RESONANCE RESPONSE OF SCANNING FORCE MICROSCOPY CANTILEVERS

A variational method is used to calculate the deflection and the funda mental and harmonic resonance frequencies of commercial V-shaped and r ectangular atomic force microscopy cantilevers. The effective mass of V-shaped cantilevers is roughly half that calculated for the equivalen t rectangular cantilevers. Damping by environmental gases, including a ir, nitrogen, argon, and helium, affects the frequency of maximum resp onse and to a much greater degree the quality factor Q. Helium has the lowest viscosity, resulting in the highest Q, and thus provides the b est sensitivity in noncontact force microscopy. Damping in liquids is dominated by an increase in effective mass of the cantilever due to an added mass of the liquid being dragged with that cantilever.