We present a method by which multi-harmonic signals acquired during a normal tapping mode (amplitude modulated) AFM scan of a sample in air or vacuum with standard microcantilevers can be used to map quantitatively the local mechanical properties of the sample such as elastic modulus, adhesion, and indentation. The approach is based on the observation that during the tapping mode operation in air or vacuum, the 0th and 2nd harmonic signals of microcantilever vibration are encountered under most operating conditions and can be mapped with sufficient signal to noise ratio. By measuring the amplitude and phase of the driven harmonic as well as the 0th and 2nd harmonic observables, we find analytical/semi-analytical formulas that relate these multi-harmonic observables to local mechanical properties for several classical tip-sample interaction models. Least squares estimation of the local mechanical properties is performed pixel by pixel. The method is validated through computations as well as experimental data acquired on a polymer blend made of Polystyrene and Polyolefin elastomer.

We introduce a multiscale model for contact mechanics between rough surfaces and apply it to characterize the force-displacement relationship for a metal-dielectric contact relevant for radio frequency micro-electromechanicl system (MEMS) switches. We propose a mesoscale model to describe the history-dependent force-displacement relationships in terms of the surface roughness, the long-range attractive interaction between the two surfaces, and the repulsive interaction between contacting asperities (including elastic and plastic deformation). The inputs to this model are the experimentally determined surface topography and the Hamaker constant as well as the mechanical response of individual asperities obtained from density functional theory calculations and large-scale molecular dynamics simulations. The model captures non-trivial processes including the hysteresis during loading and unloading due to plastic deformation, yet it is computationally efficient enough to enable extensive uncertainty quantification and sensitivity analysis. We quantify how uncertainties and variability in the input parameters, both experimental and theoretical, affect the force-displacement curves during approach and retraction. In addition, a sensitivity analysis quantifies the relative importance of the various input quantities for the prediction of force-displacement during contact closing and opening. The resulting force-displacement curves with quantified uncertainties can be directly used in device-level simulations of micro-switches and enable the incorporation of atomic and mesoscale phenomena in predictive device-scale simulations.

The measurement of the intermittent interaction between an oscillating nanotip and the sample surface is a key challenge in dynamic Atomic Force Microscopy (AFM). Accelerometers integrated onto AFM cantilevers can directly measure this interaction with minimal cantilever modification but have been difficult to realize. Here, we design and fabricate high frequency bandwidth accelerometers on AFM cantilevers to directly measure the tip acceleration in commercial AFM systems. We demonstrate a simple way of calibrating such accelerometers and present experiments using amplitude modulated AFM on freshly cleaved mica samples in water to study the response of the accelerometer.

A method is presented to enhance the optical lever sensitivity in dynamic atomic force microscopy (AFM) by nearly an order of magnitude over a wide frequency bandwidth. This is achieved by fabricating or releasing a paddle with a soft hinge close to the free end of the AFM microcantilever such that the paddle resonance frequency is well below the fundamental resonance frequency of the microcantilever. We show a significant increase in signal to noise ratio when cantilever motion is observed at the paddle for AFM systems that are not limited by thermal noise. Also, any effects due to the excitation of the second eigenmode were decoupled by locating the paddle at the node of the second eigenmode. We use these probes for higher harmonic imaging in amplitude modulated AFM (AM-AFM) on a standard polymer blend made of polystyrene and low density polyethylene. We demonstrate significantly improved contrast in higher harmonic images when observing cantilever motion at the paddle. Thus this microcantilever design can improve significantly conventional cantilever performance for dynamic AFM and is compatible with low-cost, high yield microfabrication processes.

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