GAS DAMPING OF ELECTROSTATICALLY EXCITED RESONATORS

The aim of the present investigation is to determine the influence of both pressure and cavity depth on the mechanical Q-factor for electros tatically excited and capacitively detected encapsulated microresonato rs. In this paper, we present vibration Q-factor results for bulk-micr omachined resonator structures in silicon which have been anodically b onded to glass lids of different recess depths. The parameters investi gated are the air pressure, extending from 0.1 to 1000 mbar, and the d istance between the resonator structures and the glass-lid wall, rangi ng from 15 to 45 mu m. Another structure without a glass lid has also been tested and is used as a reference. The measurements are performed inside a vacuum chamber. We also present results on low-pressure enca psulated resonators. The structures are excited electrostatically with an external electrode, while the detection is achieved optically by a He/Ne laser combined with a lateral photodetector. The measurements s how that the resonator vibration damping is dominated by 'squeeze-film ' damping for small recess depths (15 mu m or less) and that a pressur e below 1 mbar is needed to achieve Q-factors of more than 3000. We pr esent a theoretical model for the squeeze-film Q-factor which takes in to account both the pressure and the recess-depth parameters. This mod el matches very well with the measurements. For the first time, a pres sure of 1 mbar has been demonstrated inside a low-pressure encapsulate d resonator, starting from a bonding pressure of 10(-4) mbar, without using any getter material or gas evacuation after the bonding process.