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NASA NTRS2003

Continuous Tuning and Calibration of Vibratory Gyroscopes

A method of control and operation of an inertial reference unit (IRU) based on vibratory gyroscopes provides for continuously repeated cycles of tuning and calibration. The method is intended especially for application to an IRU containing vibratory gyroscopes that are integral parts of microelectromechanical systems (MEMS) and that have cloverleaf designs, as described in several previous NASA Tech Briefs articles. The method provides for minimization of several measures of spurious gyroscope output, including zero-rate offset (ZRO), angle random walk (ARW), and rate drift. These benefits are afforded both at startup and thereafter during continuing operation, in the presence of unknown rotation rates and changes in temperature. A vibratory gyroscope contains a precision mechanically resonant structure containing two normal modes of vibration nominally degenerate in frequency and strongly coupled via a Coriolis term. In the case of the cloverleaf design MEMS gyro, these normal modes of vibration are plate rocking modes. The rocking motion of the plate is described by giving two angles, theta(sub 1) and theta(sub 2). A proof mass consisting of a post orthogonal to the plate ensures a high degree of Coriolis coupling of vibratory energy from one mode into the other under inertial rotation. The plate is driven and sensed capacitively across a few-microns-wide gap, and the normal mode frequencies can be tuned electrostatically by DC voltages applied across this gap. In order to sense rotation, the resonator plate is caused to rock in the theta(sub 1) direction, then any small motions in the theta(sub 2) direction are sensed, rebalanced, and interpreted as inertial rotation. In this scenario, the "drive" has been assigned to the theta(sub 1) direction, and the "sense" has been assigned to the theta(sub 2) direction.

Hayworth, Ken↗
NASA NTRS2003

A Reactive-Ion Etch for Patterning Piezoelectric Thin Film

Reactive-ion etching (RIE) under conditions described below has been found to be a suitable means for patterning piezoelectric thin films made from such materials as PbZr(1-x)Ti(x)O3 or Ba(x)Sr(1.x)TiO3. In the original application for which this particular RIE process was developed, PbZr(1-x)Ti(x)O3 films 0.5 microns thick are to be sandwiched between Pt electrode layers 0.1 microns thick and Ir electrode layers 0.1 microns thick to form piezoelectric capacitor structures. Such structures are typical of piezoelectric actuators in advanced microelectromechanical systems now under development or planned to be developed in the near future. RIE of PbZr(1-x)Ti(x)O3 is usually considered to involve two major subprocesses: an ion-assisted- etching reaction, and a sputtering subprocess that removes reactive byproducts. RIE is favored over other etching techniques because it offers a potential for a high degree of anisotropy, high-resolution pattern definition, and good process control. However, conventional RIE is not ideal for patterning PbZr(1-x)Ti(x)O3 films at a thickness as great as that in the original intended application. In order to realize the potential benefits mentioned above, it is necessary to optimize process conditions . in particular, the composition of the etching gas and the values of such other process parameters as radio-frequency power, gas pressure, gas-flow rate, and duration of the process. Guidelines for determining optimum conditions can be obtained from experimental determination of etch rates as functions of these parameters. Etch-gas mixtures of BCl3 and Cl2, some also including Ar, have been found to offer a high degree of selectivity as needed for patterning of PbZr(1-x)Ti(x)O3 films on top of Ir electrode layers in thin-film capacitor structures. The selectivity is characterized by a ratio of approx.10:1 (rate of etching PbZr(1-x)Ti(x)O3 divided by rate of etching Ir and IrO(x)). At the time of reporting the information for this article, several experiments on RIE in BCl3 and Cl2 (and sometimes Ar) had demonstrated the 10:1 selectivity ratio, and further experiments to enhance understanding and obtain further guidance for optimizing process conditions were planned.

Yang, Eui-Hyeok↗
NASA NTRS2003

Silicon Membrane Mirrors with Electrostatic Shape Actuators

Efforts are under way to develop deformable mirrors equipped with microscopic electrostatic actuators that would be used to maintain their reflective surfaces in precise shapes required for their intended applications. Unlike actuators that depend on properties of materials (e.g., piezoelectric and electrostrictive actuators), electrostatic actuators are effective over a wide temperature range. A mirror of the present type would be denoted a MEMSDM (for microelectromechanical system deformable mirror). The reflective surface of such a mirror would be formed on a single-crystal silicon membrane that would be attached by posts to a silicon actuator membrane that would, in turn, be attached by posts to a rigid silicon base (see figure). The actuator membrane would serve as the upper electrode of a capacitor. Multiple lower electrodes, each occupying a conveniently small fraction of the total area, would be formed on an electrically insulating oxide layer on the base, thereby defining a multiplicity of actuator pixels. The actuator membrane would be corrugated in a pattern that would impart mechanical compliance needed for relaxation of operational and fabrication-induced stresses and to minimize the degree of nonlinearity of deformations. The compliance afforded by the corrugations would also help to minimize the undesired coupling of deformations between adjacent pixels (a practical goal being to keep the influence coefficient between adjacent pixels below 10 percent).

Yang, Eui-Hyeok↗
NASA NTRS2003

Micro-Ball-Lens Optical Switch Driven by SMA Actuator

The figure is a simplified cross section of a microscopic optical switch that was partially developed at the time of reporting the information for this article. In a fully developed version, light would be coupled from an input optical fiber to one of two side-by-side output optical fibers. The optical connection between the input and the selected output fiber would be made via a microscopic ball lens. Switching of the optical connection from one output fiber to another would be effected by using a pair of thin-film shape-memory-alloy (SMA) actuators to toggle the lens between two resting switch positions. There are many optical switches some made of macroscopic parts by conventional fabrication techniques and some that are microfabricated and, hence, belong to the class of microelectromechanical systems (MEMS). Conventionally fabricated optical switches tend to be expensive. MEMS switches can be mass-produced at relatively low cost, but their attractiveness has been diminished by the fact that, heretofore, MEMS switches have usually been found to exhibit high insertion losses. The present switch is intended to serve as a prototype of low-loss MEMS switches. In addition, this is the first reported SMA-based optical switch. The optical fibers would be held in V grooves in a silicon frame. The lens would have a diameter of 1 m; it would be held by, and positioned between, the SMA actuators, which would be made of thin films of TiNi alloy. Although the SMA actuators are depicted here as having simple shapes for the sake of clarity of illustration, the real actuators would have complex, partly net-like shapes. With the exception of the lens and the optical fibers, the SMA actuators and other components of the switch would be made by microfabrication techniques. The components would be assembled into a sandwich structure to complete the fabrication of the switch. To effect switching, an electric current would be passed through one of the SMA actuators to heat it above its transition temperature, thereby causing it to deform to a different "remembered" shape. The two SMA actuators would be stiff enough that once switching had taken place and the electrical current was turned off, the lens would remain latched in the most recently selected position. In a test, the partially developed switch exhibited an insertion loss of only -1.9 dB and a switching contrast of 70 dB. One the basis of prior research on SMA actuators and assuming a lens displacement of 125 m between extreme positions, it has been estimated that the fully developed switch would be capable of operating at a frequency as high as 10 Hz.

Yang, Eui-Hyeok↗
NASA NTRS2003

Wafer-Level Membrane-Transfer Process for Fabricating MEMS

A process for transferring an entire wafer-level micromachined silicon structure for mating with and bonding to another such structure has been devised. This process is intended especially for use in wafer-level integration of microelectromechanical systems (MEMS) that have been fabricated on dissimilar substrates. Unlike in some older membrane-transfer processes, there is no use of wax or epoxy during transfer. In this process, the substrate of a wafer-level structure to be transferred serves as a carrier, and is etched away once the transfer has been completed. Another important feature of this process is that two electrodes constitutes an electrostatic actuator array. An SOI wafer and a silicon wafer (see Figure 1) are used as the carrier and electrode wafers, respectively. After oxidation, both wafers are patterned and etched to define a corrugation profile and electrode array, respectively. The polysilicon layer is deposited on the SOI wafer. The carrier wafer is bonded to the electrode wafer by using evaporated indium bumps. The piston pressure of 4 kPa is applied at 156 C in a vacuum chamber to provide hermetic sealing. The substrate of the SOI wafer is etched in a 25 weight percent TMAH bath at 80 C. The exposed buried oxide is then removed by using 49 percent HF droplets after an oxygen plasma ashing. The SOI top silicon layer is etched away by using an SF6 plasma to define the corrugation profile, followed by the HF droplet etching of the remaining oxide. The SF6 plasma with a shadow mask selectively etches the polysilicon membrane, if the transferred membrane structure needs to be patterned. Electrostatic actuators with various electrode gaps have been fabricated by this transfer technique. The gap between the transferred membrane and electrode substrate is very uniform ( 0.1 m across a wafer diameter of 100 mm, provided by optimizing the bonding control). Figure 2 depicts the finished product.

Yang, Eui-Hyeok↗
NASA NTRS2003

Miniature Gas-Turbine Power Generator

A proposed microelectromechanical system (MEMS) containing a closed- Brayton-cycle turbine would serve as a prototype of electric-power generators for special applications in which high energy densities are required and in which, heretofore, batteries have been used. The system would have a volume of about 6 cm3 and would operate with a thermal efficiency >30 percent, generating up to 50 W of electrical power. The energy density of the proposed system would be about 10 times that of the best battery-based systems now available, and, as such, would be comparable to that of a fuel cell. The working gas for the turbine would be Xe containing small quantities of CO2, O2, and H2O as gaseous lubricants. The gas would be contained in an enclosed circulation system, within which the pressure would typically range between 5 and 50 atm (between 0.5 and 5 MPa). The heat for the Brayton cycle could be supplied by any of a number of sources, including a solar concentrator or a combustor burning a hydrocarbon or other fuel. The system would include novel heat-transfer and heat-management components. The turbine would be connected to an electric power generator/starter motor. The system would include a main rotor shaft with gas bearings; the bearing surfaces would be made of a ceramic material coated with nanocrystalline diamond. The shaft could withstand speed of 400,000 rpm or perhaps more, with bearing-wear rates less than 10(exp -)4 those of silicon bearings and 0.05 to 0.1 those of SiC bearings, and with a coefficient of friction about 0.1 that of Si or SiC bearings. The components of the system would be fabricated by a combination of (1) three-dimensional xray lithography and (2) highly precise injection molding of diamond-compatible metals and ceramic materials. The materials and fabrication techniques would be suitable for mass production. The disadvantages of the proposed system are that unlike a battery-based system, it could generate a perceptible amount of sound, and, if it were to burn fuel, then it would also generate exhaust, similarly to other combustion-based power sources.

Wiberg, Dean↗
NASA NTRS2003

Combining Multiple Gyroscope Outputs for Increased Accuracy

A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular-velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a virtual gyroscope) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy. The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum- variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation.

Bayard, David S.↗
NASA NTRS2003

MEMS-Based Piezoelectric/Electrostatic Inchworm Actuator

A proposed inchworm actuator, to be designed and fabricated according to the principles of microelectromechanical systems (MEMS), would effect linear motion characterized by steps as small as nanometers and an overall range of travel of hundreds of microns. Potential applications for actuators like this one include precise positioning of optical components and active suppression of noise and vibration in scientific instruments, conveyance of wafers in the semiconductor industry, precise positioning for machine tools, and positioning and actuation of micro-surgical instruments. The inchworm motion would be generated by a combination of piezoelectric driving and electrostatic clamping. The actuator (see figure), would include a pair of holders (used for electrostatic clamping), a slider (the part that would engage in the desired linear motion), a driver, a piezoelectric stack under the driver, and a pair of polymer beams centrally clamped to the flexure beam via a T bar. The holders would be held stationary. One end of the piezoelectric stack would be held stationary; the other end would be connected to the bottom of the driver, which would be free to move up and down. All of these components except the piezoelectric stack and the polymer beams would be micromachined from a 500- m-thick silicon wafer by deep reactive-ion etching. The inchworm motion would be perpendicular to the broad faces of the wafer (perpendicular to the plane of the figure). The combination of the polymer beams and the centrally clamped flexure beam would spring-bias the slider into a position such that, in the absence of electrostatic clamping, the gap between the slider on the one hand and both the driver and the holder on the other hand would be no more than a few microns. This arrangement would make it possible to electrostatically pull the slider into contact with either the holders or the driver at a clamping force of the order of 1 N by applying a reasonably small voltage (of the order of 100 V).

Yang, Eui-Hyeok↗
NASA NTRS2011

Programmable Aperture with MEMS Microshutter Arrays

A microshutter array (MSA) has been developed for use as an aperture array for multi-object selections in James Webb Space Telescope (JWST) technology. Light shields, molybdenum nitride (MoN) coating on shutters, and aluminum/aluminum oxide coatings on interior walls are put on each shutter for light leak prevention, and to enhance optical contrast. Individual shutters are patterned with a torsion flexure that permits shutters to open 90 deg. with a minimized mechanical stress concentration. The shutters are actuated magnetically, latched, and addressed electrostatically. Also, micromechanical features are tailored onto individual shutters to prevent stiction. An individual shutter consists of a torsion hinge, a shutter blade, a front electrode that is coated on the shutter blade, a backside electrode that is coated on the interior walls, and a magnetic cobalt-iron coating. The magnetic coating is patterned into stripes on microshutters so that shutters can respond to an external magnetic field for the magnetic actuation. A set of column electrodes is placed on top of shutters, and a set of row electrodes on sidewalls is underneath the shutters so that they can be electrostatically latched open. A linear permanent magnet is aligned with the shutter rows and is positioned above a flipped upside-down array, and sweeps across the array in a direction parallel to shutter columns. As the magnet sweeps across the array, sequential rows of shutters are rotated from their natural horizontal orientation to a vertical open position, where they approach vertical electrodes on the sidewalls. When the electrodes are biased with a sufficient electrostatic force to overcome the mechanical restoring force of torsion bars, shutters remain latched to vertical electrodes in their open state. When the bias is removed, or is insufficient, the shutters return to their horizontal, closed positions. To release a shutter, both the electrode on the shutter and the one on the back wall where the shutter sits are grounded. The shutters with one or both ungrounded electrodes are held open. Sub-micron bumps underneath light shields and silicon ribs on back walls are the two features to prevent stiction. These features ensure that the microshutter array functions properly in mechanical motions. The MSA technology can be used primarily in multi-object imaging and spectroscopy, photomask generation, light switches, and in the stepper equipment used to make integrated circuits and MEMS (microelectromechanical systems) devices.

Moseley, Samuel↗
NASA NTRS2012

Sampling and Control Circuit Board for an Inertial Measurement Unit

Spacesuit navigation is one component of NASA s efforts to return humans to the Moon. Studies performed at the NASA Glenn Research Center (GRC) considered various navigation technologies and filtering approaches to enable navigation on the lunar surface. As part of this effort, microelectromechanical systems (MEMS) inertial measurement units (IMUs) were studied to determine if they could supplement a radiometric infrastructure. MEMS IMUs were included in the Lunar Extra-Vehicular Activity Crewmember Location Determination System (LECLDS) testbed during NASA s annual Desert Research and Technology Studies (D-RATS) event in 2009 and 2010. The testbed included one IMU in 2009 and three IMUs in 2010, along with a custom circuit board interfacing between the navigation processor and each IMU. The board was revised for the 2010 test, and this paper documents the design details of this latest revision of the interface circuit board and firmware.

Chelmins, David↗
NASA NTRS2012

Next-Generation Microshutter Arrays for Large-Format Imaging and Spectroscopy

A next-generation microshutter array, LArge Microshutter Array (LAMA), was developed as a multi-object field selector. LAMA consists of small-scaled microshutter arrays that can be combined to form large-scale microshutter array mosaics. Microshutter actuation is accomplished via electrostatic attraction between the shutter and a counter electrode, and 2D addressing can be accomplished by applying an electrostatic potential between a row of shutters and a column, orthogonal to the row, of counter electrodes. Microelectromechanical system (MEMS) technology is used to fabricate the microshutter arrays. The main feature of the microshutter device is to use a set of standard surface micromachining processes for device fabrication. Electrostatic actuation is used to eliminate the need for macromechanical magnet actuating components. A simplified electrostatic actuation with no macro components (e.g. moving magnets) required for actuation and latching of the shutters will make the microshutter arrays robust and less prone to mechanical failure. Smaller-size individual arrays will help to increase the yield and thus reduce the cost and improve robustness of the fabrication process. Reducing the size of the individual shutter array to about one square inch and building the large-scale mosaics by tiling these smaller-size arrays would further help to reduce the cost of the device due to the higher yield of smaller devices. The LAMA development is based on prior experience acquired while developing microshutter arrays for the James Webb Space Telescope (JWST), but it will have different features. The LAMA modular design permits large-format mosaicking to cover a field of view at least 50 times larger than JWST MSA. The LAMA electrostatic, instead of magnetic, actuation enables operation cycles at least 100 times faster and a mass significantly smaller compared to JWST MSA. Also, standard surface micromachining technology will simplify the fabrication process, increasing yield and reducing cost.

Moseley, Samuel↗
NASA NTRS2013

Fully Integrated, Miniature, High-Frequency Flow Probe Utilizing MEMS Leadless SOI Technology

This work focused on developing, fabricating, and fully calibrating a flowangle probe for aeronautics research by utilizing the latest microelectromechanical systems (MEMS), leadless silicon on insulator (SOI) sensor technology. While the concept of angle probes is not new, traditional devices had been relatively large due to fabrication constraints; often too large to resolve flow structures necessary for modern aeropropulsion measurements such as inlet flow distortions and vortices, secondary flows, etc. Mea surements of this kind demanded a new approach to probe design to achieve sizes on the order of 0.1 in. (.3 mm) diameter or smaller, and capable of meeting demanding requirements for accuracy and ruggedness. This approach invoked the use of stateof- the-art processing techniques to install SOI sensor chips directly onto the probe body, thus eliminating redundancy in sensor packaging and probe installation that have historically forced larger probe size. This also facilitated a better thermal match between the chip and its mount, improving stability and accuracy. Further, the leadless sensor technology with which the SOI sensing element is fabricated allows direct mounting and electrical interconnecting of the sensor to the probe body. This leadless technology allowed a rugged wire-out approach that is performed at the sensor length scale, thus achieving substantial sensor size reductions. The technology is inherently capable of high-frequency and high-accuracy performance in high temperatures and harsh environments.

Ned, Alex↗
NASA NTRS2014

Structure and Fabrication of a Microscale Flow-Rate/Skin Friction Sensor

A floating element shear sensor and method for fabricating the same are provided. According to an embodiment, a microelectromechanical systems (MEMS)-based capacitive floating element shear stress sensor is provided that can achieve time-resolved turbulence measurement. In one embodiment, a differential capacitive transduction scheme is used for shear stress measurement. The floating element structure for the differential capacitive transduction scheme incorporates inter digitated comb fingers forming differential capacitors, which provide electrical output proportional to the floating element deflection.

Chandrasekharan, Vijay↗
NASA NTRS2014

Embedded Data Acquisition Tools for Rotorcraft Diagnostic Sensors

Rotorcraft drive trains must withstand enormous pressure while operating continuously in extreme temperature and vibration environments. Captive components, such as planetary and spiral bevel gears, see enormous strain but are not accessible to fixed instrumentation, such as a piezoelectric transducer. Thus, it is difficult to directly monitor components that are most susceptible to damage. This innovation is a self-contained data processing unit within a specialized fixture that installs directly inside the rotating pinion gear in the gearbox. From this location, it detects and transmits high-resolution prognostic data to a fixed transceiver. The sensor is based on microelectromechanical systems (MEMS) technology and uses innovative circuit designs to capture high-bandwidth data and transmit it wirelessly from inside an operational helicopter transmission. With Ridgetop's advanced MEMS-based sensor, researchers have, for the first time, been able to extract high-resolution acoustic signatures wirelessly from sensors within the transmission that would otherwise be muffled by background gear noises. Ridgetop's innovative instrument will help researchers perform dynamic analysis of gear interaction and develop improved designs for gear components. In addition, data from this instrument can be used to validate new algorithms that detect and predict faults based on external acoustic signatures, for prognostic purposes. The result of this work will be an improvement in safety, performance, and cost for future generations of rotating components.

Wagoner, Robert↗
NASA NTRS2013

Shear Stress Sensing using Elastomer Micropillar Arrays

The measurement of shear stress developed as a fluid moves around a solid body is difficult to measure. Stresses at the fluid-solid interface are very small and the nature of the fluid flow is easily disturbed by introducing sensor components to the interface. To address these challenges, an array of direct and indirect techniques have been investigated with various advantages and challenges. Hot wire sensors and other indirect sensors all protrude significantly into the fluid flow. Microelectromechanical systems (MEMS) devices, although facilitating very accurate measurements, are not durable, are prone to contamination, and are difficult to implement into existing model geometries. One promising approach is the use of engineered surfaces that interact with fluid flow in a detectable manner. To this end, standard lithographic techniques have been utilized to generate elastomeric micropillar arrays of various lengths and diameters. Micropillars of controlled length and width were generated in polydimethylsiloxane (PDMS) elastomer using a soft-lithography technique. The 3D mold for micropillar replication was fabricated using laser ablative micromachining and contact lithography. Micropillar dimensions and mechanical properties were characterized and compared to shear sensing requirements. The results of this characterization as well as shear stress detection techniques will be discussed.

Wohl, Christopher J.↗
NASA NTRS2017

Omnidirectional Inter-Satellite Optical Communicator (ISOC)

The objective of the Omnidirectional Inter-Satellite Optical Communicator (ISOC) project is to design a compact, lightweight,and energy efficient communicator module for use between satellites in space. This module will achieve continuous optical communication, with simultaneous data transmission and reception, at up to1 gigabit per second (Gbits) data rates for small spacecraft separated by up to 200 kilometers (kms). To achieve this goal,a data communicator with full spherical coverage field of view (FOV) needs to be designed. The proposed ISOC is a dodecahedron geometric array of chipscale, microelectromechanical systems (MEMS) based gimbal-less scanning mirrors that provide adjustable beam pointing and spherical FOV coverage for uninterrupted data transmission between several small spacecraft at arbitrary relative positions. This design eliminates known pointing issues and hence allows accurate direction of arrival calculations.Moreover, the proposed approach will enable data relaying between multiple satellites, and enable relative navigation control.

Inter-small satellite communication↗
NASA NTRS2017

Mars Organic Molecule Analyzer (MOMA) Laser Desorption/Ionization Source Design and Performance Characterization

The Mars Organic Molecule Analyzer (MOMA), a dual-source, ion trap-based instrument capable of both pyrolysis-gas chromatography mass spectrometry (pyr/GC-MS) and laser desorption/ionization mass spectrometry (LDI-MS), is the core astrobiology investigation on the ExoMars rover. The MOMA instrument will be the first spaceflight mass analyzer to exploit the LDI technique to detect refractory organic compounds and characterize host mineralogy; this mode of analysis will be conducted at Mars ambient conditions. In order to achieve high performance in the Martian environment while keeping the instrument compact and low power, a number of innovative designs and components have been implemented for MOMA. These include a miniaturized linear ion trap (LIT), a fast actuating aperture valve with ion inlet tube, and a Microelectromechanical System (MEMS) Pirani sensor. Advanced analytical capabilities like Stored Waveform Inverse Fourier Transform (SWIFT) for selected ion ejection and tandem mass spectrometry (MS/MS) are realized in LDI-MS mode, and enable the isolation and enhancement of specific mass ranges and structural analysis, respectively. We report here the technical details of these instrument components as well as system-level analytical capabilities, and we review the applications of this technology to Mars and other high-priority targets of planetary exploration.

Xiang Li↗
NASA NTRS1999

MEMS for Space Applications

The future of robotic space missions in ever-smaller platforms and MicroElectroMechanical Systems (MEMS) will be key in this development.

MEMS↗