Radial-contour Mode Research Articles

Design of RF MEMS Piezoelectric Disk Resonator for 5G Communication

With the growing impact of 5G communication system, Radio-Frequency Micro-Electro-Mechanical-Systems (RF MEMS) technologies are becoming increasingly important in our daily lives. Resonators have wide applications in filters for generation or selection of specific frequency signals. Bulk mode resonators have a larger rigidity than flexural mode resonators of the same size, resulting in higher frequencies that are ideal for 5G communication. Owing to this reason, bulk mode resonators are utilized for generation of frequency ranges greater than 2 GHz. As compared to electrostatic actuation, piezoelectric actuation techniques have a substantially lower motional resistance, lower operating voltages, and greater power handling capabilities. Thus, in this work, a 5 GHz piezoelectric micro-disk resonator has been designed and simulated using MEMS CAD tool. The quality factor, admittance, and scattering parameters of a radial-contour mode disk resonator are designed and tested. Along with this study, a comparative evaluation of three different piezoelectric materials based on the quality factor of the dominant resonant mode has been carried out. All three resonators are simulated for resonant frequency f0 = 5 GHz, and various analysis have been carried out. It was proposed that Lithium Niobate is preferred amongst the three piezoelectric materials for higher selectivity applications. The quality factors reported for the materials ZnO, AlN, and LiNbO3 are 1720, 1740 and 1850, respectively. Thus, this study indicates that RF piezoelectric disk resonators can achieve higher frequencies, at the cost of complicated fabrication process.

Exploration and Realization of Novel High-Q Bulk Modes Using Support Transducer Topology

This work reports an exploratory study of novel high quality factor acoustic modes that can be excited using the support transducer topology. The removal of the piezoelectric transducer layer from the high energy confinement mode eliminates the charge cancellation bottleneck. To excite the targeted modes, a frequency match between the thin film piezoelectric on substrate (TPoS) transducer arm and the central Silicon based high quality factor (Q) resonant tank is necessary. The concept of scaling up the frequency without shrinking the device dimensions by exciting higher-order modes has been verified using a third-order Lamé mode. The device exhibits a <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> of 21,632 for a resonant frequency of 58.5MHz. Unexplored modes such as the combination of a square extension mode and a radial contour mode operating in an out-of-phase manner, multiple new higher-order modes, etc. exhibiting very high- <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> have been realized. The average <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> values of these new resonator designs range between 15,000 and 50,000, which is exceptional for piezoelectric transduction-based Microelectromechanical resonators. The idea of excitation of degenerate modes using silicon aligned along non-<100> and non-<110> crystalline axes has also been verified. The proof-of-concept of going beyond the traditional approach of resonance excitation scheme will pave the way to the investigation of unexplored modes that hold immense potential across various sectors of MEMS. [2021-0075]

Effects of material and dimension on TCF, frequency, and Q of radial contour mode AlN-on-Si MEMS resonators

This paper investigates the effects of material and dimension parameters on the frequency splitting, frequency drift, and quality factor (Q) of aluminium nitride (AlN)-on-n-doped/pure silicon (Si) microelectromechanical systems (MEMS) disk resonators through analysis and simulation. These parameters include the crystallographic orientation, dopant, substrate thickness, and temperature. The resonators operate in the elliptical, higher order, and flexural modes. The simulation results show that i) the turnover points of the resonators exist at 55 ​°C, –50 ​°C, 40 ​°C, and –10 ​°C for n-doped silicon with the doping concentration of 2 ​× ​1019 ​cm–3 and the Si thickness of 3.5 ​μm, and these points are shifted with the substrate thickness and mode variations; ii) compared with pure Si, the modal-frequency splitting for n-doped Si is higher and increases from 5% to 10% for all studied modes; iii) Q of the resonators depends on the temperature and dopant. Therefore, the turnover, modal-frequency splitting, and Q of the resonators depend on the thickness and material of the substrate and the temperature. This work offers an analysis and design platform for high-performance MEMS gyroscopes as well as oscillators in terms of the temperature compensation by n-doped Si.

Bandwidth controlled weakly connected MEMS resonators based narrowband filter

Electrical tuning of bandwidth is critical for microelectromechanical system (MEMS) resonator-based narrowband filters especially at ultra-high frequency ranges and beyond. The resonance frequency of MEMS resonators is highly susceptible to fabrication process uncertainties and very small fabrication variations could result in significant shift in their resonance frequency. Although, disk resonators are the most acceptable candidates for implementing of resonators at GHz frequencies, according to their high stiffness, electrical tuning of these resonators and consequently the resulting filters is almost impossible. This study presents a novel tuning method for low velocity through anchor coupled MEMS radial contour mode disk resonators based on the coupling beam's stiffness tuning using the piezoelectric effect. As the results of this method, high bandwidth tuning ratio as 1:1.25 is achieved due to changing the tuning DC voltage from 0 to 20 V. This impressive result for a narrowband filter with 450 kHz of bandwidth is achieved due to changing the stiffness of low stiff coupling beam which is much easier to control in comparison with extremely high stiffness disk resonators. Various simulation results, as well as analytical works, verify the proposed approach.

Technique and Circuit for Contactless Readout of Piezoelectric MEMS Resonator Sensors.

A technique and electronic circuit for contactless electromagnetic interrogation of piezoelectric micro-electromechanical system (MEMS) resonator sensors are proposed. The adopted resonator is an aluminum-nitride (AlN) thin-film piezoelectric-on-silicon (TPoS) disk vibrating in radial contour mode at about 6.3 MHz. The MEMS resonator is operated in one-port configuration and it is connected to a spiral coil, forming the sensor unit. A proximate electronic interrogation unit is electromagnetically coupled through a readout coil to the sensor unit. The proposed technique exploits interleaved excitation and detection phases of the MEMS resonator. A tailored electronic circuit manages the periodic switching between the excitation phase, where it generates the excitation signal driving the readout coil, and the detection phase, where it senses the transient decaying response of the resonator by measuring through a high-impedance amplifier the voltage induced back across the readout coil. This approach advantageously ensures that the readout frequency of the MEMS resonator is first order independent of the interrogation distance between the readout and sensor coils. The reported experimental results show successful contactless readout of the MEMS resonator independently from the interrogation distance over a range of 12 mm, and the application as a resonant sensor for ambient temperature and as a resonant acoustic-load sensor to detect and track the deposition and evaporation processes of water microdroplets on the MEMS resonator surface.

Highly confined radial contour modes in phononic crystal plate based on pillars with cap layers

We investigate highly confined and isolated surface modes in a phononic crystal plate based on pillars with cap layers. The structure is made of a thin membrane supporting periodic pillars each composed of one cylinder surmounted by a disk shaped cap layer. An optimal choice of the geometrical parameters and material composition allows the structure to support isolated radial contour modes confined in the cap layer. In this study, we consider diamond and gold (Au) as the pillar and cap layers, respectively, and aluminum nitride as a thin membrane owing to the strong contrast in their elastic and density properties and to their compatibility with the integrated circuit technology and microwave electroacoustic devices. The phononic crystal based on diamond pillars allows us to induce a wide stop band frequency, and the addition of the Au disk shaped layer on diamond pillars enables us to introduce flat modes within the bandgap. We demonstrate that one can optimize the flat mode frequencies by varying the geometrical parameters of the Au cap layer. The quality factor (Q) of a cavity resonator composed of one line gold/diamond pillar surrounded by an array of diamond pillars on both sides has been investigated. These results clearly show that, using this design approach, one can (i) reduce the acoustic energy leakage out of the resonator and (ii) optimize the cavity resonator’s Q factor by varying only the geometrical parameters of the gold cap layer. The proposed design provides a promising solution for advanced signal processing and sensing applications.

Piezoelectric-on-silicon Lorentz force magnetometers based on radial contour mode disk resonators

In this paper, we realize two unique design topologies for Lorentz force magnetometers (LFMs) based on radial contour (RC) mode piezoelectric-on-silicon disk resonators for the detection of out-of-plane magnetic fields (i.e. normal to the plane of fabrication). The proposed topologies take advantage of the strong electromechanical coupling from the piezoelectric Aluminum Nitride (AlN) layer to enhance the sensitivity of the devices while operating under ambient pressure, thus avoiding the need for vacuum encapsulation. Compared to previously reported modes, we show that RC mode provides a higher coupling efficiency. This ultimately leads to higher responsivity (defined here as the ratio of the pre-amplified output resonant current to the external magnetic field strength, normalized over the excitation current applied) compared to other modes previously reported. Having shown the advantages of the disk LFM, we then extend the advantages of a single disk LFM by mechanically coupling two disk resonators to increase the responsivity. We show that the quality (Q) factor, which determines the responsivity at resonance, does not degrade substantially by mechanically coupling the disks. The responsivity of our coupled disk LFM (21.20 ppm/mT) is 8 times higher compared to a state of art vacuum sealed LFM based on capacitive readout, but without the contraint of requiring vacuum.

Radial-contour mode microring resonators: Nonlinear dynamics

This research is on the dynamics of electrostatically actuated radial-contour mode microring resonators. The governing equation of motion is derived by the minimization of the Hamiltonian and generalized to include the viscous damping effect. The Galerkin method is used to discretize the distributed-parameter model of the considered ring resonator. The periodic solutions in the vicinity of fundamental natural frequency are determined by means of shooting method; the stability of the periodic orbits are investigated by determining the well-known Floquet exponents of the perturbed motions. The influences of intermolecular forces such as van der Waals and Casimir on the dynamic behavior of the resonator are investigated. The natural frequencies and mode shapes of the ring are calculated for various values of ratio of radii (β). The effect of the design parameters including ring radius, electrostatic voltage and quality factor on the dynamic responses, is discussed. The results of present study can be used in the design of novel MEMS resonators, RF filters and channelizers.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators

A small-signal equivalent circuit for parallelplate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators.

A small-signal equivalent circuit for parallel-plate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

AlN micromechanical radial-contour disc resonator

Micromechanical resonators that have high performance and are small in size are competitive candidates for radio frequency (RF) device minimization, paving the way for high performance monolithic transceivers. A piezoelectric aluminium nitride radial-contour mode disc resonator with a CMOS-compatible fabrication process is presented. The piezoelectric properties of the resonator disc, concerning the driving voltage and resonance mode deformation, are analysed, revealing the advantages introduced when using a sputter deposited AlN thin film. The radial-contour resonance mode of the disc resonator was investigated by finite element method simulation and theoretical evaluation. The resonance frequency was found to be thickness-independent, which is beneficial for fabrication and integration. In view of CMOS compatibility, a fabrication process with a low thermal budget and a tungsten titanium sacrificial layer was designed; devices were fabricated on 4 inch silicon wafers. The RF performance of the resonators with a diameter of 150 µm was measured using a HP4395A network analyzer, yielding a resonant frequency of 14.11 MHz with a Q value of 3125 and a return loss of 31.46 dB. These results indicate that this device is attractive for use in RF frequency-selecting and generation devices in high performance wireless communication systems.

Crossed ring anchored disk resonator for self-alignment of the anchor

Misalignment is a problematic challenge in RF MEMS resonators. It causes asymmetry in the ultra symmetric radial contour mode disk resonators and degrades their performance by increasing the insertion loss and decreasing their quality factors (Q). Self-alignment method seems to be a good solution for misalignment problem, but it cannot be directly applied on high performance ring shape anchored resonators. This paper discusses misalignment effects for the ring shape anchored resonators and proposes a method for reconfiguring its anchor to be compatible with self-alignment process. Simulation results validate that the crossed ring anchor structure has the same resonance characteristics with the complete ring shape anchored resonator.

Cavity piezooptomechanics: Piezoelectrically excited, optically transduced optomechanical resonators

We present a monolithic integrated aluminum nitride (AlN) optomechanical resonator in which the mechanical motion is actuated by piezoelectric force and the displacement is transduced by a high-Q optical cavity. The AlN optomechanical resonator is excited from a radio-frequency electrode via a small air gap to eliminate resonator-to-electrode loss. We observe the electrically excited mechanical motion at 47.3 MHz, 1.04 GHz, and 3.12 GHz, corresponding to the 1st, 2nd, and 4th radial-contour mode of the wheel resonator, respectively. An equivalent circuit model is developed to describe the observed Fano-like resonance spectrum.

Electroplated nickel based micro-machined disk resonators for high frequency applications

Microelectromechanical system (MEMS) based resonators can be used for filtering and frequency synthesis applications in many subcomponents of radio frequency wireless integrated circuits due to their small size, high level of frequency selectivity, low cost batch fabrication, ease of integration with CMOS circuits. Electroplated nickel is an attractive low cost material for CMOS compatible MEMS due to their low deposition temperatures. Among the different modes of vibration, radial-contour mode resonators are preferred for high frequency applications because they offer higher effective stiffness. Two different types of electroplated nickel based radial-contour bulk-mode circular disk resonator geometries which depend on capacitive actuation and readout technique is presented in this work. Material, mechanical and electrical characterizations were performed on these structures to show their functionality.

GHz optomechanical resonators with high mechanical Q factor in air

We demonstrate wheel-shaped silicon optomechanical resonators for resonant operation in ambient air. The high finesse of optical whispering gallery modes (loaded optical Q factor above 500,000) allows for efficient transduction of the wheel resonator's mechanical radial contour modes of frequency up to 1.35 GHz with high mechanical Q factor around 4,000 in air.

Analysis and design of a high performance and low cost bio-mass sensor based on the radial contour mode disk resonator

A high performance and cost effective biosensor is designed based on a radial contour-mode disk resonator. Filling a dielectric material within the capacitive gap, we can achieve low motional resistance (Rx) in a cost-effective manner. The motional resistance of the new device is characterized analytically and validated using 3D-multiphysics simulation. Compared with other biosensors, the introduced biosensor may detect the smaller mass changes with mass sensitivity of −74.68μm2/ng (−1617Hz/ng).

Ring shape anchored RF MEMS contour mode disk resonator for UHF communication applications

A new high reliable microelectromechanical radial contour mode disk resonator is demonstrated with the ability to work at UHF range and high quality factor in both vacuum and air. This structure is capable to work at second radial mode without increasing the insertion loss and therefore lowering Q. These characteristics are achieved because of the ring shape anchor which is placed at the nodal ring of a hollow disk resonator at the equivalent second radial mode. Also the ring shape anchor seems to be more reliable than stem shape anchors reported in previous works. The motional resistance of the resonator is decreased due to displacement of electrodes, both inside and outside of the structure. In addition to providing simulation results, this paper formulates the resonance frequency and calculates the optimum location of the anchor. Transfer function, resonance frequency and anchor displacement versus inner radius are also studied.

5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million

This paper reports the design and electrical characterization of a micromechanical disk resonator fabricated in single crystal silicon using a foundry SOI micromachining process. The microresonator has been selectively excited in the radial extensional and the wine glass modes by reversing the polarity of the DC bias voltage applied on selected drive electrodes around the resonant structure. The quality factor of the resonator vibrating in the radial contour mode was 8000 at a resonant frequency of 6.34 MHz at pressure below 10 mTorr vacuum. The highest measured quality factor of the resonator in the wine glass resonant mode was 1.9 × 10 6 using a DC bias voltage of 20 V at about the same pressure in vacuum; the resonant frequency was 5.43 MHz and the lowest motional resistance measured was approximately 17 kΩ using a DC bias voltage of 60 V applied across 2.7 μm actuation gaps. This corresponds to a resonant frequency–quality factor ( f– Q) product of 1.02 × 10 13, among the highest reported for single crystal silicon microresonators, and on par with the best quartz crystal resonators. The quality factor for the wine glass mode in air was approximately 10,000.

High-Q UHF micromechanical radial-contour mode disk resonators

A micromechanical, laterally vibrating disk resonator, fabricated via a technology combining polysilicon surface-micromachining and metal electroplating to attain submicron lateral capacitive gaps, has been demonstrated at frequencies as high as 829 MHz and with Q's as high as 23 000 at 193 MHz. Furthermore, the resonators have been demonstrated operating in the first three radial contour modes, allowing a significant frequency increase without scaling the device, and a 193 MHz resonator has been shown operating at atmospheric pressure with a Q of 8,880, evidence that vacuum packaging is not necessary for many applications. These results represent an important step toward reaching the frequencies required by the RF front-ends in wireless transceivers. The geometric dimensions necessary to reach a given frequency are larger for this contour-mode than for the flexural-modes used by previous resonators. This, coupled with its unprecedented Q value, makes this disk resonator a choice candidate for use in the IF and RF stages of future miniaturized transceivers. Finally, a number of measurement techniques are demonstrated, including two electromechanical mixing techniques, and evaluated for their ability to measure the performance of sub-optimal (e.g., insufficiently small capacitive gap, limited dc-bias), high-frequency, high-Q micromechanical resonators under conditions where parasitic effects could otherwise mask motional output currents. [1051].

1.156-GHz self-aligned vibrating micromechanical disk resonator

A new fabrication methodology that allows self-alignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radial-contour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q's at this frequency >2,650 in both vacuum and air. In addition, a 734.6-MHz version has been demonstrated with Q's of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, self-alignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.