Analysis of Entrainment and Clamping Loss in an Optically Actuated MEMS

Abstract

This thesis presents a study of thin, planar, radio frequency MEMS resonators that are shown to self-oscillate in the absence of external forcing, when illuminated by a DC laser of sufficient amplitude. Entrainment or frequency locking is achieved in these devices when an external forcing strong enough and close in frequency to that of the unforced oscillations is applied. The forcing can be accomplished either parametrically, by modulating the laser beam incident on the oscillator, or nonparametrically, using inertial driving. The system exhibits both 2:1 and 1:1 resonances, as well as quasiperiodic motions and hysteresis. Dynamics of a three dimensional system of coupled thermo-mechanical model for the forced disc resonator is studied, using a perturbation scheme. Perturbation results show that the model agrees well with experiments and explain how and where transitions into and out of entrainment occur. Simpler canonical models showing similar behavior are also studied. Next a method to improve Quality factor (Q) of these devices is studied. Q is a measure of damping and models the total losses in a dynamical system. As MEMS vibrates, a fraction of its vibration energy is transmitted to the substrate upon which the MEMS are fabricated. A large component of this energy is carried away as surface acoustic waves (SAW). This energy is either scattered or dissipated into the relatively infinite expanse of the substrate and termed as anchor loss in the system. A design that improves the Q of dome shaped oscillators by up to 4 by reflecting surface wave energy back to the MEMS is demonstrated. Wave reflection occurs at trenches fabricated in a circle around the MEMS. The trench creates a ?mesa? that provides partial mechanical isolation to the MEMS. Finite element analysis (FEA) is used to model these losses with infinite elements acting as quiet boundary for the truncated substrate domain. These boundaries absorb most of the outgoing energy and model the relatively infinite expanse of the substrate. The results predicted by the model agree well with the experiments and are also able to predict the experimentally observed improvement due to the presence of a mesa.