Phase imaging with intermodulation atomic force microscopy

Abstract

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.Key words: atomic force microscopy, intermodulation, multifrequency AFM, phase imaging IntoductionSince its invention by Binnig et al. [1], the atomic force microscope (AFM) has become one of the most widely used tools in nanoscience. In the first applications of AFM only the sample topography was measured by monitoring the static deflection of the AFM cantilever. The introduction of dynamic AFM with an oscillating cantilever brought various improvements, such as much lower measurement back action which greatly reduced damage to soft samples while imaging. In addition, the ability to measure the phase lag between the cantilever response and the exciting force, opened a new information channel to record while scanning. These "phase images" enabled compositional mapping of surfaces with dynamic AFM. The standard interpretation relates the measured phase lag to the energy dissipation resulting from the tip-sample interaction [2]. This interpretation is based on the assumption that the cantilever response is sinusoidal and only at the drive frequency, as in a linear approximation.More recently, the attention of the dynamic AFM community has focused on the nonlinear nature of the tipsample interaction [3,4,5,6]. It has been realized that the higher harmonics of the tip-motion carry valuable information about the tip-sample interaction. Each higher harmonic represents two new information channels (amplitude and phase) that can be recorded while scanning. Higher harmonic amplitudes and phases have been used for imaging both under ambient conditions and in liquids [7,8,9]. With a sufficient number of these information channels, a quantitative reconstruction of the tip-sample force is possible without measuring amplitude-distance curves [10,11]. * Corresponding author Email address: haviland@kth.se (David B. Haviland) However, the signal-to-noise ratio (SNR) for higher harmonics measurements is usually very poor because the harmonics are in general not located at a cantilever resonance. Various efforts have been made to improve the signal detection, for example by modifying the cantilever design [12]. Other approaches to increase the information acquired while scanning involve multifrequency excitations like bimodal AFM [13] or band excitation [14]. With bimodal AFM, two excitation tones are applied at the first two flexural eigenmodes of the cantilever. In this driving scheme the amplitude and phase at both dri...

Effect of Material Stiffness on Intermodulation Response in Dynamic Atomic Force Microscopy

“…That all response can be accounted for by a Fourier series in ∆Ω is a valid assumption as long as the nonlinearity is not too strong, so that period doubling or other such precursors to chaos do not appear in the response. In the experiment, the phase can be determined by using the two drives signals to build a reference signal with frequency ∆Ω [10]. This measurement constituents a generalization to nonlinear systems, of a common instrument used in linear systems analysis, known as the lock-in amplifier, or network analyzer.…”

Phase imaging quality improvement by modification of AFM probes’ cantilever

“…Atomic force microscopy (AFM) is the one of the most commonly used techniques when the studies with atomic level precision of the material's surface structure and properties are considered (Binnig et al ., ; Giessibl, ; Dulebo et al ., ; Platz et al ., ). Among various AFM operational modes, tapping mode (TM), including its extension, called phase imaging (PI), is the one of the operational modes of AFM, which allows for analysis of surface properties (Mourougou‐Candoni, ), providing high‐resolution images.…”

Reconstructing Nonlinearities with Intermodulation Spectroscopy

“…Our work is motivated by the desire to understand the information content of intermodulation spectra, as measured in superconducting microresonators at GHz frequencies [11,12], and in AFM cantilevers oscillating at several hundred kHz while interacting with a surface [13,14] (see Fig. 2).…”

“…The nonlinearity is provided by the tip-surface force, F nl = F ts (ζ), which we wish to determine. Intermodulation spectroscopy can be performed while scanning over a surface, measuring the dominant IMPs at each image point [13,14]. The inversion algorithm described here can be used to rapidly determine the force-distance curve at each image pixel, while scanning at normal speeds for dynamic AFM, one of the major objectives of AFM development [5,20].…”

“…(color online). Measured intermodulation spectra taken from a nonlinear superconducting resonator[12] (left panel) and an AFM cantilever interacting with a surface[14] (right panel). In these experiments the two central peaks with largest response are the drive tones.…”