Calibration Of Atomic Force Microscope Research Articles

Lateral Force Calibration Method Used for Calibration of Atomic Force Microscope

Modern heterogeneous micro- and nanostructures usually integrate modules fabricated using various materials and technologies. Moreover, it has to be emphasized that the macro and micro nanoscale material parameters are not the same. For this reason it has become crucial to identify the nanomechanical properties of the materials commonly used in micro- and nanostructure technology. One of such tests is a nanowear test performed using the atomic force microscope (AFM). However, to obtain quantitative measurement results a precision calibration step is necessary. In this paper a novel approach to calibration of lateral force acting on the tip of an AFM cantilever is discussed. Presented method is based on application of known lateral force directly on the tip using a special test structure. Such an approach allows for measurements of nanowear parameters (force, displacement) with the uncertainty better than ±3%. The calibration structure designed specifically for this calibration method is also presented.

DNA origami structures as calibration standards for nanometrology

In this work we have studied the feasibility of DNA origami nanostructures as dimensional calibration standards for atomic force microscopes (AFMs) at the nanometre scale. The stability of the structures and repeatability of the measurement have been studied, and the applicability for calibration is discussed. A cross-like Seeman tile (ST) was selected for the studies and it was found suitable for repeatable calibration of AFMs. The height of the first height step of the ST was 2.0 nm. Expanded standard uncertainty (k = 2) of the measurement Uc was 0.2 nm. The width of the ST was 88 nm and width of its arm was 28 nm with Uc = 3 nm. In addition, prepared dry samples were found out to be stable at least for 12 months.

Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2–18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip–sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32–156 N m−1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.

Atomic force microscope caliper for critical dimension measurements of micro and nanostructures through sidewall scanning

A novel atomic force microscope (AFM) dual-probe caliper for critical dimension (CD) metrology has been developed. The caliper is equipped with two facing tilted optical fiber probes (OFPs) wherein each can be used independently to scan either sidewall of micro and nanostructures. The OFP tip with length up to 500μm (aspect ratio 10:1, apex diameter ⩾10nm) has unique features of scanning deep trenches and imaging sidewalls of relatively high steps with exclusive profiling possibilities. The caliper arms–OFPs can be accurately aligned with a well calibrated opening distance. The line width, line edge roughness, line width roughness, groove width and CD angles can be measured through serial scan of adjacent or opposite sidewalls with each probe. Capabilities of the presented AFM caliper have been validated through experimental CD measurement results of comb microstructures and AFM calibration grating TGZ3.

Atomic force microscopy deep trench and sidewall imaging with an optical fiber probe.

We report a method to measure critical dimensions of micro- and nanostructures using the atomic force microscope (AFM) with an optical fiber probe (OFP). This method is capable of scanning narrow and deep trenches due to the long and thin OFP tip, as well as imaging of steep sidewalls with unique profiling possibilities by laterally tilting the OFP without any modifications of the optical lever. A switch control scheme is developed to measure the sidewall angle by flexibly transferring feedback control between the Z- and Y-axis, for a serial scan of the horizontal surface (raster scan on XY-plane) and sidewall (raster scan on the YZ-plane), respectively. In experiments, a deep trench with tapered walls (243.5 μm deep) and a microhole (about 14.9 μm deep) have been imaged with the orthogonally aligned OFP, as well as a silicon sidewall (fabricated by deep reactive ion etching) has been characterized with the tilted OFP. Moreover, the sidewall angle of TGZ3 (AFM calibration grating) was accurately measured using the switchable scan method.

A nondestructive calibration method for maximizing the range and accuracy of AFM force measurement

In this paper, a nondestructive method for the normal and lateral sensitivity calibrations of the optical lever in atomic force microscope (AFM) is presented. The practical application of this method in a dual-probe AFM is discussed in detail. To calibrate the conversion factors between photodiode responses and probe's deflection angles accurately without applying forces to the probe, a two-degrees-of-freedom flexure-hinge-based calibration device (FHCD) is developed. The device, which mainly consists of two mutually perpendicular flexure-hinge levers that share the same rotational center, serves as a switching mechanism for precise translation-to-rotation conversions both in the normal and lateral directions. During the calibration, a probe is attached to the FHCD at the meeting of the rotational axes of two levers. The FHCD is mounted on an AFM sample platform. The probe in this method acts as a mirror to be normally and laterally tilted at nanoscale angles to deflect the reflected laser beam by twisting the corresponding flexure-hinge levers, rather than the force-inducing probe deflection in traditional AFM calibration methods. With this method, the nondestructive calibration of the local and full-range sensitivities of the optical levers can be completed without destroying the probe tip or modifying the actual system setup of an AFM. Moreover, the nonlinearities of the optical levers are accurately compensated. Experimental results show that the linear ranges (with a deviation of 5% in the full range) of the force measurement are extended to 3.6 and 4.5 times in the normal and lateral directions, respectively, increasing to over 90% of the full range of the force measurement.

Measuring the Mechanical Properties of Living Cells Using Atomic Force Microscopy

Mechanical properties of cells and extracellular matrix (ECM) play important roles in many biological processes including stem cell differentiation, tumor formation, and wound healing. Changes in stiffness of cells and ECM are often signs of changes in cell physiology or diseases in tissues. Hence, cell stiffness is an index to evaluate the status of cell cultures. Among the multitude of methods applied to measure the stiffness of cells and tissues, micro-indentation using an Atomic Force Microscope (AFM) provides a way to reliably measure the stiffness of living cells. This method has been widely applied to characterize the micro-scale stiffness for a variety of materials ranging from metal surfaces to soft biological tissues and cells. The basic principle of this method is to indent a cell with an AFM tip of selected geometry and measure the applied force from the bending of the AFM cantilever. Fitting the force-indentation curve to the Hertz model for the corresponding tip geometry can give quantitative measurements of material stiffness. This paper demonstrates the procedure to characterize the stiffness of living cells using AFM. Key steps including the process of AFM calibration, force-curve acquisition, and data analysis using a MATLAB routine are demonstrated. Limitations of this method are also discussed.

Measurement strategies and uncertainty estimations for pitch and step height calibrations by metrological atomic force microscope

Gratings and step height standards are useful transfer standards for lateral and vertical length scale calibration of atomic force microscopes (AFMs). In order to have traceability to the SI-meter, the standards must have been calibrated prior to use. Metrological AFMs (MAFMs) with online laser interferometric position measurements are versatile instruments for the calibrations. The developed task-specific measurement strategies for step height and pitch calibrations with the Centre for Metrology and Accreditation's (MIKES's) metrological AFM are described. The strategies were developed to give high accuracy and to reduce measurement time. Detailed uncertainty estimations for step height and grating pitch calibrations are also given. Standard uncertainties are 0.016 and 0.018 nm for 300 and 700 nm pitch standards, respectively, and 0.21 and 0.44 nm for 7 and 1000 nm step height standards.

Multilaboratory comparison of traceable atomic force microscope measurements of a 70-nm grating pitch standard

The National Institute of Standards and Technology (NIST), Advanced Surface Microscopy (ASM), and the National Metrology Centre (NMC) of the Agency for Science, Technology, and Research (A*STAR) in Singapore have completed a three-way interlaboratory comparison of traceable pitch measurements using atomic force microscopy (AFM). The specimen being used for this comparison is provided by ASM and consists of SiO2 lines having a 70-nm pitch patterned on a silicon substrate. For this comparison, NIST used its calibrated atomic force microscope (C-AFM), an AFM with incorporated displacement interferometry, to participate in this comparison. ASM used a commercially available AFM with an open-loop scanner, calibrated with a 144-nm pitch transfer standard. NMC/A*STAR used a large scanning range metrological atomic force microscope with He-Ne laser displacement interferometry incorporated. The three participants have independently established traceability to the SI (International System of Units) meter. The results obtained by the three organizations are in agreement within their expanded uncertainties and at the level of a few parts in 104.

Precise surface measurements at the nanoscale

Availability of self-assembly effects occurring at the atomically clean Si(1 1 1) surface during high temperature anneals in an ultrahigh vacuum chamber for fabrication of a precise calibrator at nanoscale measurements is discussed. These effects provide formation of ordered monatomic step arrays assembled by step bunches divided by almost singular surface areas with widely spaced monatomic steps suitable for calibration of atomic force microscopes. The monatomic step height at the Si(1 1 1) surface and its replication by the native oxide layer was attested by the high-resolution transmission electron microscopy followed by Digital Micrograph analysis and found to be equal to interplanar spacing (0.314 nm) in the volume of Si crystal with ±0.001 nm of accuracy. Excellent replication of the monatomic step height by oxide film covering the Si surface makes available precise AFM calibration at the nanoscale at ambient conditions. The averaged step height measured by AFM scanning of 1 × 1 µm2 is found to be 0.314 ± 0.003 nm (∼1% of uncertainty). However, when the scan area becomes bigger than 2 × 2 µm2, the height measurement uncertainty increases sharply 15 times (0.310 ± 0.034 nm). We assume that this is due to differences between piezo element calibrations at small and large scan areas. The height measurement uncertainty for step bunches with well-defined quantity of steps (28) even at a large scan area (18 × 18 µm2) turns out to be 0.3%.

DMCMN: Experimental/Analytical Evaluation of the Effect of Tip Mass on Atomic Force Microscope Cantilever Calibration

Quantitative studies of material properties and interfaces using the atomic force microscope (AFM) have important applications in engineering, biotechnology, and chemistry. Contrary to what the name suggests, the AFM actually measures the displacement of a microscale probe, so one must determine the stiffness of the probe to find the force exerted on a sample. Numerous methods have been proposed for determining the spring constant of AFM cantilever probes, yet most neglect the mass of the probe tip. This work explores the effect of the tip mass on AFM calibration using the method of Sader (1995, “Method for the Calibration of Atomic Force Microscope Cantilevers,” Rev. Sci. Instrum., 66, pp. 3789) and extends that method to account for a massive, rigid tip. One can use this modified method to estimate the spring constant of a cantilever from the measured natural frequency and Q-factor for any mode of the probe. This may be helpful when the fundamental mode is difficult to measure or to check for inaccuracies in the calibration obtained with the fundamental mode. The error analysis presented here shows that if the tip is not considered, then the error in the static stiffness is roughly of the same order as the ratio of the tip’s mass to the cantilever beam’s. The area density of the AFM probe is also misestimated if the tip mass is not accounted for, although the trends are different. The model presented here can be used to identify the mass of a probe tip from measurements of the natural frequencies of the probe. These concepts are applied to six low spring-constant, contact-mode AFM cantilevers, and the results suggest that some of the probes are well modeled by an Euler–Bernoulli beam with a constant cross section and a rigid tip, while others are not. One probe is examined in detail, using scanning electron microscopy to quantify the size of the tip and the thickness uniformity of the probe, and laser Doppler vibrometry is used to measure the first four mode shapes. The results suggest that this probe’s thickness is significantly nonuniform, so the models upon which dynamic calibration is based may not be appropriate for this probe.

Effect of contact stiffness on wedge calibration of lateral force in atomic force microscopy

Quantitative friction measurement of nanomaterials in atomic force microscope requires accurate calibration method for lateral force. The effect of contact stiffness on lateral force calibration of atomic force microscope is discussed in detail and an improved calibration method is presented. The calibration factor derived from the original method increased with the applied normal load, which indicates that separate calibration should be required for every given applied normal load to keep the accuracy of friction measurement. We improve the original method by introducing the contact factor, which is derived from the contact stiffness between the tip and the sample, to the calculation of calibration factors. The improved method makes the calculation of calibration factors under different applied normal loads possible without repeating the calibration procedure. Comparative experiments on a silicon wafer have been done by both the two methods to validate the method in this article.

Round-robin measurements of 100- and 60-nm scales among a deep-ultraviolet laser diffractometer, a scanning electron microscope and various atomic force microscopes

An intercomparison of nanometric lateral scales, which are special one-dimensional (1D) grating standards with sub-hundred-nanometre pitches, among a deep-ultraviolet (DUV) laser diffractometer, a critical dimension scanning electron microscope (CD-SEM) and different types of atomic force microscope (AFM) was performed. The reference value and its expanded uncertainty were provided by the National Metrology Institute of Japan (NMIJ) using an atomic force microscope with differential laser interferometers (DLI-AFM). The consistency of the measurement results obtained using the DUV laser diffractometer, CD-SEM and some AFMs was satisfactory; however, that in the measurement results obtained using other AFMs was unsatisfactory. An improvement in AFM calibration technology using nanometrological standards is required for both AFM manufacturers and AFM users, including metrology institutes.

A Piezoresistive Cantilever Force Sensor for Direct AFM Force Calibration

AbstractWe describe the design, fabrication, and calibration testing of a new piezoresistive cantilever force sensor suitable for the force calibration of atomic force microscopes in a range between tens of nanonewtons to hundreds of micronewtons. The sensor is calibrated using the NIST Electrostatic Force Balance (EFB) and functions either as a force reference or stiffness artifact that is traceable to the International System of Units. The cantilever has evenly spaced fiducial marks along its length. We report stiffnesses that vary quadratically with location, from a high of 12.1 N/m at the first fiducial to a low of 0.394 N/m at the last; with force sensitivities that vary linearly, ranging from 18.1 Ù/mN to 106 Ù/mN. We also test the device to transfer the unit of force to an atomic force microscope, finding that force and stiffness based approaches yield independent estimates of the contact force consistent within 2 % of each other.

Electrical, Thermal, and Mechanical Characterization of Silicon Microcantilever Heaters

Silicon atomic force microscope (AFM) cantilevers having integrated solid-state heaters were originally developed for application to data storage, but have since been applied to metrology, thermophysical property measurements, and nanoscale manufacturing. These applications beyond data storage have strict requirements for mechanical characterization and precise temperature calibration of the cantilever. This paper describes detailed mechanical, electrical, and thermal characterization and calibration of AFM cantilevers having integrated solid-state heaters. Analysis of the cantilever response to electrical excitation in both time and frequency domains aids in resolving heat transfer mechanisms in the cantilever. Raman spectroscopy provides local temperature measurement along the cantilever with resolution near 1 mum and 5degC and also provides local surface stress measurements. Observation of the cantilever mechanical thermal noise spectrum at room temperature and while heated provides insight into cantilever mechanical behavior and compares well with finite-element analysis. The characterization and calibration methodology reported here expands the use of heated AFM cantilevers, particularly the uses for nanomanufacturing and sensing

Force Curve Measurements with the AFM: Application to the In Situ Determination of Grafted Silicon-Wafer Surface Energies

The atomic force microscope (AFM) can be used to perform surface force measurements in the quasi-static mode (cantilever is not oscillating) to investigate nanoscale surface properties. Nevertheless, there is still a lack of literature proposing a complete systematic and rigorous experimental procedure that enables one to obtain reproducible and significant quantitative data. This article focuses on the fundamental experimental difficulties arising when making force curve measurements with the AFM in air. On the basis of this AFM calibration procedure, quantitative assessment values were used to determine, in situ, SAM (or Self Assembled Monolayer)-tip thermodynamic work of adhesion at a local scale, which have been found to be in good agreement with quoted values. Finally, determination of surface energies of functionalised silicon wafers (as received, CH3, OH functionalised silicon wafers) with the AFM (at a local scale) is also proposed and compared with the values obtained by wettability (at a macroscopic scale). In particular, the effect of the capillary forces is discussed.

Reinforcement of polymeric nanofibers by ferritin nanoparticles

Poly(vinyl alcohol) (PVA) nanofibers containing bimolecular ferritin nanoparticles exhibited the enhancement of elastic modulus as compared to pure PVA nanofibers due to chemical interactions between the ferritin and the PVA matrix. The elastic modulus of the nanofibers was measured using a three-point bending test employing an atomic force microscope (AFM). To improve the reliability of the AFM measurements, uniform nanofibers were oriented linearly on an AFM calibration grating by introducing parallel subelectrodes in an electrospinning system. The length to diameter ratio of the measured nanofibers was >16. The PVA nanofibers reinforced by ferritin are applicable as artificial muscles and actuators.

Traceable pico-meter level step height metrology

The atomic force microscope (AFM) increasingly being used as a metrology tool in the semiconductor industry where the features measured are at the nanometer level and continue to decrease. Usually the height sensors of the AFM are calibrated using step height specimens ranging from 8 nm to a few μm, however there are no calibration standards at the sub-nanometer level. Recently we have explored the use of stepped silicon single atom specimens as sub-nanometer height calibration artifacts. We have also developed a calibrated atomic force microscope (C-AFM), an AFM with direct traceability to the definition of length to calibrate standards for other AFMs. Earlier, we evaluated the step height of silicon single atomic steps along the (1 1 1) direction (with native oxide) using the C-AFM and obtained a value 304 ± 8 pm ( k = 2). To validate the utility of these specimens and the applicability of our analysis technique, we conducted an industry comparison to determine the reproducibility of results obtained when using our procedure. The comparison included AFM vendors and semiconductor device manufacturers. The average standard deviation was 6 pm, and indicates that these specimens and our procedure could be used for sub-nanometer height calibrations. In this paper we will present our evaluation procedure, results of the comparison, and derivation of a value for Si(1 1 1) step height. We will also explore the trends in each participant's data, its effect on the calculation of the mean value, and implications on the reproducibility of our technique. Finally, we will outline the procedure for use of these specimens.

Microelectromechanical system device for calibration of atomic force microscope cantilever spring constants between 0.01 and 4 N/m

Calibration of atomic force microscope (AFM) cantilevers is necessary for the measurement of nano-newton and pico-newton forces, which are critical to analytical application of AFM in the analysis of polymer surfaces, biological structures and organic molecules. Previously we have described microfabricated array of reference spring (MARS) devices for AFM cantilever spring-constant calibration. Hitherto, these have been limited to the calibration of AFM cantilevers above 0.03 N/m, although they can be used to calibrate cantilevers of lower stiffness with reduced accuracy. Below this limit MARS devices similar to the designs hitherto described would be fragile and difficult to manufacture with reasonable yield. In this work we describe a device we call torsional MARS. This is a large-area torsional mechanical resonator, manufactured by bulk micromachining of a “silicon-on-insulator” wafer. By measuring its torsional oscillation accurately in vacuum we can deduce its torsional spring constant. The torsional reference spring spans the range of spring constant (from 4 down to 0.01 N/m) that is important in biological AFM, allowing even the most compliant AFM cantilever to be calibrated easily and rapidly.

Quantitative analytical atomic force microscopy: a cantilever reference device for easy and accurate AFM spring-constant calibration

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. We have developed a compact and easy-to-use reference artefact for this calibration by bulk micromachining of silicon, which we call a cantilever microfabricated array of reference springs (C-MARS). Two separate reference cantilever structures, each nominally 3 µm thick, are fabricated from a single crystal silicon membrane. A binary code of surface oxide squares (easily visible in light, electron and atomic force microscopy) makes it easy to locate the position of the AFM tip along the length of the cantilevers. Uncertainty in location is the main source of error when calibrating an AFM using reference cantilevers, especially for those having spring constants greater than around 10 N m−1. This error is effectively eliminated in our new design. The C-MARS device spans the range of spring constants from 25 N m−1 down to 0.03 N m−1 important in AFM, allowing almost any contact-mode AFM cantilever to be calibrated easily and rapidly.