Higher-order dielectrically transduced bulk-mode ring resonator with low motional resistance

Abstract

This paper reports internal dielectric transduction of the 41 st radial bulk-mode of a ring resonator at 2.79GHz with a quality factor exceeding 11,500 in air. The transducer electrodes are integrated within the vibrating structure in a dense serpentine pattern, with the dielectric-filled gaps strategically placed on the nodal lines to excite the 41 st order bulk radial mode. The serpentine dielectric transduction results in a low motional resistance of less than 500Ω, which can be detected by direct two-port transmission measurements. The "notched" ring design allows for anchoring this resonator at the center nodal line of the ring, resulting in higher Q and lower motional resistance. This resonator is fabricated by a double nanogap process, where 30nm silicon nitride sidewall layers are formed using a combination of optically defined trenches and deposition of a high-κ dielectric followed by a doped polysilicon layer.

Mode- And Direction-Dependent Akhiezer Damping in Single-Crystal Silicon Resonators

“…3 shows the room temperature f × Q product as a function of the mechanical resonant frequency for the WE, SE, CE, and Lamé modes of a [100]-oriented intrinsic silicon resonator evaluated using the expression in Eq. ( 7) along with Woodruff's result for reference and a number of experimental results from silicon resonators in the literature [7][8][9][10][15][16][17][18][19][20][21][22][23][24]. Due to the quadratic dependence of Q on resonant frequency, the curves remain constant up to ∼20.5 GHz, corresponding to the condition Ωτ = 1.…”

“…This expression is often used to make an order of magnitude prediction of the internal friction limit for a given material [6]. Modern devices, however, approach and even exceed Woodruff's oversimplified limit [7][8][9][10], indicating a need for a more predictive, analytical model that can be evaluated in a straightforward manner using known material constants and reliably compared with experimental results.…”

Mode- and Direction-Dependent Mechanical Energy Dissipation in Single-Crystal Resonators due to Anharmonic Phonon-Phonon Scattering

“…The most accurate approach would be to use the branch-specific τ i , which depend on both direction and polarization; however, lack of a complete set of experimental values for these time constants prohibits calculation in this way. Figure 3 shows the room temperature f × Q product as a function of the mechanical resonant frequency for the WE, SE, CE and Lamé modes of a resonator with edges oriented along the [100] directions in intrinsic silicon evaluated using the expression in equation 24 along with Woodruff's result for reference and a number of experimental results from silicon resonators in the literature [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. As expected, given the quadratic dependence of Q on resonant frequency in the Zener model, the curves remain constant up to ∼ 20.5 GHz, corresponding to the condition Ωτ = 1.…”

“…. The dashed line is Woodruff's estimation of the Akhiezer damping limit and the points are experimental results from high quality factor resonators surveyed from the literature [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. A number of recently fabricated resonators have quality factors that exceed Woodruff's limit, indicating that the simplified, isotropic expression does not provide sufficient accuracy.…”

“…The evaluation of the anharmonic and anisotropic expression derived in this work indicates that Woodruff's order-of-magnitude result (dashed line) fails to provide an upper bound on quality factor due to Akhiezer damping. In fact, several silicon resonators with quality factors that exceed Woodruff's limit have already been fabricated and measured in the literature [26][27][28][29], indicating the important need for our more accurate damping model that provides a robust upper bound on the performance of modern micromechanical resonators.…”