Logan Sorenson

3-D micromachined hemispherical shell resonators with integrated capacitive transducers

We present a self-aligned fabrication method developed for three-dimensional (3-D) microscale hemispherical shell resonators with integrated capacitive transducers and a center post for electrical access to the shell. The self-aligned process preserves the axisymmetry for robust, balanced resonators that can potentially reach very high-Q due to suppressed anchor loss. High-Q operation of a thin polycrystalline silicon shell resonator is verified by exciting devices capacitively into a breathing resonance mode, with measured Q of 8,000 at 412 kHz in vacuum. This process can be further optimized to batch-fabricate micro-hemispherical resonator gyroscopes for portable inertial navigation.

Multi-axis AlN-on-Silicon vibration energy harvester with integrated frequency-upconverting transducers

This paper presents fully-integrated multi-axis piezoelectric-on-silicon kinetic energy harvesters (KEHs) that demonstrate enhanced power output via mechanical frequency upconversion. Mechanical energy is converted to electrical energy by out-of-plane and in-plane devices that are micromachined on the same substrate. The out-of-plane device demonstrates nearly 100× frequency upconversion of 134 Hz input vibrations, while the in-plane harvester demonstrates more than 3000× frequency upconversion of 2 Hz input vibrations. The batch-fabrication process is compatible with AlN-on-Si devices such as RF resonators and sensors. The total volume of an individual harvester is 5 mm3 (in-plane) and 1 mm3 (out-of-plane), implying that stacked arrays of such devices can easily increase power density.

An Empirical Phase-Noise Model for MEMS Oscillators Operating in Nonlinear Regime

Nonlinearity of a silicon resonator can lead to improved phase-noise performance in an oscillator when the phase shift of the sustaining amplifier forces the operating point to a steeper phase-frequency slope. As a result, phase modulation on the oscillator frequency is minimized because the resonator behaves as a high-order phase filter. The effect of the increased filtering translates into phase-noise shaping that reflects superior overall performance. Nonlinear effects in MEMS oscillators can be induced via sufficient driving power, generating low-frequency nonwhite noise processes that need to be considered in a phase-noise description. Since the phase-frequency response is not symmetric for a nonlinear detuned resonator, an empirical model based on power series is proposed to describe its effect in the noise sources and to account for the observed higher effective quality factor of the oscillator, the reduction in the corner frequency, and elevated levels of flicker noise very close-to-carrier. The applicability of the presented phase-noise model is shown for three piezoelectric MEMS oscillators, producing a relative fitting error below 1% in all cases.

One-dimensional linear acoustic bandgap structures for performance enhancement of AlN-on-Silicon micromechanical resonators

This work introduces piezo-on-silicon linear acoustic bandgap (LAB) structures, a class of compact 1D micro-scale phononic crystal (PC) which can be directly integrated with micromechanical devices. Finite element simulations with custom-derived dispersion equations predict multiple bandgaps for coupled-ring LAB structures into the GHz region. AlN-on-Si resonator are replaced with coupled-ring LAB tethers to reduce acoustic loss into the substrate; the existence of bandgaps is experimentally confirmed in transmission spectra of test structures as well as quality factor (Q) and insertion loss (IL) improvements of LAB-enhanced resonators. An IL of 3.8 dB at 178 MHz and Qs of greater than 11,000 at 600 MHz in air are reported.

Invar-36 Micro Hemispherical Shell Resonators

We report, for the first time, on the successful fabrication and operational characterization of electroplated Invar Micro-Hemispherical Shell Resonators (μHSR). The heat treatment of the samples and its effect on the quality factor (Q) of the resonators is studied. We show that thermal annealing shifts the coefficient of thermal expansion (CTE) of the alloy towards its minimum of ~2ppm/°C, as a result of which the Q of a 29kHz μHSR with diameter of 780 μm increases at least 3 times and reaches 7500 in vacuum.

Electrical characterization of ALD-coated silicon dioxide micro-hemispherical shell resonators

This paper reports on electrical characterization of ALD-coated thermally-grown silicon dioxide micro-hemispherical shell resonators (μHSRs) with capacitive electrodes. A high aspect ratio silicon dioxide μHSR with a thickness of 2.6 μm and diameter of 910 μm, uniformly coated with 30 nm of platinum using ALD process, demonstrated Q of 19,100 at 19.17 kHz and 14,300 at 55.2 kHz for m=2 and m=3 wineglass modes, respectively. An optimized isotropic dry etching recipe was developed to create highly symmetric hemispherical molds in (111) silicon substrates, from which the oxide shells were thermally grown. This resulted in a significant improvement of frequency mismatch between m=2 degenerate modes, achieving 21 Hz split as fabricated for m=2 modes of an 8kHz SiO2 μHSR that is 1240 μm in diameter and 2 μm in thickness. This creates a path for fabricating high Q and highly symmetric hemispherical shell resonators for microscale hemispherical resonator gyroscopes.

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.

Compensation, tuning, and trimming of MEMS resonators

Fundamental characteristics of MEMS resonators such as acoustic velocity and energy dissipation may have strong temperature and process dependencies that must be carefully compensated in applications requiring high degrees of stability and accuracy. This paper presents an overview of compensation, tuning, and trimming techniques for MEMS resonators. The use of these techniques in implementation of high precision and high performance MEMS resonators is described, and the benefits and challenges of different approaches are discussed and compared.

Phase noise shaping via forced nonlinearity in piezoelectrically actuated silicon micromechanical oscillators

This paper shows improved phase-noise performance of MEMS oscillators when the sustaining amplifier operates a lateral bulk acoustic wave AlN-on-Si resonator in the nonlinear regime. An empirical exponential-series-based model that closely describes the phase noise in nonlinearity is presented, reflecting the increased resonator filter order and the reduced amplifier flicker-noise contribution. An oscillator using a 23MHz in-plane shear mode resonator with a quality factor of 4,000 exhibits a phase noise of −130dBc/Hz at 1KHz offset-frequency, corresponding to an improvement of about 20dB with respect to linear operation.

Bulk and Surface Thermoelastic Dissipation in Micro-Hemispherical Shell Resonators

Thermoelastic dissipation (TED) is a fundamental energy loss process, which bears concern in all microelectromechanical resonators. High aspect ratio (R/h) 3-D micro-hemispherical shell resonators (μHSRs) have exceptionally low stiffness and are sensitive to dissipation forces both internally and at their surfaces. TED in μHSRs originating in the bulk of the shell and near its surfaces due to asperities (roughness) is investigated. Rayleighs inextensional solutions for the lowest frequency vibration modes of μHSRs in the isothermal quasistatic limit result in zero contributions to energy loss from bulk TED since no volumetric strain is generated in this approximation. After relaxing Rayleighs inextensional assumption, perturbational undulations of the shells neutral surface are found to cause non-zero bulk TED. The resulting quasi-inextensional vibration modes force the shell into an approximately anti-biaxial strain state, which stretch surface asperities along one axis and compress them along the other, generating thermal flux around the base of each asperity. Closed-form approximate analytical models are developed from the geometrical and material dependencies to predict the quality factor associated with bulk and surface TED, enabling examination of these effects across scale. Fully-coupled thermoelastic finite element models verify the above results. Finally, experimental results from fabricated μHSRs are compared with the developed models.