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.     

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.     

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.     

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.     

An integrated methodology for data processing in dynamic force spectroscopy of ligand-receptor binding

Dynamic force spectroscopy (DFS), using atomic force microscopy (AFM), is a powerful tool to study ligand-receptor binding. The interaction mode of two binding partners is investigated by exploring stochastic behaviors of bond rupture events. However, to define a rupture event from force-distance measurements is not conclusive or unique in literature. To reveal the influence of event identification methods, we have developed an efficient protocol to manage tremendous amount of data by implementing different choices of peak selection from the force-distance curve. This data processing software simplifies routinely experimental procedures such as cantilever spring constant and force-distance curve calibrations, statistical treatments of data, and analysis distributions of rupture events. In the present work, we took available experimental data from a complex between a chelate metal compound and a monoclonal antibody as a study system.     

Prototype cantilevers for quantitative lateral force microscopy

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.     

Molecular dynamics simulation of the contact process in AFM surface observations

In the present work, several molecular dynamics simulations have been performed to clarify dynamically the contact mechanism between the specimen surface and probe tip in surface observations by an atomic force microscope (SFM) or friction force microscope (FFM). In the simulation, a three‐dimensional model is proposed where the specimen and the probe are assumed to consist of monocrystalline copper and rigid diamond or a carbon atom, respectively. The effect of the cantilever stiffness of the AFM/FFM is also taken into consideration. The surface observation process is simulated on a well‐defined Cu{100} surface. From the simulation results it has been verified that the surface images and the two‐dimensional atomic‐scale stick‐slip phenomenon, just as is the case for real AFM/FFM surface observations, can be detected from the spring force acting on the cantilever. From the evaluation of the behaviour of specimen surface atoms, the importance of the specimen stiffness in deciding the cantilever properties can also be understood. The influence of the probe tip shape on the force images is also evaluated. From the results it can be verified that the behaviour of the specimen surface atoms as well as the solid surface images in AFM/FFM surface observations can be understood using the molecular dynamics simulation of the model presented.     

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.     

具有三维力反馈的原子力显微镜纳米操作系统

在基于原子力显微镜的纳米操作过程中，由于缺乏实时反馈信息，造成纳米操作效率低下且灵活性差，同时探针因受力过大而损坏。为此，本文通过对探针受力-悬臂变形进行建模，并根据实时检测到的悬臂变形信号、新的参数获取与校准方法，从而获取探针所受的实时三维纳米力。将此三力经比例放大后送人力／触觉设备进行感知，操作者就可以实时调节施加在探针上力的大小及探针的运动轨迹，使得操作的效率及灵活性明显提高，且可以避免探针因受力过大而造成损坏。纳米刻画和多壁碳纳米管的操作实验验证了系统的有效性。     

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.     

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each modes.     

Atomic force microscope probe calibration by use of a commercial precision balance

In this paper, we investigate the characteristics of a piezoresistive AFM cantilever in the range of 0–1.6 μN by using nano force calibrator (NFC), which consists of a high precision balance with resolution of 1 nN and 1-D fine positioning stage. Brief modeling of the cantilever is presented and then, the calibration results are shown. Tests revealed a linear relationship between the probing force and sensor output (resistance change), but the force vs. deflection is not as linear as the force vs. sensor output curve. The force constant of the cantilever was measured to 0.26 N/m with a standard deviation of 0.01 N/m. It shows that there is big difference between measured and nominal spring constant of 1 N/m provided by the manufacturer’s specifications.     

FORCE TRANSDUCER MODELING OF RECTANGULAR,V–SHAPED,AND DAGGER CANTILEVER PROBES BASED ON ATOMIC FORCE MICROSCOPY

Real-time monitoring of the nano-particle manipulation process by atomic force microscope (AFM) is almost impossible since the manipulator of the AFM is used as either the imaging or manipulation tool at a given instant. As one approach to this problem, researchers scan the area where the target particle exists, before and after the nano-manipulation. Thus, by using some fixed reference features, the new relative position of the particle is obtained from the images. However, this imaging is offline, and unexpected problems during nano-manipulation process cannot be detected. In this article, force transducer of the AFM rectangular, V-shaped, and dagger cantilevers, which convert the three-dimensional deflections measured by the detection system to corresponding three-dimensional force, are modeled and compared. So there would be a feedback from the real-time force system during nano-manipulation process, which can be utilized for better understanding and reliable handling of nano-particles. Furthermore, the manipulation forces are affected directly by spring constants of cantilever. Hence, the cantilever is the most significant and sensitive component of the AFM. Therefore, variations of the lateral, longitudinal, and normal spring constants of the mentioned cantilever for different geometrical parameters are analyzed and discussed.     

Study of thermal and acoustic noise interferences in low stiffness atomic force microscope cantilevers and characterization of their dynamic properties

The atomic force microscope (AFM) is a powerful tool for the measurement of forces at the micro/nano scale when calibrated cantilevers are used. Besides many existing calibration techniques, the thermal calibration is one of the simplest and fastest methods for the dynamic characterization of an AFM cantilever. This method is efficient provided that the Brownian motion (thermal noise) is the most important source of excitation during the calibration process. Otherwise, the value of spring constant is underestimated. This paper investigates noise interference ranges in low stiffness AFM cantilevers taking into account thermal fluctuations and acoustic pressures as two main sources of noise. As a result, a preliminary knowledge about the conditions in which thermal fluctuations and acoustic pressures have closely the same effect on the AFM cantilever (noise interference) is provided with both theoretical and experimental arguments. Consequently, beyond the noise interference range, commercial low stiffness AFM cantilevers are calibrated in two ways: using the thermal noise (in a wide temperature range) and acoustic pressures generated by a loudspeaker. We then demonstrate that acoustic noises can also be used for an efficient characterization and calibration of low stiffness AFM cantilevers. The accuracy of the acoustic characterization is evaluated by comparison with results from the thermal calibration.     

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.     

Calibration of AFM cantilever stiffness: a microfabricated array of reflective springs

Calibration of the spring constant of atomic force microscope (AFM) cantilevers is necessary for the measurement of nanonewton and piconewton forces, which are critical to analytical applications of AFM in the analysis of polymer surfaces, biological structures and organic molecules.

We have developed a compact and easy-to-use reference standard for this calibration. The new artifact consists of an array of 12 dual spiral-cantilever springs, each supporting a mirrored polycrystalline silicon disc of 160 μm in diameter. These devices were fabricated by a three-layer polysilicon surface micromachining method, including a reflective layer of gold on chromium. We call such an array a Microfabricated Array of Reference Springs (MARS). These devices have a number of advantages. Cantilever calibration using this device is straightforward and rapid. The devices have very small inertia, and are therefore resistant to shock and vibration. This means they need no careful treatment except reasonably clean laboratory conditions.

The array spans the range of spring constant from around 0.16 to 11 N/m important in AFM, allowing almost all contact-mode AFM cantilevers to be calibrated easily and rapidly. Each device incorporates its own discrete gold mirror to improve reflectivity. The incorporation of a gold mirror both simplifies calibration of the devices themselves (via Doppler velocimetry) and allows interferometric calibration of the AFM z-axis using the apparent periodicity in the force–distance curve before contact. Therefore, from a single force–distance curve, taking about one second to acquire, one can calibrate the cantilever spring constant and, optionally, the z-axis scale. These are all the data one needs to make accurate and reliable force measurements.     

Cleaning AFM colloidal probes by mechanically scrubbing with supersharp “brushes”

Contamination control of atomic force microscope (AFM) tips (including standard but supersharp imaging tips and particle/colloidal probes) is very important for reliable AFM imaging and surface/interface force measurements. Traditional cleaning methods such as plasma, UV–ozone and solvent treatments have their shortcomings. Here, we demonstrate that calibration gratings with supersharp spikes can be employed to scrub away contaminants accumulated on a colloidal sphere probe by scanning the probe against the spikes at high load at constant-force mode. The present method is superior to traditional cleaning methods in several aspects. First, accumulated lump-like organic/inorganic material can be removed; second, removal is non-destructive and highly efficient based on a “targeted removal” strategy; third, removal and probe shape/morphology study can be completed in a single step (we report, to our best knowledge, the first evidence of the wear of the colloidal sphere during force measurements); and fourth, both colloidal/particle probes and standard but supersharp AFM imaging tips can be treated.     

Interlaboratory round robin on cantilever calibration for AFM force spectroscopy

Single-molecule force spectroscopy studies performed by Atomic Force Microscopes (AFMs) strongly rely on accurately determined cantilever spring constants. Hence, to calibrate cantilevers, a reliable calibration protocol is essential. Although the thermal noise method and the direct Sader method are frequently used for cantilever calibration, there is no consensus on the optimal calibration of soft and V-shaped cantilevers, especially those used in force spectroscopy. Therefore, in this study we aimed at establishing a commonly accepted approach to accurately calibrate compliant and V-shaped cantilevers. In a round robin experiment involving eight different laboratories we compared the thermal noise and the Sader method on ten commercial and custom-built AFMs. We found that spring constants of both rectangular and V-shaped cantilevers can accurately be determined with both methods, although the Sader method proved to be superior. Furthermore, we observed that simultaneous application of both methods on an AFM proved an accurate consistency check of the instrument and thus provides optimal and highly reproducible calibration. To illustrate the importance of optimal calibration, we show that for biological force spectroscopy studies, an erroneously calibrated cantilever can significantly affect the derived (bio)physical parameters. Taken together, our findings demonstrated that with the pre-established protocol described reliable spring constants can be obtained for different types of cantilevers.     

An In Situ Method for Simultaneous Friction Measurements and Imaging of Interfacial Tribochemical Film Growth in Lubricated Contacts

Tribological investigations of macroscopic lubricated sliding contacts are critical for a wide range of industrial applications including automotive engines, gears, bearings, and any other contacting surfaces in relative motion. However, the inability of existing techniques to access buried sliding interfaces with high spatial resolution inhibits the development of fundamental insights into the tribological processes at play. Here we demonstrate a novel and general in situ method, based on atomic force microscopy (AFM), in which micrometer-scale spherical probes are attached to a standard microfabricated AFM cantilever which is then slid over a substrate while immersed in a liquid lubricant. In this case, steel colloidal probes and steel substrates were used, and the contact was immersed in a commercial polyalphaolefin oil with zinc dialkyl dithiophosphate (ZDDP) additive at both room temperature and 100 °C, but the method can be used for a broad range of material combinations, lubricants, and temperatures. We demonstrate that the in situ measurements of friction force and the morphological evolution of the tribochemical films on the substrate can be simultaneously achieved with nanometer-level spatial resolution. In addition, we demonstrate that the sliding zone is readily accessible for further characterization with higher spatial resolution using standard AFM probes with nanometer-scale tip radii. Ex situ characterization of the micrometer-scale probe and the sample is also feasible, which is demonstrated by acquiring high-resolution AFM topographic imaging of the final state of the probe.     

Data analysis of interaction forces measured with the atomic force microscope

The force-distance cycle mode of the atomic force microscope (AFM) allows for detection of interaction forces between the AFM-tip and a substrate (probe). This can either be a direct tip-sample interaction or an interaction between molecules coupled to the tip and probe, respectively. The interaction forces are typically in the range of a few pN to some hundred pN. In this article we describe algorithms for the analysis of force-distance cycles, to quantify interaction forces between tip and probe. Both, the direct tip-probe interaction as well as the interaction between specifically bound molecules are analyzed. The molecules bound to tip and probe have to be either long and flexible or have to be bound via a flexible cross linker. The algorithms are exemplified on direct tip-probe interactions and on unbinding events of cadherins which are bound via PEG-spacers to the AFM-tip and to the probe.