Yu Qiao Qu

Verification of the phase-noise model for MEMS oscillators operating in the nonlinear regime

We experimentally verify the phase-noise model for oscillators operating in a nonlinear regime by testing a micromechanical resonator-based oscillator (MEMS oscillator). Operation of oscillators in the nonlinear regime had been believed to induce instability [1] - a belief we have demonstrated to be mistaken [2]. As a result of this misunderstanding, little study has been devoted to the phase-noise performance of oscillators in the nonlinear regime. In this study, we compare measurements of the phase noise of MEMS oscillators far into the nonlinear regime and compare them with a recent prediction [3]. This paper provides confirmation that low phase-noise performance is possible in the nonlinear regime, and confirms that models can be used to predict and optimize performance.

Phase Lock Loop based Temperature Compensation for MEMS Oscillators

We present a new temperature compensation system for microresonator based frequency references. It consists of a phase lock loop whose inputs are derived from two microresonators with different temperature coefficients of frequency. The resonators are suspended within an encapsulated cavity and are heated to constant temperature by the phase lock loop controller, thereby achieving active temperature compensation. We show repeated real-time measurements of two prototypes which achieve frequency stability of better than ±1 ppm from -20 °C to + 80°C without calibration look-up tables and ±0.05 ppm with calibration.

Nonlinearity of hermetically encapsulated high-Q double balanced breathe-mode ring resonator

We present a hermetically encapsulated breathe-mode ring resonator with very high quality factor (∼473,000) and frequency at 10.65 MHz and 13.29 MHz. The resonators nonlinear behavior is experimentally characterized and theoretically analyzed for the first time. The maximum current handling is measured and verified using two different methods. We find that material nonlinearity (nonlinear Youngs modulus of silicon) limits the devices maximum output current. The theoretical analysis presented here is valid for any type of MEMS resonators, and the results provide guidance for future design of high current handling devices.

High-cyclic fatigue experiments of single crystal silicon in an oxygen-free environment

We report on the first study of fatigue in single crystal silicon MEMS resonators within an extremely clean and controlled environment using the ‘epi-seal’ encapsulation technology. This packaging technology provides a unique opportunity to investigate controversial issues in silicon fatigue since the devices are not exposed to air, oxygen, organics, or other residues that might complicate the initiation and observation of fatigue. We have conducted fatigue experiments on 10 devices over 1010 actuation cycles with various dynamic loadings ranging from 1.0 to 1.9 GPa at 29°C and from 0.2 to 1.1 GPa at 280°C. No fatigue related phenomena have been observed under these experimental conditions.

A novel characterization method for temperature compensation of composite resonators

We develop an efficient characterization method for temperature compensated micromechanical resonators by employing empirical data analysis with an a priori model. We have previously demonstrated that electrostatic-tuning of a composite resonator with an accurate lookup table can achieve a temperature stability of ±3.2 ppm, but this characterization method was not suitable for commercialization since it required measurements at every temperature point of interest. This paper presents a technique that can reduce the number of temperature points for calibration by 67% without compromising accuracy. We also demonstrate a one-point calibration method with which ±7 ppm calibration error can be achieved using a single temperature point measurement.

Motional impedance of resonators in the nonlinear regime

We developed a model for the motional impedance Zm of electrostatic resonators that operate in a nonlinear regime. The model predicts that the Zm at resonance has the same expression as it has in the linear case. In addition, we developed a new measurement setup, which is based on a variable-phase feedback circuit. This setup enables the measurement of Zm at operating points that are unobservable with a conventional impedance analyzer measurement. The estimation based on our model matches the measurement with errors less than 10% in the worst case.

Using encapsulated MEMS resonators to measure evolution in thin film stress

Encapsulated resonators can offer excellent long-term frequency stability, because the encapsulation provides protection from external environmental variations. Encapsulated double-anchored flexural-mode resonators exhibit a sensitive coupling between changes in stresses applied to the chip and changes in the resonant frequency while still isolated from other external variations. In this work, this sensitivity is exploited to observe stress relaxation in thin films deposited on the outside of the encapsulated resonator. Because of the high sensitivity to stress, and the insensitivity to other factors, these devices provide the first opportunity to observe film stress relaxation with nano-strain resolution. We have begun a study of film stress relaxation in LPCVD and TEOS oxides and aluminum-all of which are commonly used as structural layers in MEMS devices. Theoretical analysis, finite element analysis (FEA), as well as preliminary data on different film materials are presented herein.

Influence of the temperature dependent A-f effect on the design and performance of oscillators

In this work, we develop a theoretical explanation for the temperature dependence of the nonlinear amplitude-frequency (A-f) effect in micromechanical resonators. Using this theory, we explain the discrepancy in frequency-temperature (f-T) characteristics between open-loop observation and closed-loop measurements. We show how the temperature dependence of the A-f effect introduces bias voltage dependence in the f-T characteristics of an oscillator system. Based upon this understanding, we present a new method to remove the temperature dependence of the A-f effect from an oscillator system, thereby eliminating the bias voltage (Vbias) dependency, and enabling predictable f-T characteristics.

Influence of the A-F effect on the temperature stability of silicon micromechanical resonators

Micromechanical resonators (MEMS resonators) often show a discrepancy between the frequency-temperature (ƒ-T) characteristics they have in open-loop and closed-loop measurements. We show that this discrepancy is due to the nonlinear amplitude-frequency (A-ƒ) effect: the quality factor (Q) can increase by more than a factor of 2 when the resonators go from a high temperature to a low temperature; simple oscillators thus allow the resonator amplitude to change with temperature; then, the A-ƒ effect becomes temperature-dependent, causing the discrepancy. We also show how the discrepancy adversely affects the temperature stability of single-crystal-silicon (SCS) resonators and demonstrate a new closed-loop system that improves the stability by removing the discrepancy.