Contour-mode Resonators Research Articles

A novel high-Q contour mode resonator

This work presents a novel silicon-based capacitive Edge-Radial Contour Mode (ERCM) resonator. Various loss mechanisms of the resonators are investigated via numerical calculations and simulations, the energy loss of the ERCM resonator is mainly dominated by thermoelastic and anchor loss. To suppress thermoelastic loss and anchor loss while maintaining a larger anchor radius, a supporting structure based on a four-ring release hole array was designed, which has significantly reduced anchor loss and motional impedance. By incorporating a four-ring spoke array within the circular disk, the resonator demonstrated more than 4 times enhancement in quality factor (Q) and an 81% reduction in motional impedance. The Q factor reaches 91,000 at frequency of 23.7MHz. Besides, the nonlinear behaviors of the resonator were studied. The nonlinear coefficients of the two resonators were modulated by optimizing the doping types to be 1.93×1010m-2 and -5.62×109m-2, respectively. These studies provide a deep understanding of the nonlinear behaviors of ERCM resonators and their potential application in tunable narrow-bandwidth filters and high-sensitive sensors.

Nonlinear response of very high frequency contour mode resonators

We explore the source of nonlinearities in Aluminum Nitride (AlN) Contour Mode Resonators (CMRs) operating in the Very High Frequency (VHF) range. We demonstrate that the red-shift of the resonance frequency found in VHF CMRs when the input RF power increases is due to nonlinear stiffness appearing from self-heating, and variable damping due to geometric nonlinearities. Moreover, we find a linear relationship between the variable damping coefficient and the resonator quality factor (Q). Such nonlinear mechanisms are modeled using a spring-mass-damper physical system and, in the electrical domain, a modified Butterworth-Van Dyke (MBVD) circuit where the nonlinear stiffness and variable damping are captured by a charge-dependent motional capacitor and a charge-dependent motional resistor, respectively. Detailed guidelines are provided to accurately analyze nonlinear CMRs using full-wave numerical simulations based on a finite-element method. Such simulations allow us to isolate the influence of each independent nonlinear mechanism and establish a relation between variable damping and geometric nonlinearities. Circuit and full-wave numerical simulations are in good agreement with measured data from fabricated 225 MHz CMRs exhibiting different Q. Finally, we exploit nonlinearities in high-Q CMRs to generate frequency combs at the MHz range opening the door to new exciting applications in telecommunication and sensing.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Extending the Linearity of AlScN Contour-Mode Resonators Through Acoustic Metamaterials-Based Reflectors.

This work describes the implementation of acoustic metamaterials (AMs) made of a forest of rods at the sides of a suspended aluminum scandium nitride (AlScN) contour-mode resonator (CMR) to increase its power handling without causing degradations of its electromechanical performance. The increase in usable anchoring perimeter with respect to conventional CMR designs, enabled by the adoption of two AM-based lateral anchors, permits to achieve improved heat conduction from the resonator's active region to the substrate. Furthermore, thanks to such AM-based lateral anchors' unique acoustic dispersion features, the attained increase of anchored perimeter does not cause any degradations of the CMR's electromechanical performance, even leading to a ~15% improvement in the measured quality factor. Finally, we experimentally show that using our AM-based lateral anchors leads to a more linear CMR's electrical response, which is enabled by a 32% reduction of its Duffing nonlinear coefficient with respect to the corresponding value attained by a conventional CMR design that uses fully etched lateral sides.

Al0.78Sc0.22N Lamb Wave Contour Mode Resonators.

This article presents the lamb wave contour mode resonators (CMRs) based on 22% aluminum scandium nitride (AlScN) thin film with λ of 12-24 [Formula: see text], and operating in [Formula: see text] mode. We report the design, fabrication, and characterization of 500 nm-thick AlScN CMRs, which take advantage of optimized stress control of co-sputtered AlScN thin films and vertical inductively coupled plasma (ICP) etching profile. The experimental results are compared to theoretical predictions by finite element analysis (FEA). All Al 0.78 Sc [Formula: see text] devices show excellent agreement with simulations in piezoelectric coupling using modified AlScN film parameters. The best Al 0.78 Sc [Formula: see text] CMR has achieved an electromechanical coupling coefficient ( kt2) of 5.24% and loaded quality factor ( Q ) of 1219 with an operating frequency at approximately 300 MHz, which exhibits a high Figure-of-Merit (FoM) of 63.88 in piezoelectric microelectromechanical system (MEMS) lamb wave CMR. This article also presents the co-sputtering characteristics of the AlScN thin films under [Formula: see text] gas to achieve low-stress and high-quality piezoelectric materials, and the etching optimization of high concentration Sc doping aluminum nitride (AlN) thin films under Cl2/BCl3/Ar chemistry to obtain record profile angle of 77°, high selectivity of 1:1 with SiO2 hard mask.

CMOS-Integrated Aluminum Nitride MEMS: A Review

Aluminum nitride (AlN) has gained wide interest owing to its high values of elastic modulus, band gap, dielectric strength, resistivity, thermal conductivity and acoustic velocities, especially because it retains most of its properties and versatility in the thin-film form. This review focuses on applications where the CMOS integration of AlN MEMS has been effectively demonstrated. First, the fundamental concepts of piezoelectricity on polycrystalline <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$c$ </tex-math></inline-formula> -axis oriented thin-films are introduced and AlN is compared to other common piezoelectric materials, namely LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , LiTaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , quartz, lead zirconate titanate (PZT), ZnO and GaN by thoroughly discussing the material properties, processing and technological implications. After presenting the possible MEMS-CMOS integration strategies, recent demonstrations of AlN-based devices are reviewed, namely energy harvesters, film bulk acoustic resonators (FBAR), contour mode resonators (CMR), gas sensors, imagers, microphones, transducers for chip-scale communication and calorimetric sensors. Finally, other recent applications/integration opportunities are outlined for AlN-based micro-mirrors, flexible sensors and transducers for liquid media and harsh environments. [2022-0006]

Fully differential higher order transverse mode piezoelectric membrane resonators for enhanced liquid-phase quality factors

This paper investigates the characteristics of higher-order transverse mode fully clamped membrane resonators that are piezoelectrically transduced as a class of resonators that completely seal the domain above the resonator from the domain below. Such isolation between the top and bottom of a resonator is preferable when encasing the device in a microfluidic cell for liquid-phase sensing measurements, a setup that can be beneficial for sensing applications. Most fully clamped membrane resonators are hampered by low liquid-phase quality factor (Q) and large motional resistance (R m). This paper describes the design of higher-order transverse (2, 2) mode square membrane and (2, 0) mode circular membrane resonators, and the effect of device scaling on liquid-phase Q and R m. We show a best-case liquid-phase R m of 54 kΩ and Q of 270 among the various membrane sizes tested. This level of liquid-phase Q is higher than some contour mode resonators. Compared to other fully clamped membrane resonators in the literature, the results here represent a significant improvement in both R m and Q, highlighting the potential of these membrane resonators for liquid-phase mass sensing applications.

Curvature and Stress Effects on the Performance of Contour-Mode Resonant ΔE Effect Magnetometers.

Miniaturized piezoelectric/magnetostrictive contour-mode resonators have been shown to be effective magnetometers by exploiting the ΔE effect. With dimensions of ~100-200 μm across and <1 μm thick, they offer high spatial resolution, portability, low power consumption, and low cost. However, a thorough understanding of the magnetic material behavior in these devices has been lacking, hindering performance optimization. This manuscript reports on the strong, nonlinear correlation observed between the frequency response of these sensors and the stress-induced curvature of the resonator plate. The resonance frequency shift caused by DC magnetic fields drops off rapidly with increasing curvature: about two orders of magnitude separate the highest and lowest frequency shift in otherwise identical devices. Similarly, an inverse correlation with the quality factor was found, suggesting a magnetic loss mechanism. The mechanical and magnetic properties are theoretically analyzed using magnetoelastic finite-element and magnetic domain-phase models. The resulting model fits the measurements well and is generally consistent with additional results from magneto-optical domain imaging. Thus, the origin of the observed behavior is identified and broader implications for the design of nano-magnetoelastic devices are derived. By fabricating a magnetoelectric nano-plate resonator with low curvature, a record-high DC magnetic field sensitivity of 5 Hz/nT is achieved.

Characterization of AlN and AlScN film ICP etching for micro/nano fabrication

We investigate the inductively coupled plasma (ICP) etching characteristics of (0002) Aluminum Nitride (AlN) and Aluminum Scandium Nitride (Al0.94Sc0.06N) piezoelectric thin films as well as the implementation on piezoelectric lamb wave resonators. A profile of 84° is obtained on AlN thin film, with an etching rate of approximately 230 nm/min, and a selectivity of 0.77:1 relative to photoresist mask. A nearly 80° profile and over 30:1 selectivity are accomplished using Ni film as the etching mask. Al0.94Sc0.06N film has achieved a profile of 77° by optimizing the RF power. Finally, AlN contour mode resonators (CMRs) are fabricated and characterized, and a CMR operating at about 400 MHz with a quality factor exceeding 1600 has been demonstrated.

Liquid-Loaded Piezo-Silicon Micro-Disc Oscillators for Pico-Scale Bio-Mass Sensing

In this work, we report on the implementation of a closed-loop liquid-loaded resonant mass sensor as a test vehicle for the realization of highly sensitive miniaturized biomarker assays. Using thin-film piezoelectric-on-silicon (TPoS) contour-mode disc resonators that are specifically designed and optimized for liquid-phase operation, a liquid-loaded low power (~1.6 mW) oscillator at ~17 MHz is demonstrated with a single transistor. By proper placement of the electrodes and the supporting tethers, a high liquid-loaded quality factor (~380) and a low insertion loss (~19 dB) are concurrently achieved which enable the accurate frequency tracking of the potential mass microbalance. The frequency shifts due to the liquid-loading and the preliminary characterized frequency stability of the oscillator imply a minimum mass detection resolution in the picograms range. [2020-0177]

Evidence of Smaller 1/F Noise in AlScN-Based Oscillators Compared to AlN-Based Oscillators

In this paper we investigate the direct effect of resonator quality factor (Q) on the oscillator phase noise. We use 2-port contour mode resonators (CMRs), fabricated both with aluminum nitride (AlN) and aluminum scandium nitride (AlScN), as the frequency-determining element in the oscillator circuit. Over 70 oscillator configurations are tested using resonators with different Q and with different piezoelectric layer. The testing of so many devices is possible because, in our setup, interfacing the circuit to the resonator is streamlined using RF probes. Our results show that higher resonator Q yields better frequency stability of the oscillator, for both AlN and AlScN CMRs. Interestingly, the comparison between AlN-based oscillators and AlScN-based oscillators with equal Q shows that AlScN-based oscillators' Phase Noise is up 10 dBc/Hz better than the AlN oscillator at 1 kHz offset frequency, suggesting different intrinsic resonator flicker noise of the two piezoelectric layers.

Development of Piezoelectric One Port Contour-Mode Microelectromechanical System Resonator for Biomedical Mass/Pressure Sensing Application

This paper presents zinc oxide one port contour-mode machined resonator operated under global system for mobile communication range of frequency. TheS11 value of –38.57 dB at resonance frequency of 882 MHz in average was observed. The phase shift of the device and voltage standing wave ratio were noted as 115° and 1.18 respectively, sufficiently adopted for radio frequency communication. The device has been optimized for 21 aluminum interdigited fingers patterned over zinc oxide thin film. Two electron beam and two optical lithography were processed for fabricating the devices. Our findings are expected to provide effective approach for realizing efficient biocompatible detector for biomedical mass/pressure sensing application.

A Study on the Effects of Bottom Electrode Designs on Aluminum Nitride Contour-Mode Resonators.

This study presents the effects of bottom electrode designs on the operation of laterally vibrating aluminum nitride (AlN) contour-mode resonators (CMRs). A total of 160 CMRs were analyzed with varying bottom electrode areas at two resonant frequencies (f0) of about 230 MHz and 1.1 GHz. Specifically, we analyzed the impact of bottom electrode coverage rates on the resonator quality factor (Q) and electromechanical coupling (k2), which are important parameters for Radio Frequency (RF) and sensing applications. From our experiments, Q exhibited different trends to electrode coverage rates depending on the device resonant frequencies, while k2 increased with the coverage rate regardless of f0. Along with experimental measurements, our finite element analysis (FEA) revealed that the bottom electrode coverage rate determines the active (or vibrating) region of the resonator and, thus, directly impacts Q. Additionally, to alleviate thermoelastic damping (TED) and focus on mechanical damping effects, we analyzed the device performance at 10 K. Our findings indicated that a careful design of bottom electrodes could further improve both Q and k2 of AlN CMRs, which ultimately determines the power budget and noise level of the resonator in integrated oscillators and sensor systems.

Dynamic Q-enhancement in aluminum nitride contour-mode resonators

In this letter, we discuss a dynamic quality factor (Q)-enhancement technique for aluminum nitride (AlN) contour-mode resonators. This technique is implemented by applying an external voltage source that has a specific frequency-dependent phase relationship with respect to the driving voltage source. In this way, the effective spring, damping, and mass of the resonator become dependent on the frequency. With proper gain and phase delay between external and driving signals at resonance, 3-dB Q of the resonator's spectral admittance can be dramatically boosted beyond the fundamental limit of the AlN f-Q product. Meanwhile, the effective electromechanical coupling, kt2, is also improved regardless of the material piezoelectricity limit. These two enhancements correspond to the reduction of the effective damping and spring, respectively. Unlike other active Q-enhancement methods, which use complex electrical circuits to convert resonator displacement/output current into a feedback signal, in this approach, the external and driving signals are generated from the same source and split via a power splitter without resorting to any closed loop operation. The external signal is amplified and shifted by an amplifier and a delay line, respectively. Thus, the demonstrated dynamic Q-enhancement method is relatively simple to implement and intrinsically immune to self-oscillations.

Engineered acoustic mismatch for anchor loss control in contour mode resonators

Improving the quality factor (Q) of electromechanical resonators is of paramount importance for different applications, ranging from RF filtering to sensing. In this paper, we present a modified fabrication process flow for contour mode resonators to simultaneously obtain the (i) Q insensitive to the Si undercut geometry and (ii) in-phase reflectors for anchor loss control and Q optimization. To assess the potential of the reflector, we vary its distance from the resonator's anchor. This results in a periodic trend of Q when the distance between the anchor and the reflector changes. Further confirmation of the trend is obtained via a finite element (FE) model. Interestingly, when in the FE model, the step between consecutive reflectors is decreased by a factor of 6× with respect to the experimental step, we observe a fast modulation of Q, superimposed onto that seen experimentally. The origin of this fast modulation is likely the coexistence of waves with different wavelengths traveling through the released region. Our results show that the profile of the region undergoing Si undercutting (released area) can be easily set by design. Furthermore, engineering the introduced acoustic mismatch provides unprecedented control of anchor loss.

Al0.83Sc0.17N Contour-Mode Resonators With Electromechanical Coupling in Excess of 4.5.

In this paper, we demonstrate the fabrication of contour-mode resonators (CMRs) with Al0.83Sc0.17N as a piezoelectric layer. Moreover, we assess the electromechanical coupling and the maximum achieved quality factor from 150 to 500 MHz. In comparison to pure aluminum nitride (AlN) CMRs, our results show electromechanical coupling coefficients of more than a 2× factor higher at around 200 MHz. The highest quality factor is measured on a CMR operating at 388 MHz and is in excess of 1600. From the characterization of devices operating at different frequencies, material parameters of the Al0.83Sc0.17N are extracted such as the stiffness constant, the relative permittivity, and the piezoelectric constant. In particular, the reported d31 piezoelectric constant is equal to -3.9 pm/V. This represents a 2.25× improvement when compared to pure AlN. Finally, we report the first temperature compensation experimental results for Al0.83Sc0.17N CMRs. Our results show that about 1.5 [Formula: see text] of sputtered oxide, deposited on top of a released resonator, allows near zero temperature coefficient of frequency variation for CMRs operating up to 500 MHz.

An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements.

The importance of micro-electromechanical systems (MEMS) for radio-frequency (RF) applications is rapidly growing. In RF mobile-communication systems, MEMS-based circuits enable a compact implementation, low power consumption and high RF performance, e.g., bulk-acoustic wave filters with low insertion loss and low noise or fast and reliable MEMS switches. However, the cross-hierarchical modelling of micro-electronic and micro-electromechanical constituents together in one multi-physical design process is still not as established as the design of integrated micro-electronic circuits, such as operational amplifiers. To close the gap between micro-electronics and micro-electromechanics, this paper presents an analytical approach towards the linear top-down design of MEMS resonators, based on their electrical specification, by the solution of the mechanical wave equation. In view of the central importance of thermal effects for the performance and stability of MEMS-based RF circuits, the temperature dependence was included in the model; the aim was to study the variations of the RF parameters of the resonators and to enable a temperature dependent MEMS oscillator simulation. The variations of the resonator parameters with respect to the ambient temperature were then verified by RF measurements in a vacuum chamber at temperatures between −35 C and 85 C. The systematic body of data revealed temperature coefficients of the resonant frequency between −26 ppm/K and −20 ppm/K, which are in good agreement with other data from the literature. Based on the MEMS resonator model derived, a MEMS oscillator was designed, simulated, and measured in a vacuum chamber yielding a measured temperature coefficient of the oscillation frequency of −26.3 ppm/K. The difference of the temperature coefficients of frequency of oscillator and resonator turned out to be mainly influenced by the limited Q-factor of the MEMS device. In both studies, the analytical model and the measurement showed very good agreement in terms of temperature dependence and the prediction of fabrication results of the resonators designed. This analytical modelling approach serves therefore as an important step towards the design and simulation of micro-electronics and micro-electromechanics in one uniform design process. Furthermore, temperature dependences of MEMS oscillators can now be studied by simulations instead of time-consuming and complex measurements.

Hybrid Bandpass-Absorptive-Bandstop Magnetically Coupled Acoustic-Wave-Lumped-Element-Resonator Filters

This letter presents a novel advancement in acoustic-wave-lumped-element-resonator (AWLR) filters, which improves transmission zero isolation by over 40 dB without adding any additional components. By spacing and orienting the AWLR-lumped inductors for intentional magnetic coupling, a hybrid bandpass-absorptive-bandstop filter is generated. The filter is demonstrated in three configurations using aluminum nitride contour-mode resonators and off-the-shelf lumped elements. Measured performance of as low as 3.2-dB insertion loss, bandwidth of 0.87%, and transmission zero notch depth greater than 60 dB is shown.

Phase Noise Measurements of AlN Contour-Mode Resonators With Carrier Suppression Technique.

In this paper, the phase noise of aluminum nitride (AlN) contour-mode resonators is investigated using a passive measurement system with carrier suppression. The purpose is to make careful measurements of the performance of AlN resonators in order to better understand and clarify previously reported frequency instability in these devices. The resonant frequencies of the resonators are around 220 MHz. The motional parameters, the thermal behavior, and the nonlinear power effect of these resonators have been evaluated. Then, the principle of the noise measurement system is reviewed, and the resonator conditioning is shown. Finally, the noise measurements of the resonators are presented and discussed.

The impact of electrode materials on 1/f noise in piezoelectric AlN contour mode resonators

This paper presents a detailed analysis on the impact of electrode materials and dimensions on flicker frequency (1/f) noise in piezoelectric aluminum nitride (AlN) contour mode resonators (CMRs). Flicker frequency noise is a fundamental noise mechanism present in any vibrating mechanical structure, whose sources are not generally well understood. 1 GHz AlN CMRs with three different top electrode materials (Al, Au, and Pt) along with various electrode lengths and widths are fabricated to control the overall damping acting on the device. Specifically, the use of different electrode materials allows control of thermoelastic damping (TED), which is the dominant damping mechanism for high frequency AlN CMRs and largely depends on the thermal properties (i.e. thermal diffusivities and expansion coefficients) of the metal electrode rather than the piezoelectric film. We have measured Q and 1/f noise of 68 resonators and the results show that 1/f noise decreases with increasing Q, with a power law dependence that is about 1/Q4. Interestingly, the noise level also depends on the type of electrode materials. Devices with Pt top electrode demonstrate the best noise performance. Our results help unveiling some of the sources of 1/f noise in these resonators, and indicate that a careful selection of the electrode material and dimensions could reduce 1/f noise not only in AlN-CMRs, but also in various classes of resonators, and thus enable ultra-low noise mechanical resonators for sensing and radio frequency applications.