Squeeze-Film Damping of Flexible Microcantilevers at Low Ambient Pressures

An improved theoretical approach is presented to calculate and predict the quality factors of flexible microcantilevers affected by squeeze-film damping at low ambient pressures, and moderate to high Knudsen numbers. Veijola’s model [1], originally derived for a rigid oscillating plate near a wall, is extended to a flexible cantilever beam and both the gas inertia effect and slip boundary condition are considered in deriving resulting damping pressure. The model is used to predict the natural frequencies and quality factors of silicon microcantilevers with small gaps and their dependence on ambient pressure. In contrast to non-slip, continuum models, we find that quality factor depends strongly on ambient pressure, and that the damping of higher modes is more sensitive to ambient pressure than the fundamental.