New Formulation for Finite Element Modeling Electrostatically DrivenMicroelectromechanical Systems

The increased complexity and precision requirements of microelectromechanical systems(MEMS) have brought about the need to develop more reliable and accurate MEMS simulation tools. To better capture the physical behavior encountered, several finite elementanalysis techniques for modeling electrostatic and structural coupling in MEMS devices havebeen developed in this project. Using the principle of virtual work and an approximationfor capacitance, a new 2-D lumped transducer element for the static analysis of MEMS hasbeen developed. This new transducer element is compatible to 2-D structural and beamelements. A novel strongly coupled 3-D transducer formulation has also been developed tomodel MEMS devices with dominant fringing electrostatic fields. The transducer is compatible with both structural and electrostatic solid elements, which allows for modeling complexdevices. Through innovative internal morphing capabilities and exact element integrationthe 3-D transducer element is one of the most powerful coupled field FE analysis tools available. To verify the accuracy and effectiveness of both the 2-D and 3-D transducer elements a series of benchmark analyses were conducted. More specifically, the numerically predicted results for the misalignment of lateral combdrive fingers were compared to available analytical and modeling techniques. Electrostatic uncoupled 2-D and 3-D finite element models werealso used to perform energy computations during misalignment. Finally, a stability analysisof misaligned combdrive was performed using a coupled 2-D finite element approach. Theanalytical and numerical results were compared and found to vary due to fringing fields

Modeling the effect of microstructure on the coupled torsion/bending instability of rotational nano-mirror in Casimir regime

t has been well-established that the physical performance of nano-devices might be affected by the microstructure. Herein, a 2-degree-of-freedom model based on the modified couple stress elasticity is developed to incorporate the impact of microstructure in the torsion/bending coupled instability of rotational nano-electromechanical mirror. The governing equation of the mirror is derived incorporating the effects of electrostatic Coulomb and corrected Casimir forces with the consideration of the finite conductivity of interacting surfaces. Effect of microstructure-dependency on the instability parameters are determined as a function of the microstructure parameter, bending/torsion coupling ratio, vacuum fluctuation parameter and geometrical dimensions. It is found that the bending/torsion coupling substantially affects the stable behavior of the mirrors especially those with long rotational beam elements. Depending on the geometry and material characteristics, the presented model is able to simulate both hardening behavior (due to microstructure) and softening behavior (due to torsion/bending coupling) of the nano-mirror

Compliant Torsional Micromirrors with Electrostatic Actuation

Due to the existence of fabrication tolerance, property drift and structural stiction in MEMS (Micro Electro Mechanical Systems), characterization of their performances through modeling, simulation and testing is essential in research and development. Due to the microscale dimensions, MEMS are more susceptible and sensitive to even minor external or internal variations. Moreover, due to the current limited capability in micro-assembly, most MEMS devices are fabricated as a single integrated micro-mechanical structure composed of two essential parts, namely, mass and spring, even if it may consist of more than one relatively movable part. And in such a scale of dimensions, low resonant micro-structures or compliant MEMS structures are hard to achieve and difficult to survive. Another problem arises from the limited visibility and accessibility necessary for characterization. Both of these issues are thus attempted in this research work. An investigation on micromirrors with various actuations and suspensions is carried out, with more attention on the micromirrors with compliant suspensions, electrostatic actuation and capable of torsional out-of-plane motion due to their distinct advantages such as the low resonance and the low drive voltage. This investigation presents many feasible modeling methods for prediction and analysis, aiming to avoid the costly microfabrication. Furthermore, both linear and nonlinear methods for structure and electrostatics are all included. Thus, static and dynamic performances of the proposed models are formularized and compared with those from FEA (Finite Element Analysis) simulation. The nonlinear modeling methods included in the thesis are Pseudo Rigid Body Model (PRBM) and hybrid PRBM methods for complex framed microstructures consisting of compliant beam members. The micromachining technologies available for the desired micromirrors are reviewed and an SOI wafer based micromachining process is selected for their fabrication. Though the fabrication was executed outside of the institution at that time, the layout designs of the micro-chips for manufacture have included all related rules or factors, and the results have also demonstrated the successful fabrication. Then investigation on non-contact test methods is presented. Laser Doppler Vibrometer (LDV) is utilized for the measurement of dynamic performances of proposed micromirrors. Two kinds of photo-sensing devices (PSDs), namely, the digitized PSD formed by CCD arrays and the analog PSD composed of a monolithic photosensing cell, are used for static test set-ups. An interferometric method using Mirau objective along with microscope is also employed to perform static tests of the selected micromirrors. Comparison of the tested results and their related theoretical results are presented and discussed, leading to a conclusion that the proposed hybrid PRBM model are appropriate for prediction or analysis of compliantly suspended micromirrors including issues arising from fabrication tolerance, structural or other parametric variations

Computational Analysis of Input-Shaping Control of Microelectromechanical Mirrors

Advances in micromachining technology have enabled the design and development of high performance microelectromechanical systems (MEMS). There is a pressing need for control techniques that can be used to improve the dynamic behavior of MEMS such as the response speed and precision. In MEMS applications, open-loop control is attractive as it computes a priori the required system input to achieve desired dynamic behavior without using feedback, thus eliminating the problems associated with closed-loop MEMS control. While the input-shaping control is attractive due to its simplicity, the effectiveness of this control approach depends on the accuracy of the model that is used to compute the input voltage. Accurate modeling of MEMS dynamics is critical in the input-shaping process. Input-shaping MEMS control algorithms based on analytical lumped models have been proposed. It has been shown that step-shaped input voltages can be used to control the structural vibration of MEMS. However, several questions remain to be answered: (1) What are the effects of the higher vibrational modes on the input-shaping control of MEMS? (2) Can the input-shaping technique be improved to control these effects? In this work, a full 3-D computational code is developed for coupled electromechanical simulation and analysis of electrostatically actuated MEMS. The effect of higher vibrational modes on the input-shaping control of electrostatic micromirros is investigated. We show that, depending on the design of the micromirros, the bending mode of the micromirror structures can have significant effect on the dynamic behavior of the system, which is difficult to suppress by using the step-voltage open-loop control. We employ a numerical optimization procedure to shape the input voltage from the real time dynamic response of the mirror structures. The optimization procedure results in a periodic nonlinear input voltage design that can effectively suppress the bending mode effect

DESIGN AND FABRICATION OF MEMS ELECTROSTATIC ACTUATORS

The research presented in this thesis is focused on the design and development of MEMS (Micro Electro Mechanical System) electrostatic actuators. Different kinds of electrostatic actuators are analyzed and presented . The study of torsional electrostatic actuator is carried out and the design of an micromirrors array for beam steering optical switching in a thick polysilicon technology is presented. The main advantage of these devices is that they are realized in a commercial surface micromachining technology (THELMA by STMicrolectronics) hence they are less expensive with respect to other solutions present in literature. For the torsional actuators, a novel semi-analytical model which allows prediction of the behaviour of the structures and takes into account the flexural deformation of the structure is presented. A very good agreement between the model, FEM simulation and experimental results has been obtained. The possibility of using another competitive surface micromachining technology (developed at IMEC) which uses poly silicon germanium as structural layer to realize the micromirrors is also investigated. Poly Silicon Germanium has the advantage that can be integrated on top of commercial CMOS. The development of optimized (low stressed) layers of poly silicon germanium has been addressed and some test micromirrors using this technology have been designed. Moreover an analysis of the levitation effect in electrostatic comb fingers atcuators is presented. The use of this actuation for vertical or torsional motion of micromachined structures is exploited. Two different levitational mechanical resonators have been designed and fabricated in THELMA. Because of the high thickness of the structural layer, classic springs shows several limitation, so specifically designed suspension springs (rotated serpentines), with better performance for high thickness, have been used. A full analysis of this kind of spring and a comparison with other springs are also presented. Finally a study of the dependence of the levitation force intensity on the geometric parameters of the actuators is performed using FEM simulations, and information about critical geometrical parameters in the design of operative levitational actuators is obtained. The devices are characterized and the obtained results are compared with FEM simulations

Applications of programmable MEMS micromirrors in laser systems

The use of optical microelectromechanical systems (MEMS) as enabling devices has been shown widely over the last decades, creating miniaturisation possibilities and added functionality for photonic systems. In the work presented in this thesis angular vertical offset comb-drive (AVC) actuated scanning micromirrors, and their use as intracavity active Q-switch elements in solid-state laser systems, are investigated. The AVC scanning micromirrors are created through a multi-user fabrication process, with theoretical and experimental investigations undertaken on the influence of the AVC initial conditions on the scanning micromirror dynamic resonant tilt movement behaviour. A novel actuator geometry is presented to experimentally investigate this influence, allowing a continuous variation of the initial AVC comb-offset angle through an integrated electrothermal actuator. The experimentally observed changes of the resonant movement with varying initial AVC offset are compared with an analytical model, simulating this varying resonant movement behaviour. In the second part of this work AVC scanning micromirrors are implemented as active intra-cavity Q-switch elements of a Nd:YAG solid-state laser system. The feasibility of achieving pulsed laser outputs with pulse durations limited by the laser cavity and not the MEMS Q-switch is shown, combined with a novel theoretical model for the Q-switch behaviour of the laser when using a bi-directional intra-cavity scanning micromirror. A detailed experimental investigation of the pulsed laser output behaviour for varying laser cavity geometries is presented, also discussing the influence of thin film coatings deposited on the mirror surfaces for further laser output power scaling. The MEMS Q-switch system is furthermore expanded using a micromirror array to create a novel Q-switched laser system with multiple individual controllable output beams using a common solid-state gain medium. Experimental results showing the simultaneous generation of two laser outputs are presented, with cavity limited pulse durations and excellent laser beam quality.The use of optical microelectromechanical systems (MEMS) as enabling devices has been shown widely over the last decades, creating miniaturisation possibilities and added functionality for photonic systems. In the work presented in this thesis angular vertical offset comb-drive (AVC) actuated scanning micromirrors, and their use as intracavity active Q-switch elements in solid-state laser systems, are investigated. The AVC scanning micromirrors are created through a multi-user fabrication process, with theoretical and experimental investigations undertaken on the influence of the AVC initial conditions on the scanning micromirror dynamic resonant tilt movement behaviour. A novel actuator geometry is presented to experimentally investigate this influence, allowing a continuous variation of the initial AVC comb-offset angle through an integrated electrothermal actuator. The experimentally observed changes of the resonant movement with varying initial AVC offset are compared with an analytical model, simulating this varying resonant movement behaviour. In the second part of this work AVC scanning micromirrors are implemented as active intra-cavity Q-switch elements of a Nd:YAG solid-state laser system. The feasibility of achieving pulsed laser outputs with pulse durations limited by the laser cavity and not the MEMS Q-switch is shown, combined with a novel theoretical model for the Q-switch behaviour of the laser when using a bi-directional intra-cavity scanning micromirror. A detailed experimental investigation of the pulsed laser output behaviour for varying laser cavity geometries is presented, also discussing the influence of thin film coatings deposited on the mirror surfaces for further laser output power scaling. The MEMS Q-switch system is furthermore expanded using a micromirror array to create a novel Q-switched laser system with multiple individual controllable output beams using a common solid-state gain medium. Experimental results showing the simultaneous generation of two laser outputs are presented, with cavity limited pulse durations and excellent laser beam quality

MEMS Actuation and Self-Assembly Applied to RF and Optical Devices

The focus of this work involves optical and RF (radio frequency) applications of novel microactuation and self-assembly techniques in MEMS (Microelectromechanical systems). The scaling of physical forces into the micro domain is favorably used to design several types of actuators that can provide large forces and large static displacements at low operation voltages. A self-assembly method based on thermally induced localized plastic deformation of microstructures has been developed to obtain truly three-dimensional structures from a planar fabrication process. RF applications include variable discrete components such as capacitors and inductors as well as tunable coupling circuits. Optical applications include scanning micromirrors with large scan angles (>90 degrees), low operation voltages (<10 Volts), and multiple degrees of freedom. One and two-dimensional periodic structures with variable periods and orientations (with respect to an incident wave) are investigated as well, and analyzed using optical phased array concepts. Throughout the research, permanent tuning via plastic deformation and power-off latching techniques are used in order to demonstrate that the optical and RF devices can exhibit zero quiescent power consumption once their geometry is set

BULK-PIEZOELECTRIC TRANSDUCTION OF MICROSYSTEMS WITH APPLICATIONS TO BATCH-ASSEMBLY OF MICROMIRRORS, CAPACITIVE SENSING, AND SOLAR ENERGY CONCENTRATION

Electromechanical modeling, actuation, sensing and fabrication aspects of bulkpiezoelectric ceramic integration for microsystems are investigated in this thesis. A small-signal model that describes the energy exchange between surface micromachined beams and bulk-lead zirconium titanate (PZT) actuators attached to the silicon substrate is presented. The model includes detection of acoustic waves launched from electrostatically actuated structures on the surface of the die, as well as their actuation by bulk waves generated by piezoelectric ceramics. The interaction is modeled via an empirical equivalent circuit, which is substantiated by experiments designed to extract the model parameters. As a die level application of bulk-PZT, an Ultrasound Enhanced Electrostatic Batch Assembly (U2EBA) method for realization of 3-D microsystems is demonstrated. U2EBA involves placing the die in an external DC electric field perpendicular to the substrate and actuating the die with an off-chip, bulk-piezoelectric ceramic. Yield rates reaching up to 100% are reported from 8×8 arrays of hinged mirrors with dimensions of 180 × 100 micrometre-squared. U2EBA is later improved to provide temporary latching at intermediate angles between fully horizontal and vertical states, by using novel latching structures. It is shown that the micromirrors can be trapped and freed from different rotation angles such that zero static power is needed to maintain an angular position. The zero-idle-power positioning of large arrays of small mirrors is later investigated for energy redirection and focusing. All-angle LAtchable Reflector (ALAR) concept is introduced, and its application to Concentrated Solar Power (CSP) systems is discussed. The main premise of ALAR technology is to replace bulky and large arrays of mirrors conventionally used in CSP technologies with zeroidle- power, semi-permanently latched, low-profile, high-fill factor, micrometer to centimeter scale mirror arrays. A wirelessly controlled prototype that can move a 2-D array of mirrors, each having a side length of less than 5 cm, in two degrees of freedom to track the brightest spot in the ambient is demonstrated. Capacitive sensing using bulk-piezoelectric crystals is investigated, and a Time- Multiplexed Crystal based Capacitive Sensing (TM-XCS) method is proposed to provide nonlinearity compensation and self-temperature sensing for oscillator based capacitive sensors. The analytical derivation of the algorithm and experimental evidence regarding the validity of some of the relations used in the derivation are presented. This thesis also presents results on microfluidic particle transport as another application of bulk-PZT in microsystems. Experiments and work regarding actuation of micro-scale, fluorescent beads on silicon nitride membranes are described

MEMS Devices for Circumferential-scanned Optical Coherence Tomography Bio-imaging

Ph.DDOCTOR OF PHILOSOPH

Novel Actuation Mechanisms for MEMS Mirrors

Ph.DDOCTOR OF PHILOSOPH