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As one of the fundamental sources of noise in atomic force microscopy (AFM), thermal fluctuations of the cantilever have been studied for the case of a free tip but not much for cantilevers in contact. In this paper, using the equipartition theorem, we calculated the thermal deflection amplitude for all normal modes of an elastically supported AFM cantilever, including the free cantilever as a special case. With increasing contact stiffness, the mean thermal fluctuation amplitude decreases for all cantilever modes when in the elastic contact. In addition, considering the optical lever detection scheme used in most AFMs, we calculated the corresponding output thermal noise amplitude. The experiments validated our theoretical calculations. Our investigation facilitates a more comprehensive understanding of the thermal noise in AFM. It provides guidance for thermally excited contact-resonance AFM, which is promising for quantitative viscoelastic measurements. [ABSTRACT FROM AUTHOR]

We proposed a method for measuring undercut etching based on contact resonance atomic force microscopy (CR-AFM). Suspended undercut structures were fabricated through isotropic wet etching on a patterned SiNx/Si architecture. The materials beneath the SiNx masks with circular and rectangular shapes were partially etched to form center-supported thin plates. A clear contrast was observed between the supported and suspended regions by CR-AFM amplitude imaging, enabling accurate determination of the undercut boundary and the corresponding etched length. CR-spectroscopy measurements of the undercut dimensions were also applied by acquiring the contact stiffness distribution and by further fitting with models of analyzing the plate deflection. The etching rates given by both the imaging and spectroscopy measurements were in close accordance. The theoretical measurement error induced by finite CR-frequency to stiffness sensitivity was evaluated to be around 5% under our experimental settings. This work paves the way for in situ and real-time detection of undercut etching at the nanoscale and benefits relevant micro- and nano-fabrications. [ABSTRACT FROM AUTHOR]

Subsurface imaging capability of liquid-environment higher-harmonic atomic force microscopy (AFM) was investigated using a reference artifact. A series of cylindrical cavities with pre-known dimensions were fabricated on a silicon substrate via electron beam lithography and then covered by a set of highly oriented pyrolytic graphite (HOPG) pieces with different thicknesses. Experiments on these structures demonstrated that the higher-harmonic amplitude sensitivity to the local stiffness in liquids was at least an order of magnitude larger than that in ambient air under the same parameter settings. The harmonic AFM in liquids could detect the cavities beneath over a 200 nm thick HOPG cover. Theoretical analyses based on the cantilever dynamics and the membrane mechanical properties well interpreted the experimental results. Furthermore, it was verified that the momentary excitation of the non-driven higher eigenmode in a low-Q environment could play a critical role in the enhanced subsurface imaging capability of harmonic AFM in liquids. [ABSTRACT FROM AUTHOR]