High-Qbulk-mode SOI square resonators with straight-beam anchors

Abstract

In this paper, the performance of 6.35 MHz Lamé-mode square resonators with different dimensions of straight-beam anchor supports is presented, with quality factor values exceeding one million in ambient pressures as high as 150 Pa. A maximum Q value of 1.70 million was experimentally measured for some of the square resonators at a vacuum pressure of 36 µTorr. The Q values of square resonators were relatively independent of pressure at levels below 100 Pa, which suggests that Q is pressure limited due to air damping only when pressures become higher than 100 Pa. Dimensions of straight-beam anchors placed at the four corners of the square resonator lead to tradeoffs among achievable Q, power handling capabilities and motional resistance. Longer anchor beams generally provide good signal-to-noise performance of a square resonator at lower dc bias; however, the resonator goes into the nonlinear regime at lower ac–dc drive amplitudes, which means reduced power handling capability. The benefit of shorter anchors is that the resonator is able to operate in a linear mode under high drive conditions. Depending on the type of application, anchor dimensions can be chosen such that the resonator's performance is optimal in terms of a quality factor, motional resistance and power handling. The resonators were fabricated using the silicon-on-insulator multi-user MEMS process from MEMSCAP.

Inhomogeneous mechanical losses in micro-oscillators with high reflectivity coating

“…The higher mass is compensated by the possibility to manage high power at low temperatures, thanks to the favorable geometric factor (thicker connectors) and the high thermal conductivity of silicon at cryogenic temperature [40]. With such design, it is important to control the mechanical dissipation in the coating layers, in order to exploit the potentially very high Q of silicon oscillators [41,42]. Here we report on the losses measured in a micro oscillator covered by a highly reflective coating, and discriminate, by the use of Finite Element analysis (FEM), the contribution of thermoelastic dissipation and coating losses.…”

Design strategies for controlling damping in micromechanical and nanomechanical resonators

“…The dissipation due to all components associated with the supporting frame and package is collectively called boundary damping. There are three main mechanisms of boundary damping: (i) support losses or anchor losses due to the radiation of elastic waves (or stress waves) from the resonator into the supporting frame [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]; (ii) microsliding at the interfaces between the resonator and supporting frame, and between the supporting frame and package [61]; and (iii) viscoelasticity in the gels and adhesives used to bond the supporting frame to the package [9]. (The term clamping loss is frequently encountered in the literature.…”

“…Support losses can be reduced by using analytical and numerical models for stresswave radiation to guide the selection of materials, structures, dimensions, modes, and frequencies. Alternately, the generation and propagation of elastic waves can be disrupted by contacting the resonator at its nodal points using anchors or tethers [26][27][28][29][30][31] and incorporating phononic band-gap structures [32][33][34][35], acoustic reflectors [36,37], and vibration isolators [38,39]. In each case, well-established models from vibrations and elasticity are available to guide design.…”

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

“…For a bulk-mode resonator operating in high vacuum, it is demonstrated that anchor loss is the dominant energy-loss mechanism and limits the quality factor [25]. This loss mechanism strongly depends on the side-support beam dimensions, and it can be reduced by mechanically isolating the support beams from the substrate and optimally designing their dimensions [26,27]. However, in micromechanical ring resonators, resonant pull-in condition limits the maximum allowable quality factor and minimum initial gap spacing as shown in Figure 6.…”