Thermoelastic dissipation of nanowire resonators with surface stress

Surface stress effect on thermoelastic dissipation of nanowires is studied with a simple 1D surface stress–surface strain model. A simplified procedure is suggested to calculate the inverse quality factor for nanowires with different thermal surface conditions. Explicit formulas are derived for rectangular and circular cross-sections with adiabatic or isothermal surface condition. The accuracy of the present method is demonstrated by excellent agreement with the known classical results for rectangular and circular cross-sections under adiabatic surface condition. In the absence of surface stress, the present analysis shows that the maximum thermoelastic dissipation is determined by material constants alone, independent of the size and shape of the cross-section and thermal surface condition. On the other hand, the presence of surface stress does cause a size-dependence of the maximum thermoelastic dissipation on the cross-section, and the relative change in thermoelastic dissipation due to the surface stress effect is independent of operating frequency. In particular, the present results showed that thermoelastic dissipation with adiabatic surface condition can be a few times different than that with isothermal surface condition, and the effect of surface stress on thermoelastic dissipation becomes more significant for isothermal surface condition than for adiabatic surface condition.