Width-extensional Mode Research Articles

An oven controlled piezoelectric MEMS dual-resonator platform with frequency stability of [formula omitted]100 ppb over industrial temperature range

This work demonstrates a piezoelectric MEMS dual-resonator platform with an oven control. The platform includes a micro-oven in-chip, which integrates a frequency output resonator and a temperature sensing resonator. The two resonators operate using a phase-locked loop system, one in width-extensional (WE) mode and the other in width-shear (WS) mode. An equivalent thermal model of the dual-resonator platform is established and both resonators exhibit extremely uniform temperature distributions. The real-time temperature of the resonators is monitored by measuring the frequency difference between the two resonators and a closed-loop oven control is implemented to maintain the dual-resonator platform at an oven-set temperature. The reported oven controlled piezoelectric MEMS dual-resonator platform exhibits a measured frequency stability of ±100 ppb across the industrial temperature range of −40 to 85 °C. This result signifies the promising potential of the device in high-end timing applications.

Aspect ratio optimization of piezoelectric extensional mode resonators for quality factor and phase noise performance enhancement

Abstract This study focuses on optimizing the resonator geometry via the aspect ratio design of a width-extensional mode resonator to improve its quality factor (Q), which is one of the critical performance parameters for resonators in either sensing (Allan deviation) or frequency reference (phase noise) applications. The proposed approach uses finite element analysis to reduce the strain energy at anchor supports by altering the resonator geometric structure, thereby reducing energy loss through anchors. Moreover, process limitations on feature sizes are used as constraints to find aspect ratios that can not only increase the Q but also reduce spurious modes near the targeted frequency. The devices were fabricated using AlN thin film piezoelectric on a substrate (TPoS) process. The simulated energy dissipation trends for specific length-to-width (L/W) ratios closely match the measured changes in the resonator Q values in vacuum. In vacuum, the highest Q-factor achieved by the device is close to 8816, with a motional resistance of a few tens of ohms. Additionally, a board-level oscillator realized using a commercial low-noise amplifier exhibits phase noise performance of −141.21 dBc Hz−1 and −164.25 dBc Hz−1 at 1 kHz and 1 MHz frequency offsets, respectively. The calculated figures of merit for these offsets are 204 and 168, respectively.

A novel narrowband MEMS filter with extensional mode resonators

This work proposes a novel electrostatic mechanically coupled narrowband filter based on width extensional mode (WEM) resonators. Rectangle plate WEM resonators have the potential for high quality factor (Q) and low motional resistance. The rectangle plate was slotted to reduce thermoelastic loss and optimize mode shape coefficient of WEMs. The Q values of coupled WEM resonators exceed 80,000, enabling a narrow bandwidth filter. A 3λ/4-length coupling beam filter (CBF) was demonstrated. The 3λ/4 coupling beam filter has a center frequency of 79.79 MHz and a bandwidth of 0.024 %. The CBF exhibits an impressive 26.39 dB stopband rejection and 6.97 dB insertion loss with 5.13 dB passband ripple. The MEMS filters presented in this work hold significant potential for applications in wireless communication systems.

A mechanically coupled MEMS filter with high-Q width extensional mode resonators

This work presents a novel radio frequency (RF) narrowband Si micro-electro-mechanical systems (MEMS) filter based on capacitively transduced slotted width extensional mode (WEM) resonators. The flexibility of the plate leads to multiple modes near the target frequency. The high Q-factor resonators of around 100 000 enable narrow bandwidth filters with small size and simplified design. The 1-wavelength and 2-wavelength WEMs were first developed as a pair of coupled modes to form a passband. To reduce bandwidth, two plates are coupled with a λ-length coupling beam. The 79.69 MHz coupled plate filter (CPF) achieved a narrow bandwidth of 8.8 kHz, corresponding to a tiny 0.011%. The CPF exhibits an impressive 34.84 dB stopband rejection and 7.82 dB insertion loss with near-zero passband ripple. In summary, the RF MEMS filter presented in this work shows promising potential for application in RF transceiver front-ends.

A Q-factor Boost Strategy for High-Order Width-Extensional Mode MEMS Resonators by Varied Unit Length

A Q-factor Boost Strategy for High-Order Width-Extensional Mode MEMS Resonators by Varied Unit Length

A Micro-Oven Controlled Dual-Mode Piezoelectric MEMS Resonator With ± 190 ppb Stability Over −40 to 105 °C Temperature Range

This letter presents a dual-mode piezoelectric microelectromechanical system (MEMS) resonator with an in-chip micro-oven for resonator temperature control. The piezoelectric MEMS resonator simultaneously operates in width-extensional (WE) mode with a high temperature turnover point, and torsion-bending (TB) mode with a large temperature coefficient of frequency (TCF) based on a phase-locked loop based system. Exploiting the difference in frequency-temperature characteristics of these two modes, accurate temperature sensing and precise close-loop micro-oven heating control are achieved by phase locking the resonator at its turnover point temperature of WE mode. Measured real-time frequency stability of the reported micro-oven controlled MEMS resonator is ±190 ppb over an extended industrial temperature range of -40 °C to 105 °C, indicating potential applications in high-end timing field, such as macro base stations and instrumentations.

A GHz Silicon-Based Width Extensional Mode MEMS Resonator with Q over 10,000.

This work presents a silicon-based capacitively transduced width extensional mode (WEM) MEMS rectangular plate resonator with quality factor (Q) of over 10,000 at a frequency of greater than 1 GHz. The Q value, determined by various loss mechanisms, was analyzed and quantified via numerical calculation and simulation. The energy loss of high order WEMs is dominated by anchor loss and phonon-phonon interaction dissipation (PPID). High-order resonators possess high effective stiffness, resulting in large motional impedance. To suppress anchor loss and reduce motional impedance, a novel combined tether was designed and comprehensively optimized. The resonators were batch fabricated based on a reliable and simple silicon-on-insulator (SOI)-based fabrication process. The combined tether experimentally contributes to low anchor loss and motional impedance. Especially in the 4th WEM, the resonator with a resonance frequency of 1.1 GHz and a Q of 10,920 was demonstrated, corresponding to the promising f × Q product of 1.2 × 1013. By using combined tether, the motional impedance decreases by 33% and 20% in 3rd and 4th modes, respectively. The WEM resonator proposed in this work has potential application for high-frequency wireless communication systems.

Influence of a Tailored Oxide Interface on the Quality Factor of Microelectromechanical Resonators

AbstractPiezoelectric microelectromechanical systems (MEMS) are used as sensors, actuators, energy harvesters, accelerometers, and communication modules. Aluminum nitride (AlN) is an especially attractive piezoelectric material because its fabrication process allows it to be integrated into semiconductor circuitry to deliver a fully integrated solution. Microelectromechanical resonators with AlN sandwiched between n‐type silicon (Si) and top metal electrode with and without a silicon oxide layer are designed and fabricated. The effect of the oxide film is up to a fourfold increase in quality factor (Q) that is consistent from very high frequency (VHF) to super high frequency (SHF). This effect is demonstrated using thin plate bulk acoustic wave modes from 70–80 MHz using the second contour mode and first width extensional mode and from 9.5–10.5 GHz using high overtone thickness modes. To explore potential applications of AlN‐transduced Q‐enhanced MEMS devices in harsh environments, measurements from −200 °C to +200 °C are performed. The Q enhancement is persistent across a wide temperature range for both VHF and SHF resonators with the added oxide layer. Furthermore, AlN‐on‐Si resonators that have a comparable temperature coefficient of frequency to silicon carbide‐based resonators in commercial applications are demonstrated.

A Micro-Oven-Controlled Dual-Mode Piezoelectric MEMS Resonator With ±400 PPB Stability Over −40 to 80 °C Temperature Range

In this article, the design, implementation, and characterization of a micro-oven-controlled dual-mode piezoelectric microelectromechanical system (MEMS) resonator are presented. The designed MEMS resonator simultaneously operates in the width extensional (WE) mode and length shear (LS) mode. Both modes show high quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> ). The measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> is 15672 for the WE mode and 17781 for the LS mode. Taking advantage of the significant difference in frequency–temperature characteristics between the two modes, accurate temperature sensing and precisely closed-loop micro-oven control are implemented by phase locking the MEMS resonator at an oven-set temperature. In-plane micro-oven is composed of four folded beams and an isolation frame, which maintains an extremely uniform temperature distribution on the resonating element. The micro-oven structure requires less than 7.8 mW to maintain the resonator’s temperature at the preset temperature over variations in the external temperature range of −40 °C to 80 °C. Measured real-time frequency stability of the reported micro-oven-controlled MEMS resonator is less than ±400 ppb over a wide temperature range from −40 °C to 80 °C.

Excitation of high-frequency in-plane bulk acoustic resonance modes in geometrically engineered hafnium zirconium oxide nano-electro-mechanical membrane

A nano-electro-mechanical membrane created from atomic-layered ferroelectric hafnium zirconium oxide (Hf0.5Zr0.5O2), titanium nitride (TiN), and silicon dioxide is engineered to localize high quality factor (Q) in-plane bulk acoustic resonance modes over 80–840 MHz. The in-plane geometry of the membrane, with an overall thickness of 50 nm and an aspect ratio exceeding 104:1, is optimized to simultaneously preserve the stress profile needed for sustaining ferroelectric polarization and enable propagation and constructive interaction of extensional and shear waves to create bulk acoustic modes. A ferroelectric polarization of 11.2 μC/cm2 is measured at the transduction ports, which is consistent after nano-membrane release. The first, third, and seventh order width extensional modes (WE1,3,7) and the third order of the width shear mode (WS3) are electrically measured at 109, 389, 766, and 267 MHz, respectively, showing Qs over 50–100 that are dominated by the large electrical resistance of TiN electrodes. High mechanical Qs of 538, 407, 781, and 594 are extracted for the WE1,3,7 and WS3 modes, respectively, after de-embedding the TiN electrode impedance, resulting in large resonance frequency (f0) × Q products as high as 6 × 1011. The measured characteristics, along with numerical simulations, are used to extract a Young's modulus of ∼340 GPa for the 10 nm-thick Hf0.5Zr0.5O2 film, which is in close agreement with the reported ab initio estimations.

Growth of C-Axis Textured AlN Films on Vertical Sidewalls of Silicon Microfins

A fabrication process is developed to grow c -axis textured aluminum nitride (AlN) films on the sidewall of single-crystal silicon (Si) microfins to realize fin bulk acoustic wave resonators (FinBARs). FinBARs enable ultradense integration of high-quality-factor ( Q ) resonators and low-loss filters on a small chip footprint and provide extreme lithographical frequency scalability over ultra- and super-high-frequency regimes. Si microfins with large aspect ratio are patterned and their sidewall surfaces are atomically smoothened. The reactive magnetron sputtering AlN deposition is engineered to optimize the hexagonal crystallinity of the sidewall AlN film with c -axis perpendicular to the sidewall of Si microfins. The effect of bottom metal electrode and surface roughness on the texture and crystallinity of the sidewall AlN film is explored. The atomic-layer-deposited platinum film with (111) crystallinity is identified as a suitable bottom electrode for deposition of c -axis textured AlN on the sidewall with c -axis orientation of 88.5° ± 1.5° and arc-angle of ~12° around (002) diffraction spot over film thickness. A 4.2-GHz FinBAR prototype is implemented showing a Q of 1574 and effective electromechanical coupling ( [Formula: see text]) of 2.75%, when operating in the 3rd width-extensional resonance mode. The lower measured Q and [Formula: see text] compared to simulations highlights the effect of granular texture of sidewall AlN film on limiting the performance of FinBARs. The developed c -axis textured sidewall AlN film technology paves the way for realization and monolithic integration of multifrequency and multiband FinBAR spectral processors for the emerging carrier aggregated wireless communication systems.

Derivation of losses from impedance spectrum for contour modes of ceramic resonator

ABSTRACT Method of loss coefficients calculation from mechanical quality factors of transversal vibration modes is presented. Theoretical formulae are derived for the contour mode of thin square plate and width extensional mode of a thin rectangular plate. Mechanical quality factors are expressed as a function of loss coefficients for ceramic with known Poisson’s ratio. Measured impedance spectra are compared with calculations and used for the characterization of losses on lead-free BCZT and lead-based PZT piezoelectric ceramics. Full set of loss coefficients active for planar vibration modes is characterized on a single sample. Mechanical quality factor at resonance is the same for the contour extensional mode of a thin square plate and for the width extensional mode of a thin rectangular plate. Loss coefficients reach the biggest values for the piezoelectric losses, followed by the dielectric and elastic losses. Our results show that the BCZT ceramics have losses of the same magnitude as soft PZT ceramic.

Microresonator-on-Membrane for Real-Time Mass Sensing in Liquid Phase

Microresonator-on-membrane (MRoM) is presented in this article as a new approach to address the performance deterioration of microscale resonators in contact with a liquid media. An MRoM is composed of a rectangular piezoelectric-on-substrate resonator formed on top of an isolating membrane, which can operate in its length and width extensional (LE and WE) resonance modes. In the proposed scheme, the solution under a test is added into a microcavity on the back side of the MRoM chip. In this manner, the contact surface of the resonator to liquid is minimized to reduce mechanical losses caused by viscous damping, leading to a higher resonator quality factor ( Q ). Simultaneously, isolation caused by the membrane eliminates electrical interference of ionic solutions on a resonator performance. Despite enabling such advantages, the membrane underneath the resonator causes further anchoring losses, which reduces the Q s of MRoMs operating in air. To minimize such losses, in-plane primary and secondary circular acoustic reflectors are located around the resonator leading to higher Q s. Consequently, the MRoMs with secondary reflectors exhibit the Q s as high as 3500 for operation at both LE and WE resonance modes of 39 and 83MHz, respectively, when operating in air, showing adequate suppression of anchoring loss caused by the presence of the membrane. Also, maximum liquid phase Q s up to 410 are achieved for the MRoMs, which operate in the WE mode. As mass sensors, the MRoMs demonstrate mass sensitivity of 12 Hz.cm2ng while operating at the same mode.

A piezoelectric-on-silicon width-extensional mode Lorentz force resonant MEMS magnetometer

In this paper, we present a unique micromachined magnetometer based on a width-extensional (WE) mode thin-film piezoelectric-on-silicon (TPoS) resonator for detection of magnetic fields applied normal to the plane of fabrication. The reported device targets operation in ambient pressure rather than vacuum, which should simplify packaging requirements. To compensate for a lower quality (Q) factor when operating in ambient pressure, the strong electromechanical coupling provided by the piezoelectric Aluminium Nitride (AlN) transducer has the advantage of greatly enhancing the sensitivity performance of the device. The reported device is based on a rectangular plate that is driven into the WE resonance mode by an in-plane Lorentz force pair that results from an external out-of-plane magnetic field. Two design generations of the proposed device topology are presented herein, with the latter design generation showing a substantial improvement over the former. The resonant frequency of the most recent design generation is 18MHz, and its associated Q-factor was 1500 under ambient conditions. We have experimentally calibrated the sensitivity of the device, which was found to be 63.27mV/T under ambient conditions. The measured result agrees well with both our analytical and finite element model.

Erratum to: MEMS filter’s design and modeling based on width-extensional mode plate resonator for wireless applications

Erratum to: MEMS filter’s design and modeling based on width-extensional mode plate resonator for wireless applications

Single-resonator dual-frequency AIN-on-Si MEMS oscillators.

This paper reports on the design, implementation, and phase-noise optimization of low-power interface IC for dual-frequency oscillators that utilize two high quality factor (Q) width-extensional bulk acoustic modes of the same AlN-on-silicon resonator. Two 0.5-μm CMOS transimpedance amplifiers (TIA) have been designed, characterized, and interfaced with two dual-mode resonators operating at 35.5/105.7 MHz (first/third order modes) and 35.5/174.9 MHz (first/ fifth order modes). One TIA uses open-loop regulated cascode (RGC) topology in the first stage to enable low power operation, whereas the second one uses an inverter with shunt-shunt feedback to deliver higher gain with lower phase noise. An on-chip switching network is incorporated into each TIA to change the oscillation frequency based on the different phase shift. The effect of TIA on the phase-noise performance of oscillators is studied and compared for both topologies. The measured phase noise of low- and high-frequency modes at 1 kHz offset from carrier are -114 and -108 dBc/Hz for the 35/105 MHz oscillator, and -108 and -105 dBc/Hz for the 35/175 MHz oscillator, respectively, whereas the far-from-carrier reaches below -140 dBc/Hz in all cases.

A 76.8 MHz temperature compensated MEMS reference oscillator for wireless handsets

This paper reports on the design of a low phase noise 76.8MHz AlN-on-silicon reference oscillator using SiO2 as temperature compensation material. The paper presents profound theoretical optimization of all the important parameters for AlN-on-silicon width extensional mode resonators, filling into the knowledge gap targeting the tens of megahertz frequency range for this type of resonators. Low loading CMOS cross coupled series resonance oscillator is used to reach the-state-of-the-art LTE phase noise specifications. Phase noise of −123dBc/Hz at 1kHz, and −162dBc/Hz at 1MHz offset is achieved. The oscillator׳s integrated root mean square RMS jitter is 106fs (10kHz to 20MHz), consuming 850μA, with startup time of 250μs, and a figure-of-merit FOM of 216dB. This work offers a platform for high performance MEMS reference oscillators; where, it shows the applicability of replacing bulky quartz with MEMS resonators in cellular platforms.

MEMS filter’s design and modeling based on width-extensional mode plate resonator for wireless applications

This paper proposes a new filter's design process and modeling that can be employed in RF wireless communication systems. The filter is constructed by two similar rectangular piezoelectric plates vibrating in the width-extensional mode. Each plate is formed by a piezoelectric film and is sandwiched between two metallic electrodes. The vibrating plates are mechanically coupled by a beam linkage. The resonance frequencies of the vibrating structure are defined by the plate's lateral dimension which allows the integration of the multi-frequency filter banks on the same chip. The coupled resonators exhibit two mechanical resonance modes: in-phase and out-of-phase vibrating modes. These modes define the filter bandwidth. In the first part of this paper, we proposed a theoretical model allowing to define the desired filter bandwidth varying the coupling beams location. In the second part, we used the microwave circuit theory to calculate the generalized ABCD matrix and consequently the filter transmitted coefficient (S21). The filter bandwidth values extracted from the transmitted coefficient (S21) show a consistent agreement with the desired filter bandwidths determined by the theoretical model developed in the first part. As application, a filter with a center frequency of 217 MHz is able to operate with fractional bandwidth varying from very low value (close to 0 %) to 5.5 %. This modeling approach is very important for filter bandwidth control.

Dual-Mode AlN-on-Silicon Micromechanical Resonators for Temperature Sensing

In this paper, we present dual-mode (DM) AlN-on-silicon micromechanical resonators for self-temperature sensing. In-plane width-shear (WS) and width-extensional (WE) modes of [110]-oriented silicon resonators have been used as alternatives to first- and third-order modes to enhance DM temperature sensitivity by engineering device geometry, which reduces inherent beat frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> between the two modes. This configuration provides a 50× improvement in temperature coefficient of beat frequency (TCf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ) compared with single-mode temperature measurement and eliminates the need for additional frequency multipliers to generate f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> from its constituents. [100]-oriented WS/WE resonators provide 4× larger TCF difference between modes (ΔTCF) than first and third width-extensional resonators, which further contributes to TCf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> enhancement. WS/WE mode resonators also demonstrate the capability of operating as a temperature-stable reference f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> . The proposed modes for DM operation have high Q and low motional resistance, and are 180 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> out-of-phase when operated in two-port configuration, thus enabling mode-selective low-power oscillator interfacing for resonant temperature sensing.

PZT transduction of high-overtone contour- mode resonators

This paper presents the Butterworth-van Dyke model and quantitative comparison that explore the design space of lead zirconate titanate-only (PZT) and PZT on 3-, 5-, and 10-μm single-crystal silicon (SCS) high-overtone width-extensional mode (WEM) resonators with identical lateral dimensions for incorporation into radio frequency microelectromechanical systems (RF MEMS) filters and oscillators. A novel fabrication technique was developed to fabricate the resonators with and without a silicon carrier layer using the same mask set on the same wafer. The air-bridge metal routings were implemented to carry electrical signals while avoiding large capacitances from the bond-pads. We theoretically derived and experimentally measured the correlation of motional impedance (RX), quality factor (Q), and resonance frequency (f) with the resonators' silicon layer thickness (tSi) up to frequencies of operation above 1 GHz.