Parametric Frequency Divider Based Ising Machines.

We report on a new class of Ising machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic-injection locking (SHIL), PFD IMs do not require strong injected continuous-wave signals or applied dc voltages. Therefore, they show a significantly lower power consumption per spin compared to SHIL-based IMs, making it feasible to accurately solve large-scale combinatorial optimization problems that are hard or even impossible to solve by using the current von Neumann computing architectures. Furthermore, using high quality factor resonators in the PFD design makes PFD IMs able to exhibit a nanowatt-level power per spin. Also, it remarkably allows a speedup of the phase synchronization among the PFDs, resulting in shorter time to solution and lower energy to solution despite the resonators' longer relaxation time. As a proof of concept, a 4-node PFD IM has been demonstrated. This IM correctly solves a set of Max-Cut problems while consuming just 600 nanowatts per spin. This power consumption is 2 orders of magnitude lower than the power per spin of state-of-the-art SHIL-based IMs operating at the same frequency.

Ultra-High Interfacial Thermal Conductance via Double hBN Encapsulation for Efficient Thermal Management of 2D Electronics.

Heat dissipation is a major limitation of high-performance electronics. This is especially important in emerging nanoelectronic devices consisting of ultra-thin layers, heterostructures, and interfaces, where enhancement in thermal transport is highly desired. Here, ultra-high interfacial thermal conductance in encapsulated van der Waals (vdW) heterostructures with single-layer transition metal dichalcogenides MX2 (MoS2 , WSe2 , WS2 ) sandwiched between two hexagonal boron nitride (hBN) layers is reported. Through Raman spectroscopic measurements of suspended and substrate-supported hBN/MX2 /hBN heterostructures with varying laser power and temperature, the out-of-plane interfacial thermal conductance in the vertical stack is calibrated. The measured interfacial thermal conductance between MX2 and hBN reaches 74 ± 25 MW m-2 K-1 , which is at least ten times higher than the interfacial thermal conductance of MX2 in non-encapsulation structures. Molecular dynamics (MD) calculations verify and explain the experimental results, suggesting a full encapsulation by hBN layers is accounting for the high interfacial conductance. This ultra-high interfacial thermal conductance is attributed to the double heat transfer pathways and the clean and tight vdW interface between two crystalline 2D materials. The findings in this study reveal new thermal transport mechanisms in hBN/MX2 /hBN structures and shed light on building novel hBN-encapsulated nanoelectronic devices with enhanced thermal management.

Phase Transition of MoTe2 Controlled in van der Waals Heterostructure Nanoelectromechanical Systems.

This work reports experimental demonstrations of reversible crystalline phase transition in ultrathin molybdenum ditelluride (MoTe2 ) controlled by thermal and mechanical mechanisms on the van der Waals (vdW) nanoelectromechanical systems (NEMS) platform, with hexagonal boron nitride encapsulated MoTe2 structure residing on top of graphene layer. Benefiting from very efficient electrothermal heating and straining effects in the suspended vdW heterostructures, MoTe2 phase transition is triggered by rising temperature and strain level. Raman spectroscopy monitors the MoTe2 crystalline phase signatures in situ and clearly records reversible phase transitions between hexagonal 2H (semiconducting) and monoclinic 1T' (metallic) phases. Combined with Raman thermometry, precisely measured nanomechanical resonances of the vdW devices enable the determination and monitoring of the strain variations as temperature is being regulated by electrothermal control. These results not only deepen the understanding of MoTe2 phase transition, but also demonstrate a novel platform for engineering MoTe2 phase transition and multiphysical devices.

Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS2 Nanomechanical Resonators.

We report on experimental measurements and quantitative analyses of nonlinear dynamic characteristics in ultimately thin nanomechanical resonators built upon single-layer, bilayer, and trilayer (1L, 2L, and 3L) molybdenum disulfide (MoS2) vibrating drumhead membranes. This synergistic study with calibrated measurements and analytical modeling on observed nonlinear responses has led to the determination of nonlinear damping and stiffness coefficients at cubic and quintic orders for these two-dimensional (2D) resonators operating in the very high frequency (VHF) band (up to ∼90 MHz). We find that the quintic force can be ∼20% of the Duffing force at larger amplitudes, and thus, it generally cannot be ignored in a nonlinear dynamics analysis. This study provides the first quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators and elucidates their origins and dependency on engineerable parameters, setting a foundation for future exploration and utilization of the rich nonlinear dynamics in 2D nanomechanical systems.

Raman Spectroscopic Probe for Nonlinear MoS2 Nanoelectromechanical Resonators.

Resonant nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) semiconductors have been actively explored and engineered for making ultrascaled transducers toward applications in ultralow-power signal processing, communication, and sensing. Although the transduction of miniscule resonant motions has been achieved by low-noise optical or electronic techniques, direct probing of strain in vibrating 2D semiconductor membranes and the interplay between the spectroscopic and mechanical properties are still largely unexplored. Here, we experimentally demonstrate dynamical phonon softening in atomically thin molybdenum disulfide (MoS2) NEMS resonators by directly coupling Raman spectroscopy with optical interferometry resonance motion detection. In single-layer, bilayer, and trilayer (1L to 3L) MoS2 circular membrane NEMS resonators, we show that high-amplitude nonlinear resonances can enhance the Raman signal amplitude, as well as introduce Raman modes softening up to 0.8 cm-1. These results shall pave the way for engineering the coupling and control between collective mechanical vibrations and Raman modes of the constituent crystals in 2D transducers.

Ultrawide Frequency Tuning of Atomic Layer van der Waals Heterostructure Electromechanical Resonators.

We report on the experimental demonstration of atomically thin molybdenum disulfide (MoS2)-graphene van der Waals (vdW) heterostructure nanoelectromechanical resonators with ultrawide frequency tuning. With direct electrostatic gate tuning, these vdW resonators exhibit exceptional tunability, in general, Δf/f0 > 200%, for continuously tuning the same device and the same mode (e.g., from ∼23 to ∼107 MHz), up to Δf/f0 ≈ 370%, the largest fractional tuning range in such resonators to date. This remarkable electromechanical resonance tuning is investigated by two different analytical models and finite element simulations. Furthermore, we carefully perform clear control experiments and simulations to elucidate the difference in frequency tuning between the heterostructure and single-material resonators. At a given initial strain level, the tuning range depends on the two-dimensional (2D) Young's moduli of the constitutive crystals; devices built on materials with lower 2D moduli show wider tuning ranges. This study exemplifies that vdW heterostructure resonators can retain unconventionally broad, continuous tuning, which is promising for voltage-controlled, tunable nanosystems.

Single-crystal 3C-SiC-on-insulator platform for integrated quantum photonics.

Photonic quantum information processing and communication demand highly integrated device platforms, which can offer high-fidelity control of quantum states and seamless interface with fiber-optic networks simultaneously. Exploiting the unique quantum emitter characteristics compatible with photonic transduction, combined with the outstanding nonlinear optical properties of silicon carbide (SiC), we propose and numerically investigate a single-crystal cubic SiC-on-insulator (3C-SiCOI) platform toward multi-functional integrated quantum photonic circuit. Benchmarking with the state-of-the-art demonstrations on individual components, we have systematically engineered and optimized device specifications and functions, including state control via cavity quantum electrodynamics and frequency conversion between quantum emission and telecommunication wavelengths, while also considering the manufacturing aspects. This work will provide concrete guidelines and quantitative design considerations for realizing future SiCOI integrated photonic circuitry toward quantum information applications.

Development of Dual-Frequency PMUT Arrays Based on Thin Ceramic PZT for Endoscopic Photoacoustic Imaging.

This paper presents a dual-frequency piezoelectric micromachined ultrasonic transducer (pMUT) array based on thin ceramic PZT for endoscopic photoacoustic imaging (PAI) applications. With a chip size of 7 × 7 mm2, the pMUT array consists of 256 elements, half of which have a lower resonant frequency of 1.2 MHz and the other half have a higher resonant frequency of 3.4 MHz. Ceramic PZT, with outstanding piezoelectric coefficients, has been successfully thinned down to a thickness of only 4 µ by using wafer bonding and chemical mechanical polishing (CMP) techniques and employed as the piezoelectric layer of the pMUT elements. The diaphragm diameters of the lower-frequency and higher-frequency elements are 220 µm and 120 µm, respectively. The design methodology, multiphysics modeling, fabrication process, and characterization of the pMUTs are presented in detail. The fabricated pMUT array has been fully characterized via electrical, mechanical, and acoustic measurements. The measured maximum responsivities of the lower- and higher- frequency elements reach 110 nm/V and 30 nm/V at their respective resonances. The measured cross-couplings of the lower-frequency elements and higher-frequency elements are about 9% and 5%, respectively. Furthermore, PAI experiments with pencil leads embedded into an agar phantom have been conducted, which clearly shows the advantages of using dual-frequency pMUT arrays to provide comprehensive photoacoustic images with high spatial resolution and large signal-to-noise ratio simultaneously.

Electrodynamic Force, Casimir Effect, and Stiction Mitigation in Silicon Carbide Nanoelectromechanical Switches.

Logic switches enabled by nanoelectromechanical systems (NEMS) offer abrupt on/off-state transition with zero off-state leakage and minimal subthreshold swing, making them uniquely suited for enhancing mainstream electronics in a range of applications, such as power gating, high-temperature and high-voltage logic, and ultralow-power circuits requiring zero standby leakage. As NEMS switches are scaled with genuinely nanoscale gaps and contacts, quantum mechanical electrodynamic force (EDF) takes an important role and may be the ultimate cause of the plaguing problem of stiction. Here, combined with experiments on three-terminal silicon carbide (SiC) NEMS switches, a theoretical investigation is performed to elucidate the origin of EDF and Casimir effect leading to stiction, and to develop a stiction-mitigation design. The EDF calculation with full Lifshitz formula using the actual material and device parameters is provided. Finite element modeling and analytical calculations demonstrate that EDF becomes dominant over elastic restoring force in such SiC NEMS when the switching gap shrinks to a few nanometers, leading to irreversible stiction at contact. Artificially corrugated contact surfaces are designed to reduce the contact area and the EDF, thus evading stiction. This rational surface engineering reduces the EDF down to 4% compared with the case of unengineered, flat contact surfaces.

A MEMS lens scanner based on serpentine electrothermal bimorph actuators for large axial tuning.

Confocal microscopes and two-photon microscopes are powerful tools for early cancer diagnosis because of their high-resolution 3D imaging capability, but applying them for clinical use in internal organs is hindered by the lack of axially tunable lens modules with small size, high image quality and large tuning range. This paper reports a compact MEMS lens scanner that has the potential to overcome this limitation. The MEMS lens scanner consists of a MEMS microstage and a microlens. The MEMS microstage is based on a unique serpentine inverted-series-connected (ISC) electrothermal bimorph actuator design. The microlens is an aspheric glass lens to ensure optical quality. The MEMS microstage has been fabricated and the lens scanner has been successfully assembled. The entire lens scanner is circular with an outer diameter of 4.4 mm and a clear optical aperture of 1.8 mm. Experiments show that the tunable range reaches over 200 µm at only 10.5 V and the stiffness of the microstage is 6.2 N/m. Depth scan imaging by the MEMS lens scanner has also been demonstrated with a 2.2 µm resolution, only limited by the available resolution target.

Anisotropic Thermal Conductivity of Suspended Black Phosphorus Probed by Opto-Thermomechanical Resonance Spectromicroscopy.

Atomic layer semiconducting black phosphorus (P) exfoliated from its bulk crystals offers excellent properties and promises for emerging two-dimensional (2D) electronics, photonics, and transducers. It also possesses unique strong in-plane anisotropy among many 2D semiconductors, stemming from its corrugated crystal structure. As an important thermophysical aspect, probing the anisotropic thermal conductivity of black P is essential for device engineering, especially for energy dissipation and thermal management. Here, we report on measurement and analysis of anisotropic in-plane thermal conductivity of black P crystal, in a mechanically suspended device platform, by exploiting a novel opto-thermomechanical resonance spectromicroscopy (OTMRS) technique. With spatially resolved heating effects and thermomechanical resonance motions of suspended structures, anisotropic in-plane thermal conductivity (κAC and κZZ) is determined for black P crystals of 10-100 nm thick. This study validates a new noninvasive approach to determining anisotropic thermal conductivity without any requirement of preknowledge of crystal orientation or specific configurations of structure and electrodes according to the anisotropy.

Electrothermally Tunable Graphene Resonators Operating at Very High Temperature up to 1200 K.

The unique negative thermal expansion coefficient and remarkable thermal stability of graphene make it an ideal candidate for nanoelectromechanical systems (NEMS) with electrothermal tuning. We report on the first experimental demonstration of electrothermally tuned single- and few-layer graphene NEMS resonators operating in the high frequency (HF) and very high frequency (VHF) bands. In single-, bi-, and trilayer (1L, 2L, and 3L) graphene resonators with carefully controlled Joule heating, we have demonstrated remarkably broad frequency tuning up to Δ f/ f0 ≈ 310%. Simultaneously, device temperature variations imposed by Joule heating are monitored using Raman spectroscopy; we find that the device temperature increases from 300 K up to 1200 K, which is the highest operating temperature known to date for electromechanical resonators. Using the measured frequency and temperature variations, we further extract both thermal expansion coefficients and thermal conductivities of these devices. Comparison with graphene electrostatic gate tuning indicates that electrothermal tuning is more efficient. The results clearly suggest that the unique negative thermal expansion coefficient of graphene and its excellent tolerance to very high temperature can be exploited for engineering highly tunable and robust graphene transducers for harsh and extreme environments.

Tuning Optical Signatures of Single- and Few-Layer MoS2 by Blown-Bubble Bulge Straining up to Fracture.

Emerging atomic layer semiconducting crystals such as molybdenum disulfide (MoS2) are promising candidates for flexible electronics and strain-tunable devices due to their ultrahigh strain limits (up to ∼20-30%) and strain-tunable bandgaps. However, high strain levels, controllable isotropic and anisotropic biaxial strains in single- and few-layer MoS2 on device-oriented flexible substrates permitting convenient and fast strain tuning, remain unexplored. Here, we demonstrate a "blown-bubble" bulge technique for efficiently applying large strains to atomic layer MoS2 devices on a flexible substrate. As the strain increases via bulging, we achieve continuous tuning of Raman and photoluminescence (PL) signatures in single- and few-layer MoS2, including splitting of Raman peaks. With proper clamping of the MoS2 crystals, we apply up to ∼9.4% strain in the flexible substrate, which causes a doubly clamped single-layer MoS2 to fracture at 2.2-2.6% strain measured by PL and 2.9-3.5% strain measured by Raman spectroscopy. This study opens new pathways for exploiting 2D semiconductors on stretchable substrates for flexible electronics, mechanical transducers, tunable optoelectronics, and biomedical transducers on curved and bulging surfaces.

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy.

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.

Environmental Instability and Degradation of Single- and Few-Layer WTe2 Nanosheets in Ambient Conditions.

The ambient environmental instability and degradation mechanism of single- and few-layer WTe2 are investigated. Oxidation of W and Te atoms appears to be a main reason for degradation. Single-layer samples' Raman signals disappear within 20 min in air. Few-layer WTe2 exhibits saturating degradation behavior: only the top layer WTe2 is oxidized; the degraded layer can protect inner layers from further degradation.

Silicon carbide microdisk resonator.

We demonstrate a silicon carbide (SiC) microdisk resonator with an intrinsic optical quality factor of 6.19×10(3), fabricated on the 3C-SiC-on-Si platform. We characterize the temperature dependence of the cavity resonance and obtain a thermo-optic coefficient of 2.92×10(-5)/K for 3C-SiC. Our simulations show that the device exhibits great potential for cavity optomechanical applications.

High frequency top-down junction-less silicon nanowire resonators.

We report here the first realization of top-down silicon nanowires (SiNW) transduced by both junction-less field-effect transistor (FET) and the piezoresistive (PZR) effect. The suspended SiNWs are among the smallest top-down SiNWs reported to date, featuring widths down to ~20 nm. This has been achieved thanks to a 200 mm-wafer-scale, VLSI process fully amenable to monolithic CMOS co-integration. Thanks to the very small dimensions, the conductance of the silicon nanowire can be controlled by a nearby electrostatic gate. Both the junction-less FET and the previously demonstrated PZR transduction have been performed with the same SiNW. These self-transducing schemes have shown similar signal-to-background ratios, and the PZR transduction has exhibited a relatively higher output signal. Allan deviation (σA) of the same SiNW has been measured with both schemes, and we obtain σ(A) ~ 20 ppm for the FET detection and σ(A) ~ 3 ppm for the PZR detection at room temperature and low pressure. Orders of magnitude improvements are expected from tighter electrostatic control via changes in geometry and doping level, as well as from CMOS integration. The compact, simple topology of these elementary SiNW resonators opens up new paths towards ultra-dense arrays for gas and mass sensing, time keeping or logic switching systems on the SiNW-CMOS platform.

Five Low-Noise Stable Oscillators Referenced to the Same Multimode AlN/Si MEMS Resonator.

We report on the first experimental demonstration of five self-sustaining feedback oscillators referenced to a single multimode resonator, using piezoelectric aluminum nitride on silicon (AlN/Si) microelectromechanical systems (MEMS) technology. Integrated piezoelectric transduction enables efficient readout of five resonance modes of the same AlN/Si MEMS resonator, at 10, 30, 65, 95, and 233 MHz with quality ( Q ) factors of 18 600, 4350, 4230, 2630, and 2138, respectively, at room temperature. Five stable self-sustaining oscillators are built, each referenced to one of these high- Q modes, and their mode-dependent phase noise and frequency stability (Allan deviation) are measured and analyzed. The 10, 30, 65, 95, and 233 MHz oscillators exhibit low phase noise of -116, -100, -105, -106, and -92 dBc/Hz at 1 kHz offset frequency, respectively. The 65 MHz oscillator yields the Allan deviation of 4×10-9 and 2×10-7 at 1 and 1000 s averaging time, respectively. The 10 MHz oscillator's low phase noise holds strong promise for clock and timing applications. The five oscillators' overall promising performance suggests suitability for multimode resonant sensing and real-time frequency tracking. This work also elucidates mode dependency in oscillator noise and stability, one of the key attributes of mode-engineerable resonators.

High Quality Factors in Superlattice Ferroelectric Hf0.5Zr0.5O2 Nanoelectromechanical Resonators.

The discovery of ferroelectricity and advances in creating polar structures in atomic-layered hafnia-zirconia (HfxZr1-xO2) films spur the exploration of using the material for novel integrated nanoelectromechanical systems (NEMS). Despite its popularity, the approach to achieving high quality factors (Qs) in resonant NEMS made of HfxZr1-xO2 thin films remains unexplored. In this work, we investigate the realization of high Qs in Hf0.5Zr0.5O2 nanoelectromechanical resonators by stress engineering via the incorporation of alumina (Al2O3) interlayers. We fabricate nanoelectromechanical resonators out of the Hf0.5Zr0.5O2-Al2O3 superlattices, from which we measure Qs up to 171,000 and frequency-quality factor products (f × Q) of >1011 Hz through electrical excitation and optical detection schemes at room temperature in vacuum. The analysis suggests that clamping loss and surface loss are the limiting dissipation sources and f × Q > 1012 Hz is achievable through further engineering of anchor structure and built-in stress.

Thin ceramic PZT dual- and multi-frequency pMUT arrays for photoacoustic imaging.

Miniaturized ultrasonic transducer arrays with multiple frequencies are key components in endoscopic photoacoustic imaging (PAI) systems to achieve high spatial resolution and large imaging depth for biomedical applications. In this article, we report on the development of ceramic thin-film PZT-based dual- and multi-frequency piezoelectric micromachined ultrasonic transducer (pMUT) arrays and the demonstration of their PAI applications. With chips sized 3.5 mm in length or 10 mm in diameter, square and ring-shaped pMUT arrays incorporating as many as 2520 pMUT elements and multiple frequencies ranging from 1 MHz to 8 MHz were developed for endoscopic PAI applications. Thin ceramic PZT with a thickness of 9 µm was obtained by wafer bonding and chemical mechanical polishing (CMP) techniques and employed as the piezoelectric layer of the pMUT arrays, whose piezoelectric constant d 31 was measured to be as high as 140 pm/V. Benefiting from this high piezoelectric constant, the fabricated pMUT arrays exhibited high electromechanical coupling coefficients and large vibration displacements. In addition to electrical, mechanical, and acoustic characterization, PAI experiments with pencil leads embedded into an agar phantom were conducted with the fabricated dual- and multi-frequency pMUT arrays. Photoacoustic signals were successfully detected by pMUT elements with different frequencies and used to reconstruct single and fused photoacoustic images, which clearly demonstrated the advantages of using dual- and multi-frequency pMUT arrays to provide comprehensive photoacoustic images with high spatial resolution and large signal-to-noise ratio simultaneously.