Quantum limit of quality factor in silicon micro and nano mechanical resonators

Low-Loss GHz Frequency Phononic Integrated Circuits in Gallium Nitride for Compact Radio Frequency Acoustic Wave Devices

Guiding and manipulating GHz frequency acoustic waves in [Formula: see text]-scale waveguides and resonators open up new degrees of freedom to manipulate radio frequency (RF) signals in chip-scale platforms. A critical requirement for enabling high-performance devices is the demonstration of low acoustic dissipation in these highly confined geometries. In this work, we show that gallium nitride (GaN) on silicon carbide (SiC) supports low-loss acoustics by demonstrating acoustic microring resonators with frequency-quality factor ( fQ ) products approaching 1013 Hz at 3.4 GHz. The low dissipation measured exceeds the fQ bound set by the simplified isotropic Akhiezer material damping limit of GaN. We use this low-loss acoustics platform to demonstrate spiral delay lines with on-chip RF delays exceeding [Formula: see text], corresponding to an equivalent electromagnetic delay of ≈ 750 m. Given GaN is a well-established semiconductor with high electron mobility, this work opens up the prospect of engineering traveling wave acoustoelectric interactions in [Formula: see text]-scale waveguide geometries, with associated implications for chip-scale RF signal processing.

Electrochemical etching strategy for shaping monolithic 3D structures from 4H-SiC wafers

Silicon Carbide (SiC) is an outstanding material, not only for electronic applications, but also for projected functionalities in the realm of spin-based quantum technologies, nano-mechanical resonators and photonics-on-a-chip. For shaping 3D structures out of SiC wafers, predominantly dry-etching techniques are used. SiC is nearly inert with respect to wet etching, occasionally photoelectrochemical etching strategies have been applied. Here, we propose an electrochemical etching strategy that solely relies on defining etchable volumina by implantation of p-dopants. Together with the inertness of the n-doped regions, very sharp etching contrasts can be achieved. We present devices as different as monolithic cantilevers, disk-shaped optical resonators and membranes etched out of a single crystal wafer. The high quality of the resulting surfaces can even be enhanced by thermal treatment, with shape-stable devices up to and even beyond 1550°C. The versatility of our approach paves the way for new functionalities on SiC as high-performance multi-functional wafer platform.

Thermoelastic damping in MEMS gyroscopes at high frequencies

Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g., in modern automotive and consumer applications, and require signal stability and accuracy in rather harsh environmental conditions. In many use cases, device reliability must be guaranteed under large external loads at high frequencies. The sensitivity of the sensor to such external loads depends strongly on the damping, or rather quality factor, of the high-frequency mechanical modes of the structure. In this paper, we investigate the influence of thermoelastic damping on several high-frequency modes by comparing finite element simulations with measurements of the quality factor in an application-relevant temperature range. We measure the quality factors over different temperatures in vacuum, to extract the relevant thermoelastic material parameters of the polycrystalline MEMS device. Our simulation results show a good agreement with the measured quantities, therefore proving the applicability of our method for predictive purposes in the MEMS design process. Overall, we are able to uniquely identify the thermoelastic effects and show their significance for the damping of the high-frequency modes of an industrial MEMS gyroscope. Our approach is generic and therefore easily applicable to any mechanical structure with many possible applications in nano- and micromechanical systems.

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 (Hf_xZr_1-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 Hf_xZr_1-xO₂ thin films remains unexplored. In this work, we investigate the realization of high Qs in Hf_0.5Zr_0.5O₂ nanoelectromechanical resonators by stress engineering via the incorporation of alumina (Al₂O₃) interlayers. We fabricate nanoelectromechanical resonators out of the Hf_0.5Zr_0.5O₂-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.

A Novel Extensional Bulk Mode Resonator with Low Bias Voltages

This paper presents a novel Π-shaped bulk acoustic resonator (ΠBAR) with low bias voltages. Concave flanges were coupled with straight beams to effectively enlarge the transduction area. A silicon-on-insulator(SOI)-based fabrication process was developed to produce nanoscale spacing gaps. The tether designs were optimized to minimize the anchor loss. With a substantially improved electromechanical coupling coefficient, the high-stiffness ΠBAR can be driven into vibrations with low bias voltages down to 3 V. The resonator, vibrating at 20 MHz, implements Q values of 3600 and 4950 in air and vacuum, respectively. Strategies to further improve the resonator performance and robustness were investigated. The resonator has promising IC compatibility and could have potential for the development of high-performance timing reference devices.

Epitaxial bulk acoustic wave resonators as highly coherent multi-phonon sources for quantum acoustodynamics

Solid-state quantum acoustodynamic (QAD) systems provide a compact platform for quantum information storage and processing by coupling acoustic phonon sources with superconducting or spin qubits. The multi-mode composite high-overtone bulk acoustic wave resonator (HBAR) is a popular phonon source well suited for QAD. However, scattering from defects, grain boundaries, and interfacial/surface roughness in the composite transducer severely limits the phonon relaxation time in sputter-deposited devices. Here, we grow an epitaxial-HBAR, consisting of a metallic NbN bottom electrode and a piezoelectric GaN film on a SiC substrate. The acoustic impedance-matched epi-HBAR has a power injection efficiency >99% from transducer to phonon cavity. The smooth interfaces and low defect density reduce phonon losses, yielding (f × Q) and phonon lifetimes up to 1.36 × 10¹⁷ Hz and 500 µs respectively. The GaN/NbN/SiC epi-HBAR is an electrically actuated, multi-mode phonon source that can be directly interfaced with NbN-based superconducting qubits or SiC-based spin qubits.

Coherent electrical control of a single high-spin nucleus in silicon

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers¹ and demonstrations of quantum search² and factoring³ algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron^4-6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods^7-9 relied on transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single ¹²³Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 1961¹⁰ but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots^11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Monocrystalline Silicon Carbide Disk Resonators on Phononic Crystals with Ultra-Low Dissipation Bulk Acoustic Wave Modes

Micromechanical resonators with ultra-low energy dissipation are essential for a wide range of applications, such as navigation in GPS-denied environments. Routinely implemented in silicon (Si), their energy dissipation often reaches the quantum limits of Si, which can be surpassed by using materials with lower intrinsic loss. This paper explores dissipation limits in 4H monocrystalline silicon carbide-on-insulator (4H-SiCOI) mechanical resonators fabricated at wafer-level, and reports on ultra-high quality-factors (Q) in gyroscopic-mode disk resonators. The SiC disk resonators are anchored upon an acoustically-engineered Si substrate containing a phononic crystal which suppresses anchor loss and promises Q_ANCHOR near 1 Billion by design. Operating deep in the adiabatic regime, the bulk acoustic wave (BAW) modes of solid SiC disks are mostly free of bulk thermoelastic damping. Capacitively-transduced SiC BAW disk resonators consistently display gyroscopic m = 3 modes with Q-factors above 2 Million (M) at 6.29 MHz, limited by surface TED due to microscale roughness along the disk sidewalls. The surface TED limit is revealed by optical measurements on a SiC disk, with nanoscale smooth sidewalls, exhibiting Q = 18 M at 5.3 MHz, corresponding to f · Q = 9 · 10¹³ Hz, a 5-fold improvement over the Akhiezer limit of Si. Our results pave the path for integrated SiC resonators and resonant gyroscopes with Q-factors beyond the reach of Si.

An efficient Terahertz rectifier on the graphene/SiC materials platform

We present an efficient Schottky-diode detection scheme for Terahertz (THz) radiation, implemented on the material system epitaxial graphene on silicon carbide (SiC). It employs SiC as semiconductor and graphene as metal, with an epitaxially defined interface. For first prototypes, we report on broadband operation up to 580 GHz, limited only by the RC circuitry, with a responsivity of 1.1 A/W. Remarkably, the voltage dependence of the THz responsivity displays no deviations from DC responsivity, which encourages using this transparent device for exploring the high frequency limits of Schottky rectification in the optical regime. The performance of the detector is demonstrated by resolving sharp spectroscopic features of ethanol and acetone in a THz transmission experiment.

Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator

Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q, for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300 K. By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f · Q product for these devices approaches 2 × 10¹³, which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.

Optomechanical antennas for on-chip beam-steering

Rapid and low-power control over the direction of a radiating light field is a major challenge in photonics and a key enabling technology for emerging sensors and free-space communication links. Current approaches based on bulky motorized components are limited by their high cost and power consumption, while on-chip optical phased arrays face challenges in scaling and programmability. Here, we propose a solid-state approach to beam-steering using optomechanical antennas. We combine recent progress in simultaneous control of optical and mechanical waves with remarkable advances in on-chip optical phased arrays to enable low-power and full two-dimensional beam-steering of monochromatic light. We present a design of a silicon photonic system made of photonic-phononic waveguides that achieves 44° field of view with 880 resolvable spots by sweeping the mechanical wavelength with about a milliwatt of mechanical power. Using mechanical waves as nonreciprocal, active gratings allows us to quickly reconfigure the beam direction, beam shape, and the number of beams. It also enables us to distinguish between light that we send and receive.

Predicting the impact of structural diversity on the performance of nanodiamond drug carriers

Diamond nanoparticles (nanodiamonds) are unique among carbon nanomaterials, and are quickly establishing a niché in the biomedical application domain. Nanodiamonds are non-toxic, amenable to economically viable mass production, and can be interfaced with a variety of functional moieties. However, developmental challenges arise due to the chemical complexity and structural diversity inherent in nanodiamond samples. Nanodiamonds present a narrow, but significant, distribution of sizes, a dizzying array of possible shapes, and a complicated surface containing aliphatic and aromatic carbon. In the past these facts have been cast as hindrances, stalling development until perfectly monodispersed samples could be achieved. Current research has moved in a different direction, exploring ways that the polydispersivity of nanodiamond samples can be used as a new degree of engineering freedom, and understanding the impact our limited synthetic control really has upon structure/property relationships. In this review a series of computational and statistical studies will be summarised and reviewed, to characterise the relationship between chemical complexity, structural diversity and the reactive performance of nanodiamond drug carriers.

Efficient anchor loss suppression in coupled near-field optomechanical resonators

Elastic dissipation through radiation towards the substrate is a major loss channel in micro- and nanomechanical resonators. Engineering the coupling of these resonators with optical cavities further complicates and constrains the design of low-loss optomechanical devices. In this work we rely on the coherent cancellation of mechanical radiation to demonstrate material and surface absorption limited silicon near-field optomechanical resonators oscillating at tens of MHz. The effectiveness of our dissipation suppression scheme is investigated at room and cryogenic temperatures. While at room temperature we can reach a maximum quality factor of 7.61k (fQ-product of the order of 10¹¹ Hz), at 22 K the quality factor increases to 37k, resulting in a fQ-product of 2 × 10¹² Hz.

Optically driven ultra-stable nanomechanical rotor

Nanomechanical devices have attracted the interest of a growing interdisciplinary research community, since they can be used as highly sensitive transducers for various physical quantities. Exquisite control over these systems facilitates experiments on the foundations of physics. Here, we demonstrate that an optically trapped silicon nanorod, set into rotation at MHz frequencies, can be locked to an external clock, transducing the properties of the time standard to the rod’s motion with a remarkable frequency stability f_r/Δf_r of 7.7 × 10¹¹. While the dynamics of this periodically driven rotor generally can be chaotic, we derive and verify that stable limit cycles exist over a surprisingly wide parameter range. This robustness should enable, in principle, measurements of external torques with sensitivities better than 0.25 zNm, even at room temperature. We show that in a dilute gas, real-time phase measurements on the locked nanorod transduce pressure values with a sensitivity of 0.3%.

Nanomechanical sensors that rely on intrinsic resonance frequencies usually present a tradeoff between sensitivity and bandwidth. In this work, the authors realise an optically driven nanorotor featuring high frequency stability and tunability over a large frequency range.

Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution

The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 108 at 1 MHz to yield the highest mechanical Qf products (>1014 Hz) yet reported at room temperature.The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions.

Approaching the intrinsic quality factor limit for micromechanical bulk acoustic resonators using phononic crystal tethers

We systematically demonstrate that one-dimensional phononic crystal (1-D PnC) tethers can significantly reduce tether loss in micromechanical resonators to a point where the total energy loss is dominated by intrinsic mechanisms, particularly phonon damping. Multiple silicon resonators are designed, fabricated, and tested to provide comparisons in terms of the number of periods in the PnC and the resonance frequency, as well as a comparison with conventional straight-beam tethers. The product of resonance frequency and measured quality factor (f×Q) is the critical figure of merit, as it is inversely related to the total energy dissipation in a resonator. For a wide range of frequencies, devices with PnC tethers consistently demonstrate higher f×Q values than the best conventional straight-beam tether designs. The f×Q product improves with increasing number of PnC periods, and at a maximum value of 1.2 × 10¹³ Hz, approaches limiting values set by intrinsic material loss mechanisms.

Micromachined Resonators: A Review

This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Resonating Behaviour of Nanomachined Holed Microcantilevers

The nanofabrication of a nanomachined holed structure localized on the free end of a microcantilever is here presented, as a new tool to design micro-resonators with enhanced mass sensitivity. The proposed method allows both for the reduction of the sensor oscillating mass and the increment of the resonance frequency, without decreasing the active surface of the device. A theoretical analysis based on the Rayleigh method was developed to predict resonance frequency, effective mass, and effective stiffness of nanomachined holed microresonators. Analytical results were checked by Finite Element simulations, confirming an increase of the theoretical mass sensitivity up to 250%, without altering other figures of merit. The nanomachined holed resonators were vibrationally characterized, and their Q-factor resulted comparable with solid microcantilevers with same planar dimensions.

High-frequency and high-quality silicon carbide optomechanical microresonators

Silicon carbide (SiC) exhibits excellent material properties attractive for broad applications. We demonstrate the first SiC optomechanical microresonators that integrate high mechanical frequency, high mechanical quality, and high optical quality into a single device. The radial-breathing mechanical mode has a mechanical frequency up to 1.69 GHz with a mechanical Q around 5500 in atmosphere, which corresponds to a fm · Qm product as high as 9.47 × 10(12) Hz. The strong optomechanical coupling allows us to efficiently excite and probe the coherent mechanical oscillation by optical waves. The demonstrated devices, in combination with the superior thermal property, chemical inertness, and defect characteristics of SiC, show great potential for applications in metrology, sensing, and quantum photonics, particularly in harsh environments that are challenging for other device platforms.

Tunable micro- and nanomechanical resonators

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

Impact of distributions and mixtures on the charge transfer properties of graphene nanoflakes

Many of the promising new applications of graphene nanoflakes are moderated by charge transfer reactions occurring between defects, such as edges, and the surrounding environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity and chemical hardness can be useful indicators of the efficiency of graphene nanoflakes for different reactions, and can help identify new application areas. However, as samples of graphene nanoflakes cannot necessarily be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of flakes, and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of ensembles where restrictions have been placed on the diversity of the structures. By predicting quality factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified.

Cascaded optical transparency in multimode-cavity optomechanical systems

Electromagnetically induced transparency has great theoretical and experimental importance in many areas of physics, such as atomic physics, quantum optics and, more recent, cavity optomechanics. Optical delay is the most prominent feature of electromagnetically induced transparency, and in cavity optomechanics, the optical delay is limited by the mechanical dissipation rate of sideband-resolved mechanical modes. Here we demonstrate a cascaded optical transparency scheme by leveraging the parametric phonon-phonon coupling in a multimode optomechanical system, where a low damping mechanical mode in the unresolved-sideband regime is made to couple to an intermediate, high-frequency mechanical mode in the resolved-sideband regime of an optical cavity. Extended optical delay and higher transmission as well as optical advancing are demonstrated. These results provide a route to realize ultra-long optical delay, indicating a significant step towards integrated classical and quantum information storage devices.

Phonon-electron interactions in piezoelectric semiconductor bulk acoustic wave resonators

This work presents the first comprehensive investigation of phonon-electron interactions in bulk acoustic standing wave (BAW) resonators made from piezoelectric semiconductor (PS) materials. We show that these interactions constitute a significant energy loss mechanism and can set practical loss limits lower than anharmonic phonon scattering limits or thermoelastic damping limits. Secondly, we theoretically and experimentally demonstrate that phonon-electron interactions, under appropriate conditions, can result in a significant acoustic gain manifested as an improved quality factor (Q). Measurements on GaN resonators are consistent with the presented interaction model and demonstrate up to 35% dynamic improvement in Q. The strong dependencies of electron-mediated acoustic loss/gain on resonance frequency and material properties are investigated. Piezoelectric semiconductors are an extremely important class of electromechanical materials, and this work provides crucial insights for material choice, material properties, and device design to achieve low-loss PS-BAW resonators along with the unprecedented ability to dynamically tune resonator Q.