Optimization and calibration of atomic force microscopy sensitivity in terms of tip-sample interactions in high-order dynamic atomic force microscopy (original) (raw)
Related papers
2012
Frequency analysis and modal sensitivity of an atomic force microscope (AFM) cantilever is presented in this paper. Closed-form expressions for frequency equation and sensitivity of vibration modes are derived for the tip-cantilever system as the cantilever undergoes coupled lateral-vertical bending with torsional vibration. In this work, the effects of the sample surface contact stiffness and the cantilever to tip lengths ratio on resonant frequencies and sensitivities are assessed. The results show that the resonant frequency is constant in low and high values of the normal and lateral contact stiffnesses and there is a shift of frequency in a specific value of stiffness. Also, in comparison with the values of normal contact stiffness, frequency shift, due to the tip–sample interaction, occurs in lower values of lateral contact stiffness. In the low values of contact stiffnesses, the lower-order vibration modes are more sensitive than the higher-order modes. The situation is compl...
Contact atomic force microscopy using piezoresistive cantilevers in load force modulation mode
Ultramicroscopy, 2018
Scanning probe microscopy (SPM) encompasses several techniques for imaging of the physical and chemical material properties at nanoscale. The scanning process is based on the detection of the deflection of the cantilever, which is caused by near field interactions, while the tip runs over the sample's surface. The variety of deflection detection methods including optical, piezoresistive, piezoelectric technologies has been developed and applied depending on the measurement mode and measurement environment. There are many advantages (compactness, vacuum compatibility, etc.) of the piezoresistive detection method, which makes it very attractive for almost all SPM experiments. Due to the technological limitations the stiffness of the piezoresistive beams is usually higher than the stiffness of the cantilever detected using optical methods. This is the basic constraint for the application of the piezoresistive beams in contact mode (CM) atomic force microscopy (AFM) investigations performed at low load forces (usually less than 20 nN). Drift of the deflection signal, which is related to thermal fluctuations of the measurement setup, causes that the microscope controller compensates the fluctuations instead of compensating the strength of tip-surface interactions. Therefore, it is quite difficult to keep near field interaction precisely at the setpoint level during the whole scanning process. This can lead to either damage of the cantilever's tip and material surface or loosing the contact with the investigated sample and making the measurement unreliable. For these reasons, load force modulation (LoFM) scanning mode, in which the interaction at the tip is precisely controlled at every point of the sample surface, is proposed to enable precise AFM surface investigations using the piezoresistive cantilevers. In this article we describe the developed measurement algorithm as well as proposed and introduced hardware and software solutions. The results of the experiments confirm strong reduction of the AFM entire setup drift. The results demonstrating contactless tip lateral movements are presented. It is common knowledge that such a scanning reduces tip wear.
The interactive damping sensitivity and the resonant frequency of normal vibration and longitudinal vibration of an atomic force microscope (AFM) rectangular cantilever have been analyzed. Surface electrostatic attraction between the atoms in the tip of the probe and those in the surface is simulated with flexural and longitudinal contact stiffness. Theoretical investigation of normal and longitudinal interaction individually and both, have been presented as normal and longitudinal sensitivity. Also using the sensitivity equations the effects of material property and geometrical parameters can be specified.
Beilstein Journal of Nanotechnology, 2014
We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip–surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip–surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.
Size-dependent on vibration and flexural sensitivity of atomic force microscope
Applied and Computational Mechanics, 2019
In this paper, the free vibration behaviors and flexural sensitivity of atomic force microscope cantilevers with small-scale effects are investigated. To study the small-scale effects on natural frequencies and flexural sensitivity, the consistent couple stress theory is applied. In this theory, the couple stress is assumed skew-symmetric. Unlike the classical beam theory, the new model contains a material-length-scale parameter and can capture the size effect. For this purpose, the Euler–Bernoulli beam theory is used to develop the AFM cantilever. The tip interacts with the sample that is modeled by a spring with constant of. The equation of motion is obtained through a variational formulation based on Hamilton’s principle. In addition, the analytical expressions for the natural frequency and sensitivity are also derived. At the end, some numerical results are selected to study the effects of material-length-scale parameter and dimensionless thickness on the natural frequency and f...
Applied Physics Letters, 1996
Using an atomic force microscope ͑AFM͒ with a silicon cantilever partially covered with a layer of zinc oxide ͑ZnO͒, we have imaged in the constant force mode by employing the ZnO as both a sensor and actuator. The cantilever deflection is determined by driving the ZnO at the second mechanical resonance while the tip is in contact with the sample. As the tip-sample force varies, the mechanical boundary condition of the oscillating cantilever is altered, and the ZnO electrical admittance is changed. Constant force is obtained by offsetting the ZnO drive so that the admittance remains constant. We have also used the ZnO as an actuator and sensor for imaging in the intermittent contact mode. In both modes, images produced by using the ZnO as a sensor are compared to images acquired with a piezoresistive sensor.
A new model for investigating the flexural vibration of an atomic force microscope cantilever
Ultramicroscopy, 2010
A new model for the flexural vibration of an atomic force microscope cantilever is proposed, and a closed-form expression is derived. The effects of angle, damping and tip moment of inertia on the resonant frequency were analysed. Because the tip is not exactly located at one end of the cantilever, the cantilever is modelled as two beams. The results show that the frequency first increases with increase in angle and then decreases to a constant value for high values of the angle. Moreover, the damping is increased at lower contact positions. The tip moment of inertia is also sensitive to the resonant frequency at small values for the odd modes and large values for the even modes.
Contact mechanics and tip shape in AFM-based nanomechanical measurements
Ultramicroscopy, 2006
Stiffness-load curves obtained in quantitative atomic force acoustic microscopy (AFAM) measurements depend on both the elastic properties of the sample and the geometry of the atomic force microscope (AFM) tip. The geometry of silicon AFM tips changes when used in contact mode, affecting measurement accuracy. To study the influence of tip geometry, we subjected ten AFM tips to the same series of AFAM measurements. Changes in tip shape were observed in the scanning electron microscope (SEM) between individual AFAM tests. Because all of the AFAM measurements were performed on the same sample, variations in AFAM stiffness-load curves were attributed to differences in tip geometry. Contact-mechanics models that assumed simple tip geometries were used to analyze the AFAM data, but the calculated values for tip dimensions did not agree with those provided by SEM images. Therefore, we used a powerlaw approach that allows for a nonspherical tip geometry. We found that after several AFAM measurements, the geometry of the tips at the very end is intermediate between those of a flat punch and a hemisphere. These results indicate that the nanoscale tip-sample contact cannot easily be described in terms of simple, ideal geometries. r