Analysis of frequency locking in optically driven MEMS resonators

Thin, planar, radio frequency microelectromechanical systems (MEMS) resonators have been shown to self-oscillate in the absence of external forcing when illuminated by a direct current (dc) laser of sufficient amplitude. In the presence of external forcing of sufficient strength and close enough in frequency to that of the unforced oscillation, the device will become frequency locked, or entrained, by the forcing. In other words, it will vibrate at the frequency of the external forcing. Experimental results demonstrating entrainment for a disk-shaped oscillator under optical and mechanical excitation are reviewed. A thermomechanical model of the system is developed and its predictions explored to explain and predict the entrainment phenomenon. The validity of the model is demonstrated by the good agreement between the predicted and experimental results. The model equations could also be used to analyze MEMS limit-cycle oscillators designed to achieve specific performance objectives.