Nonlinear Dynamic Analysis of Atomic Force Microscopy

2006 ◽  
Author(s):  
Hossein Nejat Pishkenari ◽  
Mehdi Behzad ◽  
Ali Meghdari
Keyword(s):  
Atomic Force Microscopy ◽  
Equations Of Motion ◽  
Basin Of Attraction ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Behavior ◽  
Random Excitation ◽  
System Response ◽  
Force Microscopy ◽  
Atomic Force ◽  
Exciting Frequency

This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as Averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.

Singular Loss of Stability Due to Hysteretic Capillary Forces in Atomic Force Microscopy

2010 ◽  
Author(s):  
Michael Katzenbach ◽  
Harry Dankowicz
Keyword(s):  
Atomic Force Microscopy ◽  
Theoretical Analysis ◽  
Deterministic Model ◽  
Fluid Layer ◽  
Mapping Technique ◽  
System Response ◽  
Force Microscopy ◽  
Atomic Force ◽  
Critical Equilibrium ◽  
Linearized Stability

This paper considers discontinuity-induced bifurcations due to the onset and termination of hysteretic, capillary tip-sample interaction forces in a single-mechanical-mode model of intermittent-contact atomic-force microscopy. The theoretical analysis generalizes earlier results for a piecewise-linear hybrid dynamical system to establish the singular termination of branches of steady-state oscillations of the AFM cantilever at critical equilibrium separations corresponding to the grazing contact of the cantilever tip with a fluid layer deposited on the sample. It is shown that this termination is preceded by rapid changes in linearized stability characteristics with one characteristic multiplier going to plus or minus infinity in the deterministic model. The paper describes the application of a discontinuity-mapping technique that allows for unfolding the system response in the vicinity of the grazing condition and the critical equilibrium separation. Numerical simulations and results of parameter continuation are shown to closely agree with the predictions of the theoretical analysis.

Image acquisition for trolling-mode atomic force microscopy based on dynamical equations of motion

2020 ◽  
pp. 095440622097755
Author(s):  
Mohammadreza Sajjadi ◽  
Hossein Nejat Pishkenari ◽  
Gholamreza Vossoughi
Keyword(s):  
Atomic Force Microscopy ◽  
High Speed ◽  
Imaging Techniques ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
Dynamical Equations ◽  
Force Microscopy ◽  
Atomic Force ◽  
Two Degree Of Freedom ◽  
Mode Atomic Force Microscopy

Trolling mode atomic force microscopy (TR-AFM) can considerably reduce the liquid-resonator interaction forces, and hence, has overcome many imaging problems in liquid environments. This mode increases the quality factor (QF) significantly compared with the conventional AFM operation in liquid; therefore, the duration to reach the steady-state periodic motion of the oscillating probe is relatively high. As a result, utilizing conventional imaging techniques, which are based on measuring the amplitude and phase, are significantly slower when compared to our proposed method. This research presents a high-speed scanning technique based on an estimation law to obtain the topography of various samples utilizing a two-degree-of-freedom model of TR-AFM. The effect of the nanoneedle tip horizontal displacement on the estimation process is investigated, and a solution to compensate for its undesirable effect is also presented.

Localized Material Properties Through Nonlinear Dynamics Based Atomic Force Microscopy

2010 ◽  
Author(s):  
Wei Huang ◽  
Andrew J. Dick
Keyword(s):  
Atomic Force Microscopy ◽  
Material Properties ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Separation Distance ◽  
Resonance Excitation ◽  
Current Effort ◽  
Force Microscopy ◽  
Atomic Force ◽  
Local Material Properties

Due to the intrinsic nonlinearity of the tip-sample interaction forces that are utilized in atomic force microscopy, nonlinear behavior can be observed even under the most ‘ideal’ conditions. While the standard operating modes of the atomic force microscope (AFM) have been developed to minimize this nonlinear behavior, the authors’ work focuses on utilizing a nonlinear response of the AFM probe associated with off-resonance excitation in order to measure local material properties of the sample. Previously, period-doubling bifurcations were identified and studied for an off-resonance excitation condition of two-and-a-half times the fundamental frequency. A relationship was identified between the characteristics of the qualitative response transition and the properties of the probe and sample. For a given probe, the critical separation distance where the period-doubling bifurcation occurs is influenced by the local modulus properties of the sample. This paper details the current effort studying this relationship with the goal of developing a new AFM operation mode for obtaining localized material properties by scanning the sample. The influence of different system parameters on this relationship is studied and preliminary simulation results are presented for a simple scanning process.

Sign in / Sign up

Export Citation Format

Share Document