Accuracy of the spring constant of atomic force microscopy cantilevers by finite element method

Atomic force microscopy (AFM) probe with different functions can be used to measure the bonding force between atoms or molecules. In order to have accurate results, AFM cantilevers must be calibrated precisely before use. The AFM cantilever's spring constant is usually provided by the manufacturer, and it is calculated from simple equations or some other calibration methods. The spring constant may have some uncertainty, which may cause large errors in force measurement. In this paper, finite element analysis was used to obtain the deformation behavior of the AFM cantilever and to calculate its spring constant. The influence of prestress, ignored by other methods, is discussed in this paper. The variations of Young's modulus, Poisson's ratio, cantilever geometries, tilt angle, and the influence of image tip mass were evaluated to find their effects on the cantilever's characteristics. The results were compared with those obtained from other methods.     

Atomic Force Microscope Cantilever Flexural Stiffness Calibration: Toward a Standard Traceable Method

The evolution of the atomic force microscope into a useful tool for measuring mechanical properties of surfaces at the nanoscale has spurred the need for more precise and accurate methods for calibrating the spring constants of test cantilevers. Groups within international standards organizations such as the International Organization for Standardization and the Versailles Project on Advanced Materials and Standards (VAMAS) are conducting studies to determine which methods are best suited for these calibrations and to try to improve the reproducibility and accuracy of these measurements among different laboratories. This paper expands on a recent mini round robin within VAMAS Technical Working Area 29 to measure the spring constant of a single batch of triangular silicon nitride cantilevers sent to three international collaborators. Calibration techniques included reference cantilever, added mass, and two forms of thermal methods. Results are compared to measurements traceable to the International System of Units provided by an electrostatic force balance. A series of guidelines are also discussed for procedures that can improve the running of round robins in atomic force microscopy.     

Accurate analytical measurements in the atomic force microscope: a microfabricated spring constant standard potentially traceable to the SI

Calibration 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 at nanoscale lateral resolution. We have developed a compact and easy-to-use reference artefact for this calibration, using a method that allows traceability to the SI (Système International). Traceability is crucial to ensure that force measurements by AFM are comparable to those made by optical tweezers and other methods. The new non-contact calibration method measures the spring constant of these artefacts, by a combination of electrical measurements and Doppler velocimetry. The device was fabricated by silicon surface micromachining. The device allows AFM cantilevers to be calibrated quite easily by the 'cantilever-on-reference' method, with our reference device having a spring constant uncertainty of around ± 5% at one standard deviation. A simple substitution of the analogue velocimeter used in this work with a digital model should reduce this uncertainty to around ± 2%. Both are significant improvements on current practice, and allow traceability to the SI for the first time at these nanonewton levels.     

原子力显微镜用于微尺度材料力学性能表征的研究进展

原子力显微镜(AFM)是纳米科学研究的有力工具。从AFM的原理出发,分析了探针与样品之间作用力的计算过程,介绍了确定悬臂弹性常数的几种方法,并综述了AFM在生物材料、薄膜材料、纳米结构、单分子操作和纳米力学实验中的研究进展。     

Variations in properties of atomic force microscope cantilevers fashioned from the same wafer

Variations in the mechanical properties of nominally identical V-shaped atomic force microscope (AFM) cantilevers sourced from the same silicon nitride wafer have been quantified by measuring the spring constants, resonant frequencies and quality factors of 101 specimens as received from the manufacturer using the thermal spectrum method of Hutter and Bechhoefer. The addition of thin gold coatings always lowers the resonant frequency but the corresponding spring constant can either increase or decrease as a result. The observed broad spread of spring constant values and the lack of correlations between the resonant frequency and spring constant can be attributed in part to the non-uniformity of composition and material properties in the thinnest dimension of such cantilevers which arise from the manufacturing process. The effects of coatings are dictated by the competing influence of differences in mass density and Young's modulus between the silicon nitride and the gold coating. An implication of this study is that cantilever calibration methods based on the assumption of uniformity of material properties of the cantilever in the thinnest dimension are unlikely to be applicable for such cantilevers.     

Atomic force microscope cantilever calibration using a focused ion beam

A calibration method is presented for determining the spring constant of atomic force microscope (AFM) cantilevers, which is a modification of the established Cleveland added mass technique. A focused ion beam (FIB) is used to remove a well-defined volume from a cantilever with known density, substantially reducing the uncertainty usually present in the added mass method. The technique can be applied to any type of AFM cantilever; but for the lowest uncertainty it is best applied to silicon cantilevers with spring constants above 0.7?N?m(-1), where uncertainty is demonstrated to be typically between 7 and 10%. Despite the removal of mass from the cantilever, the calibration method presented does not impair the probes' ability to acquire data. The technique has been extensively tested in order to verify the underlying assumptions in the method. This method was compared to a number of other calibration methods and practical improvements to some of these techniques were developed, as well as important insights into the behavior of FIB modified cantilevers. These results will prove useful to research groups concerned with the application of microcantilevers to nanoscience, in particular for cases where maintaining pristine AFM tip condition is critical.     

随机噪声激励下轻敲式原子力显微镜动力学特性研究

针对有界随机噪声激励下轻敲式原子力显微镜 (AFM：Atomic force microscope)系统的非线性动力学问题,建立Lennard-Jones力场作用下针尖-样品的集总参数模型,应用现代微分方程和分岔理论,分析了随机扰动强度和弯月面接触角对AFM针尖-样品耦合系统动力学特性的影响。结果表明,轻敲式AFM耦合动力学系统中存在丰富的周期运动和混沌运动,表现出复杂的非线性行为,混沌特性随着随机扰动强度增大而增强,弯月面接触角越大混沌特性越明显,因此在轻敲式AFM优化设计中,随机噪声对AFM系统的影响不可忽视。     

Controlled AFM detachments and movement of nanoparticles: gold clusters on HOPG at different temperatures

The effect of temperature on the onset of movement of gold nanoclusters (diameter 27 nm) deposited on highly oriented pyrolytic graphite (HOPG) has been studied by atomic force microscopy (AFM) techniques. Using the AFM with amplitude modulation (tapping mode AFM) we have stimulated and controlled the movement of individual clusters. We show how, at room temperature, controlled detachments and smooth movements can be obtained for clusters having dimensions comparable to or smaller than the tip radius. Displacement is practically visible in real time and it can be started and stopped easily by adjusting only one parameter, the tip amplitude oscillation. Analysing the energy dissipation signal at the onset of nanocluster sliding we evaluated a detachment threshold energy as a function of temperature in the range 300-413 K. We also analysed single cluster thermal induced displacement and combining this delicate procedure with AFM forced movement behaviour we conclude that detachment threshold energy is directly related to the activation energy of nanocluster diffusion and it scales linearly with temperature as expected for a single-particle thermally activated process.     

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.     

水化膜对原子力显微镜扫描图像的影响

原子力显微镜(AFM)有接触和轻敲两种工作方式,可以在气相和液相下工作.在液相工作状态下,浸没于水中的探针和样品表面会形成一层水化膜.在探针和样品表面形成的水化膜是否会对扫描图像产生影响以及产生何种影响是一个值得研究的问题.本文用原子力显微镜对1μm标准校正光栅在空气和水两种媒质中进行了图像扫描,扫描分别采用接触和轻敲两种工作方式.扫描图像显示,在液相工作环境中,水化膜在探针和样品表面的形成将严重影响轻敲工作方式所形成的图像,而接触方式的扫描图像基本不受影响.     

原子力声显微镜成像及分析

超声检测技术与原子力显微技术相结合,构成原子力声显微镜(AFAM),能够实现样品内部纳米结构的测量,并分析如局域弹性模量、刚度等力学性能.本文在传统的原子力显微镜(AFM)的基础上初步构建了AFAM,利用AFM轻敲模式下的微悬臂梁振动激励信号来驱动样品背面的压电超声换能器,并利用轻敲模式控制系统中的锁相环检测经过样品后由探针收集的振动信号,形成振幅及相位图像.这种AFAM方法不需外接信号发生器、锁相放大器及相关控制电路,从而避免AFM内、外部的仪器及控制电路的不同步而引起的AFAM振幅/相位与形貌图像间的偏移.此外,还分析了形貌结构对AFAM振幅图像的影响,为进一步研究AFAM亚表面成像奠定了基础.     

Characterization of materials' nanomechanical properties by force modulation and phase imaging atomic force microscopy with soft cantilevers

Soft cantilevers, although having good force sensitivity, have found limited use for investigating materials' nanomechanical properties by conventional force modulation (FM) and intermittent contact (IC) atomic force microscopy. This is due to the low forces and small indentations that these cantilevers are able to exert on the surface, and to the high amplitudes required to overcome adhesion to the surface. In this paper, it is shown that imaging of local elastic properties of surface and subsurface layers can be carried out by employing electrostatic forcing of the cantilever. In addition, by mechanically exciting the higher vibration modes in contact with the surface and monitoring the phase of vibrations, the contrast due to local surface elasticity is obtained.     

Diamond-modified AFM probes: from diamond nanowires to atomic force microscopy-integrated boron-doped diamond electrodes

In atomic force microscopy (AFM), sharp and wear-resistant tips are a critical issue. Regarding scanning electrochemical microscopy (SECM), electrodes are required to be mechanically and chemically stable. Diamond is the perfect candidate for both AFM probes as well as for electrode materials if doped, due to diamond's unrivaled mechanical, chemical, and electrochemical properties. In this study, standard AFM tips were overgrown with typically 300 nm thick nanocrystalline diamond (NCD) layers and modified to obtain ultra sharp diamond nanowire-based AFM probes and probes that were used for combined AFM-SECM measurements based on integrated boron-doped conductive diamond electrodes. Analysis of the resonance properties of the diamond overgrown AFM cantilevers showed increasing resonance frequencies with increasing diamond coating thicknesses (i.e., from 160 to 260 kHz). The measured data were compared to performed simulations and show excellent correlation. A strong enhancement of the quality factor upon overgrowth was also observed (120 to 710). AFM tips with integrated diamond nanowires are shown to have apex radii as small as 5 nm and where fabricated by selectively etching diamond in a plasma etching process using self-organized metal nanomasks. These scanning tips showed superior imaging performance as compared to standard Si-tips or commercially available diamond-coated tips. The high imaging resolution and low tip wear are demonstrated using tapping and contact mode AFM measurements by imaging ultra hard substrates and DNA. Furthermore, AFM probes were coated with conductive boron-doped and insulating diamond layers to achieve bifunctional AFM-SECM probes. For this, focused ion beam (FIB) technology was used to expose the boron-doped diamond as a recessed electrode near the apex of the scanning tip. Such a modified probe was used to perform proof-of-concept AFM-SECM measurements. The results show that high-quality diamond probes can be fabricated, which are suitable for probing, manipulating, sculpting, and sensing at single digit nanoscale.     

Atomic force microscopy with nanoscale cantilevers resolves different structural conformations of the DNA double helix

Structural variability and flexibility are crucial factors for biomolecular function. Here we have reduced the invasiness and enhanced the spatial resolution of atomic force microscopy (AFM) to visualize, for the first time, different structural conformations of the two polynucleotide strands in the DNA double helix, for single molecules under near-physiological conditions. This is achieved by identifying and tracking the anomalous resonance behavior of nanoscale AFM cantilevers in the immediate vicinity of the sample.     

Conductive supports for combined AFM-SECM on biological membranes

Four different conductive supports are analysed regarding their suitability for combined atomic force and scanning electrochemical microscopy (AFM-SECM) on biological membranes. Highly oriented pyrolytic graphite (HOPG), MoS(2), template stripped gold, and template stripped platinum are compared as supports for high resolution imaging of reconstituted membrane proteins or native membranes, and as electrodes for transferring electrons from or to a redox molecule. We demonstrate that high resolution topographs of the bacterial outer membrane protein F can be recorded by contact mode AFM on all four supports. Electrochemical feedback experiments with conductive cantilevers that feature nanometre-scale electrodes showed fast re-oxidation of the redox couple Ru(NH(3))(6)(3+/2+) with the two metal supports after prolonged immersion in electrolyte. In contrast, the re-oxidation rates decayed quickly to unpractical levels with HOPG or MoS(2) under physiological conditions. On HOPG we observed heterogeneity in the re-oxidation rate of the redox molecules with higher feedback currents at step edges. The latter results demonstrate the capability of conductive cantilevers with small electrodes to measure minor variations in an SECM signal and to relate them to nanometre-scale features in a simultaneously recorded AFM topography. Rapid decay of re-oxidation rate and surface heterogeneity make HOPG or MoS(2) less attractive for combined AFM-SECM experiments on biological membranes than template stripped gold or platinum?supports.     

Routine and timely sub-picoNewton force stability and precision for biological applications of atomic force microscopy

Force drift is a significant, yet unresolved, problem in atomic force microscopy (AFM). We show that the primary source of force drift for a popular class of cantilevers is their gold coating, even though they are coated on both sides to minimize drift. Drift of the zero-force position of the cantilever was reduced from 900 nm for gold-coated cantilevers to 70 nm (N = 10; rms) for uncoated cantilevers over the first 2 h after wetting the tip; a majority of these uncoated cantilevers (60%) showed significantly less drift (12 nm, rms). Removing the gold also led to ～10-fold reduction in reflected light, yet short-term (0.1-10 s) force precision improved. Moreover, improved force precision did not require extended settling; most of the cantilevers tested (9 out of 15) achieved sub-pN force precision (0.54 ± 0.02 pN) over a broad bandwidth (0.01-10 Hz) just 30 min after loading. Finally, this precision was maintained while stretching DNA. Hence, removing gold enables both routine and timely access to sub-pN force precision in liquid over extended periods (100 s). We expect that many current and future applications of AFM can immediately benefit from these improvements in force stability and precision.     

压膜阻尼对原子力显微镜振动特性的影响研究

原子力显微镜(Atomic Force Microscope, AFM)在轻敲模式下工作时,随着探针针尖与样品距离的逐渐减小,空气压膜阻尼的作用随之增大。为研究压膜阻尼对原子力显微镜振动系统的影响,分别使用无针尖探针和微球针尖探针进行扫频实验,并基于振动理论将该过程简化,得到了两种不同的振动模型的系统刚度。在考虑压膜阻尼作用影响后,将微球针尖振动系统模型进一步简化为一维振子模型,并对压膜阻尼的影响进行讨论。实验表明空气压膜阻尼模型对于探针样品在微尺度下的作用过程是准确合理的。该结果对原子力显微镜轻敲模式研究具有重要意义。     

Electrostatic interaction forces in aqueous salt solutions of variable concentration and valency

We use atomic force microscopy (AFM) to determine electrostatic interactions between Si tips and Si wafers in aqueous electrolytes of variable composition. We demonstrate that dynamic force spectroscopy (DFS) in the frequency modulation (FM) mode with stiff cantilevers and sharp tips allows for a continuous detection of the tip-sample interactions without mechanical jump-to-contact instability and with substantially higher lateral resolution than standard colloidal probe measurements. For four different species of salt (NaCl, KCl, MgCl(2), CaCl(2)) we find repulsive electrostatic forces at the lowest salt concentrations (1 mM) that become progressively screened until they are dominated by attractive van der Waals forces at the highest concentration (100 mM). For the divalent cations the crossover from repulsive to attractive forces occurs at lower concentrations than for monovalent cations. Surface charges extracted from fits to standard Poisson-Boltzmann double layer theory indicate a rather weak dependence of the surface charge on the ion concentration. The high lateral resolution of our approach is illustrated by a 2D force field measurement over a patterned surface of a supported lipid bilayer on a mica substrate.     

Numerical simulation of nano scanning in intermittent-contact mode AFM under Q control

We investigate nano scanning in tapping mode atomic force microscopy (AFM) under quality (Q) control via numerical simulations performed in SIMULINK. We focus on the simulation of the whole scan process rather than the simulation of cantilever dynamics and the force interactions between the probe tip and the surface alone, as in most of the earlier numerical studies. This enables us to quantify the scan performance under Q control for different scan settings. Using the numerical simulations, we first investigate the effect of the elastic modulus of the sample (relative to the substrate surface) and probe stiffness on the scan results. Our numerical simulations show that scanning in an attractive regime using soft cantilevers with high effective Q factor (Q(eff)) results in a better image quality. We then demonstrate the trade-off in setting Q(eff) of the probe in Q control: low values of Q(eff) cause an increase in tapping forces while higher ones limit the maximum achievable scan speed due to the slow response of the cantilever to the rapid changes in surface profile. Finally, we show that it is possible to achieve higher scan speeds without causing an increase in the tapping forces using adaptive Q control (AQC), in which the Q factor of the probe is changed instantaneously depending on the magnitude of the error signal in oscillation amplitude. The scan performance of AQC is quantitatively compared to that of standard Q control using iso-error curves obtained from numerical simulations first and then the results are validated through scan experiments performed using a physical set-up.