A quasi-continuum thermomechanical model for phonon damping analysis of single crystal silicon nano-resonators

Abstract

In this paper, we study phonon-mediated intrinsic damping in single crystal silicon nano-resonators where the phonon transport is of partial ballistic and partial diffusive nature. For this purpose, we present a quasicontinuum thermomechanical model that accounts for both thermoelastic and Akhiezer energy dissipation mechanisms. In the model, the linearized frequency-dependent phonon Boltzmann transport equation (BTE) is coupled with continuum elasticity equations via phonon modulation theory. The model is implemented numerically by using the finite element and finite volume methods for calculating the damping ratio and quality factor of nano-resonators under forced vibration. Both flexural and axial motions are considered for single crystal silicon nano-resonators with different sizes and frequencies. The numerical results obtained from the quasi-continuum thermomechanical model are compared with those obtained from molecular dynamics simulations.

High intrinsic dissipation of graphyne nanotubes

“…3, structural support is not a dominant factor for the high dissipation of GNTs due to the fact that the same boundary condition is used for CNT and GNTs. On the other hand, intrinsic dissipation of nano/microresonators mainly includes surface damping, thermoelastic damping [31,32], and Akhiezer damping [33][34][35]. Due to the fact that CNT and GNTs are single layers of carbon atoms, surface damping may be neglected.…”

“…C v is the specificheat capacity, T is the operating temperature, γ is the Grüneisen parameter, ω is the angular frequency, τ ph is the phonon relaxation time, ρ is the material density, and c is the velocity of sound. The phonon relaxation time can be given by [35]…”