Linear-Quadratic Control of a MEMS Micromirror Using Kalman Filtering

The deflection limitations of electrostatic flexure-beam actuators are well known. Specifically, as the beam is actuated and the gap traversed, the restoring force necessary for equilibrium increases proportionally with the displacement to first order, while the electrostatic actuating force increases with the inverse square of the gap. Equilibrium, and thus stable open-loop voltage control, ceases at one-third the total gap distance, leading to actuator snap-in. A Kalman Filter is designed with an appropriately complex state dynamics model to accurately estimate actuator deflection given voltage input and capacitance measurements, which are then used by a Linear Quadratic controller to generate a closed-loop voltage control signal. The constraints of the latter are designed to maximize stable control over the entire gap. The design and simulation of the Kalman Filter and controller are presented and discussed, with static and dynamic responses analyzed, as applied to basic, 100 micrometer by 100 micrometer square, flexure-beam-actuated micromirrors fabricated by PolyMUMPs. Successful application of these techniques enables demonstration of smooth, stable deflections of 50% and 75% of the gap

Electrostatically Driven Large Aperture Micro-Mirror Actuator Assemblies for High Fill-Factor, Agile Optical Phase Arrays

Aircraft laser beamsteering is accomplished using a single gimbaled mirror housed inside a turret, which protrudes from the fuselage and causes unwanted turbulence, vibrations, and weight. The Air Force is currently investigating the use of microelectromechanical systems (MEMS) micro-mirror arrays to replace aircraft beamsteering technology. MEMS micro-mirror arrays provide a unique solution to address these issues. Unfortunately, current MEMS micro-mirror technology cannot meet all the beamsteering requirements in a single assembly. These include high fill-factor, large aperture, 25 degrees of out-of-plane deflection, 4-axis tilt, and actuation speeds below 1 ms. In this research, a novel MEMS actuation scheme to address all these requirements using electrostatically driven bimorph cantilever beams was designed, modeled, fabricated, and characterized. Modeling results show a linear relationship between the number of cantilever beams and maximum deflection. Characterization of fabricated micro-mirror assemblies supports the modeling for individual actuators as well as for micro-mirror platform assemblies. Fabricated devices reached vertical deflections greater than 170 micrometer with pull-in voltages of 20 V and an optical range of 16 degrees. These large deflections, low pull-in voltage, and reasonable optical range shown in this research demonstrate the feasibility of using MEMS micro-mirror arrays to address aircraft beamsteering issues

Cantilever beam microactuators with electrothermal and electrostatic drive

Microfabrication provides a powerful tool for batch processing and miniaturization of mechanical systems into dimensional domain not accessible easily by conventional machining. CMOS IC process compatible design is definitely a big plus because of tremendous know-how in IC technologies, commercially available standard IC processes for a reasonable price, and future integration of microma-chined mechanical systems and integrated circuits. Magnetically, electrostatically and thermally driven microactuators have been reported previously. These actuators have applications in many fields from optics to robotics and biomedical engineering. At NJIT cleanroom, mono or multimorph microactuators have been fabricated using CMOS compatible process. In design and fabrication of these microactuators, internal stress due to thermal expansion coefficient mismatch and residual stress have been considered, and the microactuators are driven with electro-thermal power combined with electrostatical excitation. They can provide large force, and in- or out-of-plane actuation. In this work, an analytical model is proposed to describe the thermal actuation of in-plane (inchworm) actuators. Stress gradient throughout the thickness of monomorph layers is modeled as linearly temperature dependent Δσ. The nonlinear behaviour of out-of-plane actuators under electrothermal and electrostatic excitations is investigated. The analytical results are compared with the numerical results based on Finite Element Analysis. ANSYS, a general purpose FEM package, and IntelliCAD, a FEA CAD tool specifically designed for MEMS have been used extensively. The experimental results accompany each analytical and numerical work. Micromechanical world is three dimensional and 2D world of IC processes sets a limit to it. A new micromachining technology, reshaping, has been introduced to realize 3D structures and actuators. This new 3D fabrication technology makes use of the advantages of IC fabrication technologies and combines them with the third dimension of the mechanical world. Polycrystalline silicon microactuators have been reshaped by Joule heating. The first systematic investigation of reshaping has been presented. A micromirror utilizing two reshaped actuators have been designed, fabricated and characterized

Stress Monitoring of Post-processed MEMS Silicon Microbridge Structures Using Raman Spectroscopy

Inherent residual stresses during material deposition can have profound effects on the functionality and reliability of fabricated Micro-Electro-Mechanical Systems (MEMS) devices. Residual stress often causes device failure due to curling, buckling, or fracture. Typically, the material properties of thin films used in surface micromachining are not well controlled during deposition. The residual stress; for example, tends to vary significantly for different deposition methods. Currently, few nondestructive techniques are available to measure residual stress in MEMS devices prior to the final release etch. In this research, micro-Raman spectroscopy is used to measure the residual stresses in polysilicon MEMS microbridge devices. This measurement technique was selected since it is nondestructive, fast, and provides the potential for in-situ stress monitoring. Raman spectroscopy residual stress profiles on unreleased and released MEMS microbridge beams are compared to analytical and FEM models to assess the viability of micro-Raman spectroscopy as an in-situ stress measurement technique. Raman spectroscopy was used during post-processing phosphorus ion implants on unreleased MEMS devices to investigate and monitor residual stress levels at key points during the post-processing sequences. As observed through Raman stress profiles and verified using on-chip test structures, the post-processing implants and accompanying anneals resulted in residual stress relaxation of over 90%

Use of Instabilities in Electrostatic Micro-Electro-Mechanical Systems for Actuation and Sensing

This thesis develops methods to exploit static and dynamic instabilities in electrostatic MEMS to develop new MEMS devices, namely dynamically actuated micro switches and binary micro gas sensors. Models are developed for the devices under consideration where the structures are treated as elastic continua. The electrostatic force is treated as a nonlinear function of displacement derived under the assumption of parallel-plate theorem. The Galerkin method is used to discretize the distributed-parameter models, thus reducing the governing partial differential equations into sets of nonlinear ordinary-differential equations. The shooting method is used to numerically solve those equations to obtain the frequency-response curves of those devices and the Floquet theory is used to investigate their stability. To develop the dynamically actuated micro switches, we investigate the response of microswitches to a combination of DC and AC excitations. We find that dynamically actuated micro switches can realize significant energy savings, up to 60 %, over comparable switches traditionally actuated by pure DC voltage. We devise two dynamic actuation methods: a fixed-frequency method and a shifted-frequency method. While the fixed-frequency method is simpler to implement, the shifted-frequency method can minimize the switching time to the same order as that realized using traditional DC actuation. We also introduce a parameter identification technique to estimate the switch geometrical and material properties, namely thickness, modulus of elasticity, and residual stress. We also develop a new detection technique for micro mass sensors that does not require any readout electronics. We use this method to develop static and dynamic binary mass sensors. The sensors are composed of a cantilever beam connected to a rigid plate at its free end and electrostatically coupled to an electrode underneath it. Two versions of micro mass sensors are presented: static binary mass sensor and dynamic binary mass sensor. Sensitivity analysis shows that the sensitivity of our static mass sensor represents an upper bound for the sensitivity of comparable statically detected inertial mass sensors. It also shows that the dynamic binary mass sensors is three orders of magnitude more sensitive than the static binary mass sensor. We equip our mass sensor with a polymer detector, doped Polyaniline, to realize a formaldehyde vapor sensor and demonstrate its functionality experimentally. We find that while the static binary gas sensor is simpler to realize than the dynamic binary gas sensor, it is more susceptible to external disturbances

CMOS-MEMS Resonant Gate Transistor-Based Devices

The development of the semiconductor industry in general and IC (Integrated Circuits) fabrication technologies in particular enabled the miniaturization of moving electro-mechanical structures down to micrometer size. This significantly reduced the cost and power consumption, and improved the performance of modern Micro-Electro-Mechanical Systems (MEMS). Electrostatically-driven MEMS-based resonators are used in a vast range of applications, including sensors, high frequency filters, time reference signal generations, etc. However, with the resonance frequency continuously increasing and the physical dimensions of the resonators shrinking, the sensitivity of capacitive detection is becoming a major problem due to decreased output signals. The Resonating Suspended Gate Field Effect Transistor (RSG-FET) is seen as a perfect solution to overcome this problem. It replaces conventional capacitive detection with FET detection when the vibrating gate modulates the channel current. This thesis presents an RSG-FET-based resonator fabricated using conventional CMOS technology with additional post-processing. The concept of RSG-FET combines the advantages of both a high mechanical quality factor and an intrinsic gain of a transistor. The physical mechanisms behind the operation principle along with its advantages and disadvantages are thoroughly investigated using distributed and lumped analysis as well as Finite Element Analysis (FEA) methods. Various approaches for tuning the resonance frequency are studied analytically and verified experimentally. The fabrication of the device is carried out through a post-processing of a conventional CMOS process (TSMC CMOSP35). Possible applications for RSG-FET-based devices in high frequency filters and atomic force microscopy are also investigated

Modeling and Control of MEMS-based Multi-layered Prestressed Piezoelectric Cantilever Beam

Piezoelectric materials are the preferred smart materials for sensing and actuation in the form of micro and nano-engineering structures like beams and plates. Cantilever beams play a significant role as key components in atomic force microscopy and bio and chemical sensors. Adding an active layer such as lead zirconate titanate (PZT) thin-film to form smart cantilever beams with sensing and actuation capabilities is highly desirable to facilitate miniaturization, enhance performance and functionali- ties such as enabling on-chip high-speed parallel AFM. During the micro-fabrication process, residual stresses develop in the different layers of the cantilever beam, causes initial deflection. The residual stress in the different layers of the cantilever beam and the application of voltage to the PZT thin-film affects their dynamics. This the- sis investigates the dynamic behaviour and develops a control technique and a novel charge readout circuit to improve the performance of a micro-fabricated multi-layer prestressed piezoelectric cantilever beam as an actuator and a deflection sensor. Firstly, the fabrication process of a unimorph PZT cantilever beam is explained. A low thermal budget Ultra-high vacuum e-beam evaporated polysilicon thin-film (UHVEEpoly) process is used for the fabrication of multi-layered PZT cantilever beam in d31 mode. The sharp peaks at resonant frequencies in the frequency response of the PZT cantilever beam show very little damping and a large settling time of the cantilever beam. Secondly, the dynamic behaviour of the prestressed PZT cantilever beam is in- vestigated subjected to change in driving voltage. Experimental investigations show a shift in resonant frequencies of a PZT cantilever beam. However, there is no reported mathematical model that predicts the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam subjected to a change in driving voltage. This work developed a mathematical model with experimental val- idation to estimate the shift in resonance frequencies of such cantilever beams with the change in the driving voltage. A very good agreement between the model predic- tions and experimental measurements for the frequency response of the cantilever beam at different driving voltages has been obtained. A novel linear formulation has been developed to predict the shift in resonance frequencies of the PZT can- i tilever beam for a wide range of driving voltages. The formulation shows that the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam per unit of applied voltage is dependent on geometric parameters and material properties. Thirdly, a robust resonant controller has been designed and implemented to re- duce the settling time of a highly vibrating PZT cantilever beam. The controller design is based on a mixed negative-imaginary, passivity, and a small-gain approach. The motivation to design a resonant controller using the above-mentioned analyti- cal framework is its bandpass nature and the use of velocity feedback, as the charge collected from a vibrating PZT cantilever beam gives the velocity information of the beam. The proposed controller design results in finite gain stability for a pos- itive feedback interconnection between two stable linear systems with a large gain and phase margin. Experimental results demonstrate that the designed resonant controller is able to effectively damp the first resonant mode of a cantilever, signifi- cantly reducing settling time from 528 ms to 32 ms. The robustness of the designed resonant controller is tested against changes in the cantilever beam dynamics due to residual stress variation and or stress variation due to driving voltage. Finally, to facilitate the miniaturization of on-chip sensors and parallel high- speed AFM, a single layer of a PZT thin-film in a cantilever beam is used as a deflection sensor and an actuator instead of bulky optical deflection sensors. A novel charge readout circuit is designed for deflection sensing by capturing the electrical charge generated due to the vibration of the PZT beam. The signal-to-noise ratio and sensitivity analysis of the readout circuit shows similar results compared to the commercially available optical deflection sensors. Our work highlights very important aspects in the dynamic behaviour and perfor- mance of a multi-layered prestressed piezoelectric cantilever beam. The agreement between the proposed theoretical formulation and experimental investigations in modeling, control design, and a novel readout circuit will provide the platform for further the development and miniaturization of microcantilever-based technologies, including on-chip parallel HS-AFM

Reduced-order models for microelectromechanical rectangular and circular plates incorporating the Casimir force

AbstractWe consider the von Kármán nonlinearity and the Casimir force to develop reduced-order models for prestressed clamped rectangular and circular electrostatically actuated microplates. Reduced-order models are derived by taking flexural vibration mode shapes as basis functions for the transverse displacement. The in-plane displacement vector is decomposed as the sum of displacements for irrotational and isochoric waves in a two-dimensional medium. Each of these two displacement vector fields satisfies an eigenvalue problem analogous to that of transverse vibrations of a linear elastic membrane. Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate in-plane motion. The reduced-order model is derived from the equation yielding the transverse deflection of a point. For static deformations of a plate, the pull-in parameters are found by using the displacement iteration pull-in extraction method. Reduced-order models are also used to study linear vibrations about a predeformed configuration. It is found that 9 basis functions for a rectangular plate give a converged solution, while 3 basis functions give pull-in parameters with an error of at most 4%. For a circular plate, 3 basis functions give a converged solution while the pull-in parameters computed with 2 basis functions have an error of at most 3%. The value of the Casimir force at the onset of pull-in instability is used to compute device size that can be safely fabricated

MEMS micromirrors for imaging applications

Strathclyde theses - ask staff. Thesis no. : T13478Optical MEMS (microelectromechanical systems) are widely used in various applications. In this thesis, the design, simulation and characterisation of two optical MEMS devices for imaging applications, a varifocal micromirror and a 2D scanning micromirror, are introduced. Both devices have been fabricated using the commercial Silicon-on-Insulator multi-users MEMS processes (SOIMUMPs), in the 10 m thick Silicon-on-Insulator (SOI) wafer. Optical MEMS device with variable focal length is a critical component for imaging system miniaturisation. In this thesis, a thermally-actuated varifocal micromirror (VFM) with 1-mm-diameter aperture is introduced. The electrothermal actuation through Joule heating of the micromirror suspensions and the optothermal actuation using incident laser power absorption have been demonstrated as well as finite element method (FEM) simulation comparisons. Especially, the optical aberrations produced by this VFM have been statistically quantified to be negligible throughout the actuation range. A compact imaging system incorporating this VFM has been demonstrated with high quality imaging results. MEMS 2D scanners, or scanning micromirrors, are another type of optical MEMS which have been widely investigated for applications such as biomedical microscope imaging, projection, retinal display and optical switches for telecommunication network, etc. For large and fast scanning motions, the actuation scheme to scan a micromirror in two axes, the structural connections and arrangement are fundamental. The microscanner introduced utilises two types of actuators, electrothermal actuators and electrostatic comb-drives, to scan a 1.2-mm-diameter gold coated silicon micromirror in two orthogonal axes. With assistance of FEM software, CoventorWare, the structure optimisation of actuators and flexure connections are presented. The maximum optical scan angles in two axes by each type of actuator individually and by actuating the two at the same time have been characterised experimentally. By programming actuation signals, the microscanner has achieved a rectangular scan pattern with 7° 10° angular-scan-field at a line-scan rate of around 1656 Hz.Optical MEMS (microelectromechanical systems) are widely used in various applications. In this thesis, the design, simulation and characterisation of two optical MEMS devices for imaging applications, a varifocal micromirror and a 2D scanning micromirror, are introduced. Both devices have been fabricated using the commercial Silicon-on-Insulator multi-users MEMS processes (SOIMUMPs), in the 10 m thick Silicon-on-Insulator (SOI) wafer. Optical MEMS device with variable focal length is a critical component for imaging system miniaturisation. In this thesis, a thermally-actuated varifocal micromirror (VFM) with 1-mm-diameter aperture is introduced. The electrothermal actuation through Joule heating of the micromirror suspensions and the optothermal actuation using incident laser power absorption have been demonstrated as well as finite element method (FEM) simulation comparisons. Especially, the optical aberrations produced by this VFM have been statistically quantified to be negligible throughout the actuation range. A compact imaging system incorporating this VFM has been demonstrated with high quality imaging results. MEMS 2D scanners, or scanning micromirrors, are another type of optical MEMS which have been widely investigated for applications such as biomedical microscope imaging, projection, retinal display and optical switches for telecommunication network, etc. For large and fast scanning motions, the actuation scheme to scan a micromirror in two axes, the structural connections and arrangement are fundamental. The microscanner introduced utilises two types of actuators, electrothermal actuators and electrostatic comb-drives, to scan a 1.2-mm-diameter gold coated silicon micromirror in two orthogonal axes. With assistance of FEM software, CoventorWare, the structure optimisation of actuators and flexure connections are presented. The maximum optical scan angles in two axes by each type of actuator individually and by actuating the two at the same time have been characterised experimentally. By programming actuation signals, the microscanner has achieved a rectangular scan pattern with 7° 10° angular-scan-field at a line-scan rate of around 1656 Hz

Design and Fabrication of Electrostatically Actuated Serpentine-Hinged Nickel-Phosphorous Micromirror Devices

A process for micromachining of micro-mirror devices from silicon-on-insulator wafers was proposed and implemented. Test methods and force applicators for these devices were developed. Following successful fabrication of these devices, a novel process for fabrication of devices out of the plane of the silicon wafer was proposed, so that the devices could be actuated electrostatically. In particular, the process makes use of thick photoresist layers as a sacrificial mold into which an amorphous nickel-phosphorous alloy may be deposited. Ideal design of the electrostatically actuated micro-mirrors was investigated, and a final design was selected and modeled using FEA software, which found that serpentine-hinged devices require approximately 33% of the actuation force of their straight-beamed counterparts. An aqueous electroless plating solution composed of nickel acetate, sodium hypophosphite, citric acid, ammonium acetate, and Triton X-100 in was developed for use with the process, and bath operating parameters of 85°C and 4.5 pH were determined. However, this electroless solution failed to deposit in the presence of the photoresist. Several mechanisms proposed for deposition failure included leaching of organic solvents from the photoresist, oxidation of the nickel-titanium seed layer on which the deposition was intended to occur, and nonlinear diffusion of dissolved oxygen in the solution