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6MHz BULK-MODE RESONATOR WITH Q VALUES EXCEEDING ONE MILLION

Lynn Khine, Moorthi Palaniapan* and Wai-Kin Wong Department of Electrical and Computer Engineering, National University of Singapore, SINGAPORE

(*Tel : +65-65168723 ; Email : elemp@nus.edu.sg)

Abstract: In this paper, we report a 6.3MHz Lamé-mode square resonator with fully differential drive and sense electronics, exhibiting quality factor, Q values exceeding 1 million in ambient pressures as high as 100Pa. A maximum Q value of 1.6 million was experimentally measured at vacuum pressure of 36 µTorr. It was also experimentally observed that the Q value for the bulk mode resonator was relatively independent for pressures below 100Pa suggesting that the Q is pressure limited for pressure higher than 100Pa. This resonator was fabricated using SOIMUMPs process from MEMSCAP.

Keywords: Bulk-mode, resonators, micromechanical, Quality factor, differential drive

1. INTRODUCTION Recent research interests have focused on the

high quality factor, Q micromechanical resonators suitable for oscillator and filter applications [1]-[7]. Bulk-mode micromechanical resonators have been shown to provide higher Q values and better power handling capabilities. The advantage of high Q micromechanical oscillator is outlined in [1], where a square resonator excited for square extensional mode, with a Q value of 130,000 in vacuum, has been shown to give a low phase noise that satisfies the GSM specification. Another possible excitation of a square resonator is to operate in Lamé mode. The benefits of differential drive and sense of square resonator in Lamé mode has been reported in [2], where differentially driven-and-sensed 173MHz Poly-SiC square had a Q of 9,300 in air. In this work, we present a 6.35MHz silicon-on-insulator (SOI) Lamé-mode square resonator with measured Q of 1.6 million in vacuum pressure of 36µTorr.

2. HIGH-Q MEMS RESONATORS

From the perspective of high Qmicromechanical resonators, bulk acoustic mode or contour mode type of resonators provide better performance than the flexural mode resonators as dimensions are scaled for higher frequency. When the dimensions for a flexural resonator become smaller, anchor losses are large, and the Q value usually goes down severely along with a decrease in power handling or maximum current output.

A 92MHz free-free beam resonator has been shown to have a Q of 7450 at 50µTorr [4] and a 72MHz flexural square plate resonator is reported with a Q of 17,500 at 200µTorr. Using the bulk or radial contour mode disk resonators, the Q could be enhanced to higher values, such as in the order of 145,000 for a 60MHz wine-glass disk resonator under 20-mtorr vacuum [4]. Other radial-contour mode disk resonators with Q values exceeding 10,000 at frequencies greater than 1GHz have also been reported, such as a 1.51GHz nanocrystalline diamond disk resonator with Q of 10,100 in air [5]. Another reported disk resonator in GHz range is 1.2GHz hollow-disk ring polysilicon resonator with a Q of 14,600 under vacuum [6]. A summary of selected resonators found in literature is listed in Table 1.

Table 1. Recently reported resonators in literature and their resonance frequency and Q values.

Resonator fo Q Pressure Free-Free beam 92MHz 7450 50µTorr

Square plate 72MHz 17,500 200µTorr Wine-glass disk 60MHz 145,780 20mTorr Diamond disk 1.51GHz 10,100 air

Hollow-disk ring 1.2GHz 14,600 vacuum Poly-SiC square 173MHz 9,300 air

Longitudinal beam 12MHz 180,000 0.01 mbar Square-extensional 13.1MHz 130,000 0.01 mbar

Quartz crystal 10MHz 1,300,000 - Our work (Lamé-mode) 6.35MHz 1,600,000 36µTorr

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Other bulk mode resonators have been shown to provide high Q’s > 100,000. A 12MHz longitudinal bulk acoustic mode silicon beam resonator with a Q of 180,000 at pressure < 0.01 mbar is reported in [7]. As mentioned before the 13.1MHz SOI square plate excited in bulk square-extensional mode is also shown to have a Q of 130,000 at pressure < 0.01 mbar [1].

Quartz crystals and surface acoustic wave (SAW) resonators with Q’s in the range of 106 are widely used for high-Q oscillators and filters. A recently reported quartz crystal at 10MHz has a Qof 1.3 million [8]. Due to very high Q, quartz crystal oscillators are well known to provide very good phase noise performance. However, the Qvalues of smaller micromechanical resonators are catching up to those of crystals, and they have become more attractive given the benefit of integration with IC electronics monolithically.

The high Q value is not the only criteria to be maximized, as it has for example trade-off issues with power handling. Tradeoffs between Q and power handling seem to be very important in setting the close-to-carrier and far-from-carrier phase noise for oscillator applications [4]. Nevertheless, Q is an important criterion for high performance oscillators and filters.

3. SQUARE RESONATOR DESIGN

The square resonator of this work is designed to operate in Lamé mode, its mode shape simulated with finite element software, ABAQUS, and a micrograph of the resonator is shown in Fig. 1. In this mode the edges of square plate bend in anti-phase while the plate volume is preserved. The length of the square edge is designed as 650µm. The anchor tether beams are placed at the nodal points of the mode, and are optimized for minimum energy losses through the anchors.

If the material of square plate is isotropic and the side length of square L is much larger than its thickness, the resonance frequency fo can be calculated as outlined in [9] as shown equation (1),

650µm650µm

Fig. 1: Micrograph of square resonator and ABAQUS simulation of Lamé mode resonance.

LGfo 2

1⋅=ρ

(1)

and elastic component term G can be expressed as

( )ν+=

12EG (2)

where E is the Young’s modulus, ν is the Poisson’s coefficient, and ρ is the density. For the silicon material used E = 180GPa, ν = 0.29, and ρ = 2330 kg/m3. According to equation (1), resonance frequency is around 6.0 MHz and is verified by ABAQUS simulation shown in Fig. 1.

The resonator was fabricated using the SOIMUMPs process provided by MEMSCAP. The cross-sectional view of different layers in SOIMUMPs process is shown in Fig. 2.

Fig. 2: Cross sectional view of different layers in SOIMUMPs process.

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The 25m thick top silicon structural layer pushes the undesirable out-of-plane resonant modes to higher frequencies. Moreover, the backside etch has the advantage of reducing substrate parasitics. The minimum feature size for top structural silicon is 2m, and therefore the electrode gap is limited to 2m as well.

4. MEASUREMENT SETUP

Fig. 3 shows the fully differential drive and sense measurement setup used for this work. The 180° degrees out of phase nature of the adjacent sides of the square is very useful in driving the resonator differentially. Resonator’s output current sensing is done using a differential transresistance amplifier. The wire-bonded resonator die and the transresistance amplifier are mounted on the same PCB which is placed inside the vacuum chamber during testing.

Fig. 3: Differential drive and sense measurement setup.

The polarization DC voltage VP is applied directly to the resonator proof-mass. The ac drive signal from network analyzer is split into positive and negative signals through a single-to-differential conversion PCB block. The drive and sense components are kept far apart on the PCB board to reduce the parasitics. The SOI substrate is grounded to reduce the parasitics caused by the feed-through capacitance. The pressure of the vacuum chamber which can be increased up to 1 atmosphere is maintained around 36µTorr for all the high vacuum measurements.

5. EXPERIMENTAL RESULTS

The measured S21 transmission curve for the square resonator of Fig. 1 is shown in Fig. 4. The resonance frequency is measured at 6.358MHz with Q value of 1.6 million in vacuum pressure of 36µTorr, when the resonator is biased with DC voltage VP of 50V and an AC drive voltage of 62mVpp. As can be seen from the Fig. 4(a) and Fig. 4(b), anti-resonance peak due to feed-through parasitic capacitances is suppressed due to fully differential drive and sense electronics. The corresponding phase plot in Fig. 4(b) shows the expected sharp drop in phase at resonance.

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Frequency (MHz)

Tran

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Q =1,589,560

Absence of anti-resonance

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Frequency (MHz)

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(dB

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AC = 62mVpp

P = 0.005Pa

Q =1,589,560

Absence of anti-resonance

(a)

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(dB

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magnitude

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0

Phas

e (D

egre

e)

3dBQ =1,589,560

DC=50V

AC=62mVpp

P=0.005Paphase

magnitude

(b)

Fig. 4: Measured transmission curve of the 6.358MHz Lame mode square resonator in large-span view and zoom- in view, biased at 50V DC, 62mVpp AC, and Q

is measured as 1.6 million.

The relationship between Q and the pressure was measured by increasing the pressure in the vacuum chamber up to one atmospheric pressure

Network Analyzer

vi vo

Single to

Differential

+VP

vd - vd+

vd -

id+

id -Ramp

Vacuum chamber

–

+

–

+

–

+

–

+

Ramp

-

Network Analyzer

vi vo

Single to

Differential

+VP

vd - vd+

vd -

id+

id -Ramp

Vacuum chamber

–

+

–

+

–

+

–

+

Ramp

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of ~105 Pa, and the results are shown in Fig. 5, where both pressure levels and Q values are plotted in log scales. The polarization voltage VPof 60V was fixed for all pressures. The Q value remained almost constant up to a pressure level of 100Pa, maintaining a value exceeding 1.0 million. However, beyond 100Pa, the measured Q value drops inversely with pressure reaching a value of about 5,100 at a pressure of ~105 Pa. The Qlimitation in this pressure range above 100Pa is mainly due to air damping [10].

Fig. 5 A plot of measured Q versus Pressure for 6.358MHz Lamé mode square resonator.

To further verify the consistency of our high Qresults, another identical resonator device from the same fabrication run was tested. The measured resonance frequency measured is 6.343MHz with the Q of about 1.2 million in vacuum pressure of 36µTorr. The magnitude and phase responses for the new device matched the results shown in Fig.4 reasonably well indicating the repeatability of the results for our 6.35MHz resonator.

With the fully differential test setup, motional and feed-through currents are drained at the resonator proof-mass node as the virtual ground, without charges passing through the anchors [2]. This fully differential drive/sense circuit setup has also reduced the anti-resonance behavior (Fig 4a).

The factors affecting the quality factor, Q of the resonator as outlined in [10] depends on various mechanisms such as thermo elastic dissipation (TED), air damping, anchor losses, surface loss, and other intrinsic material losses. When the

resonator is operated in high vacuum, Q value is limited by other loss mechanisms and not air damping. From Fig. 5, it be inferred that our bulk mode resonator’s Q value is pressure limited (air damping) for pressures higher than 100Pa. Hence, the optimal operating pressure should be 100Pa so as to achieve the maximum Q value.

6. CONCLUSION

A measured Q value of around 1.6 million for 6.35MHz square resonators have been reported in this paper and the advantages of differential drive and sense measurement architecture are also highlighted. The Q value is maintained at about 5,100 in ambient air. Pressure limited regime for Q value due to air damping was observed for pressures higher than 100Pa. Such high-Qresonators have a huge potential in improving performance of MEMS based oscillators and filters.

REFERENCES [1] V. Kaajakari, et al., “Square-extensional mode single-crystal silicon micromechanical resonator for low phase noise oscillator applications”, IEEE Electron Device Lett., vol. 25, no. 4, April 2004. [2] S. A. Bhave, et al., “Fully differential poly-SiC Lamé-mode resonator and checkerboard filter”, IEEE MEMS Conf., 2005. [3] J. R. Clark, et al., “High-Q UHF micromechanical radial-contour mode disk resonators”, J. MEMS, vol. 14, no. 6, Dec 2005. [4] Y.-W. Lin, et al., “Series-resonant VHF micromechanical resonator reference oscillators”, IEEE J. of Solid-State Cir, vol. 39, no. 12, 2004, pp. 2477-2491. [5] J. Wang, et al., “1.51-GHz nanocrystalline diamond micromechanical disk resonator with material-mismatched isolating support”, IEEE MEMS Conf., 2004, pp. 641-644. [6] S.-S. Li , et al., “Micromechanical ‘hollow-disk’ ring resonator”, IEEE MEMS Conf., 2004, pp. 821-824. [7] T. Mattila, et al., “A 12 MHz micromechanical bulk acoustic mode oscillator”, Sensors and Actuators A, vol. 101, no. 1-2, 2002, pp. 1-9. [8] F. Watanabe and T. Watanabe, “Convex quartz crystal resonator of extremely high Q in 10MHz-50MHz”, Proc. IEEE Ultrasonics Symposium, vol. 1, 02’, pp. 1007-1010. [9] Hicham Majjad, et al., “Modeling and characterization of Lamé-mode microresonators realized by UV-LIGA”, Transducers '01, vol. 1, 2001, pp. 300-3. [10] B. Kim, et al., “Temperature dependence of quality factor in MEMS resonators”, IEEE MEMS Conf., 2006, pp. 590-593

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