Mapping nanoscale elasticity and dissipation using dual frequency contact resonance AFM

Abstract

We report on a technique that simultaneously quantifies the contact stiffness and dissipation of an AFM cantilever in contact with a surface, which can ultimately be used for quantitative nanomechanical characterization of surfaces. The method is based on measuring the contact resonance frequency using dual AC resonance tracking (DART), where the amplitude and phase of the cantilever response are monitored at two frequencies on either side of the contact resonance. By modelling the tip-sample contact as a driven damped harmonic oscillator, the four measured quantities (two amplitudes and two phases) allow the four model parameters, namely, drive amplitude, drive phase, resonance frequency and quality factor, to be calculated. These mechanical parameters can in turn be used to make quantitative statements about localized sample properties. We apply the method to study the electromechanical coupling coefficients in ferroelectric materials and the storage and loss moduli in viscoelastic materials.

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“…FMM is a SFM-based mode where the tip in direct contact with the surface is forced to vibrate at a high frequency (contact resonance frequency typically of several 100's of KHz) in order to evaluate the mechanical response of the material [27][28][29]. Any variation in the contact resonance frequency is related to the local sample stiffness, i.e., a positive shift in frequency corresponds to stiffer mechanical properties.…”

Direct determination of the effect of strain on domain morphology in ferroelectric superlattices with scanning probe microscopy

“…In addition, the contribution of the local contact resonance to the amplitude of the response can be calculated and subtracted to determine the absolute value of the property. 29,33 Non-local electrostatic fields from the tip shaft and cantilever can contribute a spurious force component leading to artifacts. This effect can be minimized by imaging with a sufficiently large contact force.…”

Contact resonances of U-shaped atomic force microscope probes

“…In order for new material designs to be fully understood, measurements that can quantify behavior at appropriate scales, often down to the nanoscale, are required. The contact resonance atomic force microscope (CR-AFM) technique is a promising materials characterization approach, which can quantify the elastic [1][2][3][4][5][6][7][8][9] as well as viscoelastic [10][11][12][13][14][15][16] properties of materials with spatial resolution on the order of tens of nanometers. CR-AFM uses the vibration spectra of an AFM probe during vibrations for both the noncontact case, and when the tip is in contact with a sample.…”

“…More recently, Yuya et al 10,18 developed a method to find the viscoelastic properties of a sample from experiment by following a similar approach. CR-AFM is becoming well accepted for analyzing the properties of a wide variety of materials such as polymers, [11][12][13][14]16,18,23 biological materials, 16,25,26 composite materials, 27 dielectric materials, 28 metallic glass, 29 and metals. 6,8,9 It has shown great promise for many interesting problems especially those involving the interfaces of a multi-phase material.…”

“…17,19,20 Likewise, the change in the width of the resonances can be used to find material damping. 16,18 For both types of samples, the inversion algorithm to find the properties involves a deconvolution of the probe vibration response. Thus, the creation of quantitative images of properties from CR-AFM spectra during scanning requires simple analytical solutions of the probe vibrations in order for the inversion to be made during the experiment rather than as a post-processing step.…”