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Imaging Nanoscopic Elasticity of Thin Film Materials by Atomic Force Microscopy: Effects of Force Modulation Frequency and Amplitude J. S. Jourdan,† S. J. Cruchon-Dupeyrat,† Y. Huan,† P. K. Kuo,*,‡ and G. Y. Liu*,† Departments of Chemistry and Physics, Wayne State University, Detroit, Michigan 48202-3489 Received February 24, 1999. In Final Form: May 18, 1999 Octadecyltriethoxysilane (OTE) monolayers on mica are imaged using force modulation microscopy (FMM) and dynamic force modulation (DFM). Nanoscopic areas of mica are produced within OTE layers and serve as an internal standard for contact stiffness measurements. The contact stiffness is systematically studied as a function of imaging medium and force modulation amplitude and frequency. Measurements taken in liquid media are found to reflect more accurately the viscoelastic properties of the sample, while imaging in air is perturbed by the capillary neck at contact. Increasing modulation amplitude increases the overall signal in FMM. However, extremely large amplitudes diminish the contrast difference between OTE and mica because the sensing depth is much higher than the monolayer. The measured contact stiffness is found to depend sensitively upon the modulation frequency because of the presence of several resonances within 10-50 kHz, which cause the image contrast to vary or to flip. Collective motion of the molecules under contact is most likely responsible for these resonances. The observed amplitude and frequency dependence also allows active control of FMM image contrast.
Background and Introduction Atomic force microscopy (AFM) has been widely used in the areas of material science and biophysics because of its high spatial resolution, simplicity in operation, and the ability to image a wide range of materials under various conditions.1-4 More importantly, AFM has the potential to image the mechanical properties of these materials on a nanometer scale.3,4 Using a deflection-type configuration, researchers are able to acquire topographic and friction images simultaneously.5,8,9 In addition, a broader application of AFM has been reported, such as imaging friction, polarization, and elastic compliance.5,10,11,12 The investigation presented here focuses on measurements of nanoelasticity or contact stiffness using a force modulation technique. Contact stiffness (κ) is defined as the amount of force or load (L) per unit displacement required to compress an elastic contact along a particular direction.10 Therefore, the contact stiffness along the surface normal (or Z) direction can be calculated using eq 1, in which κ has the
κ ) dL/dZ
(1)
unit of N/m or (nN/nm) and can be understood as the “force constant” of the contact. Correlating κ with the material’s properties such as Young’s modulus requires complete characterization of the tip-surface contact. The † ‡
Department of Chemistry. Department of Physics.
(1) Sarid, D. Scanning Force Microscopy, with Applications to Electric, Magnetic and Atomic Forces; Oxford University Press, New York, 1991. (2) Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Rev. Lett. 1986, 56, 930. (3) Frommer, J. J. Angew. Chem., Int. Ltd. Engl. 1992, 31, 1298. (4) Quate, C. F. Surf. Sci. 1994, 299/300, 980. (5) Carpick, R. W.; Salmeron, M. Chem. Rev. 1997, 97, 1163. (6) Handbook of micro/nanotribology; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995. (7) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607. (8) Ruan, J. A.; Bhushan, B. J. Tribol. Trans. ASME 1994, 116, 378. (9) Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1988, 53, 2400.
simplest approach is to treat the tip-surface region as an elastic sphere-plane contact as shown in Figure 1. In the static limit, the Hertzian model may be applied,10,11
κ = 2aE*
(2)
where
E* )
[
]
(1 - ν1)2 (1 - ν2)2 + E1 E2
-1
(3)
E1 and E2 are the Young moduli of the sphere and plane, respectively, and ν1 and ν2 are the corresponding Poisson ratios. The contact radius, a, may be estimated by
a ) (3RL/4E*)1/3
(4)
From the force-distance curves, one can extract the contact stiffness κ and Young modulus of the material (E2) at the contact using the contact mechanics described above. To measure local Young moduli of materials using this approach, a force curve must be taken at every point during the scan. A more time-efficient method to map out or image the nanoscopic elasticity is the use of force modulation microscopy (FMM).12-15 During force modulation, the surface under the AFM tip is oscillated at a desired frequency and amplitude (f and ∆Z). When the surface is (10) (a) Carpick, R. W.; Ogletree, D. F.; Salmeron, M. Appl. Phys. Lett. 1997, 70, 1548. (b) Hu, J.; Xiao, X. D.; Salmeron, M. Appl. Phys. Lett. 1995, 67, 476. (11) Bar, G.; Rubin, S.; Parikh, A. N.; Swanson, B. I.; Zawodzinski, T. A.; Whangbo, M. H. Langmuir 1997, 13, 320. (12) Overney, R. M.; Meyer, E.; Frommer, J.; Gu¨ntherodt, H. J.; Fujihira, M.; Takano, H.; Gotoh, Y. Langmuir 1994, 10, 1281. (13) Maivald, P.; Butt, H. J.; Gould, S. A. C.; Prater, C. B.; Drake, B.; Gurley, J. A.; Elinis, V. B.; Hansma, P. K. Nanotechnology 1991, 2, 103. (14) DeVecchio, D.; Bhushan, B. Rev. Sci. Instrum. 1997, 68, 4498. (15) Radmacher, M.; Tillmann, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900.
10.1021/la9902183 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/13/1999
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Figure 1. Sphere-plane model describing the AFM tip-surface contact during contact mode imaging. The radii of the tip and contact are R and a, respectively, with the maximum deformation of the surface at the contact being δ. In the Hertzian model, such contact may be approximately treated as two springs in series, and the spring constants are κlever and κ or κcontact. During force modulation, the sinusoidal driving function (f and ∆Z) transfers energy, through the elastic (middle) or viscoelastic (right) motion of the contact, to the AFM cantilever.
in contact with the AFM tip, energy transfer causes the cantilever to modulate, mainly at the same frequency. The magnitude and phase of the cantilever oscillation depends on the viscoelastic properties of the contact.12-15 Ideally, if the contact is rigid and the surface is hard, the cantilever will oscillate with the same amplitude and phase as the sample. Contact with softer materials will cause the cantilever to oscillate at reduced amplitude and a different phase.12-15 Thus, the elasticity of the material may be extracted from the amplitude and phase images. In practice, many materials, especially organic or polymeric films, exhibit viscoelastic behavior.11,12 A theoretical treatment of the linear viscoelastic interaction has also been reported, in which the viscoelastic function of the sample, b‚E*(f), can also be extracted from the corresponding amplitude and phase images.16,17 In this case, the Young modulus E* is a complex number and exhibits a frequency dependence.16,17 A quantitative or even semiquantitative theory describing the contact mechanics is still lacking due to the complexity of local interactions at the contact, such as the presence of adhesion, capillary interaction,6,18-22 inertia, and resonances.23,27 The present work provides a more systematic study of the above interactions, in the hope of facilitating an understanding of the FMM and local viscoelastic properties of the materials. (16) Radmacker, M.; Tillmann, R. W.; Gaub, H. E. Biophys. J. 1993, 64, 735. (17) Stroup, E. W.; Pungor, A.; Radmacher, M.; Hlady, V.; Andrade, J. D. Polym. Prepr. 1995, 36, 125. (18) Thundat, T.; Zheng, X.-Y.; Chen, G. Y. ; Warmack, R. J. Surf. Sci. Lett. 1993, 294, L939. (19) Binggeli, M.; Mate, C. M. J. Vac. Sci. Technol., B 1995, 13, 1312. (20) Luna, M.; Colchero, J.; Baro, A. M. Appl. Phys. Lett. 1998, 72, 3461. (21) Colchero, J.; Storch, A.; Luna, M.; Gomez Herrero, J.; Baro, A. M. Langmuir 1998, 14, 2230. (22) Israelachvili, J. Intermolecular and surface forces; Academic Press: San Diego, CA, 1992. (23) Attard, P.; Schulz, J. C.; Rutland, M. W. Rev. Sci. Instrum. 1998, 69, 3852. (24) Rabe, U.; Scherer, V.; Hirsekorn, S.; Arnold, W. J. Vac. Sci. Technol. B 1997 15, 1506. (25) Burnham, N. A.; Gremaud, G.; Kulik, A. J.; Gallo, P.-J.; Oulevey, F. J. Vac. Sci. Technol. B 1996, 14, 1308. (26) Chen, G. Y.; Warmack, R. J.; Oden, P. I.; Thundat, T. J. Vac. Sci. Technol. B 1996, 14, 1313. (27) Anczykowski, B.; Kruger, D.; Babcock, K. L.; Fuchs, H. Ultramicroscopy 1996, 66, 251.
Although not discussed explicitly in previous studies, one important side product of FMM is that the amplitude and phase images provide a new contrast mechanism for the AFM imaging process. In some cases, the amplitude and phase images are more sensitive than topography and friction in resolving microscopic features.11,12,16 Successful examples include the contrast enhancement of hard sites in fully hydrated calcified tissues,28 correlation of microstructure with physical properties of polymers,29-35 and revealing viscoelastic behavior of organic thin films,36,37 proteins,38,39 and living cells.40-42 Instead of using a trialand-error method, this work provides a systematic investigation of FMM image contrast. The study provides an effective guide to selectively enhance the image contrast of desired surface features. We have investigated (i) the influence of imaging medium on FMM image contrast, (ii) the effects of force modulation frequency and amplitude on measured contact stiffness, and (iii) the effect of force modulation frequency and amplitude on FMM image contrast. (28) Kinney, J. H.; Balooch, M.; Marshall, S. J.; Marshall, G. W.; Weihs, T. P. J. Biomech. Eng. Trans. ASME 1996, 118, 133. (29) Domke, J.; Radmacher, M. Langmuir 1998, 14, 3320. (30) Overney, R. M.; Leta, D. P.; Pictroski, C. F.; Rafailovich, M. H.; Liu, Y.; Quinn, J.; Sokolov, J.; Eisenberg, A.; Overney, G. Phys. Rev. Lett. 1996, 76, 1272. (31) Nie, H. Y.; Motomatsu, M.; Mizutani, W.; Tokumoto, H. Thin Solid Films 1996, 273, 143. (32) Akari, S. O.; van der Vegte, E. W.; Grim, P. C. M.; Belder, G. F.; Koutsos, V.; ten Brinke, G.; Hadziioannou, G. Appl. Phys. Lett. 1994, 65, 1915. (33) Friedenberg, M. C.; Mate, C. M. Langmuir 1996, 12, 6138. (34) Galuska, A. A.; Poulter, R. R.; McElrath, K. O. Surf. Interf. Anal. 1997, 25, 418. (35) Chizhik, S. A.; Huang, Z.; Gorbunov, V. V.; Myshkin, N. K.; Tsukruk, V. V. Langmuir 1998, 14, 2606. (36) Overney, R. M.; Bonner, T.; Meyer, E.; Reutschi, M.; Luthi, R.; Howald, L.; Frommer, J.; Guntherodt, H. J.; Fujihira, M; Takano, H. J. Vac. Sci. Technol B. 1994, 12, 1973. (37) Salmeron, M.; Neubauer, G.; Folch, A.; Tomitori, M.; Ogletree, D. F.; Sautet, P. Langmuir 1993, 9, 3600. (38) Yamada, H.; Hirata, Y.; Miyake, J. J. Vac. Sci. Technol. A 1995, 13, 1742. (39) Radmacher, M.; Fritz, M.; Cleveland, J. P.; Walters, D. A.; Hansma, P. K. Langmuir 1994, 10, 3809. (40) Radmacher, M.; Tillman, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900. (41) Fritz, M.; Radmacher, M.; Petersen, N.; Gaub, H. E. J. Vac. Sci. Technol. B 1994, 12, 1526. (42) Radmacher, M.; Fritz, M.; Kacher, C. M.; Cleveland, J. P.; Hansma, P. K. Biophys. J. 1996, 70, 556.
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Experimental Section (1) Preparation of Octadecyltriethoxysilane Monolayers. The system used is a well-characterized self-assembled monolayer, octadecyltriethoxysilane on mica (OTE/mica). OTE/ mica was prepared following a procedure reported previously.43 A hydrolysis solution was made by adding 0.210 g of OTE (Gelest Inc., Tullytown, PA) and 0.1 mL of 1.31 N HCl to 25 mL of tetrahydrofuran (THF). After 48 h of stirring, an additional 20fold dilution was made with cyclohexane and transferred to a clean glass jar containing freshly cleaved muscovite mica pieces (MICA New York Corp., New York). After 30-60 min of immersion at room temperature, the mica pieces were removed, rinsed with fresh cyclohexane, and baked 2-3 h at 120 °C. (2) AFM and Nanoelasticity Measurements. The atomic force microscope utilizes a home-constructed deflection-type scanning head with a commercial electronic controller (RHK Technology, Troy, MI).44,45 Sharpened Si3N4 microcantilevers with a force constant of 0.1 N/m (Park Scientific Instruments, Sunnyvale, CA) were used for this study. A laser is focused on the back of the cantilever and deflected to a four-segment photosensitive detector, which can monitor the vertical deflection and lateral twisting of the cantilever as the tip scans across the surface. The tip radii are determined by imaging crystalline steps with known height, such as Au(111) steps (single atomic step height ) 2.4 Å). Prior to nanoelasticity measurements, OTE monolayers were characterized using AFM at a typical load of 5 nN in air or 1 nN in liquid. The OTE monolayers typically consist of domains separated by boundaries.43,46 Within each domain, molecules form a nearly close-packed structure without long-range order or periodicity.43,46,47 It is known that the headgroups are cross-linked into a Si-O network, and the chains tilt ∼ 15° from the surface normal.43,47 After a desired location was chosen, the imaging force was gradually increased while scanning an area of 100 × 100 Å2. As the load increased beyond 50 nN in air, or 10 nN in liquid, the image changed from a disordered OTE feature to an ordered mica surface. Once the threshold force was known, a desired area of OTE was displaced to expose a fresh mica surface.47-51 By fabricating a nanoscopic mica area inlaid in the OTE, we could measure the local elasticity of both OTE and mica sideby-side under the same imaging conditions and using the same AFM tip. Mica could then be used as an internal standard for FMM measurements. (2.1) Force Modulation Microscopy. The setup for imaging surface topography and elastic compliance has been reported previously.12,16,51 Basically, the sample is modulated in the Z-direction with a sinusoidal wave function of frequencies f and amplitude ∆Z. The modulation signal is normally set at frequencies (>10 kHz) above the response of the feedback circuit (a few kilohertz) to minimize the coupling with the electronics. The cantilever follows the sinusoidal motion when the tip is in contact with the surface. The amplitude and phase response of the cantilever is amplified by a lock-in amplifier and then recorded as a function of tip position. The viscoelastic properties of the materials at contact manifest into image contrast.12-17,51 One example of FMM imaging is shown in Figure 2. (43) Peanasky, J.; Schneider, H. M.; Granick, S.; Kessel, C. R. Langmuir 1995, 11, 953. (44) Xu, S.; Cruchon-Dupeyrat, S. J.-N.; Garno, J. C.; Liu, G.-Y.; Jennings, G. K.; Yong, T. H.; Laibinis, P. E. J. Chem. Phys. 1998, 108, 5002. (45) Liu, G.-Y.; Xu, S.; Cruchon-Dupeyrat, S. In Thin Film: SelfAssembled Monolayers of Thiols; Ulman, A., Ed.; Academic Press: New York, 1998; Vol. 24, pp 81-110. (46) Schwartz, D. K.; Steinberg, S.; Israelchvili, J.; Zasadzinski, J. A. Phys. Rev. Lett. 1992, 69, 3354. (47) Xiao, X. D.; Liu, G.-Y.; Charych, D. H.; Salmeron, M. Langmuir 1995, 11, 1660. (48) Fujii, M.; Sugisawa, S.; Fukada, K.; Kate, T.; Seimiya, T. Langmuir 1995, 11, 405. (49) Nakagama, T.; Ogawa, K.; Kurumizawa, T. Langmuir 1994, 10, 525. (50) Bierbaum, K; Grunze, M.; Baski, A. A.; Chi, L.F.; Schrepp, W.; Fuchs, H. Lamgmuir 1995, 11, 2143. (51) Kiridena, W.; Jain, V.; Kuo, P.; Liu, G.Y. Surf. Interface Anal. 1997, 25, 383.
Figure 2. Comparison of FMM and DFM images for an OTE/ mica surface in air. The total scan area in the FMM image is 3000 × 3000 Å2. The central square is a 1000 × 1000 Å2 mica area fabricated by the AFM tip under a 50 nN load. The DFM image was generated by scanning a single line, 3000 Å × 0 Å indicated in the FMM image. Therefore, the topographic image shows a dark 1000 Å band in DFM. The sharp straight edge indicates the thermal stability of the AFM. A typical scan rate is 200 ms/line with 256 lines per frame. The modulation amplitude (∆Z) here is the peak to peak value. The average value is 1/x2 of the indicated value. (2.2) Force Modulation Spectroscopy. Systematically investigating the influence of the modulation frequency and amplitude requires the collection and analysis of numerous images oneby-one if the force modulation technique is used. Such study is time-consuming if one needs to investigate the frequency or amplitude dependence in detail. A new imaging configuration, dynamic force modulation (DFM) was developed to acquire the frequency or amplitude dependence of a surface in a single image. In other words, each image represents a force modulation spectrum. This procedure is used in conjunction with FMM to map out contact stiffness and its frequency and amplitude dependence. The setup for DFM is illustrated in Figure 3, and a typical DFM image is compared to a FMM image in Figure 2. In the FMM images shown in Figure 2, topographic, amplitude, and phase images are acquired over an area of 3000 × 3000 Å2 at a single frequency and modulation amplitude. In contrast, DFM images are acquired by scanning a single line along the X-direction repeatedly while keeping the Y-scanning piezo voltage constant. Thus, the sample stage scans back and forth only in the X-direction. As illustrated in Figure 3, a function generator supplies a sinusoidal wave function to the sample stage. The frequency or amplitude varies with desired increment. In Figure 2, the frequency increases from the top to the bottom line by 0.05 kHz/line. Therefore, the X-axis represents the true X-position of the surface. The same line is displayed along the Y-axis with increasing frequency or amplitude. In the topographic image, the same X-scan is displayed 256 times along the Y-axis, resulting in a stripe like image. A cursor profile along the Y-direction in the amplitude and phase images depicts the contact stiffness at that chosen contact as a function of the frequency or amplitude.
Results and Discussion (1) Frequency Spectra. Prior to FMM and DFM measurements, frequency spectra of the cantilever are acquired to reveal the active vibrations of the system. The natural vibration of a cantilever can be measured by taking fast Fourier transform frequency spectra while the cantilever is far away, typically 50 Å above the surface. Figure 4 shows that a 0.1 N/m microsharpened cantilever (Park Scientific Instrument) exhibits a natural resonance frequency, f0, of 28 or 22 kHz when measured in air or in a 2-butanol solution, respectively. In air, f0 corresponds well with the resonance frequency provided by the cantilever manufacturers. In liquid media, the effective
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Figure 3. Schematic diagram of dynamic force modulation. A modulation signal is supplied by a DS345 function generator (SRS) to the sample stage. The increase of f (or ∆Z) is synchronized with the AFM data acquisition scan. Amplitude (A) and phase (θ) response of the cantilever deflection is amplified by an SR830 lock-in amplifier (SRS) and displayed with the corresponding topographic (Z) image. For amplitude sweeps, the DS345 is revised such that the signal output is connected only to the Z-modulation input of the STM100, and sync output is connected to the ref input of the SR830.
Figure 4. Frequency spectra of AFM cantilevers in air (left) and in 2-butanol (right). When the tip is in contact with the surface, the loads are maintained at 5 and 2 nN respectively under ambient and liquid environments. The background shown in these spectra is mainly due to the 1/f component.
mass (m*) of the cantilever is increased due to the damping by the surrounding fluid, causing f0 to shift downward
f0 )
(2π1 )xk/m*
More resonances appear when the tip is in contact with the surface, as shown in Figure 4. Each spectrum contains
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Figure 5. Topographic (Z), amplitude (A), and phase (θ) images of an OTE monolayer on mica taken under ambient conditions. The total scan area is 5000 × 5000 Å2 with the central 1500 × 1000 Å2 region being mica. Six frequencies shown here were chosen from FMM images systematically acquired at 1 kHz intervals between 10 and 50 kHz. The driving modulation amplitude is 90 Å.
the following: (i) 1/f background; (ii) peaks whose frequencies depend sensitively on the contact situation; and (iii) peaks whose frequencies are independent of the tipsurface contact, which are mainly due to the intrinsic vibrations of the scanning head assembly. In air, contact with mica and OTE regions results in an upshift of f0 ) 41 and 37 kHz, respectively. After the initial contact, this resonance shifts down with increasing load. Thus, this mode consists primarily of the cantilever vibration, which is very sensitive to the “external” or contact force field. In contrast, extra resonance peaks appearing in the 2-17 kHz region have a weak load dependence. Their location and intensity remain unchanged once an experiment is set up. It is very likely that these motions arise from the sample stage and/or piezo assembly, which are sensed by the cantilever upon contact. Liquid media damp the natural resonance of the cantilever, as shown in Figure 4. Weak resonances are still visible and remain unchanged with increased load. This observation is not surprising because the load in liquid is small due to the lack of capillary forces. Regardless of the imaging medium, modulation frequencies used during FMM experiments are normally set higher than 10 kHz to avoid coupling with the feedback circuit. (2) Influence of Environment on FMM Imaging. The topography (Z), amplitude (A), and phase (θ) images of OTE monolayers were first taken under ambient laboratory conditions: 1 atm, room temperature, and without humidity regulation. Images were acquired from 10 to 50 kHz, at 1 kHz intervals. Six representative frequencies are shown in Figure 5. Images b, c, and f were
Nanoscopic Elasticity of Thin Film Materials
chosen to represent typical images in FMM measurements taken in air.51 In the amplitude images, the mica region appears to be softer (dark regions represent smaller amplitude response) than OTE. Only at certain frequencies such as 12, 34, and 42 kHz, does mica appear to be harder. The above observations seem to conflict with the common knowledge of the mechanical properties of the materials. First, the mica region is darker in amplitude images than OTE, which appears to be inconsistent with the known Young moduli for mica (130 GPa) and OTE (300 Å). The trend is nonlinear and the rate of decay depends on the tip sharpness, modulation frequency, and humidity. Dull tips and high humidity result in slower decay. In 2-butanol and with R ∼ 125 Å, the measured relative stiffness reaches its maximum value at ∼8 Å and decays with increasing ∆Z. The contrast almost diminishes at ∼40 Å, as shown in Figure 11. The decay is nonlinear. The rate of decay is independent of the frequency and depends only on the sharpness of the tip and likely on the packing of OTE molecules at the contact. The amplitude dependence can be understood from the tip-surface contact situation. Surface molecules at contact undergo deformation under the load applied by the AFM tip. During force modulation, the contact area and molecular deformations vary. Increasing ∆Z results in larger contact area (larger a), deeper deformation (δ), and thus increasing sensing depth. At sufficiently high ∆Z, the measured stiffness reflects mostly the bulk of the substrate; therefore the elasticity difference Amica - AOTE between mica and OTE regions diminishes. In air, the tip-surface contact is preserved over a large range of ∆Z due to the water meniscus between the tip and surface. Thus, long tails are observed in the Amica - AOTE versus ∆Z plots in Figure 11. In summary, stronger signals and better signal-to-noise ratio in FMM are observed with increasing force modulation amplitude ∆Z. Increasing ∆Z results in larger contact area and Z-deformation, and thus higher sensing depth. Sharp tips reduce contact area and produce high resolution in FMM images. For OTE monolayers or other thin film systems, the optimal contrast is observed at intermediate ∆Z determined from the Alayer - Asubstrate versus ∆Z curves. (4) Influence of Force Modulation Frequency and Amplitude on Image Contrast. In contact mode AFM imaging, the feedback electronics move the sample up and down during the scan to maintain the constant bending of the cantilever. As shown in Figure 1, the surface of the sample undergoes a deformation δ, and the deformation force δ‚k has the same magnitude as the load applied by the cantilever. In air, the load is the sum of the force due to cantilever bending and the capillary force. Therefore, for homogeneous materials or samples that are much harder than the cantilever (small δ), the AFM images reflect the true surface topography. For other materials, AFM tips follow the contour of the surface morphology and are also influenced by the local capillary interaction and spring constant. In liquid media such as 2-butanol, the load is solely due to the cantilever bending, and equal to δ‚k. AFM images reflect the surface topography and are influenced by local elasticity (δ‚k). Thus, true surface structure and higher resolution are obtained at low loads (smaller δ‚k). During force modulation, e.g. in FMM or DFM, the local deformation (δ) and the cantilever deflection vary. Since our modulation is sufficiently fast (>10 kHz), the feedback circuit is not able to follow the oscillation. Topographic images depend only on the average load, and therefore are the same as the AFM images without modulation. The amplitude and phase images, however, depend on the modulation conditions (f and ∆Z) and reflect the local viscoelasticity of the materials. The amplitude and phase signals reflect efficiency of the energy transfer from the sample to the tip. The systematic studies discussed in section 3 have revealed that the contact stiffness is influenced by intrinsic factors such as structure, functionality, and packing of the molecules at contact. In addition, the amplitude and phase image contrast also depends on
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Figure 11. Amplitude spectra measured using DFM. In air (left), DFM is acquired at 17 kHz, an off-resonance frequency, and 15 and 40 kHz, which are superpositioned with the resonance. In 2-butanol (right), DFM is taken at 16, 19, and 40 kHz, respectively. The relative stiffness is extracted from the amplitude images in DFM (Amica - AOTE) and is normalized. At ∆Z smaller than 10 Å, the signal of DFM images is weak and noisy. Increasing ∆Z enhances the overall DFM signal. The relative stiffness reaches maximum at ∼20 Å and decays with the increasing ∆Z. The tip radii are 425 and 125 Å for the measurements taken in air and in 2-butanol, respectively.
Figure 12. Example of OTE detachment that occurred during FMM measurement. At f ) 25.0 kHz, a nonresonance frequency, detachment is observed at ∆Z ) 360 Å or higher. The total scan area is 3000 × 3000 Å2.
external factors such as f and ∆Z. In other words, one can control the FMM image contrast by selecting proper modulation conditions.51 For instance, the sensing depth may be controlled by changing ∆Z. Larger ∆Z enables an AFM tip to sense deeper into the material. For thin film materials such as OTE/mica shown in Figures 9, 10, and 12 the sharpest contrast is obtained when ∆Z is approximately 0.5-2 times the thickness of the film. The frequency of the force modulation has more profound effects on the FMM image contrast. Certain driving frequencies correspond to the intrinsic oscillations of the contact, i.e., resonances occur, at which energy transfer from the driving signal to the contact is most efficient. Since the resonance feature depends sensitively upon the tip-contact situation, DFM measurements are recommended to map out the frequency spectrum for each experiment as illustrated in Figures 7 and 8. From the DFM spectra, one can choose the frequency (or frequencies) to selectively enhance the contrast in FMM images for a specific surface component or a specific local surface structure. Under ambient conditions for instance, mica contrast is selectively enhanced at f ) 34 and 42 kHz (Figure 5) to surpass the amplitude of OTE. OTE contrast is clearest at 16 kHz. In FMM images taken in 2-butanol,
the image resolution and contrast also depend sensitively on the modulation frequency. In Figures 6 and 8, mica contrast is most strongly enhanced at 17, 36, 41, and 45 kHz, whereas OTE contact exhibits a resonance at 45 kHz. Domain boundaries exhibit sharpest contrast at 36 kHz. Depending upon the requirement of each experiment, one can use FMM to selectively map out the specific surface features such as mica at 41 kHz, or OTE at 45 kHz, or domain boundaries at 36 kHz. (5) Detachment of OTE during Elasticity Imaging. Although self-assembled monolayers are mechanically robust, OTE molecules can be displaced under high loads.47,51 We have also observed displacement, or detachment during FMM measurements. Conditions that facilitate detachment during force modulation include sharp tips, high ∆Z, or at OTE resonance frequencies. The location and quantity of the detachment can be seen from topographic and amplitude images. Figure 12 shows an example where damage occurs during FMM. The tip radius is ∼180 Å and the driving frequency is 25 kHz, which is not superpositioned with any resonance frequencies. The OTE monolayer is stable with modulation amplitudes smaller than 350 Å. However, when the modulation amplitude reaches 360 Å, OTE domains around the bottom of a 100 × 100 nm2 mica area started to detach. Above 360 Å, more OTE domains are removed during the scan. It is known that OTE SAMs are formed following a mechanism of nucleation growth.46,51 Since the mica surface does not have a high density of hydroxyl groups, OTE/mica SAMs contain OTE domains separated by domain boundaries. The stability of OTE/ mica arises from cross-linking of neighboring OTE molecules within the domain and a small number of anchors to the mica substrate. At high modulation amplitudes, the transient load is high, thus the lateral force during the scan becomes sufficiently large to displace OTE domains. Such an effect is similar to the wear process, which starts the displacement from defect sites, e.g. at the boundaries of the mica region and the surrounding OTE areas. Figure 13 shows an example in which detachment occurrs at a resonance frequency. At f ) 25 kHz, an offresonance frequency, no visible detachment of OTE is observed, even when the modulation amplitude is as high as 270 Å. However, at a resonance frequency of 11.5 kHz, images are full of spikes even when the modulation amplitude is lowered to 205 Å. The spikes in the topography, amplitude, and phase images indicate the
Nanoscopic Elasticity of Thin Film Materials
Figure 13. Example of OTE detachment that occurred at a resonance frequency. At f ) 25.0 kHz (top), a nonresonance frequency, the FMM images show that the monolayer can withstand a modulation amplitude as high as 270 Å. While modulating at a resonance frequency of f ) 11.5 kHz (middle), FMM images contain spikes, which indicates violent motions of the tip. At 25 kHz and 90 Å (bottom), the topographic image reveals the displacement of OTE molecules.
Figure 14. Frequency spectra acquired during OTE detachment. (a) Typical frequency spectrum of a free AFM cantilever (k ) 0.1 N/m, Park Scientific Co.). (b) Frequency spectrum when the tip is in contact with the surface. (c) Without detachment, a modulation at f ) 25 kHz and ∆Z ) 205 Å produces a sharp spike in the frequency spectrum at 25 kHz. (d) The frequency spectrum exhibits sharp peaks corresponding to the driving signal and its high harmonics. Additional broad peaks are also observed, which correspond to the oscillations of the partially detached OTE domains. The modulation condition are as follows: f ) 11.5 kHz; ∆Z ) 160 Å. (e) More peaks appear when the modulation amplitude is increased to 205 Å. The tip senses the modulations of the driving signal and the motions of the partially detached OTE domains, as well as their couplings. After OTE domains are completely detached (Figure 13), the spectrum becomes similar to (c).
instability or sudden variation in cantilever deformation during the scan. To image the detachment, force modulation conditions are changed to f ) 25 kHz and ∆Z ) 90 Å. As shown in Figure 13, detachments occurred around and below the central mica area. In the case of Figure 13, we are able to capture the detachment process from the frequency spectra shown in
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Figure 14. Without detachment, a typical frequency spectrum for a free cantilever exhibits only one intrinsic resonance. When in contact with the OTE surface, the cantilever resonance amplitude decreases and its position shifts to higher frequencies. Additional peaks may appear, which reflect the oscillation of the instrument and the contact. During modulation, the driving signal appears in the frequency spectrum as a much sharper peak than the rest of the mechanical resonances. When detachment occurs at f ) 11.5 kHz, and ∆Z ) 160 Å, the frequency spectrum suddenly changes from a spectrum similar to Figure 14c into a multiresonance spectrum shown in Figure 14d, where broad resonance peaks appear. These peaks are observed at 6, 8, 14, 17, 26, 29, 37, and 48 kHz. In addition, the driving signal and its sharp harmonics are excited as well. When modulating at larger amplitudes, 205 Å, each broad resonance peak splits into two narrower peaks. The driving signal, its higher harmonics, and two fractional harmonics are detected as a result of nonlinear and chaotic motion of the cantilever. The spectra in Figure 14d,e indicate the complicated oscillations of the AFM cantilever when OTE domains break loose. In addition to following the driving signal and its harmonics, the tip encounters the oscillating OTE domains that are partially detached from mica and adjacent domains. These OTE domains oscillate at different frequencies and phase from the driving signal. Therefore, the motion of the cantilever is influenced by both the modulation of the cantilever and these partially detached OTE domains, their harmonics and combinations. These “extra resonances” disappear once the loosened OTE domains become completely detached and wiped away from the scanned area. Summary We have presented a systematic study of FMM and DFM as a function of force modulation amplitude and frequency. OTE monolayers on mica are used as a test system. Nanoscopic areas of mica are created within OTE monolayers to serve as an internal standard for contact stiffness measurements. In air, water films are present at contacts. These water molecules form a capillary neck at the tipsurface contact that couples into the measured contact stiffness especially in the hydrophilic regions. Measurements taken in liquid media more accurately reflect the viscoelastic properties of the material at contact. The contact stiffness measured using FMM or DFM depends on the chemical functionality of the material, the configuration and packing of these molecules under contact, and their deformation. Obtaining the absolute value of Young modulus (E*) requires accurate determination of tip and contact radii (R and a), force, and force modulation amplitude. The resulting E* is valid only for specific contact and modulation conditions. Therefore we conclude that comparing relative contact stiffness or Young’s modulus under the same modulation conditions is more reliable and meaningful than comparing absolute values. One can control the image contrast by adjusting the modulation conditions: frequency and amplitude. Such effects may be assessed quantitatively by the tip-surface interactions. The surface groups under an AFM tip deform, e.g. distortion of the lattice in the case of mica and larger tilt angle and more gauche bonds in the case of OTE. These deformations vary during force modulation, resulting in resonances as low as 5-50 kHz. These resonances are responsible for observed contrast variation and sometimes reversal. When the driving signal is in resonance with those modes, the energy transfer from sample to the tip is most efficient, resulting in the enhancement in the FMM image contrast of that particular contact. Therefore, by
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modulation at resonance, one can use FMM to selectively enhance the contrast of the desired surface component or local structures. Another parameter is the modulation amplitude, ∆Z. Increasing modulation amplitude enhances the overall signal in the amplitude image. However, extremely large amplitude diminishes the contrast difference between OTE and mica as the tip senses into the bulk of the substrate. While topographic images mainly reflect the surface morphology, amplitude and phase images in DFM can probe the depth profile of local viscoelasticity. For thin films or monolayer materials, optimal contrast is achieved at intermediate modulation amplitude, which can be determined from the corresponding amplitude difference versus ∆Z curves. One caution for using FMM and DFM is that damage to monolayer materials can occur under extreme conditions, such as at very large ∆Z and at
Jourdan et al.
resonance frequencies. OTE domains may undergo nonlinear or chaotic motions, be shaken loose from surrounding domains, and finally detach. Acknowledgment. We thank Dr. Jane Frommer at IBM Almaden Research Center for many stimulating discussions. We appreciate the insightful comments from both reviewers regarding the scientific discussions and writing style of this manuscript. G.Y.L. gratefully acknowledges the Camille and Henry Dreyfus Foundation for a New Faculty Award and the Arnold and Mabel Beckman Foundation for a Young Investigator Award. This work is also supported by the Whitaker Foundations Biomedical Engineering Grant, PRF-AC and NSF-Career Award (Grant CHE-9733400). LA9902183
