Effect of pressure on the Q factor and the resonance frequency of SiN microcantilevers

A systematic study of the quality factor and resonance behavior of flexural and torsional modes of silicon nitride cantilevers vs. pressure is presented. Different anchoring, i.e., with and without undercut, is studied in the range between 3 mPa and atmospheric pressure. Thermal noise spectra of the cantilevers have been measured using a home-made optical deflection setup with an appropriately windowed vacuum chamber. The experimental data on the pressure dependence of the quality factor of the first three flexural modes is in good agreement with existing theories for the molecular and viscous regimes, for both the freestanding and suspended cantilevers. The corresponding gradual decrease in the resonance frequency to a maximum of 5% from vacuum to atmospheric pressure can be explained by the air mass effect. A small increase of the resonance frequency just prior to this downward shift might be attributed to a slight cooling away of heat from the optical beam or alternatively to a slight stiffening of the cantilever due to residual gas absorption in the near-surface region.