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

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 quasi-continuum 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.