James C. Salvia

Real-Time Temperature Compensation of MEMS Oscillators Using an Integrated Micro-Oven and a Phase-Locked Loop

We present a new temperature compensation system for microresonator-based frequency references. It consists of a phase-locked loop (PLL) 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 a constant temperature by the PLL controller, thereby achieving active temperature compensation. We show repeated real-time measurements of three 1.2-MHz prototypes that achieve a frequency stability of ± 1 ppm from -20°C to +80°C, as well as a technique to reduce steady-state frequency errors to ±0.05 ppm using multipoint calibration.

Temperature-Insensitive Composite Micromechanical Resonators

Utilizing silicon and silicon dioxides opposing temperature coefficients of Youngs modulus, composite resonators with zero linear temperature coefficient of frequency are fabricated and characterized. The resulting resonators have a quadratic temperature coefficient of frequency of approximately -20 ppb/degC2 and a tunable turnover temperature in the -55degC to 125degC range. Reduction of the temperature dependence of frequency is shown in flexural-mode resonators (700 kHz-1.3 MHz) and extensional-mode ring resonators (20 MHz). The linear temperature coefficient of Youngs modulus of silicon dioxide is extracted from measurements to be +179 ppm/degC. The composite resonators are fabricated and packaged in a CMOS-compatible wafer-scale hermetic encapsulation process. The long-term stability of the resonators is monitored for longer than six months. Although most devices exhibit less than 2 ppm frequency drift, there is evidence of dielectric charging in the silicon dioxide.

Thermal Isolation of Encapsulated MEMS Resonators

This paper presents an in-chip thermal-isolation technique for a micro-ovenized microelectromechanical-system resonator. Resonators with a microoven can be used for high-precision feedback control of temperature to compensate for the temperature dependence of resonator frequency over a wide temperature range. However, ovenization requires power consumption for heating, and the thermal time constant must be minimized for effective temperature control. This paper demonstrates an efficient local-thermal-isolation mechanism, which can reduce the power requirement to a few milliwatts and the thermal time constant to a few milliseconds. In this method, the mechanical suspension of the resonator is modified to provide thermal isolation and include an integrated resistive heater. This combination provides mechanical suspension, electrical heating, and thermal isolation in a compact structure that requires low heating power and has a small thermal time constant. A power consumption of approximately 12 mW for a 125degC temperature rise and a thermal time constant ranging from 7 to 10 ms is reported in this paper, which is orders of magnitude lower than that of commercially available ovenized quartz resonators. A CMOS-compatible wafer-scale encapsulation process is used to fabricate this device, and the thermal-isolation design is achieved without any modification to the existing resonator fabrication process.

Using the temperature dependence of resonator quality factor as a thermometer

Silicon micromechanical resonators have been designed to have a quality factor (Q) that is a strong function of temperature. This is an ideal sensor for the temperature of the resonator—it is instantaneous, consumes no power, and indicates the temperature of the resonator structure with high sensitivity. The authors present a practical implementation of an oscillator system using these resonators with a temperature resolution of better than 0.002°C. The Q(T) signal is uniquely suited for implementing feedback control of the resonator temperature, thereby stabilizing the frequency silicon micromechanical resonators and enabling their use in high-stability frequency reference applications.

Cmos-Compatible Dual-Resonator MEMS Temperature Sensor with Milli-Degree Accuracy

This paper presents a dual-resonator design which, not only enables temperature sensing of the resonators but also acts as a general-purpose temperature sensor. The frequency stability of the temperature compensated resonator depends on the accuracy with which the temperature of the resonator is measured. The dual-resonator design, described here, produces temperature-dependent beat frequency which is inherent to the resonator and thus eliminates any spatial and temporal thermal lag associated with the use of an external temperature sensor. Furthermore, this design can also be used as a CMOS-compatible digital temperature sensor. In this work, we achieved the sensor resolution of approximately 0.008degC which is comparable to that of the best CMOS temperature sensors available today.

Model and Observations of Dielectric Charge in Thermally Oxidized Silicon Resonators

This paper investigates the effects of dielectric charge on resonant frequency in thermally oxidized silicon resonators hermetically encapsulated using ¿epi-seal.¿ SiO2 coatings are effective for passive temperature compensation of resonators but make the devices more susceptible to charging-related issues. We present a theoretical model for the electromechanical effects of charge trapped in the dielectrics within the transduction gap of a resonator. Observations of resonance frequency against varying resonator bias voltage are fitted to this model in order to obtain estimates for the magnitude of the trapped oxide charge. Statistics collected from wet- and dry-oxidized devices show that lower fixed oxide charge can be expected upon dry oxidation. In addition, observations of time-varying resonator frequency indicate the presence of mobile oxide charge in a series of voltage biasing and temperature experiments.

High resolution microresonator-based digital temperature sensor

A digital temperature sensing technique using a complementary metal oxide semiconductor (CMOS) compatible encapsulated microresonator is presented. This technique leverages our ability to select the temperature dependence of the resonant frequency for micromechanical silicon resonators by adjusting the relative thickness of a SiO2 compensating layer. A dual-resonator design is described that includes a pair of resonators with differential temperature compensations so that the difference between the two resonant frequencies is a sensitive function of temperature. The authors demonstrate a temperature resolution of approximately 0.008°C for 1s averaging time, which is better than that of the best CMOS temperature sensors available today.

A High-Stability MEMS Frequency Reference

Silicon MEMS resonators with high levels of frequency stability are demonstrated in an oscillator system suitable for use as a frequency reference. The use of resonator quality factor (Q) as a temperature sensor allows us to control the temperature of the resonator with milli-degree precision, thus stabilizing the output frequency of the resonator to ~0.1 ppm. Composite Si/SiO2 resonator design has reduced the inherent frequency sensitivity of the resonator. The combination of Q(T) temperature stabilization and composite resonator design has reduced the frequency variation to ~0.01 ppm, a level that is competitive with high-performance commercial devices.

Stable Operation of MEMS Oscillators Far Above the Critical Vibration Amplitude in the Nonlinear Regime

In microelectromechanical systems resonators, nonlinear operation is feasible, but instabilities can arise if open-loop resonators operate above the critical vibration amplitude. This fact has led to a reluctance to operate resonator-based oscillators above this amplitude. This study experimentally demonstrates stable operation of these oscillators far beyond the critical vibration amplitude.

Fatigue Experiments on Single Crystal Silicon in an Oxygen-Free Environment

The fatigue lifetime of single crystal silicon (SCS) was characterized in an environment free of oxygen, humidity, and organics. Long-term (> 1010 Hz) fatigue experiments performed with smooth-walled SCS devices showed no signs of fatigue damage up to 7.5 GPa. In contrast, experiments using SCS devices with a silicon dioxide (SiO2) coating and rough sidewalls due to scalloping from deep reactive ion etching exhibited fatigue drift at 2.7 GPa and suffered from short-term (<; 1010 Hz) fatigue failure at stress levels >3 GPa. In these SCS-SiO2 experiments, the initiation of fracture occurs in the SiO2 layer. It is concluded that fatigue in this case is likely attributed to a subcritical cracking mechanism; not reaction-layer nor dislocation related. A cross-comparison with other works from literature is developed to show that packaging a pristine device in an inert environment is necessary in order to operate devices at high-stress levels.