Micromechanical Disk Resonators Research Articles

Modeling Support Loss in Torsional Mode Vibrations of a Micromechanical Disk Resonator with Two L-Shaped Support Beams

In this paper, a new micromechanical disc resonator with two L-shaped horizontal support beams in torsional mode vibrations has been proposed. The proposed micromechanical resonator has been studied in the field of natural frequencies and support loss. In order to verify the findings of natural frequencies, the analytical results are compared to the simulation results given by ANSYS software. A good agreement between analytical and simulation results is shown. In addition a closed-form equation for support loss quality factor in torsional mode vibrations of the proposed micromechanical resonator is presented. The results show that using L-shaped support beams can improve the support loss quality factor up to two times.

Modeling Support Loss in Torsional Mode Vibrations of a Micromechanical Disk Resonator with Two L-Shaped Support Beams

Modeling Support Loss in Torsional Mode Vibrations of a Micromechanical Disk Resonator with Two L-Shaped Support Beams

A 9.45 MHz micromechanical disk resonator with movable electrodes for gap reduction

A micro-electromechanical wine glass modal disk resonator with movable electrodes is presented in this paper. The movable electrodes were driven by electrostatic force for gap reduction to reduce insertion loss. By reducing the gap from 2.5μm to 0.5μm, the insertion loss improved from −104dB to −81dB at the same bias voltage of 20V. However, unstable movable electrodes caused the quality factor to decrease from 920,000 to 27,200.

Nonlinear effect of disk resonator

Radial-contour-mode micromechanical disk resonator with high frequency and high quality factor (Q) is attractive for wireless communication application. The nonlinear behaviors are usually not expected for disk resonator with high stiffness. However, when disk resonator is actuated by large bias voltage or works in vacuum, spring softening effect was observed. And spring hardening effect occurs when the resonator works in low temperature (below 110 K). In this work, the nonlinear behaviors of disk resonator are investigated. For disk resonator with high Q, the driving force should be reduced to ensure a linear operation when it works at low temperature or in vacuum.

Frequency Stability of RF-MEMS Disk Resonators

This paper systematically investigates the frequency stability of a radial-contour-mode micromechanical disk resonators with high quality factor (Q-factor) and high resonance frequency. Microelectromechanical system (MEMS)-based oscillator prototype consisting of the resonator and off-chip circuit is realized for frequency reference. The sustaining circuit is designed using impedance matching networks and two op-amp stages with automatic gain control circuit. The oscillator reaches a short-term frequency stability of ±1 ppm and a medium-term frequency stability of ±5 ppm over industrial temperature range (-40 °C-85 °C), which outperforms some of the best MEMS oscillators. Meanwhile, the phase noise is -95 dBc/Hz at 10 kHz offset and 149-MHz carrier. This paper also presents a simple and effective compensation scheme by combining built-in microoven and bias voltage tuning, which can achieve a frequency stability range of 2 ppm at temperature ranges from 20 °C to 100 °C.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

Design and fabrication of cost‐effective side‐stem micromechanical disk resonator with large capacitive gap

A high-performance micromechanical disk resonator is developed for use in mass detection biosensors. The resonator is designed to facilitate easy and cost-effective fabrication by anchoring the disk on the side stems and increasing the capacitive gap size up to 4.75 µm. The designed disk resonator operates in an elliptic contour-mode at a resonance frequency of 5.971 MHz with a quality factor of 4272 in ambient air condition and 17 221 in a 600 Torr vacuum environment.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators

A small-signal equivalent circuit for parallelplate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators.

A small-signal equivalent circuit for parallel-plate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

Analytical formulation of modal frequency split in the elliptical mode of SCS micromechanical disk resonators

This paper presents an analytical formulation of frequency splitting observed in the elliptical modes of single crystal silicon (SCS) micromechanical disk resonators. Taking the anisotropic elasticity of SCS into account, new formulae for computing modal mass and modal stiffness are first derived for accurate prediction of the modal frequency. The derived results are in good agreement with finite element simulation, showing a factor of 10 improvement in the prediction accuracy as compared to using the formula for the isotropic case. In addition, the analysis successfully explains the effect of anisotropy on the modal frequency splitting of primary elliptical modes, for which the maximum modal displacement is aligned with the directions of maximum (〈1 1 0〉) and minimum (〈1 0 0〉) elasticity respectively on a (1 0 0) SCS wafer. The measured frequency splitting of other degenerate modes is due to the manufacturing imperfections.

The Influence of Package Atmospheres on Resonance Performance of Micromechanical Radial-Contour Disk Resonator

Owing to high performance and tiny size, micromechanical radial-contour disk resonator as competitive candidate demonstrates an impressive prospect to replace traditional frequency selecting module in RF devices, so as to improve performance of modern RF transceivers. The influence of package atmospheres on resonance performance of micromechanical radial-contour disk resonator was investigated. By model construction and FEM calculation, resonance performance of micromechanical radial-contour disk resonator was analyzed, which indicate its resonance frequency as well as unique deformation style. In addition, effect on resonance performance of radial-contour disk resonator caused by package atmosphere was analyzed. The analysis result of resonance parameters variation of resonator immerged in different gases reveals that as the gas viscosity increases, the resonance frequency decreases. The phenomenon was interpreted by damping effect and recovery delay of disk deformation introduced by gases, which can be a reference for micromechanical resonator design and package selection in different applications.

Study of the out-of-plane vibrational modes in thin-film amorphous silicon micromechanical disk resonators

Thin-film silicon micro resonators are fabricated by surface micromachining at temperatures that are CMOS and large area substrate-compatible. Disk resonators offer large working surfaces and a large number of vibrational modes. The vibrational modes of micromechanical disk resonators made from hydrogenated amorphous silicon thin films were studied in this work. The dynamic behavior of these structures is shown to be mechanically described to be in the transition between a membrane and a plate due to the influence of residual stresses generated during the film growth and to thermal mismatch with underlying layers. Non-degenerate modes are observed as a consequence of the radial symmetry and their effective stiffness is related to the anchor geometry and the parity of the number of diametric nodal lines. The experimentally measured frequencies were compared with the simulated values from finite element modeling with good agreement. Investigation of the intrinsic quality factors shows that there is a dependence of the energy dissipation per cycle with the mode order that is related to the clamping anchors. Thermal annealing experiments show that enhanced quality factors can be obtained using low temperature annealing for a limited period of time.

Improvement of fabrication and characterization methods for micromechanical disk resonators

In this paper we present a novel method to fabricate reliable micro-electro-mechanical system (MEMS) disk resonators with high yield and good performance. The key breakthrough in the fabrication process is a novel approach to effectively restraining electro-chemical corrosion of polycrystalline silicon (polysilicon) electrically coupled with noble metals of MEMS devices by hydrofluoric acid (HF)-based solutions. In addition, a measurement architecture based on a differential readout topology is demonstrated. The differential circuit proposed here can effectively suppress noise and feed-through current by common-mode rejection of the differential amplifier. This differential amplifier circuit configuration is also used to build up a notch filter. The preliminary result about the temperature dependence of the resonance frequency is discussed, and the device failure is analysed.

An effective approach for restraining electrochemical corrosion of polycrystalline silicon caused by an HF-based solution and its application for mass production of MEMS devices

This paper presents a novel method to effectively protect the structural material polycrystalline silicon (polysilicon) from electrochemical corrosion, which often occurs when the MEMS device is released in HF-based solutions, especially when the device contains a noble metal. This corrosion seriously degrades the electrical and mechanical performance as well as the reliability of MEMS devices. In this method, a photoresist (PR) is employed to cover the noble metal, which is electrically coupled with the underlying polysilicon layer. This PR cover can effectually prevent an HF-based solution from diffusing through and arriving at the surface of the noble metal, thus cutting off the electrical current of the electrochemical corrosion reaction. The polysilicon is well protected for longer than 80 min in 49% concentrated HF solutions by a 3 µm-thick AZ 6130 PR film. This fabrication process is simple, reliable and suitable for mass production of high-end micromechanical disk resonators. Benefiting from the technology breakthrough mentioned above, a novel low-cost microfabrication method for disk resonators with high performance has been developed, and the VHF polysilicon disk resonators with resonance frequencies around 282 MHz and Q values larger than 2000 at atmosphere have been produced at wafer level.

SOI-based radial-contour-mode micromechanical disk resonator

This paper reports a radial-contour-mode micromechanical disk resonator for radio frequency applications. This disk resonator with a gold plated layer as the electrodes, was prepared on a silicon-on-insulator wafer, which is supported by an anchor on another silicon wafer through Au-Au thermo-compression bonding. The gap between the disk and the surrounding gold electrodes is 100 nm. The radius of the disk is 20 μm and the thickness is 4.5 μm. In results, the resonator shows a resonant frequency of 143 MHz and a quality factor of 5600 in vacuum.

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 × 10 6 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 × 10 13, 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.

Support loss in the radial bulk-mode vibrations of center-supported micromechanical disk resonators

This paper presents a comprehensive analysis of support loss, the dominant loss mechanism, in center-supported micromechanical disk resonators operating in their radial bulk-modes. Through separation and coupling between the three components (disk, support beam, and support structure) of a disk resonator, support loss is evaluated quantitatively and the closed-form expression is obtained for support quality factor ( Q support) of a center-supported disk resonator. The comparison between theoretical analysis and experimental data shows good agreement. This work provides significant insights into the geometrical design and choice of materials in high- Q center-supported disk resonant structures. To minimize support loss, a quarter wavelength rule exists for the height of the support beam in a center-supported disk resonator, similar to the length of torsion support beams of a free–free flexural beam resonator.

1.156-GHz self-aligned vibrating micromechanical disk resonator

A new fabrication methodology that allows self-alignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radial-contour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q's at this frequency >2,650 in both vacuum and air. In addition, a 734.6-MHz version has been demonstrated with Q's of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, self-alignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.