An experimental study of anharmonic micromachined silicon resonators

The use of resonant sensors with high mechanical Q factors is based on a vibrating element acting as a harmonic oscillator. The existence and consequence of non-linearity, for some special resonant structures and above critical values, are not often taken into account. For experiments in which the mechanical deflection gives basically the physical information, a lack of knowledge of possible non-linearity may have dramatic consequences for the exploitation of the results. Different free-standing silicon resonators have been micromachined and an experimental device to test the dynamical properties of these structures has been designed. The resonant structures were electrostatically excited in flexural mode. The results have revealed a spectacular non-linear behaviour of the thin films at ambient temperature. It is well established that this anharmonic behaviour is linked to the mechanical properties of these resonators rather than to the electrostatic excitation. The experiments have revealed three different types of non-linear behaviour. These experimental results are presented and analysed starting from the non-linear differential equation.