Frequency response of higher cantilever eigenmodes in bimodal and trimodal tapping mode atomic force microscopy

Abstract

We have recently implemented a trimodal tapping mode atomic force microscopy (AFM) imaging scheme for ambient air with which it is possible to simultaneously acquire topographical, phase and frequency shift contrast images. In implementing this method we have identified conditions, such as very low fundamental amplitude setpoints and very low oscillation amplitudes for the higher eigenmodes, for which the stability of the imaging process can be compromised. In this work we use numerical simulations to gain insight into the changes in the frequency response of the higher eigenmodes in bimodal and trimodal operation for different levels of sample stiffness, tip–sample dissipative forces, oscillation amplitudes for each of the eigenmodes and cantilever rest positions above the surface. Although we do not attempt to convey a complete dynamics picture of the system, the results provide general guidelines for the selection of conditions that lead to stable imaging as well as insight into the observed phase and frequency shift contrast, highlighting a few potential imaging artifacts. Our simulation results are in general agreement with our experimental observations.

Optimization of phase contrast in bimodal amplitude modulation AFM

“…This context has also stimulated other multifrequency AFM variations such as trimodal AFM [39][40][41]. In trimodal AFM the first three flexural modes are excited and detected.…”

“…Solares and co-workers have extended the bimodal scheme by introducing an additional excitation in the third mode [39][40][41]46]. The third excitation in trimodal AFM offers two additional channels for compositional contrast.…”

Particle swarm optimization used with proportional–derivative control to analyze nonlinear behavior in the atomic force microscope

“…To get the error signal ½e 1 , e 2 to approach zero, the system output y(t) is subtracted from the system input r(t), as shown in equation (6). An error signal is obtained which provides the control item u(t) through the PD controller, as shown in equation (10), and the expression satisfies the condition shown below…”

“…Solares and Chawla 6 implemented a trimodal tapping-mode atomic force microscope (AFM) imaging scheme for ambient air with which it is possible to simultaneously acquire topographical and phase and frequency shift contrast images. By implementing this method, they had identified conditions, such as very low fundamental amplitude setpoints and very low oscillation amplitudes for the higher eigenmodes, for which the stability of the imaging process can be compromised.…”

Phase contrast and operation regimes in multifrequency atomic force microscopy

“…The single frequency virial that controls the phase shift might undergo transitions in sign while the average force (modal virial) remains positive (negative). Multifrequency atomic force microscopy (AFM) is an emerging 1,2 branch of AFM where two or more frequencies 3,4 are externally excited in order to map material composition, [5][6][7] enhance resolution 8 and sensitivity, [9][10][11] and quantify material properties [12][13][14] with gentle forces. The theory that controls the response of the cantilever while simultaneously exciting several frequencies and modes however is still emerging 12,15,16 and might result complex.…”