High-Q single crystal silicon HARPSS capacitive beam...

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 12, NO. 4, AUGUST 2003 487

High-Q Single Crystal Silicon HARPSS CapacitiveBeam Resonators With Self-Aligned Sub-100-nm

Transduction GapsSiavash Pourkamali, Student Member, IEEE, Akinori Hashimura, Student Member, IEEE,

Reza Abdolvand, Student Member, IEEE, Gavin K. Ho, Student Member, IEEE, Ahmet Erbil, andFarrokh Ayazi, Member, IEEE

Abstract—This paper reports on the fabrication and charac-terization of high-quality factor (Q) single crystal silicon (SCS)in-plane capacitive beam resonators with sub-100 nm to submicrontransduction gaps using the HARPSS process. The resonating el-ement is made of single crystal silicon while the drive and senseelectrodes are made of trench-refilled polysilicon, yielding an all-silicon capacitive microresonator. The fabricated SCS resonatorsare 20–40 m thick and have self-aligned capacitive gaps. Ver-tical gaps as small as 80 nm in between 20m thick silicon struc-tures have been demonstrated in this work. A large number ofclamped-free and clamped–clamped beam resonators were fabri-cated. Quality factors as high as 177 000 for a 19 kHz clamped-freebeam and 74 000 for an 80 kHz clamped–clamped beam were mea-sured under 1 mtorr vacuum. Clamped–clamped beam resonatorswere operated at their higher resonance modes (up to the fifthmode); a resonance frequency of 12 MHz was observed for the fifthmode of a clamped–clamped beam with the fundamental modefrequency of 0.91 MHz. Electrostatic tuning characteristics of theresonators have been measured and compared to the theoreticalvalues. The measured Q values of the clamped–clamped beam res-onators are within 20% of the fundamental thermoelastic dampinglimits ( ) obtained from finite element analysis. [950]

Index Terms—Capacitive gap, HARPSS, quality factor,resonator, silicon micromachining, submicron, thermoelasticdamping.

I. INTRODUCTION

OVER the past few decades, development of silicon mi-crofabrication technologies has provided the opportunity

for batch fabrication of high-quality (Q) factor micromechanicalresonators for a variety of sensing and frequency filtering appli-cations. Due to the high sensitivity of the resonance frequency ofmicromechanical resonators to environmental parameters, thesedevices have great potential for implementation of highly sen-sitive resonant sensors such as pressure sensors, chemical sen-sors, accelerometers and gyroscopes. In addition to the sensory

Manuscript received October 24, 2002; revised January 14, 2003. This workwas supported by DARPA under Contract DAAH01-01-1-R004. Subject EditorG. B. Hocker.

S. Pourkamali, R. Abdolvand, G. K. Ho, and F. Ayazi are with the School ofElectrical and Computer Engineering, Georgia Institute of Technology Atlanta,GA 30332-0250 USA (e-mail: [email protected]).

A. Hashimura was with the School of Electrical and Computer Engineering,Georgia Institute of Technology Atlanta, GA 30332-0250 USA. He is now withPanasonic, Osaka, Japan.

A. Erbil is with the School of Physics, Georgia Institute of Technology At-lanta, GA 30332-0250 USA.

Digital Object Identifier 10.1109/JMEMS.2003.811726

applications, extreme demand for high-performance highly-in-tegrated wireless communication units has fueled interest in re-placing the off-chip bulky frequency selective components incommunication systems with integrated micromechanical reso-nant devices [1]. However, extension of the operating frequencyof capacitive MEMS resonators to the VHF and UHF rangerequires ultra-thin capacitive gaps as small as a few 10’s ofnanometers in between the electrodes and the high Q resonatingelement [2]. Therefore, fabrication technologies that can im-plement all-silicon high-Q capacitive resonators with scalablenanometer-in-size gap spacing without the need for nanolithog-raphy are of great interest.

A variety of micromechanical resonators with single crystalor polycrystalline silicon as the structural material have been sofar reported in literature. Surface micromachined polysiliconcapacitive resonators with submicron gap spacing have beendemonstrated [3], [4]. Single crystal silicon (SCS) is a moreattractive structural material for microresonators compared topolysilicon due to its low internal friction and consequentlyhigher mechanical Q, low internal stress and independencefrom various process parameters. However, fabrication ofelectrically-isolated single crystal silicon mechanical structureswith very small gaps introduces several problems and limita-tions. Silicon-on-insulator (SOI) substrates [5]–[7] or waferbonding techniques [8], [9] are usually used for implementationof SCS devices resulting in higher cost and process complexity.The single crystal silicon resonators that have been so farreported in literature use fabrication processes that are notcapable of producing sense and drive electrodes in sub-100 nmproximity of the resonant structure. They either have complexoptical [6], [7], [10] or magnetic [11] sense and actuationscheme or, in case of capacitive resonators, the gaps cannot bescaled down to sub 100-nm level using optical lithography [5],[8], [12], limiting their application to low frequencies.

This paper presents the implementation and characterizationof high-Q in-plane SCS capacitive beam resonators withsub-100 nm to submicron transduction gaps using the HARPSSprocess. An enhanced and modified version of the HARPSS(High Aspect Ratio combined Poly and Single crystal Silicon)process [13], [14] has been used in this work to fabricate 10’sof microns thick SCS resonators within submicron vicinity ofvertical polysilicon electrodes [15]. Sub-100 nm self-alignedvertical capacitive gaps are demonstrated for the first time in 20

m thick SCS capacitive resonators. Thick in-plane resonators

1057-7157/03$17.00 © 2003 IEEE

488 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 12, NO. 4, AUGUST 2003

Fig. 1. Schematic view of a two-port clamped–clamped SCS beam resonatorfabricated through the HARPSS process.

have the advantage of consuming smaller die area by extendingin the vertical direction into the silicon substrate. This provideslarger drive and sense area, which when combined with the ultrasmall gaps will reduce the equivalent motional resistance ofthe resonator (increase the signal to noise ratio). Measurementresults on the Q of clamped–clamped and clamped-free SCSbeams with various dimensions operating in their fundamentaland higher order flexural modes are reported and compared tothe theoretical values. Tuning characteristics of the fabricatedbeam resonators in the fundamental and higher order modes arealso presented. It is shown through finite-element analysis thatthe measured Q’s of the clamped–clamped beam resonatorsare very close to the fundamental thermoelastic damping limits

.

II. RESONATORFABRICATION

The HARPSS process has been previously used to fabricatethick trench-refilled polysilicon resonators and gyroscopes[14]. In this work, a modified version of the HARPSS processis deployed to implement 10’s of microns thick single crystalsilicon resonating structures with thick polysilicon elec-trodes [15]. The schematic diagram of an in-plane two-portclamped–clamped beam resonator fabricated through theHARPSS process is shown in Fig. 1.

As shown in Fig. 2, the fabrication process starts by definingthe electrically isolated bonding pads for the electrodes. A 1

m thick silicon dioxide covered by a thin layer of LPCVDsilicon nitride (3000A) is used to create the bonding pads [seeFig. 2(a)]. To define the SCS resonating beam, two adjacenthigh aspect-ratio trenches (5m wide and 20–40 m deep) areetched into the low-resistivity silicon substrate using a deep-re-active ion etching (DRIE) system. The height of the trenchesdetermines the height of the resonator. A thin conformal layer ofhigh-temperature LPCVD oxide is then deposited C[see Fig. 2(b)] and trenches are subsequently refilled withdoped LPCVD poly to form the vertical electrodes. The lateralgap spacing is defined by the thickness of the deposited oxide

layer. Polysilicon is etched back on the surface using plasmaetching to expose the sacrificial oxide layer [see Fig. 2(c)]. Sac-rificial oxide is then patterned and another doped LPCVD layerof polysilicon is deposited. Polysilicon is patterned to form thepads followed by metallization using A A[see Fig. 2(d)]. The resonator is released from the siliconsubstrate using a dry silicon etch in SF6 plasma, consistingof an anisotropic followed by an isotropic etch to undercutthe structures [see Fig. 2(e)]. During the isotropic etch stepthe sacrificial oxide layer protects the silicon structure andpolysilicon electrodes. Finally, the sacrificial oxide is removedin a (1:1) solution to release the structures [seeFig. 2(f)]. Various types of capacitive resonator with differentdimensions covering a wide frequency range can be fabricatedusing this process technology. Fig. 3 shows the SEM picture offabricated clamped–clamped and clamped-free SCS HARPSSbeam resonators. Figs. 4 and 5 are the SEM pictures of theelectrode area, showing the single crystal beam, the polysiliconelectrodes and the submicron gap in between.

A. Sub-100-nm Capacitive Gaps

The self-aligned nature of the gap formation in between theSCS and trench-refilled polysilicon structures in the HARPSSprocess allows for the reduction of the capacitive gaps to thetens of nanometer range. Single crystal silicon resonators withcapacitive gaps as small as 80 nm have been fabricated in thiswork. Fig. 6 shows SEM pictures of the cross section of 200nm and 80 nm uniform vertical gaps in between the polysil-icon inside the trench and the silicon substrate. Top view of theclamped–clamped beam resonators with 80 nm drive and sensecapacitive gaps and the close-up view of the electrode area areshown in Fig. 7. This device has been successfully operated andthe results are presented later in this paper.

B. Polysilicon Electrode Definition

In this process, the trenches are used to define: 1) theboundary of the resonating structure, and 2) the polysiliconelectrodes. At the end of the process (during the dry releasestep), all the polysilicon inside the trenches is removed, exceptfor the electrode area. To separate and protect the polysilicon inthe electrode area from the areas that only define the boundaryof the resonator, two methods were investigated which areshown in Fig. 8(a) and (b). The first method is to physicallydisconnect the polysilicon electrode by using discontinuoustrenches and etch away the polysilicon inside the trenches thatdefine the boundary of the resonator. However, this methodcreates “stubs” on the sides of the beam as shown in the SEMof Fig. 8(a), introducing residual extra mass and uncertaintyin the operating frequency of the resonators. Finite elementanalysis using ANSYS have shown that these stubs do not alterthe resonance frequency significantly. The size of these stubscan be controlled by characterizing the timing of isotropicrelease etch step. The alternative method is to use a continuoustrench to define the boundary of the resonator and reduce thewidth of the trench in certain areas between the electrode trenchand the trenches that only define the shape. The narrow trenchlocated in between the regular size trenches will be refilled byoxide only; this will subsequently create a barrier to the

POURKAMALI et al.: HIGH-Q SINGLE CRYSTAL SILICON HARPSS CAPACITIVE BEAM RESONATORS 489

(a) (b) (c)

(d) (e) (f)

Fig. 2. HARPSS fabrication process flow for single crystal silicon beam resonators.

(a) (b)

Fig. 3. SEM view of (a) clamped–clamped and (b) clamped-free single crystal silicon beam resonators fabricated through the HARPSS process.

Fig. 4. SEM of the electrode area showing the polysilicon electrodes as tall asthe beam separated by submicron gaps.

flow to protect the polysilicon electrodes as shown in Fig. 8(b).It should be noted that, due to the presence of voids in themiddle of the narrow trenches, a thin residual poly line mightbe formed, connecting the electrode poly to the boundary poly.

This parasitic polysilicon results in larger effective electrodearea and will be subsequently etched away during the isotropicetch step.

III. M EASUREMENTRESULTS

Fabricated SCS beam resonators were tested under vacuumin a two-port configuration using an Agilent 4395A networkanalyzer. The sensing interface circuits were assembled on aprinted circuit board (PCB) using surface mount components.The MEMS resonator chip was mounted on the board and theinput and output signals along with the dc polarization voltagewere applied to the resonator through wire-bonds. The PCB wasplaced inside a custom vacuum system, which keeps the pres-sure below 1 mtorr. Fig. 9 shows a schematic diagram of thesetup for testing the resonators. Two different sense circuit con-figurations were used for testing the resonators. A J-FET inputhigh frequency operational amplifier was connected in 1) nonin-verting voltage amplifier and 2) inverting trans-resistance con-figuration. Both circuit configurations are capable of detecting


Fig. 5. Close-up view of the electrode area showing the 700 nm gap spacing.

(a) (b)

Fig. 6. Cross-sectional SEM view of trench refilled with polysilicon separatedfrom the substrate with (a) 200 nm and (b) 80 nm uniform gaps.

the small output current of the resonators (in the range of a fewnA).

A. Fundamental Mode Results

Fig. 10 shows the plot of a typical frequency responsetaken from the network analyzer, showing a Q of 74 000at 80 kHz for a 700 m long, 6 m wide and 20 mtall SCS clamped–clamped beam resonator under 1 mtorrvacuum. The summary of the Q measurement results for theclamped–clamped beam resonators with various fundamentalresonance frequencies ranging from 41.5 kHz to 3.2 MHz isgiven in Table I. The Q decreases as the frequency of the beamincreases. A Q of 4500 was measured for the 3.2 MHz beamresonator.

Significantly higher quality factors are measured forclamped-free beams due to their lower resonance frequencyand reduced support loss. A quality factor of 177 000 has beenmeasured for a 500m long, 4 m wide SCS clamped-freebeam resonator at the center frequency of 19 kHz (see Fig. 11).Table II presents measured quality factors for clamped-freebeams with different dimensions.

B. Frequency Tuning

Resonance frequency of parallel plate capacitive resonatorscan be tuned by changing the dc polarization voltage appliedacross the sense and drive capacitive gaps. As the resonator vi-brates variations in the resonator to electrode distances result

in force components at the resonance frequency that oppose theforce produced by the mechanical stiffness of the structure. Thiseffect can be modeled by an equivalent negative electrical stiff-ness as expressed in (1) that partly cancels the mechanical stiff-ness and reduces the resonance frequency of the resonator

(1)

where is the dc polarization voltage applied between the elec-trodes and the resonator, and are the capacitances be-tween the beam and the drive and sense electrodes, respectively,and and are the drive and sense capacitive gaps.

Fig. 12 shows the comparison between the measured and the-oretical frequency tuning characteristics for a 300m long, 6.5

m wide resonator with 700 nm capacitive gaps by changing thedc polarization voltage . The mismatch is mainly due to un-certainties in the resonator structure caused during the isotropicetch step to undercut the structure, which alter the overall stiff-ness of the beam. The resonance frequency changed from 505to 450 kHz by changing the polarization voltage by more than40 V (the calculated pull-in voltage was 56 V), providing a largeelectrostatic tuning range (10%).

C. Sub-100-nm Gap Resonators

The capability of HARPSS to implement resonators withsub-100-nm capacitive gaps was shown by the successful char-acterization of the 80 nm gap device of Fig. 7. Fig. 13 showsthe frequency response of the 610 kHz resonator with 80 nmsense and drive gaps, demonstrating a Q of 4800 under vacuum.Much larger tuning range and significantly sharper tuningcharacteristic are observed for the devices with sub-100-nmcapacitive gaps. Measured tuning characteristic of the 610 kHzclamped–clamped beam resonator with 80 nm capacitive gapsis shown in Fig. 14, demonstrating a tuning range of 28% bychanging the polarization voltage from 0.1 to 2.0 V. The resultsare in good agreement with theory.

D. Higher Resonance Modes

In order to achieve higher operating frequencies without re-ducing the size of the structures, resonators can be operatedin their higher resonance modes. The natural frequencies ofclamped–clamped beam resonators are given by (2) [16]

(2)

where is the length of the beam, is the Young’s modulusof the beam material, is the area moment of inertia aroundthe principal axis, is the mass of the beam and is the fre-quency coefficient for each resonance mode that can be calcu-lated by solving (3)

(3)

For a clamped–clamped (C–C) beam,values for the first,third and fifth resonance modes are , and

, respectively. Therefore, the third and fifth modesshould have resonance frequencies of 5.52 and 13.3 times higherthan the fundamental mode, respectively.


Fig. 7. Top view of the 600 kHz single crystal silicon resonator and close-up view of the electrode area showing the 80 nm gap spacing.

Fig. 8. Diagram and SEM of the separation methods using (a) disconnectedtrenches and (b) narrow trenches.

Fig. 9. Test setup for measurement of resonator frequency response.

Fabricated C-C beam resonators were excited in their thirdand fifth flexural modes and the quality factors were measured.The second and the fourth modes could not be excited due to themidway position of the drive electrode. Resonance frequenciesup to 12.0 MHz have been achieved by exciting the fifth res-onance mode of a 200m long 5 m wide clamped–clampedbeam with the fundamental resonance frequency of 910 kHz.Fig. 15 shows the measured resonance peaks and Q values for

Fig. 10. Frequency response of a 700�m long, 5�m wide, 20�m thickclamped–clamped beam resonator.

TABLE IMEASUREMENT RESULTS ONRESONANCEFREQUENCY AND QUALITY

FACTOR OF THEVARIOUS SCS CLAMPED–CLAMPED BEAM RESONATORS

FABRICATED THROUGH HARPSS TECHNOLOGY

various modes of this resonator. A summary of measured centerfrequencies and quality factors for clamped–clamped beams in


Fig. 11. Frequency response of a 500�m long, 4�m wide, 20�m thickclamped-free beam resonator.

TABLE IIMEASUREMENTRESULTS ONRESONANCEFREQUENCY AND QUALITY

FACTOR OF THEVARIOUS SCS CLAMPED-FREE BEAM RESONATORS

FABRICATED THROUGH HARPSS TECHNOLOGY

their higher resonance modes is presented in Table III. Mea-sured frequencies for higher resonance modes are in good agree-ment with the values predicted by (2). Due to higher stiffnessof the beams in higher modes, excitation of resonators in thosemodes requires higher polarization voltages or smaller excita-tion and sense gaps. For the same reason, tuning capability athigher resonance modes is weaker than the fundamental modes.Fig. 16 shows tuning characteristics of a 300m long, 5 mwide clamped–clamped beam with 700 nm gaps at its third res-onance mode showing a tuning slope of 0.18 kHz/V, which issignificantly lower than that of the first resonance mode of suchresonator (2.5 kHz/V).

Comparison of the measured quality factor values for the fun-damental and higher resonance modes shows that at a certaincenter frequency and beam width measured Q for beam res-onators at higher order modes are equal or even slightly greaterthan that of the fundamental resonance modes (see Fig. 17).

As shown in Table I, the Q of the fabricated HARPSSC-C beam resonators decreases as the frequency of the beamresonator increases. This trend is similar to what is predictedby the thermoealstic damping (TED) loss. However, to verifythe results and benchmark the HARPSS process as an enablingtechnology for “high-Q” capacitive SCS resonators, the funda-mental TED-based limits of the quality factor for the fabricated

Fig. 12. Plots of measured and calculated change of frequency versuspolarization voltage for a 500 kHz clamped–clamped beam resonator with 700nm capacitive gaps.

Fig. 13. Frequency response of a 200�m long, 3�m wide, 20�m thickclamped-free beam resonator with 80 nm capacitive gaps.

Fig. 14. Plots of measured and calculated change of frequency versuspolarization voltage for a 610 kHz clamped–clamped beam resonator with 80nm capacitive gaps.

resonators were computed and compared to the measurementresults. The results are presented in the next section.


(a) (b) (c)

Fig. 15. Frequency response of a 200�m long, 5�m wide, 20�m thick with capacitive 200 nm capacitive gaps at fundamental, third and fifth resonance modes.

TABLE IIIMEASUREMENTRESULTS ONRESONANCEFREQUENCY ANDQUALITY FACTOR

OF THE VARIOUS SCS CLAMPED–CLAMPED BEAM RESONATORS AT

FUNDAMENTAL AND HIGHER RESONANCEMODES

Fig. 16. Tuning characteristic of a 300�m long, 5�m wide clamped–clampedbeam with 700 nm gaps at its third resonance mode.

IV. L OSSMECHANISMS

Various loss mechanisms in beam resonators have been in-vestigated by researchers including the thermoelastic damping(TED), support, and surface related losses [7], [12], [17]–[20].

Fig. 17. Comparison of measured quality factors for fundamental, third andfifth resonance modes for resonators with width of 5 to 6�m.

Among these, the thermoelastic damping could be the most sig-nificant loss mechanism in flexural beam resonators with largeaspect ratios [12], [17], [20]. Thermoelastic damping is a re-sult of irreversible heat flow across temperature gradients pro-duced by inhomogeneous compression and expansion of theoscillating beam. Here we present the results of a finite ele-ment analysis (FEA) to establish the limitations imposed onthe quality factor by the TED mechanism. The finite elementmethod can handle realistic device geometries without the sim-plifying assumptions that are often made in analytical methodsto reach closed form expressions [18], [21].

The thermoelastic damping mechanism is governed by thefollowing coupled partial differential equations:

(4)

and

(5)

where we assume summation over the repeated indices. The de-parture of the beam elements from equilibrium are described bya displacement field and denotes the tempera-ture field. The terms on the right hand sides provide coupling be-tween (4) and (5). The equation parameters and the values used


TABLE IVDEFINITION OF PARAMETERS IN THE COUPLED THERMAL AND

STRAIN FIELD EQUATIONS

in our simulation are provided in Table IV. In equilibrium, thebeam is unstrained and unstressed, and has a uniform tempera-ture of . The value for thermal conductivity was taken fromthe experimental plots given in [22] for a p-type low-resistivitysilicon substrate with doping levels in excess of cm .

The multiphysics TED simulation for the clamped–clampedbeam resonators was performed by using the FEMLAB [23]software. Since the width of the beams is much smaller that theother two dimensions, a plane-strain assumption was made to re-duce the computation time. A three-dimensional analysis yieldsthe same results within the uncertainties of the experiment. Fora given resonator, the amplitude at the midpoint was calculatedas a function of driving frequency. The response curve was fitto a lorentzian function to obtain the quality factor Q.

Fig. 18(a) and (b) show the results of FEA along with the ex-perimental data points for C-C beams that are 5.0m and 7.5

m wide, respectively. For each FEA plot, only the length ofthe beam was changed to obtain different resonant frequencies.The solid circles show the points obtained from FEA for the firstharmonic, and the solid line is drawn as a guide to the eye. Themeasurements for both first and third harmonic quality factorsfor various beams are shown for comparison. The agreement be-tween the measurement and the FEA prediction is excellent, andwithin the uncertainties of the measurements in both Fig. 18(a)and (b). The analytical predictions by Lifshitz and Roukes [18]are also shown on the figures for comparison (dashed lines).The resonator parameters were kept the same as the ones usedfor the FEA. The analysis by Lifshitz and Roukes [18] consis-tently overestimates the Q values predicted by FEA by a factorof about two, which might be due to the simplifying assump-tions. It should be noted that the FEA for the third harmonic wasalso performed in FEMLAB and the results were within 5% ofthe first harmonic FEA Q values for the same width beam (theplot for the third harmonic FEA was not added for the sake oflegibility).

Support loss of clamped-free (C-F) beam resonators has beenstudied in [7] and [19], and the following expression [see (6)]was derived for :

(6)

where and are length and width of the C-F beam, respec-tively, and the resonator and support are of the same material.

Fig. 18. Measurement results of Q for beams of several thicknesses (regardlessof mode number) plotted versus frequency in comparison with the theoreticallypredicted QTED.

The expression for support loss of a clamped–clamped beamis expected to have similar geometrical dependency with a dif-ferent proportionality factor. For the resonators studied in thiswork with fundamental frequencies below 1 MHz, the largelength to width ratios of the resonators result inlarger than the measured Q values, indicating that sup-port loss cannot be the major Q limiting mechanism. Howeverfor some of the higher order resonance modes of the beams, sup-port loss can become the dominant loss mechanism.

To investigate the significance of surface related losses [12]in the Q of the fabricated beam resonators, two different batchesof resonators were fabricated and characterized. For the secondbatch, after etching the trenches that define the boundary of theSCS beams, a thin layer of thermal oxide was grownon the Si surfaces and subsequently removed by wet etching inbuffered HF solution. The first batch did not undergo this ox-idation treatment. As shown in Fig. 19, the thermal oxidationsubstantially reduced the roughness of the SCS beam sidewalls(introduced during the unoptimized DRIE etch process). Mea-surement results obtained from the two batches of the resonators


(a)

(b)

Fig. 19. SEM pictures showing surface roughness of beam sidewalls beforeoxidation step (a) and its improvement after thermal oxidation and oxideremoval (b).

revealed that the surface oxidation treatment provides only aslight improvement of about 15–20% in the Q values. There-fore, considering the fact that the measured Q values are within20% of the fundamental values, we conclude that surfacerelated losses are not a major source of loss in the fabricatedHARPSS SCS resonators.

V. CONCLUSION

All-silicon high-Q capacitive micromechanical beam res-onators with sub-100 nm to submicron gap-spacing utilizingsingle crystal silicon as the resonating element and polysiliconas the electrodes have been reported. The resonators werefabricated using the HARPSS process in which capacitive gapsare defined in a self-aligned process by the thickness of thedeposited sacrificial layer. Uniform vertical capacitive gaps of80 nm are demonstrated without the need for nanolithography.Measurement results for several beam dimensions operating indifferent resonance modes have been reported. Quality factorsas high as 177 000 for a clamped-free beam at 19 kHz, andresonance frequencies as high as 12 MHz for theflexuralmode of a clamped–clamped beam with Q of 2000 have beenachieved. The possibility of operation of beam resonators intheir higher resonance modes with high quality factors hasbeen demonstrated. Investigation of various loss mechanismsrevealed that the measured quality factors for compliant

high-aspect-ratio beams follow the behavior predicted by theTED loss mechanism.

ACKNOWLEDGMENT

The authors wish to thank S. Y. No for his contributions andthe staff of Georgia Tech Microelectronics Research Center, es-pecially the CMOS group, for their assistance.

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Siavash Pourkamali(S’03) was born in 1980. He re-ceived the B.S. degree in electrical engineering fromSharif University of Technology, in 2001. Currently,he is working towards the Ph.D. degree at the Elec-trical Engineering Department, Georgia Institute ofTechnology, Atlanta.

His main research interests are in the areas of RFMEMS, silicon micromachining technologies and in-tegrated microsystems.

Akinori Hashimura (S’03) was born in 1977 atNagoya, Japan. In 2000, he received the B.S. degreein electrical engineering from the Georgia Instituteof Technology, Atlanta. Following, he continued hiseducation at the Georgia Institute of Technology,where he received the M.S. degree in electricalengineering in 2002.

His research interests were in the areas of MEMSresonators and silicon micromachining technologies.He is currently working for the Panasonic, Osaka,Japan, where he will be continuing his research in the

R&D headquarter division.

Reza Abdolvand (S’02) was born in Shiraz, Iran,in 1976. He received the B.S. and M.S. degrees inelectrical engineering both from Sharif University ofTechnology, in 1999 and 2001, respectively. He iscurrently pursuing the Ph.D. degree with the Inte-grated MEMS group of Georgia Institute of Tech-nology, Atlanta.

His research interests are in the area of MEMS withfocus on integrated microresonators.

Gavin K. Ho (S’01) was born in Vancouver,Canada, in 1980. He received the M.Eng. degreeand B.A.Sc. degree with distinction in mechanicalengineering (electromechanical design option) fromthe University of British Columbia, Canada, in2001. Following, he joined the Georgia Institute ofTechnology, Atlanta, where he is currently pursuingthe Ph.D. degree in the School of Electrical andComputer Engineering.

His research interests include the physics of lossmechanisms in MEMS resonators and MEMS res-

onator design for signal processing applications.Mr. Ho was the recipient of the UBC Letson Prize in 2001 and the Col. Oscar

P. Cleaver Award from the Georgia Institute of Technology in 2002.

Ahmet Erbil received the Ph.D. degree in physicsfrom Massachusetts Institute of Technology, Cam-bridge, in 1983.

After two years at IBM Thomas J. WatsonResearch Center, Yorktown Heights, NY, he joinedGeorgia Institute of Technology, Atlanta, Facultyto establish a program on electronic and photonicmaterials. He has been a Sloan Research Fellow anda recipient of IBM Faculty Development Award.He was a Visiting Professor at Ecole PolytechniqueFederale de Lausanne, Switzerland, in fall 1991. He

has been consultant to several large industrial firms. He has also been principalinvestigator on more than 20 projects sponsored by government agencies andcorporations. He holds five patents in the field of MOCVD chemicals and thinfilm production.

Farrokh Ayazi (S’96–M’99) was born on February19, 1972. He received the B.S. degree in electrical en-gineering from the University of Tehran, Iran, in 1994and the M.S. and the Ph.D. degrees in electrical engi-neering from the University of Michigan, Ann Arbor,in 1997 and 2000, respectively.

He joined the faculty of Georgia Institute ofTechnology in December 1999, where he is currentlyan assistant professor in the School of Electricaland Computer Engineering. His current researchinterests are in the areas of integrated MEMS, RF

MEMS, VLSI analog integrated circuits, integrated microsystems, MEMSinertial sensors, and microfabrication technologies.

Prof. Ayazi is the recipient of the Georgia Tech College of Engineering Cut-ting Edge Research Award for 2001–2002. He received a Rackham PredoctoralFellowship from the University of Michigan for 1998–1999.

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