Available online at www.sciencedirect.com
Procedia Engineering 47 (2012) 949 – 952
Proc. Eurosensors XXVI, September 9-12, 2012, Kraków, Poland
Frequency Tuning in a MEMS Resonator via an Integral Crossbar Heater Weiguan Zhanga*, Joshua E.-Y. Leeaa a
Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Abstract This paper investigates the frequency tuning effects in a MEMS resonator that employs a simple crossbar heater integral to the devices as opposed to more complex serpentine heater designs. We report tuning of up to 1.1% from an unturned frequency of 39.2 kHz with 50mW power. By utilizing comb drives instead of parallel plate transducers, frequency tuning is controlled solely using joule heating through the crossbar while electrostatic spring tuning is negligible in comparison. The frequency shifts follow a power square law at lower currents but shown to deviate towards a higher order characteristic when the power exceeds 33mW. © 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Symposium Cracoviense © 2012 Published by Elsevier Ltd. Sp. z.o.o. Open access under CC BY-NC-ND license. Keywords: MEMS resonator; frequency tuning; integral crossbar heater
1. Introduction MEMS resonators are widely used in various vibratory microsystems as an integral unit, including MEMS oscillators [1] and sensors [2]. These have the advantage of small size and a high quality factor that leads to better performance. However, fabrication tolerances cannot be avoided, which inevitably lead to infinitesimal differences between the resonant frequencies of the devices after fabrication relative to the designed value. In addition, given the non-zero temperature coefficient of modulus of silicon, frequency drift due to the temperature sensitivity of the device also is another important issue that needs to be addressed. As such, post-fabrication active frequency tuning, preferably by an electrical stimulus is highly desired especially for precision timing-control applications. In this paper, we propose a comb-shaped
* Corresponding author. Tel.: +852-3442-2107; fax: +852-3442-0562. E-mail address:
[email protected].
1877-7058 © 2012 The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Symposium Cracoviense Sp. z.o.o. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.09.303
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resonator with a simple crossbar heater capable of achieving a tuning effect of up to 1.1% tuning from the central frequency. 2. Device Design In contrast to previous work which employs more complex integrated serpentine heater designs [3], we here investigate the effectiveness on active frequency tuning afforded by a simple crossbar heater as illustrated in the schematic shown in Fig 1(a). With reference to Fig 1(a), the center part of the device with the comb-finger structure is the main resonating body. As shown in this schematic, the crossbar bounds the two clamped ends of the flexural mode resonator, which is driven to resonate in the plane of fabrication as described by the finite element (FE) eigenmode simulation shown in Fig 1(b). By injecting a DC current through the crossbar, heat is generated and distributed to the resonator thus changing its temperature. Since silicon has a negative temperature coefficient of modulus, increasing the temperature of the resonator results in material softening and thus a decrease in resonant frequency. This dependence of resonant frequency on temperature is commonly described as linear, as reported in [4] (whereby higher order terms in the temperature characteristic are neglected). In addition, temperature drift in the flexural beams will also have effect on the frequency shift due to thermal stresses arising from thermal mismatch between the layers. In the specific case of our design, the flexural beams are clamped by the crossbar which is released from the underlying substrate. As such, stresses arising from any thermal mismatch between the layers will be negligible in comparison to the temperature sensitivity of the Young’s modulus. Hence, it is reasonable to assume in our case that the frequency shift observed is mainly due to change of Young’s modulus resulting from the joule heating.
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Fig. 1. (a) Schematic of MEMS resonator with integral crossbar heaters including biasing configuration used; (b) FE eigenmode simulation in COMSOL
Weiguan Zhang and Joshua E.-Y. Lee / Procedia Engineering 47 (2012) 949 – 952
3. Measurement Result The resonator with an integral crossbar was fabricated in a foundry SOI MEMS process. Fig. 2 shows an optical micrograph of the fabricated device. After being packaged in a 28-pin DIL chip carrier and mounted on a PCB, the fabricated device was measured in a custom-built vacuum chamber for electrical characterization by following the biasing configuration illustrated in Fig 1(a). Fig. 3 (a) shows the measured electrical transmission of the resonator as the applied current through the crossbar is increased from 0mA to 5mA. To observe the relationship between resonant frequency and the applied current through the crossbar, the fraction frequency shift (in %, normalized against the resonant frequency measured at 0mA) was plotted against the current as shown in Fig. 3(b). Fig.3 (b) shows that the relationship follows polynomial curve fit that is primarily quadratic, thus indicating that the frequency shift follows a power square law with the current. This characteristic is consistent with the hypothesis and analysis in the previous section that the shifts are mainly due to joule heating.
Fig. 2. Optical micrograph of fabricated device
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Fig. 3. (a) Measured electrical transmission at different currents (de-embedded to remove feedthrough) (b) Fractional frequency shift tracked with increasing current (0mA ~ 5mA)
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Fig.4 (a) further confirms the hypothesis by showing a strong linear relationship between frequency shift and applied power, obtained by the using the product of the sourced current and measured voltage. By increasing the current further to 7mA (~ 54mW), a maximum frequency shift of about 1.1% can be obtained. The frequency shift characteristic also deviates from the initial linear behavior towards a higher order relationship as shown in Fig.4 (b). The nonlinear effect at higher tuning power is possibly due to a non-uniform of thermal distribution.
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Fig. 4. (a) Fractional frequency shift (%) tracked with increasing input power (0mW ~ 22mW) (b) Fractional frequency shift with higher input power (0mW ~ 54mW)
4. Conclusion A comb-drive MEMS resonator with an integral crossbar heater has been designed and fabricated. The reported device has a much simpler resistive heater layout compared to more common serpentine designs. We show here that despite its simple design, frequency tuning of up to 1.1% could be achieved using 50mW of power applied to the resistive heaters. A strongly linear relation between fractional frequency shift and input power (smaller than 33mW) suggests that the major tuning effect is due to the temperature sensitivity of its Young’s modulus as joule heating is applied. Acknowledgements The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU8/CRF/09). References [1] Lee JEY, Bahreyni B, Zhu Y, Seshia AA. A signle-crystal-silicon bulk-acoustic-mode microresonator oscillator. IEEE Electron Device Letters, 2008; 29:701–3. [2] Bahreyni B, Wijeweera G, Shafai C, Rajapakse A. Analysis and design of a micromachined electri-field sensor. J.Microelectromech. Syst, 2008; 17:31–6. [3] Salvia J, Melamud R, Chandorkar S, Lord S, Kenny T. Real-time temperature compensation of MEMS oscillators using an integrated micro-oven and a phase-locked loop. J. Microelectromech. Syst, 2010; 19:192–201. [4] Schoen F, Nawaz M, Bever T, Gruenberger R, Raberg W, Weber W, Winkler B, Weigel R. Temperature compensation in silicon-based microelectromechanical resonators. Proc. IEEE MEMS 2009, p. 884–7; 2009.
