Investigation of Energy Dissipation in Low Frequency Vibratory Mems Demonstrating a Resonator with 25 Minutes Time Constant

We report a conventionally batch micromachined silicon tuning fork MEMS resonator, with ultra-low energy dissipation. The dissipation time constant of 25 minutes was experimentally achieved by using a test device with natural frequency of 570 Hz and Quality factor of 2.7 million. This low level of energy dissipation was accomplished through identification and minimization of the dominating dissipation mechanisms. Results of the experimental investigation lead to the formulation of practical design guidelines and tradeoffs for low frequency resonant devices. INTRODUCTION Dissipation of energy is a fundamental characteristic of a resonance system which defines a limit of performance. For some devices, such as 1-D oscillators, frequency multiplied by Q-factor, fQ, is the figure of merit [1]. For others, such as Coriolis Vibratory Gyroscopes (CVG), the dissipation time constant, , is a parameter of interest. Macro-scale CVGs with size on the order of several inches can achieve a dissipation time constant of tens of minutes and Q-factor in the tens of millions, with bias instability on the order of 10 deg/hr [2]. Additionally, a high dissipation time constant provides advantageous mechanizations, such as continuous whole angle operation uninterrupted by power failures (i.e., electromagnetic impulse), which is not possible using optical devices, such as Fiber Optic Gyroscopes (FOGs) and Ring Laser Gyroscopes (RLGs). Low dissipation vibratory systems, especially systems with a high time constant, are generally associated with large spatial dimensions. It is often assumed that conventionally batch fabricated silicon MEMS resonators are not suitable for applications where large dissipation time is necessary due to their small mobile masses. However, state of the art MEMS devices have demonstrated time constants up to three minutes in recent reports, [3], [4]. Unlike mature RF resonators, there is a gap in the literature in the field of low dissipation micromachined vibratory gyroscopes. In this paper, an ultra-low dissipation resonator is reported and used in an experimental study of design trade-offs and formulation of practical design guidelines. The fabricated prototype has demonstrated a time constant of ~ 1/2 hour and Q-factor of 2.7 million at a natural frequency of 570 Hz, Fig. 1, as well as a high dissipation time constant and high value of Q-factor throughout a wide temperature range, from -40 C to 100 C. For low frequency resonators there are five primary energy loss mechanisms. In order of importance, these are: viscous damping, support (anchor) loss, loss due to structural asymmetry, ThermoElastic Damping (TED), and electrical damping. These mechanisms comprise the total Q-factor of the device [5]: Other El TED Asym Anchor Viscous total Q Q Q Q Q Q Q 1 1 1 1 1 1 1       . (1) Throughout this paper, each of these five dissipation mechanisms are systematically investigated, and the impact of each is quantitatively assessed. It is also experimentally validated that any additional damping mechanisms, QOther, are negligibly small for low frequency resonators. TEST-BED RESONATOR To support this theoretical investigation, a specially designed resonator was fabricated. This resonator was designed to minimize energy dissipation from viscous damping, thermoelastic damping, and support loss. With these three mechanisms sufficiently reduced, a detailed investigation into electrical damping of the detection system is conducted. To alleviate support losses, a tuning fork architecture was employed. The proposed tuning fork resonator comprises of two coupled tines (4 mm by 4 mm each), each driven in opposite directions, or anti-phase resonance. Each tine includes differential lateral comb electrodes for capacitive detection, and differential lateral comb electrodes for electrostatic excitation of the anti-phase mode. The anti-phase mode of resonator minimizes the net reaction force applied to the substrate, providing both rejection of commonmode external accelerations, and reduction of energy dissipation from the vibrating structure. Any in-phase component of motion is due to fabrication imperfection and is considered parasitic; to reduce undesirable in-phase motion the design includes nondifferential parallel plate capacitors for dynamic balancing by modulation of stiffness through the negative electrostatic spring effect, Fig. 2. Also, the parallel plate electrodes allow for the simultaneous and independent tuning of operational (resonance) frequency and Q-factor through electrical damping. The fabrication of the prototype was performed using an in-house, wafer-level, single-mask process. Devices were fabricated using Silicon-onInsulator (SOI) wafers with a 100 m single crystalline silicon device layer, a 5 m buried oxide layer, and a 500 m handle wafer, Fig. 2. After wafer fabrication and dicing, sensors were attached to a ceramic DIP-24 package through the use of a UniTemp RSS-160 solder reflow system, and a low-stress die attachment procedure. The attachment was made using an eutectic solder comprised of 80 % gold and 20 % tin. Eutectic Au/Sn solder was used in this process for three main reasons: 1) it is a low outgassing material, well suited for vacuum sealing with getter, 2) it creates a strong, rigid attachment to the package, preventing spurious degrees of freedom, and 3) it is capable of surviving high temperatures. Due to mismatches in the thermal properties between 9781940470016/HH2014/$25©2014TRF 76 Solid-State Sensors, Actuators and Microsystems Workshop Hilton Head Island, South Carolina, June 8-12, 2014 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 4 10 6 10 8 10 10 Frequency, Hz Q T E D 1 m 00 m 10 m Proposed design Figure 3: Thermoelastic Q-factor versus frequency for silicon springs of three different widths (1, 10, and 100 m). Resonator 2 Excitation Tuning Detection Tuning Excitation Excitation Tuning Detection Tuning Excitation S u sp en si o n b ea m s