Micromechanical resonators are circuits tuned to particular frequencies1 that have broad application in electronic and communication systems. Silicon-based resonators also have the advantage of economy by virtue of their compatibility with integrated-circuit fabrication technology. A key issue for these resonators is a high quality (Q) factor (a key indicator of performance), which is essential for alleviating ‘close-in’ (phase) noise in timing devices. To achieve this performance, resonator energy loss—due either to damping or radiation—needs to be kept as low as possible. Damping loss establishes the material limits to reaching an effective Q factor,2 whereas radiation loss is a byproduct of the energy transmitted by acoustic wave propagation from the resonator through its support structure into a substrate.
Figure 1. (a) Conventional design of a bar-type micromechanical resonator with simple support beams. (b) Bar-type resonator anchored by phononic crystal (PnC) strips for eliminating radiation loss. (c) Detailed drawing of a unit cell of the PnC strip. (d) Various microelectromechanical systems (MEMS) resonators supported by PnC strips can be realized using a silicon-based lithographic process. a: Lattice spacing. d: Width of the simple support beams. h: Height of the cavity. L: Length of the cavity. r: Radius. W: Width of the cavity. Vin, Vout: Voltage in and out.
Completely eliminating acoustic radiation loss is difficult, although numerous approaches have been described. The simplest of these involves supporting resonators at their nodal points of oscillation to the substrate. More effective methods are based on acoustic impedance mismatch,3 for instance, quarter-wavelength support beams for effectively reflecting outgoing waves back to the resonators. However, to thoroughly eliminate radiation loss through supports, we developed a periodic microstructure possessing an ultrasonic stop band, or phononic crystal (PnC) strip (see Figure 1). The device halts acoustic wave propagation at a particular frequency.
A PnC strip can be regarded as a 1D periodic strip structure. We explored these strips based on our experience with so-called PnC slabs, which exhibit a frequency range (or frequency bandgap) that prohibits acoustic waves of any kind from propagating.4 We combined PnC strips and acoustic resonance cavities.5, 6 Figure 1(b) shows our architecture, and Figure 1(a) a conventional design. The resonator consists of a bar-type resonance cavity anchored to the substrate by two PnC strips at its two ends. When the bar is actuated by electrostatic force at its natural frequency, it accumulates acoustic energy and resonates. Effectively trapping the resonance energy in the cavity, which our PnC strips can do, enhances the Q factor of the resonator.
Figure 2. Calculated power transmission spectra of acoustic wave incidence with particle vibrations in different directions through the designed PnC strip. Gray range denotes the ultrasonic bandgap that yields extremely low transmissions.
Figure 2 shows the theoretically predicted power transmission spectra of acoustic wave incidence with particle vibrations in different directions through the PnC strip. At frequencies of approximately 212MHz, the transmitted wave power decreases to extremely low levels (less than −100dB), regardless of the vibration. This shows the ability of the PnC strip to stop wave propagation. The underlying physics involves the PnC strip structure scattering the acoustic waves, analogous to photonic bandgaps, and forming an ultrasonic energy gap in the relevant frequency range.
PnC strips can potentially be used to engineer various micromechanical resonators for eliminating radiation loss or confining acoustic energy. Figure 1(d) shows microfabricated bar-type and ring-type resonators with PnC strips as lossless supports. We made these microstructures using a silicon-on-insulator wafer and nanogap technique.
Figure 3. Acoustic wave fields of bar-type micromechanical resonators actuated in a width-extensional resonance mode. (a) Acoustic energy radiates through the simple support beam. (b) PnC strip eliminates acoustic radiation loss when the operating frequency is inside the bandgap. (c) Acoustic radiation loss occurs when the operating frequency is not in the bandgap.
Figure 3 displays simulated acoustic radiation loss. The acoustic wave fields of the bar-type micromechanical resonator are actuated in a width-extensional resonance mode. Figure 3(a) shows the conventional design with acoustic wave energy radiating through the simple support beam. By contrast, Figure 3(b) shows a resonator anchored by our PnC strips and operated at the resonance frequency in the bandgap. The acoustic radiation loss is nearly completely suppressed, leading to a high Q factor near the material limits.6 Figure 3(c) compares the case of a resonator designed to operate outside the bandgap of the PnC strip. In this case, acoustic radiation loss may occur without meeting the bandgap.
In summary, we have described novel PnC strips that exhibit an ultrasonic bandgap and, accordingly, enable effective Q resonator architecture using the strips as lossless supports. The architecture for silicon-based micromechanical resonators provides a guideline for a variety of resonators that require support structures for practical application. We will focus our future research on developing high-performance oscillators based on high-Q resonators with PnC strips for frequency-device applications such as timers and sensors.
The authors thank the Ministry of Economic Affairs of the Republic of China, Taiwan, for financially supporting this research under contract A327HK2310. J.-C. Hsu thanks the National Science Council of Taiwan for support.
Feng-Chia Hsu, Tsun-Che Huang, Chin-Hung Wang, Pin Chang
Microsystems Technology Center
Industrial Technology Research Institute (ITRI) South
Feng-Chia Hsu is an associate engineer. He received his MS in applied mechanics from National Taiwan University (2008). His current research focuses on radio frequency microelectromechanical systems (RF MEMS), phononic crystals, and acoustics.
Tsu-Che Huang is an engineer. He received his MSEE from National Taiwan University (1994). His research interests include portable antenna design for wireless communications, satellite reflector antennas, and RF/microwave communication circuit designs.
Chin-Hung Wang is department manager. He received his MS in materials science and engineering from National Chiao-Tung University, Taiwan (1992). His research interests include wafer-level packaging for MEMS sensors, RF MEMS, and MEMS microphones.
Pin Chang is a deputy director. He received his PhD in physics from the Massachusetts Institute of Technology (1992). He works on RF MEMS, MEMS microphones employing CMOS front-end processes, lead zirconate titanate-driven MEMS scanning mirrors, and laser pico-projectors.
National Yunlin University of Science and Technology
Jin-Chen Hsu is an assistant professor in the Department of Mechanical Engineering. He received his PhD in applied mechanics from National Taiwan University (2007). His current research focuses on piezoelectric materials and phononic crystals for acoustic-wave devices.
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