On the Air Damping of Micro-Resonators in the Free-Molecular Region
S. Hutcherson and W. Ye
Georgia Institute of Technology, US
Keywords: MEMS modeling, molecular damping, resonator, disk
Predicting air damping on micromachined mechanical resonators is crucial in the design of high-performance filters used in wireless communication systems. In the past, most of the work focused on devices with minimum feature size on the order of microns. At micron scale, continuum theory is still valid and was employed in these studies. In this work, we investigate air damping on a contour-mode disk resonator that can oscillate at gage-hertz frequency range. In such a device, the gap between electrodes and disk has to be in the submicron range in order to drive the ''stiff'' disk. With such a small gap, continuum theory breaks down and a molecular approach that accounts for interactions between the disk and individual molecules must be adopted. We estimate the damping coming from the gap by calculating the energy gained for each molecule that interacts with the disk within a cycle and summing the contribution due to each molecule using the Maxwell-Boltzmann speed distribution function to obtain the total energy loss of the disk during one cycle. Quality factors are then calculated and results are consistent with the available experimental measurements.
Nanotech 2004 Conference Technical Program Abstract