Rodolphe Boisgard

Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids

We present a study of thermal noise of commercially available atomic force microscopy (AFM) cantilevers in air and in water. The purpose of this work is to investigate the oscillation behavior of a clamped AFM microlever in liquids. Up to eight vibration modes are recorded. The experimental results are compared to theoretical predictions from the hydrodynamic functions corresponding to rigid transverse oscillations of an infinitely long rectangular beam. Except for the low-frequency modes, the known hydrodynamic functions cannot describe the amount of dissipated energy due to the liquid motion induced by the cantilever oscillation. The observed variation of the damping coefficient is smaller than the one predicted. The difference at higher modes between the mentioned theoretical description and experimental results is discussed with the help of numerical solutions of the three-dimensional Navier–Stokes equation.

Nonlinear dynamical properties of an oscillating tip–cantilever system in the tapping mode

The dynamical properties of an oscillating tip–cantilever system are now widely used in the field of scanning force microscopy. The aim of the present work is to get analytical expressions describing the nonlinear dynamical properties of the oscillator in noncontact and intermittent contact situations in the tapping mode. Three situations are investigated: the pure attractive interaction, the pure repulsive interaction, and a mixing of the two. The analytical solutions obtained allow general trends to be extracted: the noncontact and the intermittent contact show a very discriminate variation of the phase. Therefore the measurement of the phase becomes a simple way to identify whether or not the tip touches the surface during the oscillating period. It is also found that the key parameter governing the structure of the dynamical properties is the product of the quality factor by a reduced stiffness. In the attractive regime, the reduced stiffness is the ratio of an attractive effective stiffness and the c...

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.

Hysteresis generated by attractive interaction: oscillating behavior of a vibrating tip–microlever system near a surface

We provide experimental evidence of hysteretic behavior of a vibrating microlever that arises when a surface approaches the microlever. An analytical solution is derived from a variational method that shows that the width of the hysteresis depends on the strength of the attractive interaction at a given driving amplitude. For a large attractive interaction, the hysteretic behavior disappears, and the oscillating amplitude of the microlever decreases as the tip is close to the surface without needing to touch the surface. As a direct consequence, the way the cycle of the hysteresis varies close to the surface can be used to measure the change in attractive interaction without disturbing the surface.

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.

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

Abstract: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 dependence 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.

Design and operation of a silicon ring resonator for force sensing applications above 1 MHz

We present an integrated force probe based on a silicon bulk-mode MEMS resonator. This device uses a silicon ring with symmetrical tips vibrating in the elliptic vibration mode. The tips enable us to make mechanical interactions with surfaces or external objects. Both excitation and detection of the resonator are integrated thanks to electrostatic actuation and capacitive detection. Apart from optical and electrical characterizations of the fabricated device, we report for the first time on the interaction between the resonator tip and a hydrodynamic force applied thanks to a water droplet. This demonstrates a first step toward high frequency atomic force probes for liquid medium applications.

GROWTH KINETICS OF A NANOPROTUBERANCE UNDER THE ACTION OF AN OSCILLATING NANOTIP

CPMOH, Universite ´Bordeaux I, 351 Cours de la Liberation, F-33405 Talence Cedex, France~!The atomic force microscope is a versatile tool that allows many routes to be used for investigating themechanical properties of soft materials on the nanometer scale. In the present work, experiments were per-formed on polystyrene polymer films of various molecular weight by approaching a vibrating nanotip towardsthe surface. The variation of the oscillating amplitude of the cantilever is interpreted as the result of the growthprocess of a nanoprotuberance. The growth rate is found to be dependent of the magnitude of the oscillatingamplitude and of the molecular weight. A model is developed describing in a very simple way the action of thetip and a viscoelastic response of the polymer. The numerical simulation helps in understanding the nonlinearrelation between the growth rate and the vibrating amplitude of the microlever and describes qualitatively mostof the experimental features. For the softer material, experimental situations are found that allow the experi-mental results to be amenable with an analytical solution. The analytical solution provides a fruitful compari-son with the experimental results showing that some of the nanoprotuberance evolution cannot be explainedwith the approximation used. The presents results show that there exists a new and fascinating route to betterunderstand the mechanical response at the local scale. PUBLISHED IN Phys. Rev. B 59(3), 2407-2416 (1999)@S0163-29~99!03003-9#I. INTRODUCTION

Reduction of the cantilever hydrodynamic damping near a surface by ion-beam milling

In this work, we evaluate the influence of the cantilever width on the hydrodynamic drag force. To do so, we present an experimental analysis of the thermal motion in air and liquid of a commercial and modified by focused ion-beam (FIB) milling silicon nitride cantilevers. From the thermal noise spectrum, we extract the damping for different cantilever-sample distances. We show that the hydrodynamic force due to the drag can be reduced by almost an order of magnitude when reducing the cantilever width. With the FIB modification (milling) one can still use conventional atomic force microscope heads with a significant reduction of the hydrodynamic forces.

Noncontact 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.