Ian B. Flader

Mode-Matching of Wineglass Mode Disk Resonator Gyroscope in (100) Single Crystal Silicon

In this paper, we present four design methods to overcome (100) silicon crystalline anisotropy and achieve mode-matching in wineglass-mode disk resonator gyroscope (DRG). These methods were validated through experimental characterization of more than 145 different devices that arose from simulations. With the proposed methods, the frequency split of the 250-kHz DRG wineglass modes in (100) silicon was reduced from >10 kHz to as low as 96 Hz (<;0.04% of 250-kHz resonant frequency) without any electrostatic tuning. Perfect mode-matching is then achieved using electrostatic tuning. Mode-matching was maintained within ±10 Hz over a temperature range from -20 °C to 80 °C. The temperature dependence of quality factor is also discussed in this paper. These results allow for the development of high-performance miniature DRGs tuned for degenerate wineglass mode operation from high-quality crystalline silicon material.

A Unified Epi-Seal Process for Fabrication of High-Stability Microelectromechanical Devices

This paper presents a thin-film wafer-level encapsulation process based on an epitaxial deposition seal that incorporates both narrow and wide lateral transduction gaps (0.7-50 μm), both in-plane and out-of-plane electrodes, and does not require release etch-holes in the device layer. Resonant structures fabricated in this process demonstrate high-quality factors ( f × Q products of up to 2.27e + 13 Hz) and exceptional stability (±18 ppb over one month) with no obvious aging trends. Studies on cavity pressure indicate that vacuum levels better than 0.1 Pa can be achieved after final encapsulation, thus reducing gas damping for high surface-to-volume devices. The vast diversity of functioning devices built in this process demonstrates the potential for combinations of high-performance MEMS devices in a single process and/or single chip.

Nonlinearity of Degenerately Doped Bulk-Mode Silicon MEMS Resonators

We present an experimental study of conservative nonlinearities in bulk acoustic mode (bulk-mode) silicon MEMS resonators with degenerate doping. Three types of bulk acoustic mode resonators oriented in (110) and (100) silicon crystalline directions are used to analyze both linear and nonlinear elastic behavior of silicon with p- (N ≅ 4.19e + 18 to 1.63e + 20 cm-3) and n-type (N ≅ 1.58e + 18 to 5.91e + 19 cm-3) doping. For accurate characterization of the amplitude-dependent nonlinear stiffness constant, we employ two methods: amplitude-frequency response and ringdown measurement. Experimental results show that the nonlinear behavior of these resonators is dominated by material-dependent mechanical nonlinearities and strongly depends on the doping type and crystal orientation. These results are useful for understanding the material-induced nonlinear properties of doped silicon and design of MEMS resonators with desired dynamic behavior, and may provide a new avenue for tailoring resonator response characteristics.

In-situ ovenization of Lamé-mode silicon resonators for temperature compensation

This paper reports an inside-encapsulation ovenization method for the temperature compensation of Lamé-mode epi-sealed silicon resonators. With this method, the square Lamé-mode resonator itself acts both as a thermometer and a heater, which allows for simultaneous in situ sensing and control of the operating temperature. In this device, only the resonating element is heated, reducing the power consumption and the thermal time constant, relative to approaches which control the temperature of an entire MEMS chip or system. Preliminary results of real-time frequency compensation achieve a frequency stability of ~5ppm over -40~+80°C without the need for sophisticated control schemes.

Epitaxially-encapsulated quad mass gyroscope with nonlinearity compensation

We present an epitaxially-encapsulated 2×2 mm2 quad-mass gyroscope (QMG). Relative to the earlier QMG which measured 8×8 mm2 and required an external vacuum package and getter [1], this device is 16x smaller in area and is vacuum-sealed at the wafer-level. Due to the devices small size, high quality factor (Q) and large oscillation amplitude are required to achieve low noise. However, the devices high Q (85,000) makes it highly sensitive to mechanical nonlinearity, resulting in amplitude-frequency dependence and instability of the oscillator loop at large amplitudes. To overcome these problems, we demonstrate electrostatic compensation of the mechanical nonlinearity, enabling 10x greater amplitude and therefore scale factor (SF). Together with closed-loop amplitude control and quadrature compensation, this enables angle-random walk of 0.42 mdeg/s/VHz, comparable to the best QMG published to date. Closed-loop amplitude control and quadrature null are used to achieve a bias instability of 1.6 deg/hr.

The long path from MEMS resonators to timing products

Research on MEMS Resonators began over 50 years ago. In just the last 10 years, there has been a series of important technological developments, and (finally!) success at commercialization. The presentation will highlight some key milestones along this path, describe some of the critical technology steps, and outline some of the important non-technological events within SiTime - all of these factors contributed to the successful outcome.

Ovenized dual-mode clock (ODMC) based on highly doped single crystal silicon resonators

This work demonstrates, for the first time, ovenization of a fully-encapsulated dual-mode silicon MEMS resonator operational over a large ambient temperature range. We maintain a localized, elevated operating temperature by utilizing the temperature coefficient of frequency (TCf) difference between two excitation modes of the same resonant body as a thermometer, and by integrating a micro-oven in the encapsulation layer. Preliminary results of real-time compensation demonstrate a stability of ±250ppb of the in-plane Lamé-mode frequency over -20°C to 80°C.

A unified epi-seal process for resonators and inertial sensors

A thin-film wafer-level encapsulation process which incorporates both narrow (0.7 μm) and wide (>50 μm) lateral transduction gaps, in-plane and out-of-plane electrodes, and does not require release etch-holes is presented. High stability, high quality factor (Q) resonant devices as well as inertial sensors are fabricated in the process. The great diversity of functioning devices built in this process demonstrates the potential for combinations of high-performance MEMS devices in a single process and even in single chips.

Q-factor optimization in disk resonator gyroscopes via geometric parameterization

We present an assortment of geometrically parameterized disk resonator gyroscopes (DRGs) individually designed for resonant frequency (f) and quality factor (Q). This work demonstrates accurate FEM-based predictions of Q for fabricated devices, and geometric optimizations that significantly improve this key performance metric for the DRG. Measurements on suites of fabricated devices confirm that losses are dominated by thermoelastic dissipation (TED). Qted is shown to account for 64-80% of the total energy dissipation. The temperature dependence of Q is also used to confirm and quantify the presence of pressure damping in the fabricated devices. At frequencies near 300 kHz, we show that Q can be increased by a factor of 2.6 and demonstrate feasibility of geometric/topological optimization of the fabricated devices with the aid of finite element software.

Epitaxially encapsulated resonant accelerometer with an on-chip micro-oven

This paper reports, for the first time, on-chip ovenization of an epitaxially encapsulated resonant accelerometer to improve the stability of scale factor and bias. A double-ended tuning fork (DETF) resonator that shares the anchor with the sensing resonators is used to measure the device temperature. The measured temperature is maintained at a fixed set point using an on-chip silicon heater defined in the encapsulation layer. Preliminary results show significant improvement beyond the devices intrinsic passive temperature compensation. Over the temperature range from −20°C to 80°C, the 0g bias error is reduced by a factor of three, and the scale factor stability is improved by over an order of magnitude.