Roozbeh Tabrizian

Effect of phonon interactions on limiting the f.Q product of micromechanical resonators

We discuss the contribution of phonon interactions in determining the upper limit of f.Q product in micromechanical resonators. There is a perception in the MEMS community that the maximum f.Q product of a microresonator is limited to a “frequency-independent constant” determined by the material properties of the resonator [1]. In this paper, we discuss that for frequencies higher than ωτ= 1/τ, where τ is the phonon relaxation time, the f.Q product is no longer constant but a linear function of frequency. This makes it possible to reach very high Qs in GHz micromechanical resonators. Moreover, we show that 〈100〉 is the preferred crystalline orientation for obtaining very high Q in bulk-acoustic-mode silicon resonators above ∼750 MHz, while 〈100〉 is the preferred direction for achieving high-Q at lower frequencies.

A 27 MHz temperature compensated MEMS oscillator with sub-ppm instability

This paper reports on the design, implementation and characterization of a low phase-noise 27 MHz MEMS oscillator with sub-ppm temperature instability based on a high-Q composite bulk acoustic wave (BAW) resonator. An array of silicon dioxide (SiO2) pillars has been uniformly embedded in the body of a piezoelectrically transduced silicon resonator to compensate its negative temperature coefficient of frequency (TCF). Using this technique, an overall frequency drift of 83 ppm is achieved for the resonator over the temperature range of -20°C to 100°C while resonator Q remains greater than 7,500 in atmospheric pressure. An electronically compensated oscillator using this resonator exhibits sub-ppm temperature instability with a consistent phase noise (PN) behavior over the entire temperature range and a value of -101 dBc/Hz at 1 kHz offset-frequency. Long-term stability measurement has been carried out for both temperature-compensated resonator and oscillator in an environmental chamber to study their stability over time.

Temperature-Stable Silicon Oxide (SilOx) Micromechanical Resonators

This paper presents a passive temperature compensation technique that can provide full cancellation of the linear temperature coefficient of frequency (TCF1) in silicon resonators. A uniformly distributed matrix of silicon dioxide pillars is embedded inside the silicon substrate to form a homogenous composite silicon oxide platform (SilOx) with nearly perfect temperature-compensated stiffness moduli. This composite platform enables the implementation of temperature-stable microresonators operating in any desired in- and out-of-plane resonance modes. Full compensation of TCF1 is achieved for extensional and shear modes of SilOx resonators resulting in a quadratic temperature characteristic with an overall frequency drift as low as 83 ppm over the industrial temperature range ( -40°C to 80°C). Besides a 40 times reduction in temperature-induced frequency drift in this range, SilOx resonators exhibit improved temperature stability of Q compared with their single crystal silicon counterparts.

Dual-Mode AlN-on-Silicon Micromechanical Resonators for Temperature Sensing

In this paper, we present dual-mode (DM) AlN-on-silicon micromechanical resonators for self-temperature sensing. In-plane width-shear (WS) and width-extensional (WE) modes of [110]-oriented silicon resonators have been used as alternatives to first- and third-order modes to enhance DM temperature sensitivity by engineering device geometry, which reduces inherent beat frequency fb between the two modes. This configuration provides a 50× improvement in temperature coefficient of beat frequency (TCfb) compared with single-mode temperature measurement and eliminates the need for additional frequency multipliers to generate fb from its constituents. [100]-oriented WS/WE resonators provide 4× larger TCF difference between modes (ΔTCF) than first and third width-extensional resonators, which further contributes to TCfb enhancement. WS/WE mode resonators also demonstrate the capability of operating as a temperature-stable reference fb. The proposed modes for DM operation have high Q and low motional resistance, and are 180 ° out-of-phase when operated in two-port configuration, thus enabling mode-selective low-power oscillator interfacing for resonant temperature sensing.

Tunable piezoelectric MEMS resonators for real-time clock

This paper reports on the design, simulation and characterization of small form factor, tunable piezoelectric MEMS resonators for real time clock applications (32.768 kHz). The structures were fabricated on a thin-film AlN-on-SOI substrate to enable piezoelectric actuation of an out-of-plane flexural mode, as well as electrostatic frequency tuning by utilizing the handle layer as a DC voltage electrode. Resonators of only a few hundred of µm in size exhibit greater than 3100 ppm of tuning using voltages no larger than 4 V; this tuning sufficiently compensates for frequency variations across temperature from −25 to 100 °C. The devices exhibit low motional impedance that is completely independent of the tuning potential.

High-Frequency AlN-on-Silicon Resonant Square Gyroscopes

This letter reports, for the first time, on a high-frequency resonant square micro-gyroscope using piezoelectric transduction. Degenerate pairs of orthogonal flexural resonance modes are used to provide energy exchange paths for the Coriolis-based resonant gyroscope in response to z-axis rotation. Aluminum nitride thin films have been used to provide highly efficient electromechanical transduction for drive and sense modes without requiring any dc polarization voltage for operation. A proof-of-concept design consisting of a 300 μm× 300 μm square gyro shows linear rate sensitivity of 20.38 μV/°/s when operating in its first flexural mode at ~ 11 MHz.

Electrostatically tunable piezoelectric-on- silicon micromechanical resonator for real-time clock

This paper reports on the design, fabrication, and characterization of a small form factor, piezoelectrically transduced, tunable micromechanical resonator for real-time clock (RTC) applications (32.768 kHz). The device was designed to resonate in an out-of-plane flexural mode to simultaneously achieve low-frequency operation and reduced motional resistance in a small die area. Finite element simulations were extensively used to optimize the structure in terms of size, insertion loss, spurious-mode rejection, and frequency tuning. Microresonators with an overall die area of only 350 × 350 μm were implemented on a thin-film AlN on silicon-on-insulator (SOI) substrate with AlN thickness of 0.5 μm, device layer of 1.5 μm, and an electrostatic tuning gap size of 1 μm. A frequency tuning range of 3100 ppm was measured using dc voltages of less than 4 V. This range is sufficient to compensate for frequency variations of the microresonator across temperature from -20°C to 100°C. The device exhibits low motional impedance that is completely independent of the frequency tuning potential. Discrete electronics were used in conjunction with the resonator to implement an oscillator, verifying its functionality as a timing reference.

Thermo-acoustic engineering of silicon microresonators via evanescent waves

A temperature-compensated silicon micromechanical resonator with a quadratic temperature characteristic is realized by acoustic engineering. Energy-trapped resonance modes are synthesized by acoustic coupling of propagating and evanescent extensional waves in waveguides with rectangular cross section. Highly different temperature sensitivity of propagating and evanescent waves is used to engineer the linear temperature coefficient of frequency. The resulted quadratic temperature characteristic has a well-defined turn-over temperature that can be tailored by relative energy distribution between propagating and evanescent acoustic fields. A 76 MHz prototype is implemented in single crystal silicon. Two high quality factor and closely spaced resonance modes, created from efficient energy trapping of extensional waves, are excited through thin aluminum nitride film. Having different evanescent wave constituents and energy distribution across the device, these modes show different turn over points of 67 °C and 87 °C for their quadratic temperature characteristic.

Energy dissipation in micromechanical resonators

Recent years have witnessed breakthrough researches in micro- and nano-mechanical resonators with small dissipation. Nano-precision micromachining has enabled the realization of integrated micromechanical resonators with record high Q and high frequency, creating new research horizons. Not too long ago, there was a perception in the MEMS community that the maximum f.Q product of a microresonator is limited to a frequency-independent constant determined by the material properties of the resonator. In this paper, the contribution of phonon interactions in determining the upper limit of f.Q product in micromechanical resonators will be discussed and shown that after certain frequency, the f.Q product is no longer constant but a linear function of frequency. This makes it possible to reach very high Qs in GHz micro- and nano-mechanical resonators and filters. Contributions of other dissipation mechanisms such as thermoelastic damping and support loss in the quality factor of a microresonator will be discussed as well.

Acoustically-engineered multi-port AlN-on-silicon resonators for accurate temperature sensing

This paper reports on a novel silicon microresonator that is acoustically engineered to facilitate simultaneous yet independent piezoelectric transduction of multiple resonance modes with large difference in their temperature coefficient of frequency (TCF) and integer frequency ratios. A three-port aluminum-nitride-on-silicon (AlN-on-Si) microresonator prototype implemented based on this technique has two energy-trapped modes at 109 MHz and 218 MHz, with a TCF difference of ~7 ppm/°C, which are separately transduced through two isolated electrical ports. A small beat frequency extracted from an integer combination of these modes has a linear TCF of ~8300 ppm/°C, suitable for sensing the resonator temperature with high accuracy and resolution.