Single cycle and transient force measurements in dynamic atomic force microscopy

Abstract

The monitoring of the deflection of a micro-cantilever, as the end of a sharp probe mounted at its end, i.e. the tip, interacts with a surface, forms the foundation of atomic force microscopy AFM. In a nutshell, developments in the field are driven by the requirement of obtaining ever increasing throughput and sensitivity, and enhancing the versatility of the instrument to simultaneously map the topography and quantify nanoscale processes and properties. In the most common dynamic mode of operation, the motion of the driven cantilever is monitored at a single point on its longitudinal axis. Here, we show that from this single point a waveform is obtained that contains all the details about conservative and dissipative interactions. Then a formalism that accounts for multiple arbitrary flexural modes is developed for an indirectly driven cantilever. The formalism is shown to allow recovery of the details of the interaction even in the presence of complex and relevant hysteretic forces when the cantilever oscillates in the steady state. In a different approach, we develop a formalism that monitors the wave profile of the cantilever, i.e. the waveform at five different points on its longitudinal axis. With this formalism the interaction can be reconstructed during a single oscillation cycle even in the transient state of oscillation. Finally, we discuss the potential and advantages of the proposed methods and future technical challenges. Other standard and state of the art techniques and methods are also discussed and compared with the ones presented here. This work should also provide insight into the current high throughput-high sensitivity developments dealing with multifrequency dynamic AFM where information is recovered from multiple eigenmodes.

Non-resonant frequency components observed in a dynamic Atomic Force Microscope

“…In the dynamic AFM mode, the probe tip is typically excited with a single frequency approximately equal to the natural frequency of the cantilever probe. The response of the probe tip has high-order frequency components due to the nonlinear interaction [12,13]. The purpose of this study is to investigate the spectral characteristic of the decaying oscillation.…”

“…In this study, we investigate the oscillatory behaviors of the probe tip with an approximated dynamical model, which is given by an ordinary differential equation with one degree of freedom [7,8,11,13,14]. We assume the magnitude of the interaction force between the probe tip and the sample surface from a Lennard-Jones potential.…”

Unlocking higher harmonics in atomic force microscopy with gentle interactions

“…Since the higher harmonic amplitudes here are externally excited, the number of harmonics N that is to be monitored can, in principle, be arbitrarily chosen up to the limits of frequency detection, i.e., of the order of MHz, without compromising detection. The main constraint is that the number of higher modes, M , that is to be considered needs to be consistent with the number of higher harmonics N that are to be analysed [22]. For simplicity, we consider M = 2 and N = 10 in the numerical analysis without loss of generality.…”

“…Thus, the simultaneous detection and interpretation of multiple higher harmonic signals while scanning [14] can lead to spectroscopy-like capabilities [15–16], such as chemical identification, with similar or higher resolution [5,17–18]. The higher harmonic approach however, and particularly in other than highly damped environments [19–20], requires dealing with the recurrent challenge of detecting higher harmonics [1,3,21–22]. Higher harmonics are a result of the non-linear tip–sample interaction in the sense that the interaction effectively acts as the driving force of each harmonic component [7].…”

“…Higher harmonics are a result of the non-linear tip–sample interaction in the sense that the interaction effectively acts as the driving force of each harmonic component [7]. Accordingly, relatively high peak forces, of the order of 1–100 nN, are required [22–23] to excite higher harmonics above the noise level. In order to address this issue, in 2004 Rodriguez and García [23] proposed to drive the second higher flexural mode of the cantilever with an external drive.…”