Enhancing higher harmonics of a tapping cantilever by excitation at a submultiple of its resonance frequency

Abstract

Cataloged from PDF version of article.In a tapping-mode atomic force microscope, the frequency spectrum of the oscillating cantilever contains higher harmonics at integer multiples of the excitation frequency. When the cantilever oscillates at its fundamental resonance frequency w(1), the high Q-factor damps the amplitudes of the higher harmonics to negligible levels, unless the higher flexural eigenmodes are coincident with those harmonics. One can enhance the nth harmonic by the Q factor when the cantilever is excited at a submultiple of its resonance frequency (w(1)/n). Hence, the magnitude of the nth harmonic can be measured easily and it can be utilized to examine the material properties. We show theoretically that the amplitude of enhanced higher harmonic increases monotonically for a range of sample stiffness, if the interaction is dominated by elastic force

High-speed dynamic atomic force microscopy by using a Q-controlled cantilever eigenmode as an actuator

“…In the simulations of a 0.1 GPa sample, we increased the set-point slightly to decrease the indentation into the sample. In fact, selecting softer cantilevers for soft samples and choosing stiffer cantilevers for stiff samples is appropriate [39]. Hence we decreased the cantilever stiffness 10 times for both eigenmodes, while keeping the resonance frequencies and the quality factors unchanged, and performed simulations on the 1 GPa sample.…”

Sensitivity vector fields for atomic force microscopes

“…Also, by enhancing and exploiting the dynamics of the higher harmonics, the resolution of AFM can be enhanced [2,3,15,21]. Stark showed [20,22] that the higher harmonics cannot be neglected in the analysis of the tapping-mode AFM.…”

Parametrically coupled multiharmonic force imaging

“…6 The main reason for this is, for a rectangular cantilever, higher order mode frequencies are not integer multiples of the fundamental mode frequency. [7][8][9][10][11] Several authors have addressed the problem of measuring the complete tip-sample interaction during tapping using special modifications to the cantilever or the scanning probe electronics. 12,13 Multifrequency excitation of the cantilever simultaneously at the two flexural resonances has also been demonstrated to give complementary material contrast.…”