Energy dissipation in tapping-mode scanning force microscopy with low quality factors

The phase angle of the cantilever oscillation in tapping mode scanning force microscopy can be related to the energy dissipated per oscillation period through an analytical model that assumes a sinusoidal movement of the cantilever @J. Tamayo and R. Garcı́a, Appl. Phys. Lett. 73, 2926 ~1998!; J. P. Cleveland, B. Anczykowski, E. Schmid, and V. Elings, Appl. Phys. Lett. 72, 2613 ~1998!#. In this work, numerical calculations of the oscillation of cantilevers with quality factors lower than 10 show a significant contribution of higher harmonics ~;5%–20%!. This contribution can lead to a significant error in the energy dissipated deduced by using the model cited above. Thus, an extended relationship between the phase shift and the energy dissipated is presented, that takes into account the higher harmonics of the oscillation. These results determine the conditions for the measurement of energy dissipation in a liquid. © 1999 American Institute of Physics. @S0003-6951~99!04548-9#