Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator

Research on Energy Dissipation Mechanism of Cobweb-like Disk Resonator Gyroscope

The micro disk resonator gyroscope is a micro-mechanical device with potential for navigation-grade applications, where the performance is significantly influenced by the quality factor, which is determined by various energy dissipation mechanisms within the micro resonant structure. To enhance the quality factor, these gyroscopes are typically enclosed in high-vacuum packaging. This paper investigates a wafer-level high-vacuum-packaged (<0.1 Pa) cobweb-like disk resonator gyroscope, presenting a systematic and comprehensive theoretical analysis of the energy dissipation mechanisms, including air damping, thermoelastic damping, anchor loss, and other factors. Air damping is analyzed using both a continuous fluid model and an energy transfer model. The analysis results are validated through quality factor testing on batch samples and temperature characteristic testing on individual samples. The theoretical results obtained using the energy transfer model closely match the experimental measurements, with a maximum error in the temperature coefficient of less than 2%. The findings indicate that air damping and thermoelastic damping are the predominant energy dissipation mechanisms in the cobweb-like disk resonant gyroscope under high-vacuum conditions. Consequently, optimizing the resonator to minimize thermoelastic and air damping is crucial for designing high-performance gyroscopes.

Anchor Loss Reduction in Micro-Electro Mechanical Systems Flexural Beam Resonators Using Trench Hole Array Reflectors

The quality factor of microelectromechanical resonators is a crucial performance metric and has thus been the subject of numerous studies aimed at maximizing its value by minimizing the anchor loss. This work presents a study on the effect of elastic wave reflectors on the quality factor of MEMS clamped-clamped flexural beam resonators. The elastic wave reflectors are a series of holes created by trenches in the silicon substrate of the resonators. In this regard, four different shapes of arrayed holes are considered, i.e., two sizes of squares and two half circles with different directions are positioned in proximity to the anchors. The impact of these shapes on the quality factor is examined through both numerical simulations and experimental analysis. A 2D in-plane wave propagation model with a low-reflecting fixed boundary condition was used in the numerical simulation to predict the behavior, and the MEMS resonator prototypes were fabricated using a commercially available micro-fabrication process to validate the findings. Notably, the research identifies that half-circle-shaped holes with their curved sides facing the anchors yield the most promising results. With these reflectors, the quality factor of the resonator is increased by a factor of 1.70× in air or 1.72× in vacuum.

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.

Thermoelastic damping in MEMS gyroscopes at high frequencies

Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g., in modern automotive and consumer applications, and require signal stability and accuracy in rather harsh environmental conditions. In many use cases, device reliability must be guaranteed under large external loads at high frequencies. The sensitivity of the sensor to such external loads depends strongly on the damping, or rather quality factor, of the high-frequency mechanical modes of the structure. In this paper, we investigate the influence of thermoelastic damping on several high-frequency modes by comparing finite element simulations with measurements of the quality factor in an application-relevant temperature range. We measure the quality factors over different temperatures in vacuum, to extract the relevant thermoelastic material parameters of the polycrystalline MEMS device. Our simulation results show a good agreement with the measured quantities, therefore proving the applicability of our method for predictive purposes in the MEMS design process. Overall, we are able to uniquely identify the thermoelastic effects and show their significance for the damping of the high-frequency modes of an industrial MEMS gyroscope. Our approach is generic and therefore easily applicable to any mechanical structure with many possible applications in nano- and micromechanical systems.

Stability of Bragg reflectors under megahertz heat load at XFELs

Modern X-ray free-electron laser (XFEL) sources can deliver photon pulses with millijoule pulse energies and megahertz repetition rate. As shown by the simulations in this work, for particular cases the dynamical heat load effects for Bragg reflectors could cause problems at these facilities. These problems would be underestimated if only quasi-static thermoelastic simulations are considered. Nevertheless, for the sake of simplicity the quasi-static approach is a common choice for estimating heat load effects. To emphasize the relevance of dynamical thermoelastic effects, the response to the partial absorption of an X-ray pulse, as provided by a saturated X-ray free-electron laser oscillator (XFELO) in a single crystal diamond with a thickness of 100 µm and lateral dimensions in the millimetre range, is discussed in this work. The outcome of the dynamic thermoelastic simulations indicates a clear dominance regarding the strain value reached, which is present for consecutive X-ray matter interactions with megahertz repetition rate.

A Novel Extensional Bulk Mode Resonator with Low Bias Voltages

This paper presents a novel Π-shaped bulk acoustic resonator (ΠBAR) with low bias voltages. Concave flanges were coupled with straight beams to effectively enlarge the transduction area. A silicon-on-insulator(SOI)-based fabrication process was developed to produce nanoscale spacing gaps. The tether designs were optimized to minimize the anchor loss. With a substantially improved electromechanical coupling coefficient, the high-stiffness ΠBAR can be driven into vibrations with low bias voltages down to 3 V. The resonator, vibrating at 20 MHz, implements Q values of 3600 and 4950 in air and vacuum, respectively. Strategies to further improve the resonator performance and robustness were investigated. The resonator has promising IC compatibility and could have potential for the development of high-performance timing reference devices.

Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers

We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65)  ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

Dominant Loss Mechanisms of Whispering Gallery Mode RF-MEMS Resonators with Wide Frequency Coverage

This work investigates the dominant energy dissipations of the multi-frequency whispering gallery mode (WGM) resonators to provide an insight into the loss mechanisms of the devices. An extensive theory for each loss source was established and experimentally testified. The squeezed film damping (SFD) is a major loss for all the WGMs at atmosphere, which is distinguished from traditional bulk acoustic wave (BAW) resonators where the high-order modes suffer less from the air damping. In vacuum, the SFD is negligible, and the frequency-dependent Akhiezer damping (AKE) has significant effects on different order modes. For low-order WGMs, the AKE is limited, and the anchor loss behaves as the dominant loss. For high-order modes with an extended nodal region, the anchor loss is reduced, and the AKE determines the Q values. Substantial Q enhancements over four times and an excellent f × Q product up to 6.36 × 1013 at 7 K were achieved.

Low-Loss Unidirectional Acoustic Focusing Transducer in Thin-Film Lithium Niobate

In this work, we present gigahertz low-loss unidirectional acoustic focusing transducers in thin-film lithium niobate. The design follows the anisotropy of fundamental symmetric (S0) waves in X-cut lithium niobate. The implemented acoustic delay line testbed consisting of a pair of the proposed transducers shows a low insertion loss of 4.2 dB and a wide fractional bandwidth of 7.5% at 1 GHz. The extracted transducer loss is 1.46 dB, and the propagation loss of the S0 waves is 0.0126 dB/ [Formula: see text]. The design framework is readily extendable to other acoustic modes, given consideration on the optimal orientation for power flow and electromechanical transduction.

Integrated optical isolators using electrically driven acoustic waves

We propose and investigate the performance of integrated photonic isolators based on non-reciprocal mode conversion facilitated by unidirectional, traveling acoustic waves. A triply-guided waveguide system on-chip, comprising two optical modes and an electrically-driven acoustic mode, facilitates the non-reciprocal mode conversion and is combined with spatial mode filters to create the isolator. The co-guided and co-traveling arrangement enables isolation with no additional optical loss, without magnetic-optic materials, and with low power consumption. The approach is theoretically evaluated with simulations predicting over 20 dB of isolation and 2.6 dB of insertion loss with a 370 GHz optical bandwidth and 1 cm device length. The isolator uses only 1 mW of electrical drive power, an improvement of 1-3 orders of magnitude over the state of the art. The electronic drive and lack of magneto-optic materials suggest the potential for straightforward integration with drive circuits, including in monolithic CMOS electronic-photonic platforms, enabling a fully contained 'black box' optical isolator with two optical ports and DC electrical power.

A Novel High Q Lamé-Mode Bulk Resonator with Low Bias Voltage

This work reports a novel silicon on insulator (SOI)-based high quality factor (Q factor) Lamé-mode bulk resonator which can be driven into vibration by a bias voltage as low as 3 V. A SOI-based fabrication process was developed to produce the resonators with 70 nm air gaps, which have a high resonance frequency of 51.3 MHz and high Q factors over 8000 in air and over 30,000 in vacuum. The high Q values, nano-scale air gaps, and large electrode area greatly improve the capacitive transduction efficiency, which decreases the bias voltage for the high-stiffness bulk mode resonators with high Q. The resonator showed the nonlinear behavior. The proposed resonator can be applied to construct a wireless communication system with low power consumption and integrated circuit (IC) integration.

Low motional impedance distributed Lamé mode resonators for high frequency timing applications

This paper presents a novel high-Q silicon distributed Lamé mode resonator (DLR) for VHF timing reference applications. The DLR employs the nature of shear wave propagation to enable a cascade of small square Lamé modes in beam or frame configurations with increased transduction area. Combined with high efficiency nano-gap capacitive transduction, it enables low motional impedances while scaling the frequency to VHF range. The DLR designs are robust against common process variations and demonstrate high manufacturability across different silicon substrates and process specifications. Fabricated DLRs in beam and frame configurations demonstrate high performance scalability with high Q-factors ranging from 50 to 250 k, motional impedances <1 kΩ, and high-temperature frequency turnover points >90 °C in the VHF range, and are fabricated using a wafer-level-packaged HARPSS process. Packaged devices show excellent robustness against temperature cycling, device thinning, and aging effects, which makes them a great candidate for stable high frequency references in size-sensitive and power-sensitive 5 G and other IoT applications.

Monocrystalline Silicon Carbide Disk Resonators on Phononic Crystals with Ultra-Low Dissipation Bulk Acoustic Wave Modes

Micromechanical resonators with ultra-low energy dissipation are essential for a wide range of applications, such as navigation in GPS-denied environments. Routinely implemented in silicon (Si), their energy dissipation often reaches the quantum limits of Si, which can be surpassed by using materials with lower intrinsic loss. This paper explores dissipation limits in 4H monocrystalline silicon carbide-on-insulator (4H-SiCOI) mechanical resonators fabricated at wafer-level, and reports on ultra-high quality-factors (Q) in gyroscopic-mode disk resonators. The SiC disk resonators are anchored upon an acoustically-engineered Si substrate containing a phononic crystal which suppresses anchor loss and promises Q_ANCHOR near 1 Billion by design. Operating deep in the adiabatic regime, the bulk acoustic wave (BAW) modes of solid SiC disks are mostly free of bulk thermoelastic damping. Capacitively-transduced SiC BAW disk resonators consistently display gyroscopic m = 3 modes with Q-factors above 2 Million (M) at 6.29 MHz, limited by surface TED due to microscale roughness along the disk sidewalls. The surface TED limit is revealed by optical measurements on a SiC disk, with nanoscale smooth sidewalls, exhibiting Q = 18 M at 5.3 MHz, corresponding to f · Q = 9 · 10¹³ Hz, a 5-fold improvement over the Akhiezer limit of Si. Our results pave the path for integrated SiC resonators and resonant gyroscopes with Q-factors beyond the reach of Si.