Effective Coupling Coefficient Research Articles

Bulk acoustic wave—Solidly mounted resonator with a-SiOCN:H as low-Z material

Bulk acoustic wave (BAW) filters have been proven to be of high demand in today's low power RF front-ends for mobile communication devices. Within the launch of 5G applications worldwide, especially in the region of new radio (nr-1) up to 6 GHz, defined frequency bands require filters of wide bandwidths, while simultaneously featuring steep edges and high out-of-band rejection. Due to the coexistence with 4G LTE (long term evolution) wireless standards as well as advanced data transfer concepts such as carrier aggregation, the increasing complexity of antenna systems forces the implementation of highly selective acoustic filters. In contrast to the widely used surface acoustic wave (SAW) technology, BAW filters appear with superior performance for frequencies above 1 GHz. This work describes the fabrication of a BAW-solidly mounted resonator (BAW-SMR) with a tailored material system of a-SiOCN:H as a low impedance (low-Z) material integrated within its acoustic Bragg mirror. A direct comparison to the widely used low-Z material of SiO2 with an acoustic impedance of around 13 MRayl is demonstrated by two equal resonator stacks by replacing only the uppermost low-Z thin film of the acoustic reflector. A single-mask design was chosen with platinum as a bottom electrode to ensure the most equal growth conditions for the piezoelectric aluminum nitride (AlN) layers on both reflectors’ surfaces featuring either the tailored a-SiOCN:H or standard SiO2. The a-SiOCN:H thin films were deposited by plasma-enhanced chemical vapor deposition and the according acoustic impedance was priorly depicted to 7.1 MRayl, which could be exploited to achieve an increase in the effective coupling coefficient beyond 7% as well as a resonator bandwidth of more than 60 MHz.

Magnetoelastic coupling for Fe–Ga thin films epitaxially grown on different substrates

This paper reports the systematic study on the structure, magnetic properties and magnetoelastic properties for the Fe100−x Ga x (001) thin films epitaxially grown on the different substrates of GaAs(001) and MgO(001) using the sputtering technique. The alloy composition dependence of effective magnetoelastic coupling coefficient B eff along the FeGa [110] direction indicated that the largest magnetoelastic coupling was obtained for the Fe–Ga layer with x = 30 grown on the MgO substrate, which was evaluated to be B eff = − 9.4 × 107 erg cm−3. Considering the results of structural analysis and magnetization measurement, the different crystallite sizes depending on the kind of substrate may give rise to the different magnetoelastic coupling strengths between the Fe–Ga layers on the MgO and the GaAs. The magnetostriction along the Fe–Ga [111] direction λ 111 was also estimated with the assumption of plausible elastic property of Fe–Ga, and showed the values comparable to the reported value of bulk Fe–Ga. This means the large magnetostriction can be obtained even for the Fe–Ga thin films epitaxially grown not only on the GaAs(001) but also on the MgO(001). The findings in this work will give a guideline for designing spintronic applications with a Fe–Ga layer exhibiting a large magnetoelastic coupling.

Impact of Grating Duty-Cycle Randomness on DFB Laser Performance

The duty-cycle randomness (DCR) of the Bragg grating of the distributed feedback (DFB) lasers introduced by the fabrication process is inevitable, even with state-of-the-art technologies such as electron beam lithography and dry or wet etching.This work investigates the impact of grating DCR on DFB laser performance through numerical simulations. The result reveals that such randomness causes a reduction in the side mode suppression ratio (SMSR), and deteriorates the noise characteristics, i.e., broadens the linewidth and increases the relative intensity noise (RIN). With the grating DCR, the effective grating coupling coefficient decreases as evidenced by the reduced Bragg stopband width. However, the longitudinal spatial hole burning (LSHB) effect in the DFB lasers can somewhat be diminished by the grating DCR. The seriousness of these effects depends on different grating structures and their coupling strengths. Our simulation shows that a degradation of 17 dB can be brought to the SMSR of the uniform grating DFB lasers with their duty cycles taking a deviation of ±25% in a uniformly distributed random fashion. It also broadens the linewidth of the quarter-wavelength phase-shifted DFB lasers by more than 2.5 folds. The impact of this effect on the RIN is moderate—less than 2%. All the performance deteriorations can partially be attributed to the effective reduction in the grating coupling coefficient of around 20% by such a DCR.

A Piezotronic and Magnetic Dual‐Gated Ferroelectric Semiconductor Transistor

AbstractPiezotronics is the coupling effect of the piezoelectric and semiconductor properties; however, the piezoelectric constant of the piezoelectric semiconductor is relatively small while the ferroelectric materials with large piezoelectric constant typically possess weak semiconductor properties, thus limiting the effective coupling coefficient of the piezotronic materials and devices. Here, a piezotronics and magnetic dual‐gated ferroelectric semiconductor transistor (PM‐FEST) is fabricated by Terfenol‐D, aluminum oxide (Al2O3), and ferroelectric semiconductor α‐In2Se3, which has a large piezoelectric coefficient, room‐temperature ferroelectricity, and dipole locking. The charge carrier transport and corresponding drain current of the PM‐FEST can be directly modulated by either the applied magnetic field or external strain. At a low magnetic field (<200 mT), the maximum current on/off ratio of α‐In2Se3 based PM‐FEST is as high as 1700%. Compared with traditional piezotronic devices, the PM‐FEST demonstrates a higher gauge factor (2.3 × 104) than that of the piezoelectric semiconductors. This work provides a possibility of realizing magnetism‐modulated electronics in semiconductors by exploiting the coupling of piezotronics and magnetostriction.

Polyimide-On-Silicon 2D Piezoelectric Micromachined Ultrasound Transducer (PMUT) Array

This paper presents a fully addressable 8 × 8 two-dimensional (2D) rigid piezoelectric micromachined ultrasonic transducer (PMUT) array. The PMUTs were fabricated on a standard silicon wafer, resulting in a low-cost solution for ultrasound imaging. A polyimide layer is used as the passive layer in the PMUT membranes on top of the active piezoelectric layer. The PMUT membranes are realized by backside deep reactive ion etching (DRIE) with an oxide etch stop. The polyimide passive layer enables high resonance frequencies that can be easily tuned by controlling the thickness of the polyimide. The fabricated PMUT with 6 µm polyimide thickness showed a 3.2 MHz in-air frequency with a 3 nm/V sensitivity. The PMUT has shown an effective coupling coefficient of 14% as calculated from the impedance analysis. An approximately 1% interelement crosstalk between the PMUT elements in one array is observed, which is at least a five-fold reduction compared to the state of the art. A pressure response of 40 Pa/V at 5 mm was measured underwater using a hydrophone while exciting a single PMUT element. A single-pulse response captured using the hydrophone suggested a 70% −6 dB fractional bandwidth for the 1.7 MHz center frequency. The demonstrated results have the potential to enable imaging and sensing applications in shallow-depth regions, subject to some optimization.

Coupling coefficient analysis of composite bar: A new idea for the design of multi-resonant longitudinal transducer

Multi-resonant longitudinal transducers are widely used in sonar technology by exciting multiple resonant modes to extend the operating bandwidth. However, the existing design methods of multi-resonant longitudinal transducers lack unified and effective theoretical guidance, and usually require extensive parameter searches and calculations, so it is not universal and difficult to popularize. Based on the one-dimensional longitudinal vibration theory, the mode analysis and harmonic analysis of the single piezoelectric bar and the composite bar are carried out, and the physical mechanism of the modes not being excited is revealed. Then, starting with the original definition of electromechanical coupling coefficient, the effective coupling coefficients of the composite bar at different resonant modes are given. Finally, a method to adjust the relative strength of resonant modes is proposed based on the relationship between dynamic conductance and effective coupling coefficient. In this paper, electromechanical coupling coefficient is taken as the core factor of transducer design, which holds the key point and provides a new idea for the design of multi-resonant longitudinal broadband transducers.

Localization effects from local phase shifts in the modulation of waveguide arrays

Artificial gauge fields enable the intriguing possibility to manipulate the propagation of light as if it were under the influence of a magnetic field even though photons possess no intrinsic electric charge. Typically, such fields are engineered via periodic modulations of photonic lattices such that the effective coupling coefficients after one period become complex-valued. In this work, we investigate the possibility of introducing randomness into artificial gauge fields by applying local random phase shifts in the modulation of lattices of optical waveguides. We first study the elemental unit consisting of two coupled single-mode waveguides and determine the effective complex-valued coupling coefficient after one period of modulation as a function of the phase shift, modulation amplitude, and modulation frequency. Thereby we identify the regime where varying the modulation phase yields sufficiently large changes of the effective coupling coefficient to induce Anderson localization. Using these results, we demonstrate numerically the onset of Anderson localization in 1D and 2D lattices of x- and helically modulated waveguides via randomly choosing the modulation phases of individual waveguides. Besides further fundamental investigations of wave propagation in the presence of random gauge fields, our findings enable the engineering of coupling coefficients without changing the footprint of the overall lattice. As a proof of concept, we demonstrate how to engineer out-of-phase modulated lattices that exhibit dynamic localization and defect-free surface states. Therefore, we anticipate that the modulation phase will play an important role in the judicious design of functional waveguide lattices.

Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN

The piezoelectric and elastic properties are critical for the performance of AlN-based 5G RF filters. The improvement of the piezoelectric response in AlN is often accompanied by lattice softening, which compromises the elastic modulus and sound velocities. Optimizing both the piezoelectric and elastic properties simultaneously is both challenging and practically desirable. In this work, 117 X0.125Y0.125Al0.75N compounds were studied with the high-throughput first-principles calculation. B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N were found to have both high C33 (>249.592 GPa) and high e33 (>1.869 C/m2). The COMSOL Multiphysics simulation showed that most of the quality factor (Qr) values and the effective coupling coefficient (Keff2) of the resonators made with these three materials were higher than those with Sc0.25AlN with the exception of the Keff2 of Be0.125Ce0.125AlN, which was lower due to the higher permittivity. This result demonstrates that double-element doping of AlN is an effective strategy to enhance the piezoelectric strain constant without softening the lattice. A large e33 can be achieved with doping elements having d-/f- electrons and large internal atomic coordinate changes of du/dε. The doping elements-nitrogen bond with a smaller electronegativity difference (ΔEd) leads to a larger elastic constant C33.

Exploring electromechanical utility of GaAs interdigitated transducers; using finite-element-method-based parametric analysis and experimental comparison

Analysis of interdigitated transducers often relies on phenomenological models to approximate device electrical performance. While these approaches prove essential for signal processing applications, phenomenological models provide limited information on the device’s mechanical response and physical characteristics of the generated acoustic field. Finite element method modeling, in comparison, offers a robust platform to study the effects of the full device geometry on critical performance parameters of interdigitated transducer devices. In this study, we fabricate a surface acoustic wave resonator on semi-insulating GaAs (100), which consists of an interdigitated transducer and acoustic mirror assembly. The device is subsequently modeled using fem software. A vector network analyzer is used to measure the experimental device scattering response, which compares well with the simulated results. The wave characteristics of the experimental device are measured by contact-mode atomic force microscopy, which validates the simulation’s mechanical response predictions. We further show that a computational parametric analysis can be used to optimize device designs for series resonance frequency, effective coupling coefficient, quality factor, and maximum acoustic surface displacement.

High-performance SH-SAW resonator using optimized 30° YX-LiNbO3/SiO2/Si

With the rapid development of 5G technology, acoustic wave filters with large bandwidths are urgently required to deal with the explosive increase in data traffic. Recently, there is extensive attention paid to shear-horizontal (SH) surface acoustic wave (SAW) resonators based on lithium niobate (LiNbO3) substrates, thanks to its large effective coupling coefficient (k2eff). However, because of the bulk acoustic wave (BAW) energy radiation into the LiNbO3 substrate, it is very challenging to obtain a high quality factor (Q) for SH-SAW resonators. In this study, a 30° YX-LiNbO3/SiO2/Si SAW resonator with the SH mode is proposed to achieve a large coupling and a high Q simultaneously. By bonding a LiNbO3 thin film onto a thermally oxidized Si(100) substrate, the velocity mismatch between the piezoelectric layer and the SiO2/Si substrate could significantly reduce the BAW energy leakage. Finite element method simulation is employed to optimize the cut angle of the LiNbO3 film and the thickness of each layer. The fabricated SH-SAW resonators with a resonant frequency of 924 MHz yield a k2eff of 24.8% and a maximum of Bode-Q (Bode-Qmax) of 1107. In comparison with the previously reported same-type SAW resonators, a higher Bode-Qmax is demonstrated in this work when their k2eff is larger than 20%, providing a potential solution to enable wideband tunable filters in the 5G communication system.

Single-crystalline LiNbO3 film based wideband SAW devices with spurious-free responses for future RF front-ends

This work demonstrates super-high frequency wave-guided surface acoustic wave (SAW) devices based on LiNbO3/SiO2/Si layered substrates. SAW resonators with fundamental operating frequency to the 7-GHz range were developed, and wave modes like the Rayleigh, Shear-horizontal (SH), Pseudo-Bulk, etc., were observed. Furthermore, effective coupling coefficients (k2eff) and quality factor (Q) of the devices have been investigated systematically. Specifically, spurious-free SAW resonators with the SH wave frequency over 7.40 GHz and the high k2eff value of ∼7.8% were obtained at a nanoscale wavelength of 480 nm. Finally, high-performance filters with a bandwidth over 300 MHz were achieved. The demonstrated filters show sharp roll-off and spurious-free responses within the passband with insertion loss <−5 dB and a small temperature coefficient of frequency of ∼−45.8 ppm/K at a super-high frequency of 7.17 GHz. Upon further optimizations, high-performance SAW devices built on a single crystalline LiNbO3 film can potentially enable the low-loss and wideband signal processing functions, promising for the next-generation radio frequency front-end system applications.

Lagrangian formulation to investigate the effect of coupling on resonant microstrip transmission line

AbstractAn analytical and a numerical study on coupling in microstrip transmission line (MTL) are reported for different split-gap orientations of a single gap square-shaped split-ring resonator (SRR). Taking both magnetic and electric couplings and adopting Lagrangian formulation for this coupled system, mathematical relations are found for each orientation of SRR to determine the connection between coupling co-efficient and resonant mode frequency. It is shown that coupling results in higher resonance frequency when the SRR, with parallel split-gap, has the gap far from the MTL. But, a lower resonance frequency is obtained when the SRR is placed at shorter distances with parallel split-gap near to the MTL. Again, for perpendicular split-gap orientation of SRR, the resonant frequency is found in terms of an effective coupling co-efficient; at shorter distances it is found to be lower than the fundamental resonance frequency of uncoupled SRR and an opposite effect is obtained at longer distances. Using CST Microwave Studio, the resonance frequency for each split-gap orientation of SRR is also studied as a function of separation between MTL and SRR. It is observed that this phenomenon strongly depends on SRR side-length, substrate height, and separation between MTL and SRR.

Evaluation of the impact of abnormal grains on the performance of Sc0.15Al0.85N-based BAW resonators and filters

Sc x Al1−x N is a promising piezoelectric material for radio frequency communication applications with excellent electro-acoustic properties. However, the growth of abnormally oriented grains is widely observed in the Sc doped AlN films deposited by sputtering. In this work, for the first time, the impact of the abnormal grains in the Sc0.15Al0.85N films on the performance of bulk acoustic wave resonators and filters is systematically evaluated by both simulations and measurements. The correlation between the device performance and the abnormal grain parameters, including the density, dimension, crystal orientation, growth height and the total volume of the abnormal grains, is evaluated and quantified. Simulation results show that the total volume of all abnormal grains in the whole device is the most critical factor among the parameters. Abnormal grains with randomly distributed parameters and around 6% total volume of the film can degrade the effective coupling coefficient of the resonator from 13.6% to 11%, leading to a 10.6% decrement of the filter bandwidth. Wafer-level device characterizations and measurements are performed, and the results are consistent with the simulations. This study provides a practical method for predicting the performance of the resonators and filters with abnormal grains, and a guideline for film quality evaluation.

Screen Printed Copper and Tantalum Modified Potassium Sodium Niobate Thick Films on Platinized Alumina Substrates.

We show how sintering in different atmospheres affects the structural, microstructural, and functional properties of ~30 μm thick films of K0.5Na0.5NbO3 (KNN) modified with 0.38 mol% K5.4Cu1.3Ta10O29 and 1 mol% CuO. The films were screen printed on platinized alumina substrates and sintered at 1100 °C in oxygen or in air with or without the packing powder (PP). The films have a preferential crystallographic orientation of the monoclinic perovskite phase in the [100] and [−101] directions. Sintering in the presence of PP contributes to obtaining phase-pure films, which is not the case for the films sintered without any PP notwithstanding the sintering atmosphere. The latter group is characterized by a slightly finer grain size, from 0.1 μm to ~2 μm, and lower porosity, ~6% compared with ~13%. Using piezoresponse force microscopy (PFM) and electron backscatter diffraction (EBSD) analysis of oxygen-sintered films, we found that the perovskite grains are composed of multiple domains which are preferentially oriented. Thick films sintered in oxygen exhibit a piezoelectric d33 coefficient of 64 pm/V and an effective thickness coupling coefficient kt of 43%, as well as very low mechanical losses of less than 0.5%, making them promising candidates for lead-free piezoelectric energy harvesting applications.

Interaction between surface acoustic waves and spin waves in a ferromagnetic thin film

We present a theoretical description of magnon–phonon interactions in a multilayer structure containing a ferromagnetic thin film. The formalism is applicable to an arbitrary direction of external magnetic field and various types of acoustic waves including Rayleigh and Love surface modes. A particular attention is paid to the spatial profile of the acoustic wave modes and analytical expressions for the effective coupling coefficients are derived taking into account the degree of mode profile overlap between spin waves and acoustic waves. The results are applied to reproduce a strongly anisotropic and non-reciprocal linewidth of acoustic ferromagnetic resonance reported in a recent experiment.

Structure-Size Optimization and Fabrication of 3.7 GHz Film Bulk Acoustic Resonator Based on AlN Thin Film

Traditional radio frequency filters cannot meet the demands of miniaturization, high frequency operation, integration, and broadband capacity in new-generation communication system owing to their larger volumes. A thin film bulk acoustic resonator (FBAR) is therefore suggested as an optimum solution because of its small volume and a good performance. In this study, the COMSOL multiphysics software was used to build 2 D and 3 D finite element models to analyze the harmonic characteristics of the FBAR. Based on the optimized structural parameters, the FBAR was fabricated with series resonant frequency, parallel resonant frequency, and effective coupling coefficient values of 3.705, and 3.82 GHz, and 7.4%, respectively. Compared with the simulated FBAR results, the effective coupling coefficient of the fabricated FBAR declined by only 0.1%, almost achieving the desired performance.

Three-Dimensional Finite Element Analysis and Characterization of Quasi-Surface Acoustic Wave Resonators.

In this work, three-dimensional finite element analysis (3D FEA) of quasi-surface acoustic wave (QSAW) resonators with high accuracy is reported. The QSAW resonators consist of simple molybdenum (Mo) interdigitated transducers (IDT) on solidly mounted stacked layers of AlN/Mo/Si. Different to the SAW resonators operating in the piezoelectric substrates, the reported resonators are operating in the QSAW mode, since the IDT-excited Rayleigh waves not only propagate in the thin piezoelectric layer of AlN, but also penetrate the Si substrate. Compared with the commonly used two-dimensional (2D) FEA approach, the 3D FEA method reported in this work shows high accuracy, in terms of the resonant frequency, temperature coefficient of frequency (), effective coupling coefficient () and frequency response. The fabricated QSAW resonator has demonstrated a of 0.291%, series resonant frequency of 422.50 MHz, and of −23.418 ppm/°C in the temperature range between 30 °C and 150 °C, for the design of wavelength at 10.4 m. The measurement results agree well with the simulations. Moreover, the QSAW resonators are more mechanically robust than lamb wave devices and can be integrated with silicon-based film bulk acoustic resonator (FBAR) devices to offer multi-frequency function in a single chip.

Impact of applied biaxial stress on the piezoelectric, elastic, and dielectric properties of scandium aluminum nitride alloys determined by density functional perturbation theory

The effects of biaxial in-plane stress on the elastic, dielectric, and piezoelectric (PE) properties of c-axis textured thin film wurtzite phase scandium aluminum nitride (w-ScxAl1−xN) alloys have been calculated with density functional perturbation theory. The in-plane stress σR was kept below 1 GPa covering compressive and tensile values and applied to alloy supercells represented with special quasi-random structures. An increasingly tensile biaxial stress (σR > 0) produces higher displacement-response internal-strain coefficients for the constituent atoms of the alloy and the related PE properties are more sensitive to σR when the fraction x increases. A significant rise of the relative dielectric permittivity ϵr,33η and softening of the stiffness coefficient c33E are also reported with σR > 0. The effective thin film PE strain coefficient d33,f and coupling coefficient k33,f2 show a relative increase of 22% and 26%, respectively, at σR = 1 GPa and x = 0.438. Both tensile σR and x tend to decrease the c/a cell parameter ratio of the wurtzite structure with a significant impact on the PE coefficients. Based on the decomposition of the stiffness, dielectric, and PE coefficients as well as the structural data, it is suggested that tensile biaxial stress enhances the hexagonal character of w-ScxAl1−xN in a qualitatively similar manner as the scandium nitride fraction x does. The manufacture and PE characterization of a beneficially stressed thin film of w-ScxAl1−xN on a substrate of w-InyAl1−yN with adjusted x, y values are suggested to confirm the calculated values of d33,f.

Monolithic DWDM source with precise channel spacing

We report a low-cost manufacturing approach for fabricating monolithic multi-wavelength sources for dense wavelength division multiplexing (DWDM) systems that offers high yield and eliminates crystal regrowth and selective area epitaxy steps that are essential in traditional fabrication methods. The source integrates an array of distributed feedback (DFB) lasers with a passive coupler and semiconductor optical amplifier (SOA). Ridge waveguide lasers with sampled Bragg side wall gratings have been integrated using quantum well intermixing to achieve a fully functional four-channel DWDM source with 0.8 nm wavelength spacing and residual errors < 0.13 nm. The output power from the SOA is > 10 mW per channel making the source suitable for use in passive optical networks (PONs). We have also investigated using multisection phase-shifted sampled gratings to both increase the effective grating coupling coefficient and precisely control the channel lasing wavelength spacing. An 8-channel DFB laser array with 100 GHz channel spacing was demonstrated using a sampled grating with two π-phase-shifted sections in each sampling period. The entire array was fabricated by only a single step of electron beam lithography.

The Effects of a Coated Material Layer on High-Overtone Bulk Acoustic Resonator and its Possible Applications.

This article describes the characterization and analysis of the effects an additional polymer layer has on a high-overtone bulk acoustic wave resonator based on Ba0.5Sr0.5TiO3 (BSTO) thin film by studying its spectral information. From both the simulation (numerical model) and experimental results of the resonator with and without coating, significant difference of both cases is evident in the spacing of the parallel resonance frequencies (SPRFs), effective coupling coefficient ( [Formula: see text]), and quality factor distribution of the resonator. The acoustic velocity of the coated material (SU-8) is calculated from the new periodicity introduced in the SPRF distribution. The SPRF distribution of the SU-8-coated resonator decreases overall as expected due to the additional layer introduced but sharply increases in regions defined by the thickness and acoustic velocity of the SU-8 layer. The mechanical loss of the added layer has significant effect on the parameters of the resonator. The study reveals that this method of characterization can be used to approximate the mechanical loss of materials such as polymers or polymer composites. The simulation with finite-element method agrees with the experimental result.