Dynamic Atomic Force Microscopy Modes Research Articles

Dielectric constant measurement sensitivity in electrostatic force and force gradient microscopy-based modes

Understanding the nanoscale electrostatic interaction between a conductive atomic force microscopy (AFM) probe and a dielectric film is central to the operation of various nanoscale dielectric microscopies and determination of dielectric properties of the film. There is no simple analytical description of the electrostatic interaction generated in the confined probe-sample geometry for neither static nor dynamic AFM modes used in dielectric measurements. An accurate description of the involved physics is obtained only by means of a finite element analysis modeling of the system. However, the alternative to using the numerical analysis is not very popular due to being slower and requiring relatively high computation resources. In this work, we revised the contributions from different parts of the AFM probe to the probe-sample capacitance by both analytical and numerical methods. We tried to reconciliate the two approaches and observed the differences as a function of geometry and material parameters. Under various noise levels, the efficiency of an analytical model was tested against a finite element analysis that captures in detail the electrostatic interaction in AFM-based dielectric measurements. The investigation was performed in both spectroscopic force-distance curves and constant height scans with measurements for deflection and frequency of the AFM probe. The obtained measurement sensitivities are relevant in selecting the optimal scanning mode and its operational parameters for a given film thicknesses and dielectric constants but also show the critical role of the numerical analysis to the correct interpretation of the measurements.

Custom-Designed Glassy Carbon Tips for Atomic Force Microscopy.

Glassy carbon is a graphenic form of elemental carbon obtained from pyrolysis of carbon-rich precursor polymers that can be patterned using various lithographic techniques. It is electrically and thermally conductive, mechanically strong, light, corrosion resistant and easy to functionalize. These properties render it very suitable for Carbon-microelectromechanical systems (Carbon-MEMS) and nanoelectromechanical systems (Carbon-NEMS) applications. Here we report on the fabrication and characterization of fully operational, microfabricated glassy carbon nano-tips for Atomic Force Microscopy (AFM). These tips are 3D-printed on to micro-machined silicon cantilevers by Two-Photon Polymerization (2PP) of acrylate-based photopolymers (commercially known as IP-series resists), followed by their carbonization employing controlled pyrolysis, which shrinks the patterned structure by ≥98% in volume. Tip performance and robustness during contact and dynamic AFM modes are validated by morphology and wear tests. The design and pyrolysis process optimization performed for this work indicate which parameters require special attention when IP-series polymers are used for the fabrication of Carbon-MEMS and NEMS. Microstructural characterization of the resulting material confirms that it features a frozen percolated network of graphene sheets accompanied by disordered carbon and voids, similar to typical glassy carbons. The presented facile fabrication method can be employed for obtaining a variety of 3D glassy carbon nanostructures starting from the stereolithographic designs provided by the user.

Simulation of dynamic modes of atomic force microscopy using a 3D finite element model

In dynamic atomic force microscopy (AFM), a cantilever is used to extract surface properties by observing the changes of its dynamic characteristics due to the tip–sample interaction. Analytical/numerical models that can accurately simulate the surface-coupled dynamics of the cantilever are essential for quantitative/qualitative understanding/explanation of measured results. In this paper, a comprehensive finite element model is developed for numerical simulation of free and surface-coupled dynamics of tip–cantilever system in dynamic modes of AFM. Representing the cantilever by three-dimensional beam elements, this model can simulate all the cantilever dynamic modes within a framework of the standard finite element method. Formulations reflecting the exact excitation mechanisms are derived for tapping mode (TM), torsional resonance (TR) mode, and lateral excitation (LE) mode. Under tip–sample interaction, the location/geometry of the tip and the tilting of the cantilever to the sample surface become important and can be easily addressed in this model. With the application of this finite element model, in TM, we show that phase shift of cantilever response and interaction force sensitively depend on in-plane mechanical properties but it is not true for cantilever vibration amplitude. The excitation of higher-order modes of vertical bending is observed in our simulation and its influence on data acquisition and interpretation is discussed. In TR and LE modes, torsion and lateral bending of the cantilever are coupled. We investigate how the torsion and lateral bending contribute to the twist of the cantilever and demonstrate that the lateral bending contribution can be ignored only if the lateral interaction is relatively weak compared to the cantilever stiffness of lateral bending. Tip eccentricity, if any, strongly affects amplitude and phase of cantilever responses and therefore cannot be ignored in TR and LE modes. The differences of TR and LE modes due to their different excitation mechanisms are also discussed. The presented model is capable of accurately simulating the cantilever dynamics under complex tip–sample interaction and might be used for quantitative extraction of surface properties.

Sensitivity of flexural and torsional vibrationmodes of atomic force microscope cantilevers to surfacestiffness variations

Dynamic modes of atomic-force microscopy offer newpossibilities for imaging because of the availability of thevarious vibrational modes of the probes. However, each mode hasa different sensitivity to variations in surface stiffness. Thissensitivity directly controls the image contrast. Low-stiffnesscantilevers have typically been unusable for imaging of stiffmaterials because of the lack of sensitivity of the firstflexural mode. In this paper, the sensitivities of theflexural and torsional modes are derived. Closed-formexpressions are obtained for cantilevers with constant cross sections. For cantilevers with other shapes, an approximatesolution is developed using the method of Rayleigh-Ritz. Theinteraction of the cantilever with the surface is modelled bylinear springs, which restricts the results to experimentsinvolving low-amplitude excitations. Both flexural and torsionalvibration modes are considered. For given nominal values ofsurface and AFM probe properties, the appropriate mode forhighest contrast may be predicted.

Experimental determination of the mechanical impedance of atomic force microscopy cantilevers in fluids up to 70 kHz

The high-frequency dynamical response of cantilevers used in atomic force microscopy (AFM) to an external force is important for applications such as dynamic AFM modes and dynamic mechanical measurements on biological tissues. In this paper we present a novel method for experimentally determining the mechanical driving-point impedance of an AFM cantilever up to frequencies of at least 70 kHz. A frequency-independent, point force was achieved by applying an electric field between the cantilever and a sharpened steel electrode positioned near (10 μm) the tip of the cantilever. The velocity of the cantilever in response to the force was measured with a laser interferometer. The method was tested in air and in tetrachloromethane (CCl4), a nonpolar, nondissociating fluid. The results agree with theoretical predictions. In addition, the mechanical impedance of a cantilever near a flat surface was measured.