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Cantilevers with interferometric high bandwidth force sensors can resolve nonlinear tip-sample interaction forces in tapping-mode atomic force microscopy. In this paper, we provide a detailed analysis of time-resolved force measurements using such cantilever. We first model the probe as a coupled spring-mass system and investigate its steady state dynamics under tapping-mode imaging conditions. Next, we analyze the optical response of the interferometric force sensor: Diffraction patterns as a function of tip displacement are obtained both analytically and by simulations. Finally, the frequency response of the force sensor is calculated, and the effects of the sensor geometry variations on the sensor mechanical response are analyzed. [ABSTRACT FROM AUTHOR]

We present a micromachined cantilever with an integrated high-bandwidth resonator for direct measurement of tip-sample interaction forces in tapping-mode atomic force microscopy. Force measurements are achieved by a diffraction grating that serves as a differential displacement sensor for the tip motion relative to the cantilever body. Time-resolved tip-sample interaction force measurement is demonstrated on a silicon sample following calibration of the probe structure. By using lock-in detection, the harmonics of periodic tip-sample interaction have been utilized to obtain high-contrast, material specific images. The harmonic images of patterned silicon/silicon nitride control samples and triblock copolymers are presented. [ABSTRACT FROM AUTHOR]

We present a micromachined scanning probe cantilever, in which a specific higher-order flexural mode is designed to be resonant at an exact integer multiple of the fundamental resonance frequency. We have fabricated such cantilevers by reducing the stiffness of the third order flexural mode relative to the fundamental mode, and we have demonstrated that these cantilevers enable sensing of non-linear mechanical interactions between the atomically sharp tip at the free end of the cantilever and a surface with unknown mechanical properties in tapping-mode atomic force microscopy. Images of surfaces with large topographical variations show that for such samples harmonic imaging has better resolution than standard tapping-mode imaging. [Copyright &y& Elsevier]