W3P.125
THE EFFECTS OF TIGHT CAPACITIVE COUPLING ON PHASE NOISE PERFORMANCE: A LAMÉ-MODE MEMS OSCILLATOR STUDY Haoshen Zhu3, Chieh-Hsu Chuang2, Cheng-Syun Li1, Ming-Huang Li1, Joshua E.-Y. Lee3,4, and Sheng-Shian Li1,2* 1 Inst. of NanoEngineering and MicroSystems, National Tsing Hua University, Hsinchu, TAIWAN 2 Dept. of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, TAIWAN 3 Dept. of Electronic Engineering, City University of Hong Kong, HONG KONG 4 State Key Laboratory of Millimeter Waves, City University of Hong Kong, HONG KONG ABSTRACT In this work, we realize low-polarization-voltage (VP) capacitive MEMS oscillators implementing vacuum packaged 50nm-gap Lamé-mode silicon micromechanical resonators and investigate their phase noise (PN) performance. Two different oscillator configurations are studied; these are here referred to as differential-in-differential-out (DIDO) and single-in-differential-out (SIDO). Clear disparities in their respective PN profiles could be observed. The DIDO outperforms the SIDO with an improved close-to-carrier PN by more than 25dB. This 17.6MHz oscillator achieves a PN of -127dBc/Hz at 1kHz offset and -132dBc/Hz far-from-carrier PN performance, which is competitive with state-of-the-art capacitive MEMS oscillators but with lowest VP in this work. The measured PN is found to be dependent on VP for our oscillators, which is probably due to the nonlinear effects augmented by the tight electromechanical coupling.
also been observed that the close-to-carrier PN deteriorates as the gap shrinks [9]. Thus understanding the possible limits of the capacitive gap on PN is crucial to engineer high performance MEMS reference oscillators. In this work, Lamé-mode microresonator-based oscillators with strong electromechanical coupling (owing to their 50-nm narrow gap capacitive transducers) are studied. We implement two versions of Lamé-mode oscillators by using two different circuit configurations and then investigate their PN performance at various VP levels. The results indicate that both configurations and drive conditions impose significant influence on the
KEYWORDS Micro-Electro-Mechanical Systems (MEMS), Phase Noise (PN), Resonator, Oscillator, Lamé mode
INTRODUCTION Recently silicon-based MEMS oscillators have begun to be a competitive alternative to the conventional quartz crystal in the quartz-dominated timing market. The newly reported MEMS products show critical features such as phase noise and frequency stability that are comparable to typical temperature compensated crystal oscillators (TCXO) [1]. Fabricated with CMOS compatible processes, these devices fulfill the goal of higher system integration with smaller form factors and higher flexibility as modern telecommunication markets expand, attracting tremendous research interests from both academia and industry [2]. Among MEMS oscillators that have been developed to date, capacitively-transduced bulk-mode microresonators [3] remain favorable for achieving high quality factor (Q), which according to Leeson’s model [4] improves the close-to-carrier PN performance of the MEMS oscillators. However, capacitive transduction generally suffers from poor electromechanical coupling efficiency; hence narrow transduction gap is normally preferable to reduce motional impedance. Various oscillators with sub-µm transduction gap (ranging from ×10~×100nm) have been demonstrated [5]-[7]. Theoretically, the nonlinear capacitive transducer couples undesired noise (like flicker noise) into the near carrier spectrum in capacitive-type MEMS oscillators [8]. It has
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Figure 1: (a) PCB implementation of the oscillator; (b) encapsulated devices packaged and wire-bonded to a DIL ceramic chip carrier; (c) SEM of an uncapped structure; (d) revealed narrow gap view after using a focused ion beam cut through the wafer-level encapsulated die.
Figure 2: Circuit schematics of the two Lamé-mode MEMS oscillator configurations: (a) single-in-differential-out (SIDO); (b) differential-in-differential-out (DIDO).
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Figure 3: Frequency response of the 50-nm gap resonator vibrating in a Lamé mode; the dashed line indicates the critical magnitude response at a higher RF power. close-to-carrier PN and should thus be fully considered in MEMS oscillator design.
RESONATOR CHARACTERIZATION AND OSCILLATOR CONFIGURATION Single-crystal-silicon square-plate microresonators were fabricated by a foundry-oriented SOI-MEMS plus a poly-Si refill process (process flow is detailed in [10]). The device was aligned against the crystal axis and perforated with uniformly distributed etch holes (2μm × 2μm) for the front-side HF release, as illustrated in the scanning electron micrograph (SEM) (Figure 1c). The 50-nm transducer gaps were realized by removing the sacrificial oxide layer between the poly-Si electrode and the resonator body. A cross-section view of the capacitive transducer is shown in Figure 1d and the formed narrow gap is clearly observed. The devices were hermetically encapsulated (measured vacuum level: ~1mTorr) at wafer-level using a eutectic bonding technique, which reduces air damping and enables high Q. The capped resonators were wired bonded to ceramic chip carriers (Figure 1b) and then combined with off-the-shelf electronics on printed circuit boards (PCBs) (Figure 1a) to sustain oscillation. The schematics of two different configurations of Lamé-mode oscillators, namely single-in-differential-out (SIDO) and differential-in-differential-out (DIDO), are illustrated in Figure 2a and 2b, respectively. The sustaining circuitries are built using off-the-shelf ICs and comprised of two stages. The first stage comprises a fixed gain transimpedance amplifier (TIA) while the voltage gaincontrollable amplifiers (VGA) form the second stage. To study the nonlinear effects on the PN performance as the device is driven beyond the mechanical critical bifurcation points, the Lamé-mode oscillators were designed to be self-limiting while amplifiers with clamped differential outputs were selected in the second stage [11]. The gain of the second stage was set to 2 in both configurations for fair comparison. For SIDO, we performed differential drive using inverted VP to reduce the parasitic feedthrough. The encapsulated device was first characterized in a probe station using a 4-port network analyzer (Agilent E5071C) at room temperature. The measured transmission
Sdd21 (i.e., fully-differential) is shown in Figure 3. The measured resonance at 17.62MHz matches the finite element (FE) simulation (~17.756MHz) of the etch-hole filled Lamé-mode resonator via COMSOL. The simulated vibration mode shape is illustrated in Figure 2 where the solid outline represents the nominal shape of the resonator. The extracted Q is around 20,000 indicating a successful vacuum package while the motional impedance (Rm) is around 6.7kΩ (VP = 3V) showing enhanced transduction via the 50-nm gaps. Prominent spring-softening Duffing behavior is detected as we increase the injected RF power. For this device, the critical RF power before the hysteresis occurs at the 3V VP is found to be ~-5dBm (refer to Figure 3). The open-loop measurements were also conducted by breaking the sustaining loop at the differential drive ports. Figure 4 depicts the measured frequency responses of the microresonator including the amplifiers after feedthrough de-embedding. It is clear that as the signal is magnified by the on-board circuitries, the transmission is elevated by over 40dB and approaches 0dB, thus meeting the unity loop-gain requirement. It is noted that the required VP to achieve the 0dB transmission peak is somewhat different (marked red in Figure 4) for the two configurations. Although the designed overall transimpedance gain equates to 20kΩ for both versions, it seems the phase mismatch of the two TIAs in the DIDO configuration lowers the total gain as they are cascaded to the differential input of the second stage, and the higher VP is needed. Therefore, a fully-differential TIA is preferred instead of two discrete TIAs. The insets in Figure 4 show the directly measured Sdd21 magnitude responses, which
Figure 4: The de-embedded open-loop measurements of the oscillator: (a) SIDO; (b) DIDO configuration. Insets: measured raw magnitude responses before de-embedding.
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from mechanical nonlinearity will be magnified, which in turn generates unwanted harmonics. The PN performance for both versions were measured by a signal source analyzer (Agilent E5052B) and plotted in Figure 6. For the SIDO configuration (Figure 6a), a VP as low as 1.8V is sufficient to provide a steady oscillation, which is the lowest value reported to date for capacitive MEMS oscillators. At VP = 1.8V, the calculated motional impedance is about 18.5kΩ, satisfying the Barkhausen criterion as the overall gain of the amplifier equals 20kΩ. As VP increases, the carrier power (CP) rises up and the PN at 1 kHz offset shows a gradual improvement (from -92 to -100dBc/Hz), as predicted by the well-known Leeson’s model [4]. At lower VP (1.8~1.9V), as expected, the near-carrier PN follows the f-3 trend line, due to the flicker noise (1/f noise) aliasing from the capacitive nonlinearity [8]. However, within 100Hz offset, it is interesting to find that the PN deviates from the f-3 trend and the slope becomes steeper (up to f-6 at 2.2V) as VP increases. As previously discussed, the resonator is working beyond its critical vibration point with this large CP. At this stage, it is believed that mechanical nonlinearity (derived from both large deformation and material nonlinearity [13]) may impose extra mixing components and contribute to this strange PN behavior. Beyond this, a comprehensive quantitative explanation is still lacking so far. While keeping a similar noise floor level, the DIDO configuration shows a dramatic improvement in the closeFigure 5: The measured spectra of the fundamental tone (centered at ~17.63 MHz) for the oscillators: (a) SIDO (VP =2.2V, span=10 kHz); (b) DIDO (VP=3.2V, span=1 kHz). Insets: time domain waveforms of the output signals. indicate substantial feedthrough are introduced after wire-bonding (compared to Figure 3). As expected, the DIDO exhibits better feedthrough rejection capability over the SIDO counterpart [11].
MEASURED RESULTS AND DISCUSSION Figure 5 presents the measured Fourier spectra around the fundamental tone using an Agilent spectrum analyzer while the insets show the corresponding time-domain waveform from an oscilloscope. Based on the previous characterization results, the critical RF power values for the specified VP levels (2.2V and 3.2V) are calculated as -2.30dBm and -5.56dBm respectively. Therefore, for the SIDO version, the measured 1.5dBm spectrum power (SP) indicates that the resonator is working beyond the critical bifurcation point. In such circumstances, the nonlinear effects from both capacitive and mechanical origins could play a significant role in the device’s dynamic behavior. A wideband spectrum reveals unusually large higher-order harmonics (listed in Figure 5) in this case, hence reflected by a highly distorted time-domain signal. In contrast, the DIDO oscillator suppresses the 2nd harmonic and keeps a much lower SP (below the critical RF power); the waveform is thus free of distortion. Theoretically, both the capacitive transducer and mechanical nonlinearities contribute to these harmonics. Thus, intuitively, we can conclude that as the device is driven too hard, the effects
Figure 6: The measured PN for the oscillators at various Vp levels: (a) SIDO; (b) DIDO. Each trace represents the corrected results based on 10 measurements.
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Table 1: A brief comparison against the state-of-the-art Lamé-mode resonator-based MEMS oscillators. (Note: the value in parentheses denotes PN normalized to 10MHz) Oscillator [14] This work [15] Configuration Fully Balanced SIDO DIDO Diff. fo [MHz] 10 100 17.6 Resonator Q 22k >200k 20k VP [V] 75 14 3.6 2.1 PN@1kHz -132 -98 -100 -127 [dBc/Hz] (-132) (-118) (-105) (-132) -110 Noise floor -138 -133 -132 (-130) [dBc/Hz] (-138) (-138) (-137) Figure 7: The measured PN for the DIDO oscillator with normalized PN performance and RMS phase jitter. to-carrier PN (Figure 6b), resulting in a 27dB reduction at 1kHz offset with VP = 3.6V. The close-to-carrier PN is also observed to be VP-dependent. As VP rises, the near-carrier PN level (f-3 portion) is also elevated. This agrees with the theory that the flicker noise aliasing is mainly due to capacitive force nonlinearity and its magnitude is proportional to VP2 [8]. Besides, this prominent shift of the f-3 level also further indicates that the flicker noise aliasing magnitude, which is inversely proportional to d4 (d: the gap spacing), is extremely sensitive to VP particularly in the case of narrow gap devices. Since the device remains in operation within a linear regime, the effects of mechanical nonlinearity are minor and no peculiar PN slope-rising behavior was detected in this case. Contrary to the case of SIDO, it was found that the PN at 1kHz offset degrades drastically at higher VP, which suggests that improvement in close-to-carrier PN over higher CP can be overshadowed by augmented flicker noise aliasing. As shown in Figure 7, the down-converted PN is now able to satisfy the GSM PN specification at 1kHz offset (-130dBc/Hz). But the noise floor remains higher than the required level, which leads to an RMS phase jitter (~7ps) that is an order larger than cutting-edge MEMS oscillators [1]. This relatively higher noise floor may be limited by the noisy buffer amplifier [13], and should be fully studied for further PN improvement. A comparison between our work and previous implementations of MEMS oscillators is summarized in Table 1. Our DIDO device maintains a competitive PN performance but requires the lowest VP. Q can be feasibly to further enhance the close-to-carrier PN level by using an etch-hole-free structure [16].
CONCLUSIONS The PN performance of two versions of self-limiting Lamé-mode MEMS oscillators is reported in this work. According to the measured results, the overdriven device shows an unusual slope change in the close-to-carrier PN portion as the resonators are working in a nonlinear regime. We have verified that VP influences flicker noise aliasing and determines the near-carrier PN levels in our strong capacitive coupled device. The oscillator with much lower CP and VP shows substantially improved PN performance, which is on par with other reported works. Benefitting from an ultralow VP, our device thus does not
require any charge pump bias generator [7], which is technically more favorable and eases a further integration with CMOS ICs.
ACKNOWLEDGEMENTS This work was supported by the National Science Council (NSC) of Taiwan under grant of NSC-101-2221-E-007-100-MY3. The authors also wish to thank the TSMC for device fabrication and National Chip Implementation Center for phase noise measurement.
REFERENCES [1] H. Lee, et al., in Proc. IEEE IFCS, Baltimore, May 21-24, 2012. [2] J. T. M. van Beek, et al., J. Micromech. Microeng., vol. 22, no. 1, 013001, 2012. [3] J. E.-Y. Lee, et al., Sens. Actuators A, Phys., vol. 156, no. 1, pp. 28-35, 2009. [4] D. B. Leeson, Proc. IEEE, vol. 54, no. 2, pp. 329-330, 1966. [5] V. Kaajakari, et al., IEEE Elect. Dev. Lett., vol. 25, pp. 173-175, 2004. [6] Y.-W. Lin, et al., IEEE J. Solid-State Circuits, vol. 39, no. 12, pp. 2477-2491, 2004. [7] K. Sundaresan, et al., in Proc. IEEE CICC, San Jose, Sept. 9-13 2006, pp. 841-844. [8] V. Kaajakari, et al., IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 52, no. 12, pp. 2322-2331, 2005. [9] M. Akgul, et al., in Tech. Digest Transducers‘09, Denver, June 21-25, 2009, pp. 798-801. [10] C.-S. Li, et al., in Proc. IEEE IFCS, Baltimore, May 21-24, 2012. [11] S. Lee, et al., in Tech. Digest Hilton Head Workshop, South Carolina, June 6-10, 2004, pp. 33-36. [12] S. A. Bhave, et al., in Proc. IEEE MEMS, Miami, Jan. 30-Feb. 3, 2005, pp. 223-226. [13] V. Kaajakari, et al., J. Microelectromech. Syst., vol. 13, pp. 715-724, 2004. [14] T. Niu, et al., in Proc. IEEE IFCS, Newport Beach, June 1-4, 2010, pp.189-194. [15] E. Colinet, et al., in Proc. IEEE IFCS, Newport Beach, June 1-4, 2010, pp.174-178. [16] C. Tu, et al., IEEE Elect. Dev. Lett., vol. 33, no. 3, pp. 450-452, 2012.
CONTACT * S.-S. Li, Tel: +886-3-516-2401;
[email protected]
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