Spurious Mode Suppression Research Articles

Suppression of Spurious Lateral Modes and Undesired Coupling Modes in Frame-Like FBARs by 2-D Theory.

Thin-film bulk acoustic wave resonators (FBARs) are of significant interest for wireless applications due to their good performance. To achieve excellent characteristics, the frame-like FBARs were previously invented by researchers in this field to suppress the resonances of spurious lateral modes (or spurious modes). Another aspect that has an impact on the working performance of FBAR is the undesired coupling modes, which were rarely studied due to the lack of proper theoretical tools. In this article, we thoroughly investigate the coupling modes and spurious modes in frame-like FBARs by 2-D theory, which was already derived in our previous work. The widely used state-vector approach is applied here and both free and forced vibration problems are analyzed. Frequency spectra and mode shapes obtained from free vibration analysis show the coupling vibration characteristics in this structure. Moreover, the admittance resonance obtained from the forced vibration analysis shows the efficiency of the designed structure on the suppression of both undesired coupling and spurious modes. Results in this article provide a thorough understanding of the vibration in frame-like FBAR, and the method presented can work as an effective tool in engineering design process.

Modeling and Electrode Design Optimizations of Plano-Plano Langasite Crystal Resonator.

The 3-D finite-element model (FEM) of a Y-cut plano-plano langasite crystal thickness shear mode (TSM) resonator is presented, and Mindlin's theory is used to investigate the optimal electrode shapes and sizes for langasite crystal resonator. Circular and elliptical electrodes of various arc lengths are studied to identify the most optimal electrode design configuration in order to achieve TSM vibration free from any anharmonic modes. Simulation results show that resonators with elliptical electrodes have noticeably better suppression of spurious modes compared to that of circular electrodes. Moreover, spurious mode suppression is accomplished for multiple electrode sizes for the same shape, which greatly differs from Mindlin's theory. Hence, three optimized designs are shortlisted and their mass loading sensitivities are investigated. Circular and elliptical electrodes of the same area show similar responses to added mass, indicating that elliptical electrodes have no apparent advantage over circular electrode in mass sensing applications.

Dispersion-Engineered Guided-Wave Resonators in Anisotropic Single-Crystal Substrates - Part I: Concept and Analytical Design.

This paper presents an analytical approach for implementation of high quality-factor (Q) resonators with arbitrary cross-sectional vibration mode-shapes in anisotropic single-crystal substrates. A closed-form dispersion relation is analytically derived to characterize the dynamics of guided waves in rectangular waveguides. Three categories of waves with propagating, standing-evanescent and propagating-evanescent dynamics are identified and used for energy localization of acoustic excitations with arbitrary cross-sectional vibration patterns. An analytical design procedure is presented for dispersion engineering of waveguides to realize high-Q resonators without the need for geometrical suspension through narrow tethers or rigid anchors. The effectiveness of the dispersion engineering methodology is verified through development of experimental test-vehicles in 20㯌m-thick single-crystal silicon substrate with 500nm aluminum nitride transducers. Various proof-of-concept resonators, representing guided waves with different dispersion types, are presented and compared to highlight the optimum design procedures for Q enhancement and spurious mode suppression. Part I of this paper presents the operation principle of guided wave resonators based on analytical derivation of dispersion relation followed by a systematic resonator design procedure. Numerical and experimental characterization for verification of the proposed design procedure and extensive measurement data on proof-of-concept resonators are presented in Part II.

A Leaky-Wave Antenna With Controlled Radiation Using a Bianisotropic Huygens’ Metasurface

In this paper, a novel concept of a leaky-wave antenna is proposed, based on the use of Huygens' metasurfaces. It consists of a parallel-plate waveguide in which the top plate is replaced by a bianisotropic metasurface of the Omega type. It is shown that there is an exact solution to transform the guided mode into a leaky-mode with arbitrary control of the constant leakage factor and the pointing direction. Although the solution turns out to be periodic, only one Floquet mode is excited and radiates, even for electrically long periods. Thanks to the intrinsic spurious Floquet mode suppression, broadside radiation can be achieved without any degradation. Simulations with idealized reactance sheets verify the concept. Moreover, physical structures compatible with PCB fabrication have been proposed and designed, considering aspects such as the effect of losses. Finally, experimental results of two prototypes are presented and discussed.

Transverse Spurious Mode Compensation for AlN Lamb Wave Resonators

Lamb wave modes with type I dispersion characteristics exhibit strong affinity toward multi transverse modes behavior above resonance frequency (f r ) in the AlN Lamb wave resonators (LWRs), especially the high-transduction-efficiency modes: S 0 and S 1 mode. For conventional interdigital transducer (IDT) design, the IDT aperture and IDT gap are the two main factors impacting the transverse mode placements and strengths, according to the wave vector analysis and finite element method (FEM) simulation. Moreover, the convex slowness curve of the Lamb wave modes propagating in AlN platelets allows the waveguiding and weak lateral leakage into busbars by the high-velocity IDT gap region. Apodization, the standard technique to suppress the transverse modes for IDT-excited resonators, suffers from drawbacks, such as additional loss and reduction of the effective coupling coefficient (k eff 2 ). Type I Lamb wave modes in AlN show positive slope in the dispersion branch so that a border region of lower Eigen-resonance frequency is required to form piston mode structure for transverse spurious mode suppression and lateral leakage reduction. Based on dispersion calculations and 2.5D FEM simulations, we demonstrate that by designing the low-velocity border region, such as simply changing the IDT layout, the guiding can be improved and a piston mode can be obtained for the type I Lamb wave modes.

Lithium Niobate Phononic Crystals for Tailoring Performance of RF Laterally Vibrating Devices.

This paper reports the first demonstration of phononic crystals (PnCs) in suspended lithium niobate thin films, which exhibit band gaps for tailoring the performance of laterally vibrating devices. Transmission and reflection properties of lithium niobate PnCs for both shear-horizontal (SH0) and length-extensional (S0) modes have been investigated and subsequently explored in two applications. In the first case, PnC-embedded delay lines were designed for filtering with stopbands, while in the second case, PnC-bounded resonators were implemented for spurious mode suppression. Equivalent circuit models incorporating acoustic scattering parameters of the designed PnCs and Mason's model of the transducers have been built for each application. Benchmarked to reference devices without PnCs, the measured PnCs embedded in delay lines show 20-dB attenuation in the stopbands and less than 2-dB loss in the passbands for the SH0 mode, and 30-dB attenuation in the stopbands and less than 10-dB loss in the passbands for the S0 mode. The fabricated piezoelectric PnC-bounded resonator has shown a quality factor of 434 at 142.7 MHz with undesired spurious modes significantly suppressed. These demonstrations show that lithium niobate PnCs for laterally vibrating devices can potentially lead to wideband and low-loss acoustic functions for radio frequency signal processing.

A Method for the Suppression of Multiple Spurious Modes

This paper reports on a novel electrode design technique for spur suppression in parallel-plate piezoelectric resonators with minimal impact on the intended vibration mode. To demonstrate this technique, fabricated two-port resonators were designed to optimally excite the first harmonic of length extension in a lead zirconate titanate-on-silicon resonator and suppress chosen higher harmonics. The targeted harmonics have been largely suppressed, while the intended mode experienced no change in magnitude. This is the first step towards a general technique for suppression of an arbitrary mode. [2017–0251]

Frame structure for thin-film piezoelectric-on-silicon resonator to greatly enhance quality factor and suppress spurious modes

Thin-film piezoelectric-on-silicon (TPoS) bulk acoustic wave resonator provides an attractive vision of system-on-chip integrated circuits by micro/nano-engineering the timing reference. However, its quality factor (Q) at high frequency is a great challenge due to the mechanical loss. Herein, a novel suspended frame structure on tethers was proposed to significantly enhance the Q and suppress spurious modes of TPoS resonator working in the 30.4 MHz fundamental mode. Compared with the pristine one, the measured Q of fabricated resonator with frame structure showed a maximum 136-fold enhancement. The systematical investigation by both finite-element-analysis (FEA) simulation and experimental comparison revealed that the existing of frame structure effectively decreases the effective coupling coefficient (k2eff) of resonator and further results in the suppression of spurious modes and the enhancement of Q. As the width of frame structure increases, the k2eff maintains a consistent value of 0.15% while the anchor loss significantly reduced, which results in the reduction of insertion loss (IL) and the enhancement of Q.

Balanced bandpass filter with spurious mode suppression

ABSTRACTThis article presents a new and simple design approach for the balanced bandpass filter (BPF) with spurious mode suppression using half‐wavelength resonators. The second harmonic of the resonator, acting as the lowest‐frequency common‐mode (CM) noise, is suppressed by using a new differential feeding scheme. Furthermore, an electrically coupled structure, exhibiting a bandstop response at the third harmonic of the resonator [acting as the lowest‐frequency differential‐mode (DM) spurious], is introduced. As a result, both wideband CM suppression and extended DM upper stopband can be realized simultaneously due to the suppression of the second and third harmonics of the resonator. For demonstration, a second‐order balanced BPF is designed, fabricated, and measured. Good agreement between simulated and measured results can be observed. © 2017 Wiley Periodicals, Inc. Microwave Opt Technol Lett 59:1188–1190, 2017

Design of spurious mode-free elliptical ring resonators

Spurious modes suppression to retain the purity of the main resonance in lateral-extensional contour modes is one of the most important requirements for commercializing vibrating RF MEMS resonators. This issue becomes much more critical for ring-shaped micromechanical resonators that are normally susceptible to both out-of-plane flexural modes and in-plane torsional modes at frequencies adjacent to that of the desired lateral-extensional mode. However, this kind of lateral-extensional mode resonators hold unique ability to achieve GHz frequencies without excessive scaling of its key dimensions, such as inner and outer radius, to facilitate strong electromechanical coupling coefficient by either capacitive or piezoelectric transducers while exhibiting high Q’s on the orders of a few thousands. This paper presents a new type of ring resonators based on a hollow ellipsoid structure operating in the extensional wine-glass mode. Due to the mode shape matching to the resonator body shape, vibration amplitude at this strategically-designed mode becomes much larger than those for other modes. Moreover, a harmonic analysis to verify the basic design principles and further discussions towards design optimization have been presented.

GHz spurious mode free AlN lamb wave resonator with high figure of merit using one dimensional phononic crystal tethers

This letter reports a spurious mode free GHz aluminum nitride (AlN) lamb wave resonator (LWR) towards high figure of merit (FOM). One dimensional gourd-shape phononic crystal (PnC) tether with large phononic bandgaps is employed to reduce the acoustic energy dissipation into the substrate. The periodic PnC tethers are based on a 1 μm-thick AlN layer with 0.26 μm-thick Mo layer on top. A clean spectrum over a wide frequency range is obtained from the measurement, which indicates a wide-band suppression of spurious modes. Experimental results demonstrate that the fabricated AlN LWR has an insertion loss of 5.2 dB and a loaded quality factor (Q) of 1893 at 1.02 GHz measured in air. An impressive ratio of the resistance at parallel resonance (Rp) to the resistance at series resonance (Rs) of 49.8 dB is obtained, which is an indication of high FOM for LWR. The high Rp to Rs ratio is one of the most important parameters to design a radio frequency filter with steep roll-off.

Harnessing Mode Conversion for Spurious Mode Suppression in AlN Laterally Vibrating Resonators

This paper reports on a spurious mode suppression technique for S0 mode aluminum nitride (AlN) laterally vibrating resonators. The technique utilizes a notch in the resonator body to convert spurious asymmetrical (A0) modes into the intended S0 mode vibration. Finite-element analyses were employed to theoretically investigate the mode conversion from A0 mode to S0 mode, and identify the optimal notch configuration. The technique has been experimentally validated to simultaneously eradicate the A0 spurious mode and enhance the S0 mode electromechanical coupling ( $k_{t}^{2}$ ) for the monolithically integrated resonators over a wide frequency range ( $100\sim 600$ MHz). It is a crucial technology development, because the spurious modes are a major bottleneck obstructing the deployment of single-chip multi-frequency AlN resonators as a commercially viable solution for radio frequency front-end filtering. [2015-0295]

Исследование моделей подавления паразитных мод оптоэлектронного СВЧ-автогенератора на основе инжекционной и многоконтурной схем

Исследование моделей подавления паразитных мод оптоэлектронного СВЧ-автогенератора на основе инжекционной и многоконтурной схем

Elimination of Spurious Modes in SH0 Lithium Niobate Laterally Vibrating Resonators

This letter reports on a spurious mode suppression technique for the shear horizontal (SH0) mode lithium niobate laterally vibrating resonators. The concept utilizes triangular and arched edge shapes on the transversal sides of a resonant cavity to effectively distribute and scatter the acoustic waves in the inactive regions, yielding the suppression of transverse spurious modes. 2D models and 3D finite-element analyses were employed to theoretically verify the technique. For devices with the arched-shape edges, complete removal of higher order transverse modes has been experimentally demonstrated with $2\times $ enhancement for quality factor ( $Q$ ). The $Q$ enhancement arises from the improved concentration of mechanical energy under the inter-digitated transducers. The fabricated device exhibits a $Q$ of 920, a large electromechanical coupling ( $k_{t}^{2}$ ) of 17.8%, and a figure of merit of 164.

Transverse Mode Spurious Resonance Suppression in Lamb Wave MEMS Resonators: Theory, Modeling, and Experiment

This paper presents a transverse mode suppression theory and its experimental verification through aluminum nitride Lamb wave resonators (LWRs) operating at 142 MHz. An effective 2-D approximation model of the LWR is proposed, based on which the origin of transverse modes in LWR is investigated. The displacement distribution, resonant frequencies, and electromechanical coupling coefficients $( k_{t}^{2})$ of the main mode and its auxiliary transverse modes are obtained. A spurious mode suppression theory in terms of the expression of $k_{t}^{2}$ in the 2-D model is proposed. Three kinds of electrodes are designed to suppress the transverse mode adjacent to the main mode, including a novel interdigital transducer gap technique that is reported for the first time. With the applicable geometries, these methods reduce the spurious response from 11.8 to <0.5 dB, without significantly affecting the figure of merit of the resonator.

Reduction of Spurious Tones and Phase Noise in Dual-Loop OEO by Loop-Gain Control

Although a long loop delay in an optoelectronic oscillator (OEO) is essential for achieving a low-phase-noise signal, it generates narrowly spaced spurious modes that cannot be filtered out. Conventional dual-loop OEOs proposed to suppress the spurious modes exhibit degraded phase-noise performance compared with single-loop OEOs because of the short fiber loop in dual-loop OEOs. To overcome the decrease in phase-noise performance, we investigated both theoretically and experimentally the open-loop characteristics of the dual-loop OEO. We found that the spurious modes can be eliminated without degradation in the phase-noise performance by properly controlling the open-loop gain of the OEO. Through gain control, we successfully demonstrated the suppression of spurious modes by more than 21 dB.

DC and Imaginary Spurious Modes Suppression for Both Unbounded and Lossy Structures

A generalization of the tree–cotree technique for the removal of imaginary and dc spurious modes in finite-element-based eigenanalysis of 3-D lossy unbounded structures is introduced. Five frequently encountered types of polynomial eigenvalue problems are tackled including: 1) closed structures with finite metals conductivity losses; 2) closed structures with material losses due to migrating charge carriers; 3) open-radiating structures using the absorbing boundary conditions of both first- and second-order; 4) open-radiating structures with finite conductivity metallic objects; and 5) any combination of the aforementioned cases. The resulting polynomial eigenvalue problems are linearized utilizing both the companion and the symmetric approaches. The different linearization techniques are being compared for their efficiency and robustness.

Opportunities for shear energy scaling in bulk acoustic wave resonators.

An important energy loss contribution in bulk acoustic wave resonators is formed by so-called shear waves, which are transversal waves that propagate vertically through the devices with a horizontal motion. In this work, we report for the first time scaling of the shear-confined spots, i.e., spots containing a high concentration of shear wave displacement, controlled by the frame region width at the edge of the resonator. We also demonstrate a novel methodology to arrive at an optimum frame region width for spurious mode suppression and shear wave confinement. This methodology makes use of dispersion curves obtained from finite-element method (FEM) eigenfrequency simulations for arriving at an optimum frame region width. The frame region optimization is demonstrated for solidly mounted resonators employing several shear wave optimized reflector stacks. Finally, the FEM simulation results are compared with measurements for resonators with Ta2O5/ SiO2 stacks showing suppression of the spurious modes.

Resonant Body Transistors in IBM's 32 nm SOI CMOS Technology

This paper presents unreleased CMOS-integrated MEMS resonators fabricated at the transistor level of IBM's 32SOI technology and realized without the need for any post-processing or packaging. In this technology, resonant body transistors (RBTs) are driven capacitively and sensed piezoresistively using an n-channel field effect transistor (FET). Acoustic Bragg Reflectors (ABRs) are used to localize acoustic vibrations in the unreleased resonators completely buried under the CMOS metal stack and surrounded by low- $\kappa$ dielectric. FET sensing is analytically compared with alternative active and passive sensing mechanisms to benchmark CMOS-MEMS resonator performance with frequency scaling. Experimental results from the first generation hybrid CMOS-MEMS RBTs show RBTs operating above 11 GHz with $Q{\rm s}$ of 24–30 and footprints of 5 $\,\times\,$ 3 $\mu{\rm m}$ . Comparative behavior of devices with design variations is used to demonstrate the effect of ABRs on spurious mode suppression. In addition, the performance of the RBTs is compared with passive electrostatic resonators, which show no discernible peak. Finally, temperature stability of ${ due to complimentary materials in the CMOS stack is analytically and experimentally verified. $\hfill{[2012\hbox{-}0309]}$

Apodization technique for spurious mode suppression in AlN contour-mode resonators

This paper reports on the application of apodization techniques to 900MHz–1GHz MEMS AlN Contour-Mode Resonators (CMRs [1–6]) to efficiently suppress spurious modes in close proximity of the main mechanical resonance. This concept has been applied with excellent results to a variety of one port resonators formed by patterned top electrodes made out of aluminum, and a floating bottom electrode made out of platinum sandwiching the AlN film. As also predicted by 3D COMSOL analysis, a complete elimination of the spurious responses (>90% suppression) is attained without significantly impacting the quality factor, Q, and electromechanical coupling coefficient, kt2, of the device. On average, the Q improves except for resonators with thick (220nm) top electrodes for which <11% degradation in Q is recorded. The kt2 reduction is <20% and it has an absolute value>1% for all designs.