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Computation Method For 3D Point-Cloud Holography

 The dynamic patterning of 3D optical point clouds has emerged as a key enabling technology in volumetric processing across a number of applications. In the context of biological microscopy, 3D point cloud patterning is employed for non-invasive all-optical interfacing with cell ensembles. In augmented and virtual reality (AR/VR), near-eye display systems can incorporate virtual 3D point cloud-based objects into real-world scenes, and in the realm of material processing, point cloud patterning can be mobilized for 3D nanofabrication via multiphoton or ultraviolet lithography. Volumetric point cloud patterning with spatial light modulators (SLMs) is therefore widely employed across these and other fields. However, existing hologram computation methods, such as iterative, look-up table-based and deep learning approaches, remain exceedingly slow and/or burdensome. Many require hardware-intensive resources and sacrifices to volume quality.To address this problem, UC Berkeley researchers have developed a new, non-iterative point cloud holography algorithm that employs fast deterministic calculations. Compared against existing iterative approaches, the algorithm’s relative speed advantage increases with SLM format, reaching >100,000´ for formats as low as 512x512, and optimally mobilizes time multiplexing to increase targeting throughput. 

Field-Programmable Ising Machines (FPIM)

Certain difficult optimization problems, such as the traveling salesman problem, can be solved using so-called analog Ising machines, in which electronic components (such as certain arrangements of diodes or electronic switches) implement an analog of a well-studied physical system known as an Ising machine. The problem is recast so that its solution can be read off from the lowest-energy configuration of the analog Ising machine, a state which the system will naturally evolve towards. While promising, this methodology suffers major drawbacks. Firstly, the number of subunits, known as “spins”, in the analog Ising machines, as well as the number of connections between these subunits, can grow substantially with problem size. Secondly, existing implementations of this principle rely on chip constructions which are optimized for one or a few problems, and are not sufficiently reprogrammable to be repurposed efficiently for other applications. To address these problems, researchers at UC Berkeley have developed a device known as a Field-programmable Ising machine which can be adapted to implement an analog Ising machine using a variety of hardware designs, such as the diodes and switches mentioned above. These Ising machines can be effectively reprogrammed to efficiently solve a wide array of problems across various domains. The inventors have shown that this design can be applied to SAT (“Satisfiability”) problems, a class known to be similar to the traveling salesman problem, in that the number of spins needed and their level of connectivity do not grow too quickly with problem size.

Adaptive Machine Learning-Based Control For Personalized Plasma Medicine

Plasma medicine has emerged as a promising approach for treatment of biofilm-related and virus infections, assistance in cancer treatment, and treatment of wounds and skin diseases. However, an important challenge arises with the need to adapt control policies, often only determined after each treatment and using limited observations of therapeutic effects. Control policy adaptation that accounts for the variable characteristics of plasma and of target surfaces across different subjects and treatment scenarios is needed. Personalized, point-of-care plasma medicine can only advance efficaciously with new control policy strategies.To address this opportunity, UC Berkeley researchers have developed a novel control scheme for tailored and personalized plasma treatment of surfaces. The approach draws from concepts in deep learning, Bayesian optimization and embedded control. The approach has been demonstrated in experiments on a cold atmospheric plasma jet, with prototypical applications in plasma medicine.

Method For The Synthesis Of Gallium Nitride With N2 Gas At Room Temperature

Gallium nitride is an essential semiconductor material that has shown great promise in electronic and optoelectronic applications. Its synthesis traditionally requires high temperatures (~300-1000℃) and/or pressures (~1-100MPa) in order to break the strong bond in molecular nitrogen. Manufacture of gallium nitride and similar semiconductor materials under these conditions is very expensive. Additionally, artificial nitrogen fixation in the form of ammonia manufacture is critical to the global food supply, but similarly requires very expensive high temperature and/or pressure synthesis. To address these problems, researchers at UC Berkeley have developed a method to synthesize gallium nitride from molecular nitrogen at approximately room temperature (30℃) and atmospheric pressure. This process can be accomplished more cheaply than traditional methods, using only standard reagents and equipment. Researchers have confirmed that prior to the synthesis of gallium nitride, atomic nitrogen is freely dissociated. This suggests that a similar method can be used in the manufacture of other nitride semiconductor materials, or even of nitrogenous substances such as ammonia.

Superlattice, Ferroic Order Thin Films For Use As High/Negative-K Dielectric

With the two-dimensional scaling of silicon field-effect transistors reaching fundamental limits, new functional improvements to transistors, as well as novel computing paradigms and vertical device integration at the architecture-level, are currently under intense study. Gate oxides play a critical role in this endeavor, as it’s a common performance booster for all devices, including silicon, new channel materials with potential for higher performance, and even materials suitable for three-dimensional integrated transistors.With the scaling of lateral dimensions in advanced transistors, an increased gate capacitance is desirable both to retain the control of the gate electrode over the channel and to reduce the operating voltage. To pursue these performance gains, UC Berkeley researchers invented a new heterostructure insulator material where: 1) the material possesses specific ferroic order such as ferroelectricity/anti-ferroelectricity or a mixture of both; 2) the overall dielectric property such as the permittivity is determined by the stacking order of different layers rather than exact volume fraction of the constituents; and 3) the material is composed of one or several repetition of ultra thin superlattice periods ranging from a few angstroms to 3 nm.

Precision Graphene Nanoribbon Wires for Molecular Electronics Sensing and Switch

The inventors have developed a highly scalable multiplexed approach to increase the density of graphene nanoribbon- (GNR) based transistors. The technology forms a single device/chip (scale to 16,000 to >1,000,000 parallel transistors) on a single integrated circuit for single molecule biomolecular sensing, electrical switching, magnetic switching, and logic operations. This work relates to the synthesis and the manufacture of molecular electronic devices, more particularly sensors, switches, and complimentary metal-oxide semiconductor (CMOS) chip-based integrated circuits.Bottom-up synthesized graphene nanoribbons (GNRs) have emerged as one of the most promising materials for post-silicon integrated circuit architectures and have already demonstrated the ability to overcome many of the challenges encountered by devices based on carbon nanotubes or photolithographically patterned graphene. The new field of synthetic electronics borne out of GNRs electronic devices could enable the next generation of electronic circuits and sensors.  

Compact Ion Gun for Ion Trap Surface Treatment in Quantum Information Processing Architectures

Electromagnetic noise from surfaces is one of the limiting factors for the performance of solid state and trapped ion quantum information processing architectures. This noise introduces gate errors and reduces the coherence time of the systems. Accordingly, there is great commercial interest in reducing the electromagnetic noise generated at the surface of these systems.Surface treatment using ion bombardment has shown to reduce electromagnetic surface noise by two orders of magnitude. In this procedure ions usually from noble gasses are accelerated towards the surface with energies of 300eV to 2keV. Until recently, commercial ion guns have been repurposed for surface cleaning. While these guns can supply the ion flux and energy required to prepare the surface with the desired quality, they are bulky and limit the laser access, making them incompatible with the requirements for ion trap quantum computing.To address this limitation, UC Berkeley researchers have developed an ion gun that enables in-situ surface treatment without sacrificing high optical access, enabling in situ use with a quantum information processor.

Reticulation Of Macromolecules Into Crystalline Networks

Covalent organic frameworks (COFs) are 2D or 3D extended periodic networks assembled from symmetric, shape persistent molecular 5 building blocks through strong, directional bonds. Traditional COF growth strategies heavily rely on reversible condensation reactions that guide the reticulation toward a desired thermodynamic equilibrium structure. The requirement for dynamic error correction, however, limits the choice of building blocks and thus the associated mechanical and electronic properties imbued within the periodic lattice of the COF.   UC Berkeley researchers have demonstrated the growth of crystalline 2D COFs from a polydisperse macromolecule derived from single-layer graphene, bottom-up synthesized quasi one-dimensional (1D) graphene nanoribbons (GNRs). X-ray scattering and transmission electron microscopy revealed that 2D sheets of GNR-COFs self-assembled at a liquid-l quid interface stack parallel to the layer boundary and exhibit an orthotropic crystal packing. Liquid-phase exfoliation of multilayer GNR-COF crystals gave access to large area bilayer and trilayer cGNR-COF films. The functional integration of extended 1D materials into crystalline COFs greatly expands the structural complexity and the scope of mechanical and physical materials properties.

High Performance Iron Electrocoagulation Systems for Removing Water Contaminants

The inventors have developed an iron electrocoagulation (Fe-EC) system for arsenic removal. The system offers a highly effective, low cost, robust method for removing arsenic from groundwater used for drinking, at community scale (10,000 liters per day).The main advance of this invention is to replace the assembly of inter-digited flat steel plates with an assembly of spiral-wound or folded and inter-digited two steel sheets separated only with perforated insulating spacers. This substantially reduces the energy consumption in comparison to other Fe-EC reactors, and allows for larger flow rates for a given reactor size than the standard inter-digited flat plate configuration. This advance is possible because the system relies on: externally added (ppm quantities) of oxidizer (H2O2), and a newly-discovered effect that allows consistent iron dissolution at high current densities. High current density also produces copious quantities of micro-bubbles of H2 gas, which flushes the space between the electrodes continuously during operation, preventing the clogging that has defeated earlier attempts.In a typical Fe-EC reactor, parallel inter-digited plates of mild steel are inserted into the contaminated water and a small DC voltage is applied between alternate plates to promote anodic dissolution of F(0) metal to release Fe(II) ions into the contaminated water. The Fe(II) ions react with dissolved oxygen in the water to produce Fe(III) that is used to capture the contaminants. Typically, an assembly of flat inter-digited parallel steel plates, with nearest neighbor spaced 2 cm to 5 cm, is used in Fe-EC reactors. Occasionally, externally added or in-situ produced oxidants may be used (e.g. externally added strong oxidants such as H2O2, O3, Chlorine, Permanganate, etc., or in-situ produced strong oxidants such as H2O2 using carbon based cathodes). 

Low Band Gap Graphene Nanoribbon Electronic Devices

This invention creates a new graphene nanoribbons (GNR)-based transistor technology capable of pushing past currently projected limits in the operation of digital electronics for combining high current (i.e. high speed) with low-power and high on/off ratio. The inventors describe the design and synthesis of molecular precursors for low band gap armchair graphene nanoribbons (AGNRs) featuring a width of N=11 and N=15 carbon atoms, their growth into AGNRs, and their integration into functional electronic devices (e.g. transistors). N is the number of carbon atoms counted in a chain across the width and perpendicular to the long axis of the ribbon.

High Electromechanical Coupling Disk Resonators

Capacitive-gap transduced micromechanical resonators routinely post Q several times higher than piezoelectric counterparts, making them the preferred platform for HF and low-VHF (e.g. 60-MHz) timing oscillators, as well as very narrowband (e.g. channel-select) low-loss filters. However, the small electromechanical coupling (as gauged by the resonator's motion-to-static capacitance ratio, Cx/Co) of these resonators at higher frequency prevents sub-mW GSM reference oscillators and complicates the realization of wider bandwidth filters. To address this situation, researchers at UC Berkeley developed a capacitive-gap transduced radial mode disk resonator with reduced mass and stiffness. This novel Berkeley disk resonator has a measured electromechanical coupling strength (Cx/Co) of 0.56% at 123 MHz without electrode-to-resonator gap scaling. This is an electromechanical coupling strength improvement of more than 5x compared with a conventional radial contour-mode disk at the same frequency. This increase should help improve the passbands of channel-select filters targeted for low power wireless transceivers and lower the power of MEMS-based oscillators.  

Stroboscopic Universal Structure-Energy Flow Correlation Scattering Microscopy

Flexible semiconductors are far less costly, resource and energy intensive than conventional silicon production. Yet, as an unintended consequence of semiconductor printing, the films produced contain structural heterogeneities, or defects, which can limit their capacity to shuttle energy, or, information, over device-relevant scales. To be able to fully embrace this new, greener process, it is essential to elucidate which physical material properties most influence energy flow and which defects are most deleterious to efficient energy transport so that they can be targeted for elimination at the materials processing stage. Although some rather complex approaches have recently been used to track energy flow, the applicability of each one depends on specifics of the semiconductor properties (bandgap, excitonic vs charge carrier form of excitation, strong absorption or emission). Existing techniques cannot therefore be applied to a broad range of materials, and often necessitate adapting samples to fit the specific requirements of the technique. A broadly applicable approach is therefore needed to non-invasively and simultaneously reveal and correlate material morphology and energy flow patterns across many scales.    Researchers at the University of California, Berkeley have developed a new high-sensitivity, non-invasive, label-free, time-resolved optical scattering microscope able to map the flow of energy in any semiconductor, and correlate it in situ to the semiconductor morphology. This device has been shown as a far simpler approach to spatio-temporally characterize the flow of energy in either charge or exciton form, irrespective of the electronic properties of the material, and with few-nm precision. Furthermore, built into this approach is the unprecedented capability to perform in situ correlation to the underlying physical structure of the material. 

Printable Repulsive-Force Electrostatic Actuator Methods and Device

Flexible electrostatic actuators are well designed for a range of commercial applications, from small micro-mechanical robotics to large vector displays or sound wall systems. Electrostatic actuation provides efficient, low-power, fast-response driving and control of movable nano-, micro-, and macro-structures. While commercially available electrostatic actuators have the requisite high levels of mechanical energy / force for some applications, their energy requirements are typically orders of magnitude higher than what is needed in large-area, low-power applications. Moreover, conventional approaches to these types of electrostatic actuators have limited design geometries and are prone to reliability issues like electrical shorts. To address these problems, researchers at the University of California, Berkeley, have experimented with planar electrostatic actuators using novel printing and electrode patterning and engineering techniques. The team has demonstrated a repulsive-force electrostatic actuator device (100 mm x 60 mm achieved) with extremely high field strength and high voltage operation and without insulator coatings or air breakdown.

RF-Powered Micromechanical Clock Generator

Realizing the potential of massive sensor networks requires overcoming cost and power challenges. When sleep/wake strategies can adequately limit a network node's sensor and wireless power consumption, then the power limitation comes down to the real-time clock (RTC) that synchronizes sleep/wake cycles. With typical RTC battery consumption on the order of 1µW, a low-cost printed battery with perhaps 1J of energy would last about 11 days. However, if a clock could bleed only 10nW from this battery, then it would last 3 years. To attain such a clock, researchers at UC Berkeley developed a mechanical circuit that harnesses squegging to convert received RF energy (at -58dBm) into a local clock while consuming less than 17.5nW of local battery power. The Berkeley design dispenses with the conventional closed-loop positive feedback approach to realize an RCT (along with its associated power consumption) and removes the need for a sustaining amplifier altogether. 

Apparatus and Method for 2D-based Optoelectronic Imaging

The use of electric fields for signaling and manipulation is widespread, mediating systems spanning the action potentials of neuron and cardiac cells to battery technologies and lab-on-a-chip devices. Current FET- and dye-based techniques to detect electric field effects are systematically difficult to scale, costly, or perturbative. Researchers at the University of California Berkeley have developed an optical detection platform, based on the unique optoelectronic properties of two-dimensional materials that permits high-resolution imaging of electric fields, voltage, acidity, strain and bioelectric action potentials across a wide field-of-view.

Enhancing Photoluminescence Quantum Yield for High Performance Optoelectrics

Surface defects dominate the behavior of minority carriers in semiconductors and optoelectronic devices. Photoluminescence quantum yield (QY), which dictates efficiency of optoelectrics such as LEDs, lasers, and solar cells, is extremely low in materials with a large number of surface defects. Researchers at UC Berkeley and Lawrence Berkeley National Laboratory have developed a bis(trifluoromethane) sulfonamide (TFSI) solution for passivation/repair of surface defects in 2D transition metal dichalcogenide (TMDC). This air-stable solution-based chemical treatment provides unmatched photoluminescence QY enhancement to values near 100% without changing the surface morphology. The treatment eliminates defect-mediated non-radiative recombination, which eliminates the low performance limit of TMDC and enhances its minority carrier lifetime. This novel development can address surface passivation in numerous semiconductors which will lead to highly efficient light emitting diodes, lasers and solar cells based on 2D materials.

Enhanced Patterning Of Integrated Circuits

Information and communication technologies rely on integrated circuits (ICs) or “chips.” Increased integration has improved system performance and energy efficiency, and lowered the manufacturing cost per component. Moore’s Law predicts that the number of transistors on an IC will double every two years, yet industry experts predict that we are reaching economic limits of traditional circuit patterning processes. Photolithographic patterning is best suited to print linear features that are evenly spaced. The smaller or more complex the shape, the more likely the printed pattern will be blurred and unusable. Although multiple-patterning techniques can be used to increase feature density on ICs, they bring a high additional cost to the process. This means that the most advanced ICs available today have a high density of features, but are restricted to having simple patterns and are increasingly expensive to produce. Without innovations in production techniques, Moore’s Law will reach its end in the near future.  To address this issue, researchers at UC Berkeley have developed a one-step method to increase feature density on chips. This method is capable of achieving arbitrarily small feature size, and self-aligns to pre-existing features on the surface formed by other techniques. 

Methods to Produce Ultra-Thin Copper Nanowires for Transparent Conductors

The disclosure provides innovative synthesis methods to produce uniform, ultrathin and high-quality metal nanostructures. In certain embodiments, the synthesis methods disclosed herein are solution based, therefore affording scalability and allowing for the production of metal nanostructures (e.g. Cu-nanowires ) that can have varying diameters, e.g., between 1 nm to 70 nm. The resulting metal nanostructures can be used to construct transparent electrodes that have lower costs, better transparency, and superior flexibility in comparison to conventional metal-oxide conductors, such as indium tin oxide (ITO) .

Chemical-Sensitive Field-Effect Transistor

Conventional metal-oxide semiconductor field-effect transistor (MOSFET) technology consists of a source, drain, gate, and substrate. The chemical field-effect transistor (chemFET) is a type of a field-effect transistor acting as a chemical sensor, and is similar to MOSFET except for the gate structures. Modern industrial players seek higher-sensitivity technologies which are small, durable, efficient, and versatile. Further advances in these materials and structures could enable many new kinds of layered semiconductors and devices. To address need, researchers at the University of California, Berkeley, have developed chemical-sensitive field-effect transistor (CS-FET) platform technology. By exploiting selective thin films incorporated into the CS-FET, researchers have created chemical sensors with commercial promise in terms of chemical-versatility and low-power. 

A Thin Film Vls Semiconductor Growth Process

A team of Berkeley Lab researchers has invented the first vapor-liquid-solid (VLS) growth technology yielding III-V photovoltaics. The photovoltaics achieve 25% power conversion efficiency at a cost significantly lower than current approaches due to the non-epitaxial processing approach and high material utilization rate. The films have grain sizes of 100-200 microns (100 times larger than yielded from conventional growth processes), minority carrier lifetimes up to 2.5 nanoseconds and electron mobilities reaching 500 cm2/V-s. Under one-sun equivalent illumination, an open circuit voltage of up to 930 mV can be reached, just 40 mV lower than measured on a single crystal wafer. Berkeley Lab researchers fabricated continuous thin films of polycrystalline indium phosphide (InP) directly on metal foils by, first, depositing an indium (In) thin film directly on molybdenum (Mo) foil. Next, they deposit a thin capping layer to prevent dewetting of the indium from the substrate during subsequent high temperature processing steps. The resulting stack (Mo – In – capping layer) is then heated in the presence of phosphorous precursors causing supersaturation of the liquid indium with phosphorous, followed by precipitation of InP, thus turning all the In into InP. III-V photovoltaics deliver the highest power conversion efficiencies, but significant processing costs (expensive materials and equipment, low precursor utilization rate) have limited their use. Berkeley Lab’s non-epitaxial growth technology overcomes these limitations to deliver a promising low cost solar cell.

Novel Porous Organic Polymers for Ammonia Adsorption

Ammonia is used in many industrial and commercial applications, for example in the manufacture of fertilizers and cleaners.  However, ammonia is toxic at high concentrations and, therefore, safe storage and transportation of ammonia is required. In addition, trace amounts of ammonia in the atmosphere contaminate and interfere with certain industrial processes, such as semiconductor fabrication, which requires ultra-pure air. Proper ammonia management includes the adsorption of the gas under each of these pressure regimes: high-pressure adsorption for safe storage and transportation and low-pressure adsorption for the removal of trace contaminants from the ambient air. Current methods of adsorption include simple salts, such as MgCl2, but these are not efficient for low-pressure adsorption and furthermore their ammonia cycle is inefficient, requiring significant heat exchange and large changes in volume. Investigators at UC Berkeley have developed a novel polymer for ammonia adsorption that uses acidic materials placed in a spatial arrangement that allows for cooperative adsorption. This not only increases the efficiency of adsorption but also is effective at both high-pressure and low-pressure ammonia adsorption, resulting in multiple applications of the technology. 

Pyroelectric MEMS Infrared Sensor with Numerous Wavelength Absorptions

In recent years, gas sensors for industrial applications have experienced great advances through rapid evolution of microelectromechanical systems (MEMS). As a result of increased government legislative pressure on industrial health and safety, commercial customers are demanding integrated smart sensor technology and systems which leverage MEMS for small footprint, low cost, and high-performance features. Market researchers suggest double-digit compound annual growth rates for MEMS sensors through 2018, with the fastest growth is expected in the semiconductor sensor base. Traditional infrared gas analyzers determine the absorption of an emitted infrared light source through a certain air sample. Nondispersive infrared technology (NDIR) detects certain gas by detecting the absorption of infrared wavelengths that is characteristic of that gas. NDIR detectors are the industry standard method of measuring the concentration of carbon oxides. Researchers at UC Berkeley and Davis have successfully demonstrated pyroelectric infrared detectors that exhibit high sensitivity and reliable performance for advanced gas analyses. The MEMS technology is well suited for constant monitoring in harsh environments where long term stability is important, such as petroleum, medical, and industrial monitoring settings.

Flexible Wound Healing Monitor

Pressure ulcers are formed when constant pressure or rubbing results in breakdown of the skin. Hospitals and nursing homes spend billions of dollars each year to prevent formation of pressure ulcers in their patients, as many current solutions (pressure-distributing beds, re-positioning patients every few hours, etc.) are very expensive and labor-intensive. Additionally, chronic cutaneous wounds affect millions of people each year, costing billions of dollars to treat. These ailments represent critical, unmet needs in clinical medical practice, and result in increased morbidity and mortality at a high human and financial cost.In response to this challenge, investigators and University of California, Berkeley have developed a flexible wound healing monitor. As an objective measurement, wound progression is monitored remotely. Otherwise undetectable features are identified visually. The flexible wound healing monitor uses impedance spectroscopy to measure and characterize tissue health, allowing physicians to identify high-risk areas of skin to prevent formation of pressure ulcers or to objectively monitor progression of wound healing. Uniquely, the flexible wound healing monitor takes measurements across nearest neighbor electrodes in an array to create a visually intuitive map of electrical impedance. Data visualization is through a map resembling the electrode array. Spaces between every two electrodes are filled with a color corresponding to the impedance magnitude or phase as determined by an intuitive color scale. The flexible wound healing monitor can be integrated into the Wound VAC, a current standard-of-care wound treatment. In addition, impedance measurements taken at high-risk sites can allow for early detection of impending pressure ulcer formation. First prototypes of the flexible wound healing monitor were fabricated on rigid FR4 printed circuit boards. The investigators are transferring this technology onto a flexible substrate using inkjet printing of conductive metal ink. 

MEMS-Based Charge Pump

The reduction of power supply voltage with each new generation of CMOS technology continues to complicate the design of charge pumps needed for high voltage applications that integrate into systems alongside transistor chips -- such as the increasing number of MEMS-based gyroscopes, timing oscillators, and gas sensors. Moreover, the aggressive scaling in CMOS resulting in lower dielectric and junction breakdown voltages has compelled the use of customized CMOS processes -- including increased gate oxide thickness and/or added deep-n-wells. Clearly, advances in transistor technology are moving in the opposite direction of the needs of high voltage MEMS applications. To address this trend, researchers at UC Berkeley have developed a MEMS-based charge pump. This design avoids the turn-on voltage and breakdown limitation of CMOS. With much higher breakdown voltages than transistor counterparts, the demonstrated MEMS charge pump implementation should eventually allow voltages higher than 50V desired for capacitive-gap transduced resonators that currently dominate the commercial MEMS-based timing market.

Micro Electromechanical Switch Design with Self Aligning and Sub-Lithographic Properties

Shrinking of integrated circuit (IC) device dimensions provides for enhanced functionality and performance  of computers and electronics. Researchers at Berkeley are exploring nano-mechanical information processing as a means to overcome the energy-efficiency limits of CMOS technology and recently have directed their efforts toward the development of device designs suitable for implementation in the cross-point array architecture for minimal footprint.  To that end, our researchers have designed a novel process for fabricating ultimately scaled electro-mechanical relays with decananometer lateral dimensions. Their innovation includes a compact electro-mechanical switch design which has self-aligned features with a minimum dimension not defined lithographically. By incorporating multiple sets of output electrodes, the area required to implement a complex logic gate is reduced by a factor of 2. 

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