High-Fidelity Modeling of MEMS Resonators—Part I: Anchor Loss Mechanisms Through Substrate

Nonlinear damping and dephasing in nanomechanical systems

“…Parameter δr q gives the momentum uncertainty in the momentum conservation condition (20), δk ∼ (δr q ) −1 . Similar arguments apply to the matrix elements v κκ of the coupling of the considered low-frequency mode to high-frequency modes κ,κ [see Eq.…”

“…However, Eq. (20) indicates that, locally, the quasimomentum of the system of phonons is conserved. Short-range disorder breaks down this conservation; in each scattering event, the local momentum of a phonon is transferred to a short-range scatterer.…”

“…The relaxation mechanisms include radiation into the bulk modes of the medium surrounding the nanosystem [19][20][21][22][23], nonlinear coupling between the modes localized inside the system [10,[24][25][26][27][28], and coupling with electronic excitations [29][30][31][32] and two-level defects [33][34][35].…”

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.…”

“…This phenomenon is effectively a source of damping because the ordered mechanical energy of the resonator is transferred to the substrate in the form of stress waves, and eventually dissipated in the substrate. By assuming that the radiated energy does not reflect back into the resonator, damping can be estimated by performing calculations solely in the elastic domain without specifying the detailed mechanisms by which energy is dissipated in the substrate [20][21][22][23][24][25]. One of the first models for support loss is an analysis by Jimbo and Itao in 1968 of a two-dimensional system consisting of an isotropic, homogeneous, linear elastic cantilever of length L, width w, and thickness h that is attached to an elastic halfspace.…”