Piezoelectric Disk Resonators Based on Epitaxial ... - IEEE Xplore

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Ken Deng, Parshant Kumar, Member, IEEE, Member, ASME, Lihua Li, and Don L. DeVoe. Abstract—A new design for anisotropic piezoelectric disk res-.
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 1, FEBRUARY 2007

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Piezoelectric Disk Resonators Based on Epitaxial AlGaAs Films Ken Deng, Parshant Kumar, Member, IEEE, Member, ASME, Lihua Li, and Don L. DeVoe

Abstract—A new design for anisotropic piezoelectric disk resonators is demonstrated using single-crystal Al0 3 Ga0 7 As films. The shape of the disk resonator is based on the velocity propagation profile of the elastic wave in the plane of the piezoelectric film, with lateral dimensions scaled to the half wavelength of the desired resonance frequency. The resonators are designed with supports which emulate free-free boundary conditions. Prototype resonators are fabricated using a three-layer Al0 3 Ga0 7 As heterostructure containing silicon-doped electrodes and an undoped piezoelectric Al0 3 Ga0 7 As layer. Quality factors as high as 11 200 are measured in air for a 23.25 MHz fundamental resonant . A mode, with a corresponding motional resistance of 1.67 finite-element model for the resonator design is also described. Simulation results agree well with both theoretical calculations and experimental data. [2006-0008]

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Index Terms—AlGaAs, piezoelectric resonator, radio-frequency (RF) microelectromechanical systems (MEMS).

I. INTRODUCTION HERE is strong demand in the wireless communications industry for highly integrated, low-power, and low-cost oscillators and high-frequency filters for applications such as mobile phones and GPS receivers. Radio-frequency (RF) microelectromechanical system (MEMS) resonators are being explored as a promising solution to fulfill this need. While dramatic progress has been made, to date there is no ideal solution that can meet all the requirements for communication applications. Resonators and resonant filters based on capacitively transduced silicon have been the subject of great attention. A variety of silicon resonators based on bending-mode and planar one-dimensional longitudinal-mode or two-dimensional (2-D) radial-mode designs have been described [1]–[6]. From the application perspective, there are five important metrics that specify resonator performance: maximum resonance frequency , minimum series motional resistance , maximum quality factor (Q), maximum power-handling ability, and stability [1]. By taking advantage of the low material losses inherent in both single-crystal and polycrystalline silicon, bending-mode capacitive resonators with high Q’s have been reported. For example, Wang et al. [3] achieved a Q over 10 000 at around 100 MHz in vacuum for a bending-mode beam with free–free boundary conditions. In contrast to such

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Manuscript received February 3, 2006; revised May 3, 2006. This work was supported by the DARPA/MTO Nanomechanical Array Signal Processors program under Contract F3060202C0016. Subject Editor K. Najafi. The authors are with the Center of Micro Engineering, University of Maryland, College Park, MD 20742 USA. Color versions of Figs. 1–5, 8, and 10 are available online at http://ieeexplore. ieee.org. Digital Object Identifier 10.1109/JMEMS.2006.886006

bending-mode designs, planar resonators offer the benefit of higher stiffness and lower viscous damping when operating in and quality factor Q air. The highest product of frequency reported for a microresonator in air is a planar-mode device [1]. In addition, 2-D planar-mode with resonators tend to offer better power handling capability than bending-mode designs. A single crystal silicon planar resonator with a maximum power handling level up to 0.12 mW at 13.1 MHz was recently described [2]. Although this remains the highest power handling level reported for a capacitive resonator, it is still lower than the demands of wireless communication systems, with requirements on the order of several milliwatts based on typical incident power levels as well as phase noise limitations [7]. Another drawback of capacitive resonators is that they require extremely small capacitive gap spacings on the order of 100 nm or below to provide sufficient electromechanical coupling strength. This requirement can introduce substantial fabrication and packaging complexities. To further increase the electromechanical coupling strength in capacitive resonators, and thereby lower the series motional resistance , high bias voltages ( 10 V) are generally required, introducing an additional limitation. For example, a motional was reported for an electrostatic resistance of only 1.46 resonator with an 80 nm capacitive gap and 12 V bias voltage [3]. Upon increasing the gap to 160 nm, the fabrication requirements are relaxed but motional resistance is sacrificed, with an of 43.3 under 17 V bias [1]. Compared to capacitively transduced devices, microresonators based on piezoelectric transduction can potentially offer a number of advantages. Due to the inherently linear nature of piezoelectric transduction, rather than the quadratic relationship in electrostatic coupling, piezoelectric-based microresonators can handle substantially higher power levels. Because piezoelectric transduction is based on absolute strain rather than relative displacement, high electromechanical coupling can be realized without resorting to nanoscale gaps, resulting in simpler design and implementation. Furthermore, the electromechanical transduction coefficients for many piezoelectric materials provide more effective coupling than capacitive transduction, offering low values of motional resiswithout the need for large bias voltages. However, tance most piezoelectric materials used for microresonators exhibit higher internal losses compared to silicon. Furthermore, the piezoelectric films must be sandwiched between conductive electrodes to apply the electric field and sense the electric charge produced at resonance. Metal electrodes tend to exhibit high levels of thermoelastic damping and can reduce the overall Q of a resonator by an order of magnitude of more [8], [9]. Consequently, relatively low Q’s have been reported in several

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previous efforts at demonstrating piezoelectric microresonators [10], [11]. A number of planar-mode piezoelectric resonator designs have recently been demonstrated [12]–[15], with superior performance over their bending-mode counterparts. For example, Li et al. demonstrated extensional-mode piezoelectric bar resonators operating up to 25 MHz with Q’s as high as 25,390 and motional resistance between 4–18 [15], and Piazza et al. presented a ring-shaped piezoelectric contour-mode resonator with a Q of 2,900 at 472.7 MHz and motional resistance around based on their reported admittance plots [13]. Despite 2.6 these advances, comparatively little effort has been spent on planar piezoelectric microresonators, in part because of the difficulty in integrating high quality single-crystal piezoelectric materials and lack of an effective design methodology to accommodate the anisotropy inherent in these materials. Epitaxially grown III–V materials are widely used for the production of high-speed VLSI circuits. With the exception of AlN, the use of the piezoelectric effect in III–V materials has not been widely used in MEMS devices. Recently, a fabrication process [16] for realizing bending-mode [17] and longitudinal-mode [15] resonators based on single-crystal piezoelectric Al Ga As combined with Si-doped Al Ga As electrodes has been reported by our group. The lattice-matched single-crystal heterostructure essentially eliminates residual stress-induced curvature. This is an important consideration for the planar disk resonators described here, since out-of-plane curvature can degrade the quality factor due to excitation of unwanted vibrational modes. In addition, Al Ga As heterostructures exhibit relatively low material damping compared to traditional devices using polycrystalline piezoelectric films such as PZT, ZnO, or AlN combined with metal electrodes. The use of Al Ga As for the resonator structure also holds promise for future integration with high-speed III–V electronics. In this paper the single-crystal Al Ga As fabrication process is combined with a 2-D planar-mode resonator model to realize a new structure for piezoelectric disk resonators. The epitaxially grown single-crystal AlGaAs films possess cubic symmetry and exhibit orthotropic elastic behavior. Traditional design approaches for isotropic piezoelectric materials cannot be employed since acoustic propagation speed is a function of the crystal orientation. The appropriate shape of the 2-D resonator is derived from the radial elastic wave velocity profile, with radial dimensions set to the half wavelength of the designated resonant frequency. A finite-element model of the resonator is also developed, allowing mode shapes, resonance frequencies, optimal anchor locations, and equivalent circuit parameters to be predicted. Prototype disk resonators are are fabricated, and measured results show that both Q and greatly improved compared with equivalent longitudinal-mode beam resonators.

, orthotropic elastic wafers with theoretical piezoelectric , and relative dielectric constant matrices given stiffness by

(1)

(2)

(3) , , , , , and is the Al mole fraction [18]. Within the Al Ga As crystal plane, both the mechanical and piezoelectric properties vary with crystal direction. To obtain these properties, tensor rotation is required. Using indicial and piezoelecnotation, the transformed stiffness tensor can be found from the original tensors for an tric tensor arbitrary azimuthal angle as [19] where

(4) (5) where is the direction cosine determined from the direction cosine matrix

(6) Using Matlab, the rotation calculations were performed within the film plane, with the results shown in Fig. 1. As shown in this figure, the transverse piezoelectric coefficient reaches its maximum value 3.0 pC/N in the direction as the shear piezoelectric coefficient diminishes to zero, direction achieves its maximum value while in the drops to zero. 3.0 pC/N as Waves propagating in a piezoelectric crystal are a combination of elastic and dielectric polarization modes with wavespeeds , which can be determined from the well-known Christoffel equation [20]

(7) II. DISK RESONATOR DESIGN The III–V family of materials possesses a cubic zincblende structure (group 43 m). The single-crystal Al Ga As films used here are grown by molecular beam epitaxy on (100) GaAs

where

(8)

DENG et al.: PIEZOELECTRIC DISK RESONATORS BASED ON EPITAXIAL AlGaAs FILMS

Fig. 2. Velocity of wave propagation in Al

Fig. 1. (a) Elastic stiffness coefficients C and C and (b) piezoelectric coefficients d and d in the (001) Al Ga As plane.

and

is the average density of Al Ga As given by [18]. In (8), are the direction cosines satisfying , such that a vector describing the . wave propagation direction may be defined as The piezoelectric coefficient tensor is related to piezoelectric coefficient tensor by (9)

are directly related to the three The eigenvalues of wavespeeds, with one corresponding to the wave parallel to (longitudinal wave) and the other two corresponding to the waves perpendicular to (transverse or shear waves). In the (100) Al Ga As plane, the direction vector has the

157

Ga

As (001) plane.

, , 0). Using MatLab, the velocities of wave format ( propagation were calculated from (7)to (9). The results are presented as a function of azimuthal angle in the (100) plane in Fig. 2. The longitudinal elastic wave speed given in this figure is of particular interest for the disk resonator design. Unlike an in-plane isotropic material, whose speed profile is an ideal circle, the Al Ga As crystal has a speed profile similar to a rounded square due to the inherent material anisotropy. An ideal, longitudinally vibrating, piezoelectric plate should have the same profile as the velocity profile of its elastic wave propagation to ensure a pure resonating mode with spurious modes excluded. When the longitudinal, fundamental mode of a boundary-free plate is excited at resonance, a standing elastic wave is created when the radial dimensions are equal to the half wavelength of the resonance frequency. Inspired by this concept, a new design methodology for a disk-shaped planar resonator is proposed in which the free boundary of the 2-D resonator is shaped proportional to the profile of elastic wave propagating speed, and then scaled to set its radial dimensions equal to the half wavelength of the desired resonating frequency, i.e., (10) is the radial dimension, is the elastic wave propwhere agating speed in same direction, and is desired resonant frequency. To verify the design concept and gain more insight on the planar disk resonator, a finite-element model was created in ANSYS 8.0. In this model, the piezoelectric three-dimensional element SOLID98 was used for the piezoelectric material, with Al Ga As properties given by (1)–(3). For this simulation, continuous electrodes are applied to the top and bottom surfaces of the piezoelectric plate. Modal analysis was conducted to determine resonant frequencies and mode shapes for a 5- m-thick resonator with lateral dimensions varying between 80 m in the 001 direction and 89 m in the 011 direction. The first

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Fig. 4. Simulated admittance spectrum for an 80 m disk resonator.

plying an electric field between the top and bottom electrodes, modes 1 and 3 will not be excited. This observation results directly from the form of the piezoelectric matrix in (1), which dictates that only shear strains are produced in the 001 directions upon application of an electric field across the thickness ( -axis) of the resonator. Since modes 1 and 3 are excited only by normal strains in the 001 directions, these modes are suppressed for the chosen resonator geometry. Thus the undesired modes are effectively eliminated as a direct result of the AlGaAs anisotropy and proposed design approach. This can be further validated by observing the electrical admittance spectrum. The admittance predicted from the finite-element model for a 1 V amplitude sinusoidal voltage applied to the top electrode is shown in Fig. 4. Only one resonant peak is visible in this figure, at a frequency (29.8 MHz) very close to the predicted second mode frequency (30.8 MHz), while the predicted first and third modes do not appear. The fact that the antisymmetric 011 breathing mode shown in Fig. 3(b) is the only mode to appear in the spectral response offers another practical benefit. Because this mode possesses four nodal points where the disk boundary intersects the 001 axes, the anchors may be placed at these points rather than the center of disk, enabling anchor losses to be minimized in a manner that is compatible with the AlGaAs microfabrication process. III. RESULTS AND DISCUSSION A. Fabrication Process

Fig. 3. Displacement contours of the first three in-plane resonant modes predicted by finite-element analysis. (a) First mode, f = 23:1 MHz; (b) second mode, f = 29:8 MHz; (c) third mode, f = 33:6 MHz.

three in-plane vibration modes resulting from this analysis are shown in Fig. 3. However, when the plate is actuated by ap-

Disk resonators with cross-sections similar to that shown in Fig. 5 were fabricated with varying geometries using a modified version of a previously reported Al Ga As micromachining process [16]. In this process, a 1- m-thick sacrificial Al Ga As layer is first grown on a (100) GaAs wafer by molecular beam epitaxy. Next, a three-layer Al Ga As heterostructure is grown, with top and bottom Al Ga As layers heavily Si-doped to achieve high conductivity. The electrodes are each 0.5 m thick, and the undoped piezoelectric layer is 4.0 m thick. A four-mask process is used to fabricate the suspended disk and metal contact pads. First, a window is opened

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B. Quality Factor

Fig. 5. Cross-sectional schematic of an Al

Ga

Fig. 6. Electron micrograph of a released 80 m Al

As disk resonator.

Ga

As disk resonator.

to the bottom Al Ga As layer by inductively coupled plasma reactive-ion etching (ICP RIE). This opening is used to define the bottom electrode contact. Next, the top Al Ga As layer is patterned by ICP RIE to define top electrode geometries. In the third step, bond pads defined by liftoff of a Au/Ni/Ge/Au multilayer stack to contact the top and bottom Al Ga As layers. After metallization, another mask is used to define the resonator geometry, and the full Al Ga As stack is etched through to the sacrificial Al Ga As layer by ICP IRE. Finally, the resonator is released by etching the underlying sacrificial Al Ga As film in a solution of concentrated hydrofluoric acid (HF) diluted 50% with deionized water. The HF etch provides excellent selectivity between the sacrificial Al Ga As layer and structural Al Ga As films [21]. Using this process, resonators were fabricated with lateral didirection of 80 and 100 m. An SEM mensions in the image of a fabricated 80 m disk resonator is shown in Fig. 6. While all anchors were 5 m wide, different anchor lengths were fabricated to explore the relationship between anchor geometry on resonator performance. The 80 m resonators were fabricated with lengths ranging from 50 to 130 m, and the 100 m resonators were fabricated with lengths ranging from 110 to 150 m.

Fabricated chips were characterized in air on an RF-1 probe station (Cascade Microtech, Beaverton, OR), with electrical contacts made using coaxial RF probes placed on adjacent metal bond pads. Qualify factors were measured using an impedance bridge scheme [17], in which the resonator acts as one branch of a capacitive bridge circuit, with the opposite defined by matched an on-chip piezoelectric capacitor defined by an identical resonator that has not been released from the substrate. The remaining two branches are defined by passive off-chip capacitors that may be tuned to balance the bridge. When fully balanced, the output voltage between the two branches is zero, but as the device impedance drops near resonance the bridge becomes unbalanced, and the resulting output voltage is fed to a differential voltage amplifier monitored using an HP 4395A network analyzer. Referring to Fig. 6, the anchor beams connecting the four nodal points of the resonator to the substrate are relatively long compared to other resonator designs, which attempt to minimize anchor losses through resonant impedance matching [3], [4], [6]. Impedance matching is difficult for a high-Q resonator, since any mismatch between the resonance frequencies of the device and anchor will result in poor performance. A different approach for reducing anchor losses has been applied in the present case. For a flexural mode beam, it has been shown that the energy transmitted through the anchor to the substrate is proportional to (b/L) [22], [23], where b and L are the width and length of the anchor, respectively. Thus, long and narrow beams are chosen here to reduce anchor losses. The experimental relationship between quality factor and anchor length is summarized in Fig. 9. As expected, increasing the beam length resulted in an improvement in quality factor, particularly for the 100 m resonator. The highest measured value of Q is 11 200 as shown in Fig. 8 for a 100 m disk resonator with 150- m-long anchors. Regardless of the anchor length, the resonant frequencies for each disk size remained virtually unchanged, with less than 0.2% variation. C. Motional Resistance The equivalent circuit model of a single-port piezoelectric resonator may be represented by the classical Butterworth–Van Dyke model shown in Fig. 7. At resonance, the overall resonator in parimpedance is equivalent to the motional resistance allel with the static capacitance . The motional resistance dominates, since the capacitive impedance due to is much at resonance. Motional resistance is a critical larger than resonator parameter, with impedance matching to 50 RF electronics generally desired. Motional resistance for the fabricated resonators was measured using a transmission/reflection test set (HP 87512A) connected to a network analyzer (HP 4395A), with the resonators directly connected to the 50 input and output ports of the network analyzer. Values for motional resistance were determined through the measurement of insertion loss at resonance (IL), and applying the following relationship [5]: (11)

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TABLE I SUMMARY OF THEORETICAL AND EXPERIMENTAL RESONATOR PERFORMANCE IN AIR

Overall, the motional resistance measurements show substantial improvement (at least 4 ) compared to piezoelectric extensional-mode beam resonators operating in the same frequency range [15]. D. Temperature Stability Fig. 7. Butterworth–Van Dyke equivalent circuit model for a piezoelectric resonator.

Fig. 8. Frequency response of 100 m disk resonator with 150-m-long quadsymmetric anchors.

In this equation, is the total parasitic resistance in series with the device under test, which must be subtracted from the total measured resistance to determine the intrinsic value . The total transmission impedances were measured from of an 80 m resonator with 50- m-long anchors and a 100 m resonator with 150- m-long anchors, with resulting values of 4.40 and 4.50 , respectively. For our resonators, the parasitic impedance is primarily defined by the resistance of the electrodes connecting the bond pads with Al Ga As the resonator. Using a measured value of resistivity for the silicon-doped Al Ga As electrodes of 0.005 cm, together is estimated as 2.18 with the known electrode geometries, for the 80 m resonator and 2.83 for the 100 m resonator. After removing the parasitic resistance values from the measured transmission impedances, the intrinsic motional resistance for the 80 m resonator and values are determined to be 2.22 for the 100 m resonator. The measured values of , 1.67 are summarized in Table I, together with the anaQ, and lytical and finite-element predictions for resonance frequency.

Temperature-induced variations in resonant frequency were measured from room temperature to 95 C for the 80 and 100 m resonators. The temperature coefficient of frequency (TCF) for the resonators should be independent of resonant frequency. As expected, the interpolated TCF is similar for the two resonators, TCF values of 44.7 and 47.3 ppm/ C for the 80 and 100 m resonators, respectively. The variation in TCF values between the two resonators is likely due to slight differences in alignment between the as-fabricated disk structures and the AlGaAs crystal planes. The data for the 80 m resonator are presented in Fig. 10. The average TCF value is comparable to other microfabricated resonators, although significantly larger than that of AT-cut quartz crystal resonators [24]. Frequency stabilization and compensation schemes may ultimately be needed to minimize temperature-induced frequency drifts of the AlGaAs resonators. IV. CONCLUSION The development of 2-D resonators based on single crystal piezoelectric materials is complicated by the anisotropic nature of both elastic and the piezoelectric properties. The methodology presented here, which is based on evaluating the profile of the elastic wave propagation speeds to achieve a pure standing wave in the resonant structure, addresses this challenge by defining a formal approach to 2-D planar resonator design. While Al Ga As was used as the piezoelectric material used to validate the model, the methodology is equally applicable to other single-crystal piezoelectric materials such as AlN. While high-quality single-crystal AlN employing appropriate low-loss electrode layers may be expected to provide better performance due to its higher wavespeed, the current Al Ga As devices exhibit encouraging results. The best performance measured from the prototype resonators includes a quality factor of intrinsic motional resistance 11 200 at 23.2 MHz with 1.67 and a quality factor of 6500 at 29.0 MHz with 2.22 intrinsic motional resistance. Further improvements in AlGaAs resonator performance may be realized by reducing the width of the anchor beams. For the devices presented here, a minimum beamwidth of 5 m

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REFERENCES

Fig. 9. Measured quality factors as a function of anchor length for resonators with h001i lateral dimensions of 80 and 100 m.

Fig. 10. Measured temperature-induced frequency drift for an 80 m piezoelectric disk resonator.

was imposed by the use of contact lithography during fabrication. Future resonators defined by projection lithography will allow substantially thinner anchors with lower anticipated energy losses to the substrate. In addition, the quad-symmetric anchors used for the prototype resonators can be replaced by a single anchor beam to reduce anchor losses, and longer anchors can further improve Q, as demonstrated in Fig. 9. While using fewer, more narrow, and longer anchors can reduce energy loss to the substrate, this also has the effect of increasing the parasitic impedance due to the higher electrical resistance of the electrodes running along the anchors. This disadvantage may be offset by using Si-doped GaAs rather than Al Ga As for the electrode layers, since GaAs:Si offers nearly an order of mag. nitude higher electron mobility than Al Ga As ACKNOWLEDGMENT The authors would like to thank L. C. Calhoun of the NSA Laboratory for Physical Sciences for his assistance with AlGaAs/GaAs wafer preparation.

[1] S. Pourkamali, Z. Hao, and F. Ayazi, “VHF single crystal silicon capacitive elliptic bulk-mode disk resonator—Part II: Implementation and characterization,” J. Microelectromech. Syst., vol. 13, no. 6, pp. 1054–1062, 2004. [2] V. Kaajakari, T. Mattila, A. Oja, J. Kiihamaki, and H. Seppa, “Squareextensional mode single-crystal silicon micromechanical resonator for low-phase-noise oscillator applications,” IEEE Electron Device Lett., vol. 25, no. 4, pp. 173–175, 2004. [3] K. Wang, A.-C. Wong, and C. T.-C. Nguyen, “VHF free-free beam high-Q micromechanical resonators,” J. Microelectromech. Syst., vol. 9, no. 3, pp. 347–360, 2000. [4] F. D. Bannon, III, J. R. Clark, and C. T.-C. Nguyen, “High-Q HF microelectromechanical filters,” IEEE J. Solid State Circuits, vol. 35, no. 4, pp. 512–526, 2000. [5] J. Wang, Z. Ren, and C. T.-C. Nguyen, “1.156-GHz self-aligned vibrating micromechanical disk resonator,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 51, no. 12, pp. 1607–1628, 2004. [6] S. A. Bhave, D. Gao, R. Mabhoudian, and R. T. Howe, “Fully-differential poly-SiC lame-mode resonator and checkerboard filter,” in Proc. 18th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2005), Miami, FL, 2005, pp. 223–226. [7] C. T.-C. Nguyen, “Vibrating RF MEMS for next generation wireless applications,” in Proc. 2004 IEEE Custom Integr. Circuits Conf., Orlando, FL, 2004, pp. 257–264. [8] S. Vengallatore, “Analysis of thermoelastic damping in laminated composite micromechanical beam resonators,” J. Micromech. Microeng., vol. 15, pp. 2398–2404, 2005. [9] R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng., vol. 15, pp. 2249–2254, 2005. [10] D. L. DeVoe, “Piezoelectric thin film micromechanical beam resonators,” Sens. Actuators A, vol. 88, pp. 263–272, 2001. [11] M. Hara, J. Kuypers, T. Abe, and M. Esashi, “Surface micromachined AlN thin film 2 GHz resonator for CMOS integration,” Sens. Actuators A, vol. 117, pp. 211–216, 2005. [12] G. Piazza, R. Abdolvand, G. K. Ho, and F. Ayazi, “Voltage-tunable piezoelectrically-transduced single-crystal silicon micromechanical resonators,” Sens. Actuators A, vol. 111, pp. 71–78, 2004. [13] G. Piazza, P. J. Stephanou, J. M. Porter, M. B. J. Wijesundara, and A. P. Pisano, “Low motional resistance ring-shaped contour-mode aluminum nitride piezoelectric micromechanical resonators for UHF applications,” in Proc. 18th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2005), Miami, FL, 2005, pp. 20–23. [14] S. Humad, R. Abdolvand, G. K. Ho, G. Piazza, and F. Ayazi, “High frequency micromechanical piezo-on-silicon block resonators,” in Proc. IEEE Int. Electron Devices Meeting, 2003, pp. 957–960. [15] L. Li, P. Kumar, L. Calhoun, and D. L. DeVoe, “Piezoelectric Al Ga As longitudinal mode beam resonators,” J. Microelectromech. Syst., accepted for publication. [16] P. Kumar, L. Li, L. Calhoun, P. Boudreaux, and D. L. DeVoe, “Fabrication of piezoelectric Al Ga As microstructures,” Sens. Actuators A, vol. 115, pp. 96–103, 2004. [17] L. Li, P. Kumar, L. Calhoun, and D. L. DeVoe, “Piezoelectric miAs films,” in Proc. crobeam resonators based on epitaxial Al Ga IMECE’03, Washington, DC, Nov. 2003, p. 41307. As: Material parameters for [18] S. Adachi, “GaAs, AlAs, and Al Ga use in research and device applications,” J. Appl. Phys., vol. 58, pp. R1–R29, 1985. [19] J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford, U.K.: Oxford Univ. Press, 1985. [20] M. J. P. Musgrave, Crystal Acoustics. San Francisco, CA: HoldenDay, 1970. [21] P. Kumar, S. Kanakaraju, and D. L. DeVoe, “Sacrificial etching of As for surface micromachining,” Appl. Phys. Lett., subAl Ga mitted for publication. [22] Z. Hao, A. Erbil, and F. Ayazi, “An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations,” Sens. Actuators A, vol. 109, pp. 156–164, 2003. [23] M. C. Cross and R. Lifshitz, “Elastic wave transmission at an abrupt junction in a thin plate with application to heat transport and vibrations in mesoscopic systems,” Phys. Rev. B, vol. 64, pp. 1–22, 2001. [24] M. E. Frerking, Crystal Oscillator Design and Temperature Compensation. New York: Van Nostrand, 1978.

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Ken Deng received the B.S. degree in mechanical engineering from Beijing University of Posts & Telecommunications (BUPT) in 1985, the M.S. degree in mechanical engineering from the University of Maryland at College Park (UMCP) in 1995, and the Ph.D. degree in MEMS from the University of Maryland at College Park (UMCP) in 2006. In 1996, he joined Wilcoxon Research, Inc., working in the field of piezoelectric transducers and underwater acoustic sensors, and he held four patents in this area. Since 2000, he has also participated in several MEMS projects in the area of MEMS piezoelectric transducers, RF resonator, and filter. His research interests are in the field of bulk and MEMS transducers and electromechanical system modeling and simulation.

Parshant Kumar (M’04) received the Ph.D. degree in Microelectronics and Instruments from Central Scientific Instruments Organization and Panjab University Chandigarh in 1998, with a specialization in ECR process development and etching of Si and III–V materials. He is a Research Scientist in the Department of Mechanical Engineering, University of Maryland, College Park. His current research interests include the development of III–V MEMS for filter technology, biosensing using piezoelectric MEMS, biomolecular electronics for hybrid device fabrication, nanofabrication and system integration of MEMS with electronics. Dr. Kumar is Member of American Society of Mechanical Engineers (ASME).

Lihua Li received the B.S. and M.S. degrees in precision instruments and mechanology from Tsinghua University, China, in 1997 and 2000, respectively, and the Ph.D. degree in mechanical engineering from the University of Maryland, College Park, in 2005. Her Ph.D. research was focused on piezoelectric microresonators and actuators. She joined MEMSCap, Inc., in 2006.

Don L. DeVoe received the Ph.D. degree in Mechanical Engineering from U.C. Berkeley in 1997, with a specialization in MEMS and piezoelectric microsystems. He is an Associate Professor of Mechanical Engineering and a core faculty member of the Bioengineering Department at the University of Maryland, College Park. His current research interests include microfluidic systems for biomolecular analysis and novel polymer-based microfabrication methods. Dr. DeVoe is a recipient of the Presidential Early Career Award for Scientists and Engineers from the National Science Foundation, and currently serves the MEMS community as a subject editor for the IEEE/ASME JOURNAL OF MICROELECTROMECHANICAL SYSTEMS.