Phase Measurements of Non - Linear Response in Mems Oscillators

We have fabricated several varieties of micro and nanomechanical resonators and have studied their phase response when driven at their natural frequency with and without parametric pumping. We found that micron-sized paddle oscillators with submicron-sized supports had resonant frequencies in the 3-10 MHz range for their translational mode. Due to the stretching of the support beams, the effective stiffness of the system increases with amplitude and distorts the response curve. The phase response vs. frequency has a sharper slope with increasing drive amplitudes, and develops a discontinuity at very large amplitudes. We explored another system, which consisted of silicon disks supported by an oxide pillar at the disk center, with a resonant frequency near 1 MHz. A low power laser beam, (about 100 μW), focused at the periphery of the disk, results in a change of the effective spring constant due to heating, which allows us to realize degenerate parametric amplification of the disk’s vibrations through a double frequency modulation of the laser power. We measured the phase response while varying the drive amplitude, the pump amplitude, and the phase angle between the drive and the pump. We also simulated the system with numerical modeling. We have studied the phase response vs. frequency for various pump conditions. For the condition of maximum amplification, the phase response displays a shallower slope with increasing pump frequency. Thus, importantly, we find that while the width of the resonance peak narrows with more amplification, the frequency stability degrades.