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In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes of electromechanical nonlinearity to an external tone generated by a secondary oscillator. The micromechanical oscillator exhibits a combination of mechanical and electrostatic nonlinearities that were tuned using a bias voltage to adjust the relative importance of third-order and fifth-order stiffness nonlinearities. While it is well-known that third-order stiffness (Duffing) nonlinearity results in a synchronization range that increases with an oscillator’s amplitude, little is known about the impact of other nonlinearities. We show that when using Duffing nonlinearity cancellation, higher order nonlinearities dominate, the synchronization range is smaller but has a greater rate-of-increase with oscillation amplitude. When both mechanical stiffness-hardening and electrostatic stiffness-softening nonlinearities are present, the frequency response follows an “s-curve” and, unlike the other conditions, the synchronization range does not increase monotonically with amplitude but instead reaches a minimum when both nonlinearities have similar magnitude. We develop a nonlinear resonator model and show that this model achieves good quantitative prediction of the measured synchronization range in all nonlinear operating regimes studied. [ABSTRACT FROM AUTHOR]

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is to construct the resonator from a material with a low temperature coefficient, such as AT-cut quartz, which can achieve absolute frequency stability on the order of 625 ppm over commercial temperature ranges. In comparison, Si microresonators suffer from the disadvantage that silicon's temperature coefficient of frequency (TCF) is approximately two orders of magnitude greater than that of AT-cut quartz. In this paper, we present an in situ passive temperature compensation scheme for Si microresonators based on nonlinear amplitude-frequency coupling which reduces the TCF to a level comparable with that of an AT-quartz resonator. The implementation of this passive technique is generic to a variety of Si microresonators and can be applied to a number of frequency control and timing applications. [ABSTRACT FROM AUTHOR]

This paper presents an ultrasonic fingerprint sensor based on a 24 × 8 array of 22MHz piezoelectric micromachined ultrasonic transducers (PMUTs) with 100 lm pitch, fully integrated with 180 nm complementary metal oxide semiconductor (CMOS) circuitry through eutectic wafer bonding. Each PMUT is directly bonded to a dedicated CMOS receive amplifier, minimizing electrical parasitics and eliminating the need for through-silicon vias. The array frequency response and vibration mode-shape were characterized using laser Doppler vibrometry and verified via finite element method simulation. The array's acoustic output was measured using a hydrophone to be ~14 kPa with a 28V input, in reasonable agreement with predication from analytical calculation. Pulse-echo imaging of a 1D steel grating is demonstrated using electronic scanning of a 20 × 8 sub-array, resulting in 300mV maximum received amplitude and 5:1 contrast ratio. Because the small size of this array limits the maximum image size, mechanical scanning was used to image a 2D polydimethylsiloxane fingerprint phantom (10mm × 8mm) at a 1.2mm distance from the array. [ABSTRACT FROM AUTHOR]

This work investigates the closed-loop operation of microelectromechanical oscillators in the presence of both cubic (Duffing) nonlinearities and parametric amplification. We present a theoretical model for this system that enables us to predict oscillation amplitude and instability and experimentally verify it using a silicon disk resonator with a quality factor (Q) of 85 000 and a natural frequency of 251 kHz. We determine that, contrary to previous understanding gained from analyzing the open-loop system, the presence of cubic nonlinearities does not limit the maximum stable oscillation amplitude if the resonator is operated in a closed loop. In addition, the stability and amplitude behavior predicted by our theoretical model are independent of the presence or severity of cubic nonlinearities, or on drive amplitude. [ABSTRACT FROM AUTHOR]

This paper presents an 8 x 24 element, 100 μm-pitch, 20 MHz ultrasound imager based on a piezoelectric micromachined ultrasonic transducer (PMUT) array having integrated acoustic waveguides. The 70 im diameter, 220 μm\ long waveguides function both to direct acoustic waves and to confine acoustic energy, and also to provide mechanical protection for the PMUT array used for surface-imaging applications such as an ultrasonic fingerprint sensor. The imager consists of a PMUT array bonded with a CMOS ASIC using wafer-level conductive eutectic bonding. This construction allows each PMUT in the array to have a dedicated front-end receive amplifier, which together with on-chip analog multiplexing enables individual pixel read-out with high signal-to-noise ratio through minimized parasitic capacitance between the PMUT and the front-end amplifier. Finite element method simulations demonstrate that the waveguides preserve the pressure amplitude of acoustic pulses over distances of 600 μm\. Moreover, the waveguide design demonstrated here enables pixel-by-pixel readout of the ultrasound image due to improved directivity of the PMUT by directing acoustic waves and creating a pressure field with greater spatial uniformity at the end of the waveguide. Pulse-echo imaging experiments conducted using a one-dimensional steel grating demonstrate the array's ability to form a two-dimensional image of a target. [ABSTRACT FROM AUTHOR]

This paper presents a 3-axis Lorentz force magnetometer based on an encapsulated micromechanical silicon resonator having three orthogonal vibration modes, each measuring one vector component of the external magnetic field. One mode, with natural frequency fn) of 46.973 kHz and quality factor (Q) of 14918, is operated as a closed-loop electrostatically excited oscillator to provide a frequency reference for 3-axis sensing and Lorentz force generation. Current, modulated at the reference frequency, is injected into the resonator, producing Lorentz force that is centered at the reference frequency. Lorentz force in the first axis is nulled by the oscillator loop, resulting in force-rebalanced operation. The bandwidth and scale-factor of this force-rebalanced axis are independent of resonator Q, improving the sensor's temperature coefficient from 20 841ppm/°C to 424ppm/°C. The frequencies of the other two modes are closely spaced to the first mode's reference frequency and are demonstrated to track this frequency over temperature within 1 ppm/K. Field measurements in these two axes are conducted open-loop and off-resonance, ensuring that the scale-factor is independent of Q to first order and producing a measurement bandwidth of over 40 Hz. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effects of electrostatic parametric amplification on a high quality factor (Q>100 000) encapsulated disk resonator gyroscope (DRG), fabricated in h100i silicon. The DRG was operated in the n=2 degenerate wineglass mode at 235 kHz, and electrostatically tuned so that the frequency split between the two degenerate modes was less than 100mHz. A parametric pump at twice the resonant frequency is applied to the sense axis of the DRG, resulting in a maximum scale factor of 156.6 µV/(°/s), an 8.8x improvement over the non-amplified performance. When operated with a parametric gain of 5.4, a minimum angle random walk of 0.034°/√h and bias instability of 1.15°/h are achieved, representing an improvement by a factor of 4.3°x and 1.5x, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a Lorentz force magnetometer employing a micromechanical oscillator. The oscillator, actuated by both electrostatic force and Lorentz force, is based on a 370 μm by 230 μm silicon micromechanical resonator with quality factor (Q) of 13 000. This field-sensitive micromechanical oscillator eliminates the need for an external electronic oscillator and improves magnetometer's stability over temperature. The resonator uses no magnetic materials and is encapsulated using an epitaxial polysilicon layer in a process that is fully compatible with complementary metal-oxide-semiconductor manufacturing. The sensor has a magnetic field resolution of 128 nT/rt-Hz with 2.1 mA bias current. [ABSTRACT FROM AUTHOR]