University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

We present studies on squeeze film effects in dynamic MEMS devices with a special emphasis on the development of compact analytical models. First, the efficacy of lumped parameter modelling of dynamic MEMS devices is illustrated in MATLAB/SIMULINK software environment using a MEMS gyroscope and a MEMS microphone as examples. This is followed by a comparative study of equivalent electrical circuit models for a MEMS microphone wherein the importance of accurate extraction of lumped mass, stiffness and damping is brought into focus. In this context, a need for an in depth study of squeeze film behaviour in MEMS structures is highlighted and a strong motivation is drawn for the development of compact squeeze film models. A 2D analytical model for estimating squeeze film damping and spring force in perforated MEMS structures is presented. The governing equations based on isothermal compressible Reynolds equation are derived by considering an approximate circular pressure cell around a hole which is representative of the spatially invariant pressure pattern over the interior of the flow domain. The advantages and limitations of the solution are discussed with relevance to MEMS structures. Next, a comprehensive analytical model for 3D MEMS structures that includes effects of compressibility, inertia, and rarefaction in the flow between two parallel plates forming the squeeze region as well as the flow through perforations is developed. A modified Reynolds equation that includes the unsteady inertial term is derived from the Navier-Stokes equation to model the flow in the circular cell and the losses through the holes are modelled using Poiseuille flow. Rarefaction effects in the flow through the air-gap as well as the holes are accounted for by considering the slip boundary conditions. The analytical results are compared with extensive numerical simulations carried out using full 3-D Navier-Stokes equation solver in a commercial simulation package (ANSYS-CFX). We show that the analytical solution performs very well in tracking the net force up to the first resonant frequency of the entrapped air.

Micromachined biosensors are used in chemical and biological applications. A biosensor which uses mass based transduction is called a mass sensor. Mass sensors are used to detect extremely small mass of biomolecules such as proteins, viruses or even parts of DNA in the range of femtograms (10-15 gm) to zeptograms (10−21 gm). Highly effective and reliable microcantilevers are used for detecting the mass of biomolecules using either static deflection or dynamic resonant peak shifts. The main objective of our work is to investigate the effect of elasticity of the attached mass on the shift in the resonant frequency and examine the validity of the rigid mass assumption used in the literature. The natural frequencies of a resonator are either found by solving the governing differential equation or approximately using Rayleigh-Ritz method. The mass of a body, attached to a resonator beam is determined using resonant frequency shift method. In our study, we derive an analytical expression for ‘δm’ based on the shift in frequency ‘δf’ that accounts for the elasticity of the added mass and the location of the mass on the beam. We study the simplest model to incorporate these effects where the added mass is itself modeled as a single degree of freedom spring-mass system. The entire system is represented as a 2-DOF lumped model of cantilever and the attached elastic mass. The natural frequencies are obtained using eigenvalue analysis. We study the mass estimation of Escherichia Coli (E. Coli), a food borne pathogen, using experimental results reported in the literature. We treat E.Coli as an elastic mass and model it as a single degree of freedom system to account for its elasticity. We use the elastic model as well as the rigid mass model to check the results available in the literature and point out the difference that results in mass estimation using the two models. To demonstrate the effect of elasticity on mass sensing using the resonant peak shift technique, we conduct mesoscale experiments. Since the fundamental principle does not depend on any phenomenon exclusively dependent on micro scales, the mesoscale experiments are justified. For this purpose, an experimental set-up with metallic cantilevers and flexible rubber strands as attached masses are used. We also use our experimental set-up to study the effect of positional inaccuracy of the added mass (rigid) in the computation of its mass from the shift in the resonance frequency. The results obtained show that elasticity of the added mass as well as its position on the resonator affect the computed mass but this effect is dependent on the relative stiffness and mass of the resonator and the added mass. We also observe the limitations of the experiments in carrying out studies over the desired range of parameters. We also create a computational model of the system and carry out simulations to explore a larger range of parameter values. In particular, we create an FEM model of our system in ANSYS, and carry out modal analysis for the cantilever beam resonator with and without the added mass, varying the relative stiffness and mass of the two components (the cantilever beam and the added mass). We compare the results of shift in the resonant frequency with those obtained from the rigid mass model. The results show the effect of elasticity clearly in certain ranges of relative stiffness and mass.

There are many ways in which the surrounding media, such as air between an oscillating MEMS structure and a fixed substrate, can affect the dynamic response of a MEMS transducer. Some of these effects involve dissipation while others involve energy transfer. Transverse oscillations of a planar structure can cause a lateral air flow in small gaps that results in pressure gradients. The forces due to the built–up pressure are always against the vibration of the structure and have characteristics of damper and stiffener. In this work, we study the squeeze film phenomenon due to the interaction between the air–film and the structure in the presence of restrictive flow boundary conditions. It is known that the squeeze film damping due to the air trapped between the oscillating MEMS structure and the fixed substrate often contributes to maximum energy dissipation. We carry out an analysis to estimate damping and stiffness in cases with restrictive flow boundaries in dynamic MEMS devices. While the studies reported in the present work address fluid flow damping with restrictive flow boundaries, the analysis of air-flow shows another important phenomenon of enhanced air-spring stiffness. This study is discussed separately in the context of spring stiffening behavior in MEMS devices exhibiting squeeze film phenomenon. First a theoretical framework for modeling squeeze film flow is established and this is followed with analytical and numerical solutions of problems involving squeeze film phenomenon. Modeling of squeeze film effects under different flow conditions is carried out using Reynold’s equation. The problem of squeeze film damping in MEMS transducers is more involved due to the complexities arising from different boundary conditions of the fluid flow. In particular, we focus our attention on estimation of damping in restricted flow boundaries such as only one side vented and no side vented passive boundary conditions. Damping coefficient for these cases are extracted when the fluid is subjected to an input velocity profile according to a specific mode shape at a given frequency of oscillation. We also explain the squeeze film flow in restricted boundaries by introducing the concept of passive and active boundary conditions and analyzing the pressure gradients which are related to the compressibility of the air in the cavity. Passive boundary conditions is imposed by specifying the free flow or no flow along one of the edges of the cavity, whereas, active boundary condition is imposed by the velocity profile being specified at the interface of the cavity with the oscillating structure. Some micromechanical structures, such as pressure sensors and ultrasound transducers use fully restricted or closed boundaries where the damping for such cases, even if small, is very important for the determination of the Q–factor of these devices. Our goal here is to understand damping due to flow in such constrained spaces. Using computational fluid dynamics (ANSYS–FLOTRAN), the case of fully restricted boundaries is studied in detail to study the effect of important parameters which determines the fluid damping, such as flow length of the cavity, air–gap height, frequency of oscillations and the operating pressure in the cavity. A simulation strategy is developed using macros programming which overcomes some of the limitations of the existing techniques and proves useful in imposing a non–uniform velocity and the extraction of damping coefficient corresponding to the flexibility of the structure in specific oscillation modes. Rarefaction effects are also accounted for in the FEM model by introducing the flow rate coefficient, or, alternatively using the concept of effective viscosity. The analysis carried out for the fully restricted case is motivated by the analytical modeling of squeeze film phenomenon for a wide range of different restricted boundaries, and analyzing the resulting pressure gradient patterns. We show that significant damping exists even in fully restricted boundaries due to lateral viscous flow. This is contrary to known reported results, which neglect damping in such cases. The result indicates that in fully restrictive fluid flow boundaries or in a closed cavity, air damping cannot be neglected at lower oscillation frequencies and large flow length to air-gap ratio if the active boundary has a non-uniform velocity profile. Analysis of air-flow in the case of restricted flow boundaries shows another important phenomenon of enhanced air-spring stiffness. It is found that fluid film stiffness has a nonlinear dependence on various parameters such as air-gap to length ratio, fluid flow boundary conditions and the frequency of oscillation. We carry out analysis to obtain the dynamic response of MEMS devices where it is significantly affected by the frequency dependent stiffness component of the squeeze film. We show these effects by introducing frequency dependent stiffness in the equation of motion, and taking examples of fluid boundary conditions with varying restriction on flow conditions. The stiffness interaction between the fluid and the structure is shown to depend critically on stiffness ratios, and the cut-off frequency. It is also inferred that for a given air–gap to flow length ratio, the spring behaviour of the air is independent of the flow boundary conditions at very high oscillation frequencies. Hence, we limit our focus on studying the effect of fluid stiffness in the regime where it is not fully compressible. For non-resonant devices, this study finds its utility in tuning the operating frequency range while for resonant devices it can be useful to predict the exact response. We show that it is possible to design or tune the operating frequency range or shift the resonance of the system by appropriate selection of the fluid flow boundary conditions. The emphasis of the present work has been toward studying the effect of squeeze film flow on dynamic response of MEMS structures with restrictive flow boundary conditions. Estimation of energy dissipation due to viscous flow cannot be ignored in the design of MEMS which comprise of restricted flow boundaries. We also remark that modeling of a system with squeeze film flow of the trapped air in terms of frequency independent parameters, viz. damping and stiffness coefficient, is unlikely to be very accurate and may be of limited utility in specific cases. Although the central interest in studying squeeze film phenomenon is on the damping characteristics because of their direct bearing on energy dissipation or Q–factor of a MEMS device, the elastic behaviour of the film also deserves attention while considering restrictive flow boundary conditions.

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In this thesis, we have designed and optimized strip waveguide based micro-ring and micro-ring and micro-racetrack resonators for biosensing applications. Silicon-On-Insulator (SOI) platform which offers several advantages over other materials such as Lithium Niobate, Silica on Silicon and Silicon nitride is considered here. High index contrast enables us to miniaturize the biosensor devices and monolithic integration of source and detectors on the same chip. We have considered the dispersive nature of the waveguide and proceeded towards optimization. Finite difference schemes and Finite Difference Time Domain (FDTD) methods are the primary tools used to model the biosensor. Various structures such as channel waveguides and beam structures are analyzed on the basis of their suitability for sensing applications. Strip and Rib waveguides are the two geometries considered in our studies. In an optical guiding structure, effective index of the propagating optical mode can be induced by two different phenomena: i. Homogeneous Sensing In this category, effective index of a propagating optical mode changes with uniformly distributed analytes extending over a distance well exceeding the evanescent field penetration depth. The sample serves as the waveguide cover. ii. Surface Sensing In the case of surface sensing, analytes bound to the surface of the waveguide. The effective index of an optical mode changes with the refractive index as well as the thickness of an adlayer. A thin layer of adsorbed or bound molecules transported from liquid or gaseous medium serving as waveguide cover is referred as an adlayer. Both homogeneous and surface sensing schemes are addresses in this work. By bulk sensing method, the characteristics of bioclad covering the device are studied. Optimization of the resonator structure involves the analysis of following parameters: • Gap between the ring and bus waveguides • Free spectral range • Extinction ratio • Quality factor We have achieved a maximum bulk sensitivity of 115 nm / RIU with ring waveguide width of 450 nm and bus width of 350 nm which is better than an earlier reported value of 70 nm/ RIU. We have proposed a novel detection scheme consisting of a micro-racetrack resonator formed over a cantilever structure. The devoice works on the principle of opto-mechanical coupling to detect conformational changes due to biomolecular adherence. BSA (Bovine Serum Albumin) and IgG ( Immuno Globulin G) are the two proteins considered in the work. Mechanical analysis of the beam for tensile and compressive stresses and corresponding spectral responses of the racetrack resonators are analyzed both by semi-analytical and method and numerical analyzes. We compared various aspects of rib and strip waveguide racetrack resonators. We have proved by numerical simulation, that the device is capable of distinguishing tensile and compressive stress. Two strip waveguides of dimensions : 450 nm X 220 nm and 400 nm X 180 nm, former supporting both Quasi-TE and Quasi-TM modes where as the second configuration allows only Quasi-TE mode alone. Sensitivity of the cantilever sensor is : 0.3196 x 10-3 nm/ µɛ at 1550 nm wavelength.