Josep Font

The intrinsic resolution limit in the atomic force microscope: implications for heights of nano-scale features

Background Accurate mechanical characterization by the atomic force microscope at the highest spatial resolution requires that topography is deconvoluted from indentation. The measured height of nanoscale features in the atomic force microscope (AFM) is almost always smaller than the true value, which is often explained away as sample deformation, the formation of salt deposits and/or dehydration. We show that the real height of nano-objects cannot be obtained directly: a result arising as a consequence of the local probe-sample geometry. Methods and Findings We have modeled the tip-surface-sample interaction as the sum of the interaction between the tip and the surface and the tip and the sample. We find that the dynamics of the AFM cannot differentiate between differences in force resulting from 1) the chemical and/or mechanical characteristics of the surface or 2) a step in topography due to the size of the sample; once the size of a feature becomes smaller than the effective area of interaction between the AFM tip and sample, the measured height is compromised. This general result is a major contributor to loss of height and can amount to up to ∼90% for nanoscale features. In particular, these very large values in height loss may occur even when there is no sample deformation, and, more generally, height loss does not correlate with sample deformation. DNA and IgG antibodies have been used as model samples where experimental height measurements are shown to closely match the predicted phenomena. Conclusions Being able to measure the true height of single nanoscale features is paramount in many nanotechnology applications since phenomena and properties in the nanoscale critically depend on dimensions. Our approach allows accurate predictions for the true height of nanoscale objects and will lead to reliable mechanical characterization at the highest spatial resolution.

Bi-stability of amplitude modulation AFM in air: deterministic and stochastic outcomes for imaging biomolecular systems

The dynamics of the oscillating microcantilever for amplitude modulation atomic force microscopy (AM AFM) operating in air is well understood theoretically but the experimental outcomes are still emerging. We use double-stranded DNA on mica as a model biomolecular system for investigating the connection between theory and experiment. A demonstration that the switching between the two cantilever oscillation states is stochastic in nature is achieved, and it can be induced by means of topographical anomalies on the surface. Whether one or the other attractor basin is accessed depends on the tip-sample separation history used to achieve the imaging conditions, and we show that the behaviour is reproducible when the tip is stable and well characterized. Emergence of background noise occurs in certain regions of parameter space regardless of whether two cantilever oscillation states coexist. The low state has been explored in detail and we note that at low to intermediate values of the free amplitude, noise-free imaging is achieved. The outcomes shown here are general and demonstrate that a thorough and systematic experimental approach in conjunction with standard modelling gives insight into the mechanisms behind image contrast formation in AM AFM in air.

How localized are energy dissipation processes in nanoscale interactions

We describe fundamental energy dissipation in dynamic nanoscale processes in terms of the localization of the interactions. In this respect, the areal density of the energy dissipated per cycle and the effective area of interaction in which each process occurs are calculated for four elementary dissipative processes. It is the ratio between these two, which we term M, that provides information about how localized the interactions are. While our results are general, we use concepts from dynamic atomic force microscopy to describe the physical phenomenon. We show that neither the phase lag, nor the magnitude of the energy dissipated alone provide information about how dissipative processes are localized. Instead, M has to be considered.

Stability, resolution, and ultra-low wear amplitude modulation atomic force microscopy of DNA: Small amplitude small set-point imaging

A way to operate fundamental mode amplitude modulation atomic force microscopy is introduced which optimizes stability and resolution for a given tip size and shows negligible tip wear over extended time periods (∼24u2009h). In small amplitude small set-point (SASS) imaging, the cantilever oscillates with sub-nanometer amplitudes in the proximity of the sample, without the requirement of using large drive forces, as the dynamics smoothly lead the tip to the surface through the water layer. SASS is demonstrated on single molecules of double-stranded DNA in ambient conditions where sharp silicon tips (Ru2009∼u20092–5u2009nm) can resolve the right-handed double helix.

Cantilever dynamics in amplitude modulation AFM: continuous and discontinuous transitions

Transitions between the attractive and the repulsive force regimes for amplitude modulation atomic force microscopy (AFM) can be either discontinuous, with a corresponding jump in amplitude and phase, or continuous and smooth. During the transitions, peak repulsive and average forces can be up to an order of magnitude higher when these are discrete. Under certain circumstances, for example, when the tip radius is relatively large (e.g. R > 20–30 nm) and for high cantilever free amplitudes (e.g. A0 > 40–50 nm), the L state can be reached with relatively low set-points only (e.g. Asp/A0 < 0.30). We find that these cases do not generally lead to higher resolution but increase the background noise instead. This is despite the fact that the imaging can be non-contact under these conditions. The appearance of background noise is linked to increasing cantilever mean deflection and tip–surface proximity with increasing free amplitude in the L state. n nCantilever dynamics in amplitude modulation AFM: Continuous and discontinuous transitions (PDF Download Available). Available from: https://www.researchgate.net/publication/231025693_Cantilever_dynamics_in_amplitude_modulation_AFM_Continuous_and_discontinuous_transitions [accessed Mar 27, 2017].

Mobile robot localization. Revisiting the triangulation methods

Localization is one of the fundamental problems in mobile robot navigation. In nthis context, triangulation is used to determine the robot pose from landmarks position and angular measurements. The method based on circle intersection is the preferred one because it is independent of the robot heading. Nevertheless, it becomes undetermined when the robot point is on the circumference that contains the landmarks used. To cope with it, a triangulation method based on straight lines intersection is presented in this paper. The robot heading angle, which is needed in this method, can be accurately determined by means of a geometrical procedure. The accuracy of the presented approach is evaluated and compared to that of alternative methods by means of experimental results and computer simulations.

Dynamic positioning of a mobile robot using a laser-based goniometer

Positioning is a fundamental problem in mobile robot navigation. Several napproaches to cope with the dynamic positioning problem have been made. Most of them are based on the inconsistent use of the algorithm for static positioning enhanced by predictive algorithms. In this paper, a method that guarantees the consistent use of this algorithm at any time under dynamic condition is presented. It combines vehicle kinematics and laser-based goniometer data for real time simulation of the evolution of the straight lines between the laser-based goniometer and the set of artificial landmarks used.

Investigation of nanoscale interactions by means of subharmonic excitation

Multifrequency atomic force microscopy holds promise as a method to provide qualitative and quantitative information about samples with high spatial resolution. Here, we provide experimental evidence of the excitation of subharmonics in ambient conditions in the regions where capillary interactions are predicted to be the mechanism of excitation. We also experimentally decouple a second mechanism for subharmonic excitation that is highly independent of environmental conditions such as relative humidity. This implies that material properties could be mapped. Subharmonic excitation could lead to experimental determination of surface water affinity in the nanoscale whenever water interactions are the mechanism of excitation.

The additive effect of harmonics on conservative and dissipative interactions

Multifrequency atomic force microscopy holds promise as a tool for chemical and topological imaging with nanoscale resolution. Here, we solve the equation of motion exactly for the fundamental mode in terms of the cantilever mean deflection, the fundamental frequency of oscillation, and the higher harmonic amplitudes and phases. The fundamental frequency provides information about the mean force, dissipation, and variations in the magnitude of the attractive and the repulsive force components during an oscillation cycle. The contributions of the higher harmonics to the position, velocity, and acceleration can be added gradually where the details of the true instantaneous force are recovered only when tens of harmonics are included. A formalism is developed here to decouple and quantify the viscous term of the force in the short and long range. It is also shown that the viscosity independent paths on tip approach and tip retraction can also be decoupled by simply acquiring a FFT at two different cantilever separations. The two paths correspond to tip distances at which metastability is present as, for example, in the presence of capillary interactions and where there is surface energy hysteresis.

Unlocking higher harmonics in atomic force microscopy with gentle interactions

Summary In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.