Lame-mode Resonator Research Articles

Investigating Elastic Anisotropy of 4H-SiC Using Ultra-High Q Bulk Acoustic Wave Resonators

Hexagonal 4H-silicon carbide (4H-SiC) is a transversely isotropic substrate garnering interest for precision MEMS devices such as resonant gyroscopes. This paper investigates the elastic anisotropy of 4H-SiC by utilizing capacitive bulk acoustic wave (BAW) resonators with ultra-high mechanical quality factors ( $Q$ ) enabled by phononic crystals. We directly measure the value of $C_{66}$ using Lame mode resonators for the first time and numerically fit the values of $C_{11}$ and $C_{12}$ using BAW elliptical modes in center-supported solid disk resonators. We compare (0 0 0 1) 4H-SiC to (1 1 1) Si, another in-plane isotropic material and validate (0 0 0 1) 4H-SiC’s superior robustness to fabrication and design variations. Measurement of in-plane BAW elliptical modes in multiple disk resonators with as-born frequency splits as low as 3 ppm reveal (0 0 0 1) 4H-SiC’s transverse isotropy across process corners. Lame mode resonators display a temperature coefficient of frequency (TCF) three times lower compared to its Si counterpart. Finally, this paper provides a modified set of elastic constants for 4H-SiC with a view towards monocrystalline SiC MEMS devices. [2020-0254]

High-Q Support Transducer MEMS Resonators Enabled Low-Phase-Noise Oscillators.

Structural and electrode material engineering methodology to attain quality factor enhancement in a support transducer enabled Wine-glass and Lamé mode resonator has been demonstrated in this work. To boost the quality factor, a series of short mechanical couplers is utilized to link the central resonant structure with the piezoelectric transducer arms. Two different top electrode materials are investigated, and the effect of metal loading on the performance of aluminum nitride (AlN)-on-Si-based resonator is investigated in detail. The new resonator design strategy improves the quality factor of the Wine-glass resonator from 9800 to 16 300 while still being able to maintain a spurious-free spectrum for a 200-MHz span, which is crucial for oscillator applications. An optimized oscillation system is realized using a commercially available low-noise amplifier. Careful positioning of the passive components is utilized to attain an ideal operating point for the resonator in the closed-loop condition. Using this scheme, Wine-glass and Lamé mode resonator-based high-performance oscillators with a low phase noise of -133.6 and -132.7dBc/Hz at 1-kHz offset and -153.7 and -150.4 dBc/Hz at 1-MHz offset, respectively, which satisfy that the Global System for Mobile (GSM) communication requirements are attained when normalized to a 13-MHz carrier frequency.

Anchor Design Affects Dominant Energy Loss Mechanism in a Lamé Mode MEM Resonator

We present a Lame mode resonator whose limiting damping mechanism depends on its anchor geometry. The device is anchor-limited when the anchors are stiffer and is Akhiezer-limited with more compliant anchors. This result is determined by observing the temperature dependence of the quality factor (Q) for devices with different lateral dimensions and different anchor designs. The total measured Q increases by an order of magnitude with the more compliant anchors and reaches a room temperature fxQ product of $\boldsymbol {2.2\times 10^{13}}$ . We studied the relationship between the device design and the anchor design and the measured Q(T) results to identify the contributions from different dissipation mechanisms. This investigation provides insight into how anchor design affects anchor damping. [2020-0195]

Low-Power Dual Mode MEMS Resonators With PPB Stability Over Temperature

We demonstrate two novel dual-mode ovenized MEMS resonators, each with an in-chip device layer micro-oven that utilizes less than 30mW for resonator temperature control over variations in external temperature from −40°C to +60°C. The device layer micro-oven enables correction for ambient temperature variations and achieves a 1-week frequency stability for the output mode over temperature near 1.5 ppb for the Lame-mode resonator. The devices were built in the Epi-Seal fabrication process and take advantage of the exceptional long-term stability of MEMS resonators built in that process. These results exceed all prior reports for frequency stability over time and temperature for MEMS resonators and have the potential to impact the development of miniature, low-power time references. [2019-0054]

Investigation of modified Lamé mode resonator with high coupling coefficient

This paper presents a modified Lamé-mode resonator (MLMR) with a high, effective electromechanical coupling coefficient (Keff2). With trapezoidal grooves introduced by etching the superficial piezoelectric material between interdigitated electrodes (IDTs), the MLMR can remarkably improve Keff2, eliminate spurious modes, and reduce the internal stress of piezoelectric material. The Lamé mode resonator (LMR) with four different electrode configurations is investigated by using finite element method simulation first; then, the impact of the groove's vertical (h) and horizontal (θ) size on Keff2 and spurious modes of MLMRs is theoretically analyzed and optimized. It is noted that all the modified structures can improve Keff2 except the IDT-Ground structure. This work demonstrates a simulated Keff2 as high as 10.47% in the modified IDT-Floating structure, and 10.73% in the modified IDT-IDT structure, which is the highest ever reported in S0 mode AlN LMR. The MLMR shows great prospect for fabricating broad bandwidth filters.

Transducer design for AlN Lamb wave resonators

AlN Lamb wave resonators enjoy advanced and attractive properties for enabling the next-generation single-chip radio frequency front-end, but their moderate effective electromechanical coupling coefficient (k2eff) poses a limit to their application in filters and multiplexers. Despite the fact that the reported k2eff enhancement techniques of doped AlN thin films which are expensive and trade off the quality factor (Q), the transducer topology itself extensively impacts the k2eff value. Although an AlN cross-sectional Lame mode resonator exhibiting a k2eff of 6.34% has been demonstrated without the need for changing the piezoelectric material, a detailed study of transducer design for AlN Lamb wave resonators has not been conducted. In this work, we investigate the impact of (i) transducer configurations, (ii) electrode materials, (iii) electrode thicknesses, and (iv) interdigital transducer duty factors on the k2eff dispersive characteristics of one-port AlN Lamb wave resonators by using the finite element analysis approach. By properly designing and optimizing the transducers, the k2eff of one-port AlN Lamb wave resonators can be boosted to as high as 7.7%, showing great potential for applications of cellular frequency selection.

RF Passive Components Based on Aluminum Nitride Cross-Sectional Lamé-Mode MEMS Resonators

This paper presents a new class of monolithic integrated RF passive components based on the recently developed aluminum nitride (AlN) MEMS cross-sectional Lame-mode resonator (CLMR) technology. First, we experimentally demonstrate a 920-MHz CLMR showing the values of electromechanical coupling coefficient ( $k_{t}^{\mathbf {2}}$ ) and quality factor ( $Q_{\mathrm{ load}}$ ) in excess of 6.2% and 1750, respectively. To the best our knowledge, the resulting figure of merit ( $= Q\cdot k_{t}^{2}$ ), in excess of 108, is the highest ever reported for AlN-based piezoelectric resonators using interdigitated metallic electrodes (IDTs) and operating in the same frequency range. Second, we report the measured performance of an 870-MHz ladder filter, synthesized using three degenerate CLMRs. This device shows the values of fractional bandwidth (BW $_{3\,\text {dB}}$ ) in excess of 3.8% and an insertion loss of ~1.5 dB. Finally, we report the performance of the first piezoelectric transformer (PT) based on the CLMR technology. This device, dubbed “cross-sectional Lame-mode transformer,” exploits the high- $\text{k}_{t}^{\mathbf {2}}$ of the CLMR technology to achieve high values of open-circuit voltage-gains ( $G_{v}$ ) in excess of 39. To the best of our knowledge, such a high $G_{v}$ -value is the highest ever reported for MEMS-based PTs operating in the microwave frequency range.

Cross-Sectional Lamé Mode Ladder Filters for UHF Wideband Applications

This letter reports on the first demonstration of ladder filters based on the recently demonstrated cross-sectional Lame mode resonator (CLMR) technology. These filter prototypes show a fractional bandwidth (BW $_{\mathrm {3dB}})$ as high as 3.3% and an insertion loss as low as 0.4 dB. As the resonance frequency of CLMRs can be lithographically controlled without significantly degrading their electromechanical coupling coefficient ( $\text{k}_{t}^{2})$ , multiple contiguous frequency bands can be covered by this filter technology without adding fabrication complexity. This unique feature addresses one of the most crucial challenges associated with the development of miniaturized mobile platforms adopting carrier-aggregation. Furthermore, the capability of achieving large BW3dB, around lithographically defined center frequencies, enables the fabrication of transmit and receive modules of the next-generation radio-frequency front ends on the same chip without adding fabrication steps.

Piezoresistive Readout Mechanically Coupled Lamé Mode SOI Resonator With $Q$ of a Million

This paper describes the use of the coupling beam in a pair of mechanically coupled Lame mode resonators to enhance electromechanical transduction by piezoresistive sensing, while at the same time maintaining a high quality factor of a million. This corresponds to an $f\!Q$ product of $1.3 \times 10^{13}$ , which approaches the Akhiezer limit of silicon. With a 15 mA bias current, electrical characterization of the array using the piezoresistive readout via the coupling-beam provides a 25 dB enhancement over a single Lame mode resonator using capacitive readout. In this paper, we have modeled the piezoresistive electromechanical frequency response function of the device both analytically and by finite elements. The models mutually agree and are experimentally verified by measured results of fabricated resonators. The model indicates that the transduction factor is independent of the lateral dimensions and thickness of the resonator. [2015-0009]

3J2-1 Resonant Frequency Analysis of a Lame Mode Resonator on a Quartz Plate by the Finite-Difference Time-Domain Method with the Collocated Grid Points of Velocities

3J2-1 Resonant Frequency Analysis of a Lame Mode Resonator on a Quartz Plate by the Finite-Difference Time-Domain Method with the Collocated Grid Points of Velocities

Design and fabrication of a square shape bulk mode MEMS resonators

This paper reports the design, simulation and fabrication of a micromechanical square shape resonators fabricated in single crystal silicon using a silicon on isolator wafer. Two different types of excitation for square shape resonators were used to stimulate Lame mode and square mode of resonance. The fabricated devices were studied under different bias voltage and in air at room temperature. The highest quality factor measured for the Lame mode resonator was 11,121 and for the square mode was 9,120 for square mode at 3.17 and 4.01 MHz, under the 80 V DC bias voltage across 1.5 μm actuation gap. It has been shown that by adding raggedy edge, the coupling capacitor has increased. Mass detection capabilities of these resonators were also investigated by adding an extra layer of gold. Frequency and quality factor variation was observed for each of the fabricated resonators. Adding a mass of 76 pgr leads to resonance frequency shift of 3.1 kHz in Lame mode structure. In this experiment quality factor drop was observed because of continues film layer of gold metal, with a thickness of 100 nm.

Design and Simulation of MEMS Based Gyroscope

This paper represents a MEMS based gyroscope to measure orientation. Silicon-micro-machined gyro is fabricated on the basis of resonators and they use vibrating mechanical element to sense rotation. The vibratory measurement can be done by measuring the change in capacitance with respect to the voltage or force applied in particular axis. Here MEMS based gyroscope has been designed from Lame mode resonator which is a square plate. The additional benefits by using the gyroscope are lower sensor cost, power consumption, more robustness, higher shock resistance. In this paper, also sensitivity of the geometry and change of capacitance has been shown. Index Terms –Coriolis Force, Gyroscope, MEMS.

High $Q$ Single Crystal Silicon Micromechanical Resonators With Hybrid Etching Process

This letter presents a hybrid silicon etching-based technique for single crystal silicon micromechanical resonators fabrication. The proposed method differs from previous works by combining a front-side wet anisotropic pre-etching and a front-side DRIE dry anisotropic post-etching in micromachining micromechanical resonators. The wet etching is used to pre-etch a cavity for structure release in the substrate, while the post- dry etching is employed to fabricate and release the resonator structures simultaneously. A 4.126-MHz square plate Lame-mode resonator has been successfully fabricated using this approach. An impressive quality factor (Q) as high as 5.34×106 is experimentally measured at a pressure of 0.06 mbar, corresponding to a frequency Q product of 2.2×1013.