It has previously been shown that bimodal tapping-mode AFM can provide increased compositional contrast. Here we discuss the addition of a third eigenmode to this scheme in order to acquire simultaneous topography, phase and frequency shift. The results suggest that, in general, the phase and frequency shift contrast exhibit anti-parallel behavior, although deviations from this trend are often observed in the experiments, such that all sources of contrast can provide complementary information.
The recent development of multi-frequency atomic force microscopy (AFM), whereby more than one cantilever eigenmode is excited and controlled simultaneously has made new characterization channels available to the user, in addition to the fundamental eigenmode response used in amplitude-modulation mode (AM-AFM, tapping-mode AFM) [1-4]. Since the response variables acquired through the various channels (oscillation frequency, amplitude and phase of each eigenmode) are sensitive to different material properties and since the higher eigenmodes are not controlled by the topographical acquisition loop, multi-frequency operation effectively increases the amount of information that can be acquired during each scan of the sample. Since its introduction within non-contact AM-AFM , bimodal tapping mode operation has been extended to repulsive mode imaging, both in air and liquid environments [3, 5]. Bimodal AFM characterization has also been successfully implemented in ultra-high vacuum through the simultaneous operation of two eigenmodes in frequency-modulation mode (FM-AFM) using phase-locked-loop (PLL) controllers [1, 6]. Since the frequency shift in FM-AFM is sensitive to the average tip-sample force gradient but not highly sensitive to local dissipation forces, while the phase shift is highly sensitive to both the average tip-sample force gradient and dissipative interactions , it seems advantageous to incorporate a third, frequency-modulated eigenmode into the bimodal tapping mode scheme. In this way, two different sources of higher-order contrast (phase and frequency shift) can be obtained simultaneously, in addition to the topography, from which the user could in principle obtain rich information about the stiffness and dissipative properties of the tip-sample junction.
Implementation of Trimodal AFM
We implemented trimodal AFM [8, 9] by integrating an Asylum Research (Santa Barbara, California, USA) MFP3D atomic force microscope with an RHK Technologies (Troy, Michigan, USA) PLL Pro2 Controller, as shown in figure 1.
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In our setup, the MFP3D controller produces a dual-frequency excitation signal, which is provided to the PLL Pro2 Controller as a bias signal. Using the filtered cantilever deflection signal, the PLL Pro2 Controller produces a frequency-modulated excitation for the additional eigenmode, which is added to the bias signal received from the MFP3D controller and sent to the cantilever shaker through an amplifier (if needed). The PLL Pro2 Controller also provides the MFP3D controller with the instantaneous frequency shift signal of the new eigenmode for imaging. All imaging is done by the MFP3D controller and computer, and no modifications of the operating system are required.
Due to the complex tip trajectory in trimodal operation, which consists of the superposition of three waves, the exact mathematical interpretation of the phase and frequency shift is not straightforward and the contrast does not always behave as for single-eigenmode operation . Nonetheless, harmonic oscillator dynamics [7, 9] predict that the phase and frequency shift should vary in anti-parallel directions, with the dependence on the force gradient being linear when the latter is close to zero. This relationship is illustrated in figure 2 for a harmonic oscillator having a free resonance frequency of 420 kHz and a quality factor of 450, similar to the second eigenmode of an Olympus AC240TS cantilever (used in several of our experiments).
Figure 3 shows typical experimental images for a Kraton triblock copolymer, obtained using eigenmodes 1, 2 and 3 for topographical, phase and frequency shift contrast, respectively. The leftmost and center images show that, for the case considered, the contrast observed in the phase of the first two eigenmodes is similar. The rightmost image shows the negative of the frequency shift, which exhibits a trend similar to that of the phase (in agreement with figure 2) although it displays sharper segregation. Additionally, it is often possible to vary the imaging conditions such that phase and frequency shift signals provide nearly identical contrast. This is most easily achieved by varying the relative amplitudes of the three eigenmodes [8, 9]. Qualitatively similar results to those of figure 3 were obtained for the phase and the frequency shift using bimodal operation (that is, operating only two eigenmodes simultaneously and collecting the phase and frequency shift images in separate scans of the same region of the sample). The similarity between the phase and frequency shift contrast obtained using bimodal operation and the results obtained for trimodal operation (figure 3) suggests that conditions can be found in trimodal operation, such that the artifacts introduced by the complex motion of the cantilever tip can be minimized and meaningful results can be obtained.
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