Polymeric Thermal Microactuator With Embedded Silicon Skeleton: Part II—Fabrication, Characterization, and Application for 2-DOF Microgripper

This paper presents the fabrication, characterization, and application of a novel silicon-polymer laterally stacked electrothermal microactuator. The actuator consists of a deep silicon skeleton structure with a thin-film aluminum heater on top and filled polymer in the trenches among the vertical silicon parts. The fabrication is based on deep reactive ion etching, aluminum sputtering, SU8 filling, and KOH etching. The actuator is 360 $muhbox{m}$ long, 125 $mu hbox{m}$ wide, and 30 $muhbox{m}$ thick. It generates a large in-plane forward motion up to 9 $muhbox{m}$ at a driving voltage of 2.5 V using low power consumption and low operating temperature. A novel 2-D microgripper based on four such forward actuators is introduced. The microgripper jaws can be moved along both the $x$- and $y$ -axes up to 17 and 11 $muhbox{m}$, respectively. The microgripper can grasp a microobject with a diameter from 6 to 40 $muhbox{m}$ . In addition, the proposed design is suitable for rotation of the clamped object both clockwise and counterclockwise. $hfill$[2007-0192]      

Thin-Film PZT Lateral Actuators With Extended Stroke

Many microelectromechanical system applications require large in-plane actuation forces, with stroke lengths ranging from submicrometer to tens of micrometers in distance. Piezoelectric thin films are capable of generating very large actuation forces, but their motion is not easily directed into lateral displacement in microscale devices. A new piezoelectric thin-film actuator that uses a combination of piezoelectric unimorph beams to generate lateral displacement has been developed. The piezoelectric actuators were fabricated using chemical-solution-derived lead zirconate titanate thin films. These actuators have demonstrated forces greater than 7 mN at displacements of nearly 1 $muhbox{m}$, with maximum stroke lengths at 20 V greater than 5 $muhbox{m}$ in a 500- $muhbox{m}$-long by 100-$mu hbox{m}$-wide actuator. Force and displacement capabilities can be manipulated through simple changes to the actuator design, while actuator nonlinearity can produce dramatic gains in work capacity and stroke length for longer actuators.$hfill$[2007-0298]      

Radioisotope Thin-Film Fueled Microfabricated Reciprocating Electromechanical Power Generator

A radioisotope power generator with a potential lifetime of decades is demonstrated by employing a 100.3-year half-lifetime $^{63}hbox{Ni}$ radioisotope thin-film source to electrostatically actuate and cause reciprocation in a microfabricated piezoelectric unimorph cantilever. The radioisotope direct-charged electrostatic actuation of the piezoelectric unimorph cantilever results in the conversion of radiation energy into mechanical energy stored in the strained unimorph cantilever. The gradual accumulation of the actuation charges leads to the pull-in of the unimorph cantilever into the radioisotope thin-film, and the resulting discharge leads to vibrations in the unimorph cantilever. During the vibrations, the stored mechanical energy is converted into electrical energy by the piezoelectric thin-film. The generator was realized by using both microfabricated lead zirconate titanate oxide–silicon (PZT–Si) and aluminum nitride–silicon (AlN–Si) unimorph cantilevers. The radioisotope direct-charged electrostatic actuation of the AlN–Si unimorph cantilevers by a 2.9-mCi $^{63}hbox{Ni}$ thin-film radiating 0.3 $muhbox{W}$ led to charge–discharge–vibrate cycles that resulted in the generation of 0.25% duty cycle 12.95- $muhbox{W}$ power pulses (across an optimal load impedance of 521 $hbox{k}Omega$) at an overall energy conversion efficiency of 3.97%. These electrical power pulses can potentially be useful for periodically sampling sensor microsystems. $hfill$[2008-0009]      

On the NP-Hardness of Checking Matrix Polytope Stability and Continuous-Time Switching Stability

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of $k$ matrices in $R^{n times n}$ are stable. In particular, we are interested whether there exist algorithms which can solve this problem in time polynomial in $n$ and $k$. We show that if $k= lceil n^{d} rceil $ for any fixed real $d>0$, then the problem is NP-hard, meaning that no polynomial-time algorithm in $n$ exists provided that $P ne NP$, a widely believed conjecture in computer science. On the other hand, when $k$ is a constant independent of $n$ , then it is known that the problem may be solved in polynomial time in $n$. Using these results and the method of measurable switching rules, we prove our main statement: verifying the absolute asymptotic stability of a continuous-time switched linear system with more than $n^{d}$ matrices $A_{i} in R^{n times n}$ satisfying $0 succeq A_{i} + A_{i}^{T}$ is NP-hard.      

$ {cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

We investigate the $ {cal L}_{2}$ gain of periodic linear switched systems under fast switching. For systems that possess a suitable notion of a time-average system, we characterize the relationship between the ${cal L}_{2}$ gain of the switched system and the ${cal L}_{2}$ gain of its induced time-average system when the switching rate is sufficiently fast. We show that the switched system ${cal L}_{2}$ gain is in general different from the average system ${cal L}_{2}$ gain if the input or output coefficient matrix switches. If only the state coefficient matrix switches, the input-output energy gain for a fixed ${cal L}_{2}$ input signal is bounded by the ${cal L}_{2}$ gain of the average system as the switching rate grows large. Additionally, for a fixed ${cal L}_{2}$ input, the maximum pointwise in time difference between the switched and average system outputs approaches zero as the switching rate grows.      

How to Make $T$-Transitive a Proximity Relation

Three ways to approximate a proximity relation $R$ (i.e., a reflexive and symmetric fuzzy relation) by a $T$ -transitive one where $T$ is a continuous Archimedean $t$-norm are given. The first one aggregates the transitive closure $overline{R}$ of $R$ with a (maximal) $T$-transitive relation $B$ contained in $R$ . The second one computes the closest homotecy of $overline{R}$ or $B$ to better fit their entries with the ones of $R$. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for $T$ the $Lstrok$ukasiewicz or the product $t$-norm. The previous methods do not apply for the minimum $t$-norm. An algorithm to approximate a given proximity relation by a ${rm Min}$-transitive relation (a similarity) is given in the last section of the paper.      

Tungsten-Based SOI Microhotplates for Smart Gas Sensors

This paper is concerned with the design, fabrication, and characterization of novel high-temperature silicon on insulator (SOI) microhotplates employing tungsten resistive heaters. Tungsten has a high operating temperature and good mechanical strength and is used as an interconnect in high temperature SOI-CMOS processes. These devices have been fabricated using a commercial SOI-CMOS process followed by a deep reactive ion etching (DRIE) back-etch step, offering low cost and circuit integration. In this paper, we report on the design of microhotplates with different diameters (560 and 300 $muhbox{m}$) together with 3-D electrothermal simulation in ANSYS, electrothermal characterization, and analytical analysis. Results show that these devices can operate at high temperatures (600 $^{circ}hbox{C}$ ) well beyond the typical junction temperatures of high temperature SOI ICs (225 $^{circ}hbox{C}$), have ultralow dc power consumption (12 mW at 600 $^{circ}hbox{C}$), fast transient time (as low as 2-ms rise time to 600 $^{circ}hbox{C}$), good thermal stability, and, more importantly, a high reproducibility both within a wafer and from wafer to wafer. We also report initial tests on the long-term stability of the tungsten heaters. We believe that this type of SOI microhotplate could be exploited commercially in fully integrated microcalorimetric or resistive gas sensors. $hfill$[2007-0275]      

Post-CMOS-Compatible Aluminum Nitride Resonant MEMS Accelerometers

This paper describes the development of aluminum nitride (AlN) resonant accelerometers that can be integrated directly over foundry CMOS circuitry. Acceleration is measured by a change in resonant frequency of AlN double-ended tuning-fork (DETF) resonators. The DETF resonators and an attached proof mass are composed of a 1- $muhbox{m}$ -thick piezoelectric AlN layer. Utilizing piezoelectric coupling for the resonator drive and sense, DETFs at 890 kHz have been realized with quality factors $(Q)$ of 5090 and a maximum power handling of 1 $muhbox{W}$. The linear drive of the piezoelectric coupling reduces upconversion of $1/f$ amplifier noise into $1/f^{3}$ phase noise close to the oscillator carrier. This results in lower oscillator phase noise, $-$96 dBc/Hz at 100-Hz offset from the carrier, and improved sensor resolution when the DETF resonators are oscillated by the readout electronics. Attached to a 110-ng proof mass, the accelerometer microsystem has a measured sensitivity of 3.4 Hz/G and a resolution of 0.9 $hbox{mG}/surdhbox{Hz}$ from 10 to 200 Hz, where the accelerometer bandwidth is limited by the measurement setup. Theoretical calculations predict an upper limit on the accelerometer bandwidth of 1.4 kHz.$hfill$ [2008-0190]      

Fracture Toughness, Fracture Strength, and Stress Corrosion Cracking of Silicon Dioxide Thin Films

The fracture toughness, fracture strength, and stress corrosion cracking behavior of thin-film amorphous silicon dioxide $(hbox{SiO}_{2})$ deposited on silicon wafers via plasma-enhanced chemical vapor deposition have been measured using specimens with length scales comparable to micromachined devices. Clamped–clamped microtensile specimens were fabricated using standard micromachining techniques. These devices exploit residual tensile stresses in the film to create stress intensity factors at precrack tips and stress concentrations at notches, in order to measure fracture toughness and fracture strength, respectively. The fracture toughness of thin-film $hbox{SiO}_{2}$ was $0.77 pm 0.15 hbox{MPa}cdot hbox{m}^{1/2}$, and the fracture strength was $0.81 pm 0.06 hbox{GPa}$. Stress corrosion cracking (slow crack growth) was also measured in the $hbox{SiO}_{2}$ devices with sharp precracks subjected to residual tensile stresses. These data are used to predict lifetimes for a $hbox{SiO}_{2}$-based microdevice. $hfill$[2007-0304]      

Thermal Degradation of Electroplated Nickel Thermal Microactuators

In this paper, the thermal degradation of laterally operating thermal actuators made from electroplated nickel has been studied. The actuators investigated delivered a maximum displacement of ca. 20 $muhbox{m}$ at an average temperature of $sim!! 450 ,^{circ}hbox{C}$ , which is much lower than that of typical silicon-based microactuators. However, the magnitude of the displacement strongly depended on the frequency and voltage amplitude of the pulse signal applied. Back bending was observed at maximum temperatures as low as 240 $^{circ}hbox{C}$. Both forward and backward displacements increase as the applied power was increased up to a value of 60 mW; further increases led to reductions in the magnitudes of both displacements. Scanning electron microscopy clearly showed that the nickel beams began to deform and change their shape at this critical power level. Compressive stress is responsible for nickel pileup, while tensile stresses, generated upon removing the current, are responsible for necking at the hottest section of the hot arm of the device. Energy dispersive X-ray diffraction analysis also revealed the severe oxidation of Ni structure induced by Joule heating. The combination of plastic deformation and oxidation was responsible for the observed thermal degradation. Results indicate that nickel thermal microactuators should be operated below 200 $^{circ}hbox{C}$ to avoid thermal degradation.$hfill$[2009-0015]      

Discharge-Based Pressure Sensors for High-Temperature Applications Using Three-Dimensional and Planar Microstructures

Two versions of microdischarge-based pressure sensors, which operate by measuring the change, with pressure, in the spatial current distribution of pulsed dc microdischarges, are reported. The inherently high temperatures of the ions and electrons in the microdischarges make these devices amenable to high-temperature operation. The first sensor type uses 3-D arrays of horizontal bulk metal electrodes embedded in quartz substrates with electrode diameters of 1–2 mm and 50–100-$muhbox{m}$ interelectrode spacing. These devices were operated in nitrogen over a range of 10–2000 torr, at temperatures as high as 1000 $^{circ}hbox{C}$. The maximum measured sensitivity was 5420 ppm/torr at the low end of the dynamic range and 500 ppm/torr at the high end, while the temperature coefficient of sensitivity ranged from $-$925 to $-$550 ppm/K. Sensors of the second type use planar electrodes and have active areas as small as 0.13 $hbox{mm}^{2}$. These devices, when tested in a chemical sensing system flowing helium as a carrier gas, had a maximum sensitivity of 9800 ppm/torr, a dynamic range of 25–200 torr, and a temperature coefficient of sensitivity of approximately $-$1412 ppm/K.$hfill$ [2008-0262]      

Serially Connected Weight-Balanced Digital Actuators for Wide-Range High-Precision Low-Voltage-Displacement Control

This paper presents the design, fabrication, and characterization of a new serial digital actuator, achieving an improvement in range-to-precision and range-to-voltage performance. We propose a weight-balanced design for the serial actuators with serpentine springs with a serial arrangement of unit digital actuators. We have measured the displacement range, precision, and drive voltage of unit and serial actuation at 1 Hz. The serial digital actuators produce a full-range displacement of $28.44 pm 0.02 muhbox{m}$ , accumulating unit displacements of $2.8 pm 0.5 muhbox{m}$ at an operating voltage of 4.47 $pm$ 0.07 V. In addition, the serial digital actuators that have a displacement precision of 37.94 $pm$ 6.26 nm do not accumulate the displacement errors of the unit actuators, i.e., 36.0 $pm$ 17.7 nm. We experimentally verify that the serial digital actuators achieve a range-to-squared-voltage ratio of 1.423 $muhbox{m/V}^{2}$ and a range-to-precision ratio of 749.6.$hfill$ [2009-0020]      

Analytical Model of Valveless Micropumps

The flow driven by a valveless micropump with a single cylindrical pump chamber and two diffuser/nozzle elements is studied theoretically using a 1-D model. The pump cavity is driven at an angular frequency $omega$ so that its volume oscillates with an amplitude $V_{rm m}$. The presence of diffuser/nozzle elements with pressure-drop coefficients $zeta_{+}$, $zeta_{-}( ≫ zeta_{+})$ and throat cross-sectional area $A_{1}$ creates a rectified mean flow. In the absence of frictional forces the maximum mean volume flux (with zero pressure head) is $Q_{0}$ where $Q_{0}/V_{rm m}omega = (zeta_{-} -break zeta_{+})pi/16(zeta_{-}+zeta_{+})$, while the maximum pressure that can be overcome is $Delta P_{max}$ where $ Delta P_{max}A_{1}^{2}/V_{rm m}^{2} omega^{2} !=! (zeta_{-} -break zeta_{+})/16$. These analytical results agree with numerical calculations for the coupled system of equations and compare well with the experimental results of Stemme and Stemme.$hfill$ [2008-0244]      

Design, Modeling, and Fabrication of MEMS-Based Multicapillary Gas Chromatographic Columns

This paper describes different approaches to achieve high-performance microfabricated silicon-glass separation columns for microgas chromatography systems. The capillary width effect on the separation performance has been studied by characterization of 250-, 125-, 50-, and 25-$muhbox{m}$ -wide single-capillary columns (SCCs) fabricated on a $10 times 8 hbox{mm}^{2}$ die. The highest plate number (12 500/m), reported to date for MEMS-based silicon-glass columns, has been achieved by 25-$muhbox{m}$-wide columns coated by a thin layer of polydimethylsiloxane stationary phase using static coating technique. To address the low sample capacity of these narrow columns, this paper presents the first generation of MEMS-based “multicapillary” columns (MCCs) consisting of a bundle of narrow-width rectangular capillaries working in parallel. The theoretical model for the height-equivalent-to-a-theoretical-plate $(HETP)$ of rectangular MCCs has been developed, which relates the $HETP$ to the discrepancies of the widths and depths of the capillaries in the bundle. Two-, four-, and eight-capillary MCCs have been designed and fabricated to justify the separation ability of these columns. These MCCs capable of multicomponent gas separation provide a sample capacity as large as 200 ng compared to 5.5 ng for 25-$muhbox{m}$-wide SCCs.$hfillhbox{[2007-0309]}$      

Controlled Thermophoresis as an Actuation Mechanism for Noncantilevered MEMS Devices

A microelectromechanical system actuator based on thermophoretic, or Knudson, forces is proposed using analytical calculations. It can potentially execute scanning or spinning motions of a body that is not mechanically attached to the reference substrate. For a silicon device of 100-$muhbox{m}$ diameter, it is calculated that it can be levitated at a distance of about 0.5 $muhbox{m}$ from a substrate and that it can execute scanning motion and use quasi-springs by laterally acting thermal forces. In this way, an engine with spinning motion of a floating body having a diameter of 200 $muhbox{m}$ with up to 5 kHz can be achieved.$hfill$[2008-0013]      

On Compensating Long Actuator Delays in Nonlinear Control

We are interested in finite-escape open-loop unstable plants that are globally stabilizable in the absence of actuator delay but require controller redesign in the presence of delay. The simplest such plant is $ {mathdot Z} (t)= Z(t)^{2} + U(t-D)$, where $D$ is actuator delay of arbitrary length. For this system we present a control law that compensates the delay and achieves feedback linearization (of the entire ODE+delay infinite-dimensional cascade). However, even though exponential stability is achieved, the result is not global because the plant can have a finite escape with an initial condition $Z(0)geq 1/D$ before the feedback control “reaches” it at $t=D$ . We prove a stability result whose region of attraction is essentially $Z(0)≪ 1/D$ and for which we derive an asymptotic stability bound in terms of the system norm $Z(t)^{2} + int _{t-D}^{t} U(theta )^{2} dtheta $.      

Cryogenic Etching of Silicon: An Alternative Method for Fabrication of Vertical Microcantilever Master Molds

This paper examines the use of deep reactive ion etching of silicon with fluorine high-density plasmas at cryogenic temperatures to produce silicon master molds for vertical microcantilever arrays used for controlling substrate stiffness for culturing living cells. The resultant profiles achieved depend on the rate of deposition and etching of an $hbox{SiO}_{x}hbox{F}_{y}$ polymer, which serves as a passivation layer on the sidewalls of the etched structures in relation to areas that have not been passivated with the polymer. We look at how optimal tuning of two parameters, the $ hbox{O}_{2}$ flow rate and the capacitively coupled plasma power, determine the etch profile. All other pertinent parameters are kept constant. We examine the etch profiles produced using electron-beam resist as the main etch mask, with holes having diameters of 750 nm, 1 $muhbox{m}$ , and 2 $muhbox{m}$. $hfill$[2008-0317]      

Real-Time Temperature Compensation of MEMS Oscillators Using an Integrated Micro-Oven and a Phase-Locked Loop

We present a new temperature compensation system for microresonator-based frequency references. It consists of a phase-locked loop (PLL) whose inputs are derived from two microresonators with different temperature coefficients of frequency. The resonators are suspended within an encapsulated cavity and are heated to a constant temperature by the PLL controller, thereby achieving active temperature compensation. We show repeated real-time measurements of three 1.2-MHz prototypes that achieve a frequency stability of $pm$ 1 ppm from $-20 ^{circ}hbox{C}$ to $+80 ^{circ}hbox{C}$, as well as a technique to reduce steady-state frequency errors to $pm$0.05 ppm using multipoint calibration.$hfill$[2009-0074]      

A Laterally Movable Gate Field Effect Transistor

A laterally movable gate field effect transistor (LMGFET) device that directly couples lateral mechanical gate motion to drain current of a FET is presented in this paper. Lateral motion of the FET gate results in a change in channel width, keeping the channel length and the gap between the gate and the oxide layer constant. This results in a change in channel current that, in principle, is linearly proportional to mechanical motion. The operating principle of an LMGFET, along with details of the fabrication process for a depletion-type LMGFET device, is described. Fabricated LMGFET shows an average drain current sensitivity to gate motion of $-5.8 muhbox{A}/muhbox{m}$ at $V_{rm DS} = 20 hbox{V}$ and $V_{rm GS} = 0 hbox{V}$ for 60-$muhbox{m}$ gate motion. A model for the fabricated LMGFET is developed based on electrical measurements. The device shows promise both as a sensor and as an actuator in MEMS and other related applications.$hfill$ [2008-0147]      

11-Megapixel CMOS-Integrated SiGe Micromirror Arrays for High-End Applications

In this paper, we report on the design, fabrication, packaging, and testing of very reliable CMOS-integrated 10-$hbox{cm}^{2}$ 11-megapixel SiGe-based micromirror arrays on top of planarized six-level metal 0.18-${rm mu}hbox{m}$ CMOS wafers. The array, which is to be used as a spatial light modulator (SLM) for optical maskless lithography, consists of $8 {rm mu}hbox{m} times 8 {rm mu}hbox{m}$ pixels, which can be individually addressed by an analog voltage to enable accurate tilt angle modulation. Due to very stringent requirements on mounted-die flatness ($< hbox{0.01}$ mrad), the first level packaging of SLM die is done using specially designed SiC holders. To avoid trapped particles between the die and holder, which would jeopardize the flatness spec, special backside cleaning of the dies (less than or equal to one 0.8-${rm mu}hbox{m particle/cm}^{2}$ ) is needed before mounting the SLM die on the holder. To enable this backside cleaning and to avoid front-side particles during dicing, handling, and wire bonding, a temporary wafer- or zero-level packaging cap, which can be placed and removed at room temperature, was developed. The dynamic white light interferometer measurements of packaged dies showed that 99.5% of the 123 648 mirrors tested are within the spec. In addition, a stable average cupping of below 7 nm, an rms roughness of below 1 nm, and a stable actuation of over 2.5 teracycles are demonstrated.$hfill$[2009-0169]