Characterization of silicon micro-oscillators by scanning laser vibrometry

Abstract

The dynamics of single-crystal silicon ∼100 μm size rectangular paddle oscillators at room temperature have been studied using a recently developed high-resolution scanning laser vibrometer. The dynamic mechanical behavior is determined by scans of the entire device, providing both amplitude and phase spatial maps of the vibratory response. These reveal more than 16 normal modes below 500 kHz. In addition to simple translation and torsional motion, flexural modes of the paddle plate are observed. Quality factors ranging from ${\text{1×10}}^3$ to ${\text{2×10}}^4$ are measured and are found to be significantly lower than those expected from well-known intrinsic absorption mechanisms. The measurements reveal that there exists significant modification of the expected eigenfrequencies and mode shapes. It is speculated that this is caused by excessive undercutting of the support structure, and that the resulting energy flow into the support leads to increased oscillator loss. Indeed, some correlation is found between observed loss and energy levels resident in the supports. At frequencies where there is relatively little support motion, three-dimensional finite-element modeling accurately predicts the paddle modal behavior.