Toward a better modulus at shallow indentations—Enhanced tip and sample characterization for quantitative atomic force microscopy

Approximations of the geometry of indenting probes, particularly when using shallow indentations on soft materials, can lead to the erroneous reporting of mechanical data in atomic force microscopy (AFM). Scanning electron microscopy (SEM) identified a marked change in geometry toward the tip apex where the conical probe assumes a near linear flat-punch geometry. Polydimethylsiloxane (PDMS) is a ubiquitous elastomer within the materials and biological sciences. Its elastic modulus is widely characterized but the data are dispersed and can display orders of magnitude disparity. Herein, we compare the moduli gathered from a range of analytical techniques and relate these to the molecular architecture identified with AFM. We present a simple method that considers sub-100 nm indentations of PDMS using the Hertz and Sneddon contact mechanics models, and how this could be used to improve the output of shallow indentations on similarly soft materials, such as polymers or cells.     

AFM的纳米硬度测试与分析

基于原子力显微镜(AFM)和金刚石针尖建立了一套纳米压痕测量系统。通过向系统发送控制电压使金刚石针尖在完成加载和卸载全过程的同时进行实时的数据采集并直接绘出载荷-压深曲线。利用该系统,对单晶铝和单晶铜薄膜材料进行了单点压痕实验,用美国Hysitron公司的纳米原位测量仪(TriboIndenter)做了验证试验。实验结果表明,该系统适合测量较软材料的纳米硬度。分析了基体材料对薄膜硬度和弹性模量的影响,在薄膜厚度低于5~10倍压入深度时,基体对薄膜材料的力学性能影响很大;并根据获得的载荷－压深曲线分析得出由于尺度效应的影响,随着压痕深度的减小,薄膜的硬度值呈明显的上升趋势,弹性模量没有这个趋势。     

Quantitative measurement of indentation hardness and modulus of compliant materials by atomic force microscopy

An atomic force microscopy (AFM) based technique is proposed for the characterization of both indentation modulus and hardness of compliant materials. A standard AFM tip is used as an indenter to record force versus indentation curves analogous to those obtained in standard indentation tests. In order to overcome the lack of information about the apex geometry, the proposed technique requires calibration using a set of reference samples whose mechanical properties have been previously characterized by means of an independent technique, such as standard indentation. Due to the selected reference samples, the technique has been demonstrated to allow reliable measurements of indentation modulus and hardness in the range of 0.3-4.0 GPa and 15-250 MPa, respectively.     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

Comparing microscopic with macroscopic elastic properties of polymer gel

Measurements of the local elastic modulus of agar gels obtained with atomic force microscope (AFM) force mapping were compared with values obtained by the tensile creep method. The observed spatial distributions of the local elastic modulus over the gel surface in AFM elastic images clearly corresponded to the network structure of agar fibers observed both in AFM topographic and scanning electron microscope (SEM) images. Both peak and average values of distribution functions in the histograms of local elastic modulus increase monotonically with the agar concentration. Values obtained by AFM force mapping were found to be proportional to values obtained from creep experiments.     

Mechanical property measurements of nanoscale structures using an atomic force microscope

This paper describes nanometer-scale bending tests of fixed single-crystal silicon (Si) and silicon dioxide (SiO2) nanobeams using an atomic force microscope (AFM). The technique is used to evaluate elastic modulus of the beam materials and bending strength of the beams. Nanometer-scale Si beams with widths ranging from 200 to 800 nm were fabricated on a Si diaphragm using field-enhanced anodization using an AFM followed by anisotropic wet etching. Subsequent thermal oxidation of Si beams was carried out to create SiO2 beams. Results from the bending tests indicate that elastic modulus values are comparable to bulk values. However, the bending strength appears to be higher for these nanoscale structures than for large-scale specimens. Observations of the fracture surface and calculations of the crack length from Griffith's theory appear to indicate that the maximum peak-to-valley distance on the beam top surfaces influence the values of the observed bending strengths.     

基于单片机的AFM纳米机械性能测试系统

摘要：目的：为解决采用AFM系统进行纳米机械性能测试中存在的不能够直接获得载荷——压深曲线以及不能够随意改变加载、保载、卸载时间等问题,对AFM系统进行改造。方法：开发了一套基于单片机的信号输入输出模块。将该模块与AFM控制系统相联,形成新的纳米机械性能测试系统。结果：该系统可以实现动态改变垂直载荷,并依据相应算法,可以实现载荷——压深曲线的实时获得。通过单片机设置模拟信号的输出速率可以实现加载、保载和卸载速率的改变。并结合二维微动精密工作台,可以实现较大范围内点阵的压痕测试。结论：通过在聚碳酸酯、聚二甲基硅氧烷等材料表面进行试验测试表明：该系统可以进行高速高精度的测量样品的纳米机械性能参数,包括对样品进行纳米压痕测试和对样品的纯弹性变形过程进行检测如聚二甲基硅氧烷或者各种微梁等微小构件。     

Indentation modulus and hardness of viscoelastic thin films by atomic force microscopy: A case study

We propose a nanoindentation technique based on atomic force microscopy (AFM) that allows one to deduce both indentation modulus and hardness of viscoelastic materials from the force versus penetration depth dependence, obtained by recording the AFM cantilever deflection as a function of the sample vertical displacement when the tip is pressed against (loading phase) and then removed from (unloading phase) the surface of the sample. Reliable quantitative measurements of both indentation modulus and hardness of the investigated sample are obtained by calibrating the technique through a set of different polymeric samples, used as reference materials, whose mechanical properties have been previously determined by standard indentation tests. By analyzing the dependence of the cantilever deflection versus time, the proposed technique allows one to evaluate and correct the effect of viscoelastic properties of the investigated materials, by adapting a post-experiment data processing procedure well-established for standard depth sensing indentation tests. The technique is described in the case of the measurement of indentation modulus and hardness of a thin film of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate), deposited by chronoamperometry on an indium tin oxide (ITO) substrate.     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

The comparison between force volume and peakforce quantitative nanomechanical mode of atomic force microscope in detecting cell's mechanical properties

Atomic force microscope (AFM) has been widely used in the biological field owing to its high sensitivity (subnanonewton), high spatial resolution (nanometer), and adaptability to physiological environments. Nowadays, force volume (FV) and peakforce quantitative nanomechanical (QNM) are two distinct modes of AFM used in biomechanical research. However, numerous studies have revealed an extremely confusing phenomenon that FV mode has a significant difference with QNM in determining the mechanical properties of the same samples. In this article, for the case of human benign prostatic hyperplasia cells (BPH) and two cancerous prostate cells with different grades of malignancy (PC3 and DU145), the differences were compared between FV and QNM modes in detecting mechanical properties. The results show measured Young's modulus of the same cells in FV mode was much lower than that obtained by QNM mode. Combining experimental results with working principles of two modes, it is indicated that surface adhesion is highly suspected to be a critical factor resulting in the measurement difference between two modes. To further confirm this conjecture, various weight ratios of polydimethylsiloxane (PDMS) were assessed by two modes, respectively. The results show that the difference of Young's modulus measured by two modes increases with the surface adhesion of PDMS, confirming that adhesion is one of the significant elements that lead to the measurement difference between FV and QNM modes.     

Dual resonance excitation system for the contact mode of atomic force microscopy

We propose an improved system that enables simultaneous excitation and measurements of at least two resonance frequency spectra of a vibrating atomic force microscopy (AFM) cantilever. With the dual resonance excitation system it is not only possible to excite the cantilever vibrations in different frequency ranges but also to control the excitation amplitude for the individual modes. This system can be used to excite the resonance frequencies of a cantilever that is either free of the tip-sample interactions or engaged in contact with the sample surface. The atomic force acoustic microscopy and principally similar methods utilize resonance frequencies of the AFM cantilever vibrating while in contact with the sample surface to determine its local elastic modulus. As such calculation demands values of at least two resonance frequencies, two or three subsequent measurements of the contact resonance spectra are necessary. Our approach shortens the measurement time by a factor of two and limits the influence of the AFM tip wear on the values of the tip-sample contact stiffness. In addition, it allows for in situ observation of processes transpiring within the AFM tip or the sample during non-elastic interaction, such as tip fracture.     

Evaluating local elasticity of the metal nano-films quantitatively based on referencing approach of atomic force acoustic microscopy

Traditional technique such nanoindenter(NI) can’t measure the local elastic modulus at nano-scale(lateral). Atomic force acoustic microscopy (AFAM) is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper(Cu) film with 110 nm thickness, zinc(Zn) film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples (it’s elastic modulus is known), and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values MCu=105-130 GPa, MZn=88.44 GPa and MGlass=50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160μm, 225μm and 520μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.     

Contact-resonance atomic force microscopy for nanoscale elastic property measurements: Spectroscopy and imaging

Quantitative measurements of the elastic modulus of nanosize systems and nanostructured materials are provided with great accuracy and precision by contact-resonance atomic force microscopy (CR-AFM). As an example of measuring the elastic modulus of nanosize entities, we used the CR-AFM technique to measure the out-of-plane indentation modulus of tellurium nanowires. A size-dependence of the indentation modulus was observed for the investigated tellurium nanowires with diameters in the range 20–150 nm. Over this diameter range, the elastic modulus of the outer layers of the tellurium nanowires experienced significant enhancement due to a pronounced surface stiffening effect. Quantitative estimations for the elastic moduli of the outer and inner parts of tellurium nanowires of reduced diameter are made with a core–shell structure model. Besides localized elastic modulus measurements, we have also developed a unique CR-AFM imaging capability to map the elastic modulus over a micrometer-scale area. We used this CR-AFM capability to construct indentation modulus maps at the junction between two adjacent facets of a tellurium microcrystal. The clear contrast observed in the elastic moduli of the two facets indicates the different surface crystallography of these facets.     

Complex approach to investigate mechanical and tribological characteristics of microcontacting objects for MEMS

Abstract

A complex approach based on atomic force microscopy (AFM) is developed to establish influence of nanoscale layer thickness on its elastic, adhesive and frictional properties of polymeric coatings for microelectromechanical systems. Thermoheating element was applied to perform AFM measurements with thermal effects in the temperature range from 20 to 120°C. Friction coefficients at high velocities of sliding and dependences of friction coefficient on the temperature of heated films at low velocities of sliding are defined. This study concludes that the Young’s modulus of ultrathin polymeric films on silicon substrate is reduced when thickness or temperature is increased.     

Comparison of friction measurements using the atomic force microscope and the surface forces apparatus: the issue of scale

Results are presented of lateral force measurements using the atomic force microscope (AFM) and the surface forces apparatus (SFA). Two different probes are used in the AFM measurements; a sharp silicon nitride tip (radius R20 nm) and a glass ball (R15 m). The lateral force is measured between the (silicon nitride or glass) probe and a mica surface which has been coated by a thin lubricant film. In the SFA, a thin lubricant film separates two molecularly smooth mica surfaces (R1 cm) which are slid relative to each other. Perfluoropolyether (PFPE) and polydimethylsiloxane (PDMS) were used as the lubricant films. In the SFA where the contact diameter is largest, the PFPE film shows much lower friction than PDMS. As the size of the probe decreases, the difference in the measured friction decreases. For sharp AFM tips, no clear distinction between the tribological properties of the films can be made. Hence, the measured coefficient of friction varies according to the length scale probed, at least for small dimensions.     

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.     

Mechanical properties of L929 cells measured by atomic force microscopy: Effects of anticytoskeletal drugs and membrane crosslinking

To shed light on the architecture of the cytoskeleton, we used the atomic force microscope (AFM) to measure the elasticity, viscoelasticity, and plasticity of L929 cells. The initial elastic response (Young's modulus ～ 4,000 Pa) of the cells to an applied force was followed by a slow compression of the cytoskeleton (τ_1/2 ≈ 10 s). When force application was terminated, the cytoskeleton underwent a sudden partial decompression and a subsequent slow, incomplete recovery. The role of the cytoskeletal elements in cell mechanics was accessed in AFM measurements carried out on cells treated with cytochalasin D, nocodazole, or col-cemid. Cytochalasin D treatment reduced both elasticity (～45%) and cytoplasmic viscosity (～65%), whereas cells treated with nocodazole or colcemid exhibited a marked increase in elasticity (～100%) and a slight increase in viscosity (～15%). The AFM force measurements also provided evidence that the cell membrane and the cytoskeleton are mechanically coupled. Tightly adherent cells were stiffer than cells that were loosely attached. Moreover, cells crosslinked with either glutaraldehyde, 3,3 ‘-dithiobis’sul-fosuccinimidylpropionate] (DTSSP), or Concanavalin A were more rigid than untreated cells. It is of interest that cells crosslinked with Concanavalin A, but not DTSSP, displayed plastic behaviors that may reflect the induction of cytoskeletal reorganization by Concanavalin A.     

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.     

Combined quantitative ultrasonic and time-resolved interaction force AFM imaging

The authors describe a method where quantitative ultrasonic atomic force microscopy (UAFM) is achieved during time-resolved interaction force (TRIF) imaging in intermittent contact mode. The method uses a calibration procedure for quantitative UAFM. It improves elasticity measurements of stiff regions of surfaces while retaining the capabilities of the TRIF mode for topography, adhesion, dissipation, and elasticity measurements on soft regions of sample surfaces. This combination is especially advantageous when measuring and imaging samples with broad stiffness range in a nondestructive manner. The experiments utilize an active AFM probe with high bandwidth and the UAFM calibration is performed by measuring the magnitude of the time-resolved UAFM signal at a judiciously chosen frequency for different contact stiffness values during individual taps. Improved sensitivity to stiff surface elasticity is demonstrated on a special sample. The results show that combining UAFM with TRIF provides 2.5 GPa (5%) standard deviation on the silicon surface reduced Young's modulus, representing 5× improvement over using only TRIF mode imaging.     

Influence of antifriction fillers on the surface properties of elastomers based on propylenoxide rubbers

Novel compositions of frost-resistant rubbers (elastomers) are investigated. The possibilities of modifying the basic elastomer using several different fillers are studied. A PTFE-based filler (Forum), technical carbon (TC), and graphene oxide (GO) are tested as fillers. Mechanical, tribological, and microscopic investigations (SEM with elemental analysis and an atomic force microscope (AFM) using different modes) are performed. In order to investigate the operating parameters of these samples, the sample surface was studied before and after the friction tests. The surface topography and the distribution of individual elements over the surface are estimated. Microscopic sections of the samples are studied to obtain information concerning the bulk distribution of the chemical elements. It is shown that the use of fillers such as Forum and technical carbon leads to a better result when they are used together. Their elastic, viscous, and adhesive properties are studied using AFM (the force curve mode—“force-distance curve” and the force modulation mode—“magnitude-distance curve”). It is shown that a distinctive feature of rubber samples having the best tribological properties consists of an increase in rigidity and a decrease in adhesion in the course of tribological testing.