Influence of Fluid-Structure Interaction on Microcantilever Vibrations: Applications to Rheological Fluid Measurement and Chemical Detection

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include inplane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range

Effect of Hydrodynamic Force on Microcantilever Vibrations: Applications to Liquid-Phase Chemical Sensing

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include in-plane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no in-situ measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range

Theoretical Analysis of Torsionally Vibrating Microcantilevers for Chemical Sensor Applications in Viscous Liquids

Dynamically driven microcantilevers excited in the transverse (or out-of-plane) direction are widely used as highly sensitive chemical sensing platforms in various applications. While these devices work very well in air, their performance in liquids is not efficient because of the combination of increased viscous damping and effective fluid mass. In order to improve the characteristics of microcantilevers in liquid environments, some other vibration modes such as the torsional mode and lateral (or in-plane) flexural mode have been proposed.In this work, the characteristics of torsionally vibrating rectangular microcantilevers with length L, width b and thickness h in viscous liquids are investigated taking into account the thickness effects. Finite element models are used to obtain the hydrodynamic loading (torque per unit length) and thus calculate values of the hydrodynamic function. An analytical expression of the hydrodynamic function in terms of the Reynolds number and aspect ratio, h/b, is then obtained by fitting the numerical results. This allows for the characteristics to be investigated as a function of both beam geometry and fluid properties, considering thickness effects on the torsional constant, the hydrodynamic function and the polar moment of area. For high aspect ratios, (h/b\u3e0.16) microcantilevers vibrating in the 1st torsional mode, ignoring thickness effects could result in a minimum error of 9%, 5%, 20%, 7% for the resonance frequency, quality factor, mass sensitivity, and normalized mass limit of detection, respectively. Clearly, for many sensing applications based on analyzing the resonance frequency and mass sensitivity, thickness effects should be taken into account. The resonance frequency is found to be dependent on h/(bL) and the quality factor is found to be dependent on h/L1/2 for microcantilevers vibrating in the 1st torsional mode in viscous liquids. In comparison, for microcantilevers vibrating in the 1st lateral mode, the resonance frequency is dependent on b/L2 and the quality factor is dependent on hb1/2/L. Such different trends can be used to optimize device geometry and liquid property, thus maximizing quality factor and sensitivity in chemical sensing applications. Compared with microcantilevers in the 1st transverse mode, microcantilevers that vibrate in their first torsional mode have higher resonance frequency and quality factor. The increase in resonance frequency and quality factor results in higher sensitivity and reduced frequency noise, respectively. This will yield much lower limits of detection in liquid-phase chemical sensing applications

Analytical Modeling of a Novel Microdisk Resonator for Liquid-Phase Sensing: An All-Shear Interaction Device (ASID)

Extensive research on micro/nanomechanical resonators has been performed recently due to their potential to serve as ultra-sensitive devices in chemical/biosensing. These applications often necessitate liquid-phase sensing, introducing significant fluid-induced inertia and energy dissipation that reduces the resonator’s performance. To minimize the detrimental fluid effects on such devices, a novel microdisk resonator supported by two tangentially-oriented, axially-driven “legs” is investigated analytically and effects of the system parameters on the resonator/sensor performance are explored. Since the device surface vibrates primarily parallel to the fluid-structure interface, it is referred to here as an “all-shear interaction device,” or ASID. Analytical modeling of the ASID includes a single-degree-of-freedom model, in which the leg mass and associated fluid resistance are neglected relative to their disk counterparts, and a generalized continuous-system, multi-modal model, in which inertial and fluid effects are included for the entire structure. The resulting analytical formulae along with the parametric studies predict that ASID designs with slender legs yield a global maximum in the quality factor (Qmax) at a “critical” disk radius approximately twice the device thickness, whereas stiffer legs correspond to Qmax occurring for the axial-mode microcantilever (the no-disk limit of the ASID). Additionally, the highest mass and chemical sensitivities (Sm, Sc) and lowest mass limit of detection (LODm) of an ASID-based sensor correspond to the axial-mode microcantilever limit, whereas the chemical LOD (LODc) has a relative minimum at the critical disk size; thus, the “optimal-Q” disk size may be different than the “optimal-sensing” counterpart. The results also show that utilizing stiffer legs will improve Q, Sm, Sc, LODm, and LODc. The theoretical results show both qualitative and quantitative agreement with existing experimental data on liquid-phase quality factor in heptane and in water, while the corresponding theoretical predictions for the fluid-induced resonant frequency shift (typically \u3c 1%) indicate the effectiveness of this novel design. Moreover, the results suggest that appropriately designed ASIDs are capable of achieving unprecedented levels of liquid-phase quality factor in the 300-500 range or even higher. The new theoretical formulae also enable one to easily map experimental data on ASID performance in one liquid to behaviors in other media without performing additional experiments

A Geometrical Study on the Roof Tile-Shaped Modes in AlN-Based Piezoelectric Microcantilevers as Viscosity–Density Sensors

Cantilever resonators based on the roof tile-shaped modes have recently demonstrated their suitability for liquid media monitoring applications. The early studies have shown that certain combinations of dimensions and order of the mode can maximize the Q-factor, what might suggest a competition between two mechanisms of losses with different geometrical dependence. To provide more insight, a comprehensive study of the Q-factor and the resonant frequency of these modes in microcantilever resonators with lengths and widths between 250 and 3000 µm and thicknesses between 10 and 60 µm is presented. These modes can be efficiently excited by a thin piezoelectric AlN film and a properly designed top electrode layout. The electrical and optical characterization of the resonators are performed in liquid media and then their performance is evaluated in terms of quality factor and resonant frequency. A quality factor as high as 140 was measured in isopropanol for a 1000 × 900 × 10 µm3 cantilever oscillating in the 11th order roof tile-shaped mode at 4 MHz; density and viscosity resolutions of 10−6 g/mL and 10−4 mPa·s, respectively are estimated for a geometrically optimized cantilever resonating below 1 MH

Microcantilever: Dynamical Response for Mass Sensing and Fluid Characterization

A microcantilever is a suspended micro-scale beam structure supported at one end which can bend and/or vibrate when subjected to a load. Microcantilevers are one of the most fundamental miniaturized devices used in microelectromechanical systems and are ubiquitous in sensing, imaging, time reference, and biological/ biomedical applications. They are typically built using micro and nanofabrication techniques derived from the microelectronics industry and can involve microelectronics-related materials, polymeric materials, and biological materials. This work presents a comprehensive review of the rich dynamical response of a microcantilever and how it has been used for measuring the mass and rheological properties of Newtonian/non-Newtonian fluids in real time, in ever-decreasing space and time scales, and with unprecedented resolution

Dynamics of oscillating piezoelectric micro resonators : hydrodynamic loading effect and intrinsic damping

Micro resonators are important components in many micro electro mechanical system (MEMS) applications. The quality factor is a key parameter for MEMS resonators and is determined by the system damping of the devices. Aluminum nitride (AlN) based piezoelectric Si micro resonators with different geometries are fabricated and measured with an all-electrical excitation and detection method, to study the energy dissipation mechanisms. The dynamic behavior of these resonators is analyzed in gases as well as in high vacuum by developing and applying specific experimental, computational and analytical tools. We investigate the hydrodynamic loading in detail by exploring how factors, such as ambient pressure, the nature of the surrounding gas, the resonator geometry, higher mode operation and the presence of a nearby surface, effect the resonance behaviour of micro resonators. The resonator fluid interaction can be broadly divided into: i) resonators vibrating in an unbounded fluid, and ii) resonators vibrating close to a surface. For the first case, we systematically investigate the performance in different resonant modes. Incompressible flow is expected for the first few resonant modes. However, as the resonant mode number increases, the acoustic wavelength reduces and the energy loss is found to be diluted through mixing of viscous and acoustic effects. For the second case, most prior efforts to investigate this hydrodynamic loading have focused on squeeze film damping with very narrow gaps. In this research we investigate the case that a resonator vibrates close to a surface with a moderate distance. When a resonator is operated in high vacuum, intrinsic damping inside the solid materials dominates the quality factor. We focus on the three major intrinsic damping effects, which are thermoelastic damping (TED), anchor losses and coating losses. TED and anchor losses are investigated by using a combination of both analytical and numerical methods, while the coating loss mechanism is explored by measuring a series of cantilevers with a piezo-electrode stack coverage varying from 20%-100% of the beam length. Experimental validations are conducted on different structures of piezoelectric micro resonators, showing that the analysis yields qualitative matches with measurements and the contributions of the three mechanisms can be separated to a reasonable extent.Mikroresonatoren sind wichtige Komponenten in vielen Anwendungen der Mikrosystemtechnik. Der Gütefaktor ist ein Schlüsselparameter für MEMS-Resonatoren und wird durch die Systemdämpfung der Bauelemente bestimmt. Um die Mechanismen des Energieverlusts zu untersuchen, wurden piezoelektrische Si-Mikroresonatoren auf Basis von Aluminiumnitrid (AlN) mit unterschiedlichen Designs hergestellt und mit einem elektrischen Anregungs- und Detektionsverfahren charakterisiert. Experimentelle, theoretische und analytische Werkzeuge wurden entwickelt, um die Dynamik von piezoelektrischen Mikroresonatoren in Gasen sowie im Hochvakuum zu analysieren. Die hydrodynamischen Energieverluste wurden in Abhängigkeit von verschiedenen Faktoren, wie dem Umgebungsdruck, der Gasart, der Resonatorgeometrie, der Mode und dem Vorhandensein von nahegelegenen Oberflächen untersucht. Die Wechselwirkung zwischen Resonator und Fluid kann in zwei verschiedene Gruppen aufgeteilt werden. Zum einen das Schwingen von Resonatoren in einem unbegrenzten Fluid, zum anderem das Schwingen der Resonatoren in der Nähe einer benachbarten Oberfläche. Für den ersten Fall wurde das Verhalten in verschiedenen Resonanzmoden untersucht, wobei eine inkompressible Strömung für die niedrigeren Moden erwartet wird. Für höhere Moden reduziert sich jedoch die Schallwellenlänge und der Energieverlust kann durch ein Mischen von viskosen und akustischen Effekten beschrieben werden. Bezogen auf den zweiten Fall haben sich fast alle bisherigen Arbeiten auf die Squeeze-Film-Dämpfung in einem sehr engen Spalt fokussiert. Unsere Untersuchung konzentriert sich auf die Dämpfungseigenschaften von Resonatoren in der Nähe einer Oberfläche mit einem moderaten Spaltabstand. Wenn ein Resonator im Hochvakuum schwingt, dominiert die intrinsische Dämpfung im Festkörpermaterial den Gütefaktor. Die vorliegende Arbeit konzentriert sich auf die drei Hauptbeiträge zur intrinsischen Dämpfung, nämlich auf die thermoelastische Dämpfung (TED), den Ankerverlust und den Beschichtungsverlust. TED und Ankerverluste wurden durch die Verwendung einer Kombination von analytischen und numerischen Methoden untersucht. Der Verlustmechanismus durch Beschichtung mit dem AlN-Piezo-Stack wurde durch durch eine experimentelle Reihe von Resonatoren mit zwanzig- bis hundertprozentiger Schichtabdeckung bezogen auf die Resonatorlänge charakterisiert. Experimentelle Validierungen zeigen eine qualitative Übereinstimmung mit den simulierten bzw. analytischen Ergebnissen. Ferner können die Dämpfungsbeiträge der drei Mechanismen in nachvollziehbarer Weise qualitativ voneinander getrennt werden

Design of a tri-axial surface micromachined MEMS vibrating gyroscope

Gyroscopes are one of the next killer applications for the MEMS (Micro-Electro-Mechanical-Systems) sensors industry. Many mature applications have already been developed and produced in limited volumes for the automotive, consumer, industrial, medical, and military markets. Plenty of high-volume applications, over 100 million per year, have been calling for low-cost gyroscopes. Bulk silicon is a promising candidate for low-cost gyroscopes due to its large scale availability and maturity of its manufacturing industry. Nevertheless, it is not suitable for a real monolithic IC integration and requires a dedicated packaging. New designs are supposed to eliminate the need for magnets and metal case package, and allow for a real monolithic MEMS-IC (Integrated Circuit) electronic system. In addition, a drastic cost reduction could be achieved by utilizing off-the-shelf plastic packaging with lead frames for the final assembly. The present paper puts forward the design of a novel tri-axial gyroscope based on rotating comb-drives acting as both capacitive sensors and actuators. The comb-drives are comprised of a single monolithic moving component (rotor) and fixed parts (stators). The former is made out of different concentrated masses connected by curved silicon beams in order to decouple the motion signals. The sensor was devised to be fabricated through the PolyMUMPs® process and it is intended for working in air in order to semplify the MEMS-IC monolithic integration

Theoretical Analysis of Laterally Vibrating Microcantilever Sensors in a Viscous Liquid Medium

Dynamically driven microcantilevers are normally excited into resonance in the out-of-plane flexural mode. The beam\u27s resonant frequency and quality factor are used to characterize the devices. The devices are well suited for operation in air, but are limited in viscous liquid media due to the increased viscous damping. In order to improve these characteristics, other vibration modes such as the in-plane (or lateral) flexural mode are investigated. In this work, microcantilevers vibrating in the in-plane flexural mode (or lateral direction) in a viscous liquid medium are investigated. The hydrodynamic forces on the microcantilever as a function of both Reynolds number and aspect ratio (thickness over width) are first calculated using a combination of numerical methods and Stokes\u27 solution. The results allowed for the resonant frequency, quality factor, and mass sensitivity to be investigated as a function of both beam geometry and medium properties. The predicted resonant frequency and quality factor for several different laterally vibrating beams in water are also found to match the trends given by experimentally determined values found in the literature. The results show a significant improvement over those of similar devices vibrating in the out-of-plane flexural mode. The resonant frequency increases by a factor proportional to the inverse of the beam\u27s aspect ratio. Moreover, the resonant frequency of a laterally vibrating beam shows a smaller decrease when immersed in water (5-10% compared to ~50% for transversely vibrating beams) and, as the viscosity increases, the resonant frequency decreases slower compared to beams excited transversely. The quality factor is found to increase by a factor of 2-4 or higher depending on the medium of operation and the beam geometry. Due to the increased resonant frequency and the decreased effective mass of the beam (compared to beams excited transversely), the estimated mass sensitivity of a laterally excited microcantilever is found to be much larger (up to two orders of magnitude). The improvement in these characteristics is expected to yield much lower limits of detection in liquid-phase bio-chemical sensing applications

Development and experimental analysis of a micromachined Resonant Gyrocope

This thesis is concerned with the development and experimental analysis of a resonant gyroscope. Initially, this involved the development of a fabrication process suitable for the construction of metallic microstructures, employing a combination of nickel electroforming and sacrificial layer techniques to realise free-standing and self-supporting mechanical elements. This was undertaken and achieved. Simple beam elements of typically 2.7mm x 1mm x 40µm dimensions have been constructed and subject to analysis using laser doppler interferometry. This analysis tool was used to implement a fill modal analysis in order to experimentally derive dynamic parameters. The characteristic resonance frequencies of these cantilevers have been measured, with 3.14kHz, 23.79kHz, 37.94kHz and 71.22kHz being the typical frequencies of the first four resonant modes. Q-factors of 912, 532, 1490 and 752 have been measured for these modes respectively at 0.01mbar ambient pressure. Additionally the mode shapes of each resonance was derived experimentally and found to be in excellent agreement with finite element predictions. A 4mm nickel ring gyroscope structure has been constructed and analysed using both optical analysis tools and electrical techniques. Using laser doppler interferometry the first four out-of-plane modes of the ring structure were found to be typically 9.893 kHz, 11.349 kHz, 11.418 kHz and 13.904 kHz with respective Q-factors of 1151, 1659, 1573 and 1407 at 0.01 mbar ambient pressure. Although electrical measurements were found to be obscured through cross coupling between drive and detection circuitry, the in-plane operational modes of the gyroscope were sucessfully determined. The Cos2Ө and Sin2Ө operational modes were measured at 36.141 kHz and 36.346 kHz, highlighting a frequency split of 205kHz. Again all experimentally derived modal parameters were in good agreement with finite element predictions. Furthermore, using the analysis model, the angular resolution of the gyroscope has been predicted to be approximately 4.75º/s