Micromechanical resonators or microresonators have a limit to the maximum usable vibration amplitude. This limit may be set by material strength, or as is often case for a MEMS resonator, by unwanted nonlinear effects. Figure 1 shows how the microresonator resonance response is changed in the presence of nonlinear restoring forces (=nonlinear springs). As the vibration amplitude increases, the resonance peak frequency shifts from the linear resonance frequency. This is often referred to as the Duffing effect. At sufficiently large amplitudes, the amplitude-frequency curve shows hysteresis; the vibration amplitude depends on the direction of frequency sweep (up/down). Although there has been some ideas of taking advantage of nonlinear effects (e.g parametric excitation), usually the devices need to be operated below the hysteresis point in order to obtain predictable performance. Translated to electrical engineering terms, the drive level (or power handling capacity) of MEMS devices is limited by the nonlinear effects. As the signals levels from microresonators are small in general, it is of fundamental interest to know the maximum achievable drive level for micro-sized devices. This determines, for example, whether one can make a MEMS oscillator with small enough phase noise for reference applications.

The nonlinearities can be of either mechanical or electrical origin. Most fundamentally, the MEMS materials are nonlinear due nonlinearities in atomic interactions. Luckily, silicon is quite linear material and other nonlinear effects typically dominate. For further information on nonlinear vibrations and nonlinear effects in MEMS resonators in particular, please refer to the publications.

Practical MEMS book