Temperature dependence of the force sensitivity of silicon cantilevers

Abstract

The resonance frequency ω and internal friction Q−1 of the first eigenmode of microfabricated silicon cantilevers are measured in the temperature range of 15-300 K. The analysis shows that variation of Young’s modulus is responsible for the temperature dependence of the resonance frequency, whereas the dependence of the geometrical dimensions can be neglected. Accordingly, the data can be fitted by the Wachtman equation, yielding a Debye temperature ΘD = 634K. The temperature variation of internal friction Q−1 is analyzed in terms of Zener’s theory of thermoelastic damping. Due to the temperature dependence of the thermal expansion coefficient α, thermoelastic damping is expected to vanish at 20 K and 125 K. A minimum of internal friction is observed at 20 K, whereas the minimum at 125 K appears to be hidden by other dissipation effects. A maximum of internal friction at 160 K is observed, which is an activation peak due to phonon scattering by atomic-scale defects. The best force sensitivity is achieved at 20 K, where a factor of 10 is gained compared to room temperature. © 2004 The American Physical Society.