Reversed Nonlinear Oscillations in Lame-Mode Single-Crystal-Silicon Microresonators

The spring hardening effect is reported here for the first time in a single-crystal-silicon bulk mode resonator. Reversing nonlinear behaviors (changing from spring softening to hardening) has been observed in fabricated silicon-on-insulator square-plate resonators of identical dimensions but aligned against different crystal orientations. This orientation-dependent reversal in the nonlinearity is explained using a dynamic model which incorporates a nonlinear strain-stress relation. The frequency response of the devices (with different dimensions) under various driving conditions can be closely predicted using the model.