitivity of its performance with respect to the de-vice design parameters using the developed model. Since theoutput vertical displacement and natural frequency of actu-ators are most commonly specified for various applications [7],[16], [28]–[29], we choose them as the performance evaluationparameters in our analysis.

We first took the values of the design parameters in Table IIas nominal ones in our parametric analysis, which yield a nat-ural frequency about 5 kHz and an vertical displacement of ap-proximately 5 at a 40 V peak-to-peak voltage applied oneach of two facing comb drives. Then we varied each of the de-sign parameters from 0.6 to 1.4 times its nominal value. Thecalculated results are shown in Fig. 10 and Fig. 11 and indi-cate that the static vertical displacement and the natural fre-quency are most sensitive to the length and width of the

(21)



Fig. 10. Predicted variation of static vertical displacement of the hybridactuator with design parameters.

Fig. 11. Predicted variation of natural frequency of the hybrid actuator withdesign parameters.

comb-drive suspension beam. In general, there exists a tradeoffbetween and the natural frequency with the varying param-eters. For instance, increases with an increasing value ofwhile the natural frequency becomes smaller at the same time.This tradeoff results from the reciprocal relationship betweenthe displacement and the natural frequency for a given mechan-ical stiffness of the entire system. The actuator design processneeds to account for this tradeoff. However, it is not observedfor and . The decrease of the spacing between the comb fin-gers increases the actuation force at constant applied voltage,and decreases the mass of the structure at the same time. Thisleads to a simultaneous increase of both and the natural fre-quency. Similarly, the decrease of flexural microjoint thickness

leads to the same result due to the decrease of both of thestructural stiffness and mass. The minimum values of these pa-rameters would be mainly limited by the fabrication capability.By carefully choosing the device dimensions according to the

analysis, the microactuator can be designed to yield a fast re-sponse and large out-of-plane displacement at a relatively smallactuation voltage.

VI. CONCLUSION

This paper has proposed a new electrostatic actuator incor-porating a 3-D PDMS microstructure that can achieve multi-axis out-of-plane motion driven by simple single-layer siliconcomb drives. A mechanical model of the PDMS structure usinga four-bar linkage analogy was developed and validated by FEAsimulation. Combing this four-bar linkage model and a par-allel-plate capacitor model for the comb drives, the static anddynamic performances of the entire actuator were evaluated.Parametric analysis of the static vertical displacement and nat-ural frequency of the proposed actuator were also conducted tostudy the influence of design parameters on them. The microactuator with dimensions that we select is expected to yield avertical motion of nearly 5 and an out-of-plane tilting mo-tion of 1.2 at a 40-V dc actuation voltage, and a resonant fre-quency of about 5 kHz. All the analytical models developed inthis work effectively serve for predicting the actuator perfor-mance in the parametric analysis. With its estimated fast dy-namic response and multi-axis motion capability with relativelylarge displacement, the proposed PDMS-on-silicon hybrid ac-tuator is promising for various MEMS applications requiringon-chip actuation functions.

This paper demonstrates the technological potential ofcombining the polymer material (PDMS) and silicon MEMSdevices. The unique material properties of the polymer canincrease the functionality of various MEMS devices with asimple structural design. The flexibility of the polymer wouldhelp a MEMS actuator generate large displacement at a limitedactuation force. Its mechanical robustness would increase thedevice reliability. In addition, the polymer material can be usedfor optical components such as optical lenses [30] and gratings[31] due to its optical transparency, and can help achievereconfigurable microoptical devices embedded with electron-ically controllable silicon-based actuators. Consequently, thepresented results promote the development of a wide variety ofnovel polymer/silicon hybrid MEMS devices.

REFERENCES

[1] S. Hollar, A. Flynn, C. Bellew, and K. S. J. Pister, “Solar powered 10 mgsilicon robot,” in Proc. 16th Annual Int. Conf. Microelectromech. Syst.,Kyoto, Japan, 2003.

[2] K.-F. Böhringer, B. R. Donald, and N. C. MacDonald, “Single-crystalsilicon actuator arrays for micro manipulation tasks,” in Proc. 9th AnnualInt. Workshop on Microelectromech. Syst., San Diego, CA, 1996.

[3] H. Kanayama, T. Tsuruzawa, N. Mitsumoto, T. Idogaki, and T. Hat-tori, “Micromanipulator utilizing a bending and expanding motion actu-ator,” in Proc. 10th Annual Int. Workshop on Microeelectromech. Syst.,Nagoya, Japan, 1997.

[4] J. C. Chiou and Y.-C. Lin, “Micromirror device with tilt and piston mo-tions,” in Proc. Design, Characterization, and Packaging for MEMS andMicroelectron., Gold Coast, Australia, 1999.

[5] P. F. V. Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “AMEMS-based projection display,” in Proc. 11th Annual Int. Conf. Mi-croelectromech. Syst., 1998.

[6] S. Kwon, V. Milanovic, and L. P. Lee, “Vertical microlens scanner for3D imaging,” in Proc. Solid-State Sens. Actuator Workshop, Hilton HeadIsland, SC, 2002.



[7] S. Kwon and L. P. Lee, “Micromachined transmissive scanning confocalmicroscope,” Opt. Lett., vol. 29, pp. 706–708, 2004.

[8] A. Tuantranont and V. M. Bright, “Segmented silicon-micromachinedmicroelectromechanical deformable mirrors for adaptive optics,” J. Se-lect. Topics in Quantum Electron., vol. 8, pp. 33–45, 2002.

[9] J. I. Young and A. M. Shkel, “Comparative study of 2-DOF micromirrorsfor precision light manipulation,” in Proc. Smart Structures and Mate-rials 2001: Smart Electron. MEMS, Newport Beach, CA, 2001.

[10] C.-H. Kim and Y.-K. Kim, “Integration of a microlens on a microXY-stage,” in Proc. Device and Process Technologies for MEMS andMicroelectron., Gold Coast, Australia, 1999.

[11] Y. Sun, D. Piyabongkarn, A. Sezen, B. J. Nelson, and R. Rajamani,“A high-aspect-ratio two-axis electrostatic microactuator with extendedtravel range,” Sens. Actuators A: Phys., vol. 102, pp. 49–60, 2002.

[12] J. A. Walraven and B. Jokiel, “Failure analysis of a multi-degree-of-freedom spatial microstage,” in Proc. Reliability, Testing, and Charac-terization of MEMS/MOEMS II, San Jose, CA, 2003.

[13] C. Chen, C. Lee, Y.-J. Lai, and W. Chen, “Development and applicationof lateral comb-drive actuator,” Japan. J. Appl. Phys., Part 1: RegularPapers and Short Notes and Review Papers, vol. 42, pp. 4059–4062,2003.

[14] R. Legtenberg, A. W. Groeneveld, and M. Elwenspoek, “Comb-driveactuators for large displacements,” J. Micromechan. Microeng., vol. 6,pp. 320–329, 1996.

[15] J. D. Grade, H. Jerman, and T. W. Kenny, “Design of large deflectionelectrostatic actuators,” J. Microelectromech. Syst., vol. 12, pp. 335–343,2003.

[16] W. Piyawattanametha, P. R. Patterson, D. Hah, H. Toshiyoshi, and M. C.Wu, “A 2D scanner by surface and bulk micromachined angular verticalcomb actuator,” in Proc. IEEE/LEOS Int. Conf. Opt. MEMS, 2003.

[17] H. Xie, Y. Pan, and G. K. Fedder, “A CMOS-MEMS with curled-hingecomb drives,” J. Microelectromech. Syst., vol. 12, pp. 450–457, 2003.

[18] D. Hah, S. T.-Y. Huang, J.-C. Tsai, H. Toshiyoshi, and M. C. Wu, “Low-voltage, large scan angle MEMS analog micromirror arrays with hiddenvertical comb-drive actuators,” J. Microelectromech. Syst., vol. 13, pp.279–289, 2004.

[19] Y. Xia and G. M. Whitesides, “Soft lithography,” Ann. Rev. Mater. Sci.,vol. 28, pp. 153–184, 1998.

[20] C. S. Effenhauser, G. J. M. Bruin, A. Paulus, and M. Ehart, “Integratedcapillary electrophoresis on flexible silicone microdevices: analysis ofDNA restriction fragments and detection of single DNA molecules onmicrochips,” Analyt. Chem., vol. 69, pp. 3451–3457, 1997.

[21] B.-H. Jo, L. M. Van Lerberghe, K. M. Motsegood, and D. J. Beebe,“Three-dimensional micro-channel fabrication in polydimethylsiloxane(PDMS) elastomer,” J. Microelectromech. Syst., vol. 9, pp. 76–81, 2000.

[22] Y.-C. Tung, M. Zhang, C.-T. Lin, K. Kurabayashi, and S. J. Skerlos,“PDMS-based opto-fluidic micro flow cytometer with two-color, multi-angle fluorescence detection capability using PIN photodiodes,” Sens.Actuators B: Chem., vol. 98, pp. 356–367, 2004.

[23] D. Huh, Y.-C. Tung, H.-H. Wei, J. B. Grotberg, S. J. Skerlos, K.Kurabayashi, and S. Takayama, “Use of air-liquid two-phase flow inhydrophobic microfluidic channels for disposable flow cytometers,”Biomed. Microdev., vol. 4, pp. 141–149, 2002.

[24] S. J. Clarson and J. A. Semlyen, Siloxane Polymer. Englewood Cliffs,NJ: Prentice-Hall, 1993.

[25] J. C. Lötters, W. Olthuis, P. H. Veltink, and P. Bergveld, “Polydimethyl-siloxane as an elastic material applied in a capacitive accelerometer,” J.Micromechan. Microeng., vol. 6, pp. 52–54, 1996.

[26] , “The mechanical properties of the rubber elastic polymer poly-dimethylsiloxane for sensor applications,” J. Micromech. Microeng., vol.7, pp. 145–147, 1997.

[27] S. Katagiri, T. Takamatsu, T. Minamikawa, and S. Fujita, “Secretagogue-induced calcium wave shows higher and prolonged transients of nuclearcalcium concentration in mast cells,” FEBS Lett., vol. 334, pp. 343–346,1993.

[28] W. Piyawattanametha, P. R. Patterson, D. Hah, H. Toshiyoshi, and M. C.Wu, “A surface and bulk micromachined angular vertical combdrive forscanning micromirrors,” in Conf. Opt. Fiber Commun., 2003.

[29] H. Oku and M. Ishikawa, “A variable-focus lens with 1 kHz bandwidthapplied to axial-scan of a confocal scanning microscope,” in Proc. 16thAnnual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS),Tucson, AZ, 2003.

[30] K. Wang, K.-S. Wei, M. Sinclair, and K. F. Böhringer, “Micro-opticalcomponents for a MEMS integrated display (invited paper),” in Proc.12th Int. Workshop on The Physics of Semiconductor Devices (IWPSD),Chennai, India, 2003.

[31] K. Hosokawa, K. Hanada, and R. Maeda, “A polydimethylsiloxane(PDMS) deformable diffraction grating for monitoring of local pressurein microfluidic devices,” J. Micromechan. Microeng., vol. 12, p. 1,2002.

Yi-Chung Tung (S’02) received the B.S. and M.S.degrees in mechanical engineering from the NationalTaiwan University, Taiwan, in 1996 and 1998,respectively. His Master’s degree research is fo-cused on piezoelectric actuator design, piezoelectricMEMS device analysis, and fabrication.

He is currently a Ph.D. degree candidate in me-chanical engineering at the University of Michigan,Ann Arbor. His Ph.D. studies include polymer andsilicon hybrid MEMS devices design and fabrication,as well as their applications in microoptics and bio-

logical detection.

Katsuo Kurabayashi (M’98) received the B.S.degree in 1992 in precision machinery engineeringfrom the University of Tokyo, Japan, and theM.S. and Ph.D. degrees in materials science andengineering with an electrical engineering minorfrom Stanford University, CA, in 1994 and 1998,respectively. His dissertation work focused onmeasurement and modeling of the thermal transportproperties of electronic packaging and organic ma-terials for integrated circuits under the contract withthe Semiconductor Research Corporation (SRC).

Upon completion of the Ph.D. program, he joined the Department of Me-chanical Engineering, Stanford University, as a Research Associate for 1 year.In January 2000, he joined the University of Michigan, Ann Arbor, where heis an Assistant Professor with the Department of Mechanical Engineering. AtMichigan, he mentors five doctoral students who are investigating thermal trans-port phenomena in MEMS structures and electronic devices, novel actuator,and micromechanism design for MEMS optical detection devices, multiphysicsmodeling, and characterization of RF MEMS, integration of biomolecular mo-tors in NEMS/MEMS.

Dr. Kurabayashi is a recipient of the 2001 NSF CAREER Award.


Documents

548 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL…katsuokurabayashi.com/wp-content/uploads/2010/06/EOS-Actuator... · 548 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14,