Transfer Function Analysis of Atomic Force Microscope Cantilevers

Current methods to study atomic force microscope (AFM) cantilever dynamics use model simplification, or are based on the non-trivial solutions of the equation of motion. As an alternative method, transfer function analysis gives a complete description of system dynamics. In this work, we derive the exact, analytical expression for the multivariable infinite dimensional transfer function of a surface coupled cantilever system. The inputs of the system are punctual force at the tip end and distributed force along the cantilever, whereas the outputs are the position and slope at the tip end. A linearization of the surface coupling force is considered. Free cantilever and pinned end are considered as limit cases of the surface coupling. Frequency response Bode plots are shown, and transfer function infinite product expansion are obtained, which allow to derive the exact location of poles and zeros of the system, as a function of the level of surface coupling. This is shown in a root locus kind of plot. Transfer function analysis gives insight into optimal input/output configurations of the system and enables the possibility of model-based AFM operation

The measurement of intermolecular forces at the liquid-solid interface is key to many studies of electrochemistry, wetting, catalysis, biochemistry, and mechanobiology. The atomic force microscope (AFM) is unique in its ability to measure and map these forces with nanometer resolution using the oscillating sharp tip of an AFM cantilever. These surface forces are only measured by observing the changes they induce in the dynamics of the resonant AFM probe. However, AFM cantilever dynamics at this interface can be significantly different when compared to air/vacuum environments due to the nature of nanoscale forces at the interface and the low-quality factors in liquids. In this work, we study the nonlinear dynamics of magnetically excited AFM microcantilevers on graphite and mica immersed in deionized water, high-concentration buffers, and methanol. By combining theory and experiments, a wealth of nonlinear dynamical phenomena such as superharmonic resonance, hysteretic jumps, and multimodal interactions are demonstrated and their dependence on hydration/solvation forces is clarified. These results are expected to aid ongoing efforts to link liquid-solid interface properties to cantilever dynamics and lead to accurate interpretation of data from experiments.

This paper reports a thermal sensor assembled by two multi-walled carbon nanotubes (MWCNTs) inside a field emission scanning electron microscope (FESEM) which constructed a probe tip in order to detect the local environment of single cell. An atomic force microscope (AFM) cantilever was used for substrate which is composed by Si3N4, and double side was covered by gold layer. Two MWCNTs were assembled to both side of AFM cantilever individually by employing a nanorobotic manipulation. Then another AFM cantilever was used as an end effector to manipulate the MWCNTs to touch, and used electron beam induced deposition (EBID) to bonding the two MWCNTs. The MWCNTs probe thermal sensor was evaluation inside a thermostated container for 30°C to 60°C. The experimental results show the positive characteristics of the temperature coefficient of resistance (TCR). We hope this result will be used rapidly in future. © 2012 IEEE.

Calibration of AFM cantilever stiffness: a microfabricated array of reflective springs

This paper explores strategies for fabricating and maintaining a sharp atomic force microscope (AFM) tip suitable for AFM data storage applications. To this end, AFM cantilevers have been incorporated into micromachined sled carriers and air-bearing sliders. These supports act to limit the maximum loading force on the AFM tip and allow for improved vibration immunity for the AFM cantilever in comparison to macroscopic loading schemes. Readback from a patterned rotating disk has been demonstrated using these devices. Silicon-carbide AFM cantilevers with diamond tips have been fabricated in a process compatible with that of the sleds and sliders. Molded silicon-nitride tips defined by the intersection of three surfaces have also been fabricated for AFM cantilevers. The molds for plane-plane-concave tips are defined by two silicon {111} planes and a silicon-dioxide curved surface. By geometry, the three surfaces necessarily have a unique intersection point, which may improve the consistency in sharpness of these tips relative to conventional pyramidal tips.

This paper presents a study on the dynamic response of an atomic force microscope (AFM) cantilever with a solid state heating element in liquid and its application for measuring the temperature-dependent viscosity of liquids. A finite difference model (FDM) predicts the frequency response of a heated cantilever immersed in liquid and calibrates the liquid viscosity from the measured cantilever resonant frequency (f0) at different cantilever heater temperatures. The technique measures a wide range of liquid viscosities (0.0005–0.005 kgm−1s−1) at temperatures ranging from 20 to 55 °C with high sensitivity (7.1 × 10−7 kgm-1s-1/Hz for 50 wt% ethylene glycol/water). The measurement requires heating a liquid volume of about 10 nl, which is more than 1000X smaller than other microcantilever-based viscosity measurements.

We investigate in theory and experiment the intermittent contact interaction between an atomic force microscope (AFM) cantilever and a nanowire under ambient conditions. The nanowire is modeled as a spring reacting instantaneously to any change of the force between the wire and the cantilever. This implies that the cantilever is subject to an “effective” force-distance relation, containing not only the surface forces but also the deflection of the nanowire. Experimentally, CVD-grown tin oxide nanowires and lithographically structured silicon nanowire arrays were investigated by intermittent contact AFM. By comparison of experimental and simulated distance-dependent resonance curves it is found that the nanowires behave like “fast nanosprings” and that the adhesion force is one of the key factors determining distance-dependent resonance curves. The results are fully applicable to a scenario in which a cantilever equipped by a nanowire interacts with a surface.

Mechanical characterization of nanofibers using a nanomanipulator and atomic force microscope cantilever in a scanning electron microscope

In this study we present measurements of the hydrodynamic force exerted on a glass sphere glued to an atomic force microscopy (AFM) cantilever approaching a mica surface in water. A large sphere was used to reduce the impact of the cantilever beam on the measurement. An AFM cantilever with large stiffness was used to accurately determine the actual contact position between the sphere and the sample surface. The measured hydrodynamic force with different approach velocities is in good agreement with the Taylor force calculated in the lubrication theory with the no-slip boundary conditions, which verifies that there is no boundary slip on the glass and mica surfaces. Moreover, a detailed procedure of how to subtract the electrostatic double-layer force is presented.

An atomic force microscope (AFM) cantilever based coordinate measuring probe applicable for true three dimensional measurements of microstructures is presented. The probe has a shaft glued to a commercial AFM cantilever and a probing sphere located at the free end of the shaft. A conventional optical lever method is applied to detect the bending, torsion, and the dynamic behavior of the AFM cantilever which will change dramatically when the probe sphere is in proximity to the object to be measured. The probe has advantages such as small probing force (<1μN), high probing sensitivity allowing nanometer measurement resolution, easy exchange of probing elements, and low cost. Measurements of a microgear and a fuel injection nozzle using the developed probe are demonstrated, indicating its promising application potential.

Nanomechanical test instruments can precisely measure force and displacement and produce repeatable load-unload curves that can be used in characterizing mechanical behaviour at the nanoscale. In this study, a newly developed translucent nanomechanical test instrument was used in deriving reproducible stiffness values for ultra nano crystalline diamond (UNCD)-made atomic force microscope (AFM) cantilevers that are used for mechanical properties characterization of DLC films. The instrument which is calibrated according to the ISO-14577 standard is integrated with nano/micropositioners and multi-view optical microscopes to facilitate precise manipulation of those AFM cantilevers that were dozens of micrometers in size. Experimental results on UNCD-made AFM cantilever stiffness measurements are provided and compared with theoretical and batch production values.

The necessity for development of new drug delivery systems for poorly soluble drugs and therapeutics which targets directly the pathogenic area requires the design of complex systems in nanoscale. Atomic Force Microscopy (AFM) since its discovery offers a unique tool to develop novel drug delivery systems. Its capability to investigate, characterise surfaces and measure forces with spatial resolution at nano-scale respectively contributes to develop and analyse pharmaceutical systems and biomedical devices with complex structures and chemistries. Specifically, polymeric nanoparticles and liposomal drug formulation have been studied extensively by using AFM where their size and morphology where revealed [1]. However, apart from topographical information, AFM can provide details on the local compositions of the sample. There are many modes that can be used to achieve this but the most common is to monitor the phase shift of the oscillating cantilever in tapping mode Such ‘Phase imaging’ can be used to detect nanoscale variation in composition, adhesion, friction, viscoelasticity, and other properties of the materials. Changes in the phase lag often indicate changes in the properties of the sample surface. Phase imaging has proved an extremely useful tool for pharmaceutical characterization. Phase imaging has been used to reveal polymeric forms from single crystal measurements [2] to confirm phase separation of two copolymers for drug delivery [3], to establish the stability of the formulation on different environments [4] and to identify formation of amorphous domains during milling of crystalline salbutamol [5]. Moreover, the ability of AFM to operate on different conditions of temperature humidity and in liquid allows studying the kinetics of range of phenomena. An interesting work was published from Miyazaki et al. where the crystal growth rate of Nifedipine, dispersed in PEG polymer matrix, was quantified [6]. Also, the dissolution process of aspirin on different facets of the crystal was studied by Danesh et al . showing their differences in dissolution rate [7]. The ability of AFM to measure force measurements have been used to investigate interactions among the different compounds in the formulation. To achieve this, the AFM cantilever is modified by attaching a particle directly onto the probe tip and is brought in contact with the substrate of interest, the force required to separate them is the measure of their adhesion. This application of AFM has been used extensively to aerosol drug formulation where the API is associated with a carrier which is released in the site of actions. For instance, AFM has been used to investigate the adhesion force of salbutamol with different excipients [8]. Moreover, localised surface energy and young’s modulus of various compounds have been measured. For example, Young’s modulus were derived from both PLA and PLA/everolimus directly from stent surface on different temperatures. The results showed that everolimus does not affect the mechanical properties of PLA up to 1/1 (w/w) drug loading of the mixture. Also, a significant drop of the Young’s modulus in solution was observed at 36°C, suggests that in vivo the Tg of the polymer is below body temperature [9]. Furthermore, force measurements have been used to identify the encapsulation the efficiency of liposomes as the rigidity of encapsulating liposomes is higher [10].

The measurement of small forces by atomic force microscopy (AFM) is of increasing importance in many applications. For example, in analytical applications where individual molecules are probed, or nanoindentation measurements as a source of information about materials properties on a nanometer scale. The fundamentals of AFM force measurement, and some of these applications, are briefly reviewed. In most cases absolute, not relative, measurements of forces are needed for valid comparisons with theory and other measurement techniques (such as optical tweezers). We review methods of AFM force calibration and the major uncertainties involved. The force range considered in this work is roughly from 10 pN to around 500 nN. We describe some issues of the repeatability of force measurements that can be important in common AFM instruments. In most cases the aspect that then limits the accuracy with which forces can be measured is the uncertainty in the stiffness (more specifically the normal force constant) of the atomic force microscope cantilever at the center of the instrument. It is known that commercially available microfabricated atomic force microscope cantilevers have a wide range of force constant, for cantilevers of nominally the same type and even the same production batch. Calibration is necessary, and many methods have been used over the years. We compare the accuracy that can be achieved and the ease of use of these different methods, including theoretical (dimensional), thermal, static and dynamic methods and their variants. A device developed at NPL should help overcome many of the problems of force constant calibration, at least for the most common AFM configurations. This is a microfabricated silicon device, which, because of its very small mass, is not susceptible to vibration as a larger device would be. A new calibration method based on electrical and Doppler measurements allows the calibration of the force constant of this device traceable to the SI newton. It can then be sent to AFM users for straightforward calibration of AFM force constants. We conclude with a brief discussion of the special problems of calibration of lateral forces, such as those obtained in frictional force measurements.

Successful deep and alignment-free patterned etching on GaN using atomic force microscope (AFM) local oxidation followed by in-situ chemical etching is demonstrated. Oxide ridges are grown on GaN on an AFM by applying positive sample bias at 80% humidity, with the oxidation reaction expedited by UV light. The oxide ridges are then etched by HCl solution, leaving troughs in the GaN surface. A dripping strategy for the in-situ chemical etching is recommended that allows deep, alignment-free multiple AFM oxidation/etching works on the GaN surface without any need of substrate removal from the AFM platform. Repeated etching followed by AFM oxidation on a spot on a GaN surface resulting in a hole as deep as 800 nm was also demonstrated. Further, a preliminary evaluation of the porosity of the AFM-grown oxide indicates that the oxide ridges grown on GaN at an AFM cantilever moving speed of 300 nm/s are porous in structure, with an estimated porosity of 86%, which porosity could be reduced if longer resident time of the AFM cantilever on the target oxidation region was used.

Investigation of influence of gas atmosphere and pressure upon non-contact atomic force microscopy