Calculation of the effect of tip geometry on noncontact atomic force microscopy using a qPlus sensor

Characteristics and Functionality of Cantilevers and Scanners in Atomic Force Microscopy

In this paper, we provide a systematic review of atomic force microscopy (AFM), a fast-developing technique that embraces scanners, controllers, and cantilevers. The main objectives of this review are to analyze the available technical solutions of AFM, including the limitations and problems. The main questions the review addresses are the problems of working in contact, noncontact, and tapping AFM modes. We do not include applications of AFM but rather the design of different parts and operation modes. Since the main part of AFM is the cantilever, we focused on its operation and design. Information from scientific articles published over the last 5 years is provided. Many articles in this period disclose minor amendments in the mechanical system but suggest innovative AFM control and imaging algorithms. Some of them are based on artificial intelligence. During operation, control of cantilever dynamic characteristics can be achieved by magnetic field, electrostatic, or aerodynamic forces.

Fundamental and higher eigenmodes of qPlus sensors with a long probe for vertical-lateral bimodal atomic force microscopy

The detection of vertical and lateral forces at the nanoscale by atomic force microscopy (AFM) reveals various mechanical properties on surfaces. The qPlus sensor is a widely used force sensor, which is built from a quartz tuning fork (QTF) and a sharpened metal probe, capable of high-resolution imaging in viscous liquids such as lubricant oils. Although a simultaneous detection technique of vertical and lateral forces by using a qPlus sensor is required in the field of nanotribology, it has still been difficult because the torsional oscillations of QTFs cannot be detected. In this paper, we propose a method to simultaneously detect vertical and lateral force components by using a qPlus sensor with a long probe. The first three eigenmodes of the qPlus sensor with a long probe are theoretically studied by solving a set of equations of motion for the QTF prong and probe. The calculation results were in good agreement with the experimental results. It was found that the tip oscillates laterally in the second and third modes. Finally, we performed friction anisotropy measurements on a polymer film by using a bimodal AFM utilizing the qPlus sensor with a long probe to confirm the lateral force detection.

A simple method for the determination of qPlus sensor spring constants

qPlus sensors are widely used to measure forces at the atomic scale, however, confidence in these measurements is limited by inconsistent reports of the spring constant of the sensor and complications from finite tip heights. Here we combine a numerical investigation of the force reconstruction with an experimental characterization of the flexural mechanics of the qPlus sensor. Numerical studies reveal significant errors in reconstructed force for tip heights exceeding 400 μm or one sixth of the cantilever length. Experimental results with a calibrated nanoindenter reveal excellent agreement with an Euler-Bernoulli beam model for the sensor. Prior to the attachment of a tip, measured spring constants of 1902 ± 29 N/m are found to be in agreement with theoretical predictions for the geometry and material properties of the sensor once a peaked ridge in the beam cross section is included. We further develop a correction necessary to adjust the spring constant for the size and placement of the tip.

Optimal geometry for a quartz multipurpose SPM sensor

We propose a geometry for a piezoelectric SPM sensor that can be used for combined AFM/LFM/STM. The sensor utilises symmetry to provide a lateral mode without the need to excite torsional modes. The symmetry allows normal and lateral motion to be completely isolated, even when introducing large tips to tune the dynamic properties to optimal values.