Deborah J. Kirby

A MEMS-based quartz resonator technology for GHz applications

We report on the development of a new MEMS quartz resonator technology that allows for the processing and integration of VHF to UHF high-Q oscillators and filters with high-speed silicon or III-V electronics. The paper describes the successful demonstration of new wafer bonding and dry plasma etching processes that make quartz-MEMS technology possible. We present impedance, Q, and temperature sensitivity data along with comparison to 3D harmonic and thermal analysis of VHF-UHF resonators. We also show Coventor simulation data of our first two- and three-pole monolithic crystal filter designs as well as a filter array layout which facilitates integration with front-end RF electronics and switches. Finally, we demonstrate a mechanical tuning technique for our resonators utilizing focused-ion-beam (FIB) technology.

Nonlinear UHF quartz MEMS oscillator with phase noise reduction

Stable local oscillators with low phase noise are extremely important elements in high performance communication and navigation systems. We present the development of compact UHF-band frequency sources capable of maintaining low phase noise for handheld portable systems. We also explored nonlinearity in MEMS resonators and attempted to use nonlinear dynamics to enhance phase noise performance. Using the quartz MEMS technology, we have thus far demonstrated a 635 MHz oscillator with -112 dBc/Hz phase noise at 1 kHz offset frequency. The controlled oscillation of this nonlinear Duffing resonator in a closed-loop system with improved phase noise is described.

Optimizing UHF quartz MEMs resonators for high thermal stability

A 1 GHz AT-cut quartz thickness shear mode resonator is modeled for the first time with thermally induced bonding stresses and their effect on the device frequency-temperature (f-T) characteristic. Without the details of the bonding configuration, modeling indicates the f-T characteristic slightly rotates as a function of the change in stiffness of a simplified absorbing mount. However, if details of the bonding configuration are included, our modeling predicts the potential for a significant distortion in the f-T curve. High or varying stress over temperature in the device active region is found to lead to an undesirable increase in the f-T slope. The origin of the active region stress can be varied, but in practice it frequently originates from a temperature dependent bonding stress, or from fabrication steps such as metal depositions. In this paper we highlight the magnitude of the thermal stress effect on the f-T curve, and offer design methods that mitigate the thermally induced bonding stress by de-coupling the active resonator area from high stress regions of the quartz device.

UHF quartz MEMS oscillators for dynamics-based system enhancements

Processes for fabricating full wafers of UHF quartz MEMS oscillators bonded to Si have been developed at HRL over the past several years. These devices have shown state-of-the-art noise and stability along with extremely small vacuum packaged die size of less than 3 mm. An interesting by-product of the high frequency, small size, and wafer-scale fabrication of these devices is that several novel dynamics-based enhancements can be considered. These include the use of nonlinear dynamics for reducing oscillator phase noise at CMOS capable voltages and co-integration with more complex structures for sensing vibration and serving as a local timing reference for reducing thermally-induced sensor drifts. Several of these novel concepts made possible by wafer-scale MEMS-based processing will be reviewed.

Nonlinear behavior of an UHF quartz resonator in an oscillating system

Characterization of a quartz resonator operating at 553 MHz in a closed loop oscillating system has been performed under various drive levels to characterize its nonlinear behavior. The voltage and current were measured across the resonator using differential active probes and used to calculate the magnitude of the admittance under drive. Our results show that nonlinear resonator operation widens the bandwidth of low phase noise operation. At the low frequency end of the operating range, where overall phase noise is degraded, phase noise improvement is ~ 20dB. However, the overall phase noise levels do not improve significantly over the linear case.

On the acceleration sensitivity and its active reduction by edge electrodes in at-cut Quartz resonators

Incremental piezoelectric equations for small vibrations superposed on initial deformations are presented. The equations are implemented in COMSOL finite element models (FEA). Equations are validated by comparing the results for the force sensitivity coefficient Kf of a circular quartz plate subjected to a pair of diametrical forces with measured data. The model results show a consistent trend with the experimental results, and the relative difference between our FEA results and Ballatos measured result is about 13%. A detailed study of the acceleration sensitivity of a rectangular AT-cut quartz plate is presented. The plate resonator is fixed along one edge as a cantilever. For AT-cut quartz resonators with the crystal digonal X-axis perpendicular to plate X-axis, the in-plane acceleration sensitivity is found to be negligible compared with the out-of-plane (Y-axis) acceleration sensitivity. For AT-cut quartz resonators with the crystal digonal X-axis parallel to plate X-axis, the Y-axis acceleration sensitivity is found to be rectified, that is the fractional change in frequency is positive with respect to both positive and negative Y-axis accelerations. The Y-axis acceleration sensitivity is small in comparison with the in-plane acceleration sensitivity for small body forces. However, for large body forces, the Y-axis acceleration sensitivity dominates because it increases nonlinearly with the Y-axis acceleration. The resonator rectified acceleration sensitivity is confirmed by phase noise measurements. For reduced acceleration sensitivity, two pairs of electrodes along the plate edges reduce the bending of the plate resonator and subsequently reduce acceleration sensitivity. We present a new method using these edge electrodes in which a dc bias field is employed to control the resonant frequency of resonator subjected to g body forces. A dc bias field with an appropriate dc bias voltage could potentially yield a reduction of acceleration sensitivity in Y-axis direction of about two orders of magnitude.

Modeling approach to analyze bonding stress in UHF quartz resonators

We have observed a phenomenon of high precision MEMS quartz resonators to change their frequency-temperature characteristics when they are mounted or bonded onto a substrate. This is due to the difference in thermal expansion coefficients between the quartz and substrate. When the temperature is changed, the mounting points between the quartz resonator and substrate become a source of mounting stress/strain in the resonator. We have defined a zero-stress temperature as the temperature at which the mounting stress is zero. We could determine the zero-stress temperature from the aging data of the resonator. We have derived a set of incremental equations for small vibrations superposed on mounting stress/strain that included the zero-stress temperature. The equations were employed in a COMSOL model of a UHF quartz resonator. The resonator frequency versus temperature profile was calculated by the change in eigenfrequency of the thickness shear mode as a function of the temperature. The eigenvalue problem of the resonator was modeled in COMSOL. The frequency-temperature curve of the resonator was shown to rotate counter-clockwise with the mounting stiffness and zero-stress temperature with respect to the frequency-temperature curve of the same resonator with no bonding stress. Furthermore the frequency-temperature curve of a bonded resonator will intersect the frequency-temperature curve of the same resonator without bonding stress at the zero-stress temperature.

MEMS-Based UHF Monolithic Crystal Filters for Integrated RF Circuits

We report our work in developing microelectromechanical systems (MEMS)-based Ultra High Frequency (UHF) AT-cut quartz monolithic crystal filters operating between 350 and 400 MHz for integration with Si electronics for highly compact Radio Frequency (RF) front-end electronics. Our narrow bandwidth (0.2%) high Q filters have measured insertion losses of -2 dB with temperature stability of roughly 50 ppm over a temperature range of 10°- 80°C. Wafer-level optical metrology and ion milling techniques have been developed to provide enhanced accuracy of the filter center frequency and resonator parameters for optimized performance and improved yields.

A 995MHz fundamental nonlinear quartz MEMS oscillator

A quartz resonator operating at 995 MHz in the fundamental mode has been characterized in a closed loop oscillating system under different drive levels to determine its nonlinear behavior and optimum phase noise performance. The best phase noise achieved was -106 dBc/Hz at a 1 kHz offset frequency. The same quartz technology was used to build VCXOs in both the Colpitts and Pierce configurations at several frequencies above 650 MHz. The lowest phase noise level achieved in the Colpitts configuration operating at 705 MHz is -111 dBc/Hz at a 1 kHz offset frequency while a Pierce Oscillator operating at 662 MHz achieved a phase noise of -112.8 dBc/Hz at the same offset. Power consumption in these VCOs is typically on the order of 30-90 mW.

Electric gradient force drive mechanism for novel microscale all-dielectric gyroscope

MEMS vibratory gyroscopes have recently shown great promise in the field of micro-scale position, navigation, and timing (μPNT), yet their performance often falls short of navigation grade due to losses in the vibratory structure. This paper reports a novel drive mechanism used to excite a cylindrical, all-dielectric micro-shell gyroscope structure. The drive mechanism operates by generating a gradient electric field force from a set of interdigitated electrodes placed adjacent to the gyroscope structure. This novel transduction mechanism enables mechanical actuation of a pristine dielectric structure without the need for direct metallization which could degrade the quality factor (Q) and mechanical performance. Mode spectroscopy in the range of 5-50 kHz is demonstrated with mode amplitudes as large as 0.3 μm for a 10 V drive signal. Quality factors of 12,000 have been measured. Design, fabrication, and experimental demonstration are presented.