A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscopy

A method is proposed for quantitatively measuring the elastic modulus of materials using atomic force microscopy (AFM) nanoindentation. In this method, the cantilever deformation and the tip-sample interaction during the early loading portion are treated as two springs in series, and based on Sneddon's elastic contact solution, a new cantilever-tip property α is proposed which, together with the cantilever sensitivity A, can be measured from AFM tests on two reference materials with known elastic moduli. The measured α and A values specific to the tip and machine used can then be employed to accurately measure the elastic modulus of a third sample, assuming that the tip does not get significantly plastically deformed during the calibration procedure. AFM nanoindentation tests were performed on polypropylene (PP), fused quartz and acrylic samples to verify the validity of the proposed method. The cantilever-tip property and the cantilever sensitivity measured on PP and fused quartz were 0.514?GPa and 51.99?nm?nA(-1), respectively. Using these measured quantities, the elastic modulus of acrylic was measured to be 3.24?GPa, which agrees well with the value measured using conventional depth-sensing indentation in a commercial nanoindenter.     

System modelling of a lateral force microscope

To quantitatively analyse lateral force microscope measurements one needs to develop a model able to relate the photodiode signal to the force acting on the tip apex. In this paper we focus on the modelling of the interaction between the cantilever and the optical chain. The laser beam is discretized by a set of rays which propagates in the system. The analytical equation of a single ray's position on the optical sensor is presented as a function of the reflection's state on top of the cantilever. We use a finite element analysis on the cantilever to connect the optical model with the force acting on the tip apex. A first-order approximation of the constitutive equations are derived along with a definition of the system's crosstalk. Finally, the model is used to analytically simulate the 'wedge method' in the presence of crosstalk in 2D. The analysis shows how the torsion loop and torsion offset signals are affected by the crosstalk.     

Accurate and precise calibration of AFM cantilever spring constants using laser Doppler vibrometry

Accurate cantilever spring constants are important in atomic force microscopy both in control of sensitive imaging and to provide correct nanomechanical property measurements. Conventional atomic force microscope (AFM) spring constant calibration techniques are usually performed in an AFM. They rely on significant handling and often require touching the cantilever probe tip to a surface to calibrate the optical lever sensitivity of the configuration. This can damage the tip. The thermal calibration technique developed for laser Doppler vibrometry (LDV) can be used to calibrate cantilevers without handling or touching the tip to a surface. Both flexural and torsional spring constants can be measured. Using both Euler-Bernoulli modeling and an SI traceable electrostatic force balance technique as a comparison we demonstrate that the LDV thermal technique is capable of providing rapid calibrations with a combination of ease, accuracy and precision beyond anything previously available.     

Determining Mechanical Properties of Carbon Microcoils Using Lateral Force Microscopy

Mechanical properties of amorphous carbon microcoil (CMC) synthesized by thermal chemical vapor deposition method were examined in compression and tension tests, using the lateral force mode of atomic force microscope (AFM). The AFM cantilever tip was manipulated by a piezoelectric scanner to contact, pull, and push an individual CMC. The lateral force that was exerted by the CMC deformation causes the twist of the AFM cantilever. It was monitored by the laser and photodetector of the AFM during the experiments. A linear response of the CMC was observed in the range of 25 nm to 5 mum of tension experiments. The results show that the spring constant of the CMC is reasonably proportional to the coil number. The shear modulus of the amorphous CMC is estimated to be 3 plusmn 0.2 GPa. The proposed method is promising to manipulate the compression and tension of the CMC and to measure the lateral force exerted in an ambient environment.     

Thermoelectric voltage at a nanometer-scale heated tip point contact

We report thermoelectric voltage measurements between the platinum-coated tip of a heated atomic force microscope (AFM) cantilever and a gold-coated substrate. The cantilevers have an integrated heater-thermometer element made from doped single crystal silicon, and a platinum tip. The voltage can be measured at the tip, independent from the cantilever heating. We used the thermocouple junction between the platinum tip and the gold substrate to measure thermoelectric voltage during heating. Experiments used either sample-side or tip-side heating, over the temperature range 25-275?°C. The tip-substrate contact is ～4?nm in diameter and its average measured Seebeck coefficient is 3.4?μV?K(-1). The thermoelectric voltage is used to determine tip-substrate interface temperature when the substrate is either glass or quartz. When the non-dimensional cantilever heater temperature is 1, the tip-substrate interface temperature is 0.593 on glass and 0.125 on quartz. Thermal contact resistance between the tip and the substrate heavily influences the tip-substrate interface temperature. Measurements agree well with modeling when the tip-substrate interface contact resistance is 10(8)?K?W(-1).     

Nanomachining by rubbing at ultrasonic frequency under controlled shear force

This study proposes a new method of proximal-probe machining that uses a rubbing process by introducing concentrated-mass (CM) cantilevers. At the second resonance of the CM cantilever vibration, the tip site of the cantilever becomes a node of the standing deflection wave because of the sufficient inertia of the attached concentrated mass. The tip makes a cyclic motion that is tangential to the sample surface, not vertical to it, as in a tapping motion. This lateral tip motion that is selectively excited by CM cantilevers was effective for the material modification of a sample due to the friction between the tip and the sample. Imaging and nanomachining under controlled shear force were demonstrated by means of the modified cantilever and a normal atomic force microscope. We were able to write a micron-sized letter "Z" having a line width of 30-100 nm on a resin surface.     

极浅压入下纳米压痕仪针尖面积函数校准方法的研究

采用原子力显微镜直接扫描纳米压痕仪针尖法、球面拟合法和熔融石英标准样块的间接测量法对极浅压入下纳米压痕仪的针尖面积函数进行比较分析。实验表明,在极浅压入下,原子力显微镜直接法由于真实地反映了针尖尖端的几何形貌因而获得的面积函数更为准确可靠。建立了相应的数学模型,对于直接法测量中主要的误差,即由于原子力显微镜针尖曲率半径带来的误差进行了分析,结果表明在极小压入深度下压入深度越小,原子力显微镜针尖曲率半径带来的压痕仪针尖面积函数相对误差越大。     

Finite element simulation for the effect of loading rate on visco‐hyperelastic characterisation of soft materials by spherical nanoindentation

Nanoindentation test performed by atomic force microscopy is highly recommended for the characterisation of soft materials at nanoscale. The assumption proposed in the characterisation is that the material is pure elastic with no viscosity. However, this assumption does not represent the real characteristics of soft materials such as bio tissue or cell. Therefore, a parametric finite element simulation of nanoindentation by spherical tip was carried out to investigate the response of cells with different constitutive laws (elastic, hyperelastic and visco‐hyperelastic). The investigation of the loading rate effect on the characterisation of cell mechanical properties was performed for different size of spherical tip. The selected dimensions of spherical tips cover commercially available products. The viscosity effects are insensitive to the varied dimensions of spherical tip in this study. A limit loading rate was found above which viscous effect has to be considered to correctly determine the mechanical properties. The method in this work can be implemented to propose a criterion for the threshold of loading rate when viscosity effect can be neglected for soft material characterisation.Inspec keywords: atomic force microscopy, viscoelasticity, finite element analysis, nanoindentation, viscosity, biomechanics, indentation, elasticityOther keywords: spherical tip, viscosity effect, viscous effect, soft material characterisation, visco‐hyperelastic characterisation, spherical nanoindentation, nanoindentation test, atomic force microscopy, bio tissue, parametric finite element simulation, loading rate effect, cell mechanical properties, constitutive laws     

Nanometer-scale flow of molten polyethylene from a heated atomic force microscope tip

We investigate the nanometer-scale flow of molten polyethylene from a heated atomic force microscope (AFM) cantilever tip during thermal dip-pen nanolithography (tDPN). Polymer nanostructures were written for cantilever tip temperatures and substrate temperatures controlled over the range 100-260?°C and while the tip was either moving with speed 0.5-2.0 μm s(-1) or stationary and heated for 0.1-100 s. We find that polymer flow depends on surface capillary forces and not on shear between tip and substrate. The polymer mass flow rate is sensitive to the temperature-dependent polymer viscosity. The polymer flow is governed by thermal Marangoni forces and non-equilibrium wetting dynamics caused by a solidification front within the feature.     

The elastic modulus of spruce wood cell wall material measured by an in situ bending technique

Using a novel in situ testing technique, the elastic modulus of wood cell wall material can be determined with great accuracy. The method relies on a focussed ion beam system (FIB) to prepare samples from individual structural components at a length scale which otherwise is hardly, if at all, accessible for testing. To determine the elastic modulus of cell wall material, cantilevers are cut with the FIB from wood cells for beam bending experiments inside the FIB or a scanning electron microscope (SEM). This type of sample preparation is site-specific and, at the same time, minimises the usual sample mounting problems. Once cut, the cantilever is tested by applying a known force with a piezoresistive AFM tip that is mounted on a micromanipulator. The resulting displacement is determined from SEM micrographs taken during the test. The cross-sectional area of the cantilever is determined for a number of positions along its length using the FIB as a cutting tool. Applying this method, we measured the elastic modulus of spruce wood cell wall material to be ∼28 GPa.     

Aspect ratio dependence of the elastic properties of ZnO nanobelts

The Young's modulus of ZnO nanobelts was measured with an atomic force microscope by means of the modulated nanoindentation method. The elastic modulus was found to depend strongly on the width-to-thickness ratio of the nanobelt, decreasing from about 100 to 10 GPa, as the width-to-thickness ratio increases from 1.2 to 10.3. This surprising behavior is explained by a growth-direction-dependent aspect ratio and the presence of stacking faults in nanobelts growing along particular directions.     

Time-dependent contact behavior between diamond and a CNT turf

The elastic and adhesive properties of nominally vertically aligned carbon nanotube?(CNT) turfs have been measured using nanoindentation. The perceived stiffness of a CNT turf is dependent on the unloading rate, which decreases at slower unloading rates. Depth-controlled nanoindentation was used to examine adhesion effects. Adhesive loads between the turf and the probe tip increased as the time the tip is in contact with the turf increased. As these effects could be from either more tubes coming into contact with the tip due to relaxation and motion of CNTs relative to one another or each tube in contact increasing its adhesive behavior and sub-contact stiffness due to tube-tube interactions within the turf, electrical resistance measurements during nanoindentation were carried out. When the tip is held at a fixed nominal depth, the current remains constant while the contact load decreases, suggesting the number of tubes in contact with the tip stays constant with time while the relaxation mechanisms in the turf occur at positions lower than the contact surface. These observations, in conjunction with in situ TEM compression test of CNT arrays, are used to describe the relative effects the various length and time scales may have on the perceived properties measured during experiments, including elastic modulus and adhesion for gecko-like dry adhesives.     

The interaction of an atomic force microscope tip with a nano-object: a model for determining the lateral force

A calculation of the lateral force interaction between an atomic force microscope (AFM) tip and a nano-object on a substrate is presented. In particular, the case where the AFM tip is used to manipulate the nano-object is considered; i.e., the tip is displaced across the nano-object with the feedback off. The Hamaker equations are used to calculate the force when the tip and sample are not in contact and the Johnson, Kendall and Roberts (JKR) or Derjaguin, Muller and Toporov (DMT) formalisms are used for the contact force. The effect of the material parameters, the choice of contact theory and the shape of the nano-object on the resulting lateral forces are explored. The calculation is applied to an experimental system consisting of a cadmium selenide nanorod on graphite.     

AFM indentation method used for elastic modulus characterization of interfaces and thin layers

Atomic force microscopy (AFM) is increasingly being used as a nanoindentation tool to measure local elastic properties of surfaces. In this article, a method based on AFM in force volume (force curve mapping) mode is employed to measure the elastic modulus distribution at the interface of a glass flake-reinforced polypropylene sample and at a lead-free Cu–solder joint. Indentation arrays are performed using a diamond AFM tip. The processing of experimental AFM indentation data is automated by customized software that can analyse and calibrate multiple force curves. The analysis algorithm corrects the obtained force curves by selecting the contact point, discarding the non-contact region and subtracting the cantilever deflection from the measured force curve in order to obtain true indentation curves. A Hertzian model is then applied to the resulting AFM indentation data. Reference materials are used to estimate the tip radius needed to extract the elastic modulus values. With the proposed AFM measurement method, we are able to obtain high-resolution maps showing elastic modulus variations around a composite interface and a Cu–solder joint. No distinct interphase region is detected in the composite case, whereas a separate intermetallic layer (1–2 μm thick) of much higher Young’s modulus (~131 GPa) than Cu and solder material is identified in the Cu–solder joint. Elastic modulus results obtained for the Cu (~72 GPa), solder (~50 GPa) and glass (~65 GPa) materials are comparable to the results obtained by instrumented indentation [~73, ~46 and ~61 GPa], which accentuates the potential of this method for applications requiring high lateral resolution.     

Atomic force microscopy for the measurement of flexibility of single softwood pulp fibres

A new method based on the atomic force microscope has been developed to measure the lateral flexibility of single wood pulp fibres. In this method, individual wet pulp fibres from earlywood and latewood of Pinus radiata were placed on a newly designed two-point support, and the load and the deflection of fibres were measured under three-point bending test using a modified cantilever probe. The lateral flexibility values of the fibres were then calculated using propped cantilever beam theory. The results obtained indicate that earlywood fibres are substantially more flexible, and have a greater range of flexibility values than latewood fibres.     

Adaptable End Effector for Atomic Force Microscopy Based Nanomanipulation

Nanomanipulation using the atomic force microscope (AFM) has been extensively investigated for many years. But the efficiency and accuracy of AFM-based nanomanipulation are still major issues due to the nonlinearities and uncertainties in nanomanipulation operations. The deformation of the cantilever caused by manipulation force is one of the most major nonlinearities and uncertainties. It causes difficulties in accurately controlling the tip position, and results in missing the position of the object. The softness of the conventional cantilevers also causes the failure of manipulation of sticky nano-objects because the tip can easily slip over the nano-objects. In this paper, an active atomic force microscopy probe is used as an adaptable end effector to solve these problems by actively controlling the cantilever's flexibility or rigidity during nanomanipulation. A control voltage is applied to the piezo layer of the adaptable end effector to exert a reverse bending moment on the cantilever to balance the bending moment caused by the interaction force during manipulation. Thus, the adaptable end effector is controlled to maintain straight shape during manipulation. A detailed model of the adaptable end effector is presented in the paper. Control of the adaptable end effector employing an optimal LQR control law is derived and implemented. The experimental results verify the validity of the model and effectiveness of the controller. The nanomanipulation results also prove the increased efficiency of AFM-based nanomanipulation using the adaptable end effector     

Elastic property of vertically aligned nanowires

An atomic force microscopy (AFM) based technique is demonstrated for measuring the elastic modulus of individual nanowires/nanotubes aligned on a solid substrate without destructing or manipulating the sample. By simultaneously acquiring the topography and lateral force image of the aligned nanowires in the AFM contacting mode, the elastic modulus of the individual nanowires in the image has been derived. The measurement is based on quantifying the lateral force required to induce the maximal deflection of the nanowire where the AFM tip was scanning over the surface in contact mode. For the [0001] ZnO nanowires/nanorods grown on a sapphire surface with an average diameter of 45 nm, the elastic modulus is measured to be 29 +/- 8 GPa.     

High-resolution and large dynamic range nanomechanical mapping in tapping-mode atomic force microscopy

High spatial resolution imaging of material properties is an important task for the continued development of nanomaterials and studies of biological systems. Time-varying interaction forces between the vibrating tip and the sample in a tapping-mode atomic force microscope contain detailed information about the elastic, adhesive, and dissipative response of the sample. We report real-time measurement and analysis of the time-varying tip-sample interaction forces with recently introduced torsional harmonic cantilevers. With these measurements, high-resolution maps of elastic modulus, adhesion force, energy dissipation, and topography are generated simultaneously in a single scan. With peak tapping forces as low as 0.6?nN, we demonstrate measurements on blended polymers and self-assembled molecular architectures with feature sizes at 1, 10, and 500?nm. We also observed an elastic modulus measurement range of four orders of magnitude (1?MPa to 10?GPa) for a single cantilever under identical feedback conditions, which can be particularly useful for analyzing heterogeneous samples with largely different material components.     

A single electron transistor on an atomic force microscope probe

We report fabrication as well as proof-of-concept experiments of a noninvasive sensor of weak nanoscale electric fields. The sensor is a single electron transistor (SET) placed at the tip of a noncontact atomic force microscope (AFM). This is a general technology to make any nanometer-sized lithography pattern at edges or tips of a cantilever. The height control of the AFM allows the SET to hover a few nanometers above the substrate, improving both the electric field sensitivity and lateral resolution of the electrometer. Our AFM-SET sensor is prepared by a scalable technology. It means that the probe can be routinely fabricated and replaced, if broken.     

原子力显微镜探针原位有效参数对线宽测量的修正

针对原子力显微镜（AFM）的线宽和轮廓的精确测量，对AFM探针的原位有效参数进行了定义和表征，提出使用AFM探针的原位有效参数对AFM的线宽测量结果进行修正的模型。采用有效半径和半内角表征AFM探针的复合形状，悬臂轴倾角表征探针的安装状态，设计了具有不同梯形截面的两个表征样板，通过对表征样板进行AFM和扫描电子显微镜（SEM）的比对测量获得了探针的原位有效参数。提出了在线宽测量中，当AFM的扫描轮廓线具有不同的斜度时分别采用的不同的修正公式。采用此公式和探针的原位参数对掩膜板的AFM线宽测量结果进行了修正。