Direct parameter extraction in capacitively transduced micromechanical resonators using the anti-resonance

This paper presents a method for the fast and direct extraction of model parameters for capacitive MEMS resonators from their measured transmission response such as quality factor, resonant frequency, and motional resistance. We show that these parameters may be extracted without having to first de-embed the resonator motional current from the feedthrough. The series and parallel resonances from the measured electrical transmission are used to determine the MEMS resonator circuit parameters. The theoretical basis for the method is elucidated by using both the Nyquist and susceptance frequency response plots, and applicable in the limit where CF > CmQ; commonly the case when characterizing MEMS resonators at RF. The method is then applied to the measured electrical transmission for capacitively transduced MEMS resonators, and compared against parameters obtained using a Lorentzian fit to the measured response. Close agreement between the two methods is reported herein. © 2010 IEEE.

Enhancing parametric sensitivity using mode localization in electrically coupled mems resonators

We use vibration localization as a sensitive means of detecting small perturbations in stiffness in a pair of weakly coupled micromechanical resonators. For the first time, the variation in the eigenstates is studied by electrostatically coupling nearly identical resonators to allow for stronger localization of vibrational energy due to perturbations in stiffness. Eigenstate variations that are orders of magnitude greater than corresponding shifts in resonant frequency for an induced stiffness perturbation are experimentally demonstrated. Such high, voltagetunable parametric sensitivities together with the added advantage of intrinsic common mode rejection pave the way to a new paradigm of mechanical sensing. ©2009 IEEE.

A surface acoustic wave-based immunosensing device using a nanocrystalline ZnO film on Si

The novelty of this study resides in the fabrication of a bio-sensing device, based on the surface acoustic wave (SAW) on a nanocrystalline ZnO film. The ZnO film was deposited using an rf magnetron sputtering at room temperature on silicon. The deposited films showed the c-axisoriented crystallite with grain size of ∼40 nm. The immunosensing device was fabricated using photolithographic protocols on the film. As a model biomolecular recognition and immunosensing, biospecific interaction between a 6-(2,4-dinitrophenyl) aminohexanoic acid (DNP) antigen and its antibody was employed, demonstrating the shifts of resonant frequencies on SAW immunosensing device. The device exhibited a linearity as a function of the antibody concentration in the range of 20∼20,000 ng/ml. © 2009 American Scientific Publishers. All rights reserved.

Parasitic feedthrough cancellation techniques for enhanced electrical characterization of electrostatic microresonators

Capacitive parasitic feedthrough is an impediment that is inherent to all electrically interfaced micron scale resonant devices, resulting in increased challenges to their integration in more complex circuits, particularly as devices are scaled to operate at higher frequencies for RF applications. In this paper, a technique to cancel the undesirable effects of capacitive feedthrough that was previously proposed is here developed for an on-chip implementation. The method reported in this paper benefits from the simplicity of its implementation, and its effectiveness is demonstrated in this paper. This technique is demonstrated for two disk-plate resonators that have been excited in the wine glass mode at 5.4 MHz, though applicable to almost any electrically interfaced resonator. Measurements of the electrical transmission from these resonators show that the magnitude of the frequency response of the system is enhanced by up to 19 dB, while the phase is found to shift through a full 180° about the resonant frequency. This method is proposed as a useful addition to other techniques for enhancing the measured response of electrostatic micromechanical resonators. © 2009 Elsevier B.V. All rights reserved.

5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million

This paper reports the design and electrical characterization of a micromechanical disk resonator fabricated in single crystal silicon using a foundry SOI micromachining process. The microresonator has been selectively excited in the radial extensional and the wine glass modes by reversing the polarity of the DC bias voltage applied on selected drive electrodes around the resonant structure. The quality factor of the resonator vibrating in the radial contour mode was 8000 at a resonant frequency of 6.34 MHz at pressure below 10 mTorr vacuum. The highest measured quality factor of the resonator in the wine glass resonant mode was 1.9 × 106 using a DC bias voltage of 20 V at about the same pressure in vacuum; the resonant frequency was 5.43 MHz and the lowest motional resistance measured was approximately 17 kΩ using a DC bias voltage of 60 V applied across 2.7 μm actuation gaps. This corresponds to a resonant frequency-quality factor (f-Q) product of 1.02 × 1013, among the highest reported for single crystal silicon microresonators, and on par with the best quartz crystal resonators. The quality factor for the wine glass mode in air was approximately 10,000. © 2009 Elsevier B.V. All rights reserved.

Binary excitation of a high-Q bulk acoustic microresonator by actuation polarity inversion

We present a technique for independently exciting two resonant modes of vibration in a single-crystal silicon bulk mode microresonator using the same electrode configuration through control of the polarity of the DC actuation voltage. Applications of this technique may include built-in temperature compensation by the simultaneous selective excitation of two closely spaced modes that may have different temperature coefficients of resonant frequency. The technique is simple and requires minimum circuit overhead for implementation. The technique is implemented on square plate resonators with quality factors as high as 3.06 × 106. Copyright © 2008 by ASME.

Low loss HF band SOI wine glass bulk mode capacitive square-plate resonator

This paper reports on the design and electrical characterization of a single crystal silicon micromechanical square-plate resonator. The microresonator has been excited in the anti-symmetrical wine glass mode at a resonant frequency of 5.166 MHz and exhibits an impressive quality factor (Q) of 3.7 × 106 at a pressure of 33 mtorr. The device has been fabricated in a commercial foundry process. An associated motional resistance of approximately 50 kΩ using a dc bias voltage of 60 V is measured for a transduction gap of 2 νm due to the ultra-high Q of the resonator. This result corresponds to a frequency-Q product of 1.9 × 1013, the highest reported for a fundamental mode single-crystal silicon resonator and on par with some of the best quartz crystal resonators. The results are indicative of the superior performance of silicon as a mechanical material, and show that the wine glass resonant mode is beneficial for achieving high quality factors allowed by the material limit. © 2009 IOP Publishing Ltd.

Thin film monitoring with silicon bulk acoustic resonators

Abstract-This paper reports a single-crystal silicon mass sensor based on a square-plate resonant structure excited in the wine glass bulk acoustic mode at a resonant frequency of 2.065 MHz and an impressive quality factor of 4 million at 12 mtorr pressure. Mass loading on the resonator results in a linear downshift in the resonant frequency of this device, wherein the measured sensitivity is found to be 175 Hz cm2/μg. The silicon resonator is embedded in an oscillator feedback loop, which has a short-term frequency stability of 3 mHz (approximately 1.5 ppb) at an operating pressure of 3.2 mtorr, corresponding to an equivalent mass noise floor of 17 pg/cm2. Possible applications of this device include thin film monitoring and gas sensing, with the potential added benefits of scalability and integration with CMOS technology. © 2008 IEEE.

Square wine glass mode resonator with quality factor of 4 million

We report on the experimental characterization of a single crystal silicon square-plate microresonator. The resonator is excited in the square wine glass (SWG) mode at a mechanical resonance frequency of 2.065 MHz. The resonator displays quality factor of 9660 in air and an ultra-high quality factor of Q = 4.05 × 106 in 12 mtorr vacuum. The SWG mode may be described as a square plate that contracts along one axis in the fabrication plane, while simultaneously extending along an orthogonal axis in the same plane. The resonant structure is addressed in a 2-terminal configuration by utilizing equal and opposite drive polarities on surrounding capacitor electrodes, thereby decreasing the motional resistance of the resonator. The resonant micromechanical device has been fabricated in a commercial silicon-on-insulator process through the MEMSCAP foundry utilising a minimum electrostatic gap of 2 μm. © 2008 IEEE.

Anchor limited q in flexural mode resonators

This paper reports a preliminary examination of the effect of anchor geometry design on the quality factor of flexural mode resonators operating in vacuum using both FE simulation and measurements of resonator frequency response. Three types of structures have been considered in this study: an elliptical mode ring, a double ended tuning fork, and a doubly-clamped beam. We consider the relative distribution of strain energies in both the resonant structure and the connecting stem, which is indicative of the measured quality factor. The measured quality factors of the different structures are compared against each other, based on which suggestions are proposed for optimizing the anchor limited quality factor (Q) in flexural mode micromechanical resonators. ©2008 IEEE.

Direct parameter extraction in feedthrough-embedded capacitive MEMS resonators

This paper presents a method for fast and accurate determination of parameters relevant to the characterization of capacitive MEMS resonators like quality factor (Q), resonant frequency (fn), and equivalent circuit parameters such as the motional capacitance (Cm). In the presence of a parasitic feedthrough capacitor (CF) appearing across the input and output ports, the transmission characteristic is marked by two resonances: series (S) and parallel (P). Close approximations of these circuit parameters are obtained without having to first de-embed the resonator motional current typically buried in feedthrough by using the series and parallel resonances. While previous methods with the same objective are well known, we show that these are limited to the condition where CF ≪ CmQ. In contrast, this work focuses on moderate capacitive feedthrough levels where CF > CmQ, which are more common in MEMS resonators. The method is applied to data obtained from the measured electrical transmission of fabricated SOI MEMS resonators. Parameter values deduced via direct extraction are then compared against those obtained by a full extraction procedure where de-embedding is first performed and followed by a Lorentzian fit to the data based on the classical transfer function associated with a generic LRC series resonant circuit. © 2011 Elsevier B.V. All rights reserved.