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The effect of an external bias voltage and fluctuating electromagnetic fieldson both the fundamental frequency and damping of cantilever vibrations isconsidered. An external voltage induces surface charges causingcantilever-sample electrostatic attraction. A similar effect arises fromcharged defects in dielectrics that cause spatial fluctuations of electrostaticfields. The cantilever motion results in charge displacements giving rise toJoule losses and damping. It is shown that the dissipation increases withdecreasing conductivity and thickness of the substrate, a result that ispotentially useful for sample diagnostics. Fluctuating electromagnetic fieldsbetween the two surfaces also induce attractive (Casimir) forces. It is shownthat the shift in the cantilever fundamental frequency due to the Casimir forceis close to the shift observed in recent experiments of Stipe et al. Both theelectrostatic and Casimir forces have a strong effect on the cantilevereigenfrequencies, and both effects depend on the geometry of the cantilevertip. We consider cylindrical, spherical, and ellipsoidal tips moving parallelto a flat sample surface. The dependence of the cantilever effective mass andvibrational frequencies on the geometry of the tip is studied both numericallyand analytically

Effects of electrostatic fields and Casimir force on cantilever vibrations