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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 61, NO. 2, FEBRUARY 2014
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Dual-Mode AlN-on-Silicon Micromechanical Resonators for Temperature Sensing Jenna L. Fu, Member, IEEE, Roozbeh Tabrizian, Member, IEEE, and Farrokh Ayazi, Fellow, IEEE
Abstract— In this paper, we present dual-mode (DM) AlNon-silicon micromechanical resonators for self-temperature sensing. In-plane width-shear (WS) and width-extensional (WE) modes of [110]-oriented silicon resonators have been used as alternatives to first- and third-order modes to enhance DM temperature sensitivity by engineering device geometry, which reduces inherent beat frequency fb between the two modes. This configuration provides a 50× improvement in temperature coefficient of beat frequency (TC fb ) compared with single-mode temperature measurement and eliminates the need for additional frequency multipliers to generate fb from its constituents. [100]-oriented WS/WE resonators provide 4× larger TCF difference between modes (TCF) than first and third widthextensional resonators, which further contributes to TC fb enhancement. WS/WE mode resonators also demonstrate the capability of operating as a temperature-stable reference fb . The proposed modes for DM operation have high Q and low motional resistance, and are 180° out-of-phase when operated in two-port configuration, thus enabling mode-selective low-power oscillator interfacing for resonant temperature sensing. Index Terms— Beat frequency, dual-mode (DM) resonator, piezoelectric-on-silicon, self-temperature sensing.
I. I NTRODUCTION
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ICROELECTROMECHANICAL system (MEMS) oscillators based on monocrystalline silicon resonators are especially promising candidates for integrated timing and sensing applications. Achieving a highly stable oscillator output using silicon resonators is challenging given their large native temperature coefficient of frequency (TCF), which is approximately −30 ppm/°C. Passive compensation techniques, such as engineering device geometry [1] and substrate doping profile [2], have shown to reduce silicon resonator TCF to a few ppm/°C. Traditional methods using a layer of positive-TCF silicon dioxide to counteract the negative silicon TCF [3] are effective but require additional process steps and are limited to thin silicon substrates. It has been demonstrated that bulk compensation rather than surface compensation, which exploits uniformly distributed silicon Manuscript received July 28, 2013; revised October 19, 2013; accepted December 5, 2013. Date of current version January 20, 2014. This work was supported by Integrated Device Technology, Inc. The review of this paper was arranged by Editor A. M. Ionescu. J. L. Fu was with the Georgia Institute of Technology, Atlanta, GA 30332 USA. She is now with System Planning Corporation, Arlington, VA 22201 USA (e-mail: [email protected]). R. Tabrizian and F. Ayazi are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2013.2295613
dioxide pillars in thick silicon completely eliminates the first-order TCF of high-Q bulk acoustic resonators, resulting in 90–180 ppm frequency drift over the entire industrial temperature range of −40 °C–85 °C [4], [5]. However, device- and circuit-level tuning are inevitable to achieve subppm instability levels required for temperature-compensated and/or oven-controlled crystal oscillator applications [6]. Such dynamic tuning should continuously monitor device operating temperature to apply the necessary frequency pulling in the tolerance range. Therefore, oscillator stability is mainly, although indirectly, defined by precision of the temperature sensing procedure. Accurate temperature measurement requires the sensor and temperature-sensitive frequency reference to be in very close proximity, thereby minimizing discrepancies caused by thermal gradients. Since oscillator frequency is measurable with high accuracy, the temperature-sensitive resonating element is an outstanding candidate to be used as a self-thermometer. Although the finite TCF of a single resonance mode can be used to track temperature, measuring a linear combination of two modes with different TCF values in a single device provides greater sensitivity. Therefore, dual-mode (DM) excitation, which has been widely employed in quartz resonators to simultaneously monitor stress, mass, pressure, and temperature [7]–[9], is of particular interest for measurement and compensation of temperature-induced oscillator frequency shift. DM excitation provides local temperature measurement without external thermometers, which significantly reduces system footprint when integrated with CMOS electronics. In this paper, DM AlN-on-Si resonator designs based on alternatives to fundamental and harmonic modes are investigated. II. DM T EMPERATURE M EASUREMENT A. Principle of Operation DM temperature sensing requires simultaneous excitation of two modes in a single resonator, which causes both modes to experience identical changes in ambient temperature [10]. The unique frequency-temperature characteristics of each mode can be used to compensate reference frequency over temperature. Beat frequency fb is defined as a linear combination of f 1 and f 2 fb = α · f 1 − f2 . (1) Multiplicative constant α is an integer when f 2 is an α-order harmonic of f 1 [10]. If the modes are close in frequency,
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Careful design of resonators with proper phase, low Rm , and high Q ensures successful DM oscillator interfacing. III. AlN- ON -Si DM R ESONATORS
Fig. 1. (a) Single-loop Colpitts oscillator with one-port resonator. (b) Dualloop DM oscillator with two-port MEMS resonator in feedback with TIAs followed by mixing, multiplication, and filtering to generate output frequency fb .
f 1 and f2 are directly mixed to generate f b , thus obviating the need for integer/fractional frequency multipliers [11]. The relative change in resonance frequency f 0 with respect to temperature, or TC f 0 , can be expressed as TCn f 0 =
1 ∂ n f0 . f0 ∂ T n
(2)
Silicon has a dominant first-order temperature coefficient, TC1 F (denoted as TCF in this paper). Based on (1) and (2), DM temperature sensitivity is defined as TC f b =
α · f 1 · TC f 1 − f 2 · TC f 2 fb
(3)
suggesting that beat frequency reduction is one method to improve temperature sensitivity. The linear TCF of silicon ensures that TC f b would also be a strongly linear function of temperature.
Self-temperature sensing techniques have been previously demonstrated within dual-resonator [14] as well as singleresonator [15] configurations. However, both implementations utilized capacitive resonators, whose high motional resistance introduces difficulties in oscillator implementation. The required dc polarization voltage (V p ) further increases power consumption and may contribute to undesired measurement inaccuracies via temperature-induced V p variations On the other hand, piezoelectric actuation enables multiplemode excitation in a single device without dc voltages. Thin film piezoelectric-on-substrate (TPoS) technology combines the advantages of piezoelectric transduction with a low-loss material such as silicon, which exhibits high-Q and enhanced power handling over piezoelectric-only resonators [16]. A. Resonance Modes for DM Operation When f b approaches a minimum (α · f 1 ∼ = f2 ), (3) can be approximated as f2 TC f 1 − TC f 2 . (4) TC f b ∼ = fb Based on frequency ratio f2 / f b , a large f 2 combined with small fb provides enhanced DM temperature sensitivity, which can be realized by exploiting high-frequency in-plane bulk modes of AlN-on-Si resonators with lithographically defined frequencies. Geometrical engineering can be used to bring together two linearly independent resonance modes to increase TC f b . Further TC fb improvements are achievable by maximizing TCF (TC f 1 − TC f 2 ), which in TPoS resonators is primarily determined by temperature coefficients of independent elastic constants (TCc11 , TCc12 , and TCc44 ) and their contributions to the selected modes [17].
B. DM Oscillator Considerations Real-time measurement and compensation requires circuitry to drive and sustain oscillations across a wide temperature range. Various architectures have been used to implement quartz DM oscillators, which can be categorized as either single-loop or dual-loop configuration [11], [12]. Single-loop (Colpitts) oscillators [Fig. 1(a)] require fewer components than a dual-loop oscillator and can exploit transistor nonlinearities to inherently provide f b as an output [11], [12]. Dual-loop DM oscillators [Fig. 1(b)] can be implemented if separate gain and phase control are required. The Barkhausen stability criterion, which states that a circuit will sustain oscillations under certain loop gain and phase conditions, must be satisfied at both frequencies in a DM oscillator. Unity loop gain is achieved by ensuring that the transimpedance amplifier (TIA) provides sufficient gain to compensate resonator electrical losses. Phase conditions are met if the combined TIA and resonator phase results in zero loop phase shift. In addition to resonator phase and motional resistance Rm , Q of both modes directly affects oscillator phase noise and consequently, temperature measurement linearity [13].
B. Limitations of Fundamental and Higher Order Harmonics for DM Operation DM quartz thermometers based on first- and third-harmonic C-modes have demonstrated fb values in the 150-kHz range ( f b = 3 · f 1 − f 3 ) [10], [11]. In previous DM demonstrations, TPoS resonators employed first and third width-extensional (WE/WE3) modes [13], [18], which tend to suffer from larger f b . A major factor causing WE/WE3 DM resonators to deviate from the ideal situation (α = 3) is their finite support size, which does not scale similarly for the two modes, creating nonuniformities in the f1 strain pattern and shifting the frequency from the nominal value. However, finite element simulations show that even with zero support size, f b reaches a lower limit for the given dimensions (Fig. 2). This can be attributed to the finite thickness and length of the resonator, resulting in deviation of WE harmonics from their bulk acoustic plane wave counterparts. Since width W determines frequency, the only variable dimension is length L, which also provides minimal fb reduction as measured in fabricated resonators (Fig. 3). Therefore, benefits of using
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Fig. 4.
ANSYS mode shapes of WS and WE modes for DM operation.
Fig. 2. Left: strain distribution for DM AlN-on-Si resonator based on WE/WE3 modes. Right: simulated f b versus support width for a 27-MHz resonator (W = 156 μm).
Fig. 5. Simulated frequency of WS and WE modes versus L for W = 156 μm, corresponding to f WE = 27 MHz.
Fig. 3.
Measured f b versus length L for AlN-on-Si WE/WE3 resonator.
high-frequency mode f 3 are negated by the inability to minimize f b in WE/WE3 resonators. Furthermore, since f 1 and f3 have the same elastic dependences, small TCF is also expected. For the devices measured in Fig. 3, TCF = –0.5 ppm/°C yields TC fb ∼ −37 ppm/°C, which provides virtually no improvement over single-mode measurement. Since extensional modes in TPoS resonators possess similar temperature-frequency behavior and large fb , alternative modes for TC f b enhancement are investigated. IV. TC fb E NHANCEMENT BY B EAT F REQUENCY R EDUCTION A. In-Plane WE and WS Modes The WE mode can be attributed to the longitudinal quasiplane wave propagating in width direction and reflecting back from stress-free boundaries. Therefore, its frequency is nearly independent of resonator length (L) and is defined by v (5) f WE = 2W where v is the effective longitudinal wave velocity. On the other hand, the width-shear (WS) mode (Fig. 4) exhibits a significant dependence on L, which can be explained by considering the 180° phase difference between particle polarizations at two boundaries along the resonator length direction. This suggests the WS mode is a standing wave formed by the interaction of Lamb waves propagating in length direction and
reflecting back from stress-free boundaries. Considering the dependence of Lamb wave velocity on resonator width, the WS mode frequency can occur in close proximity of the WE mode. Therefore, the f WS dependence on both W and L can be exploited to define specific f b values by controlling the distance between WS and WE modes ( f b = f WS − f WE ) (Fig. 5). Utilizing WS and WE modes for DM operation provides inherently small f b by directly mixing two frequencies rather than utilizing fractional multiplication to obtain a desired f b [12], thus introducing additional complexity and noise to the system. L/W = 1.31 corresponds to the case when f WS = fWE , or zero f b . Because f b is determined by ratios rather than absolute dimensions, DM excitation using WS and WE modes is less sensitive to lithography and process variations. Furthermore, the WS/WE resonator electrode configuration provides a 180° phase shift between modes when operated in two-port configuration [19], thus effectively isolating one mode from the other in a dual-loop oscillator. TCci j (1 ≤ i j ∈ N ≤ 4) values from [17] for single crystal silicon and [20] for aluminum nitride elastic properties were used to accurately model the TPoS resonator in ANSYS static structural simulations with varying temperature loads. Subsequent modal analyses performed on the resonator were prestressed with static structural results to predict f WS and f WE over temperature (TC f WS = −31.1 ppm/°C and TC f WE = −32.5 ppm/°C). WS/WE resonators with f WE = 27 MHz were designed by the methodology described, with f b ranging from 17 kHz to 1.5 MHz. Resonators were fabricated on a 20-μm-thick SOI substrate using a process similar to [21] and characterized in an ESPEC temperature chamber. The measured
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Fig. 6. Measured versus simulated f b for WS/WE resonator designs with W = 156 μm, various L values ( f b = f WS − f WE ); (inset) SEM image of WS/WE resonator (W = 156 μm, L = 204 μm).
Fig. 9. WS/WE resonator terminal configurations for DM oscillator interfacing. (a) Two-port operation. (b) Single-port operation. TABLE I W IDTH -S HEAR /W IDTH -E XTENSIONAL D UAL -M ODE R ESONATORS
Fig. 7. Extracted TC f b of WS/WE DM resonator with f b = 17 kHz; measured TC f WS = −30.1 ppm/°C, TC f WE = −31.1 ppm/°C.
B. WS/WE Mode Oscillator Interfacing
Fig. 8. Measured response of DM resonators with | f b | = 1.5 MHz and 134 kHz (| f b | = | f WS − f WE |), showing Q WE degradation when f WS and f WE converge.
frequency response of several devices, obtained with an Agilent E8364B network analyzer, agreed well with simulated f b values (Fig. 6, Table 1). The slightly lower measured TC f WS and TC f WE values (–30.1 and –31.1 ppm/°C) can be attributed to variation in doping concentration (simulations assumed boron-doped silicon with 4 cm resistivity; fabricated device resistivity ranged from 1 to 20 -cm). The highest extracted TC f b was 1480 ppm/°C for a device with f b = 17 kHz (Fig. 7), nearly 50× larger than single-mode measurement of TC fWS or TC f WE .
Acoustic coupling between modes as a result of nonlinear effects [22] can cause significant Q WE degradation when WS and WE modes converge (Fig. 8). Since Q affects frequency stability through oscillator phase noise, interference between modes must be minimized for simultaneous operation. Devices with smaller f b may benefit from one-port excitation using two single-loop oscillators, which effectively isolates one mode from the other [Fig. 9(b)]. However, transduction isolation for f b constituent modes could also be achieved using a multiport configuration with common input and separate output electrodes [23] [rather than the two-port layout shown in Fig. 9(a)]. V. E FFECT OF O RIENTATION ON WS/WE R ESONATOR TCF AlN-on-Si WS/WE resonators provide substantial f b reduction as well as a 2× larger TCF than the WE/WE3 configuration. However, further TCF enhancement would contribute to increased sensitivity as well as relaxed f b requirements, thus reducing mechanical destructive interference of the two modes.
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Fig. 10. Measured TC f WS and TC f WE for [100]-aligned WS/WE resonator, exhibiting 2× larger TCF than [110]-aligned devices. Fig. 11. Measured response of [100]-oriented WS/WE resonator with f b = 120 kHz (W = 156 μm, L = 268 μm).
The dissimilar temperature characteristic of silicon elastic constants ci j , combined with their contribution to the acoustic wave velocity in different directions, results in different TCF for similar modes when the device is aligned in another crystallographic orientation. While WE-mode resonators on (100) substrates have exploited the [100] direction for nearly full compensation of TC f WE [24], devices in this paper are reoriented to increase the WS/WE resonator TCF beyond 1 ppm/°C. WS/WE resonators aligned to the [100] direction had a simulated TC f WS = −30.6 ppm/°C and TC fWE = −32.7 ppm/°C (TCF = 2.1 ppm/°C). Devices were designed by a similar methodology to [110]-aligned devices, yielding a matched f b ratio L/W of 1.71. In the [100] direction, W = 156 μm corresponds to f WE = 25 MHz (E [100] < E [110] ). Fabricated devices had a measured TCF = 1.9 (Fig. 10), nearly 2× greater than [110] devices and 4× greater than WE/WE3 resonators. TCF can be further increased using substrates with higher doping levels, which would exhibit a larger difference between E [100] and E [110] . Because f WS is easily driven into nonlinear operation [19], f WE is more likely to be used as a reference and requires lower Rm , which is achieved through increased electrode area by the required L/W ratio (Fig. 11). VI. DM E XCITATION FOR T EMPERATURE -S TABLE B EAT F REQUENCY While DM WS/WE mode resonators are applicable to highsensitivity on-chip thermometry, they can also be employed as temperature-stable references, which are required for counter circuits that would be ultimately used to measure resonance frequency change with temperature. Equating the right-hand side of (3) to zero provides the requirements for temperature-insensitive f b in DM resonators f 2 = α · f1
TC f 1 . TC f 2
(6)
Although α · f 1 and f 2 have nonzero TCF, f b (generated by mixing the two signals) will remain constant over temperature. For a DM resonator with known values of TC f 1 and TC f 2 , α · f 1 and f 2 must be designed to satisfy conditions in (6).
Fig. 12. Measured response for f WS and f WE of [100]-aligned device with temperature-insensitive f b = 1.5 MHz (W = 156 μm, L = 242 μm).
For temperature-insensitive DM resonators, f 2 /α · f1 (rather than f2 / f b ) determines the behavior. Because f WS can be tailored to a specific ratio of f W E , WS/WE resonators (α = 1) can provide f b that is either temperature-sensitive or temperature-insensitive. A [100]-aligned WS/WE resonator with TC f WS = −29.6 ppm/°C and TC f WE = −31.5 ppm/°C was designed to fulfill the aforementioned conditions ( f WS = 26.8 MHz, f WE = 25.3 MHz), fabricated, and characterized over
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Fig. 13. Extracted TC f b of [100]-aligned WS/WE DM resonator with nearly temperature-stable f b .
temperature (Fig. 12). The extracted first-order TC1 f b of 2.4 ppm/°C and second-order TC2 f b of 3.3 ppb/°C2 correspond to a frequency drift of 266 ppm from –20 °C to 100 °C (Fig. 13), which is lower than degenerately doped resonators [25] or geometrically engineered capacitive resonators [26]. VII. C ONCLUSION In this paper, DM AlN-on-Si resonators were optimized for enhanced TC f b by overcoming previous DM implementation challenges. WS and WE mode resonators provided 50× greater TC f b compared with single-mode measurement. Oscillator configurations to address mechanical coupling concerns were suggested. The versatility of WS/WE resonators was further demonstrated through [100]-oriented resonators, which exhibited 4× larger TCF than previous WE/WE3 resonators and also demonstrated the capability to provide temperature-insensitive f b without heavy doping or structural modifications. The flexible design attributes enable WS/WE resonators to operate as either a temperature sensor or reference, depending on application requirements. ACKNOWLEDGMENT The authors would like to thank the Georgia Tech Institute for Electronics and Nanotechnology cleanroom staff for fabrication support and the OEM Group, Inc., for AlN deposition. R EFERENCES [1] A. K. Samarao, G. Casinovi, and F. Ayazi, “Passive TCF compensation in high Q silicon micromechanical resonators,” in Proc. IEEE 23rd Int. Conf. Microelectromech. Syst., Hong Kong, Jan. 2010, pp. 116–119. [2] A. K. Samarao and F. Ayazi, “Temperature compensation of silicon resonators via degenerate doping,” IEEE Trans. Electron Devices, vol. 59, no. 1, pp. 87–93, Jan. 2012. [3] K. Lakin, K. McCarron, and J. McDonald, “Temperature compensated bulk acoustic thin film resonators,” in Proc. IEEE Ultrason. Symp., Oct. 2000, pp. 855–858. [4] R. Tabrizian, G. Casinovi, and F. Ayazi, “Temperature-stable high-Q AlN-on-silicon resonators with embedded array of oxide pillars,” in Proc. Solid-State Sensors, Actuat., Microsyst. Workshop, Hilton Head, SC, USA, Jun. 2010, pp. 100–101.
[5] R. Tabrizian, G. Casinovi, and F. Ayazi, “Temperature-stable silicon oxide (SilOx) micromechanical resonators,” IEEE Trans. Electron Devices, vol. 60, no. 8, pp. 2656–2663, Aug. 2013. [6] R. Tabrizian, M. Pardo, and F. Ayazi, “A 27 MHz temperature compensated MEMS oscillators with sub-ppm instability,” in Proc. IEEE 25th Int. Conf. MEMS, Jan./Feb. 2012, pp. 23–26. [7] J. A. Kusters, M. C. Fischer, and J. G. Leach, “Dual mode operation of temperature and stress compensated crystals,” in Proc. 32nd Annu. Symp. Freq. Control, 1978, pp. 389–397. [8] B. K. Sinha, “Stress compensated orientations for thickness-shear quartz resonators,” in Proc. 35th Annu. Freq. Control Symp., 1981, pp. 213–221. [9] R. Besson, J. Boy, B. Glotin, Y. Jinzaki, B. Sinha, and M. Valdois, “A dual-mode thickness-shear quartz pressure sensor,” IEEE Trans. Ultrason. Ferroelect. Freq. Control, vol. 40, no. 5, pp. 584–591, Sep. 1993. [10] D. E. Pierce, Y. Kim, and J. R. Vig, “A temperature insensitive quartz microbalance,” IEEE Trans. Ultrason. Ferroelect. Freq. Control, vol. 45, no. 5, pp. 1238–1245, Sep. 1998. [11] A. V. Kosykh, I. V. Abramson, and R. P. Bagaev, “Dual-mode crystal oscillators with resonators excited on B and C modes,” in Proc. IEEE Int. Freq. Control Symp., Jun. 1994, pp. 578–586. [12] S. S. Schodowski, “Resonator self-temperature-sensing using a dualharmonic-mode crystal oscillator,” in Proc. 43rd Annu. Symp. Freq. Control, 1989, pp. 2–7. [13] M. J. Dalal, J. L. Fu, and F. Ayazi, “Simultaneous dual-mode excitation of piezo-on-silicon micromechanical oscillator for selftemperature sensing,” in Proc. IEEE 24th Int. Conf. MEMS, Jan. 2011, pp. 489–492. [14] C. Jha, G. Bahl, R. Melamud, S. Chandorkar, M. Hopcroft, B. Kim, et al., “CMOS-compatible dual-resonator MEMS temperature sensor with milli-degree accuracy,” in Proc. Int. Solid-State Sensors, Actuat. Microsyst. Conf., Jun. 2007, pp. 10–14. [15] M. Koskenvuori, V. Kaajakari, T. Mattila, and I. Tittonen, “Temperature measurement and compensation based on two vibrating modes of a bulk acoustic mode microresonator,” in Proc. IEEE 21st Int. Conf. MEMS, Jan. 2008, pp. 78–81. [16] R. Abdolvand and F. Ayazi, “7E-4 enhanced power handling and quality factor in thin-film piezoelectric-on-substrate resonators,” in Proc. IEEE Ultrason. Symp., Oct. 2007, pp. 608–611. [17] C. Bourgeois, E. Steinsland, N. Blanc, and N. F. de Rooij, “Design of resonators for the determination of the temperature coefficients of elastic constants of monocrystalline silicon,” in Proc. IEEE Int. Freq. Control Symp., May 1997, pp. 791–799. [18] R. Abdolvand, H. Mirilavasani, and F. Ayazi, “Single-resonator dualfrequency thin-film piezoelectric-on-substrate oscillator,” in Proc. IEEE IEDM, Dec. 2007, pp. 419–422. [19] M. Pardo, L. Sorenson, and F. Ayazi, “An empirical phase-noise model for MEMS oscillators operating in nonlinear regime,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 5, pp. 979–988, May 2012. [20] K. Tsubouchi and N. Mikoshiba, “Zero-temperature-coefficient SAW devices on AlN epitaxial films,” IEEE Trans. Sonics Ultrason., vol. 32, no. 5, pp. 634–644, Sep. 1985. [21] W. Pan and F. Ayazi, “Thin-film piezoelectric-on-substrate resonators with Q enhancement and TCF reduction,” in Proc. IEEE 23rd Int. Conf. MEMS, Jan. 2010, pp. 727–730. [22] J. P. Valentin, C. P. Guerin, and R. J. Besson, “Indirect amplitude frequency effect in resonators working on two frequencies,” in Proc. 35th Annu. Freq. Control Symp., 1981, pp. 122–129. [23] R. Tabrizian and F. Ayazi, “Acoustically-engineered multi-port AlN-on-silicon resonators for accurate temperature sensing,” in Proc. IEEE IEDM, Washington, DC, USA, 2013, pp. 1811–1814, Dec. 2013. [24] H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves–data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys., vol. 24, pp. 988–997, Aug. 1953. [25] T. Pensala, A. Jaakkola, M. Prunnila, and J. Dekker, “Temperature compensation of silicon MEMS resonators by heavy doping,” in Proc. IEEE IUS, Oct. 2011, pp. 1952–1955. [26] A. K. Samarao, G. Casinovi, and F. Ayazi, “Passive TCF compensation in high Q silicon micromechanical resonators,” in Proc. IEEE 23rd Int. Conf. MEMS, Hong Kong, Jan. 2010, pp. 116–119.
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Jenna L. Fu (S’03–M’13) received the B.S. degree in electrical and computer engineering from Carnegie Mellon University, Pittsburgh, in 2006, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2008 and 2013, respectively. Since July 2013, she has been a research scientist with System Planning Corporation in Arlington, Virginia, USA.
Roozbeh Tabrizian (S’06) received the B.S. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2007, and the Ph.D. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2013. His research interests include design, fabrication and characterization of piezoelectricallytransduced micromechanical resonators for timing, signal processing and sensing applications.
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Farrokh Ayazi (S’96–M’00–SM’05–F’13) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. In December 1999, he joined the faculty of Georgia Institute of Technology, Atlanta, where he is currently a Professor in the School of Electrical and Computer Engineering.
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Dual-Mode AlN-on-Silicon Micromechanical Resonators for Temperature Sensing Jenna L. Fu, Member, IEEE, Roozbeh Tabrizian, Member, IEEE, and Farrokh Ayazi, Fellow, IEEE
Abstract— In this paper, we present dual-mode (DM) AlNon-silicon micromechanical resonators for self-temperature sensing. In-plane width-shear (WS) and width-extensional (WE) modes of [110]-oriented silicon resonators have been used as alternatives to first- and third-order modes to enhance DM temperature sensitivity by engineering device geometry, which reduces inherent beat frequency fb between the two modes. This configuration provides a 50× improvement in temperature coefficient of beat frequency (TC fb ) compared with single-mode temperature measurement and eliminates the need for additional frequency multipliers to generate fb from its constituents. [100]-oriented WS/WE resonators provide 4× larger TCF difference between modes (TCF) than first and third widthextensional resonators, which further contributes to TC fb enhancement. WS/WE mode resonators also demonstrate the capability of operating as a temperature-stable reference fb . The proposed modes for DM operation have high Q and low motional resistance, and are 180° out-of-phase when operated in two-port configuration, thus enabling mode-selective low-power oscillator interfacing for resonant temperature sensing. Index Terms— Beat frequency, dual-mode (DM) resonator, piezoelectric-on-silicon, self-temperature sensing.
I. I NTRODUCTION
M
ICROELECTROMECHANICAL system (MEMS) oscillators based on monocrystalline silicon resonators are especially promising candidates for integrated timing and sensing applications. Achieving a highly stable oscillator output using silicon resonators is challenging given their large native temperature coefficient of frequency (TCF), which is approximately −30 ppm/°C. Passive compensation techniques, such as engineering device geometry [1] and substrate doping profile [2], have shown to reduce silicon resonator TCF to a few ppm/°C. Traditional methods using a layer of positive-TCF silicon dioxide to counteract the negative silicon TCF [3] are effective but require additional process steps and are limited to thin silicon substrates. It has been demonstrated that bulk compensation rather than surface compensation, which exploits uniformly distributed silicon Manuscript received July 28, 2013; revised October 19, 2013; accepted December 5, 2013. Date of current version January 20, 2014. This work was supported by Integrated Device Technology, Inc. The review of this paper was arranged by Editor A. M. Ionescu. J. L. Fu was with the Georgia Institute of Technology, Atlanta, GA 30332 USA. She is now with System Planning Corporation, Arlington, VA 22201 USA (e-mail: [email protected]). R. Tabrizian and F. Ayazi are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2013.2295613
dioxide pillars in thick silicon completely eliminates the first-order TCF of high-Q bulk acoustic resonators, resulting in 90–180 ppm frequency drift over the entire industrial temperature range of −40 °C–85 °C [4], [5]. However, device- and circuit-level tuning are inevitable to achieve subppm instability levels required for temperature-compensated and/or oven-controlled crystal oscillator applications [6]. Such dynamic tuning should continuously monitor device operating temperature to apply the necessary frequency pulling in the tolerance range. Therefore, oscillator stability is mainly, although indirectly, defined by precision of the temperature sensing procedure. Accurate temperature measurement requires the sensor and temperature-sensitive frequency reference to be in very close proximity, thereby minimizing discrepancies caused by thermal gradients. Since oscillator frequency is measurable with high accuracy, the temperature-sensitive resonating element is an outstanding candidate to be used as a self-thermometer. Although the finite TCF of a single resonance mode can be used to track temperature, measuring a linear combination of two modes with different TCF values in a single device provides greater sensitivity. Therefore, dual-mode (DM) excitation, which has been widely employed in quartz resonators to simultaneously monitor stress, mass, pressure, and temperature [7]–[9], is of particular interest for measurement and compensation of temperature-induced oscillator frequency shift. DM excitation provides local temperature measurement without external thermometers, which significantly reduces system footprint when integrated with CMOS electronics. In this paper, DM AlN-on-Si resonator designs based on alternatives to fundamental and harmonic modes are investigated. II. DM T EMPERATURE M EASUREMENT A. Principle of Operation DM temperature sensing requires simultaneous excitation of two modes in a single resonator, which causes both modes to experience identical changes in ambient temperature [10]. The unique frequency-temperature characteristics of each mode can be used to compensate reference frequency over temperature. Beat frequency fb is defined as a linear combination of f 1 and f 2 fb = α · f 1 − f2 . (1) Multiplicative constant α is an integer when f 2 is an α-order harmonic of f 1 [10]. If the modes are close in frequency,
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Careful design of resonators with proper phase, low Rm , and high Q ensures successful DM oscillator interfacing. III. AlN- ON -Si DM R ESONATORS
Fig. 1. (a) Single-loop Colpitts oscillator with one-port resonator. (b) Dualloop DM oscillator with two-port MEMS resonator in feedback with TIAs followed by mixing, multiplication, and filtering to generate output frequency fb .
f 1 and f2 are directly mixed to generate f b , thus obviating the need for integer/fractional frequency multipliers [11]. The relative change in resonance frequency f 0 with respect to temperature, or TC f 0 , can be expressed as TCn f 0 =
1 ∂ n f0 . f0 ∂ T n
(2)
Silicon has a dominant first-order temperature coefficient, TC1 F (denoted as TCF in this paper). Based on (1) and (2), DM temperature sensitivity is defined as TC f b =
α · f 1 · TC f 1 − f 2 · TC f 2 fb
(3)
suggesting that beat frequency reduction is one method to improve temperature sensitivity. The linear TCF of silicon ensures that TC f b would also be a strongly linear function of temperature.
Self-temperature sensing techniques have been previously demonstrated within dual-resonator [14] as well as singleresonator [15] configurations. However, both implementations utilized capacitive resonators, whose high motional resistance introduces difficulties in oscillator implementation. The required dc polarization voltage (V p ) further increases power consumption and may contribute to undesired measurement inaccuracies via temperature-induced V p variations On the other hand, piezoelectric actuation enables multiplemode excitation in a single device without dc voltages. Thin film piezoelectric-on-substrate (TPoS) technology combines the advantages of piezoelectric transduction with a low-loss material such as silicon, which exhibits high-Q and enhanced power handling over piezoelectric-only resonators [16]. A. Resonance Modes for DM Operation When f b approaches a minimum (α · f 1 ∼ = f2 ), (3) can be approximated as f2 TC f 1 − TC f 2 . (4) TC f b ∼ = fb Based on frequency ratio f2 / f b , a large f 2 combined with small fb provides enhanced DM temperature sensitivity, which can be realized by exploiting high-frequency in-plane bulk modes of AlN-on-Si resonators with lithographically defined frequencies. Geometrical engineering can be used to bring together two linearly independent resonance modes to increase TC f b . Further TC fb improvements are achievable by maximizing TCF (TC f 1 − TC f 2 ), which in TPoS resonators is primarily determined by temperature coefficients of independent elastic constants (TCc11 , TCc12 , and TCc44 ) and their contributions to the selected modes [17].
B. DM Oscillator Considerations Real-time measurement and compensation requires circuitry to drive and sustain oscillations across a wide temperature range. Various architectures have been used to implement quartz DM oscillators, which can be categorized as either single-loop or dual-loop configuration [11], [12]. Single-loop (Colpitts) oscillators [Fig. 1(a)] require fewer components than a dual-loop oscillator and can exploit transistor nonlinearities to inherently provide f b as an output [11], [12]. Dual-loop DM oscillators [Fig. 1(b)] can be implemented if separate gain and phase control are required. The Barkhausen stability criterion, which states that a circuit will sustain oscillations under certain loop gain and phase conditions, must be satisfied at both frequencies in a DM oscillator. Unity loop gain is achieved by ensuring that the transimpedance amplifier (TIA) provides sufficient gain to compensate resonator electrical losses. Phase conditions are met if the combined TIA and resonator phase results in zero loop phase shift. In addition to resonator phase and motional resistance Rm , Q of both modes directly affects oscillator phase noise and consequently, temperature measurement linearity [13].
B. Limitations of Fundamental and Higher Order Harmonics for DM Operation DM quartz thermometers based on first- and third-harmonic C-modes have demonstrated fb values in the 150-kHz range ( f b = 3 · f 1 − f 3 ) [10], [11]. In previous DM demonstrations, TPoS resonators employed first and third width-extensional (WE/WE3) modes [13], [18], which tend to suffer from larger f b . A major factor causing WE/WE3 DM resonators to deviate from the ideal situation (α = 3) is their finite support size, which does not scale similarly for the two modes, creating nonuniformities in the f1 strain pattern and shifting the frequency from the nominal value. However, finite element simulations show that even with zero support size, f b reaches a lower limit for the given dimensions (Fig. 2). This can be attributed to the finite thickness and length of the resonator, resulting in deviation of WE harmonics from their bulk acoustic plane wave counterparts. Since width W determines frequency, the only variable dimension is length L, which also provides minimal fb reduction as measured in fabricated resonators (Fig. 3). Therefore, benefits of using
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Fig. 4.
ANSYS mode shapes of WS and WE modes for DM operation.
Fig. 2. Left: strain distribution for DM AlN-on-Si resonator based on WE/WE3 modes. Right: simulated f b versus support width for a 27-MHz resonator (W = 156 μm).
Fig. 5. Simulated frequency of WS and WE modes versus L for W = 156 μm, corresponding to f WE = 27 MHz.
Fig. 3.
Measured f b versus length L for AlN-on-Si WE/WE3 resonator.
high-frequency mode f 3 are negated by the inability to minimize f b in WE/WE3 resonators. Furthermore, since f 1 and f3 have the same elastic dependences, small TCF is also expected. For the devices measured in Fig. 3, TCF = –0.5 ppm/°C yields TC fb ∼ −37 ppm/°C, which provides virtually no improvement over single-mode measurement. Since extensional modes in TPoS resonators possess similar temperature-frequency behavior and large fb , alternative modes for TC f b enhancement are investigated. IV. TC fb E NHANCEMENT BY B EAT F REQUENCY R EDUCTION A. In-Plane WE and WS Modes The WE mode can be attributed to the longitudinal quasiplane wave propagating in width direction and reflecting back from stress-free boundaries. Therefore, its frequency is nearly independent of resonator length (L) and is defined by v (5) f WE = 2W where v is the effective longitudinal wave velocity. On the other hand, the width-shear (WS) mode (Fig. 4) exhibits a significant dependence on L, which can be explained by considering the 180° phase difference between particle polarizations at two boundaries along the resonator length direction. This suggests the WS mode is a standing wave formed by the interaction of Lamb waves propagating in length direction and
reflecting back from stress-free boundaries. Considering the dependence of Lamb wave velocity on resonator width, the WS mode frequency can occur in close proximity of the WE mode. Therefore, the f WS dependence on both W and L can be exploited to define specific f b values by controlling the distance between WS and WE modes ( f b = f WS − f WE ) (Fig. 5). Utilizing WS and WE modes for DM operation provides inherently small f b by directly mixing two frequencies rather than utilizing fractional multiplication to obtain a desired f b [12], thus introducing additional complexity and noise to the system. L/W = 1.31 corresponds to the case when f WS = fWE , or zero f b . Because f b is determined by ratios rather than absolute dimensions, DM excitation using WS and WE modes is less sensitive to lithography and process variations. Furthermore, the WS/WE resonator electrode configuration provides a 180° phase shift between modes when operated in two-port configuration [19], thus effectively isolating one mode from the other in a dual-loop oscillator. TCci j (1 ≤ i j ∈ N ≤ 4) values from [17] for single crystal silicon and [20] for aluminum nitride elastic properties were used to accurately model the TPoS resonator in ANSYS static structural simulations with varying temperature loads. Subsequent modal analyses performed on the resonator were prestressed with static structural results to predict f WS and f WE over temperature (TC f WS = −31.1 ppm/°C and TC f WE = −32.5 ppm/°C). WS/WE resonators with f WE = 27 MHz were designed by the methodology described, with f b ranging from 17 kHz to 1.5 MHz. Resonators were fabricated on a 20-μm-thick SOI substrate using a process similar to [21] and characterized in an ESPEC temperature chamber. The measured
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Fig. 6. Measured versus simulated f b for WS/WE resonator designs with W = 156 μm, various L values ( f b = f WS − f WE ); (inset) SEM image of WS/WE resonator (W = 156 μm, L = 204 μm).
Fig. 9. WS/WE resonator terminal configurations for DM oscillator interfacing. (a) Two-port operation. (b) Single-port operation. TABLE I W IDTH -S HEAR /W IDTH -E XTENSIONAL D UAL -M ODE R ESONATORS
Fig. 7. Extracted TC f b of WS/WE DM resonator with f b = 17 kHz; measured TC f WS = −30.1 ppm/°C, TC f WE = −31.1 ppm/°C.
B. WS/WE Mode Oscillator Interfacing
Fig. 8. Measured response of DM resonators with | f b | = 1.5 MHz and 134 kHz (| f b | = | f WS − f WE |), showing Q WE degradation when f WS and f WE converge.
frequency response of several devices, obtained with an Agilent E8364B network analyzer, agreed well with simulated f b values (Fig. 6, Table 1). The slightly lower measured TC f WS and TC f WE values (–30.1 and –31.1 ppm/°C) can be attributed to variation in doping concentration (simulations assumed boron-doped silicon with 4 cm resistivity; fabricated device resistivity ranged from 1 to 20 -cm). The highest extracted TC f b was 1480 ppm/°C for a device with f b = 17 kHz (Fig. 7), nearly 50× larger than single-mode measurement of TC fWS or TC f WE .
Acoustic coupling between modes as a result of nonlinear effects [22] can cause significant Q WE degradation when WS and WE modes converge (Fig. 8). Since Q affects frequency stability through oscillator phase noise, interference between modes must be minimized for simultaneous operation. Devices with smaller f b may benefit from one-port excitation using two single-loop oscillators, which effectively isolates one mode from the other [Fig. 9(b)]. However, transduction isolation for f b constituent modes could also be achieved using a multiport configuration with common input and separate output electrodes [23] [rather than the two-port layout shown in Fig. 9(a)]. V. E FFECT OF O RIENTATION ON WS/WE R ESONATOR TCF AlN-on-Si WS/WE resonators provide substantial f b reduction as well as a 2× larger TCF than the WE/WE3 configuration. However, further TCF enhancement would contribute to increased sensitivity as well as relaxed f b requirements, thus reducing mechanical destructive interference of the two modes.
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Fig. 10. Measured TC f WS and TC f WE for [100]-aligned WS/WE resonator, exhibiting 2× larger TCF than [110]-aligned devices. Fig. 11. Measured response of [100]-oriented WS/WE resonator with f b = 120 kHz (W = 156 μm, L = 268 μm).
The dissimilar temperature characteristic of silicon elastic constants ci j , combined with their contribution to the acoustic wave velocity in different directions, results in different TCF for similar modes when the device is aligned in another crystallographic orientation. While WE-mode resonators on (100) substrates have exploited the [100] direction for nearly full compensation of TC f WE [24], devices in this paper are reoriented to increase the WS/WE resonator TCF beyond 1 ppm/°C. WS/WE resonators aligned to the [100] direction had a simulated TC f WS = −30.6 ppm/°C and TC fWE = −32.7 ppm/°C (TCF = 2.1 ppm/°C). Devices were designed by a similar methodology to [110]-aligned devices, yielding a matched f b ratio L/W of 1.71. In the [100] direction, W = 156 μm corresponds to f WE = 25 MHz (E [100] < E [110] ). Fabricated devices had a measured TCF = 1.9 (Fig. 10), nearly 2× greater than [110] devices and 4× greater than WE/WE3 resonators. TCF can be further increased using substrates with higher doping levels, which would exhibit a larger difference between E [100] and E [110] . Because f WS is easily driven into nonlinear operation [19], f WE is more likely to be used as a reference and requires lower Rm , which is achieved through increased electrode area by the required L/W ratio (Fig. 11). VI. DM E XCITATION FOR T EMPERATURE -S TABLE B EAT F REQUENCY While DM WS/WE mode resonators are applicable to highsensitivity on-chip thermometry, they can also be employed as temperature-stable references, which are required for counter circuits that would be ultimately used to measure resonance frequency change with temperature. Equating the right-hand side of (3) to zero provides the requirements for temperature-insensitive f b in DM resonators f 2 = α · f1
TC f 1 . TC f 2
(6)
Although α · f 1 and f 2 have nonzero TCF, f b (generated by mixing the two signals) will remain constant over temperature. For a DM resonator with known values of TC f 1 and TC f 2 , α · f 1 and f 2 must be designed to satisfy conditions in (6).
Fig. 12. Measured response for f WS and f WE of [100]-aligned device with temperature-insensitive f b = 1.5 MHz (W = 156 μm, L = 242 μm).
For temperature-insensitive DM resonators, f 2 /α · f1 (rather than f2 / f b ) determines the behavior. Because f WS can be tailored to a specific ratio of f W E , WS/WE resonators (α = 1) can provide f b that is either temperature-sensitive or temperature-insensitive. A [100]-aligned WS/WE resonator with TC f WS = −29.6 ppm/°C and TC f WE = −31.5 ppm/°C was designed to fulfill the aforementioned conditions ( f WS = 26.8 MHz, f WE = 25.3 MHz), fabricated, and characterized over
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Fig. 13. Extracted TC f b of [100]-aligned WS/WE DM resonator with nearly temperature-stable f b .
temperature (Fig. 12). The extracted first-order TC1 f b of 2.4 ppm/°C and second-order TC2 f b of 3.3 ppb/°C2 correspond to a frequency drift of 266 ppm from –20 °C to 100 °C (Fig. 13), which is lower than degenerately doped resonators [25] or geometrically engineered capacitive resonators [26]. VII. C ONCLUSION In this paper, DM AlN-on-Si resonators were optimized for enhanced TC f b by overcoming previous DM implementation challenges. WS and WE mode resonators provided 50× greater TC f b compared with single-mode measurement. Oscillator configurations to address mechanical coupling concerns were suggested. The versatility of WS/WE resonators was further demonstrated through [100]-oriented resonators, which exhibited 4× larger TCF than previous WE/WE3 resonators and also demonstrated the capability to provide temperature-insensitive f b without heavy doping or structural modifications. The flexible design attributes enable WS/WE resonators to operate as either a temperature sensor or reference, depending on application requirements. ACKNOWLEDGMENT The authors would like to thank the Georgia Tech Institute for Electronics and Nanotechnology cleanroom staff for fabrication support and the OEM Group, Inc., for AlN deposition. R EFERENCES [1] A. K. Samarao, G. Casinovi, and F. Ayazi, “Passive TCF compensation in high Q silicon micromechanical resonators,” in Proc. IEEE 23rd Int. Conf. Microelectromech. Syst., Hong Kong, Jan. 2010, pp. 116–119. [2] A. K. Samarao and F. Ayazi, “Temperature compensation of silicon resonators via degenerate doping,” IEEE Trans. Electron Devices, vol. 59, no. 1, pp. 87–93, Jan. 2012. [3] K. Lakin, K. McCarron, and J. McDonald, “Temperature compensated bulk acoustic thin film resonators,” in Proc. IEEE Ultrason. Symp., Oct. 2000, pp. 855–858. [4] R. Tabrizian, G. Casinovi, and F. Ayazi, “Temperature-stable high-Q AlN-on-silicon resonators with embedded array of oxide pillars,” in Proc. Solid-State Sensors, Actuat., Microsyst. Workshop, Hilton Head, SC, USA, Jun. 2010, pp. 100–101.
[5] R. Tabrizian, G. Casinovi, and F. Ayazi, “Temperature-stable silicon oxide (SilOx) micromechanical resonators,” IEEE Trans. Electron Devices, vol. 60, no. 8, pp. 2656–2663, Aug. 2013. [6] R. Tabrizian, M. Pardo, and F. Ayazi, “A 27 MHz temperature compensated MEMS oscillators with sub-ppm instability,” in Proc. IEEE 25th Int. Conf. MEMS, Jan./Feb. 2012, pp. 23–26. [7] J. A. Kusters, M. C. Fischer, and J. G. Leach, “Dual mode operation of temperature and stress compensated crystals,” in Proc. 32nd Annu. Symp. Freq. Control, 1978, pp. 389–397. [8] B. K. Sinha, “Stress compensated orientations for thickness-shear quartz resonators,” in Proc. 35th Annu. Freq. Control Symp., 1981, pp. 213–221. [9] R. Besson, J. Boy, B. Glotin, Y. Jinzaki, B. Sinha, and M. Valdois, “A dual-mode thickness-shear quartz pressure sensor,” IEEE Trans. Ultrason. Ferroelect. Freq. Control, vol. 40, no. 5, pp. 584–591, Sep. 1993. [10] D. E. Pierce, Y. Kim, and J. R. Vig, “A temperature insensitive quartz microbalance,” IEEE Trans. Ultrason. Ferroelect. Freq. Control, vol. 45, no. 5, pp. 1238–1245, Sep. 1998. [11] A. V. Kosykh, I. V. Abramson, and R. P. Bagaev, “Dual-mode crystal oscillators with resonators excited on B and C modes,” in Proc. IEEE Int. Freq. Control Symp., Jun. 1994, pp. 578–586. [12] S. S. Schodowski, “Resonator self-temperature-sensing using a dualharmonic-mode crystal oscillator,” in Proc. 43rd Annu. Symp. Freq. Control, 1989, pp. 2–7. [13] M. J. Dalal, J. L. Fu, and F. Ayazi, “Simultaneous dual-mode excitation of piezo-on-silicon micromechanical oscillator for selftemperature sensing,” in Proc. IEEE 24th Int. Conf. MEMS, Jan. 2011, pp. 489–492. [14] C. Jha, G. Bahl, R. Melamud, S. Chandorkar, M. Hopcroft, B. Kim, et al., “CMOS-compatible dual-resonator MEMS temperature sensor with milli-degree accuracy,” in Proc. Int. Solid-State Sensors, Actuat. Microsyst. Conf., Jun. 2007, pp. 10–14. [15] M. Koskenvuori, V. Kaajakari, T. Mattila, and I. Tittonen, “Temperature measurement and compensation based on two vibrating modes of a bulk acoustic mode microresonator,” in Proc. IEEE 21st Int. Conf. MEMS, Jan. 2008, pp. 78–81. [16] R. Abdolvand and F. Ayazi, “7E-4 enhanced power handling and quality factor in thin-film piezoelectric-on-substrate resonators,” in Proc. IEEE Ultrason. Symp., Oct. 2007, pp. 608–611. [17] C. Bourgeois, E. Steinsland, N. Blanc, and N. F. de Rooij, “Design of resonators for the determination of the temperature coefficients of elastic constants of monocrystalline silicon,” in Proc. IEEE Int. Freq. Control Symp., May 1997, pp. 791–799. [18] R. Abdolvand, H. Mirilavasani, and F. Ayazi, “Single-resonator dualfrequency thin-film piezoelectric-on-substrate oscillator,” in Proc. IEEE IEDM, Dec. 2007, pp. 419–422. [19] M. Pardo, L. Sorenson, and F. Ayazi, “An empirical phase-noise model for MEMS oscillators operating in nonlinear regime,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 5, pp. 979–988, May 2012. [20] K. Tsubouchi and N. Mikoshiba, “Zero-temperature-coefficient SAW devices on AlN epitaxial films,” IEEE Trans. Sonics Ultrason., vol. 32, no. 5, pp. 634–644, Sep. 1985. [21] W. Pan and F. Ayazi, “Thin-film piezoelectric-on-substrate resonators with Q enhancement and TCF reduction,” in Proc. IEEE 23rd Int. Conf. MEMS, Jan. 2010, pp. 727–730. [22] J. P. Valentin, C. P. Guerin, and R. J. Besson, “Indirect amplitude frequency effect in resonators working on two frequencies,” in Proc. 35th Annu. Freq. Control Symp., 1981, pp. 122–129. [23] R. Tabrizian and F. Ayazi, “Acoustically-engineered multi-port AlN-on-silicon resonators for accurate temperature sensing,” in Proc. IEEE IEDM, Washington, DC, USA, 2013, pp. 1811–1814, Dec. 2013. [24] H. J. McSkimin, “Measurement of elastic constants at low temperatures by means of ultrasonic waves–data for silicon and germanium single crystals, and for fused silica,” J. Appl. Phys., vol. 24, pp. 988–997, Aug. 1953. [25] T. Pensala, A. Jaakkola, M. Prunnila, and J. Dekker, “Temperature compensation of silicon MEMS resonators by heavy doping,” in Proc. IEEE IUS, Oct. 2011, pp. 1952–1955. [26] A. K. Samarao, G. Casinovi, and F. Ayazi, “Passive TCF compensation in high Q silicon micromechanical resonators,” in Proc. IEEE 23rd Int. Conf. MEMS, Hong Kong, Jan. 2010, pp. 116–119.
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Jenna L. Fu (S’03–M’13) received the B.S. degree in electrical and computer engineering from Carnegie Mellon University, Pittsburgh, in 2006, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2008 and 2013, respectively. Since July 2013, she has been a research scientist with System Planning Corporation in Arlington, Virginia, USA.
Roozbeh Tabrizian (S’06) received the B.S. degree in electrical engineering from Sharif University of Technology, Tehran, Iran, in 2007, and the Ph.D. degree in electrical and computer engineering from the Georgia Institute of Technology, Atlanta, in 2013. His research interests include design, fabrication and characterization of piezoelectricallytransduced micromechanical resonators for timing, signal processing and sensing applications.
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Farrokh Ayazi (S’96–M’00–SM’05–F’13) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. In December 1999, he joined the faculty of Georgia Institute of Technology, Atlanta, where he is currently a Professor in the School of Electrical and Computer Engineering.
