Zhili Hao

A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability

In this paper, we report on the design, fabrication, and characterization of an in-plane mode-matched tuning-fork gyroscope (M2-TFG). The M2-TFG uses two high-quality-factor (Q) resonant flexural modes of a single crystalline silicon mi- crostructure to detect angular rate about the normal axis. Operating the device under mode-matched condition, i.e., zero-hertz frequency split between drive and sense modes, enables a Q -factor mechanical amplification in the rate sensitivity and also improves the overall noise floor and bias stability of the device. The M2 -TFG is fabricated on a silicon-on-insulator substrate using a combination of device and handle-layer silicon etching that precludes the need for any release openings on the proof-mass, thereby maximizing the mass per unit area. Experimental data indicate subdegree-per-hour Brownian noise floor with a measured Allan deviation bias instability of 0.15deg /hr for a 60-mum-thick 1.5 mm X 1.7 mm footprint M2-TFG prototype. The gyroscope exhibits an open-loop rate sensitivity of approximately 83 mV/deg/s in vacuum. [2007-0100].

VHF single crystal silicon capacitive elliptic bulk-mode disk resonators-part II: implementation and characterization

This work, the second of two parts, reports on the implementation and characterization of high-quality factor (Q) side-supported single crystal silicon (SCS) disk resonators. The resonators are fabricated on SOI substrates using a HARPSS-based fabrication process and are 3 to 18 /spl mu/m thick. They consist of a single crystal silicon resonant disk structure and trench-refilled polysilicon drive and sense electrodes. The fabricated resonators have self-aligned, ultra-narrow capacitive gaps in the order of 100 nm. Quality factors of up to 46 000 in 100 mTorr vacuum and 26000 at atmospheric pressure are exhibited by 18 /spl mu/m thick SCS disk resonators of 30 /spl mu/m in diameter, operating in their elliptical bulk-mode at /spl sim/150 MHz. Motional resistance as low as 43.3 k/spl Omega/ was measured for an 18-/spl mu/m-thick resonator with 160 nm capacitive gaps at 149.3 MHz. The measured electrostatic frequency tuning of a 3-/spl mu/m-thick device with 120 nm capacitive gaps shows a tuning slope of -2.6 ppm/V. The temperature coefficient of frequency for this resonator is also measured to be -26 ppm//spl deg/C in the temperature range from 20 to 150/spl deg/C. The measurement results coincide with the electromechanical modeling presented in Part I.

VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators-part I: design and modeling

This work, the first of two parts, presents the design and modeling of VHF single-crystal silicon (SCS) capacitive disk resonators operating in their elliptical bulk resonant mode. The disk resonators are modeled as circular thin-plates with free edge. A comprehensive derivation of the mode shapes and resonant frequencies of the in-plane vibrations of the disk structures is described using the two-dimensional (2-D) elastic theory. An equivalent mechanical model is extracted from the elliptic bulk-mode shape to predict the dynamic behavior of the disk resonators. Based on the mechanical model, the electromechanical coupling and equivalent electrical circuit parameters of the disk resonators are derived. Several considerations regarding the operation, performance, and temperature coefficient of frequency of these devices are further discussed. This model is verified in part II of this paper, which describes the implementation and characterization of the SCS capacitive disk resonators.

Support loss in micromechanical disk resonators

In light of recent efforts to implement micromechanical resonators with high-Q and high frequency, an analytical model for support loss in micromechanical disk resonators has been developed and verified with experimental results. The derived model is general and applicable to various structures and support schemes (side-supported and center-supported disks), providing significant insight to the geometrical design and choice of materials in high-Q disk resonant structures. The methodology presented in this paper can be extended to evaluate support loss in other high-frequency bulk-mode structures such as length-extensional blocks and bars.

A design methodology for a bulk-micromachined two-dimensional electrostatic torsion micromirror

This paper presents a design methodology for a two-dimensional (2-D) electrostatic torsion micromirror fabricated with bulk-micromachining technology. The theoretical models in mechanical and electrostatic fields presented here provide insights into the influences of different design parameters on micromirror performance. Parametric numerical models built in ANSYS are used to more accurately predict its performance and further refine the design parameter values derived from the theoretical models. By use of the electrical analogy method, an equivalent electrical circuit is built in PSPICE to predict the static and dynamic performance of this micromirror, with the numerical simulation results as the input parameters. The equivalent electrical circuit has been demonstrated to be a simple and powerful approach to characterize the performance of this 2-D torsion micromirror. The test results for this micromirror reveal very good agreement between experimental and numerical results, taking into account fabrication tolerances and experimental accuracies. Incorporating the fabrication tolerances of bulk-micromachining technology, this design methodology can be readily applied to performance characterization and design optimization.

Modeling air-damping effect in a bulk micromachined 2D tilt mirror

Abstract This paper proposes an analytical model for calculating air-damping effect in a bulk micromachined 2D tilt mirror. The theory for air-damping effect in this tilt mirror is derived from the nonlinear Reynold’s equation. The boundary conditions are assumed at the ambient pressure on the sidewall of the mirror cavity. The analytical solution is obtained with Green’s function for a rectangle mirror, which provides the insight of different influence of design parameters on the air-damping effect. Due to the similarity of the air damping and heat diffusion equations, the air-damping effect for arbitrary shaped mirrors is numerically simulated with a thermal-analog model, where the harmonic tilt motion of the mirror is substituted by a heat source varying with time and distance from the tilt axis. Results obtained from the experiments on prototype 2D octagon and circular tilt mirrors show excellent agreement with this air-damping model. Therefore, this model provides a simple approach to accurately calculate the air-damping effect experienced by a bulk micromachined 2D tilt mirror.

A Temperature-Compensated ZnO-on-Diamond Resonant Mass Sensor

This paper reports on the fabrication and measurement of ZnO-on-diamond length-extensional resonant mass sensors. Improved mass sensitivity due to the higher frequency of operation as well as lower motional impedance compared to capacitively-transduced sensors of the same type is demonstrated. Measured mass sensitivity of ~1 kHz/pg is shown at ~39 MHz operation frequency. Moreover, a small temperature coefficient of frequency (TCF) of -6 ppm/degC is achieved by incorporating a layer of silicon dioxide in the resonator structure.

A High-Q Length-Extensional Bulk-Modemass Sensor with Annexed Sensing Platforms

This paper presents a length-extensional bulk-mode mass sensor with annexed sensing platforms and on-chip integrated capacitive transducers. The utilization of the bulk-mode vibrations of a resonant microstructure enables higher mass sensitivity at the micro-scale and high quality factor (Q) in air. Besides overcoming technical issues inherent with cantilever-based mass sensors, the annexed sensing platforms cover a large range of mass sensitivity within a single sensor-array chip. The measured highest mass sensitivity of this device is 215Hz/pg operating at 13MHz with a Q~ 4,000 in air.

THERMOELASTIC DAMPING IN FLEXURAL-MODE RING GYROSCOPES

This paper provides a comprehensive derivation for thermoelastic damping (TED) in flexural-mode ring gyroscopes, in light of recent efforts to design high rateresolution gyroscopes. Imposing an upper limit on the attainable mechanical noise floor of a vibratory gyroscope, thermoelastic damping in a ring gyroscope is extracted from the equations of linear thermoelasticity. By assuming that it is small and therefore has negligible effect on the flexural-mode vibrations in a ring, thermoelastic damping manifests itself through temporal attenuation, where a complex frequency is used to quantitatively evaluate this damping. The exact solution to thermoelastic damping is derived and verified with experimental data in the literature. This work not only provides significant insight to the geometrical design in high-Q ring gyroscopes, but also defines their performance limit.

Detection of distributed static and dynamic loads with electrolyte-enabled distributed transducers in a polymer-based microfluidic device

This paper reports on the use of electrolyte-enabled distributed transducers in a polymer-based microfluidic device for the detection of distributed static and dynamic loads. The core of the device is a polymer rectangular microstructure integrated with electrolyte-enabled distributed transducers. Distributed loads acting on the polymer microstructure are converted to different deflections along the microstructure length, which are further translated to electrical resistance changes by electrolyte-enabled distributed transducers. Owing to the great simplicity of the device configuration, a standard polymer-based fabrication process is employed to fabricate this device. With custom-built electronic circuits and custom LabVIEW programs, fabricated devices filled with two different electrolytes, 0.1 M NaCl electrolyte and 1-ethyl-3-methylimidazolium dicyanamide electrolyte, are characterized, demonstrating the capability of detecting distributed static and dynamic loads with a single device. As a result, the polymer-based microfluidic device presented in this paper is promising for offering the capability of detecting distributed static and dynamic loads in biomedical/surgical, manufacturing and robotics applications.