Lateral force microscope calibration using a modified atomic force microscope cantilever

A proof-of-concept study is presented for a prototype atomic force microscope (AFM) cantilever and associated calibration procedure that provide a path for quantitative friction measurement using a lateral force microscope (LFM). The calibration procedure is based on the method proposed by Feiler et al. [Rev. Sci. Instrum. 71, 2746 (2000)] but allows for calibration and friction measurements to be carried out in situ and with greater precision. The modified AFM cantilever is equipped with lateral lever arms that facilitate the application of normal and lateral forces, comparable to those acting in a typical LFM friction experiment. The technique allows the user to select acceptable precision via a potentially unlimited number of calibration measurements across the full working range of the LFM photodetector. A microfabricated version of the cantilever would be compatible with typical commercial AFM instrumentation and allow for common AFM techniques such as topography imaging and other surface force measurements to be performed.     

Improved lateral force calibration based on the angle conversion factor in atomic force microscopy

A novel calibration method is proposed for determining lateral forces in atomic force microscopy (AFM), by introducing an angle conversion factor, which is defined as the ratio of the twist angle of a cantilever to the corresponding lateral signal. This factor greatly simplifies the calibration procedures. Once the angle conversion factor is determined in AFM, the lateral force calibration factors of any rectangular cantilever can be obtained by simple computation without further experiments. To determine the angle conversion factor, this study focuses on the determination of the twist angle of a cantilever during lateral force calibration in AFM. Since the twist angle of a cantilever cannot be directly measured in AFM, the angles are obtained by means of the moment balance equations between a rectangular AFM cantilever and a simple commercially available step grating. To eliminate the effect of the adhesive force, the gradients of the lateral signals and the twist angles as a function of normal force are used in calculating the angle conversion factor. To verify reliability and reproducibility of the method, two step gratings with different heights and two different rectangular cantilevers were used in lateral force calibration in AFM. The results showed good agreement, to within 10%. This method was validated by comparing the coefficient of friction of mica so determined with values in the literature.     

Influence of Poisson's ratio variation on lateral spring constant of atomic force microscopy cantilevers

Atomic force microscopy (AFM) can be used to measure the surface morphologies and the mechanical properties of nanostructures. The force acting on the AFM cantilever can be obtained by multiplying the spring constant of AFM cantilever and the corresponding deformation. To improve the accuracy of force experiments, the spring constant of AFM cantilever must be calibrated carefully. Many methods, such as theoretical equations, the finite element method, and the use of reference cantilever, were reported to obtain the spring constant of AFM cantilevers. For the cantilever made of single crystal, the Poisson's ratio varies with different cantilever-crystal angles. In this paper, the influences of Poisson's ratio variation on the lateral spring constant and axial spring constant of rectangular and V-shaped AFM cantilevers, with different tilt angles and normal forces, were investigated by the finite element analysis. When the cantilever's tilt angle is 20 degrees and the Poisson's ratio varies from 0.02 to 0.4, the finite element results show that the lateral spring constants decrease 11.75% for the rectangular cantilever with 1muN landing force and decrease 18.60% for the V-shaped cantilever with 50nN landing force, respectively. The influence of Poisson's ratio variation on axial spring constant is less than 3% for both rectangular and V-shaped cantilevers. As the tilt angle increases, the axial spring constants for rectangular and V-shaped cantilevers decrease substantially. The results obtained can be used to improve the accuracy of the lateral force measurement when using atomic force microscopy.     

Development of a microlateral force sensor and its evaluation using lateral force microscopy

A microlateral force sensor (MLFS) was developed and evaluated using atomic force microscopy (AFM). The sensor was attached to a sensing table supported by a suspension system. The lateral motion of the sensing table was activated by a comb actuator. The driving voltage to the comb actuator was controlled to maintain a constant position of the sensing table by detecting the tunneling current at a detector, which consisted of two electrodes where the bias voltage was applied. An AFM was used to apply a lateral force to the sensing table of the sensor. When the probe of a cantilever was pressed against the sensing table and a raster scanning was conducted, the driving voltage of the comb actuator changed to compensate the friction force between the probe and sensing table. AFM measurements of an asperity array on the sensing table were conducted, and a lateral force microscopy image (LFM) was obtained from the change in driving voltage. The image by MLFS was very similar to the LFM image that was conventionally obtained from torsion of the cantilever. The LFM image strongly correlated with the gradient image calculated from the AFM topographic image. The force sensitivity of the MLFS was determined by comparing the LFM image obtained by using the MLFS with the tangential force derived from the gradient of the AFM image.     

Easy and direct method for calibrating atomic force microscopy lateral force measurements

We have designed and tested a new, inexpensive, easy-to-make and easy-to-use calibration standard for atomic force microscopy (AFM) lateral force measurements. This new standard simply consists of a small glass fiber of known dimensions and Young's modulus, which is fixed at one end to a substrate and which can be bent laterally with the AFM tip at the other end. This standard has equal or less error than the commonly used method of using beam mechanics to determine a cantilever's lateral force constant. It is transferable, thus providing a universal tool for comparing the calibrations of different instruments. It does not require knowledge of the cantilever dimensions and composition or its tip height. This standard also allows direct conversion of the photodiode signal to force and, thus, circumvents the requirement for a sensor response (sensitivity) measurement.     

Quantitative comparison of two independent lateral force calibration techniques for the atomic force microscope

Two independent lateral-force calibration methods for the atomic force microscope (AFM)--the hammerhead (HH) technique and the diamagnetic lateral force calibrator (D-LFC)--are systematically compared and found to agree to within 5?% or less, but with precision limited to about 15?%, using four different tee-shaped HH reference probes. The limitations of each method, both of which offer independent yet feasible paths toward traceable accuracy, are discussed and investigated. We find that stiff cantilevers may produce inconsistent D-LFC values through the application of excessively high normal loads. In addition, D-LFC results vary when the method is implemented using different modes of AFM feedback control, constant height and constant force modes, where the latter is more consistent with the HH method and closer to typical experimental conditions. Specifically, for the D-LFC apparatus used here, calibration in constant height mode introduced errors up to 14?%. In constant force mode using a relatively stiff cantilever, we observed an ≈?4?% systematic error per μN of applied load for loads ≤?1 μN. The issue of excessive load typically emerges for cantilevers whose flexural spring constant is large compared with the normal spring constant of the D-LFC setup (such that relatively small cantilever flexural displacements produce relatively large loads). Overall, the HH method carries a larger uncertainty, which is dominated by uncertainty in measurement of the flexural spring constant of the HH cantilever as well as in the effective length dimension of the cantilever probe. The D-LFC method relies on fewer parameters and thus has fewer uncertainties associated with it. We thus show that it is the preferred method of the two, as long as care is taken to perform the calibration in constant force mode with low applied loads.     

Low temperature ultrahigh vacuum noncontact atomic force microscope in the pendulum geometry

A noncontact atomic force microscope (nc-AFM) operating in magnetic fields up to ±7 T and liquid helium temperatures is presented in this article. In many common AFM experiments the cantilever is mounted parallel to the sample surface, while in our system the cantilever is assembled perpendicular to it; the so called pendulum mode of AFM operation. In this mode measurements employing very soft and, therefore, ultrasensitive cantilevers can be performed. The ultrahigh vacuum conditions allow to prepare and transfer cantilevers and samples in a requested manner avoiding surface contamination. We demonstrate the possibility of nc-AFM and Kelvin force probe microscopy imaging in the pendulum mode. Ultrasensitive experiments on small spin ensembles are presented as well.     

Precise atomic force microscope cantilever spring constant calibration using a reference cantilever array

A method for calibrating the stiffness of atomic force microscope (AFM) cantilevers is demonstrated using an array of uniform microfabricated reference cantilevers. A series of force-displacement curves was obtained using a commercial AFM test cantilever on the reference cantilever array, and the data were analyzed using an implied Euler-Bernoulli model to extract the test cantilever spring constant from linear regression fitting. The method offers a factor of 5 improvement over the precision of the usual reference cantilever calibration method and, when combined with the Systeme International traceability potential of the cantilever array, can provide very accurate spring constant calibrations.     

Developments for inverted atomic force microscopy

Atomic force microscopy (AFM) has been used to study a wide range of systems. Chemically and biologically modified probes have extended AFM by coupling chemical and biological information with the physical measurements. In an effort to further expand the capabilities of modified AFM probes, previous studies investigated the use of an inverted AFM design (i-AFM), wherein a microfabricated tip array is used to image a cantilever-supported sample. This report details developments in cantilever and tip array fabrication which are aimed at improving the applicability and performance of this i-AFM design. Using an epoxy-based procedure, commercial cantilevers were modified with a series of standard substrates, including template-stripped gold, highly oriented pyrolytic graphite, and mica. The samples on these cantilevers were imaged with i-AFM, and lateral force images are obtained. This paper demonstrates the first use of i-AFM for measuring friction.     

Reproducible lateral force microscopy measurements for quantitative comparisons of the frictional and chemical properties of nanostructures

Atomic force microscopy (AFM) is a widely used technique for characterizing the topography and frictional properties of nanostructures. Inherent misalignments between the AFM cantilever and the feedback hardware lead to crosstalk between topography data and lateral force microscopy (LFM) data. Because the degree of crosstalk depends on the positioning of the cantilever, LFM and topography data of the same structure can vary from one experiment to the next. For nanostructures with large LFM contrast, errors as large as 50% in topography and LFM can be observed. This paper describes an empirical strategy for correcting this alignment error. The technique is used to characterize the frictional properties of scanning probe-induced oxide nanostructures and the hydrogen-terminated Si(111) surfaces on which they are patterned. Reproducible differences in the frictional properties of the oxide nanostructures patterned on HF-treated and NH4F-treated Si(111) surfaces are observed and attributed to the mixed-hydride versus monohydride termination of each surface. The observed frictional contrast is consistent with known differences in surface reactivity and demonstrates how LFM measurements can provide insight into the frictional and chemical properties of nanostructures     

Cantilever spring constant calibration using laser Doppler vibrometry

Uncertainty in cantilever spring constants is a critical issue in atomic force microscopy (AFM) force measurements. Though numerous methods exist for calibrating cantilever spring constants, the accuracy of these methods can be limited by both the physical models themselves as well as uncertainties in their experimental implementation. Here we report the results from two of the most common calibration methods, the thermal tune method and the Sader method. These were implemented on a standard AFM system as well as using laser Doppler vibrometry (LDV). Using LDV eliminates some uncertainties associated with optical lever detection on an AFM. It also offers considerably higher signal to noise deflection measurements. We find that AFM and LDV result in similar uncertainty in the calibrated spring constants, about 5%, using either the thermal tune or Sader methods provided that certain limitations of the methods and instrumentation are observed.     

High-resolution constant-height imaging with apertured silicon cantilever probes

We present high-resolution aperture probes based on non-contact silicon atomic force microscopy (AFM) cantilevers for simultaneous AFM and near-infrared scanning near-field optical microscopy (SNOM). For use in near-field optical microscopy, conventional AFM cantilevers are modified by covering their tip side with an opaque aluminium layer. To fabricate an aperture, this metal layer is opened at the end of the polyhedral probe using focused ion beams (FIB). Here we show that apertures of less than 50 nm can be obtained using this technique, which actually yield a resolution of about 50 nm, corresponding to λ/20 at the wavelength used. To exclude artefacts induced by distance control, we work in constant-height mode. Our attention is particularly focused on the distance dependence of resolution and to the influence of slight cantilever bending on the optical images when scanning at such low scan heights, where first small attractive forces exerted on the cantilever become detectable.     

Improved parallel scan method for nanofriction force measurement with atomic force microscopy

Based on Ruan and Bhushan's study [J. Ruan and B. Bhushan, J. Tribol. 116, 378 (1994)], an improved method for quantitative nano/microfriction force measurements with the atomic force microscope (AFM) is presented. The related theoretical derivation is given in detail. The coefficient of friction can be calculated by scanning in the direction parallel to the long axis of the AFM cantilever. Then conversion factor, which can convert the lateral deflection response of the photodetector into corresponding friction force, is identified with the Meyer and Amer method [G. Meyer and N. M. Ame, Appl. Phys. Lett. 57, 2089 (1990)]. Like Ruan and Bhushan method, the advantage of this approach is that the coefficient of friction can be obtained with the plan-view geometry of AFM cantilevers and some common uncertainties, such as thickness, coating, and material properties, are not necessary. The result of the experiments performed utilizing rectangular cantilevers of different lengths shows that this improved method produces an accurate agreement for cantilevers of different lengths, thus the method can be used to measure nano/microfriction force.     

Friction property study of the surface of ZDDP and MoDTC antiwear additive films using AFM/LFM and force curve methods

The friction properties and material differences of the surface of ZDDP and MoDTC antiwear additive films, which give clear evidence of different friction coefficients in a pin-on-disc test, have been studied using atomic force microscopy (AFM)/lateral force microscopy (LFM) and force curve methods. The AFM/LFM observations show that the friction force on the surface of MoDTC additive films over the sliding area of a steel disc is lower and the friction force of ZDDP additive films is higher than that of afilmless area. Lateral force scope-trace evaluations reveal that the ratio of the friction forces on the surface of the ZDDP film, the filmless area, and the MoDTC film under the same normal force is approximately 1.5:1.0:0.7. Force curve measurements indicate that the surface materials of the ZDDP film, thefilmless area, and the MoDTC film differ according to their attractive forces, that is 29 nN for the ZDDP film, 22 nN for the filmless area, and 12 nN for the MoDTC film. These results correspond to the friction behaviour in the pin-on-disc test and also agree with the idea of the formation of solid MoS₂ lubricant from MoDTC additives on the surface of the antiwear film.     

Experimental observation of contact mode cantilever dynamics with nanosecond resolution

We report the use of a laser Doppler vibrometer to measure the motion of an atomic force microscope contact mode cantilever during continuous line scans of a mica surface. With a sufficiently high density of measurement points the dynamics of the entire cantilever beam, from the apex to the base, can be reconstructed. We demonstrate nanosecond resolution of both rectangular and triangular cantilevers. This technique permits visualization and quantitative measurements of both the normal and lateral tip sample interactions for the first and higher order eigenmodes. The ability to derive quantitative lateral force measurements is of interest to the field of microtribology/nanotribology while the comprehensive understanding of the cantilever's dynamics also aids new cantilever designs and simulations.     

Spring constant calibration of atomic force microscopy cantilevers with a piezosensor transfer standard

We describe a method to calibrate the spring constants of cantilevers for atomic force microscopy (AFM). The method makes use of a "piezosensor" composed of a piezoresistive cantilever and accompanying electronics. The piezosensor was calibrated before use with an absolute force standard, the NIST electrostatic force balance (EFB). In this way, the piezosensor acts as a force transfer standard traceable to the International System of Units. Seven single-crystal silicon cantilevers with rectangular geometries and nominal spring constants from 0.2 to 40 Nm were measured with the piezosensor method. The values obtained for the spring constant were compared to measurements by four other techniques: the thermal noise method, the Sader method, force loading by a calibrated nanoindentation load cell, and direct calibration by force loading with the EFB. Results from different methods for the same cantilever were generally in agreement, but differed by up to 300% from nominal values. When used properly, the piezosensor approach provides spring-constant values that are accurate to +/-10% or better. Methods such as this will improve the ability to extract quantitative information from AFM methods.     

AFM悬臂定位系统中光干涉误差及减小方法研究

光杠杆法是原子力显微镜（AFM）悬臂定位的主要方法。由于悬臂自身的尺寸和材料特性、检测光路系统等因素制约，悬臂弯曲测量时存在光泄露。被试样表面反射的部分泄露光与悬臂反射光产生干涉，在探针一试样接近曲线中产生光干涉误差。基于轻触模式AFM，分析了光干涉误差的产生原因，并对其引起的AFM测量误差进行了数学分析和仿真、提出了减小光干涉误差的方法。实验结果和理论分析表明，为了进一步提高AFM的测量精度，有必要克服定位系统中的光干涉误差。     

Quantitative measurement of in-plane cantilever torsion for calibrating lateral piezoresponse force microscopy

A simple quantitative measurement procedure of in-plane cantilever torsion for calibrating lateral piezoresponse force microscopy is presented. This technique enables one to determine the corresponding lateral inverse optical lever sensitivity (LIOLS) of the cantilever on the given sample. Piezoelectric coefficient, d(31) of BaTiO(3) single crystal (-81.62 ± 40.22 pm/V) which was calculated using the estimated LIOLS was in good agreement with the reported value in literature.     

Frictional forces between cohesive powder particles studied by AFM

A range of commercially important powders (hydrated alumina, limestone, titania and zeolite) and glass ballotini were attached to atomic force microscope cantilevers, and inter-particle friction forces studied in air using lateral force microscopy (LFM). The in situ calibration procedure for friction forces is described. LF images, line profiles, LF histograms, surface roughness, pull-off forces, and the load dependence of friction in the range 0-25 nN were studied for both particle-particle and particle-wall (steel) contacts. The single-particle friction results are discussed in terms of contact mechanics theory. Particle-particle contacts showed load-dependent friction, involving single asperity contacts (non-linear behaviour) or multi-asperity contacts (linear behaviour). Particle-wall contacts usually showed little load dependence and were more adhesive. The results are also related to shear stress-normal stress data (yield loci) for the same materials from bulk shear testers.     

A New AFM Nanotribology Method Using a T-Shape Cantilever with an Off-Axis Tip for Friction Coefficient Measurement with Minimized Abbé Error

A new AFM (atomic force microscopy) nanotribology method using a T-shape cantilever with an off-axis tip (Nat Nanotechnol 2:507–514, 2007) has been developed for measuring friction coefficient at nanometer scale. In this method, signals due to both bending and twisting of the T-shape AFM cantilever are detected simultaneously. For a T-shape AFM cantilever, the bending is caused by the normal load and the twisting is caused by both the normal and the lateral loads. The twisting generated by the normal load is calibrated in advance. Consequently, the twisting only due to the lateral load can be decoupled from the total lateral voltage signal. And the friction coefficient can be finally determined based on a conversion relationship between the normal and lateral voltage signals of the AFM photodetector. A practical procedure for minimizing Abbé error in friction coefficient measurement has also been introduced. The proposed new method is simple and accurate, and requires the least operation for friction coefficient measurement at nanometer scale.