Patent Grant
12091313
Each reference cited herein is expressly incorporated herein by reference in its entirety. With increasing demand for high performance and technologically advanced electronic devices, more efficient and reliable sensors are needed to achieve the performance that has come to be expected of new technology. Sensors play a vital role in these devices by enabling them to interact with and acquire information from the user, their environment, and from themselves. Because of the demand for fast, simple, and energy efficient electronic devices, microelectromechanical systems (MEMS) are often used as sensors for their fast response time, low bulk fabrication costs, and low power consumption [1].
MEMS have a tremendous range of applications and can be used as sensors [2-4], switches [5,6], energy harvesters [7-11], signal filters [12-15], etc., or for multiple applications at once [16,17] (e.g. a sensor-switch). Many of these devices use electrostatic actuation because it can be easily fabricated, consumes minimal power, and can be integrated in electronic circuits without much difficulty [1]. Traditional electrostatic actuation utilizes a parallel plate capacitor configuration with electrostatic forces pulling a movable electrode (typically a beam or plate) towards a fixed one. This can cause the electrodes to collapse if the voltage potential between them is high enough (pull-in). For switches, this is desirable because it closes a circuit between the electrodes if the contacting faces are conductive. Therefore, a MEMS switch can be toggled to closed by applying the pull-in voltage between the electrodes. While pull-in is necessary for switches, it is usually undesirable for sensors, which in many cases need the ability to move freely.
Some effort has been made to eliminate the pull-in instability by exploiting electrostatic levitation [18-30]. This creates an effectively repulsive force between the two electrodes instead of an attractive one. Lee and Cho [18] first applied a similar concept to a MEMS device in 2001 where they demonstrated that two grounded electrodes would be pulled away from each other when in close proximity to a charged electrode on their side. He and Ben-Mrad flipped this design on its side to create out of plane actuation [21]. This configuration, shown in
Triboelectricity has been investigated in recent years as a possible transduction mechanism for converting mechanical energy to electrical energy because of its high energy conversion efficiency and large voltage output [31-39]. Triboelectric charging occurs when two materials with different affinities to gain or lose electrons are brought into contact with each other. Electrons are passed from one material to another at the contact area to equalize the potential at the interface. These materials retain their charge even after the materials have been separated. Despite its large voltage, the current produced is on the order of nanoamps. However, the repulsive force electrode configuration from [21] acts as a completely open circuit between the side electrodes and beam/center electrode, requiring no current. This means the high output voltage of a tribolelectric generator can be exploited for this purpose without the downside of a low power output. Triboelectric MEMs are shown in [42, 59].
The working principle of a triboelectric generator (TEG) is based on coupling between triboelectrification and electrostatic induction [40]. A 3D model of the generator can be seen in
Nonlinearity in electrostatic microelectromechanical systems (MEMS) presents a challenging obstacle in the design of many MEMS sensors and actuators. Electrostatic MEMS convert electrical energy in the form of a voltage potential to kinetic and strain energy in a microstructure or vice versa. In most cases, MEMS are interfaced with electronic circuits to supply power or read the signal from a MEMS sensor. Ideally, sensors and actuators would have a linear relationship between voltage and the electrode position to simplify and miniaturize the electronic circuit. However, the electrostatic force is inherently nonlinear and typically has the relationship Force ˜voltage2/gap2, where the gap is the distance between electrodes. Nonlinearity effectively causes the devices to behave differently at different voltage levels and gaps, so the working range of a device is normally limited to small motions where the force can be treated as effectively linear. However, a smaller range creates less actuation distance for actuators and a smaller signal-to-noise ratio in sensors.
The most common structure of an electrostatic MEMS device consists of two electrodes that act like parallel plates. One electrode is fixed and the other is movable, such as a micro-beam that deflects under the influence of an external force. Applying a voltage potential between the two electrodes creates an electric field that pulls them together. This is the most common method of actuation and sensing in commercial MEMS because it has low bulk fabrication costs, very fast response times, and can be easily integrated into an electronic circuit [45]. However, the electrostatic force is highly nonlinear and can create instability that leads to pull-in (when the two electrodes collapse together), stiction [46], and even chaos [47]. Alternative electrode arrangements have been proposed to avoid instability in electrostatic MEMS [48-51], but all are hampered by the nonlinearity associated with electrostatic forces.
U.S. Pat. No. 7,225,674, discusses a MEMS proof mass that is levitated without any anchoring points. It depends on two electrodes with the same charge repelling each other. The switch uses the attractive electrostatic force with opposite charges to pull two electrodes away from each other. The electric fringe field from the side electrodes pulls on the top of the beam more than the bottom as a result of the shielding that center fixed electrode provides to the bottom face of the beam, and induces a net force upwards. If the beam travels too far away from the center electrode then it would once again be pulled back down with an attractive force because the electric field starts pulling on the bottom face of the beam as it would with a parallel plate. However, the geometry is designed such that this cross over point does not happen until the beam reaches a substantially large deflection.
US20180262843 provides a system and method for a multi-electrode MEMS device, in which electrostatic repulsive forces may be used between the backplate and the membrane to prevent collapse or pull-in.
U.S. Pat. No. 8,963,659 provides electrostatic MEMS devices with high reliability.
Weimin Wang, Qiang Wang, Hao Ren, Wenying Ma, Chuankai Qiu, Zexiang Chen & Bin Fan, “Electrostatic repulsive out-of-plane actuator using conductive substrate”, Scientific Reports volume 6, Article number: 35118 (2016), discloses an electrostatic actuator suspended above a ground plane, as shown in
Matthias Imboden, Jessica Morrison, Evan Lowell, Han Han, and David J. Bishop, “Controlling Levitation and Enhancing Displacement in Electrostatic Comb Drives of MEMS Actuators”, IEEE J. Microelectromechanical Systems (2014) also provides levitation with respect to a set of raised electrodes. See also, Liao, Yunn-Shivan, Shiang-Woei Chyuan, and Jeng-Tzong Chen. “An alternatively efficient method (DBEM) for simulating the electrostatic field and levitating force of a MEMS combdrive.” Journal of Micromechanics and Microengineering 14, no. 8 (2004): 1258, and U.S. Pub. App. 20090322260.
Mark Pallay, Meysam Daeichin, and Shahrzad Towfighian, “Dynamic behavior of an electrostatic MEMS resonator with repulsive actuation”, Nonlinear Dyn (2017) 89:1525-1538, DOI 10.1007/s11071-017-3532-z, discloses a repulsive force actuator similar to that shown in
Liu, Zengtao, Myongseob Kim, Nick Shen, and Edwin C. Kan. “Novel electrostatic repulsion forces in MEMS applications by nonvolatile charge injection.” In Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No. 02CH37266), pp. 598-601. IEEE, 2002 employ non-volatile charge injection to produce levitation actuation of a MEMS beam.
Suzuki, Yuji, Daigo Miki, Masato Edamoto, and Makoto Honzumi. “A MEMS electret generator with electrostatic levitation for vibration-driven energy-harvesting applications.” Journal of Micromechanics and Microengineering 20, no. 10 (2010): 104002, utilizes the levitation force, for the purpose of energy harvesting. The design requires use of an electret.
MEMS microphones are well known. The pull-in problem is well-known, and therefore many configurations employ interdigital fingers with balanced forces in a plane of the diaphragm, to permit capacitive sensing. See, US 20170127189; 20160157025; 20150350790; 20140226841; 20120189151; 20120076329; 20110286610; 20110150260; 20110038492; 20090262958; 20090046883; 20090016557; 20080235079; 20080101641; 20070297631; 20070165896; 20060026054; U.S. Pat. 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Scanning probe microscopes and related devices are well known. Many designs employ a probe which is driven into a surface, and its height of contact measured. One way to measure the height is to propel the probe with a known and dynamically stable motion profile into the surface, and record the timing of contact. Other techniques employ optical sensing, piezoelectric sensing, etc. See, U.S. Pat. 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The present technology relates to an electrostatic levitation MEMS device, which may be used as an actuator, or sensor, for example a switch or accelerometer. In an actuator embodiment, the device is compatible with use of a triboelectric generator to provide actuation. The MEMS device is, for example, a MEMS cantilever/beam, which does not employ a traditional parallel plate electrode configuration and thus avoids the typical pull-in susceptibility which is caused by applying a voltage above a pull-in threshold.
In a typical embodiment, an electrode is fixed to a substrate on each side of a beam, with a conductive plate below the beam, which is held at a controlled potential with respect to the moving electrode, to allow electrostatic levitation and enabling bi-directional actuation.
Advantageously, triboelectricity addresses the voltage requirement to generate an electrostatic levitation force, and may be used to toggle the beam/switch from closed to open. The triboelectric layers of a generator may generate a large enough voltage (˜200 V) between center and side electrodes that creates levitation. The beam tip of a 500 μm bean is capable of, for example a 25 μm deflection.
A threshold shock sensor-switch is provided which consists of a triboelectric generator connected to a MEMS cantilever with a repulsive-force electrode configuration. A small bias voltage is applied between the beam and center electrode to initiate pull-in. The generator is connected between the side and center electrodes and creates a large voltage potential between them when the generator receives an impact. The amount of voltage the generator produces is a function of the impact force magnitude, with a larger impact generating more voltage. This creates a large repulsive force that pulls the beam off of the substrate and opens the switch if the impact force is large enough. Dimples may be placed on the underside of the beam to reduce contact forces, and prevent the beam from sticking to the substrate.
Over the course of a few minutes after actuation, the charge on the generator electrodes decays, which reduces the repulsive force until the switch pulls back in and closes itself. The sensor-switch can be designed such that when the impact force passes a threshold level, the switch is triggered and the beam is released from its pulled-in position. The repulsive-force electrode configuration allows for a very large dynamic range and can be exploited to eliminate the pull-in instability in electrostatic sensors. The triboelectric generator is capable of overcoming the large threshold voltage to actuate the beam via the electrostatic fringe field, and the multi-electrode repulsive-force sensor allows the generator to remain completely open circuit, eliminating the issue with low power output. This opens the possibility for a wide range of novel sensors with increased performance and functionality.
In one embodiment, the center electrode is given a small bias voltage to initiate pull-in and bring the center electrode and cantilever beam into contact with each other, which acts as a closed switch. The side electrodes are then supplied with a voltage relative to the center electrodes, which creates an electric field that pulls the cantilever upwards, employing electrostatic levitation. When the side voltage passes a threshold value, the beam releases from its pulled in position and settles to a stable equilibrium position above the center electrode.
Because the contact or non-contact is a binary condition, the combination of the triboelectric generator and the electrostatic levitation MEMS device provides a shock sensor, since the peak voltage of the triboelectric generator is dependent on the force the triboelectric generator receives. Thus, a lower force generates a lower peak, which may be sub-threshold for changing the state of the electrostatic levitation MEMS device, while a sufficiently larger force will cause a change in state. Further, the triboelectric generator naturally produces a sufficient voltage for actuation, thus presenting a simple configuration without requirement for level shifting, amplification, or other electronic devices. Of course, in other configurations, additional electronics may be provided.
The switch is inherently miniaturized and could easily fit in a miniature electronic device, such as a cell phone.
Alternates to the triboelectric generator are piezoelectric, pyroelectric, and other types of electrically responsive materials. Typically, the electrostatic levitation MEMS device requires voltages in excess of those which typical logic-signal integrated circuits may supply, though various technologies are available which may supply the necessary voltages from a logic circuit. Further, the voltage may also be supplied by inductive or switch capacitor converters.
By driving the potential between the underlying center electrode and the moving electrode, the system is tunable, and may be used as a switch, since a pull-in state is provided. The side electrodes enable a lift-off force, allowing switching between on/off states more readily than electrostatic beams with pull-in forces but no repulsive forces, without failure. This overcomes collapse of the two parallel plate electrodes, and alleviates being stuck in alternating pulled-in positions of a sandwiched beam technique. Further, the design does not add another layer in the fabrication process, and the side electrodes are not in the path of motion of the beam.
The system operates at relatively high voltages, e.g., on the order of 100V, permitting direct use in applications with high voltages present, such as triboelectric, piezoelectric, pyroelectric, and line current.
Advantageously, the use of triboelectric generation/transduction permits a robust and simple design to generate operative conditions for the actuator, and addresses the high voltage requirement of electrostatic levitation by coupling the systems and the contact pressure between the triboelectric layers.
Levitation-based MEMS avoid limiting issues involving pull-in, and draw no current, which allows the triboelectric generator to remain a completely open circuit, and maintain high voltage, which enables synergy between the generation and usage of the voltage.
The system may be used in various electrostatic devices that operate directly from mechanical vibration or shock (i.e., cell phones & safety switches in air bag deployment devices), within safety helmets to provide information on the severity of impacts, to detect severe weather to trigger an immediate response such as shutting off power lines and sounding alarms. For example, the electrostatic levitation may operate from meteorological electrical potentials.
The system may provide a MEMS switch which is normally closed, i.e., pulled-in, which is released (circuit opened) when a sufficient voltage is applied to the side electrodes.
The system may also provide a MEMS sensor, allows the device to move in response to the quantity is sensing, with the possibility of a threshold limit that triggers an action when the sensed quantity exceeds a certain value. The large range of movement of the moving electrode permits application as a sensor, such as an accelerometer, microphone, atomic force microscope probe, force sensor, displacement sensor, or the like. The output may be capacitive, between the moving electrode and the substrate, or the moving electrode may be servo driven to a desired position, and the drive voltage to maintain the position used as a basis for an output, for example.
The moving electrode will typically oscillate, and for many applications, the resonant frequency may be above the sensing frequency. On the other hand, when driven in resonance, modulation of the oscillations may be used as an input or output. While in an oscillatory regime of operation, pull-in may be undesirable, there are cases where this is a desired outcome, and the state which allows pull-in may be tuned by the operative parameters and external conditions, such as inertial forces.
A scanning microscope probe, e.g., atomic force microscope, scanning-tunneling microscope, etc., may be implemented using the repulsive actuator. See, 10,048,289, expressly incorporated herein by reference. The device may have multiple tips, and integrated electronics, e.g., integrated JFETs (junction field effect transistors) as preamplifiers. The JFET device may be monolithically integrated into the MEMS apparatus to reduce the effect of parasitic circuit elements, signals and mismatches. The JFETs also provide on-chip gain and impedance transformation for low noise operation.
A nano-probe tip whose position is freely movable with respect to a substrate (i.e., the nano-probe tip is not attached to the substrate) is coupled to JFET electrodes through electrostatic energy sustaining gaps, and can be sensed by the JFET in two ways. First, the electrostatic force on the JFET induces a strain in the channel which tends to modify the channel carrier mobility of the JFET. Second, the coupled charges across the probe beam of a nano-probe apparatus generate a floating potential on one of the gates of a JFET, which modulates the transistor channel current as a signal that can be measured. The tip is driven repulsively, and the repulsive drive may be displaced from the sensing electrodes. The nano-probe tip position may be coupled to JFET electrodes through a meander spring so that a JFET and a meander spring together may be regarded as a motion sensor with respect to a freely movable nano-probe tip position and movement.
A particular probing method in accordance with the embodiments includes positioning with respect to a sample at least one movable probe tip within a probe apparatus comprising: a substrate; at least one movable probe tip located over the substrate, the at least one movable probe tip being movable with respect to the substrate; at least one motion sensor located over the substrate, the at least one motion sensor comprising at least one pressure sensitive component and at least one spring, the at least one motion sensor being operatively coupled with the at least one movable probe tip, and a repulsive electrostatic drive to displace the probe tip. This particular probing method also includes moving the at least one movable probe tip with respect to the sample while measuring a signal output at the at least one motion sensor.
The MEMS Sensors may be used in gyroscopes, accelerometers, pressure sensors, in smartphones, wearable devices, cars, and various medical devices.
The levitation actuator may act as a sensor by sensing contact, such as by passage of an electric current, an optical sensing of the beam displacement, a resonant frequency change, a beam damping change, an amplitude change (static or dynamic), or other known means. In addition, the large voltage ratio between displacement and side-electrode voltage, a closed loop feedback between the side electrodes (driven) and a displacement error, from a null position, provides a high-level output. The displacement error may be sensed electrostatically, optically, magnetically, or by other means. When the actuator is in resonance, the dynamic mechanical response of the actuator may vary depending on environmental conditions, such as inertia, chemical absorption, etc. For example, a secondary set of electrodes may be provided to measure a motion parameter. Further, the electrostatic potential of a conductive portion of the actuator will vary depending on the repulsive field and the reaction to that field. Thus, for example, a current flowing through the conductor, or a voltage fluctuation through an impedance, may be measured.
One alternative to parallel-plate actuation is electrostatic levitation [52-56]. The electrode configuration shown in
Much effort has been spent characterizing this system, and it has been shown to eliminate the pull-in instability and increase travel ranges by more than an order of magnitude. However, this comes at the expense of requiring a large actuation voltage because the levitation force is relatively weak compared to the attractive force between a pair of parallel plates.
This system can act as a switch by applying a bias voltage to the center electrode [57]. This allows the switch to toggle to and from the pulled-in position for the purpose of creating a more durable switch.
The present technology relates to a repulsive-force actuated electrodynamic microelectromechanical element, which may be used, for example, as a switch, accelerometer, or atomic force microscopy probe.
A key feature of one implementation of the design is that a cantilever beam is suspended over a base plate, held at approximately equipotential with the beam, and is actuated by laterally located electrodes which induce a repulsive force between the beam and the base plate electrode. The system is laterally symmetric, so the net force on the beam is normal to the baseplate.
This approach takes advantage of a fringe electrostatic field to generate a repulsive force that pushes the cantilever beam, or other movable structure, away from the substrate, which essentially eliminates the possibility of pull-in. Because the movable electrode has about the same voltage as the substrate, the possibility of micro-welding is reduced or eliminated. This failure mode happens when two microstructures with different voltages contact each other [43].
The electrostatic force on the moving element differs considerably from that found in conventional parallel-plate electrode designs, and cannot be estimated using simple analytical expressions. The dynamics of the system are nonlinear. However, the combined system can provide a linear relationship with the side electrode voltage for the static response and first natural frequency. See, M. Pallay, R. Miles, S. Towfighian (2019) Merging parallel-plate and levitation actuators to enable linearity and tunability in electrostatic MEMS, Journal of Applied Physics, 126 (1), 014501. This addresses the issues with the nonlinearity of electrostatic systems and can aid in the creation of highly tunable, linear, electrostatic MEMS with large travel ranges.
It is therefore an object to provide a microelectromechanical actuator, comprising: a substrate, having a surface; a beam having a conductive portion, freely suspended over the substrate, and having a long axis parallel to a surface of the substrate, and being displaceable along an axis normal to the surface of the substrate; a center electrode, provided on the substrate under the beam; a pair of side electrodes, axisymmetric with respect to the beam, provided on the substrate; wherein: the pair of side electrodes are configured, when charged, to exert an electrostatic force normal to the surface of the substrate on the beam, that repulses the beam from the substrate, and exerts a balanced electrostatic force on the beam in a plane of the surface of the substrate, the center conductive electrode is configured to shield the beam from electrostatic forces induced by the side electrodes from beneath the beam, and the center electrode is configured to have a voltage different from a voltage on the beam, to thereby induce an attractive electrostatic force on the beam.
The beam may have a first state in which the beam is pulled in to the center electrode by the attractive electrostatic force on the beam, and a second state in which the attractive electrostatic force on the beam by the center electrode is overcome by the repulsive electrostatic force exerted by the side electrodes.
The microelectromechanical actuator may further comprise a triboelectric generator, configured to induce an electrostatic voltage on the pair of side electrodes with respect to the beam, to thereby selectively overcome the attractive electrostatic force on the beam induced by the center electrode.
The beam may have an inertial mass, subject to displacement by inertial forces, and wherein a voltage on at least one of the center electrode and the side electrodes with respect to the beam is adjusted to control an inertial state which triggers pull-in of the beam to the center electrode.
It is a further object to provide a microelectromechanical actuator, comprising: a substrate, having a surface; an electrostatically displaceable conductive element, suspended over the substrate; a center electrode, provided on the substrate under the electrostatically displaceable conductive element; and a peripheral electrode provided on the substrate; wherein: the center electrode is larger than a projection of the electrostatically displaceable conductive element on the substrate, and is configured to shield the electrostatically displaceable conductive element from electrostatic forces induced by the peripheral electrode from beneath the electrostatically displaceable conductive element, the peripheral electrode is configured to exert an electrostatic force normal to the surface of the substrate on the electrostatically displaceable conductive element that repulses the electrostatically displaceable conductive element from the substrate, and the center electrode is configured to have a voltage different from a voltage on the electrostatically displaceable conductive element, to thereby induce an attractive electrostatic force on the beam.
The electrostatically displaceable conductive element may comprise a beam having a conductive portion, freely suspended over the substrate, and having a long axis parallel to the surface of the substrate, and being displaceable along an axis normal to the surface of the substrate; the peripheral electrode may comprise a pair of side electrodes, axisymmetric with respect to the beam, provided on the substrate, configured to exert an electrostatic force normal to the surface of the substrate on the beam, that repulses the beam from the substrate, and to exert a balanced electrostatic force on the beam in a plane of the surface of the substrate, and the center electrode may be provided on the substrate under the beam, configured to shield the beam from electrostatic forces induced by the side electrodes from beneath the beam, and to have a voltage different from a voltage on the beam, to thereby induce an attractive electrostatic force on the beam.
A triboelectric generator may be provided, configured to induce an electrostatic voltage on the peripheral electrode with respect to the center electrode, to thereby selectively overcome the attractive electrostatic force on the electrostatically displaceable conductive element induced by the center electrode, wherein the electrostatically displaceable conductive element has a first state in which the electrostatically displaceable conductive element is pulled in to the center electrode by the attractive electrostatic force on the electrostatically displaceable conductive element, and a second state in which the attractive electrostatic force on the electrostatically displaceable conductive element by the center electrode is overcome by the repulsive electrostatic force exerted by the peripheral electrode from activation of the triboelectric generator.
The electrostatically displaceable conductive element may have an inertial mass, subject to displacement by inertial forces, wherein a voltage on at least one of the center electrode and the peripheral electrode with respect to the electrostatically displaceable conductive element may be adjusted to control an inertial state which triggers pull-in of the electrostatically displaceable conductive element to the center electrode.
It is a further object to provide a method of actuating a microelectromechanical actuator, comprising: providing the microelectromechanical actuator comprising: a substrate having a surface, a conductive element, suspended over the substrate, and being electrostatically displaceable normal to the surface of the substrate, a center electrode, provided on the substrate under the conductive element, and a peripheral electrode, provided on the substrate outside the center electrode, wherein the center electrode is larger than a projection of the conductive element on the substrate, and is configured to selectively shield the conductive element from electrostatic forces induced by the peripheral electrode from beneath the conductive element, and to permit electrostatic forces induced by the peripheral electrode to interact with the conductive element from above the conductive element; applying an electric potential between the conductive element and the center electrode; and repulsing the conductive element from the substrate by applying an electric potential between the conductive element and the peripheral electrode. The conductive beam may comprise a beam having a conductive portion, freely suspended over the substrate, and having a long axis parallel to the surface of the substrate, and being displaceable along an axis normal to the surface of the substrate; the center electrode is provided on the substrate under the beam; the peripheral electrode may comprise a pair of side electrodes, disposed on either side of the center electrode, axisymmetric with respect to the beam and configured to produce an axisymmetric electrostatic force on beam; the center conductive electrode may be configured to selectively shield the beam from electrostatic forces induced by the side electrodes from beneath the beam, and not to shield the beam from electrostatic forces induced by the side electrodes from above the beam; the electric potential between the beam and the center electrode may be sufficient to cause pull-in; and the electrostatic force on the beam induced by the pair of side electrodes may repulse the beam from the substrate.
It is also an object to provide a method of actuating an microelectromechanical actuator, comprising: providing the microelectromechanical actuator comprising a substrate, having a surface, a beam having a conductive portion, freely suspended over the substrate, and having a long axis parallel to a surface of the substrate, and being displaceable along an axis normal to the surface of the substrate, a center electrode, provided on the substrate under the beam, and a pair of side electrodes, axisymmetric with respect to the beam, wherein the center conductive electrode is configured to shield the beam from electrostatic forces induced by the side electrodes from beneath the beam provided on the substrate; applying an electric potential between the beam and the center electrode to cause an electrostatic attraction sufficient to cause a pull-in; and inducing an axisymmetric electrostatic force on the pulled-in beam by the pair of side electrodes, normal to the surface of the substrate on the beam, that repulses the beam from the substrate, to release the beam from a pulled-in position contacting the substrate to a suspended position displaced from the substrate.
It is a further object to provide a method, comprising: providing an electrostatically-repositionable tip of an actuator beam; displacing the actuator beam away from a supporting substrate of the actuator beam, by applying a bias voltage potential with respect to an actuator beam potential between a bias electrode on the supporting substrate beneath the actuator beam, and a side voltage potential between a pair of laterally located electrodes on the supporting substrate and the actuator beam, wherein the side voltage potential produces a force to levitate the actuator beam away from the supporting substrate, toward the surface; and detecting a displacement of the actuator beam. The pair of laterally located electrodes on the supporting substrate may exert a laterally balanced force on the actuator beam in response to the side voltage potential. The actuator beam may be displaced to contact a surface.
The surface contact may be detected by electrical conduction between the actuator beam than the surface. The tip of the actuator beam may be displaced to contact the surface a plurality of times at a plurality of relative positions, further comprising determining a surface profile of a surface. The tip may be scanned over a portion of the surface, and the detected displacement of the actuator beam determined for a plurality of scan positions, to map a surface profile of the surface.
Contact of the tip with the surface may be determined by a piezoelectric transducer.
The side voltage potential may be increased, to thereby increase an actuator beam deflection, until the tip contacts the surface, and the deflection determined based on the voltage potential at a time of tip contact.
The side voltage potential may be oscillatory, and temporal characteristics of the actuator beam determined.
The bias voltage may be tuned to control a response of the actuator beam to the side voltage.
The side voltage may be generated by a triboelectric generator.
The displacement of the actuator beam may be oscillatory, and a dynamic displacement of the actuator beam detected.
It is a further object to provide a method of determining a surface profile of a surface, comprising: providing an electrostatically-repositionable tip of an actuator beam; displacing the actuator beam away from a supporting substrate of the actuator beam, by applying a bias voltage potential with respect to an actuator beam potential between a bias electrode on the supporting substrate beneath the actuator beam, and a side voltage potential between a pair of laterally located electrodes on the supporting substrate and the actuator beam, wherein the side voltage potential produces a laterally balanced force to levitate the actuator beam away from the supporting substrate, toward the surface; and detecting a displacement of the actuator beam at which the tip contacts the surface.
The tip may be scanned over a portion of the surface, and the detected displacement of the actuator beam is determined for a plurality of scan positions, to map a surface profile of the surface.
A contact of the tip may be determined by a piezoelectric transducer.
The side voltage potential may be increased, to thereby increase an actuator beam deflection, until the tip contacts the surface, and the deflection determined based on the voltage potential at a time of tip contact.
The side voltage potential may be oscillatory (AC), and temporal characteristics of contact of the tip and the surfaced may be determined.
The bias voltage may be further tuned to control a response of the actuator beam to the side voltage.
The side voltage may be generated by a triboelectric generator.
It is another object to provide a method of determining an inertial state of a mass, comprising: providing an electrostatically-repositionable actuator; controlling a force on the actuator with respect to a supporting substrate of the actuator, by applying a bias voltage potential with respect to an actuator potential between a bias electrode on the supporting substrate beneath a beam portion of the actuator, and a side voltage potential between a pair of laterally located electrodes on the supporting substrate and the beam portion of the actuator, wherein the side voltage potential produces a laterally balanced force tending to levitate the beam portion of the actuator away from the supporting substrate; detecting a displacement of the actuator; and controlling at least the side voltage potential, wherein a side potential voltage required to maintain a position of the actuator is responsive to the inertial state of the mass.
The inertial mass may be supported by a plurality of beam portions, each having a respective bias electrode and a pair of respective side electrodes.
The inertial mass may be configured to detect an acceleration, a rotation, and/or a shock, for example.
It is a further object to provide a method of determining an inertial state of a mass, comprising: providing an electrostatically-repositionable actuator; controlling a force on the actuator with respect to a supporting substrate of the actuator, by applying a bias voltage potential with respect to an actuator potential between a bias electrode on the supporting substrate beneath a beam portion of the actuator, and a side voltage potential between a pair of laterally located electrodes on the supporting substrate and the beam portion of the actuator, wherein the side voltage potential produces a laterally balanced force tending to levitate the beam portion of the actuator away from the supporting substrate; and detecting a displacement of the actuator while subject to the controlled force.
The detected displacement may comprise a contract between the actuator and the bias electrode.
The method may further comprise levitating the actuator away from the bias electrode by increasing the side voltage.
A force between the bias electrode and the actuator may be an attractive force toward the substrate, and a force between the side electrodes and the actuator may be a repulsive force away from the substrate.
The actuator may be subject to pull-in to the bias electrode, and the side electrodes may have a range of operation which produces a sufficient force to overcome the pull-in and release the actuator from the bias electrode.
The side electrodes may have a voltage dependent on a force, such that the actuator and bias electrode form a force-activated switch.
The side electrodes may have a voltage dependent on a force impulse, such that the actuator and bias electrode form a force-impulse activated switch.
The side electrodes may have a voltage dependent on a shock, such that the actuator and bias electrode form a shock-activated switch.
To model the actuator, the system can be treated as an Euler-Bernoulli beam with the governing equation of motion defined as,
where {circumflex over (v)} is the transverse beam deflection (z-direction beam displacement) that depends on the position along the length x of the beam, and time t, I is the moment of inertia, and {circumflex over (f)}e (ŵ, {right arrow over (V)}) is the electrostatic force, which depends on the transverse deflection and applied voltages. Because there are multiple electrodes with different voltages, V is a vector of voltages that are applied to the beam, side electrodes, and center electrode.
The out of plane deflection governing equation of motion for a clamped-clamped beam is:
where γ indicates the mid-plane stretching effect. γ is −1 for the clamped-clamped beam and 0 for the cantilever. Because of the small scale of the beams, a nondimensional form of Eq. (1A) may be used. The nondimensional substitutions and parameters are shown below, and the non-dimensional equation of motion is given as:
where pj are constants from the 5th-order polynomial forcing profile fit. In Table II and Eq. (1B), the nonaccented variables refer to the non-dimensional quantities. Equation (1B) is then discretized using Galerkin's method. The deflection of the beam is approximated as:
where φi(x) are the linear mode shapes of the beam, qi(t) are the time-dependent generalized coordinates, and n is the number of degrees of freedom (DOF) to be considered. In our case, the mode shapes for a cantilever (CL) and clamped-clamped (CC) microbeam are well known and are of the form φi(x)=cos h(αi x)−cos(αi x)−σi (sin h(αi x)−sin(αi x)), where αi are the square roots of the non-dimensional natural frequencies, and σi are constants determined from the boundary conditions and mode to be considered. Values of αi and σi for the first four modes are obtained from [39]. Once the mode shapes are known, Eq. (1B) becomes a coupled set of ordinary differential equations (ODE) in time for qi(t). Multiplying through by φk and integrating between 0 and 1 decouples the linear terms because of the orthogonality of the mode shapes and results in a set of ODEs, coupled through the nonlinear forcing terms. See, Pallay, Mark, Meysam Daeichin, and Shahrzad Towfighian. “Dynamic behavior of an electrostatic MEMS resonator with repulsive actuation.” Nonlinear Dynamics 89, no. 2 (2017): 1525-1538.
For a classic electrostatic beam with a parallel-plate electrode configuration, {circumflex over (f)}e can be represented analytically with an inverse polynomial of order two that has a singularity when the gap between electrodes goes to zero. However, in the system examined here, the simple analytical expression for the electrostatic force is not valid because of the different electrode arrangement, and the force must be calculated numerically. One way this can be achieved is to calculate the potential energy of the beam at each position, then take the derivative with respect to the direction of motion (ŵ). In this case, the potential energy is calculated from the voltage vector and capacitance matrix, the latter of which is simulated with a 2D finite-element analysis in COMSOL. The potential energy can be represented by,
where ĉij are the capacitances between each pair of electrodes, and Vside, Vbias, and Vbeam, are the voltages on the side electrodes (1), center electrode (2), and beam (3) respectively. The capacitance matrix is symmetric with cij=cji, which results in 6 independent capacitances in the system. Expanding Equation (2), setting Vbeam=0 because the beam is assumed to be the reference ground voltage level, and taking the derivative with respect to the transverse beam deflection, yields,
In Equation (3), the derivatives of the COMSOL simulated capacitance, ĉij, can be estimated with a simple central difference method.
can be fit with 9th order polynomials to create an analytical representation of the numerical data that can be used in Equation (1)
however, would require upward of a 20th order polynomial for an adequate fit, and therefore requires more consideration regarding its representation in Equation (1).
which represents the electrostatic levitation force. Conversely, if the side voltage is set to zero, only
remains and the system acts as a parallel-plate. By observing the c11 and c22 capacitances, it is clear that c22 has a much larger nominal capacitance and the magnitude of the slope is greater, especially at small gaps. This shows the parallel-plate force from the bias voltage is by far the dominant force component in this system. To counter this, much larger side voltages are needed to overcome the effect of the bias voltage.
After the force is calculated, Equation (3) is plugged into Equation (1) yielding the dimensionalized equation of motion for the cantilever,
where αi and βi are fitting coefficients for the c11 and c12 terms respectively. Equation (4) is then nondimensionalized with the substitutions shown in Table II, which yields the final nondimensional equation of motion shown in Equation (5).
When the time-derivative terms in Equation (5) are set to zero, it becomes a fourth-order ordinary differential equation, with x being the only independent variable. Despite the complicated forcing term, this equation can be solved directly as a boundary value problem. First, however, a form for
must be determined. Because this force component behaves similarly to the parallel-plate force, a fitting function with a similar form can be used. Because this force component behaves similarly to the parallel-plate force, a fitting function with a similar form can be used.
is fit with the function shown in Equation (6).
Plugging this into Equation (5) after dropping the time derivatives gives the static equation of motion that can be solved with the boundary value solver, bvp4c, in MATLAB.
Cantilevers with the electrode arrangement in
Another interesting result is the linear relationship between tip deflection and side voltage, especially at higher bias voltages. The slope is approximately 90 nm per volt on the side electrodes. This linear relationship is maintained for more than 10 μm of static displacement. (Because high voltages cannot be applied in devices created using the PolyMUMPs fabrication procedure, 190V was not exceeded.) The tip displacement shows no signs of saturating near 190V and the linear voltage relationship most likely extends much further. When there is no bias voltage, an approximately linear relationship exists for deflections above around 4 μm. However, when 4V bias is added to the center electrode, the linearity extends all the way down to 0 μm. If the bias voltage is too large, such as at 6V, pull-in will occur at small gaps. Therefore, there exists an optimal bias voltage, 4V for the dimensions shown in Table I, that yields a linear response over the entire static range.
The reason for the linearization between side voltage and tip displacement can be seen by analyzing the force and its associated components.
The reason for the linearization of the force is different when at larger voltages as opposed to smaller voltages. When the side voltage is above 80V, the c11 and c22 are negligible compared to the c11 component. In this case, the system acts like as if there was just a pure levitation force with no bias voltage. When the side voltage is increased, the upward electrostatic force on the beam also increases. If the beam was completely rigid, this force would scale with the square of the side voltage. But the beam is not rigid and deflects upwards when the side voltage is increased. This deflection increases the gap between the beam and fixed electrodes, which in turn causes the upward electrostatic force to decrease. When the side voltage is large, the decrease in the upward electrostatic force from increasing the gap counteracts the nonlinearly increasing force with voltage and the result is an effectively linear scaling of the total force with side voltage. This can be seen in the static position in
To achieve linearity at low side voltages, a bias voltage on the center electrode must be used. Comparing the upward levitation (c11) and downward parallel-plate (c22) components of the force in
Natural frequency is an important property of oscillators and sensors that determines their resolution and sensitivity. To calculate the natural frequency, we must return to the dynamic partial differential equation from Equation (5). Now w becomes a function of time and position so it must be reduced to an ordinary differential equation in time before we can calculate the natural frequency. This can be achieved by performing Galerkin's method, which is a modal analysis using separation of variables and integration over x to get a set of second-order ordinary differential equations that are coupled through nonlinear terms. If just a single mode is to be considered, this will yield a single ordinary differential equation that can be used to calculate the natural frequency.
First, the transverse deflection of the beam is assumed to have separate spatial and time-dependent functions as shown in Equation (8).
w(x,t)=φ(x)q(t) (8)
The mode shapes, φ(x), can be solved from the eigenvalue problem, which depends on the boundary conditions. The mode shapes for a simple cantilever are well known and can be expressed by,
φi(x)=cos h(λix)−cos(λix)−σi(sin h(λix)−sin(λix)) (9)
where λi is the square root of the ith nondimensional natural frequency, and σi is a constant. For the first mode, φ1 (herein referred to as φ), σi and λ1 are 0.7341 and 1.875 respectively. However, to account for fabrication imperfections the natural frequency may be identified from an experiment and nondimensionalized to use with Equation (9).
After separation of variables, the governing equation is multiplied by φ and integrated over x to yield Equation (10), which is a second-order ordinary differential equation that depends only on the time-dependent component of the solution, q,
The last term in Equation (10) can be problematic if it is not dealt with appropriately. For the static problem, this term could be fitted with the function given in Equation (6). However, the integration on x from the modal analysis will create a singularity at x=0, which will make the differential equation impossible to solve. A standard parallel-plate has a similar problem; however, it can be mitigated by multiplying the entire equation by the denominator, expanding the polynomial, and then performing Galerkin's method. In this case, two complications prevent that from working. First, the order of the polynomial in the denominator of Equation (6) is not an integer, so it cannot be expanded. Second, multiplying the two 9th order polynomials by a noninteger polynomial will be extraordinarily difficult and tedious later in the problem when solving for the natural frequency. Therefore, this term can be treated numerically as a list of numbers, where linear interpolation is used to estimate the values between data points. This is more computationally expensive, but computation time is not an issue for the natural frequency calculation. Before that can be done, the integration on x must be performed.
The derivative,
can be rewritten using the relationship,
When substituting Equation (13) into Equation (10), the φs cancel and the integration becomes 1. Now that x has been integrated out of the equation, q represents the deflection of the beam instead of w. The derivative of the numerical c22 data from COMSOL with respect to the deflection can be substituted in for
The final equation becomes,
To find the natural frequency, the eigenvalues of the Jacobian matrix can be calculated by decomposing Equation (14) to two first-order ODEs with y1=q and
setting the damping coefficient to zero, and plugging the equations into the relationship,
which is the Jacobian matrix. The eigenvalues of Equation (15) are,
where the natural frequency is the imaginary part of the eigenvalue. The only variable that is unknown in this equation is y1, which is the beam deflection. The value of y1 at each voltage level can be determined from the static model results at the given side and bias voltage, after which the natural frequency can be calculated.
In order to experimentally measure the values, white noise was superimposed on the DC side voltage while holding the bias voltage constant, and the beam tip velocity was recorded with the laser vibrometer. A fast-Fourier transform (FFT) was performed on the velocity signal to extract the natural frequency. Unlike the static case, the side voltage was not swept up continuously to 190V. Instead, the side and bias voltage were kept constant and the natural frequency was extracted at 10-volt intervals.
The model agrees well with the natural frequency experiment. The square root of the natural frequency, λ1, was 1.7998. The curling of the beam tip in the fabricated beam needs to be incorporated into the model to obtain a better fit with the experiment. Because the beams are very long, residual stress from fabrication causes them to curl upward when released. This increases the gap between the beam and center electrodes and reduces the total electrostatic force. In this case, the beam tip was curled up approximately 2 μm out of plane. Ideally, this would be incorporated into both q and the mode shapes. However, the easiest way of addressing this problem is to simply add 2 μm of deflection to q.
When no bias voltage is applied,
The system can therefore be tuned to capture a wide range of frequencies, which is highly desirable in many sensors.
At an optimum value of the bias voltage, the highest linearity of natural frequency and the side voltage is achieved. If the bias voltage is set to approximately 2V, the downward bending of the natural frequency curve at low side voltage reaches a point where it matches the slope at higher side voltages. This creates a linear shift in natural frequency with side voltage. Unlike the static solution, the natural frequency is related to the slope of the force at the equilibrium position instead of the magnitude. The slope of the force is the linear stiffness, which is related to the natural frequency through the relationship,
where ωn is the natural frequency, m is the mass, and keff is the effective stiffness, which is the sum of the mechanical stiffness of the beam (kmech) and the added stiffness from the electrostatic force (kelec), where kelec is much larger than kmech. Because m and kelec are constant, kelec must be related to the side voltage. If ωn is linearly related to side voltage, then kelec must be related to the square of the side voltage. This is confirmed to be true by analyzing the slope of the force at each static equilibrium position. The linear relationship in frequency is approximately 16 Hz per volt and is maintained for more than 2.9 kHz of frequency shift. The combination of parallel-plate and electrostatic levitation enables a wider range of capabilities that is not possible with each mechanism on its own.
To obtain the model frequency response, the dynamic equation of motion must be solved. Much of the procedure for calculating the natural frequency of Equation (5) can be used for the frequency response as well. Equation (14) can be integrated directly using linear interpolation to determine
However, the computation expense of using linear interpolation becomes problematic and creates very long solve times. To reduce the integration time,
can be fit with the inverse non-integer polynomial in Equation (6) with q replacing w. This is not problematic, because the substitution is occurring after the modal analysis, which is where the problems were occurring initially. This significantly reduces the computation time so that the frequency response can be calculated. The final dynamic equation is given in Equation (18).
The damping coefficient is estimated from the experiment, which was conducted at approximately 300 mTorr, which correlates to a quality factor of 500. The quality factor is used in Equation (18) by the relationship c=λ12/Q.
To conduct the experiment, the side voltage is given an AC voltage on top of the DC offset. The DAQ supplies the AC voltage, and the DC offset function of the Krohn-Hite amplifier applies the DC side voltage. The bias was held constant at the same 0V, 2V, 4V, and 6V values used in the static and natural frequency tests. For the frequency response, the tip velocity was measured with the vibrometer.
As with the static and natural frequency results, the frequency response model agrees with the experiment. In the experiment, the backsweep branch continues to grow until it starts tapping on the center electrode and falls back down to the lower branch. If the bias voltage is high enough, instead of falling back down to the lower branch, it pulls in, as is the case at 6V bias. Before pull-in occurs, the backsweep branch becomes very flat and increases in size. This extension of higher branch oscillation is because of the quadratic nonlinearity that causes excessive softening from electrostatic levitation and parallel-plate schemes. With no bias, the backsweep branch ends around 11 kHz, but with 6V bias the branch travels back to 10 kHz before pulling in. The high amplitude vibration could be useful for the development of high-resolution oscillators. The triggering of dynamic pull-in near the resonant peak can help create combined systems that act as a sensor and a switch, which triggers when the sensed quantity increases past a threshold. The levitation force can be used to release the pulled-in structure and reuse the device.
To get more insight into the motion of the beam, the model displacement was calculated and is shown in
However, other applications that are less hindered by the nonlinear frequency response may be able to exploit other behaviors of the combined system, such as dynamic pull-in shown in
The relationship between static tip displacement and natural frequency with side voltage can be linearized by choosing an appropriate bias voltage, which can greatly simplify and minimize the electronic circuitry for processing information from sensors and controlling actuator motion. The natural frequency for the design according to Table I can be tuned from 6 kHz up to 12 kHz, increasing tunability, which gives sensors a larger spectrum of detectable frequencies with large signal-to-noise ratios. The softening branch of the frequency response can be flattened and extended by adding a larger bias voltage. The larger bias also triggers dynamic pull-in near the resonant peak, which permits use of the technology for combined sensors and switches that use pull-in to close a circuit. The levitation force enables the system to release from its pulled-in position, allowing the combined sensor and switch system to be reused many times without failure.
MEMS sensors and actuators have replaced their macro counterparts in many applications including, for example, pressure sensors, inertial navigation systems, and adaptive optic systems [61-63]. They have enabled consumer electronic products like smartphones, laptops, virtual reality headsets, and health monitoring wearable devices to deliver more enriched functionality. Their reliable performance, low cost, low power consumption, and more importantly, their compatibility with semiconductor fabrication technology have made MEMS technology popular.
Electrostatic actuation and detection is the most common transduction method in MEMS [64], and almost all the current commercially available electrostatic MEMS devices are based on parallel-plate [65] or interdigitated comb drive configurations [66]. In a parallel-plate configuration, the electrostatic force attracts a movable electrode to the substrate or bottom electrode. One can apply a specific voltage to move an electrode to a desired position in the case of an actuator (like micromirrors), or exert an excitation and sense change in the capacitance between two electrodes in the case of a sensor (like accelerometers).
The main drawback of this electrostatic force is pull-in instability. Pull-in happens when the restoring force of the microstructure is no longer able to overcome the attractive electrostatic force and as a result, the microstructure collapses to its substrate. Capacitive MEMS transducers are designed to operate far from the pull-in region and this limits the device operation range; for example, it limits the travel range in micro-mirrors [67]. This issue is a significant constraint that needs to be considered in designing the microstructure geometry. Particularly, the initial gap between the movable electrode and the substrate is affected by this design limitation. This initial gap plays a crucial role in squeeze film damping [64] and the magnitude of the electrostatic force. As a result, it has a significant effect on the device sensitivity and performance in general.
As a new design paradigm, the repulsive capacitive sensing configuration is an alternative to parallel-plate or comb-drive configurations [68-70]. This approach takes advantage of the fringe electrostatic field to generate a repulsive force that pushes the movable structure away from the substrate, which essentially eliminates the possibility of pull-in (
Lee et al. first introduced the repulsive approach [72]. A new generation of repulsive actuators was developed by He and Ben Mrad [73,74,68,69]. The nonlinear dynamics of microstructures under a repulsive force has also been investigated [75-77].
The repulsive approach is exploited to build a capacitive accelerometer. There are numerous applications for accelerometers. They are main components of inertial navigation systems used in cars, airplanes, smartphones, etc. For example, they are used to deploy airbags in automobiles in an accident [78] or, as a part of wearable health monitoring technologies, to detect the sudden fall of elderly people [79] to provide them with necessary medical attention as soon as possible. For a comprehensive study on accelerometer sensors based on the parallel-plate scheme, see [80].
The electrostatic force on the moving element in the system examined here differs considerably from that found in conventional parallel-plate electrode designs and cannot be estimated using simple analytical expressions. This, along with the large amplitude vibration of the proof-mass, makes the dynamics of the system fully nonlinear and complicated.
The general schematic of the structure under base excitation is shown in
The dimensions of all these beams and their electrostatic field are illustrated in
When the base of the plate accelerates, the plate tends to stay at rest because of its inertia and this leads to a relative displacement between the base and the plate. Because of this displacement, the capacitance between the electrodes will change as well. This change in capacitance can be measured and related to the relative motion of the plate. If the load is large enough, the fingers can hit the bottom electrodes. However, because of the repulsive nature of the force, they will bounce back and will remain free to move. This collision can be detected with the aid of an electrical circuit.
A simple single degree of freedom model [76] may be used as a very powerful tool to predict the response of the system and capture the inherent nonlinearity caused by the electrostatic force. A lumped parameter oscillator is considered:
I{umlaut over ({circumflex over (θ)})}+c{dot over ({circumflex over (θ)})}+k{circumflex over (θ)}=Mes({circumflex over (θ)})+Msh (19)
in which {circumflex over (θ)} is the rotation of the proof-mass plate about its anchors' axis, I, c and k are the moment of inertia, torsional damping, and torsional stiffness coefficients, respectively. On the right-hand side, Mes and Msh represent the electrostatic moment and inertial moment because of the base excitation, respectively.
The electrostatic force has a nonlinear dependence on the position of the moving fingers in the electric field. To obtain an expression for the electrostatic moment, first we calculate the force profile for a unit-cell using a 2D finite element analysis in COMSOL. Such a unit cell consists of the moving electrode, bottom electrode and two side electrodes as shown in
where z is the gap between the bottom electrode and moving fingers in each cross section. In order to write the electrostatic force as a function of θ, we use the following trigonometric equation.
which yields
where z is the gap between the bottom electrode and moving electrode. In order to write the electrostatic force as a function of θ, we use the following trigonometric equation.
Integrating Eq. (22) over the beam (finger) length results in the total electrostatic force on each beam.
where the parameters are given in Table III. To calculate the corresponding moment caused by this force, the distance between the acting point of the resultant force and the axis of rotation (xc) is needed, which can be calculated as follows:
Therefore, the moment of electrostatic force on the tip fingers about the axis of rotation can be written as
where Nt is the number of fingers on the tip side of the proof mass. Following a similar approach and assuming that the electrostatic force on the fingers on the sides of the proof-mass does not change over the finger length, we can calculate the moment of the electrostatic force on these fingers as follows:
where uj is the distance of the jth side finger from the axis of rotation and Ns is the number of fingers on each side. So, the total electrostatic moment in Eq. (19) can be written as:
Mes({circumflex over (θ)})Mes-tip+2·Mes-side (27)
The factor 2 in Eq. (27) accounts for the fact that there are two sets of side fingers, one on each side of the proof-mass. The moment from acceleration (Msh) also can be written as:
where the first bracket is the moment caused by proof mass acceleration, the second shows the moment caused by the tip fingers acceleration, and the third is for the side fingers. In Eq. (28), mp, mb, and a(t) are the mass of the rotational plate, mass of the moving electrode, and the acceleration load that is exerted on the microstructure through base excitation. This mechanical load can be modeled as a harmonic base excitation or as a shock load. There are different shock profiles commonly used for modeling shock loads such as square, saw-tooth, half-sine or full-sine shock profiles. The most commonly used shock load is the half-sine with the profile given in Eq. (29), which will be used in the following description of the experiment on the fabricated device,
where
is the step function. Dividing Eq. (19) by I and using Eqs. (27) and (28) and following non-dimensional parameters (Eq. (30), we can rewrite the governing equation of motion in nondimensional format (Eq. (31).
By applying a DC voltage on the side electrodes, the proof-mass rotates around its anchors' axis and goes to an equilibrium point away from the substrate. To obtain this static rotation, all the time derivative terms in Eq. (31) are set to zero and then the equation is solved for static rotation (θst). The static rotation can be used to solve for the dynamic solution (θdyn) of Eq. (31) in the presence of any time-varying load using the following change of variable.
θ=θst+θdyn (32)
The moment of inertia, I, in Eq. (31) can be calculated as
The natural frequency of the first mode, ωn is obtained from the ANSYS finite element package. The first mode is a rotational mode as expected. The corresponding natural frequency for this mode is predicted to be 1320 Hz. After examining subsequent experimental data, this value can be modified for the natural frequency to account for all the fabrication imperfections, residual stresses and mathematical simplification in this 1 DOF model.
Eq. (31) can be solved numerically using the Runge-Kutta method for various damping conditions. However, it is likely that a simple linear damping does not capture the physics of energy dissipation in this problem. In general, modeling energy dissipation in the repulsive scheme is more challenging compared to the attractive scheme because of two reasons. First, the amplitude of vibration can get very large compared to the initial fabrication gap because the initial static deflection of the structure (from Vdc) moves the structure away from the substrate, providing more space for vibration. Therefore, those damping models available in the literature [81-83] that are based on Reynolds' equation are not valid because the underlying assumptions such as negligible pressure change across the fluid film or small gap to lateral dimension ratio are not valid here. Second, because there is no limitation from pull-in, the device can get very close to the substrate while having a large amplitude vibration. So, in each cycle of vibration, when the moving part is far away from the substrate the dominant damping mechanism is the drag force in free air. However, when the structure gets close to the substrate, the squeeze film damping mechanism starts to play a significant role in energy dissipation. Thus, the damping force is likely to be quite nonlinear.
Another challenge in modeling damping in this problem is that the continuity assumption for the air breaks down when the microstructure gets very close to the substrate, especially at low pressures. In this situation, the characteristic length of the problem is even smaller than the initial fabrication gap, and the characteristic length of the problem becomes comparable with the mean free path of air molecules. The Knudson number is the parameter to check to see if the continuity assumption is valid (Eq. (34)). This number is defined as the ratio of the mean free path of air (gas) molecules to the characteristic length of the problem, which is usually the gap between moving and stationary parts of the microstructure. The mean free path of air molecules depends on the air temperature and pressure. Assuming the room temperature condition (25° C.), the dependence of the molecules' mean free path on pressure can be written as in Eq. (34)
Using the Knudsen number, the flow is divided into four regimes: continuum flow, slip flow, transitional flow and free molecular flow. Assuming the characteristic length to be equal to the initial gap and using Eqs. (34) we can categorize the flow according to pressure (Table IV). As the experiment is performed at very low pressure on the device (P<350 mTorr), the flow regime would be in the free molecular regime. Also, as the microstructure gets very close to the substrate, the characteristic length of the problem becomes even smaller than 2 μm, which leads to higher threshold pressure for the molecular region. The modular damping depends on the ratio of vibration amplitude to the initial gap (initial fabrication gap+static deflection caused by DC voltage). When the vibration amplitude is small compared to the initial gap, the damping is dominated by linear viscous damping. However, as the vibration amplitude becomes comparable with the initial gap, the squeeze film damping increases as the air molecules are trapped between the proof mass and substrate. The equation accounting for this variable damping that modulates itself with the amplitude-gap ratio is given in Eq. (35) [76]. I
With the description of damping above, all the parameters in Eq. (31) have been defined.
The process flow of the device fabrication is depicted in
Experiments were conducted on the fabricated sensor to investigate the accelerometer dynamical performance and verify the mathematical model described above. The sensor was subjected to two different mechanical loads, harmonic excitations and shock loads. For harmonic loading, the dynamic response of the microstructure in the resonance region is considered that sheds light on the effects of inherent nonlinearities in the electrostatic force. Also, the mechanical sensitivity of the accelerometer is obtained, which is an important parameter with a significant contribution to the overall sensitivity of the sensor. This mechanical sensitivity is obtained from the frequency response before reaching the resonance region, because accelerometers are always used at frequencies below their resonance range. The robustness of the accelerometer against mechanical shocks is another important parameter to be analyzed.
The printed circuit board containing the MEMS chip is mounted to the head of the shaker and placed inside the vacuum chamber at 200 mTorr. A laser vibrometer (Polytec MSA-500) is used to monitor the time-response of the sensor. This set up is shown in
The output acceleration of the shaker depends on the amplitude and frequency of the voltage signal given to the shaker. To conduct a frequency sweep on the microstructure, the shaker needs to provide a base acceleration with a constant amplitude at different frequencies. Usually, a closed loop system is used with the shaker where the output acceleration of the shaker is constantly monitored so acceleration amplitude can be kept constant by modifying the amplitude of the voltage signal. Here, the shaker is used in an open loop mode. To identify the required voltage needed to send to the shaker at each frequency (f), the shaker is characterized in a separate setup where a laser vibrometer is used to measure the shaker velocity. For example, if a harmonic base acceleration with 1 g amplitude at 3000 Hz from the shaker is required, voltages with 3000 Hz frequency and different amplitudes are sent to the shaker until a voltage amplitude that results in 1 g±1% acceleration is found. Then, the same procedure is repeated for the next frequency step (3010 Hz). To characterize the shaker for half-sine shock excitations with different time duration, the shaker response is measured with a commercial accelerometer (PCB-352A24). If the shock amplitude is within ±1% range of the desired amplitude, the voltage will be recorded to be used for the shock experiment.
After the shaker characterization, the device is tested by applying harmonic base excitation and performing a frequency sweep. Such an analysis is helpful to investigate the accelerometer dynamical performance and verify the mathematical model described above.
The motion of the sensor proof-mass relative to the substrate is obtained by subtracting the substrate response from the device response for each excitation frequency (f). As the motion of the substrate does not depend on the electrical voltage on the device, for each mechanical loading scenario, the substrate motion was measured by reading its velocity with the laser vibrometer. The device response, on the other hand, depends on the mechanical load and electrical voltage on the side electrodes. For each loading case, the proof-mass response was measured again by reading its velocity using the laser vibrometer. Then, the velocity of the substrate for each mechanical load was subtracted from the device response for the corresponding mechanical load to obtain the relative velocity of the proof-mass. Subsequently, the fast Fourier transform (FFT) of this relative velocity signal was calculated to extract the velocity amplitude in the steady-state region. Dividing this velocity amplitude by 2πf results in the displacement amplitude for the corresponding frequency.
The softening behavior in the frequency response at a high voltage of 50V and 60V can be explained by the even-order terms in electrostatic force (A2, A4, A6, A8). Simulation results are presented in
The nonlinearity in the device response when the bias voltage is 40V is slightly hardening while the lumped model predicts softening. This discrepancy between the simulation results and experimental data can be reconciled by introducing a cubic nonlinear term for mechanical stiffness for this specific voltage but such a nonlinearity makes the response hardening for higher voltages which does not match the experimental data. Also, because the vibration amplitudes with different voltages for the same mechanical loads are very close to each other (for example, the resonance amplitudes for 40V and 50V when the acceleration amplitude is 3 g), this difference in behavior cannot be attributed to the nonlinearities in the electrostatic force or stiffness caused by air in squeeze film regime.
Although the model does not catch the nonlinear behavior of the microstructure in the resonance region for low voltages, it matches the experimental data away from this region with good accuracy. Because inertial sensors are generally operated in frequency ranges away from their natural frequency the model still could be used to simulate the device response at low frequencies.
The sensitivity of the device for different voltages is shown in
Robustness of accelerometers against mechanical shocks is an important parameter. Under mechanical shocks, a force is transmitted to the microstructure through its anchors during a short period of time compared to the natural period of the microstructure. These loads are usually characterized by the induced acceleration on the affected structure with three parameters: maximum acceleration (amplitude), time duration, and pulse shape, also called shock profile. Here, half-sine shock loads are used with different amplitudes and time durations to investigate the response of microstructure to a shock load. The actual output of the shaker is measured with the PCB accelerometer, which is mounted on the shaker.
The time responses of the microstructure for 60 V bias voltage on the side electrode to shock loads with different time durations and amplitudes are given in
The simulation results are in good agreement with the shock-experiment outcomes as shown in
The mechanical sensitivity to shock is an important factor in the performance of shock sensors. According to
Because of the limitation on the shock amplitudes that could be generated by the shaker, the device could not be tested under more severe shocks. However, the model may be used to predict the threshold shock at different voltages. These threshold shock amplitudes are given in Table VII for different voltages on side electrodes. The sensor resilience against mechanical shock could be improved by increasing the voltage on the side electrodes. This also means the threshold shock the sensor can detect can be tuned by varying the DC voltage on the side electrodes.
A capacitive electrode system is provided that achieves a repulsive electrostatic force for acceleration-sensing. A single degree of freedom lumped parameter model is described that captures the nonlinear dynamics of the system. As the presented accelerometer does not suffer from pull-in, the DC voltage can be increased to increase the fundamental natural frequency. This capability enables the accelerometer to become tunable. That means the detection range of the accelerometers, which is often below one third of their natural frequency, can be tuned by changing the DC voltage of the side electrodes. This is superior to current commercial accelerometers that often have a fixed resonance frequency, which limits their performance. Here, because the resonance frequency of the accelerometer can be tuned, it has the potential to be used in a wider range of applications. Furthermore, the initial gap between the proof-mass and the substrate is increased by increasing the voltage on the side electrodes, which improves the accelerometer robustness against mechanical shocks without sacrificing its stability. This device also has the potential to be designed and used as a shock sensor. By changing the voltage difference between the side and bottom electrodes, the threshold shock amplitude needed to collide the structure with the substrate can be tuned. Also, the natural period of the sensor can be tuned to use the sensor for shock loads with different time duration.
A tunable MEMS electrostatic accelerometer is provided that uses a repulsive electrode configuration so that the design is not hampered by capacitive pull-in instability. The repulsive force configuration enables the increase of DC bias voltage without suffering from the pull-in failure mode. This flexibility in increasing voltage can be employed as a tuning parameter to widen the working frequency range and to improve the robustness of the accelerometer.
A lumped parameter model was developed to simulate the response of the microstructure under a combination of electrostatic and dynamic mechanical loading. The electrostatic force is estimated using a finite element simulation. The nonlinear equations of motion are solved for harmonic base excitations and half-sine shock loads using the shooting and the long-time integration methods, respectively. To validate the model, a sensor is fabricated and characterized under harmonic base excitation and mechanical shocks. A mechanical sensitivity of 0.1 μmig is achieved when the bias voltage is 40 V. The experimental data are in good agreement with the simulation results.
Another flavor of the described accelerometer is an accelerometer with translational degree of freedom. A fabricated MEMS accelerometer with translational degree of freedom is depicted in
First, the pull-in voltage for the cantilever is calculated, per Pallay, Mark, Alwathiqbellah I. Ibrahim, and Shahrzad Towfighian. “A MEMS Threshold Acceleration Switch Powered by a Triboelectric Generator.” In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. V004T08A010-V004T08A010. American Society of Mechanical Engineers, 2018. This is the minimum required voltage for the switch to start in the closed state. Since the cantilever and center electrode act as a simple parallel plate actuator, the pull-in voltage can be calculated with the relationship shown in Equation (36).
where ε is the permittivity of air and A is the area of the underside of the beam. From Equation (36), the pull-in voltage should be approximately 1.9 V. Therefore 2.2 V (Vbias) is applied between the beam and center electrode so that the starting position of the switch is in the closed state. A voltage slightly higher than the pull-in voltage is necessary for the switch to stay closed because the dimples (0.75 μm long) do not allow the beam to travel the entire 2 μm gap. If the voltage is too low the beam will start to pull-in, but the force will be too weak to hold it in the pulled in position of −1.25 μm.
Next, the threshold generator voltage to open the switch when given an initial bias of 2.2 V is calculated. This can be estimated by calculating the potential energy and phase portrait. If the voltage is too low the beam should have an unstable trajectory in the phase plane. However, when the voltage exceeds a threshold it becomes stable and wants to settle to an equilibrium position somewhere above the substrate. The phase portrait will then show a periodic orbit about the equilibrium point.
To calculate the potential energy, Equation (37) is integrated. The damping has a small effect on the stability and is set to zero.
In Equation (38) the first term is the kinetic energy, while the second two terms are the potential energy. H is the total energy of the system, which can be varied to view various trajectories in the phase portrait.
Next, the side voltage is gradually increased until the system becomes stable again. This occurs when the pulled-in position of the beam (indicated in the phase portrait by the intersection of the red line and zero velocity axis) moves inside of a closed loop in the phase portrait. A loop in the phase portrait occurs when a local minimum appears in the potential energy plot. If the side electrode voltage is increased past a threshold, the potential well will grow large enough to allow the beam to oscillate in a stable orbit and the beam will release.
As can be seen in the phase portrait (
Next, the generator output was experimentally extracted using a prototype triboelectric generator from [40]. The generator was struck with a 1 lb. weight to see the open circuit voltage produced from a single impact.
In
Both cases produced a voltage that was large enough to open the switch. This is a result of the generator size, which has approximately 20 cm2 of contact area between triboelectric layers. This means that even a light impact will produce enough voltage to open the switch. To tune the output voltage such that it is closer to the threshold voltage level, a new, smaller generator should be made so that lower level impacts will produce small voltages that will not open the switch.
The voltage from
The simplified step voltages are then applied to Equation (37) to see the beam response. The generator output is not applied directly to Equation (37) because the electrostatic force does not scale with the square of the generator voltage. The voltage is approximated as a series of two steps so that the electrostatic force only needs to be simulated at three voltage levels for each plot. If the voltage is assumed to start at 0 V, then only two simulations are necessary to achieve the stepped voltage response. The electrostatic force coefficients in Equation (37)), pi, become piecewise functions that change suddenly at each jump in
For the smaller impact (
Because the delay between each voltage step is much longer than the response period, the beam has time to settle to its static position between the two voltage spikes. If the device is operated at very low pressure, this may not be the case. However, for a quality factor of 70, the beam settles to its equilibrium point in about 10 ms, which is roughly the time between voltage steps in
The sensor uses a triboelectric generator to convert mechanical energy from an impact to an electrical signal that opens a switch when the impact passes a threshold value. The switch consists of a MEMS cantilever beam with a multi-electrode configuration that can generate both attractive and repulsive forces on the beam. The center electrode is given a small bias voltage to initiate pull-in, and the side electrodes receive voltage from the generator. If the impact is large enough, the repulsive force from the side electrodes releases the beam from pull-in and opens the switch. After a few minutes, the charge on the generator decays and the switch resets to its closed state.
The levitation force is capable of balancing the parallel plate electrostatic force when the beam is in its pulled-in position without tremendously high voltage levels. It has also been experimentally demonstrated that a triboelectric transducer can generate voltages well above this threshold level and will not immediately discharge when the generator electrodes are left as an open circuit.
A microelectromechanical system (MEMS) beam is experimentally released from pull-in using electrostatic levitation. A MEMS cantilever with a parallel plate electrode configuration is pulled-in by applying a voltage above the pull-in threshold. An electrode is fixed to the substrate on each side of the beam to allow electrostatic levitation. Large voltage pulses upwards of 100 V are applied to the side electrodes to release the pulled-in beam. A large voltage is needed to overcome the strong parallel plate electrostatic force and stiction forces, which hold the beam in its pulled-in position. See, Pallay, Mark, and Shahrzad Towfighian. “A reliable MEMS switch using electrostatic levitation.” Applied Physics Letters 113, no. 21 (2018): 213102.
One common undesirable phenomenon associated with electrostatic actuation is the pull-in instability. Pull-in failure occurs when the electrostatic force pulling the two electrodes together overcomes the mechanical forces separating them and the structure collapses. In many cases, pull-in results in permanent damage to the device as the electrodes become stuck together and cannot be separated even if the voltage is removed. Stiction forces such as van der Waals become much more significant at the micro-scale, and the parallel plate electrostatic force is only capable of pulling objects together, so release is often impossible. Stiction can be mitigated by placing dimples on the bottom face of the beam or movable plate, thus reducing the contact area and minimizing the force holding the plates together. However, even beams with dimples can frequently become stuck after pull-in, and therefore, many electrostatic devices are designed to avoid pull-in entirely.
Much effort has been placed in creating electrostatic MEMS designs that do not experience pull-in at all. One method actuates a structure with electrostatic levitation. Electrostatic levitation involves a slightly different electrode configuration than the standard parallel plate design, with two extra electrodes that help induce an effectively repulsive force instead of an attractive one.
The beam and the fixed middle electrode are kept at similar voltage level, while the fixed side electrodes are supplied with a large voltage. When the beam is close enough to the middle electrode, the electrostatic fringe-field produced by the side electrodes pulls on the top of the beam more than the bottom, resulting in a net force upwards. It is not the case of a purely repulsive force that would occur between two positively charged particles but rather an attractive force that acts in the opposite direction of the substrate and is commonly referred to as repulsive to differentiate it from the attractive parallel plate force. The middle electrode acts as a shield protecting the bottom face of the beam from the electric field and associated electrostatic force. As shown in
If the beam is held to just one degree of freedom, which is common for thin, wide beams, it will not pull-in at all because the side electrodes are not in the beams' path of motion. The middle electrode will not create attractive electrostatic forces on the beam because they are both at the same voltage potential, and thus, pull-in will not occur.
A major drawback to electrostatic levitation is that it requires a very high voltage potential because it utilizes the weak fringe fields. To generate an electrostatic levitation force comparable to the one generated by a standard parallel plate configuration, the voltage must be more than an order of magnitude larger than the parallel plate voltage. Voltages upwards of 150 V may be applied to achieve around 10 μm of static tip deflection for a 500 μm long beam. However, the large voltage potential and elimination of the pull-in instability allow repulsive actuators to move more than an order of magnitude farther than their initial gap, as opposed to parallel plate actuators, which are typically limited to one-third of the initial gap because of pull-in.
Another advantage of electrostatic levitation is that it can be easily combined with parallel plate electrodes to enable bi-directional actuation. Applying a bias to the middle electrode, along with the voltage on the side electrodes, creates attractive and repulsive forces on the beam. The beam and middle electrode act as parallel plates, while the side electrodes produce the levitation force. As with other bidirectional devices, such as double-sided parallel plates, bidirectional actuation requires multiple voltage inputs with each controlling the magnitude of the force in a single direction.
According to the present technology, a MEMS beam may be toggled between its pulled-in and released positions using a combination of parallel plate actuation and electrostatic levitation. A bias voltage is applied to the middle electrode to induce pull-in, and release the beam from its pulled-in state. The repulsive force is capable of overcoming the stiction forces holding the beam to the substrate. The capability of recovering from what was once permanent pull-in failure of a MEMS structure is a great advancement and addresses a fundamental issue that has existed since the inception of electrostatically actuated MEMS. This feature can make MEMS devices more reliable and reusable. It also opens the possibility of new applications for electrostatic MEMS by allowing them to use the pulled-in state as a functional element of the device, rather than a limitation. Almost all electrostatic MEMS are designed around pull-in, and by using a combination of attractive and repulsive forcing, this limitation can be relaxed or removed entirely. This attribute has great potential for MEMS switches that will be normally closed, as opposed to current MEMS switches, which are normally open. It also has a promising application in micromechanical memories to read and erase bits as it can switch back and forth between two functional states: pulled-in and released.
MEMS cantilevers are fabricated using PolyMUMPs standard fabrication by MEMSCAP. Dimples are placed on the bottom of the beam to reduce the contact area and the associated stiction forces. While dimples can aid with release, the beams still suffer from stiction when pulled-in. The cantilevers have the electrode layout shown in
The beam can be modeled as an Euler-Bernoulli beam with electrostatic forcing, which can be calculated numerically with a 2D COMSOL simulation. A comparison of pure repulsive, pure attractive, and combined repulsive and attractive forces can be seen in
A schematic for the experimental setup is shown in
In the experiment, a bias voltage is applied to the middle electrode to start the beam in its pulled-in position. The bias is then adjusted to a specified level and held constant before a series of short, high voltage pulses are applied to the side electro des. The beam displacement is observed to determine whether the beam was released during the voltage pulses. A relationship between bias voltage and release side voltage is obtained to demonstrate the working principle of the repulsive switch.
The experiment was repeated by adjusting the bias voltage and determining the associated release voltage.
A MEMS cantilever is experimentally released from its pulled-in position using electrostatic levitation. This method provides a safe and effective way of releasing and reusing pulled-in MEMS beams, which would have otherwise been permanently stuck to the substrate, rendering them unusable.
Several types of transducers have been used to convert mechanical energy to electrical energy including electromagnetic, piezoelectric, electrostatic and triboelectric generators. Recent advances in triboelectric generation show energy conversion efficiency of ˜60% and higher energy densities compared with other transducers. The prefix “tribo” comes from the Greek word for “rub” and more friction generates more electricity. That triboelectricity is contact-induced electrification and has been known for thousands of years, but just recently with the development of micro-patterned surfaces, it has been employed to convert wasted mechanical energy into electrical energy. Despite plenty of research on triboelectric material, there is little research that models the correlation of vibration and triboelectric mechanism. Our team was among the first who discovered the coupled characteristics of triboelectricity and mechanical vibrations. These generators have the advantages of low-cost, high energy density, and flexibility. Two recent studies proposed a triboelectric accelerometer for monitoring the health of railways, in-plane sliding acceleration and motion tracking of a ball.
The triboelectric generators produce surface charges when two materials with opposite electron affinities contact each other. Although the contacting materials can be two polymers, the system works best when contacting materials consists of a polymer and a conductor. The high output energy density of triboelectric generators is attributed to several factors including: (i) the use of surface patterning to increase contacting areas of the polymer and conductor and to generate more surface charges; (ii) the use of a deformable polymer as one of the triboelectric materials to ensure conformal contact. Continuous contact and separation simultaneously create contact electrification and electrostatic induction, which creates a large potential difference or open circuit voltage.
The contact surfaces can be made of a polymer, e.g. polydimethylsiloxane (PDMS) layer and a conductor, e.g. aluminum. Another Al layer covers the back of the PDMS layer. The charge generated on the surfaces is directly proportional to the area of the contact. The key to generating more charges is to make micro-textured surfaces. This leads to a larger contact area, more friction at the microsurfaces and consequently more charges and larger output voltage.
Upon applied mechanical pressure, the Al layer is pressed against the PDMS surface. Because of its flexibility, the PDMS layer fills the gaps between the patterns. The micro-textured surface penetration causes equal but opposite charges to accumulate on both surfaces as electrons are injected into the PDMS from the top Al layer. The triboelectric effect here is not due to macroscopic sliding, but mostly from macroscopic compression, which leads to microscopic sliding. Upon release, the load is removed, and the layers separate as the top surface comes back to its initial position because of the restoring force of an external spring. There will be a large electrical potential difference between the two Al conductors that can directly be used to drive an electrostatic actuator.
Despite the high voltage that triboelectric generators produce, the current generated by these generators is very low in the nano and micro-amp ranges (high impedance generator). This drawback makes powering an electrical circuit difficult. The high voltage creates a strong electrostatic field that could be useful for running electrostatic devices.
To overcome the limitations of the typical two-electrode parallel-plate configuration, electrostatic levitation may be employed, where there are four electrodes: a beam above a center electrode and two side electrodes (
The dynamic behavior of levitation actuators is highly nonlinear.
The bias voltage on the bottom center electrode determines the minimum side voltage needed to open the switch. When the bias voltage is removed completely, the beam continues to stick to the middle electrode and a relatively low voltage of 70 V is required to release the beam (open the switch).
The triboelectric generator controls the levitation actuator. Once the impact occurs, the voltage magnitude steps up quickly and the beam begins to move, see
The output of the generator changes when connected to an actuator, although they are connected with an open circuit. As shown in
Further embodiments can be envisioned to one of ordinary skill in the art from the specification and figures. In other embodiments, combinations or sub-combinations of the above-disclosed invention can be advantageously made. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the invention as set forth in the claims.
The present application is a Non-provisional of, and claims benefit of priority from, U.S. Provisional Patent Application No. 62/891,915, filed Aug. 26, 2019, the entirety of which is expressly incorporated herein by reference.
This invention was made with government support under ECCS 16086921IP and CMMI 1919608 awarded by the National Science Foundation. The government has certain rights in the invention.
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