Temperature and pressure dependence of resonance in multi-layer microcantilevers

The resonance frequency of the fundamental and four higher order modes of a silicon dioxide microcantilever is measured. The effect on these modes of depositing a 400 nm gold coating is investigated theoretically and experimentally. We derive an analytical solution to the eigenmodes of a multi-layered cantilever and verify its validity by comparison to finite-element analysis as well as the experimentally obtained results. The temperature and pressure dependence of the resonance frequencies is investigated experimentally and found to be in good agreement with theoretical models. An experimentally obtained value for the temperature dependence of Young's modulus of elasticity for thermally grown SiO2 is presented.