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.     

Calibration of silicon atomic force microscope cantilevers

We present a comparison of three different methods to calibrate the spring constant of two different types of silicon beam shaped atomic force microscope (AFM) cantilevers to determine each method's accuracy, ease of use and potential destructiveness. The majority of research in calibrating AFM cantilevers has been concerned with contact mode levers. The two types of levers we have studied are used in force modulation and tapping mode in air. Not only can these types of cantilevers have spring constants an order of magnitude greater than contact mode levers, but also their geometries can be quite different from the standard V-shape contact lever. In this work we experimentally determine the correction factors for two of the calibration methods when applied to the tapping mode cantilevers and also demonstrate that the force modulation levers can be calibrated easily and accurately using these same techniques.     

Calibration of higher eigenmode spring constants of atomic force microscope cantilevers

Standard spring constant calibration methods are compared when applied to higher eigenmodes of cantilevers used in dynamic atomic force microscopy (dAFM).?Analysis shows that Sader's original method (Sader et al 1999 Rev. Sci. Instrum. 70 3967-9), which relies on a priori knowledge of the eigenmode shape, is poorly suited for the calibration of higher eigenmodes. On the other hand, the thermal noise method (Hutter and Bechhoefer 1993 Rev. Sci. Instrum. 64 1868-73) does not require knowledge of the eigenmode and remains valid for higher eigenmodes of the dAFM probe. Experimental measurements of thermal vibrations in air for three representative cantilevers are provided to support the theoretical results.     

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.     

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.     

Hydrodynamic methods for calibrating the normal spring constant of microcantilevers

Knowledge of the spring constants of microcantilevers is vital in atomic force microscopy and for cantilever-based devices that are, for example, employed as probes in biomedical applications. We compare two recently developed hydrodynamic methods for the determination of the normal spring constant of microcantilevers. Both approaches are non-invasive when determining the spring constant and require only knowledge of the thermal noise response of the cantilever in a fluid and its plan view dimensions. The methods do not bear the risk of damaging the cantilever and are therefore attractive for example in mass sensing applications in cases where the cantilever has been modified, e.g.?with a coating. The specific strengths of the methods are discussed and the results for a variety of cantilevers are presented and compared.     

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.     

A new detection system for extremely small vertically mounted cantilevers

Detection techniques currently used in scanning force microscopy impose limitations on the geometrical dimensions of the probes and, as a consequence, on their force sensitivity and temporal response. A new technique, based on scattered evanescent electromagnetic waves (SEW), is presented here that can detect the displacement of the extreme end of a vertically mounted cantilever. The resolution of this method is tested using different cantilever sizes and a theoretical model is developed to maximize the detection sensitivity. The applications presented here clearly show that the SEW detection system enables the use of force sensors with sub-micron size, opening new possibilities in the investigation of biomolecular systems and high speed imaging. Two types of cantilevers were successfully tested: a high force sensitivity lever with a spring constant of 0.17?pN?nm(-1) and a resonant frequency of 32?kHz; and a high speed lever with a spring constant of 50?pN?nm(-1) and a resonant frequency of 1.8?MHz. Both these force sensors were fabricated by modifying commercial microcantilevers in a focused ion beam system. It is important to emphasize that these modified cantilevers could not be detected by the conventional optical detection system used in commercial atomic force microscopes.     

Atomic Force Microscopy as a Universal Means of Measuring Physical Quantities in the Mesoscopic Length Range

Data are given on recent advances in atomic force microscopy, which is used in precision measurements of various physical quantities and fields at solid surfaces. New designs are considered for micromechanical cantilevers, which are used as physical, chemical, and biological sensors.     

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。     

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.     

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.     

Magnetomechanical detection of the specific activities of endonucleases by cantilevers

Thiolated nucleic acids 1 or 2 are immobilized on Au-coated cantilevers and hybridized with the complementary nucleic acids 1a or 2a associated with magnetic particles. The duplexes 1/1a or 2/2a include specific sequences for the scission by Apa I or Mse I, respectively. The cantilevers positioned in a flow cell are subjected to an external magnetic field, leading to the deflection of the cantilevers. Upon the specific scission of the DNA duplexes by Apa I or Mse I, the magnetic particles are disconnected from the cantilevers leading to their retraction to the rest position. The deflection/retraction of the cantilevers are followed by a conventional atomic force microscope optical detection system.     

Force microscopy experiments with ultrasensitive cantilevers

Force microscopy experiments with the pendulum geometry are performed with attonewton sensitivity (Rugar et al 2004 Nature 43 329). Single-crystalline cantilevers with sub-millinewton spring constants were annealed under ultrahigh-vacuum conditions. It is found that annealing with temperatures below 500?°C can improve the quality factor by an order of magnitude. The high force sensitivity of these ultrasoft cantilevers is used to characterize small magnetic and superconductive particles, which are mounted on the end of the cantilever. Their magnetic properties are analysed in magnetic fields as a function of temperature. The transition of a superconducting sample mounted on a cantilever is measured by the detection of frequency shifts. An increase of dissipation is observed below the critical temperature. The magnetic moment of ferromagnetic particles is determined by real time frequency detection with a phase-locked loop (PLL) as a function of the magnetic field. The dissipation between the probing tip and the sample is another important ingredient for ultrasensitive force measurements. It is found that dissipation increases at separations of 30?nm. The origins of this type of dissipation are poorly understood. However, it is predicted theoretically that adsorbates can increase this dissipation channel (Volokitin and Persson 2005 Phys.?Rev.?Lett. 94 086104). First experiments are performed under ultrahigh vacuum to investigate this type of dissipation. Long-range dissipation is closely related to long-range forces. The distance dependence of the contact potential is found to be an important aspect.     

Control of curvature in highly compliant probe cantilevers during carbon nanotube growth

Direct growth of a sharp carbon nanotube (CNT) probe on a very thin and highly flexible cantilever by plasma-enhanced chemical vapor deposition (PECVD) is desirable for atomic force microscopy (AFM) of nanoscale features on soft or fragile materials. Plasma-induced surface stresses in such fabrication processes, however, tend to cause serious bending of these cantilevers, which makes the CNT probe unsuitable for AFM measurements. Here, we report a new tunable CNT growth technique that controls cantilever bending during deposition, thereby enabling the creation of either flat or deliberately curved AFM cantilevers containing a CNT probe. By introducing hydrogen gas to the (acetylene + ammonia) feed gas during CNT growth and adjusting the ammonia to hydrogen flow ratio, the cantilever surface stress can be altered from compressive to tensile stress, and in doing so controlling the degree of cantilever bending. The CNT probes grown under these conditions have high aspect ratios and are robust. Contact-mode imaging has been demonstrated using these probe tips. Such CNT probes can be useful for bio-imaging involving DNA and other delicate biological features in a liquid environment.     

Micromechanical testing of SU-8 cantilevers

SU‐8 is a photoplastic polymer with a wide range of possible applications in microtechnology. Cantilevers designed for atomic force microscopes were fabricated in SU‐8. The mechanical properties of these cantilevers were investigated using two microscale testing techniques: contact surface profilometer beam deflection and static load deflection at a point on the beam using a specially designed test machine. The SU‐8 Young's modulus value from the microscale test methods is approximately 2–3 GPa.     

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.     

Modeling Piezoresistive Microcantilever Sensor Response to Surface Stress for Biochemical Sensors

This paper considers mechanical stress and strain in a piezoresistive cantilever sensor under surface stress loading, which is the loading condition that occurs in biochemical sensing applications. Finite element simulations examine the piezoresistor sensitivity due to changes in cantilever length, width, and thickness, and piezoresistor size, location, and depth. A few unexpected results are found. Unlike cantilevers designed for atomic force microscopy, cantilevers for biochemical sensing should be short and wide. While shallow piezoresistors offer good sensitivity, the piezoresistor may extend far into the thickness of the cantilever and still be quite effective. The paper concludes with comments on design guidelines for piezoresistive cantilever sensors.     

Mapping nanomechanical properties of live cells using multi-harmonic atomic force microscopy

The nanomechanical properties of living cells, such as their surface elastic response and adhesion, have important roles in cellular processes such as morphogenesis, mechano-transduction, focal adhesion, motility, metastasis and drug delivery. Techniques based on quasi-static atomic force microscopy techniques can map these properties, but they lack the spatial and temporal resolution that is needed to observe many of the relevant details. Here, we present a dynamic atomic force microscopy method to map quantitatively the nanomechanical properties of live cells with a throughput (measured in pixels/minute) that is ～10-1,000 times higher than that achieved with quasi-static atomic force microscopy techniques. The local properties of a cell are derived from the 0th, 1st and 2nd harmonic components of the Fourier spectrum of the AFM cantilevers interacting with the cell surface. Local stiffness, stiffness gradient and the viscoelastic dissipation of live Escherichia coli bacteria, rat fibroblasts and human red blood cells were all mapped in buffer solutions. Our method is compatible with commercial atomic force microscopes and could be used to analyse mechanical changes in tumours, cells and biofilm formation with sub-10?nm detail.     

Toward Carbon Nanotube-Based AFM Cantilevers

The mechanical properties of carbon nanotubes have been widely employed to enhance the performance of atomic force microscopy (AFM) cantilever tips. Utilizing the electromechanical properties of carbon nanotubes, this paper investigates the potential of using carbon nanotubes as active strain sensing elements on AFM cantilevers. A batch microfabrication process was developed to construct silicon microcantilevers. Multiwalled carbon nanotubes were dielectrophoretically assembled between electrodes. Based on the characterization results of 12 devices, the CNT-based cantilevers demonstrated a linear relationship between resistance changes and externally applied strain. The gauge factor ranged from 78.84 to 134.40 for four different device configurations.