Contour Mode Research Articles

The Impact of Damping on Flicker Frequency Noise of AlN Piezoelectric MEMS Resonators

This paper presents a detailed study on the effect of damping on flicker frequency (1/f) noise of 1.1-GHz aluminum nitride (AlN) contour mode resonators (CMRs). A total of 52 different AlN CMRs with different sizes, electrode designs, and anchor types are systemically designed and fabricated to give a wide range of quality factors ( $Q)$ from 300 to 3500, allowing the study of how two major damping mechanisms in AlN CMRs: 1) anchor losses; and 2) thermoelastic damping affect the resonator 1/f noise. In total, we have measured 1/f noise of 104 CMRs using the modified homodyne noise measurement setup and the results confirm that 1/f noise shows a clear power law dependency ranging from 1/ $Q^{2.7}$ to 1/ $Q^{3.5}$ , depending on the main nature of the damping mechanism. Additionally, we have measured 1/f noise of 25 CMRs at 10 K and the results follow the trend observed at ambient temperature. Understanding and accounting for the effect of damping on 1/f noise are crucial for building ultra-low noise microelectromechanical systems resonators for sensing, timing, and frequency applications. [2016-0204]

Design of spurious mode-free elliptical ring resonators

Spurious modes suppression to retain the purity of the main resonance in lateral-extensional contour modes is one of the most important requirements for commercializing vibrating RF MEMS resonators. This issue becomes much more critical for ring-shaped micromechanical resonators that are normally susceptible to both out-of-plane flexural modes and in-plane torsional modes at frequencies adjacent to that of the desired lateral-extensional mode. However, this kind of lateral-extensional mode resonators hold unique ability to achieve GHz frequencies without excessive scaling of its key dimensions, such as inner and outer radius, to facilitate strong electromechanical coupling coefficient by either capacitive or piezoelectric transducers while exhibiting high Q’s on the orders of a few thousands. This paper presents a new type of ring resonators based on a hollow ellipsoid structure operating in the extensional wine-glass mode. Due to the mode shape matching to the resonator body shape, vibration amplitude at this strategically-designed mode becomes much larger than those for other modes. Moreover, a harmonic analysis to verify the basic design principles and further discussions towards design optimization have been presented.

Analytical study on effect of piezoelectric patterns on frequency shift and support loss in ring-shaped resonators for biomedical applications

One of the most vital issue in FBAR is enhancing mass sensitivity and restraining energy loss. A ring-shaped piezoelectric resonator was proposed for biomedical applications. The proposed ring-shaped resonator comprises with a multilayer of Pt/Ti/PZT/Ti/Pt/SiO2, deposited on the silicon-on-insulator wafer and expected to be a contour mode. The ring-shaped resonator reacts to certain voltage vibration with a mass perturbation to get Eigenstate vibration or frequency shifts which could be transferred to electrical signals by converse piezoelectric effect. In this paper, vibration modes with high-frequency shift due to a small mass perturbation of 10 ng are analytical evaluated to achieve a higher sensitivity. In order to estimate the sensitivity of the ring-shaped resonator against the mass perturbation, the simulated analysis is conducted by COMSOL from two aspects including (a) the effect of PZT pattern miniaturization and distribution on frequency shift (from viewpoint of vibration mode shape); (b) achieving low support energy loss through analyzing the support displacement. It is found that frequency shift of PZT pattern C with Eigenstate mode 5 is higher than that of others and the support displacement is also small for this combination.

Analytical and Numerical Methods to Model Anchor Losses in 65-MHz AlN Contour Mode Resonators

This paper presents and experimentally validates two different approaches to describe the quality factor ( $Q$ ) due to anchor losses in 65-MHz aluminum nitride (AlN) contour mode resonators (CMRs). The first method is an approach that can be considered qualitative in nature, as it consists of a simplified analytical model that assumes quasi-static anchor conditions and a semi-infinite substrate. Despite its simplicity, it effectively provides designers with some guidelines on how to layout resonator anchors. The second approach is quantitative and consists of a numerical technique that can be considered as an alternative to the use of perfectly matched layers (PMLs). The new finite-element method imposes fixed-constraint (FC) boundary conditions at the edges of the released regions, and the $Q$ is calculated as the ratio of strain energy in both resonator and anchors and the total acoustic energy transferred to the substrate. The two approaches (analytical and numerical) are experimentally validated through measurements of 216 AlN CMRs operating at their fundamental resonance frequency (around 65 MHz). The proposed numerical approach is also compared with the results obtained using PML. This comparison shows that the FC technique has a similar accuracy to PML in predicting $Q$ , but it is superior to the latter when reflections from the clamped boundaries become relevant. [2015-0336]

Electrical characterization of piezoelectric-on-silicon contour mode resonators fully immersed in liquid

Biological sensing in the mechanical domain offers novel opportunities to measure cellular processes. Operating mechanical resonators in liquid environment for the detection of mass presents a challenge at least for electrical characterization. In this paper, we demonstrate the full electrical characterization of a micromechanical resonator that is fully immersed in DI-water. The reported device uses piezoelectric transduction through an Aluminium Nitride (AlN) film sputtered on a low damping silicon substrate to provide strong electromechanical coupling. The effect of viscous damping in DI-water is lowered by exciting the resonator to vibrate in an in-plane contour mode. We believe that incorporating a 10μm thicker silicon substrate layer stiffens the resonant system and thereby increases the energy storage capacity in relation to a resonator structured purely by a thin AlN film. The 14MHz length extensional (LE) mode resonator presented in this paper shows a quality factor (Q) of 200 when fully immersed in DI-water, which is twice that of previously reported resonators structured purely in AlN. The associated motional resistance of the device in DI-water is 40 kΩ. We have also measured the values of Q for several other in-plane resonant modes with higher resonant frequencies (up to 141.69MHz) when immersed in DI-water. Having found that the high dielectric constant of DI-water significant affects the characterization setup, we have also modeled the various sources of parasitics involved in the setup.

Synthesis and analysis of multi‐mode profile horn using mode matching technique and evolutionary algorithm

This study presents the design and analysis of linear as well as cubic spline interpolated profiled smooth-wall multimode horn using mode matching (MM) technique along with genetic algorithm (GA) and particle swarm optimisation (PSO). To apply the MM technique, the smooth profile conical geometry is assumed to consist of cascaded sections of large number of small symmetrical radial steps. Scattering matrix for each section has been calculated using MM technique and over all scattering matrix of the cascaded junctions has been calculated using generalised scattering matrix technique. The radiation pattern has been calculated using hybrid boundary contour mode matching technique. Optimisation of the linear/spline profile horn has been carried out using GA as well as PSO. Detailed modal analysis along with the convergence of the present technique for the smooth profile structure has also been carried out. A spline profile multimode horn working at 89 GHz has been designed and developed. The present analysis has been verified with the measured results. There is a very good agreement between theoretical and measured results.

Size effect in gas forming a hot-bent AA5xxx V-shaped trough trimmed for an airplane strakelet skin panel

Superplastic forming or gas forming is favorable method for the manufacture of sheet metal for making airplane skin panels. However, a major challenge in applying this method is controlling the thickness distribution in the formed product. Here, we explore a hot-bending-assisted process for gas forming of a deep trough with a complex shape for use in airplane wings. We propose the deliberate arrangement of wrinkles to achieve uniform thickness distribution. Because full-scale experiments are costly, sub-scale specimens are preferred for collecting experimental data. In linking sub-scale data to full-scale manufacturing, the size effect on wrinkle formation sites is important. The cause of the pre-form contour and larger-size specimen could be the greater variations in contour modes due to plastic buckling during the pre-forming stage.

Modeling of MEMS Resonator Piezoelectric Disc Partially Covered with Electrodes

The Legendre polynomial method has been extended to the modeling of MEMS resonator disc partially covered with electrodes. The disc has been divided into two areas: one with electrodes and the other without electrodes. For each area, The Maxwell equations and the piezoelectric constitutive equations of motion are studied and solved to yield a frequency response and electrical behavior of the MEMS resonator applying a semi analytical method based on a Legendre polynomials series and trigonometric functions. However, the method allows incorporating the boundary conditions directly into the governing equations by assuming position-dependent of elastic constants, mass density and delta functions. The alternating electrical source is described by specific terms which are also introduced into the equation of motion. The formalism has been developed which allows for both harmonic and modal analyses. In order to validate our polynomial approach, numerical results are presented such as resonant and anti-resonant frequencies, electric input admittance, electromechanical coupling coefficient and field profiles of fully and partially metallized PZT5A resonator discs. The results obtained were compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the contour modes of all orders.

Effects of Thermoelastic Damping on The Operation of The Ring Shape Anchored Contour Mode Disk Resonators

Thermoelastic damping is one of the most important energy loss mechanisms in MEMS resonators especially when the resonator is miniaturized to achieve higher frequencies. Based on thermal energy produced as the result of the resonator expansion and contraction, by considering the thermoelastic coupled equation, this article presents a solution to thermoelastic damping for previously demonstrated ring shape anchored contour mode disk RF MEMS resonator. This research proves that the thermoelastic damping has a negligible effect on the quality factor of the resonator. In addition the results mention that this effect becomes stronger when the surface to volume ratio is decreased for achieving higher frequency resonators. Obtained results reveal that the resonator could be utilized for ultra-low far-from-carrier phase noise oscillators.

Quality Factor Dependence on the Inactive Regions in AlN Contour-Mode Resonators

This paper investigates the dependence of the quality factor $({Q})$ of AlN contour mode resonators (CMRs) on the characteristics of the inactive regions located between the main resonator body (active region) and the stress-free surfaces placed beside the anchors. This paper shows that it is possible to reduce the energy leakage through the anchors by optimally sizing the width of such regions. To validate this concept, we built 16 different configurations of 225-MHz AlN CMRs, differing just by the size of the resonator inactive regions.

Reducing anchor loss In thin-film aluminum nitride-on-diamond contour mode MEMS resonators with support tethers based on phononic crystal strip and reflector

In this paper, we report on (1) the proposed support tether configuration based on phononic crystal (PnC) strip to reduce the anchor loss in the thin-film piezoelectric-on-diamond (TPoD) contour mode microelectromechanical systems (MEMS) resonators, namely the $$100^0$$1000 oriented thin-film aluminum nitride (AlN)-on-diamond wine glass (WG) and width shear (WS) mode MEMS resonators, (2) impacts of the geometrical dimensions on the band gaps of the proposed PnC structure, (3) evaluation of the performance of the Q improvement between the proposed support tether configuration and the one based on the reflector presented by B P Harrington and R Abdolvand. The designed resonators operate at approximately 115 and 156 MHz corresponding with the WG and WS modes. The band gap width covering these two operating frequencies is 30.2 and 20.6 MHz, respectively. The maximum Q of the WG mode resonator with five-unit cell PnC strip based support tethers achieves up to 398.5 % over that of the same resonator with reflector based support tethers. Similar to the WS mode one with three-unit cell PnC strip based support tethers, this Q is up to 591.1 %. The average Q of the WG mode resonator with PnC strip based support tethers over the maximum Q of the same one with different reflectors is enhanced about 964.4, 952.9, 364.2 and 4599.5 %. For the WS mode resonator, these Q values are up to 2388.8, 1830.4, 528.2 and 2384.5 %. The finite element (FE) analysis in COMSOL Multiphysics software (COMSOL) is utilized to simulate the proposed PnC strip as well as the WG and WS mode resonators.

Piezoelectric actuation of aluminum nitride contour mode optomechanical resonators.

We present a fully-integrated monolithic aluminum nitride optomechanical device in which lateral vibrations generated by a piezoelectric contour mode acoustic ring resonator are used to produce amplitude modulation of an optical signal in a whispering gallery mode photonic ring resonator. Acoustic and optical resonances are independently characterized in this contour mode optomechanical resonator (CMOMR). Electrically driven mechanical modes are optically detected at 35MHz, 654MHz and 884MHz.

Fourth-Order Contour Mode ZnO-on-SOI Disk Resonators for Mass Sensing Applications

In this work, we have investigated the design, fabrication and testing of ZnO-on-SOI fourth-order contour mode disk resonators for mass sensing applications. This study aims to unveil the possibility for real-time practical mass sensing applications by using high-Q ZnO-on-SOI contour-mode resonators while taking into account their unique modal characteristics. Through focused ion beam (FIB) direct-write metal deposition techniques, the effects of localized mass loading on the surface of three extensional mode devices have been investigated. Ten microfabricated 40 mm-radius disk resonators, which all have a 20 mm-thick silicon device layer and 1 mm-thick ZnO transducer layer but varied anchor widths and numbers, have exhibited resonant frequencies ranging from 84.9 MHz to 86.7 MHz with Q factors exceeding 6000 (in air) and 10,000 (in vacuum), respectively. It has been found that the added mass at the nodal locations leads to noticeable Q-factor degradation along with lower induced frequency drift, thereby resulting in reduced mass sensitivity. All three measured devices have shown a mass sensitivity of ~1.17 Hz·fg−1 at the maximum displacement points with less than 33.3 ppm of deviation in term of fractional frequency change. This mass sensitivity is significantly higher than 0.334 Hz·fg−1 at the nodal points. Moreover, the limit of detection (LOD) for this resonant mass sensor was determined to be 367 ag and 1290 ag (1 ag = 10−18 g) for loaded mass at the maximum and minimum displacement points, accordingly.

Anchor Losses in AlN Contour Mode Resonators

In this paper, we analyze possible sources of dissipation in aluminium nitride (AlN) contour mode resonators for three different resonance frequency devices (fr) (220 MHz, 370 MHz, and 1.05 GHz). For this purpose, anchors of different widths (W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ) and lengths (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> ) proportional to the acoustic wavelength (λ) are designed as supports for resonators in which the dimensions of the vibrating body are kept fixed. The Q extracted experimentally confirms that anchor losses are the dominant source of damping for most anchor designs when f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is equal to 220 and 370 MHz. For specific anchor dimensions (W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> /λ is in the range of 1/4-1/2) that mitigate energy leakage through the supports, a temperature-dependent dissipation mechanism dominates as seen in higher f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> resonators operating close to 1.05 GHz. To describe the Q due to anchor losses, we use a finite-element method with absorbing boundary conditions. We also propose a simple analytical formulation for describing the dependence of the temperature-dependent damping mechanism on frequency. In this way, we are able to quantitatively predict Q due to anchor losses and qualitatively describe the trends observed experimentally.

Design and Fabrication of S&lt;sub&gt;0&lt;/sub&gt; Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Commercial markets desire integrated multifrequency band-select duplexer and diplexer filters with a wide fractional bandwidth and steep roll-off to satisfy the ever-increasing demand for spectrum. In this paper, we discuss the fabrication and design of lithium niobate (LN) thin-film S0 Lamb-wave resonators on a piezoelectric-on-piezoelectric platform. Filters using these resonators have the potential to fulfill all the above requirements. In particular, we demonstrated one-port high-order S0 Lamb-wave resonators with resonant frequencies from $\sim 400$ MHz to $\sim 1$ GHz on a black rotated y-136 cut LN thin film. The effective electromechanical coupling factor ( $k_{eff}^{2}$ ) ranges from 7% to 12%, while the measured quality factor ranges from 600 to 3300. The highest $k_{eff}^{2} \times Q$ achieved on this chip is 194, significantly surpassing contour mode resonators manufactured in other technologies. [2014-0280]

Optimization of Piezoelectric Pattern Design in Ring-shaped Resonators for Health-care and Environmental Applications

A ring-shaped piezoelectric resonator was proposed for health monitoring. The proposed ring-shaped resonator is comprised with a multilayer of Pt/Ti/PZT/Ti/Pt/SiO2, deposited on the silicon-on-insulator wafer and expected to be a contour mode. The ring-shaped resonator reacts to certain voltage vibration with a mass perturbation to get eigenstate vibration or frequency shifts which could be transferred to electrical signals by piezoelectric effect. In this paper, vibration modes with high frequency shift due to a small mass perturbation of 0.74 ng are analyzed. It is found that the relatively lower displacement at the support can be obtained, and the desirable vibration can be reproduced with two eigenstate modes.

Finite Element Analysis of Influence of Nanoparticle on Hybrid Composites Reinforced by Fiber and Nanoparticle

In order to improve the strength and toughness of materials, nanoparticle is always embedded into epoxy resin and fiber composite materials. The influence of the number, distribution and mechanical property of nanoparticle arranged around the fiber on fiber reinforced composites is evaluated in this paper. A finite element analysis under a tensile load is performed by using commercial finite element software named as ABAQUS. Both the stress contour and progressive damage failure mode of the representative volume element (RVE) model of fiber reinforced composites are obtained. A series of computational experimental results indicate that both the space geometry property and mechanical property of nanoparticle have a significant effect on the stiffness and strength properties of these composite materials.

Modelling and Characterization of Planar Components

An approach for modeling and numerical simulation of planar components using the edge line concept is developed. With this method, we develop an efficient modeling technique for microstrip discontinuities. The structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included showing the efficiency of the new method proposed.

The use of 3D power Doppler ultrasound in the quantification of blood vessels in uterine fibroids: feasibility and reproducibility.

To evaluate the interobserver agreement and discriminating value of three-dimensional power Doppler ultrasound (3D PDUS) in patients with fibroids. An observational prospective cohort study in 19 patients with fibroids. 3D PDUS was performed by one examiner and evaluated by three independent examiners in order to evaluate various vascular parameters: vascular index (VI), flow index, and vascular flow index of the fibroid, the vascular capsule and of its highest vascular area, using both manual and automatic contour modes. The intraclass correlation coefficient and discriminating values were calculated. The correlation between VI and volume was studied using Kendall's Tau test. In the manual contour mode, the VIs of the fibroid and of the vascular capsule had the highest interobserver agreements (intraclass correlation coefficients of 0.89 and 0.87, respectively). Both parameters seem to have good discriminating values, given the large range of these parameters between different fibroids, independent of their volume. The vascularity of the fibroid and capsule was related. VI was not related to the volume of the fibroid. VI assessed using 3D PDUS is a reproducible parameter in the assessment of fibroid vascularization with discriminating abilities. Additional studies are needed to further evaluate its validity and clinical relevance.

Design of a novel MEMS resonator based neuromorphic oscillator

A novel MEMS based neuromorphic oscillator is presented. Due to compatibility with CMOS process, on-chip integration of electro-statically actuated microresonators is possible with very small size. Also, taking advantage of sacrificial sidewall spacer technique for fabrication of 100nm vertical gap, as low actuation voltages as 0.5V is enough for such resonators. Oscillatory neuron dynamics are also studied and design of the resonator and its characteristics are described as a neuromorphic oscillator. There are several practical barriers associated with MEMS implementation of neuromorphic oscillators such as existence of near-to-main mode spurious modes, requiring of UHF high gain trans-impedance amplifier because of very high motional resistance of such resonators, and automatic amplitude control circuit which all investigated in the paper and surmounted as well. A coupling technique for weak connection of such resonators is also described in the paper which allows mechanical low velocity connection of UHF contour mode disk resonators for the first time.