On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

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.

Methods for enhanced electrical transduction and characterization of micromechanical resonators

This paper details the design and enhanced electrical transduction of a bulk acoustic mode resonator fabricated in a commercial foundry MEMS process utilizing 2.5 μm gaps. The I-V characteristics of electrically addressed silicon resonators are often dominated by capacitive parasitics, inherent to hybrid technologies. This paper benchmarks a variety of drive and detection principles for electrostatically driven square-extensional mode resonators operating in air via analytical models accompanied by measurements of fabricated devices with the primary aim of enhancing the ratio of the motional to feedthrough current at nominal operating voltages. In view of ultimately enhancing the motional to feedthrough current ratio, a new detection technique that combines second harmonic capacitive actuation and piezoresistive detection is presented herein. This new method is shown to outperform previously reported methods utilizing voltages as low as ±3 V in air, providing a promising solution for low voltage CMOS-MEMS integration. To elucidate the basis of this improvement in signal output from measured devices, an approximate analytical model for piezoresistive sensing specific to the resonator topology reported here is also developed and presented. © 2010 Elsevier B.V. All rights reserved.

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.

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.

Disentangling mechanical and mass effects on nanomechanical resonators

Micro and nanomechanical resonators are powerful and label-free sensors of analytes in various environments. Their response, however, is a convolution of mass, rigidity, and nanoscale heterogeneity of adsorbates. Here we demonstrate a procedure to disentangle this complex sensor response, to simultaneously measure both mass and elastic properties of nanometer thick samples. This turns an apparent disadvantage of these resonators into a striking and unique asset, enabling them to measure more than mass alone.

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.

Simulation and fabrication of the SiC-based clamped-clamped filter

In this paper, the SiC-based clamped-clamped filter was designed and fabricated. The filter was composed of two clamped-clamped beam micromechanical resonators coupled by a spring coupling beam. Structural geometries, including the length and width of the resonator beam and coupling beam, were optimized by simulation for high frequency and high Q, under the material properties of SiC. The vibrating modes for the designed filter structure were analyzed by finite element analysis (FEA) method. For the optimized structure, the geometries of resonator beams and coupling beams, as well as the coupling position, the SiC-based clamped-clamped filter was fabricated by surface micromaching technology.

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. © 2014 IOP Publishing Ltd.

In-situ Boron-doped Low-stress LPCVD Polysilicon for Micromechanical Disk Resonator

Polycrystalline silicon (polysilicon) has been used as an important structural material for microelectro-mechnical systems (MEMS) because of its compatibility with standard integrated circuit (IC) processes. As the structural layer of micromechanical high resonance frequency (high-f) and high quality factor (high-Q) disk resonators, the low residual stress and low resistivity are desired for the polysilicon thin films. In the present work, we investigate the effect of deposition and annealing conditions on the residual stress and resistivity for in-situ deposited low pressure chemical vapor deposition (LPCVD) polysilicon films. Low residual stress (-100 MPa) was achieved in in-situ boron-doped polysilicon films deposited at 570 degrees C and annealed at 1000 degrees C for 4 hr. The as-deposited amorphous polysilicon films were crystallized by the rapid thermal annealing and have the (111)-preferred orientation, the low tensile residual stress is expected for this annealed film, the detailed description on this work will be reported soon. The controllable residual stress and resistivity make these films suitable for high-Q and bigh-f micro-mechanical disk resonators.

Yielding of sensitive clays: micromechanical considerations

Test results reported on several natural sensitive soils show significant anisotropy of the yield curves, which are generally oriented along the coefficient of earth pressure at rest (K-0) axis. An attempt is made in this paper to explain the anisotropy in yielding from microstructural considerations. An elliptic pore, with particle domains aligned along the periphery of the pore, and with the major axis of the pore being oriented along the direction of the in situ major principal stress, is chosen as the unit of microstructure. An analysis of forces at the interdomain contacts around the ellipse is carried out with reference to experimentally determined yield stress conditions of one soil, and a yield criteria is defined. The analysis, with the proposed yield criteria, enables one to define the complete yield curve for any other soil from the results of only two tests (one constant eta compression test with eta close to eta(K?0), where eta is the stress ratio (= q/p) and eta(K?0) is the stress ratio corresponding to anisotropic K-0 compression, and another undrained shear test). Predicted yield curves are compared with experimental yield curves of several soils reported in the literature.

Effect of metal coating and residual stress on the resonant frequency of MEMS resonators

MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant frequency of the final fabricated structure can be a denting factor for its suitability towards a desired application. There are numerous factors which alter the designed resonant frequency of the fabricated resonator such as the metal layer deposited on top of the beam and the residual stresses present in the fabricated structure. While the metal coating, which acts as electrode, increases the stiffness and the effective mass of the composite structure, the residual stress increases or decreases the net stiffness if it is a tensile or compressive type respectively. In this paper, we investigate both these cases by taking two different structures, namely, the micro cantilever beam with gold layer deposited on its top surface and the MEMS gyroscope with residual stresses. First, we carry out experiments to characterize both these structures to find their resonant frequencies. Later, we analytically model those effects and compare them with the experimentally obtained values. Finally, it is found that the analytical models give an error of less than 10% with respect to the experimental results in both the cases.

Ring Resonators and Micro Fluidics: Novel Design for Drug/Disease Detection

MEMS systems are technologically developed from integrated circuit industry to create miniature sensors and actuators. Originally these semiconductor processes and materials were used to build electrical and mechanical systems, but expanded to include biological, optical fluidic magnetic and other systems 12]. Here a novel approach is suggested where in two different fields are integrated via moems, micro fluidics and ring resonators. It is well known at any preliminary stage of disease onset, many physiological changes occur in the body fluids like saliva, blood, urine etc. The drawback till now was that current calibrations are not sensitive enough to detect the minor physiological changes. This is overcome using optical detector techniques 1]. The basic concepts of ring resonators, with slight variations can be used for optical detection of these minute disease markers. A well known fact of ring resonators is that a change in refractive index will trigger a shift in the resonant wavelength 5]. The trigger for the wavelength shift in the case discussed will be the presence of disease agents. To trap the disease agents specific antibody has to be used (e. g. BSA).