Raviv Perahia

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.

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.

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.

UHF piezoelectric quartz mems magnetometers based on acoustic coupling of flexural and thickness shear modes

This paper reports the design, fabrication, and characterization of piezoelectric quartz MEMS magnetometers based on acoustic coupling between resonance modes. The magnetic sensors described herein employ a novel transduction scheme to upconvert the desired near-DC magnetic field signal (using the fundamental flexural mode) onto frequency modulated (FM) sidebands of the primary quartz thickness shear (TS) oscillation at frequencies above 500 MHz. First-generation devices exhibit flexural and TS resonances at 2.77 kHz and at 583.31 MHz, respectively, and magnetic sensitivity of 63.6 V/T was measured with an AC loop current of 9.2 mA. This novel sensing method, intended for electronic compassing, illuminates the interactions between low and high frequency acoustic modes within resonant devices.