Yushi Yang

Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

Temperature Dependence of the Elastic Constants of Doped Silicon

Resonators fabricated in heavily doped silicon have been noted to have a reduced frequency-temperature dependence compared with lightly doped silicon. The resonant frequency of silicon microelectromechanical systems (MEMS) resonators is largely governed by the materials elastic properties, which are known to depend on doping. In this paper, a suite of different types and orientations of resonators were used to extract the first- and second-order temperature dependences of the elastic constants of p-doped silicon up to 1.7e20 cm-3, and n-doped up to 6.6e19 cm-3 . It is shown that these temperature-dependent elastic constants may be used in finite element analysis to predict the frequency-temperature dependence of similarly doped silicon resonators.

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.

100K Q-factor toroidal ring gyroscope implemented in wafer-level epitaxial silicon encapsulation process

This paper reports a new type of degenerate mode gyroscope with measured Q-factor of > 100,000 on both modes at a compact size of 1760 μm diameter. The toroidal ring gyroscope consists of an outer anchor ring, concentric rings nested inside the anchor ring and an electrode assembly at the inner core. Current implementation uses n = 3 wineglass mode, which is inherently robust to fabrication asymmetries. Devices were fabricated using high-temperature, ultra-clean epitaxial silicon encapsulation (EpiSeal) process. Over the 4 devices tested, lowest as fabricated frequency split was found to be 8.5 Hz (122 ppm) with a mean of 21 Hz (Δf/f = 300 ppm). Further electrostatic tuning brought the frequency split below 100 mHz (<; 2 ppm). Whole angle mechanization and pattern angle was demonstrated using a high speed DSP control system. Characterization of the gyro performance using force-rebalance mechanization revealed ARW of 0.047°/√hr and an in-run bias stability of 0.65 deg/hr. Due to the high Q-factor and robust support structure, the device can potentially be instrumented in whole angle mechanization for applications which require high rate sensitivity and robustness to g-forces.

Encapsulated high frequency (235 kHz), high-Q (100 k) disk resonator gyroscope with electrostatic parametric pump

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 〈100〉 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 100 mHz. 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 8.8× 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× and 1.5×, respectively.

Lorentz force magnetometer using a micromechanical oscillator

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 magnetometers 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.

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.

Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response

We present a technique for estimation of the model parameters for a single-mode vibration of symmetric micromechanical resonators, including the coefficients of conservative and dissipative nonlinearities. The nonlinearities result in an amplitude-dependent frequency and a nonexponential decay, which are characterized from the ringdown response. An analysis of the amplitude of the ringdown response allows one to estimate the linear damping constant and the dissipative nonlinearity, and the zero-crossing points in the ringdown measurement can be used for characterization of the linear natural frequency and the Duffing and quintic nonlinearities of the vibrational mode, which arise from a combination of mechanical and electrostatic effects.

Multifunctional Integrated Sensors for Multiparameter Monitoring Applications

We present multifunctional integrated sensors (MFISES) that combine temperature, humidity, pressure, air speed, chemical gas, magnetic, and acceleration sensing on a single 2-mm × 2-mm die. We fabricate the MFISES in a wafer scale encapsulation process to hermetically seal the sensor functions with moving parts at low vacuum, and then surface micromachine the environmental sensors on top of the sealed layer. The encapsulation process provides very stable conditions for the pressure, magnetic, and acceleration sensors, and enables the deployment of the MFISES in dynamic environmental conditions without special postprocess packaging. We quantify the performance requirements for sensor applications in weather stations, indoor climate control, road activity monitoring, chemical sensing, and parking monitoring. We compare the performance of the MFISES to the application requirements to demonstrate the utility of an integrated sensor in a wide range of applications.

Single-structure 3-axis lorentz force magnetometer with sub-30 nT/√HZ resolution

This work demonstrates a 3-axis Lorentz force magnetometer for electronic compass purposes. The magnetometer measures magnetic flux in 3 axes using a single structure. With 1 mW power consumption, the sensor achieves sub-30 nT/√Hz resolution in each of the 3 axes. Compared to the 3-axis Hall sensors currently used in smartphones, the 3-axis magnetometer shown here has the advantages of 10× lower noise floor and the ability to be co-fabricated with MEMS inertial sensors.