Dynamics and Control of Tapping Tip in Atomic Force Microscope for Surface Measurement Applications

S. I. Lee', J. M. Lee S. H. Hong2

Department of Mechanical and Information Engineering, University of Seoul, Seoul, Korea School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea

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Abstract In tapping mode atomic force microscopy (TM-AFM), the vibro-contact response of a resonating tip is used to measure the nanoscale topology and other properties of a sample surface. However, the nonlinear tip-surface interactions can affect the tip response and destabilize the tapping mode control. Especially it is difficult to obtain a good scanned image of high adhesion surfaces such as polymers and biomolecules using conventional tapping mode control. In this study, theoretical and experimental investigations are made on the nonlinear dynamics and control of TM-AFM. Also we report the surface adhesion is an additional important parameter to determine the control stability of TM-AFM. In addition, we proved that it was adequate for the soft and high adhesion sample to be modeled with JKR contact to obtain a reasonable tapping response in AFM.

Keywords: Atomic force microscopy (AFM), Tapping mode, Nonlinear dynamics

1 INTRODUCTION Atomic force microscopy (AFM) or scanning probe microscopy (SPM) is a breakthrough in nanoscale measurement technique with its ultra-high resolution. [ I - 31 Especially, the tapping mode has become important in scanning probe studies as a method to reduce damage to soft substrates. [4] The vibro-contact response of a resonating AFM tip is used in the tapping mode to image the surface topography and characterize the surface properties of a wide range of materials at the nanoscale.[l] Besides the contact or non-contact mode, the feedback control loop between the tip response (which is generally picked up from the photodiode array using the reflected laser) and the Z scanner in the tapping mode maintains a constant oscillation amplitude by leveling of the Z piezotube scanner at the base of the microcantilever during XY scanning. However, the intrinsic nonlinear tip- surface interactions and additional adhesion can affect the tip response, and destabilize the tapping mode control. [5] To address this instability issue in tapping mode control, we have combined both experimental and theoretical analysis of a tapping mode AFM microcantilever. In the experiment, the tapping tip amplitude and phase were measured using a silicon tip on a hard sample (HOPG: highly oriented pyrolytic graphite) and a soft polymer sample (PDMS: polydimethylsiloxane). Also the surface images for each sample (HOPG and PDMS) were obtained using the same control setpoint in the tapping mode. In the theoretical modeling, a discretized model of the AFM microcantilever with long-range attractive van der Waals force and DMT (Derjaguin-Muller-Toporov) [6] and JKR (Johnson-Kendall-Roberts) [7] contact mechanics are used to model the tip-surface interactions including adhesion as well as sample deformation during tip-sample contact. Numerical simulation of this model reveals the complex nonlinear features of the tapping mode microcantilevers. The main contribution of this paper, which is apparently distinct from the previous work [5], is the implication of the imaging instability linked to the nonlinear responses of the tapping tip due to the surface properties. To reveal this, we compared the tapping response and images for two representative samples (HOPG and PDMS) with extremely different elasticity and surface adhesion. In experiment, we

used AFM's system lock-in amplifier to capture the amplitude and phase signals of the tapping tip without additional electronics and software. This means that it can be developed seamlessly from the original configuration of commercial AFM in the tapping mode control scheme on the soft and high adhesion surfaces. In addition, we proved that it was adequate for the soft and high adhesion sample such as PDMS to be modeled with JKR contact in the tip- sample interaction to obtain a reasonable tapping response in AFM.

2 EXPERIMENT A diving-board type Si tip and a standard configuration of an AFM system are utilized to demonstrate the effects of dynamic and control characteristics on the tip response in the tapping mode. A microcantilever, which is designed for non-contact or tapping mode (NCHR probe by Nanosensors Inc., resonance frequency = 259 kHz, spring constant = 20 N/m), is employed on a PSlA XE-lOOTM scanning probe microscope (Figure 1). The XE-100 system is designed with separate XY and Z scanner. The experimental setup is similar to the previous study [5] except that the tapping tip signal is captured using system internal lock-in amplifier.

Figure 1: Scanner head and sample in measurement (PSIAXE-lOOTM AFM system)

Three sets of experiments will be described: (a) a force- distance curve, (b) the frequency response of the cantilever amplitude as the excitation is swept up through resonance, and (c) a sample surface are scanned with different tapping mode setpoints. All experiment performs both on a HOPG and on a PDMS sample. The effects on tip-sample interaction can be clearly demonstrated by measuring the force-distance curve which records the force on the tip as a function of the Z travel distance (Figure 2 and Figure 3). Figure 2 and Figure 3 show the force-distance curves on a HOPG and a PDMS sample. Even though the tapping mode uses the resonating response of the tip, the XE-100 AFM captures the tapping deflection signal of the tip. Therefore, the Y axis in Figure 2 and 3 can be regarded as the static deflection or mid-point in oscillating amplitude of the tapping microcantilever during the tip approaches and retracts from the surface. In Figure 2, as the tip approaches HOPG surface (from A to C along the red line), the cantilever first maintains no deflection and then deflects linearly from point B to C as the tip pushes against the surface. At the retraction (D + E), the curve follows along the approach case even though there exists a thermal Z drifts (the amount is about 20 nm). In contrast, the force-distance curve of a PDMS sample (Figure 3) shows quite different features from that of HOPG sample. As the tip approaches the sample (from A to C along the red line), the tip deflects after it maintains no deflection without tapping. At the region from B to C, the deflection increases almost linearly, but a little noisy. At point C, the deflection suddenly decreases into point D. This is interpreted that the tip may snap into the surface due to the high adhesive interactions. As the tip retracts from E to F, however, the deflection does not follow the approach curve. At the region between E and F, the tip shows small but unstable deflection. At this point we note that the hysteretic deflection (B + C + D and E + F) is due to the high adhesive forces of PDMS and the complex nature of the tip-surface interactions.

Figure 3: Force-distance curve for PDMS sample

In the second set of experiments, we find that the dynamic response of the tapping tip is highly nonlinear and considerably depends on the sample properties and tip- surface interactions. To demonstrate this, for each tip- sample separation distance, the excitation frequency of the microcantilever is swept up through the microcantilever's resonance frequency. The excitation level of the dither piezoactuator is maintained constant for all these experiments. For each frequency increment (Af = 10 Hz), the amplitude and phase of the cantilever oscillation (referenced to the excitation frequency) are measured by an AFM control software when the feedback is turned off. Figure 4 and 5 show representative results of the near resonant response in air. In Figure 4(a) and (b), the amplitude and phase of the tapping tip response on HOPG sample are shown when i) the tip is far away from the sample (No tapping); ii) the tapping setpoint - 450 nm (HOPG-SPI); iii) - 250 nm (HOPG-SP2); and iv) - 150 nm (HOPG-SP3). When the tip is far away from the sample, the response is essentially linear. As the tapping setpoint is reduced to HOPG-SPI, the amplitude of oscillation is reduced, and saturates in the frequency range where the tip taps on the sample. At HOPG-SP2, the amplitude response is further reduced in the amplitude saturation region. At HOPG-SP3, the amplitude is suppressed further in the whole frequency range.

Figure 4: Frequency response of tapping tip on HOPG sample: (a) amplitude; and (b) phase.

Figure 5: Frequency response of tapping tip on PDMS sample: (a) amplitude; and (b) phase.

The same procedures are performed on the PDMS sample surface. Figure 5(a) and (b) show the amplitude and phase response when i) no tapping; ii) the tapping setpoint is - 480 nm (PDMS-SPI); and iii) - 250 nm (PDMS-SP2). An important feature of the response due to the setpoint is considerably different from that observed on HOPG. When the tapping tip approaches to PDMS surface via reducing the tapping setpoint from PDMS-SP1 to -SP2 (which is the similar amount of the setpoint as HOPG-SP1 to -SP2), the amplitude of the tip unexpectedly jumps down and suppressed the whole frequency range. This makes the tapping mode control unstable and has more chances to produce the unwanted artifacts in tapping mode imaging. From the dynamic responses in frequency range with respect to the tapping setpoint, it is regarded that the instability of the tapping control is partly due to the surface adhesive forces of the material. It is because the tapping amplitude instability with respect to the tapping setpoint easily accompanies on a polymer (PDMS) sample rather than a HOPG surface. To investigate the implication for reliable imaging and the amplitude jump due to the surface forces, the effect on the tapping mode imaging stability as a function of amplitude setpoint was studied. Specifically, the HOPG and the PDMS samples are also imaged with amplitude-based tapping control at the amplitude setpoint between SP1 and SP2 for HOPG and PDMS respectively. Figure 6 and 7 show the scanned images with different materials. The scan size is 1 pm x 1 pm and the fast scan (x direction) rate is 1 Hz. The tapping image on HOPG (Figure 6) shows good surface topography, but the image on PDMS (Figure 7) shows overestimated height and imaging artifacts at the surface. The X marked points in Figure 6 and 7 indicate the measured points for the tapping responses (Figure 4 and 5) with frequency range.

Figure 6: Surface topography of HOPG sample

Figure 7: Surface topography of PDMS sample

In Figure 6, we can find the graphite layer of HOPG at near edge of the image. Also the slightly embedded wave pattern over the surface is due to the interference from the reflected laser on the cantilever and the graphite surface. In Figure 7, however, the sudden appearance of imaging artifacts across the surface indicates that the height is overestimated in standard tapping mode control due to the unexpected reduction of tapping amplitude. We can find the implication for the tapping image instability from the earlier results for the force-distance curves and the frequency responses with respect to the different tapping setpoi nt.

3 THEORETICAL MODELING To analyze the nonlinear response of the tapping tip, we model the tapping microcantilever as a Bernoulli-Euler beam. As the tip-surface interaction, van der Waals and contact forces between a sphere (as a tip) and a flat surface (as a sample surface) are assumed. To model the case of high surface adhesion between tip and sample, the JKR contact model is adopted and the proposed JKR interaction shows interaction hysteresis during the tip approaches and retracts from the sample. (Figure 8) In JKR interaction model, the tip-sample forces are divided into two regimes with the interaction hysteresis. During the tip approaches ( Z < 0) , the interaction forces Fint(z) are

while the tip retracts ( i > 0) ,

r A R I . \

where z , A , R , and a. are the tip-sample gap, Hamaker constant, the tip radius, and the intermolecular distance, respectively. Those quantities are also used in DMT model. In Equation (Ib), bo is the JKR retract

distance which is normally different from a. . Fm(z) satisfies the following relations [8]:

J 3R a3 ==LFJKR + 3 n R W + 6nRWFJKR + ( ~ z R W ) ~

where W , a , and E" are the surface adhesion energy, the contact area, and the effective elastic modulus, respectively. Because Fm(z) is expressed implicitly in Equation (2a-c), we apply the JKR contact force into Equation (la-b) after expanding the JKR contact force up to 5th order polynomials with respect to z . Figure 8 shows the approximated JKR interaction model compared to the DMT contact. The main feature of the JKR model is the interaction hystersis by the tip-sample adhesion forces which are not considered at DMT contact model.

Figure 8: Tip-surface interactions incorporating DMT (blue) and JKR (red) contact models.

Figure 9: Numerical simulation of tapping response on PDMS sample with DMT (blue) and JKR (red) contact

model: (a) amplitude; and (b) phase.

Value

I A = 2.37 X J I I Hamaker constant (Si-PDMS)

Table 1: Properties of the microcantilever and sample used in numerical computation

Next, we perform MATLAB simulation to solve the dynamic equation of the resonating tip with the tip-sample interactions incorporating DMT and JKR contact models. The dynamic equation and the detailed procedure for obtaining the tapping response are well described in [5]. The parameter values of the numerical computation in this paper are tabulated in Table 1. Figure 9(a) and (b) show the amplitude and phase response of the tapping tip on PDMS sample. In Figure 9, we note that the essential nonlinear features using both DMT and JKR contact models are qualitatively same as the experiment result in Figure 5. However, only the tapping response using JKR model is well agreed to the

amplitude response in Figure 5. Because the difference due to the selection of contact models on PDMS sample is clear in Figure 9, we can predict that JKR contact model is more adequate to simulate the tapping response on the high adhesive polymers such as PDMS. Further investigations are performing on the differences in the phase response due to the contact models.

4 CONCLUSIONS In conclusion, we have investigated both experimentally and theoretically the dynamic features and imaging instability of a tapping tip on a hard (HOPG) and a soft (PDMS) sample. Experimental measurements are presented of the force-distance data and the frequency response of a tapping tip to demonstrate the nonlinear features including tip amplitude saturation and unexpected tapping amplitude change due to the setpoints. To verify the effects of the surface adhesion and tip-sample interactions on the tapping mode imaging, HOPG and PDMS surfaces are imaged by Si tip. By the connection between the nonlinear response of the tapping tip and the scanned surface images, the effects of the amplitude setpoints and extent of surface adhesion on the imaging instability is demonstrated. Based on this study it appears the optimal setpoint for stable imaging need to be set such that the sample surface contains high adhesive forces. Also to implement a special tapping mode control is recommended to extend the surface measurement applications to soft and high adhesive samples such as polymers. Through the theoretical modeling of the tapping mode process, an appropriate tip-sample interaction model, such as JKR contact, must be required due to the sample properties. Using MATLAB simulation we proved that the soft and high adhesion sample should be modeled with JKR contact to obtain a reasonable tapping response in AFM.

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