Anisotropy Reversal of Thermal Conductivity in Silicon Nanowire Networks Driven by Quasi-Ballistic Phonon Transport

Nanostructured semiconductors promise functional thermal management for microelectronics and thermoelectrics through a rich design capability. However, experimental studies on anisotropic in-plane thermal conduction remain limited, despite the demand for directional heat dissipation. Here, inspired by an oriental wave pattern, a periodic network of bent wires, we investigate anisotropic in-plane thermal conduction in nanoscale silicon phononic crystals with the thermally dead volume. We observed the anisotropy reversal of the material thermal conductivity from 1.2 at 300 K to 0.8 at 4 K, with the reversal temperature of 80 K mediated by the transition from a diffusive to a quasi-ballistic regime. Our Monte Carlo simulations revealed that the backflow of the directional phonons induces the anisotropy reversal, showing that the quasi-ballistic phonon transport introduces preferential thermal conduction channels with anomalous temperature dependence. Accordingly, the anisotropy of the effective thermal conductivity varied from 2.7 to 5.0 in the range of 4-300 K, indicating an anisotropic heat manipulation capability. Our findings demonstrate that the design of nanowire networks enables the directional thermal management of electronic devices.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.

Reem-Shape Phononic Crystal for Q Anchor Enhancement of Thin-Film-Piezoelectric-on-Si MEMS Resonator

This paper proposes a reem-shaped phononic crystal for the performance enhancement of TPoS resonators. The proposed phononic crystal offers an ultra-wide acoustic band gap that prevents energy leakage through the supporting substrate upon its placement at the anchoring boundary, resulting in significant improvements in the resonator quality factor. Simulated results show reem-shape phononic crystals generate a band gap up to 175 MHz with a BG of 90% and enhance the anchor quality factor from 180,000 to 6,000,000 and the unloaded quality factor from 133,000 to 160,000, representing 33.3-fold and 1.2-fold improvements, respectively.

Enhanced Sensitivity of Binary/Ternary Locally Resonant Porous Phononic Crystal Sensors for Sulfuric Acid Detection: A New Class of Fluidic-Based Biosensors

This research presented a comprehensive study of a one-dimensional (1D) porous silicon phononic crystal design as a novel fluidic sensor. The proposed sensor is designed to detect sulfuric acid (H₂SO₄) within a narrow concentration range of 0-15%. Sulfuric acid is a mineral acid extensively utilized in various physical, chemical, and industrial applications. Undoubtedly, its concentration, particularly at lower levels, plays a pivotal role in these applications. Hence, there is an urgent demand for a highly accurate and sensitive tool to monitor even the slightest changes in its concentration, which is crucial for researchers. Herein, we presented a novel study on the optimization of the phononic crystal (PnC) sensor. The optimization process involves a comparative strategy between binary and ternary PnCs, utilizing a multilayer stack comprising 1D porous silicon (PSi) layers. Additionally, a second comparison is conducted between conventional Bragg and local resonant PnCs to demonstrate the design with the highest sensitivity. Moreover, we determine the optimum values for the materials' thickness and number of periods. The results revealed that the ternary local resonant PnC design with the configuration of {silicone rubber/[PSi1/PSi2/PSi3]^N/silicone rubber} is the optimal sensor design. The sensor provided a super sensitivity of 2.30 × 10⁷ Hz for a concentration change of just 2%. This exceptional sensitivity is attributed to the presence of local resonant modes within the band gap of PnCs. The temperature effects on the local resonant modes and sensor performance have also been considered. Furthermore, additional sensor performance parameters such as quality factor, figure of merit, detection limit, and damping rate have been calculated to demonstrate the effectiveness of the proposed liquid sensor. The transfer matrix method was utilized to compute the transmission spectra of the PnC, and Hashin's expression was employed to manipulate the porous silicon media filled with sulfuric acid at various concentrations. Lastly, the proposed sensor can serve as an efficient tool for detecting acidic rain, contaminating freshwater, and assessing food and liquid quality, as well as monitoring other pharmaceutical products.

Frequency-selective valley edge routing of elastic wave in topological phononic crystals with different symmetries

The control of propagation direction or path of edge states is difficult when the chirality of the excitation source and the boundary structures are determined. Here, we studied a frequency-selective routing for elastic wave based on two types of topological phononic crystals (PnCs) with different symmetries. By constructing multiple types of interfaces between different PnCs structures with distinct valley topological phases, the valley edge states of elastic wave could be realized at different frequencies in the band gap. Meanwhile, based on the simulation of topological transport, it is found that the routing path of elastic waves valley edge states highly depends on the operating frequency and the inputting port of the excitation source. By varying the excitation frequency, the transport path can be switched. The results provide a paradigm for the control of elastic wave propagation paths that could be employed for designing the frequency-dependent ultrasonic division devices.

One-Dimensional Phononic Crystals: A Simplified Platform for Effective Detection of Heavy Metals in Water with High Sensitivity

Recently, the pollution of fresh water with heavy metals due to technological and industrial breakthroughs has reached record levels. Therefore, monitoring these metals in fresh water has become essentially urgent. Meanwhile, the conventional periodic one-dimensional phononic crystals can provide a novel platform for detecting the pollution of heavy metals in fresh water with high sensitivity. A simplified design of a defective, one-dimensional phononic crystals (1D-PnC) structure is introduced in this paper. The sensor is designed from a lead-epoxy multilayer with a central defect layer filled with an aqueous solution from cadmium bromide (CdBr₂). The formation of a resonant peak through the transmittance spectrum is highly expected. This study primarily aims to monitor and detect the concentration of cadmium bromide in pure water based on shifting the position of this resonant peak. Notably, any change in cadmium bromide concentration can affect the acoustic properties of cadmium bromide directly. The transfer matrix method has been used to calculate the transmission spectra of the incident acoustic wave. The numerical findings are mainly based on the optimization of the cadmium bromide layer thickness, lead layer thickness, epoxy layer thickness, and the number of periods to investigate the most optimum sensor performance. The introduced sensor in this study has provided a remarkably high sensitivity (S = 1904.25 Hz) within a concentration range of (0-10,000 ppm). The proposed sensor provides a quality factor (QF), a resolution, and a figure of merit of 1398.51752, 48,875,750 Hz, and 4.12088 × 10^-5 (/ppm), respectively. Accordingly, this sensor can be a potentially robust base for a promising platform to detect small concentrations of heavy metal ions in fresh water.

Tuning the decay of sound in a viscous metamaterial

Using analytical results for viscous dissipation in phononic crystals, we calculate the decay coefficient of a sound wave propagating at low frequencies through a two-dimensional phononic crystal with a viscous fluid background. It is demonstrated that the effective acoustic viscosity of the phononic crystal may exceed by two to four orders of magnitude the natural hydrodynamic viscosity of the background fluid. Moreover, the decay coefficient exhibits dependence on the direction of propagation; that is, a homogenized phononic crystal behaves like an anisotropic viscous fluid. Strong dependence on the filling fraction of solid scatterers offers the possibility of tuning the dissipative decay length of sound, which is an important characteristic of any acoustic device. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Design and Optimization of a Novel SAW Gyroscope Structure Based on Amplitude Modulation with 1-D Phononic Crystals

Surface acoustic wave gyroscopes (SAWGs), as a kind of all-solid-state micro-electro-mechanical system (MEMS) gyroscopes, can work normally under extremely high-impact environmental conditions. Among the current SAWGs, amplitude-modulated gyroscopes (AMGs) are all based on the same gyro effect, which was proved weak, and their sensitivity and intensity of the output are both lower than frequency-modulated gyroscopes (FMGs). However, because FMGs need to process a series of frequency signals, their signal processing and circuits are far less straightforward and simple than AMGs. In order to own both high-sensitivity and simple signal processing, a novel surface acoustic traveling wave gyroscope based on amplitude modulation is proposed, using one-dimensional phononic crystals (PCs) in this paper. In view of its specific structure, the proposed gyroscope consists of a surface acoustic wave oscillator and a surface acoustic wave delay line within a one-dimensional phononic crystal with a high-Q defect mode. In this paper, the working principle is analyzed theoretically through the partial wave method (PWM), and the gyroscopes with different numbers of PCs are also designed and studied by using the finite element method (FEM) and multiphysics simulation. The research results demonstrate that under a 1 V oscillator voltage output, the higher sensitivity of −23.1 mV·(rad/s)⁻¹ in the linear range from −8 rad/s to 8 rad/s is reached when the gyro with three PC walls, and the wider linear range from −15 rad/s to 17.5 rad/s with the sensitivity of −6.7 mV·(rad/s)⁻¹ with only one PC wall. Compared with the existing AMGs using metal dots to enhance the gyro effect, the sensitivity of the proposed gyro is increased by 15 to 112 times, and the linear range is increased by 4.6 to 186 times, even without the enhancement of the metal dots.

Graphene-Based Nanoelectromechanical Periodic Array with Tunable Frequency

Phononic crystals (PnCs) have attracted much attention due to their great potential for dissipation engineering and propagation manipulation of phonons. Notably, the excellent electrical and mechanical properties of graphene make it a promising material for nanoelectromechanical resonators. Transferring a graphene flake to a prepatterned periodic mechanical structure enables the realization of a PnC with on-chip scale. Here, we demonstrate a nanoelectromechanical periodic array by anchoring a graphene membrane to a 9 × 9 array of standing nanopillars. The device exhibits a quasi-continuous frequency spectrum with resonance modes distributed from ∼120 MHz to ∼980 MHz. Moreover, the resonant frequencies of these modes can be electrically tuned by varying the voltage applied to the gate electrode sitting underneath. Simulations suggest that the observed band-like spectrum provides an experimental evidence for PnC formation. Our architecture has large fabrication flexibility, offering a promising platform for investigations on PnCs with electrical accessibility and tunability.

Numerical Investigation of Phononic Crystal Based Film Bulk Acoustic Wave Resonators

Film bulk acoustic resonator (FBAR)-based filters have attracted great attention because they can be used to build high-performance RF filters with low cost and small device size. Generally, FBARs employ the air cavity and Bragg mirror to confine the acoustic energy within the piezoelectric layer, so as to achieve high quality factors and low insertion loss. Here, two-dimensional (2D) phononic crystals (PhCs) are proposed to be the acoustic energy reflection layer for an FBAR (PhC-FBAR). Four kinds of PhC structures are investigated, and their bandgap diagrams and acoustic wave reflection coefficients are analyzed using the finite element method (FEM). Then, the PhCs are used as the acoustic wave reflectors at the bottom of the piezoelectric stack, with high reflectivity for elastic waves in the specific frequency range. The results show that the specific PhC possesses a wide bandgap, which enables the PhC-FBAR to work at a broad frequency range. Furthermore, the impedance spectra of PhC-FBARs are very smooth with few spurious modes, and the quality factors are close to those of traditional FBARs with air cavities, showing the application potential of the PhC-FBAR filters with wide bandwidth and high power capability.

Critical couplings in topological-insulator waveguide-resonator systems observed in elastic waves

Waveguides and resonators are core components in the large-scale integration of electronics, photonics and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e. no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting and intense wave-matter interactions, using phonons, photons or even electrons. The present work further enhances confidence in using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Q-Factor Enhancement of Thin-Film Piezoelectric-on-Silicon MEMS Resonator by Phononic Crystal-Reflector Composite Structure

Thin-film piezoelectric-on-silicon (TPoS) microelectromechanical (MEMS) resonators are required to have high Q-factor to offer satisfactory results in their application areas, such as oscillator, filter, and sensors. This paper proposed a phononic crystal (PnC)-reflector composite structure to improve the Q factor of TPoS resonators. A one-dimensional phononic crystal is designed and deployed on the tether aiming to suppress the acoustic leakage loss as the acoustic wave with frequency in the range of the PnC is not able to propagate through it, and a reflector is fixed on the anchoring boundaries to reflect the acoustic wave that lefts from the effect of the PnC. Several 10 MHz TPoS resonators are fabricated and tested from which the Q-factor of the proposed 10 MHz TPoS resonator which has PnC-reflector composite structure on the tether and anchoring boundaries achieved offers a loaded Q-factor of 4682 which is about a threefold improvement compared to that of the conventional resonator which is about 1570.

Directional Ultrasound Source for Solid Materials Inspection: Diffraction Management in a Metallic Phononic Crystal

In this work, we numerically investigate the diffraction management of longitudinal elastic waves propagating in a two-dimensional metallic phononic crystal. We demonstrate that this structure acts as an "ultrasonic lens", providing self-collimation or focusing effect at a certain distance from the crystal output. We implement this directional propagation in the design of a coupling device capable to control the directivity or focusing of ultrasonic waves propagation inside a target object. These effects are robust over a broad frequency band and are preserved in the propagation through a coupling gel between the "ultrasonic lens" and the solid target. These results may find interesting industrial and medical applications, where the localization of the ultrasonic waves may be required at certain positions embedded in the object under study. An application example for non-destructive testing with improved results, after using the ultrasonic lens, is discussed as a proof of concept for the novelty and applicability of our numerical simulation study.

Deep-Subwavelength Holey Acoustic Second-Order Topological Insulators

Higher-order topological insulators (HOTIs) belong to a new class of materials with unusual topological phases. They have garnered considerable attention due to their capabilities in confining energy at the hinges and corners, which is entirely protected by the topology, and have thus become attractive structures for acoustic wave studies and control. However, for most practical applications at audible and low frequencies, compact and subwavelength implementations are desirable in addition to providing robust guiding of sound beyond a single-frequency operation. Here, a holey HOTI capable of sustaining deeply confined corner states 50 times smaller than the wavelength is proposed. A remarkable resilience of these surface-confined acoustic states against defects is experimentally observed, and topologically protected sound is demonstrated in three different frequency regimes. Concerning this matter, the findings will thus have the capability to push forward exciting applications for robust acoustic imaging way beyond the diffraction limit.

Spider Web-Like Phononic Crystals for Piezoelectric MEMS Resonators to Reduce Acoustic Energy Dissipation

Phononic crystals (PnC) are a remarkable example of acoustic metamaterials with superior wave attenuation mechanisms for piezoelectric micro-electro-mechanical systems (MEMS) resonators to reduce the energy dissipation. Herein, a spider web-like PnC (SW-PnC) is proposed to sufficiently isolate the wave vibration. Finite-element analysis is performed to gain insight into the transmission property of finite PnC, and band characteristics by infinite periods. In comparison with the circle hole PnC at a similar bandgap, due to its already very lightweight PnC structure compared with previously reported PnCs, the proposed PnC offers a significantly lighter weight, smaller lattice constant, and greater energy leakage inhibition. More specifically, the resonator with the SW-PnC plate as the anchoring substrate exhibited a quality factor as high as 66569.7 at 75.82 MHz.

Coherent Thermal Conduction in Silicon Nanowires with Periodic Wings

Artificial periodic nanostructures, known as phononic crystals, promise to control the thermal properties of nanostructures in the coherent regime, which can be achieved in semiconductors at low temperatures. Here, we study coherent thermal conduction in silicon nanowires with added periodic wings at sub-Kelvin temperature. Our simulations show that the added periodic wings flatten the phonon dispersion and thus reduce the thermal conductance. We investigate the dependence of this reduction on the size of the wings and conclude that the reduction is mainly caused by the periodicity of the wings, rather than by local resonances in them. These findings help to better understand the mechanisms controlling coherent heat conduction in periodic resonant nanostructures.

Nonlinear Bloch waves and balance between hardening and softening dispersion

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

The Use of Phononic Crystals to Design Piezoelectric Power Transducers

It was recently proposed that the lateral resonances around the working resonance band of ultrasonic piezoelectric sandwich transducers can be stopped by a periodic array of circular holes drilled along the main propagation direction (a phononic crystal). In this work, the performance of different transducer designs made with this procedure is tested using laser vibrometry, electric impedance tests and finite element models (FEM). It is shown that in terms of mechanical vibration amplitude and acoustic efficiency, the best design for physiotherapy applications is when both, the piezoceramic and an aluminum capsule are phononic structures. The procedure described here can be applied to the design of power ultrasonic devices, physiotherapy transducers and other external medical power ultrasound applications where piston-like vibration in a narrow band is required.

Composite 3D-printed metastructures for low-frequency and broadband vibration absorption

Architected materials that control elastic wave propagation are essential in vibration mitigation and sound attenuation. Phononic crystals and acoustic metamaterials use band-gap engineering to forbid certain frequencies from propagating through a material. However, existing solutions are limited in the low-frequency regimes and in their bandwidth of operation because they require impractical sizes and masses. Here, we present a class of materials (labeled elastic metastructures) that supports the formation of wide and low-frequency band gaps, while simultaneously reducing their global mass. To achieve these properties, the metastructures combine local resonances with structural modes of a periodic architected lattice. Whereas the band gaps in these metastructures are induced by Bragg scattering mechanisms, their key feature is that the band-gap size and frequency range can be controlled and broadened through local resonances, which are linked to changes in the lattice geometry. We demonstrate these principles experimentally, using advanced additive manufacturing methods, and inform our designs using finite-element simulations. This design strategy has a broad range of applications, including control of structural vibrations, noise, and shock mitigation.

Ballistic phonon transport in holey silicon

When the size of semiconductors is smaller than the phonon mean free path, phonons can carry heat with no internal scattering. Ballistic phonon transport has received attention for both theoretical and practical aspects because Fourier's law of heat conduction breaks down and the heat dissipation in nanoscale transistors becomes unpredictable in the ballistic regime. While recent experiments demonstrate room-temperature evidence of ballistic phonon transport in various nanomaterials, the thermal conductivity data for silicon in the length scale of 10-100 nm is still not available due to experimental challenges. Here we show ballistic phonon transport prevails in the cross-plane direction of holey silicon from 35 to 200 nm. The thermal conductivity scales linearly with the length (thickness) even though the lateral dimension (neck) is as narrow as 20 nm. We assess the impact of long-wavelength phonons and predict a transition from ballistic to diffusive regime using scaling models. Our results support strong persistence of long-wavelength phonons in nanostructures and are useful for controlling phonon transport for thermoelectrics and potential phononic applications.

Probing thermomechanics at the nanoscale: impulsively excited pseudosurface acoustic waves in hypersonic phononic crystals

High-frequency surface acoustic waves can be generated by ultrafast laser excitation of nanoscale patterned surfaces. Here we study this phenomenon in the hypersonic frequency limit. By modeling the thermomechanics from first-principles, we calculate the system's initial heat-driven impulsive response and follow its time evolution. A scheme is introduced to quantitatively access frequencies and lifetimes of the composite system's excited eigenmodes. A spectral decomposition of the calculated response on the eigemodes of the system reveals asymmetric resonances that result from the coupling between surface and bulk acoustic modes. This finding allows evaluation of impulsively excited pseudosurface acoustic wave frequencies and lifetimes and expands our understanding of the scattering of surface waves in mesoscale metamaterials. The model is successfully benchmarked against time-resolved optical diffraction measurements performed on one-dimensional and two-dimensional surface phononic crystals, probed using light at extreme ultraviolet and near-infrared wavelengths.