Ultimate Decoupling between Surface Topography and Material

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Ultimate Decoupling Between Surface Topography and Material Functionality in Atomic Force Microscopy Using an Inner-Paddled Cantilever Sajith M Dharmasena, Zining Yang, Seok Kim, Lawrence A Bergman, Alexander F. Vakakis, and Hanna Cho ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b01319 • Publication Date (Web): 25 May 2018 Downloaded from http://pubs.acs.org on May 25, 2018

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Ultimate Decoupling Between Surface Topography and Material Functionality in Atomic Force Microscopy Using an Inner-Paddled Cantilever Sajith M. Dharmasena1, Zining Yang2, Seok Kim2, Lawrence A. Bergman3, Alexander F. Vakakis2, Hanna Cho1,* 1

Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, Ohio, USA 2

Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois, USA 3

Department of Aerospace Engineering, University of Illinois, Urbana, Illinois, USA *Corresponding author: [email protected]

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Abstract Atomic Force Microscopy (AFM) has been widely utilized to gain insight into various material and structural functionalities on the nanometer scale, leading to numerous discoveries and technologies. Despite the phenomenal success in applying AFM to the simultaneous characterization of topological and functional properties of materials, it has continuously suffered from the crosstalk between the observables, causing undesirable artifacts and complicated interpretations. Here, we introduce a two-field AFM probe, namely an innerpaddled cantilever integrating two discrete pathways such that they respond independently to the variations in surface topography and material functionality. Hence, the proposed design allows reliable and potentially quantitative determination of functional properties. In this paper, the efficacy of the proposed design has been demonstrated via Piezoresponse Force Microscopy (PFM) of periodically poled lithium niobate (PPLN) and collagen, although it can also be applied to other AFM methods such as AFM-based Infrared (AFM-IR) spectroscopy and Electrochemical Strain Microscopy (ESM). Keywords: atomic force microscopy, contact-mode functional AFM, piezoresponse force microscopy, contact resonance, inner-paddled microcantilever.

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Detecting and characterizing nanoscale material functionalities of emerging materials is of rapidly growing interest as it is critical for the advancement of nano- and bio-technology. Atomic Force Microscopy (AFM) has emerged as a powerful technique for obtaining nano-scale information on functional materials. Since its invention in the mid-1980’s1 as a topographical imaging technique, the capabilities of AFM have been extended to include nano-scale mapping of various material characteristics such as electrical,2–8 mechanical,9–12 chemical,13–16 electrochemical17–20 and electromechanical8,21–26 properties over a broad range of materials, paving the way for major advances in many fields including material science, physics, biomechanics, chemistry and the life sciences. For instance, Piezoresponse Force Microscopy (PFM)27,28 has been pivotal toward understanding complex material behaviors of piezoelectric and ferroelectric materials and extending their use to various applications such as very high speed, high density memory devices,29,30 ferroelectric lithography,31,32 and high efficiency solar cells.33,34 In addition, ferroelectric perovskites,35,36 multiferroic materials,33,37,38 and biological systems8,25,39,40 have been investigated using PFM. Furthermore, AFM-based Infrared (AFM-IR) spectroscopy14,41 has recently become an important tool for nano-scale chemical mapping of biomedical materials,42,43 polymer blends,44 multilayer films45 and thin films,46 providing critical insights into the distribution of the different chemical and polymer components in materials. Potential profiles of metal/semiconductor materials obtained using Kelvin Probe Force Microscopy (KPFM)47 have enabled researchers to detect nano-scale processing-induced defects, and study their effects on the performance of electrical devices.48,49 Similarly, the capabilities of Electrochemical Strain Microscopy (ESM)50 have enabled investigations of nano-scale electrochemical functionalities of energy storage systems18,20,51 used in a broad range of applications including fuel cells, automotive systems and portable electronics.

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The traditional approach to AFM functional imaging involves the use of lock-in amplifiers to determine the amplitude and phase of the cantilever response at a single welldefined excitation frequency. The input to activate the material functionality can be in the form of a harmonic excitation applied to the base of the sample or directly to the tip, while the resulting cantilever deflections provide a measure of the functional properties of the sample. Depending on the functional response under investigation, either the cantilever tip needs to remain in contact with the sample over the entirety of the oscillation cycle in a mode known as Contact AFM (C-AFM)1 or make no contact during the oscillation cycle in a mode known as Non-Contact AFM (NC-AMF).52 The C-AFM approach is the functional basis of AFM techniques such as PFM, ESM, and AFM-IR, in which the dimensional changes of a sample in response to the functional input are measured by the tip in contact. Similarly, NC-AFM is used in Electrostatic Force Microscopy (EFM),3 KPFM, and Magnetic Force Microscopy (MFM),53 in which the reacting force with respect to functional properties is measured by the non-contacting tip. The intrinsic limitation of many functional AFM techniques is the low Signal-to-Noise Ratio (SNR), especially when measuring materials of lower responsivity. The obvious approach to improving the SNR is to increase the strength of the excitation. However, using a higher excitation input may be undesirable in many applications. For example, the high voltage input in PFM may cause polarization switching in ferroelectric materials or even damage to the sample. Alternatively, the SNR can be improved by utilizing resonance of the cantilever. By operating the cantilever near resonance, its response can be increased by a factor of 10~100 (i.e., the Q factor of the cantilever resonance), thus significantly improving the SNR. Operating near resonance has proven beneficial in many AFM techniques such as single-frequency PFM,54

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AFM-IR,55 KPFM47 and Atomic Force Acoustic Microscopy (AFAM).56 However, in C-AFM methods that utilize contact resonance for signal amplification, the resonance frequency is primarily determined by the local tip-sample contact stiffness. This represents a major limitation of current contact-mode functional AFM techniques, since the contact stiffness varies due to topographic and material variations of the sample, consequently causing the resonant frequency to vary as well. Thus, there can be significant crosstalk between sample topography and the functional response, leading to undesirable artifacts and complicated interpretations of the functional properties. Moreover, in the absence of an invariant resonant frequency, calibration of the tip geometry and/or the force-sensor configuration can be extremely difficult, making quantitative measurements in AFM challenging to perform. In order to overcome the limitations of the aforementioned techniques, recent efforts have been devoted to developing methods to track changes in the contact resonant frequencies of the cantilever as it scans over the surface: Phase Locked Loop (PLL),57 Dual Frequency Resonance Tracking (DFRT)58 and Band Excitation (BE)59 methods. While these techniques enable the locking of the cantilever dynamics near resonance during the AFM operation, they require additional data and signal processing. Especially in the case of highly heterogeneous samples, BE requires a broader range of frequency inputs, and DFRT may fail to track any large scale resonant frequency changes. Here, we propose to optimize the design of the mechanical transducer of the AFM, i.e., the cantilever system as depicted in Figure 1a, named the inner-paddled cantilever. Unlike the unibody design of a conventional micro-cantilever, this proposed design consists of an inner “paddle” in the form of a silicon nano-membrane integrated with a base cantilever system. The two-field design of this base cantilever-paddle system allows for the free oscillation of the inner

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paddle over the middle cavity during C-AFM operation. Since the inner paddle is not in physical contact with the sample surface, the design should minimize the effect of local contact stiffness on the resonance frequency of the inner paddle, while still delivering the dimensional changes of the sample to its dynamics. Therefore, the proposed inner-paddled cantilever should provide a stable (invariant) contact resonant frequency, independent of the changes in the local contact stiffness, which is the basis of ultimate decoupling between topographic changes and functional response. RESULTS AND DISCUSSION A scanning electron microscope (SEM) image of the fabricated inner-paddled cantilever system is shown in Figure 1a. The proposed design consists of an inner silicon nano-membrane (acting as the inner-paddle) suspended from a base microcantilever having a middle cavity. The approximate thicknesses of the inner paddle and base microcantilever are 300 nm and 1.6 µm, respectively. To demonstrate the efficacy of our design in C-AFM, we performed PFM measurements using an inner-paddled cantilever with a metal-coated tip, and compared the results to the ones obtained for the same samples by a conventional cantilever. An overview of PFM operation with an inner-paddled cantilever is shown in Figure 1b. The AC voltage is applied to the metal-coated cantilever base to supply an electric field to a piezoelectric sample through the cantilever tip. The response of the cantilever system is measured by the AFM laser system by focusing the laser near the free end of the inner-paddle. The size of the laser spot of the AFM system employed in this work (MFP-3D Infinity by Asylum Research) is several tens of µm, large enough to cover the full width of both the inner-paddle and base cantilever. Therefore, the photodetector signal contains the deflections of both the inner-paddle and the base cantilever. The static deflection signal of the base cantilever is used as the topographic feedback

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component to generate the topography, while the inner-paddle oscillations in response to the sample deformation are processed through a lock-in amplifier to extract the amplitude and phase of the piezoelectric response. PFM imaging of PPLN and Collagen. Figure 2 illustrates PFM results of periodically poled Lithium Niobate (PPLN, Model 900.241 by Asylum Research). We intentionally measured a contaminated sample to produce the topological variations on the flat PPLN sample. Figures 2a-b depict the results obtained using a commercially available conventional cantilever (MikroMasch NSC18/Pt) in single-frequency PFM (SFPFM) and DFRT-PFM, respectively, while Figure 2c depicts the result obtained using an inner-paddled cantilever in SFPFM. The deflection images depicted in Figures 2a-c clearly show variations in the topography (~2-5 nm), presumably due to non-piezoelectric surface contaminations. The crosstalk associated with a contact resonant frequency shift is typically caused by variations in the tip-sample contact stiffness due to changes in the topography or material. This topographic-material crosstalk, often encountered in PFM when operating near resonance, is illustrated in the PFM amplitude and phase images depicted in Figures 2a-b, where the artifacts observed are consistent with the topographic variations in the corresponding deflection images as indicated by the arrows in the line scans. Even though DFRT-PFM was shown to be effective in eliminating crosstalk when imaging fairly flat and homogenous lead zirconate-titanate (PZT) polycrystalline and PPLN where frequency shifts of up to 5 kHz were observed,58 it is evident from this result that any large-scale variations in the topography could cause instabilities. In contrast, no artifacts are observed in the PFM amplitude and phase images obtained by the inner-paddled cantilever system (Figure 2c), even though the same-level of variations in the topography are seen here as well.

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In order to quantify the variations due to crosstalk observed in the PFM responses, the histograms of PFM amplitude and phase data within the PPLN domains (i.e., excluding data in the domain boundaries) are plotted in the bottom row of Figure 2. Note that all amplitude data are normalized such that the averaged responses on the domains and domain boundaries of the trace data correspond to values of 1 and 0, respectively. The histograms of Figures 2a-b show a wider distribution of the measured amplitudes and phases compared to the histograms of Figure 2c: the commercial cantilever yields standard deviations of the amplitude and phase (σa, σp) of (0.8, 6.4º) and (1.1, 6.0º) for SFPFM and DFRT-PFM, respectively, while the inner-paddled cantilever results in a reduced standard deviation of (0.3, 2.9º). In addition, we quantified the disagreement between the trace and retrace PFM data sets of amplitude and phase, (∆a, ∆p), which should be zero during ideal operation without crosstalk and errors. The SFPFM results in significant disagreement of (∆a, ∆p) = (1.94, 21.6º), although it is somewhat mitigated to (0.33, 2.64º) in DFRT-PFM. Notably, for the inner-paddled cantilever, the trace and retrace data show excellent agreement with (∆a, ∆p) = (0.06, 1.15º). These measures demonstrate by quantitative comparison that the inner-paddled cantilever is capable of significantly reducing crosstalk. Additional PFM imaging of PPLN performed at the same drive amplitudes for all three cases are presented in the Supporting Information (see Figure S1). The performance enhancement of the inner-paddled cantilever is further demonstrated in PFM imaging of collagen (Sigma Aldrich SLBG4268V) on a glass substrate as illustrated in Figure 3. Compared with solid-state samples, PFM of bio-materials is more challenging since they are, by nature, heterogeneous in terms of topography and material and display weak piezoelectricity. Figures 3a-b depict results obtained using a commercial cantilever (MikroMasch XSC11/Pt, cantilever A) and Figures 3c-d depict results obtained using the inner-paddled

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cantilever, on the collagen sample. The mapping results in Figures 3a, c show the characteristic periodicity of collagen fibrils with very high spatial resolution in their respective deflection, PFM amplitude and phase images. The corresponding frequency response curves in Figures 3b, d show the contact resonance obtained on regions of the collagen fibrils (marked as A, B) and the glass substrate (marked as C) while the frequency of the voltage applied to the tip was swept. The contact resonance curves of the commercial cantilever in Figure 3b show strong variations of the contact resonant frequency depending on the changes in topographic and material stiffness features. In comparison, the contact resonance of an inner-paddled cantilever in Figure 3d shows no variations in the resonant frequency with respect to topographical changes, again demonstrating the reproducibility of the invariant contact resonant frequency on different surfaces. In these contact resonance curves, we obtained the large resonance amplitudes not only on the piezoelectric collagen but also on the non-piezoelectric glass substrate, indicating that the measured response is primarily due to the electrostatic forces between the surface and the conductive tip, rather than the intrinsic electromechanical response of collagen itself. The low voltage used to obtain these results (Vac = 4V) cannot induce a strong electromechanical response in weakly piezoelectric materials such as collagen. When combined with amplitude changes caused by the shift in the contact resonant frequency, this electrostatic effect causes artifacts in PFM results. The expected complications associated with probing weakly piezoelectric bio-samples is immediately apparent in the PFM amplitude image obtained using the conventional cantilever illustrated in Figure 3a; the non-piezoelectric glass surface shows a higher PFM amplitude than the collagen fibrils, and the collagen fibrils A and B exhibit a significant difference in their piezoelectric amplitudes. The frequency response curves in Figure 3b reveal that this artifact is

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due to the strong electrostatic force and variations in the contact resonance frequency. Besides, the yellow arrow indicates a sudden change in contrast in the PFM amplitude and phase images in Figure 3a. This change in contrast indicates a jump in the contact resonance most likely caused by the cantilever tip picking up a contaminant. Indeed, picking up contaminants is commonly encountered in C-AFM techniques, and usually results in an irreversible change in the contact resonance frequency and, accordingly, the PFM responses. In comparison, the PFM images obtained by an inner-paddled cantilever in Figure 3c show larger PFM amplitudes on all collagen fibrils compared with those of the glass substrate, which is consistent with expectations for this sample. In spite of the strong interference from the electrostatic forces, in the inset of Figure 3d we see a clear difference in the amplitudes of the frequency response curves obtained over the collagen fibrils (regions A and B) and the surrounding area (region C). This difference in the amplitudes is an indication of the piezoelectric strain of collagen. In fact, the invariant contact resonance enabled by our innerpaddled design allows us to qualitatively characterize minute changes in the response even in the presence of the strong effect of electrostatics. This pattern was observed in several other measurements of collagen and are presented in the Supporting Information (see Figure S2). Furthermore, since the resonant frequency of the inner-paddled cantilever is immune to changes in the tip-surface contact, it can effectively eliminate artifacts associated with picking up contaminants. Indeed, the sudden change in contrast as seen in Figure 3a has never been encountered when using an inner-paddled cantilever. This result further emphasizes the efficacy of our design in that it ultimately decouples the topological and functional information for functional imaging of not only solid-state samples but also highly heterogeneous bio-samples.

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Potential for Quantitative Measurements in PFM. In many areas of functional AFM, quantitative measurements are believed to be very challenging largely due to extreme sensitivity to imaging conditions, therefore requiring extensive calibration of the probe geometry and/or force-sensor configuration to relate the material functional response and cantilever deflection. Even with careful calibration, in most cases the changes in the resonant frequency make it impossible to perform accurate quantitative measurements. As a demonstration, we experimentally investigated the stability and linearity of the contact resonance peaks of a commercial cantilever while varying the magnitude of the excitation force. Figures 4a-b depict the resonance curves of two commercial cantilevers, MikroMasch XSC11/Pt cantilevers A (nominal k=0.2 N/m) and B (nominal k=2.7 N/m), measured as the applied AC voltage was varied from 0.5V to 5V while the cantilever tip was held in contact with PPLN. The resonance curves of the two commercial cantilevers appear to shift toward lower frequencies as the drive amplitude increases. Therefore, neither the response amplitude at a fixed frequency (blue) nor the peak amplitude (red) provide a linear relationship with respect to the drive amplitude as shown in the bottom row of Figure 4. These observations demonstrate that the variations of the resonant peaks make quantitative measurements fundamentally challenging to perform in C-AFM modes not only for the single frequency scheme but also for DFRT and BE schemes that track the resonance shift. Such difficulties mainly originate from the unibody design of a conventional cantilever, which is not suitable to carry independently more than one type of information. We repeated the experiment with an inner-paddled cantilever to compare its results with those of the commercial cantilevers as shown in Figure 4c. As expected, the inner-paddled cantilever exhibits an invariant resonant frequency when the input is varied and, more

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importantly, the resulting peak amplitudes and amplitudes at a fixed frequency vary linearly with respect to the drive voltage and overlap perfectly. Additionally, the invariant resonant frequency observed here eliminates the need for frequency tracking thus avoiding complicated signal and data processing. The linearity observed by the stable contact resonance for our design can enhance the reliability and accuracy of quantitative measurements of PFM which, as mentioned previously, still represents a significant challenge when utilizing the contact resonance of a conventional cantilever as an amplifier. Description of the dynamical behavior of the inner-paddled cantilever. We employ an analytical approach as a complement to the PFM scanning results presented in the previous section to provide a detailed dynamic analysis of the proposed inner-paddled cantilever. Based on the dynamic structure of our design, a two-degree-of-freedom (two-DOF) reduced order model (ROM) is constructed in the form of a discrete spring-mass system as shown in Figure 5c. This model is based on the assumption that the base cantilever and the inner paddle oscillate in their own fundamental, linearized bending modes while being linearly coupled to each other. The base cantilever is modeled as a spring-damper system with effective mass m1, effective spring constant k1, and effective damping coefficient c1. The mass of the base cantilever (m1) interacts with the sample surface while the tip scans over the sample during contact mode operation. The tip-sample interaction is modeled as a spring-damper system (ks, cs). The inner paddle is modeled as a second spring-mass-damper system (k2, m2, c2), linearly coupled to the base cantilever. Based on this ROM the equations of motion are given by

m1&& x1 + c1 x&1 + k1 x1 + k2 ( x1 − x2 ) + c2 ( x&1 − x&2 ) + ks x1 + cs x&1 = ks u + cs u& m2 && x2 + k2 ( x2 − x1 ) + c2 ( x&2 − x&1 ) = 0

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(1)

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The functional response of a sample to a certain applied stimulus is modeled as an input displacement (u) to the cantilever system. Since the inner paddle is not in physical contact with the sample surface, the tip sample-interaction is assumed to be applied to mass m1. For instance, in PFM, u is the piezoelectric strain of the sample caused by a modulation sinusoidal voltage applied to the sample surface via a conductive tip; in AFM-IR, u is the photothermal expansion on the sample caused by a pulsed IR laser source incident to it. The addition of the inner-paddle gives the system an additional degree of freedom (as opposed to a single-DOF representing the fundamental mode of the conventional cantilever, as shown in Figure 5a), thus providing an additional resonant frequency which can be exploited for contact resonance enhanced functional imaging techniques. Performing a modal analysis of the ROM shown in Figure 5c, we obtain the expression for the two modal frequencies (ω1 and ω2) of the integrated system,

ω1 =

ω2 =

k1m2 + k2 m1 + k2 m2 + k s m2 − α 2m1m2

(2)

k1m2 + k2 m1 + k2 m2 + ks m2 + α 2m1m2

where, α = ( k1m2 ) 2 − 2k1k 2 m1m2 + 2k1k 2 m22 + 2k1k s m22 + ( k2 m1 ) 2 + 2k22 m1m2 + (k 2 m2 ) 2 − 2k2 k s m1m2 + 2k2 k s m22 + ( k s m2 ) 2

These modal frequencies represent the two leading natural frequencies of the experimental fixture of Figure 1a. Equation (2) serves as a convenient tool for investigating the effect of contact conditions on the modal frequencies of the system since both frequencies are functions of the tip-surface contact stiffness (ks). The variations in the modal frequencies with respect to the

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contact stiffness for an inner-paddled cantilever are shown in Figure 5d. Here, the frequencies are normalized by the first modal frequency of the free oscillation (ks=0) of each cantilever to facilitate comparison. The parameters of the inner-paddled cantilever used in the calculation of the modal frequencies are as follows: m1 = 6.28 ng, m2 = 0.05 ng, k1 = 4.94 N/m, k2 = 0.66 N/m It is important to note here that the appreciable differences in the parameters between the base cantilever and inner paddle (m1 vs. m2, k1 vs. k2) allow us to model our system with two–DOF under the assumption that the inner paddle and the base cantilever vibrate in their own fundamental bending modes and the two resonance regions of the base cantilever and the inner paddle are well separated. In fact, in our previous works60,61 we have verified the use of a similar two-DOF lumped parameter ROM for predicting the dynamical behavior of an inner-paddled cantilever system in tapping mode (or AC mode) AFM. Other previous works employing similar inner-paddles62,63 have shown that, when the dimensional parameters are of the same order, the entire inner-paddled microcantilever behaves like a unitary structure, in which case the above modeling approach would fail. A detailed discussion of the effect of dimensional parameters on the dynamics of the system can be found in the Supporting Information. Referring to Figure 5d, for lower values of ks, we note that an increase in the stiffness of the tip-surface contact results in an increase in the first modal frequency, whereas the second modal frequency appears to remain unchanged. Yet, for higher values of ks the reverse happens, with the first modal frequency remaining unchanged while the second modal frequency increases as the contact stiffness is increases. Furthermore, the first modal frequency saturates at a frequency that matches the second modal frequency when ks=0 (i.e., when there is no contact between the cantilever tip and sample surface). To summarize, one of the two contact resonance frequencies of this paddle-

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cantilever system does not appear to vary with respect to the tip-sample stiffness. This result provides theoretical support to the experimental observations of Figures 2c and 3c-d and further confirms that an invariant contact resonant frequency is attainable by the inner-paddle that is not in physical contact with the sample surface. For comparison with the inner-paddled cantilever design, the conventional cantilever with the tip in contact with the sample is modeled as shown in Figure 5a; the cantilever is modeled as a single damped harmonic oscillator (m, k, c) while the tip-sample interaction is again modeled by a spring-damper system (ks, cs). In this model, the effective stiffness of the system is simply k+ks. Hence, the fundamental frequency is calculated as ඥሺks +kሻ/m, which continuously increases with respect to the tip-sample stiffness (ks) as shown in Figure 5b. This analysis demonstrates the strong dependence of the contact resonant frequency on the local mechanical contact conditions, which aligns with the observations of Figures 2a-b and 3a-b. To better understand the dynamics involving contact resonance in both a conventional cantilever and the inner-paddled cantilever design, we also performed a linear modal analysis using commercial finite element analysis (FEA) software (ANSYS v17.2). We modeled the three-dimensional structures of the two systems based on their physical configurations as seen in the SEM. The modal analyses were performed with the cantilevers fixed at the base and simply supported by a linear spring element at the tip, representative of the tip-sample contact stiffness. In order to study the behavior of the cantilevers with respect to the contact conditions, we obtained the mode shapes of the systems and their corresponding mode frequencies while varying the stiffness of the spring element. Figure 6a shows the fundamental mode shape of a conventional cantilever for the non-contact (free oscillations, ks=0) and contact (ks=200 N/m) cases. We note that the change in the boundary condition at the tip from free end to elastically

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restrained end results in changes in the mode shape and the corresponding mode frequency. As the contact stiffness increases, the mode shape and corresponding resonant frequency continue to vary, once again demonstrating the strong dependence of the contact resonant frequency on the local mechanical contact conditions for a conventional cantilever. It is noteworthy that this change in the mode shapes and frequencies continues only until a certain critical contact stiffness, after which the cantilever will behave like a fixed-simply supported beam whose mode shapes and resonant frequencies are not affected by any further increase in the contact stiffness. However, this frequency saturates at higher values of contact stiffness, which are beyond the practical range realized experimentally. Figure 6b depicts the first and second mode shapes of the inner-paddled cantilever for the non-contact (free oscillations, ks=0) and contact (ks=200 N/m) cases. The first mode shape of the free oscillations corresponds to the base cantilever and inner paddle vibrating in-phase with nearly the same amplitudes. The second mode shape coincides with the base cantilever and inner paddle vibrating out-of-phase where only the oscillations of the inner paddle are observed while the oscillation amplitude of the base cantilever appears to be negligibly small. Initially (for smaller values of ks), the change in the boundary condition affects the first mode shape and its corresponding natural frequency, whereas the second mode shape and its frequency are not affected because the dynamic motion is localized to the inner paddle, which is not directly connected to the tip. As the contact stiffness increases, however, the second mode frequency remains unchanged while the first mode frequency gradually increases to the point where the first and second mode frequencies are nearly the same. Further increases in the contact stiffness do not affect the first mode shape and its corresponding frequency, whereas the second mode shape and its frequency are now susceptible to further changes in the contact stiffness. Note that

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the first mode frequency of our inner-paddled cantilever design saturates at a lower contact stiffness value as compared to a conventional cantilever, which is easily realizable in actual AFM operation. This observation emphasizes the superiority of our design over the conventional AFM cantilever. We note that the computational FEA results fully agree with our previous analysis based on the ROM of Figure 5, thus validating the accuracy and predictive capacity of the proposed ROM for the dynamics of the inner-paddled microcantilever in the considered frequency range. Furthermore, the analytically and numerically obtained results were validated by the experimental results depicted in Figure 7. In Figures 7b-c, the frequency is normalized by the first mode frequency of the free response to facilitate comparison with the analytical result of Figure 7a. Figure 7b shows the frequency spectrum of a fabricated paddled cantilever obtained by measuring the thermomechanical vibration when the tip is not in contact with the surface. The two dominant peaks observed at frequencies 135 kHz (f1,nc at normalized frequency 1) and 548 kHz (f2,nc at normalized frequency ~ 4) correspond to the first and second modal frequencies, respectively, when ks =0. In Figure 7c, the frequency response of the paddled cantilever was obtained while the tip of this cantilever was in contact with a surface. We note that the first peak (f1,c) observed in Figure 7c, located at 548 kHz (normalized frequency ~ 4), matches the second modal frequency of the free response (f2,nc) in Figure 7b. Therefore, the experimental results show good agreement with the theoretical predictions shown in Figure 7a, when comparing the non-contact resonance of Figure 7b for the case of ks =0 in Figure7a, and the contact resonance of Figure 7c for the case of ks ≈240 N/m in Figure 7a. These experimental results provide a final conclusive validation of the proposed concept based on the inner-paddled microcantilever. CONCLUSIONS

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Herein, we have proposed an inner-paddled cantilever design to eliminate the coupling between the functional response and topographic effects in C-AFM without the need for additional signal or data processing while utilizing resonance. These characteristics make this a convenient and promising approach for imaging highly heterogeneous materials that display weak functional properties such as biological tissues, where investigations are challenging due to strong frequency variations caused by the heterogeneity of the sample surface. The efficacy of our design was demonstrated through PFM imaging of PPLN where the results yielded greatly reduced crosstalk as compared to single frequency PFM and DFRT-PFM measurements obtained using a conventional cantilever. Then, PFM imaging of collagen fibrils using a commercial cantilever showed strong variations in the resonant frequency at the topographic changes, whereas the proposed design showed no variation in the resonant frequency, illustrating effective decoupling of the material response and topographic effects. Furthermore, we demonstrated the potential of our design to provide quantitative measurements in functional AFM, which can ultimately enable numerous studies that have previously been impractical or challenging.

METHODS Device Fabrication A Point Probe Force Modulation (PPFM) cantilever from NanoWorld was selected as the base cantilever for the inner-paddled cantilever design. A rectangular cavity was carved out with a Focused Ion Beam (FIB) based machining process, followed by assembling a 300nm thick silicon membrane on the base cantilever using transfer printing-based microassembly, i.e., micro-LEGO.64,65 After a silicon membrane was transfer printed over the cavity, an annealing

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process was carried out in a furnace at 500 0C for 15 min. Subsequent cooling to room temperature slowly over ~ 1 hr resulted in a strong bond, thus forming the assembled cantilever. After assembly, the inner paddle was carved out of the silicon membrane with a FIB. For PFM measurements, the tip-side of the cantilever and inner paddle were coated with a 5 nm thick layer of gold in a sputter-coater system to provide sufficient conductance. A schematic diagram of the cantilever fabrication process is provided in the Supporting Information (see Figure S7). Sample Preparation 1. PPLN. The PPLN sample was mounted on a 15mm AFM specimen steel disk using conductive silver paint, which served as a suitable ground path with respect to the conductive cantilever tip. 2. Collagen. In this study, Type I collagen was prepared from bovine Achilles tendon (SigmaAldrich, SLBG4268V). About 50mg of the extract was mixed with 100 mL of 0.01 M sulfuric acid and swollen overnight below 4 0C. The resulting solution was then shredded by a blender for about 10 min at below 4 0C. The desired dilution was made by adding the appropriate amount of phosphate buffered saline (PBS, PH 7.4). Collagen fibrils were collected on the surface of a charged microscope glass slide (Globe Scientific, 1358Y) by dipping it into the final solution. Finally, the surface of the slide was rinsed several times with deionized water to wash away any contaminants and allowed to dry at room temperature.39,40 Piezoresponse Force Microscopy (PFM) All measurements were performed in a commercial AFM system (MFP-3D Infinity by Asylum Research) in an ambient environment at room temperature. During PFM operation, a sinusoidal (AC) voltage, with frequency corresponding to the first contact resonance mode, was applied to

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the tip (through the fixed end of the base cantilever) as it scanned the sample in contact mode. The amplitude of the applied AC voltage is indicated in the caption of each figure in the Results and Discussion section.

ACKNOWLEDGEMENTS This work was supported in part by National Science Foundation Grants CMMI-1619801 at The Ohio State University and CMMI-1463558 at the University of Illinois at Urbana-Champaign. This support is gratefully acknowledged. We also acknowledge the Ohio Supercomputing Center for providing computational resources.

Supporting Information Available: Comparison of PFM scanning results of a contaminated PPLN sample obtained by a commercial cantilever and the proposed inner-paddled cantilever design; PFM imaging of collagen obtained by a commercial cantilever and the proposed innerpaddled cantilever design; a parametric study of the inner-paddled cantilever design; schematic diagram showing the fabrication process for the inner-paddled cantilever. This material is available free of charge via the Internet at http://pubs.acs.org.

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FIGURE CAPTIONS Figure 1: The Inner-paddled Cantilever. (a) A scanning electron microscope image of the proposed inner-paddled cantilever. The system consists of a base cantilever and a thinner inner paddle, allowing two discrete pathways to respond independently to the variations in surface topography and material functionality. The paddle is free to oscillate over the middle cavity during AFM operation, making it possible to separate local contact stiffness variations from the functional response of the sample. (b) Experimental schematic showing the inner-paddled cantilever in PFM operation. Figure 2: PFM imaging of periodically poled Lithium Niobate (PPLN). Deflection, PFM amplitude and phase images of PPLN and the corresponding line scans along the white dashed lines indicated on each image, for a commercial AFM cantilever in (a) single frequency PFM, (b) DFRT-PFM, and (c) for an inner-paddled cantilever design in single frequency PFM. The green arrows in (a) and (b) indicate where crosstalk between topography and PFM response is observed. In comparison, no crosstalk is observed in (c). Corresponding histograms of the response within the PPLN domain are shown in the bottom row. The histograms of (a) and (b) show wider distributions of the measured data (σa, σp) and greater disagreements between the trace and retrace data (∆a, ∆p), illustrating the contrast variations due to crosstalk. (a)-(b) were obtained using a MikroMasch NSC18/Pt cantilever at 3.5V. PFM images in (c) were obtained at 5V. Figure 3: PFM imaging of collagen. Deflection, PFM amplitude, PFM phase images of collagen and the frequency response curves on regions indicated by the markers on the deflection image for (a)-(b) a commercial AFM cantilever (MikroMasch XSC11/Pt, cantilever A) in single frequency PFM, (c)-(d) an inner-paddled cantilever in single frequency PFM. Strong variations in the contact resonant frequency of the commercial cantilever results in incorrect interpretations of the samples properties as seen in (a). The yellow arrows in (a) indicate a change in contrast in the PFM amplitude and phase images caused by a sudden change in the contact resonant frequency. Results in (c) are more consistent with expectations for this sample, owed to the invariant contact resonant frequency attainable by the inner-paddled cantilever as shown in (d). The inset of (d) illustrates the difference in the amplitudes of the frequency response curves obtained over the regions marked A, B and C in (c). This difference in the amplitudes is an indication of the piezoelectric strain of collagen. The images were obtained at Vac ≈ 4V. Figure 4: Comparison between the resonance curves of a commercial cantilever and the proposed inner-paddled cantilever. (top) Contact resonance curves measured on Lithium Niobate using (a) a commercial probe of stiffness k=0.2 N/m, (b) a commercial probe of stiffness k=2.7 N/m and (c) an inner-paddled cantilever system. The gray vertical solid line indicates the frequency at which the response amplitudes shown in the bottom row were measured. (bottom) Piezoresponse amplitudes with respect to the drive AC amplitude. The blue curve indicates the piezoresponse amplitude at a fixed drive frequency, while the red curve indicates the peak amplitude. The measured responses show nonlinear curves with respect to excitation strength for (a) and (b) demonstrating the difficulty in quantitative calibrations for a conventional cantilever. In comparison, the linearity observed by the stable contact resonance for the inner-paddled cantilever can enhance the reliability and accuracy of quantitative measurements of PFM.

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Figure 5: Comparison of the dynamical behavior in C-AFM between a commercial AFM cantilever and the proposed inner-paddled cantilever. The analytical model with lumped parameters shows that the inner-paddled cantilever system provides an invariant contact resonance frequency with respect to the variation of tip-sample stiffness while a conventional cantilever’s contact resonance frequency is continuously varied by the tip-sample stiffness. (a) the representative lumped parameter model of a conventional AFM cantilever in the form of a single damped harmonic oscillator, (b) variations of the system’s fundamental mode frequency with respect to the tip-sample contact stiffness for three different cantilever stiffness’s, (c) the representative two-degree-of-freedom reduced order model of the inner paddle-base cantilever system, and (d) variations of the first and second mode frequencies of the system with respect to the tip-sample contact stiffness. Figure 6: Investigation of the dynamic behavior using finite element analysis (FEA). FEA simulations of the mode shapes of a conventional cantilever (a) and inner-paddled cantilever system (b) for non-contact and contact cases. Variations in each system’s modal frequencies with respect to the tip-sample contact stiffness (ks) as predicted by the FEA simulations is shown to the right. The FEA results fully agree with that of the reduced order model and provide further insight into the dynamical behavior of the two systems. Figure 7: Experimental verification of the model. (a) Variations of the analytically obtained modal frequencies of the reduced order model of Figure 5c with respect to the tip-sample contact stiffness (ks), (b) the frequency spectrum of an inner-paddled cantilever system obtained experimentally by measuring the thermomechanical vibration when the tip was not in contact with the surface, corresponding to the region highlighted in gray in Figure 7(a) (i.e., ks=0), and (c) the frequency response of the same inner-paddled cantilever system when the cantilever tip was in contact with a surface, corresponding to the region highlighted in green in Figure 7(a) (i.e., ks ≈ 220 N/m). The experimental results agree with the theoretical prediction and provide a final conclusive validation of the proposed design.

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36x16mm (300 x 300 DPI)


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ACS Nano

108x65mm (300 x 300 DPI)


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

76x33mm (300 x 300 DPI)


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ACS Nano

108x65mm (300 x 300 DPI)


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

73x65mm (300 x 300 DPI)


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ACS Nano

119x94mm (300 x 300 DPI)


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

52x15mm (300 x 300 DPI)


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ACS Nano

Table of contents graphic 49x28mm (300 x 300 DPI)


Ultimate Decoupling between Surface Topography and Material

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