Modification of Akhieser mechanism in Si nanomembranes and thermal conductivity dependence of the Q-factor of high frequency nanoresonators

We present and validate a reformulated Akhieser model that takes into account the reduction of thermal conductivity due to the impact of boundary scattering on the thermal phonons' lifetime. We consider silicon nanomembranes with mechanical mode frequencies in the GHz range as textbook examples of nanoresonators. The model successfully accounts for the measured shortening of the mechanical mode lifetime. Moreover, the thermal conductivity is extracted from the measured lifetime of the mechanical modes in the high-frequency regime, thereby demonstrating that the Q-factor can be used as an indication of the thermal conductivity and/or diffusivity of a mechanical resonator.