Clamped-clamped Beam Resonator Research Articles

Vibration Mode Suppression in Micromechanical Resonators Using Embedded Anti- Resonating Structures

This paper presents a technique for suppressing specific resonance modes of micromechanical resonators by mechanical means. In particular, attaching multiple miniaturized beam structures with properly designed dimensions acting as anti-resonating tuned mass dampers (TMD's) to a micromechanical clamped-clamped beam (CC-beam) resonator based on a CMOS-MEMS process platform successfully attenuate the dynamic frequency response of the fundamental mode while retaining the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> harmonic mode of the CC-beam. The measured results show that the frequency transmission response of the TMD-embedded CC beam drops as much as ~12 dB compared to that of a reference resonator. An analytical model is used to study the effects of the parameter variations of the TMD structures. This technique provides an alternative approach to mechanically suppressing vibration modes for the micromechanical resonators that cannot employ the conventional quarter-wavelength support technique.

Fabrication of clamped-clamped beam resonators with embedded fluidic nanochannel

Suspended nanochannel resonators (SNRs) are promising devices able to characterize mass down to the attogram scale, thus being able to detect nanoparticles or biomolecules. In this paper, we present a flexible fabrication process for SNRs based on a sacrificial layer approach that allows to easily tailor the dimensions of the nanochannel by changing the thickness of the sacrificial layer or its patterning during the lithographic step. The resonance properties of the fabricated SNR are investigated in terms of resonance frequency and frequency stability (Allan deviation). Liquids of different densities are injected in the device and, from the shift of the resonance peaks, the mass responsivity of the resonators is assessed to be up to 3.90 mHz/ag. To the best of our knowledge, the devices here presented are the first example of suspended nanochannel resonators with a channel height as low as 50 nm fabricated with a top-down approach.

A chip-scale frequency down-conversion realized by MEMS-based filter and local oscillator

A wide-width clamped-clamped beam (CC-beam) resonator and a filter realized using mechanically-coupled resonator tanks have been extensively characterized to attain mixler (i.e., mixer-filter) functionality for a chip-scale frequency translation. Such a resonator has been driven into the nonlinear regime to explore its effect on the mixler operation as well as to obtain the best phase noise performance using the phase-feedback method. The proposed electrostatically transduced mixler operates by utilizing the local oscillator (LO) signal generated from the resonator itself, thus eliminating the need of a function generator or an external quartz crystal oscillator. This technique implemented with all the components on the same silicon substrate shows great potential for miniaturization in wireless communication while achieving 14.4 dB overall mixler loss.

Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance

The dynamic response of a nonlinear resonator in the presence of resonant mode coupling is studied experimentally and theoretically. For the case of a clamped-clamped beam resonator in the presence of a 1:3 internal resonance, we show that at the onset of internal resonance, steady state oscillations cannot be sustained. At higher drive levels, stable oscillations can be maintained but the resonator amplitude undergoes amplitude modulated responses. We use these dynamic responses to build a bifurcation diagram that can be described remarkably well with a simple model consisting of a Duffing resonator coupled to a linear one.

Nonlinear cc-beam microresonator model for system level electrical simulations: Application to bistable behavior analysis

Microelectromechanical resonators nonlinearities can be exploited in many ways to obtain a set of diverse new applications. In particular, some applications of bistable behavior includes threshold mechanical switches, memory cells, energy harvesting and chaotic signal generators. A key step for practical and efficient design for bistability behavior involves accounting for accurate and efficient models. In this paper we present a nonlinear electromechanical model for capacitive clamped-clamped beam resonators implemented in an analog hardware description language (AHDL) enabling system level electrical simulations. The model accounts for nonlinearities from variable resonator-electrode gap, residual fabrication stress, fringing field contributions as well as an accurate resonator deflection profile in contrast to parallel plate approximations. The model has been applied to derive for first time accurate analytical expressions for bistability design conditions. The work includes FEM analysis and experimental data that corroborates the correctness of the model in describing the required bias voltage conditions for bistability.

Dual frequency MEMS resonator through mixed electrical and mechanical coupling scheme

Miniaturised transceivers are essential in multiband wireless communication systems for higher data rates and low power consumption. Microelectromechanical system (MEMS) resonator filters are actively considered for deployment in transceivers for radio frequency and intermediate frequency (IF) signal filter and oscillator applications. In this study, the authors propose dual frequency capacitive transduced MEMS resonator with two-port electrical configuration. Clamped-clamped beam resonator was selected to serve as a basic resonant tank for the filter concept validation. Five design strategies low loss structural material, array design, mixed electrical and mechanical coupling scheme, sub-micro meter transduction gap and large transduction area were explored. With these strategies, the device achieves dual band filter characteristics, narrow pass band, desired bandwidth, low insertion loss and better stop band rejection. Dual frequency response of the proposed resonator is demonstrated at centre frequencies 400 kHz and 2.57 MHz with a narrow pass band of 3 and 20 kHz, respectively. Low insertion loss of 19.8 and 25.6 dB for frequencies centred at 400 kHz and 2.57 MHz, respectively and stop band rejection >35 dB was achieved. The proposed MEMS resonator may be incorporated in the implementation of dual band pass filter for IF signal filter and dual frequency oscillator applications.

Frequency latching in nonlinear micromechanical resonators

The resonance frequency of a nonlinear micromechanical resonator has a dependence on its modal amplitude known as the A–f effect. Here, we experimentally demonstrated that the A–f effect can be limited by the mode interaction in micromechanical resonators. The clamped-clamped beam resonator investigated in this work has a nonlinear in-plane (IP) vibration mode and a linear out-of-plane (OOP) vibration mode. In the case of single ended driving with various Vdc, the resonance frequency of the IP mode tuned through the A–f effect reaches that of the OOP mode and is limited by the OOP mode due to the modal interaction and electrostatic softening effect. In the case of double ended driving, however, the resonance frequency of the IP mode is latched to that of the OOP mode after A–f tuning and a frequency stabilized region is observed. A theoretical model is also put forward to explain this phenomenon through numerical simulations.

Temperature-Compensated CMOS-MEMS Oxide Resonators

Integrated CMOS-MEMS clamped-clamped beam resonators using metal wet etching technique are demonstrated with passive temperature compensation through the use of SiO2 and large stopband rejection via circuit integration. Such performance is enabled by the high- Q structural material (i.e., SiO2) and embedded electrodes (i.e., metal) for capacitive transduction without the need of complex post-CMOS processes. In virtue of exceptional selectivity of metal wet etchant to SiO2 among CMOS layers, the use of release holes needed for most of isotropic etching processes could be eliminated, hence substantially preserving the integrity of resonator structures. In this paper, CMOS-MEMS clamped-clamped beams with SiO2-rich structural design are fabricated and tested in vacuum under a two-port measurement configuration, exhibiting the lowest temperature coefficient of frequency (TCf) in CMOS-MEMS-based resonators with a turnover point at room temperature. Such a resonator monolithically integrated with readout circuitry using a standard CMOS 0.35 μm 2P4M process is tested with significantly enhanced performance, showing resonator Q's up to 6100, stopband rejection ~60 dB, and low noise floor at center frequency ~8 MHz, therefore benefiting future timing references and RF-MEMS building blocks for next-generation wireless communication applications.

A Versatile Instrument for the Characterization of Capacitive Micro- and Nanoelectromechanical Systems

This paper presents a laboratory prototype of an instrument developed for electromechanical characterization of capacitive micro- and nanoelectromechanical systems (M/NEMS). The instrument aims at filling the gap between commercial electrical instrumentation (impedance meters) and optical instrumentation: For most M/NEMS devices, impedance meters allow only quasi-stationary measurements (i.e., capacitance-voltage C-V curves) with a bandwidth limited to few hundreds of hertz; optical instrumentation allows dynamic characterization (Bode diagrams) but, besides being bulky and extremely costly, does not allow the measurement on packaged devices-and packaging is often an issue for the device performance and reliability. The proposed versatile characterization platform, controlled by LabVIEW libraries, monitors the capacitance variation, resulting from different kinds of electrical stimuli, via real-time capacitive sensing. The measurements are both stationary C-V curves and dynamic responses to input steps in the time domain, which are convertible into Bode plots in the frequency domain. Measurements can be done on bare or packaged and on wafer-level or diced devices, in a differential or single-ended configuration, with a good immunity to parasitic capacitances, a sensing resolution on the order of ≈1 aF/√(Hz), and a maximum testable device mechanical bandwidth around 100 kHz. A characterization of two sample structures, a micromachined magnetometer and a clamped-clamped beam resonator, is given as an example, followed by a discussion on future improvements.

Cancellation of the parasitic feedthrough current in an integrated CMOS–MEMS clamped-clamped beam resonator

This work presents a technique to cancel the parasitic feedthrough current in a fully CMOS integrated electrostatic micromechanical resonator. A four-electrode balanced topology has been proven to enhance the measured response of a polysilicon clamped-clamped beam resonator. The test results obtained show a pure RLC behavior of the resonator at 10.98MHz.

Electroplated Ni-CNT Nanocomposite for Micromechanical Resonator Applications

In this letter, electroplated Ni-CNT nanocomposite is synthesized and utilized as a structural material for micromechanical resonator fabrication. Pretreated by sulfate sodium dodecyl, carbon nanotubes (CNTs) disperse well in electrolyte and can be incorporated in an electroplated Ni film. Clamped-clamped beam resonators fabricated using the nanocomposite show 27% resonant frequency enhancement (from 498.75 to 634.72 kHz). Meanwhile, the Q factors of 781 and 760 for Ni and Ni-CNT nanocomposite resonators, which are comparable with the prior art, indicate that the anchor loss could dominate the Q performance of the beam resonators.

Interactions between directly- and parametrically-driven vibration modes in a micromechanical resonator

The interactions between parametrically and directly driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric amplification and oscillation of a single mode are analyzed by the power and phase dependence below and above the threshold for parametric oscillation. Then, the motion of a parametrically driven mode is detected by the induced change in resonance frequency in another mode of the same resonator. The resonance frequency shift is the result of the nonlinear coupling between the modes by the displacement-induced tension in the beam. These nonlinear modal interactions result in the quadratic relation between the resonance frequency of one mode and the amplitude of another mode. The amplitude of a parametrically oscillating mode depends on the square root of the pump frequency. Combining these dependencies yields a linear relation between the resonance frequency of the directly driven mode and the frequency of the parametrically oscillating mode.

A design methodology for fully integrated MEMS and NEMS Pierce oscillators

This work proposes a generic methodology to evaluate the feasibility of designing a Pierce oscillator based on a micro or nanoresonator fabricated with any given CMOS technology and with the constraint of using only one single active transistor. Both the design and the transimpedance gain of the electronics are analytically determined for resonators with capacitive or resistive detection. This approach is applied and validated in the case of (a) an electrostatically actuated clamped-clamped beam resonator using a capacitive transduction, and (b) a piezoresistive crossbeam, both based on a standard 0.13μm CMOS technology.

Electrically Enhanced Readout System for a High-Frequency CMOS-MEMS Resonator

The design of a CMOS clamped-clamped beam resonator along with a full custom integrated differential amplifier, monolithically fabricated with a commercial 0.35 μm CMOS technology, is presented. The implemented amplifier, which minimizes the negative effect of the parasitic capacitance, enhances the electrical MEMS characterization, obtaining a 48×10 8 resonant frequency-quality factor product (Q×fres) in air conditions, which is quite competitive in comparison with existing CMOS-MEMS resonators. DC voltage (VDC) is applied to the suspended structure, while an AC excitation voltage (VAC) is applied to the excitation electrode. The resulting electrostatic force induces the movement of the suspended structure at the excitation frequency. This oscillation generates a change in the capacitance constituted by the readout electrode and the suspended structure that can be quantified by measuring the induced output current:

A CMOS–MEMS RF-Tunable Bandpass Filter Based on Two High- $Q$ 22-MHz Polysilicon Clamped-Clamped Beam Resonators

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter presents the design, fabrication, and demonstration of a CMOS–MEMS filter based on two high- <formula formulatype="inline"><tex Notation="TeX">$Q$</tex></formula> submicrometer-scale clamped–clamped beam resonators with resonance frequency around 22 MHz. The MEMS resonators are fabricated with a 0.35-<formula formulatype="inline"> <tex Notation="TeX">$\mu\hbox{m}$</tex></formula> CMOS process and monolithically integrated with an on-chip differential amplifier. The CMOS–MEMS resonator shows high-quality factors of 227 in air conditions and 4400 in a vacuum for a bias voltage of 5 V. In air conditions, the CMOS–MEMS parallel filter presents a programmable bandwidth from 100 to 200 kHz with a <formula formulatype="inline"><tex Notation="TeX">$ ≪ \hbox{1}$</tex></formula>-dB ripple. In a vacuum, the filter presents a stop-band attenuation of 37 dB and a shape factor as low as 2.5 for a CMOS-compatible bias voltage of 5 V, demonstrating competitive performance compared with the state of the art of not fully integrated MEMS filters. </para>

Electrothermal actuation studies on silicon carbide resonators

The electromechanical behavior of SiC clamped-clamped beam (bridge) resonators with u-shaped aluminium (Al) electrodes on top has been studied as a function of electrode length, width, and spacing. Negative and positive deflections have been observed, indicating a complex interplay exhibited by the combined single material and bimorph characteristics of the resonator structures. It has been found that, both experimentally and theoretically, devices with electrodes applied on the root of the beam have similar or higher displacement amplitudes compared to devices with electrodes covering the half or the entire beam. Moreover, the displacement and vibration amplitudes can be maximized by increasing the electrode width and/or decreasing the spacing.

The nonlinearity cancellation phenomenon in micromechanical resonators

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

Fully integrated MIXLER based on VHF CMOS-MEMS clamped-clamped beam resonator

The design and test of a fully integrated CMOS-MEMS-MIXLER, using a commercial technology (AMS 0.35 mum) is presented. The MEMS structure is basically a clamped-clamped beam resonator implemented with the polysilicon capacitance module of the selected technology, showing a fundamental lateral resonance frequency of 22.5 MHz. Two different approaches based, respectively, on the nonlinearity of the voltage against the excitation force and on the amplitude modulation of the excitation signal, have been proposed in order to operate the MEMS as a MIXLER

Artificial neural network modeling of RF MEMS resonators

In this article, a novel and efficient approach for modeling radio-frequency microelectromechanical system (RF MEMS) resonators by using artificial neural network (ANN) modeling is presented. In the proposed methodology, the relationship between physical-input parameters and corresponding electrical-output parameters is obtained by combined circuit/full-wave/ANN modeling. More specifically, in order to predict the electrical responses from a resonator, an analytical representation of the electrical equivalent-network model (EENM) is developed from the well-known electromechanical analogs. Then, the reduced-order, nonlinear, dynamic macromodels from 3D finite-element method (FEM) simulations are generated to provide training, validating, and testing datasets for the ANN model. The developed ANN model provides an accurate prediction of an electrical response for various sets of driving parameters and it is suitable for integration with an RF/microwave circuit simulator. Although the proposed approach is demonstrated on a clamped-clamped (C-C) beam resonator, it can be readily adapted for the analysis of other micromechanical resonators. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14: 302–316, 2004.

High-Q single crystal silicon HARPSS capacitive beam resonators with self-aligned sub-100-nm transduction gaps

This paper reports on the fabrication and characterization of high-quality factor (Q) single crystal silicon (SCS) in-plane capacitive beam resonators with sub-100 nm to submicron transduction gaps using the HARPSS process. The resonating element is made of single crystal silicon while the drive and sense electrodes are made of trench-refilled polysilicon, yielding an all-silicon capacitive microresonator. The fabricated SCS resonators are 20-40 /spl mu/m thick and have self-aligned capacitive gaps. Vertical gaps as small as 80 nm in between 20 /spl mu/m thick silicon structures have been demonstrated in this work. A large number of clamped-free and clamped-clamped beam resonators were fabricated. Quality factors as high as 177000 for a 19 kHz clamped-free beam and 74000 for an 80 kHz clamped-clamped beam were measured under 1 mtorr vacuum. Clamped-clamped beam resonators were operated at their higher resonance modes (up to the fifth mode); a resonance frequency of 12 MHz was observed for the fifth mode of a clamped-clamped beam with the fundamental mode frequency of 0.91 MHz. Electrostatic tuning characteristics of the resonators have been measured and compared to the theoretical values. The measured Q values of the clamped-clamped beam resonators are within 20% of the fundamental thermoelastic damping limits (Q/sub TED/) obtained from finite element analysis.