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.     

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.     

微摩擦测试仪力传感器的研究

讨论了微尺度构件的摩擦力测试问题.Bhushan和Koinkar分别对硅材料的宏观摩擦系数和纳米摩擦系数进行了对比实验,实验表明纳米摩擦系数远远低于宏观摩擦系数.而在微机械构件中,零件的大小一般为微米级,甚至更大,接触面积也较大.载荷介于宏观和微观之间,有时会大于nN范围,因此其摩擦特殊,有可能不完全等同于宏观摩擦和纳米摩擦,因此需进一步研究.但现有的微摩擦测试仪器不管是载荷还是测量范围都是基于纳米量级,因此需要一种用于研究微机械样品间摩擦的专用仪器.本文主要对这种微摩擦测试仪中关键技术之一力传感器进行了研究.由于普通传感器在测量精度较高时,分辨率、灵敏度等均较低,不能满足系统的要求.针对普通传感器的不足,本文采用微机械工艺加工微力传感器可以大批量制量制造,且具有低成本、高精度、低驱动、高可靠性、低功耗、占用空间小、重量轻和响应速度快等优点.最后对力传感器的性能进行了分析.     

Calibration of atomic force microscope cantilevers using piezolevers

The atomic force microscope (AFM) can provide qualitative information by numerous imaging modes, but it can also provide quantitative information when calibrated cantilevers are used. In this article a new technique is demonstrated to calibrate AFM cantilevers using a reference piezolever. Experiments are performed on 13 different commercially available cantilevers. The stiff cantilevers, whose stiffness is more than 0.4 N/m, are compared to the stiffness values measured using nanoindentation. The experimental data collected by the piezolever method is in good agreement with the nanoindentation data. Calibration with a piezolever is fast, easy, and nondestructive and a commercially available AFM is enough to perform the experiments. In addition, the AFM laser must not be calibrated. Calibration is reported here for cantilevers whose stiffness lies between 0.08 and 6.02 N/m.     

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.     

Microfabricated torsion levers optimized for low force and high-frequency operation in fluids

We developed a mass production fabrication process for making symmetrically supported torsion cantilevers/oscillators with highly compliant springs. These torsion probes offer advantages in atomic force microscopy (AFM) because they are small, have high optical gain, do not warp and can be made with two independent axes. Compared to traditional AFM cantilevers, these probes have higher frequency response, higher Q, lower noise, better optics (since the mirror does not bend) and two data channels. Soft small levers with sub-pN force resolution can resonate cleanly above 10 kHz in water. When fabricated with a ferromagnetic coating on the rigid reflecting pad, they can be driven magnetically or serve as high-resolution magnetometers. Asymmetric levers can be tapping mode probes or high-resolution accelerometers. The dual axis gimbaled probes with two orthogonal axes can operate on a standard AFM with single beam illumination. These probes can be used as self-referencing, drift free, cantilevers where one axis senses the substrate position and the other the sample position. These levers can be optimized for differential contrast or high-resolution friction imaging.     

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.     

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.     

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.     

Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid

Investigation of morphology and mechanical properties of biological specimens using atomic force microscopy (AFM) often requires its operation in liquid environment. Due to the hydrodynamic force, the vibration of AFM cantilevers in liquid shows dramatically different dynamic characteristics from that in air. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions, and evaluation of sample's mechanical properties. In this study, a finite element (FE) model is used for frequency and transient response analysis of AFM cantilevers in tapping mode (TM) operated in air or liquid. Hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The additional mass and hydrodynamic damping matrices corresponding to beam elements are derived. With this model, numerical simulations are performed for an AFM cantilever to obtain the frequency and transient responses of the cantilever in air and liquid. The comparison between our simulated results and the experimentally obtained ones shows good agreement. Based on the simulations, different characteristics of cantilever dynamics in air and liquid are discussed.     

Focused ion beam-nanomachined probes for improved electric force microscopy

Nanomachining and beam-assisted Pt deposition by a focused ion beam (FIB) was used to modify AFM probes for improved electric force measurements. Si(3)N(4) cantilevers have been endowed with a nano-electrode at the tip apex to confine the electro-sensitive area at the very tip. This action results in both a marked decrease of the parasitic capacitive effect and in an improved electric force microscopy (EFM) contrast and resolution, with respect to usual, full metal-coated cantilevers. This fabrication approach is suited to the development of innovative electro-sensitive probes, useful in different scanning probe techniques.     

Improvement of thermally induced bending of cantilevers used for atomic force microscopy

The microfabricated silicon nitride cantilevers that are used for atomic force microscopy (AFM) are, unfortunately, sensitive thermometers. They bend with ambient temperature changes and those due to laser heating. The bend can result in displacements for the silicon nitride cantilevers of an order several hundred nanometers at the tip of the cantilever. If, however, the silicon nitride cantilevers are treated by removing the metallization and annealing at 500°C for 30 min, these displacements can be reduced by one or two orders of magnitude. Silicon cantilevers have approximately a one order of magnitude smaller drift than silicon nitride cantilevers as received from vendors and are improved less by treatment.     

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.     

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。     

激光检测摩擦力显微镜的定量标定

本文简要描述了激光检测摩擦力显微镜的工作原理，探索出一种横向力标定的有效方法，可以从横向力信号中提取摩擦力信号，从而能够定量地对试样表面的形貌和力学性质进行纳米量级的评定，以获取微观表面真实的三维形貌图和微观摩擦系数等信息，为纳米摩擦学设计提供依据。实验结果表明，用该方法测得未清洗单晶硅表面的微观摩擦系数约为０．０６，和Ｂｈｕｓｈａｎ等人的结果吻合的很好。     

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.     

A novel AFM based method for force measurements between individual hair strands

Interactions between hairs and other natural fibers are of broad interest for both applications and fundamental understanding of biological interfaces. We present a novel method, that allows force measurements between individual hair strands. Hair fragments can be laser-cut without altering their surface chemistry. Subsequently, they are glued onto Atomic force microscopy (AFM) cantilevers. This allows carrying out measurements between the hair fragment and surface immobilized hair in a well-defined crossed-cylinder geometry. Both force–distance and friction measurements are feasible. Measurements in air with controlled humidity and in aqueous environment show clear differences which can be explained by the dominating role of capillary interactions in air. Friction is found to be anisotropic, reflecting the fine structure of hair cuticula. While the investigations are focused on the particular example of human hair, we expect that the approach can be extended to other animal/plant fibers and thus offers perspectives for broad spectrum systems.     

Exploiting cantilever curvature for noise reduction in atomic force microscopy

Optical beam deflection is a widely used method for detecting the deflection of atomic force microscope (AFM) cantilevers. This paper presents a first order derivation for the angular detection noise density which determines the lower limit for deflection sensing. Surprisingly, the cantilever radius of curvature, commonly not considered, plays a crucial role and can be exploited to decrease angular detection noise. We demonstrate a reduction in angular detection shot noise of more than an order of magnitude on a home-built AFM with a commercial 450 μm long cantilever by exploiting the optical properties of the cantilever curvature caused by the reflective gold coating. Lastly, we demonstrate how cantilever curvature can be responsible for up to 45% of the variability in the measured sensitivity of cantilevers on commercially available AFMs.     

Friction and wear effects on a micro/nano‐scale

In this paper are described tribological effects which can be found in micro‐tribological systems, and in those macro‐systems which can be analysed by micro‐methods, e.g., by atomic force microscopy (AFM) or related methods. Micro‐tribology systems have friction contacts with loads in the micro/nano‐newton range and/or dimensions in the micro/nanometre range. Experiments on the micro/nano‐scale should be easier to explain by theoretical modelling due to their simpler system structure. An example is discussed of adhesion and friction measurements between AFM tips and clean, flat, solid surfaces in ultra‐high vacuum, which shows some of the special aspects of micro/nano‐tribology. Surprising friction characteristics on surfaces with an artificial micro‐structure can be explained by skilled and careful topographical analysis of the friction path with an AFM. In micro‐sensor contacts, ‘single wear events’ can be detected using AFM analysis of the contact region. For ceramic compounds, different friction levels for the components of the material can be found. The problems, difficulties, and dangers of misinterpretation are also discussed.     

Investigation of human hair fibers using lateral force microscopy

Atomic force microscopy (AFM) and lateral force microscopy (LFM) were used to investigate the morphologic and surface changes associated with various surface modifications to human hair. These included extraction with a series of solvents, bleaching, and treatment with a cationic copolymer. The study assessed the ability of these techniques to distinguish the changes in surface properties, including morphology and friction coefficient, as manifested in changes brought about by the indicated surface modifications. While topographic morphology can easily be investigated with contact AFM. LFM offers an additional tool for probing the surface distribution of oils and waxes. The removal of surface lipids from the fiber surface was accomplished using soxhlet extraction with t-butanol and n-hexane, while the free internal lipids (within the fiber structure) were removed by extraction with a mixture of chloroform and methanol (70:30, v/v). In addition, the surface of hair was modified with the cationic polymer, co(vinyl pyrrolidone-methacrylamidopropyl trimethylammonium chloride [PVP/MAPTAC]), and its distribution on the surface was monitored. Ambient AFM and LFM studies of surface modified and native fibers clearly indicate that when investigated as a function of tip loading force, the different modifications result in changes of the friction coefficient, which increase in this order: native, bleached, solvent extracted, and polymer-treated hair. Friction images show surface variations that are interpreted as areas of varying lipid film coverage. In addition, topographic images of the fibers show the presence of small pores, which become increasingly prevalent upon solvent extraction.