arXiv subjects

Laurent Nony

Publications and source records attributed to Laurent Nony.

At least 19 recordsLinked to original sources

arXiv2026

Inverse heterodyne effect in bimodal Kelvin probe force microscopy

Heterodyne Kelvin probe force microscopy (He-KPFM) enables high-sensitivity electrostatic measurements by converting a bias-modulated interaction into a resonant response at a higher cantilever eigenmode. While the "direct" heterodyne actuation of the second eigenmode is well established, the dynamical back-action of this heterodyne-driven motion on the fundamental eigenmode has remained largely unexplored, particularly in open-loop operation where the second mode is excited to a finite amplitude. Here, we demonstrate an inverse heterodyne effect: a force component generated by heterodyne frequency conversion acts back on the first eigenmode and produces measurable inter-mode energy exchange. The analysis combines a bimodal virial and power-balance framework with a non-truncated description of the tip-surface capacitance-gradient dynamics developed and validated in a companion manuscript submitted concurrently to the same journal. On this basis, we derive closed-form expressions linking inverse heterodyne coupling to the experimentally accessible observables of non-contact AFM open-loop amplitude-modulated He-KPFM. The theory predicts that inverse heterodyne coupling appears predominantly in the dissipation channel, with a sharply resonant dependence on the demodulation frequency near the second-eigenmode resonance, while its conservative contribution to the frequency shift remains comparatively weaker under typical conditions. Ultrahigh-vacuum experiments validate these predictions and isolate the inverse heterodyne signature through frequency- and voltage-dependent measurements. Beyond KPFM, this work connects heterodyne force microscopy to a broader class of driven multimode systems in which nonlinear coupling and frequency conversion produce inter-mode energy transfer, back-action, and dissipation-based observables.

cond-mat.mtrl-sci↗

arXiv2026

On the capacitance gradient description in Heterodyne Kelvin Probe Force Microscopy

Kelvin probe force microscopy (KPFM) probes local surface-potential variations through the electrostatic force between a conductive tip and a surface, which depends on the potential difference and the tip-surface capacitance gradient (CG). In heterodyne KPFM, the oscillating tip is usually treated by combining a bias-modulated electric field with a first-order truncated Taylor-series expansion of the CG. Although convenient, this treatment is limited to a poorly defined small-amplitude regime and leaves the convergence of the series unresolved. Here, we establish a rigorous spectral description of the CG dynamics and of the resulting electrostatic force beyond this approximation. We formulate a non-truncated Taylor-series description of the CG and prove its convergence for a realistic Hudlet-based capacitance model in both monomodal and bimodal motion. In the monomodal case, we show the equivalence between Fourier-series and Taylor-series descriptions, derive explicit expressions for the dominant Fourier coefficients, and introduce order-truncation criteria that replace the usual qualitative notion of a small-amplitude regime. We then extend the formalism to bimodal motion and derive the effective CG coefficients governing the static, first-eigenmode, and second-eigenmode components of the electrostatic interaction. Numerical simulations confirm the convergence of the Taylor-based coefficients toward the Fourier coefficients and support the truncation-regime hierarchy in both configurations. This work establishes the formal basis for describing electrostatic force components and AFM observables in open-loop heterodyne experiments and provides a general framework for CG dynamics in multimode force microscopy involving nonlinear electromechanical coupling and frequency conversion.

cond-mat.mtrl-sci↗

arXiv2009

Understanding the atomic-scale contrast in Kelvin Probe Force Microscopy

A numerical analysis of the origin of the atomic-scale contrast in Kelvin probe force microscopy (KPFM) is presented. Atomistic simulations of the tip-sample interaction force field have been combined with a non-contact Atomic Force Microscope/KPFM simulator. The implementation mimics recent experimental results on the (001) surface of a bulk alkali halide crystal for which simultaneous atomic-scale topographical and Contact Potential Difference (CPD) contrasts were reported. The local CPD does reflect the periodicity of the ionic crystal, but not the magnitude of its Madelung surface potential. The imaging mechanism relies on the induced polarization of the ions at the tip-surface interface owing to the modulation of the applied bias voltage. Our findings are in excellent agreement with previous theoretical expectations and experimental observations.

physics.atm-clus↗

arXiv2008

Analytical Approach to the Local Contact Potential Difference on (001) Ionic Surfaces: Implications for Kelvin Probe Force Microscopy

An analytical model of the electrostatic force between the tip of a non-contact Atomic Force Microscope (nc-AFM) and the (001) surface of an ionic crystal is reported. The model is able to account for the atomic contrast of the local contact potential difference (CPD) observed while nc-AFM-based Kelvin Probe Force Microscopy (KPFM) experiments. With the goal in mind to put in evidence this short-range electrostatic force, the Madelung potential arising at the surface of the ionic crystal is primarily derived. The expression of the force which is deduced can be split into two major contributions: the first stands for the coupling between the microscopic structure of the tip apex and the capacitor formed between the tip, the ionic crystal and the counter-electrode; the second term depicts the influence of the Madelung surface potential on the mesoscopic part of the tip, independently from its microscopic structure. These short-range electrostatic forces are in the range of ten pico-Newtons. When explicitly considering the crystal polarization, an analytical expression of the bias voltage to be applied on the tip to compensate for the local CPD, i.e. to cancel the short-range electrostatic force, is derived. The compensated CPD has the lateral periodicity of the Madelung surface potential. However, the strong dependence on the tip geometry, the applied modulation voltage as well as the tip-sample distance, which can even lead to an overestimation of the real surface potential, makes quantitative KPFM measurements of the local CPD extremely difficult.

physics.atm-clus↗

arXiv2007

Noncontact atomic force microscopy simulator with phase-locked-loop controlled frequency detection and excitation

A simulation of an atomic force microscope operating in the constant amplitude dynamic mode is described. The implementation mimics the electronics of a real setup including a digital phase-locked loop (PLL). The PLL is not only used as a very sensitive frequency detector, but also to generate the time-dependent phase shifted signal driving the cantilever. The optimum adjustments of individual functional blocks and their joint performance in typical experiments are determined in detail. Prior to testing the complete setup, the performances of the numerical PLL and of the amplitude controller were ascertained to be satisfactory compared to those of the real components. Attention is also focused on the issue of apparent dissipation, that is, of spurious variations in the driving amplitude caused by the nonlinear interaction occurring between the tip and the surface and by the finite response times of the various controllers. To do so, an estimate of the minimum dissipated energy that is detectable by the instrument upon operating conditions is given. This allows us to discuss the relevance of apparent dissipation that can be conditionally generated with the simulator in comparison to values reported experimentally. The analysis emphasizes that apparent dissipation can contribute to the measured dissipation up to 15% of the intrinsic dissipated energy of the cantilever interacting with the surface, but can be made negligible when properly adjusting the controllers, the PLL gains and the scan speed. It is inferred that the experimental values of dissipation usually reported in the literature cannot only originate in apparent dissipation, which favors the hypothesis of "physical" channels of dissipation.

physics.atm-clus↗

arXiv2005

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules.

physics.atm-clus↗

arXiv2005

Cu-TBPP and PTCDA molecules on insulating surfaces studied by ultra-high-vacuum non-contact AFM

The adsorption of two kinds of porphyrin (Cu-TBPP) and perylene (PTCDA) derived organic molecules deposited on KBr and Al2O3 surfaces has been studied by non-contact force microscopy in ultra-high vacuum, our goal being the assembly of ordered molecular arrangements on insulating surfaces at room temperature. On a Cu(100) surface, well ordered islands of Cu-TBPP molecules were successfully imaged. On KBr and Al2O3 surfaces, it was found that the same molecules aggregate in small clusters at step edges, rather than forming ordered monolayers. First measurements with PTCDA on KBr show that nanometre-scale rectangular pits in the surface can act as traps to confine small molecular assemblies.

physics.atm-clus↗

arXiv2005

Distance dependence of force and dissipation in non-contact atomic force microscopy on Cu(100) and Al(111)

The dynamic characteristics of a tip oscillating in the nc-AFM mode in close vicinity to a Cu(100)-surface are investigated by means of phase variation experiments in the constant amplitude mode. The change of the quality factor upon approaching the surface deduced from both frequency shift and excitation versus phase curves yield to consistent values. The optimum phase is found to be independent of distance. The dependence of the quality factor on distance is related to 'true' damping, because artefacts related to phase misadjustment can be excluded. The experimental results, as well as on-resonance measurements at different bias voltages on an Al(111) surface, are compared to Joule dissipation and to a model of dissipation in which long-range forces lead to viscoelastic deformations.

physics.atm-clus↗

arXiv2005

Non-contact atomic force microscopy: Stability criterion and dynamical responses of the shift of frequency and damping signal

The aim of this article is to provide a complete analysis of the behavior of a noncontact atomic force microscope (NC-AFM). We start with a review of the equations of motion of a tip interacting with a surface in which the stability conditions are first revisited for tapping mode. Adding the equations of automatic gain control (AGC), which insures constant amplitude of the oscillations in the NC-AFM, to the equations of motion of the tip, a new analytical stability criterion that involves proportional and integral gains of AGC is deduced. Stationary solutions for the shift of frequency and for the damping signal are obtained. Special attention is paid to the damping signal in order to clarify its physical origin. The theoretical results are then compared to those given by a virtual machine. The virtual machine is a set of equations solved numerically without any approximation. The virtual machine is of great help in understanding the dynamical behavior of the NC-AFM as images are recorded. Transient responses of the shift in frequency and of the damping signal are discussed in relation to the values of proportional and integral gains of AGC.

physics.atm-clus↗

arXiv2005

Stability analysis of an oscillating tip-cantilever system in NC-AFM

This paper is a theoretical and a numerical investigation of the stability of a tip-cantilever system used in noncontact atomic force microscopy (NC-AFM) when it oscillates close to a surface. No additional dissipative force is considered. The theoretical approach is based on a variational method exploiting a coarse grained operation that gives the temporal dependance of the non-linear coupled equations of motion in amplitude and phase of the oscillator. Stability criterions for the resonance peak are deduced and predict a stable behavior of the oscillator in the vicinity of the resonance. The numerical approach is based on the results obtained with a virtual NC-AFM developed by our group. The effect of the size of the stable domain in phase is investigated. These results are in particularly good agreement with the theoretical predictions. Also they show the influence of the phae shifter in the feedback loop and the way it can affect the damping signal.

physics.atm-clus↗

arXiv2005

Relationship between the non linear dynamic behaviour of an oscillating tip-microlever system and the contrast at the atomic scale

In this paper, the dynamic behaviour of an oscillating tip-microlever system at the proximity of a surface is discussed. The attractive tip-surface interaction is simply described with a Van der Waals dispersive term and a sphere-plane geometry. We show that the non linear behaviour of the oscillator is able to explain the observed shifts of the resonance frequency as a function of the tip-surface distance without the need of introducing a particular short range force.

physics.atm-clus↗

arXiv2005

Growth kinetics of a nanoprotuberance under the action of an oscillating nanotip

The atomic force microscope is a versatile tool that allows many routes to be used for investigating the mechanical properties of soft materials on the nanometer scale. In the present work, experiments were performed on polystyrene polymer films of various molecular weight by approaching a vibrating nanotip towards the surface. The variation of the oscillating amplitude of the cantilever is interpreted as the result of the growth process of a nanoprotuberance. The growth rate is found to be dependent of the magnitude of the oscillating amplitude and of the molecular weight. A model is developed describing in a very simple way the action of the tip and a viscoelastic response of the polymer. The numerical simulation helps in understanding the nonlinear relation between the growth rate and the vibrating amplitude of the microlever and describes qualitatively most of the experimental features. For the softer material, experimental situations are found that allow the experimental results to be amenable with an analytical solution. The analytical solution provides a fruitful comparison with the experimental results showing that some of the nanoprotuberance evolution cannot be explained with the approximation used. The presents results show that there exists a new and fascinating route to better understand the mechanical response at the local scale.

physics.atm-clus↗

arXiv2005

Nonlinear Dynamic Behavior of an Oscillating Tip-Microlever System and Contrast at the Atomic Scale

In this paper the dynamic behavior of an oscillating tip-microlever system at the proximity of a surface is discussed. We show that the nonlinear behavior of the oscillator is able to explain the high sensitivity of the oscillating tip microlever and the observed shifts of the resonance frequency as a function of the tip surface distance without the need of introducing a particular short range force.

physics.atm-clus↗

arXiv2005

DNA properties investigated by dynamic force microscopy

In this work, we show that by varying the experimental conditions, the driving amplitude, a dynamic force microscope allows DNA properties to be selectively imaged. The substrate on which the DNA is fixed is a silica surface grafted with silanes molecules ended with amine groups. Use of small oscillation amplitudes favors the attractive interaction between the tip and the sample, while use of large amplitudes renders the contribution of the attractive interaction negligible. Particularly, at small amplitudes, the images show that the attractive interaction is strongly enhanced along the DNA. This enhancement is found to be amenable with a model considering a narrow strip of randomly oriented dipoles on each side of the molecule. This work should provide new insights on the DNA interaction and conformational changes with localized charges.

physics.bio-ph↗

arXiv2005

Structural Characterization of Self-Assembled Monolayers of Organosilanes Chemically Bonded on Silica Wafers by Dynamical Force Microscopy

In this article, a dynamical force microscopy study of self-assembled monolayers of organosilanes, grafted on a silica support, is reported. Organosilanes, terminated either with a functional group (ethylene glycol) or with a methyl group, were used. The influence of the reaction time and the solvent composition on the grafting was investigated to improve the homogeneity of the self-assembled monolayers. Numerical simulations of approach-retract curves, obtained in the tapping mode, were performed and compared to experimental ones. Informations, such as mechanical response and height of the grafted organic layers, have been obtained.

physics.atm-clus↗

arXiv2005

Stability criterions of an oscillating tip-cantilever system in dynamic force microscopy

This work is a theoretical investigation of the stability of the non-linear behavior of an oscillating tip-cantilever system used in dynamic force microscopy. Stability criterions are derived that may help to a better understanding of the instabilities that may appear in the dynamic modes, Tapping and NC-AFM, when the tip is close to a surface. A variational principle allows to get the temporal dependance of the equations of motion of the oscillator as a function of the non-linear coupling term. These equations are the basis for the analysis of the stability. One find that the branch associated to frequencies larger than the resonance is always stable whereas the branch associated to frequencies smaller than the resonance exhibits two stable domains and one unstable. This feature allows to re-interpret the instabilities appearing in Tapping mode and may help to understand the reason why the NC-AFM mode is stable.

physics.atm-clus↗

arXiv2005

Dissipation induced by attractive interaction in dynamic force microscopy : contribution of adsorbed water layers

At room temperature and under ambient conditions, due to the adsorption, a water film is always present on silica surfaces. If the surface is investigated with a scanning probe method in Contact mode, this causes the formation of a meniscus between the tip and the surface. This liquid neck generates additional capillary forces between the nano-tip and the surface. In dynamic mode, due to the action of the oscillating tip on the surface, the mechanical response of the adsorbed water layers can induce additional dissipation that is probed through the phase variations of the oscillator. In the present work, we analyze by dynamic force microscopy the growth of a water film on a silica surface as a function of time. The silica sample is first cleaned and heated at $420^\circ$C, then is exposed to dry conditions. The influence of the water film is checked with the dynamic mode by using intermittent contact and noncontact situations. To describe the experimental observations, additional dissipation is taken into account when the tip approaches the surface. The results of the fits allow the evaluation of the dissipation induced by the attractive interaction between the tip and the silica surface related to the adsorption of water molecules on surface as a function of time. Results are compared to previous tribological studies performed in Contact mode and infra-red spectroscopy measurements on the silica for which the key parameter was the surface temperature instead of time. The two experimental results are in good agreement.

physics.chem-ph↗

arXiv2005

Influence of noncontact dissipation in the tapping mode: Attempt to extract quantitative information on the surface properties with the local force probe method

In the Tapping mode, a variation of the oscillation amplitude and phase as a function of the tip sample distance is the necessary measurement to access quantitatively to the properties of the surface. In the present work, we give a systematic comparison between experimental data recorded on two surfaces, phase and amplitude, and theoretical curves. With an interaction between the tip and the surface taking into account an attractive and a repulsive term, the analytical approach is unable to properly describe the relationship between the phase variation and the oscillation amplitude variation. When an additional dissipation term is involved, due to the attractive interaction between the tip and the surface, the model gives a good agreement with the recorded data. Particularly, the trends in the phase variations related to the noncontact situations have been found to be amenable to an analysis based upon a simple viscoelastic behavior of the surface.

physics.atm-clus↗