Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy

Abstract

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10 nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75 GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.

Resonance tracking atomic force acoustic microscopy quantitative modulus mapping of carbon nanotubes‐reinforced acrylonitrile–butadiene–styrene polymer

“…Figure (b) shows the relation between contact resonance frequency of sixth flexural mode as a function of normal stiffness (kN). This frequency showed high sensibility with kN, which is consistent with results from Killgore and Hurley, and was used to transform the map of resonance frequency into a map of normal stiffness. A reduced elastic modulus of tip–sample, E *, was obtained from normal stiffness by using the formula kN = 2aC E *, where aC is the radius of the contact area (assumed as circular) and E * can be expressed as 1/ E * = 1/MT + 1/MS, where MT is the indentation modulus of cantilever tip and MS is the indentation modulus of the sample.…”

Realization and direct observation of five normal and parametric modes in silicon nanowire resonators by in situ transmission electron microscopy

“…However, it is still challenging to realize high-order resonances at high frequencies due to the large energy dissipation and strict resonant conditions. 15,16 By using the top-down approach, high-order normal and parametric resonances were demonstrated, 17,18 with a resonant frequency of several MHz. 17 Bottom-up grown nanowires (NWs) are attractive as high frequency resonators because of their high crystallinity and small mass.…”

Numerical verification of the hydrodynamic reconstruction method for contact resonance atomic force microscopy

“…Here, we have chosen a nondimensional stiffness value representative of an experimental case is which sensitivity of the first in-contact eigenmode of vibration is desired. 22 We have foregone analysis of higher nondimensional stiffness values for the triangular cantilever. Table III shows the computed results.…”