Langmuir 1997, 13, 4861-4864
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Interpretation of Direct and Indirect Force Modulation Methods Using Polymer Films Shin-ichi Yamamoto*,† and Hirofumi Yamada‡ Semiconductor Research Center, Matsushita Electric Industrial Co., Ltd, 3-1-1, Yagumo-Nakamachi, Moriguchi, Osaka 570, Japan, and Department of Electronics Science and Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 619-02, Japan Received January 21, 1997. In Final Form: May 13, 1997X We have investigated regional variations of elastic properties using magnetic force-controlled atomic force microscopy (AFM). A piece of small magnet was fixed at the end of the backside of the AFM cantilever so as to apply forces directly to the tip through the external magnetic field of a coil. When the forces applied to the tip are modulated with direct force modulation and the resulting amplitude of oscillation is measured, a sensitive measurement of the local contact stiffness can be made. We have applied this technique to polymer films of poly(ethylene oxide) (PEO) on mica. The soft PEO was measured easily with the faint magnetic forces between the tip and sample. The contrast of the image can selectively be enhanced on the basis of the local elasticity difference, when a soft cantilever was used. On the contrary the spring constant of the cantilever which we should use is determined by the elasticity of materials using indirect force modulation by modulating the sample displacement. The direct force modulation technique is a convenient method to investigate, especially, the elasticity of unknown materials on the nanometer scale.
1. Introduction Atomic force microscopy (AFM)1 has been applied to the nanometer-scale investigation of various materials including hard ceramics and soft polymer samples. Several techniques using force microscopy have been developed for the investigation of surface mechanical properties,2,3 such as the force modulation technique4-7 and indentation.8 The measured properties include hardness,9 adhesion,10 friction,11 and energy dissipation.12 At the same time, elastic deformation is becoming important, especially for the investigation of soft materials like polymer specimens.13 An AFM tip in contact mode deforms both the tip and sample, and the resulting image may thus not correspond to actual surface structure and also cause the loss of true atomic resolution.14 Recently, attempts were made to extract the substrate’s elastic * To whom correspondence should be addressed. † Matsushita Electric Industrial Co., Ltd. ‡ Kyoto University. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Rev. Lett. 1986, 56, 930. (2) Pethica, J. B.; Oliver, W. C. Mater. Res. Soc. Symp. Proc. 1989, 130, 13. (3) Weihs, T. P.; Pethica, J. B. Mater. Res. Soc. Symp. Proc. 1992, 239, 325. (4) Maivald, P.; Butt, H. J.; Gould, S. A. C.; Prater, C. B.; Drake, B.; Grurley, J. A.; Elings, V. B.; Hansma, P. K. Nanotechnology 1991, 2, 103. (5) Radmacher, M.; Tillmann, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900. (6) Nie, H.-Y.; Motomatsu, M.; Mizutani, W.; Tokumoto, H. J. Vac. Sci. Technol. 1995, B13, 1163. (7) Nie, H.-Y.; Motomatsu, M.; Mizutani, W.; Tokumoto, H. To appear in Thin Solid Films. (8) Bhushan, B.; Koinkar, V. N. Appl. Phys. Lett. 1994, 64, 1653. (9) Hues, S. M.; Draper, C. F.; Colton, R. J. To be published in J. Vac. Sci. Technol. (10) Burnham, N. A.; Colton, R. J.; Pollock, H. M. Nanotechnology 1993, 4, 64. (11) Mayer, E.; Heinzelmann, H.; Grutter, P.; Jung, T.; Hidber, H.; Guntherrodt. Thin Solid Films 1989, 181, 52. (12) Boschung, E.; Heuberger, M.; Dietler, G. Appl. Phys. Lett. 1994, 64, 3566. (13) Nysten, B.; Legras, R. J. Appl. Phys. 1995, 78, 5953. (14) Weihs, T. P.; Nawaz, Z.; Jarvis, S. P.; Pethica, J. B. Appl. Phys. Lett. 1991, 59, 3536. (15) Motomatsu, M.; Nie, H.-Y.; Mizutani, W.; Tokumoto, H. Jpn. J. Appl. Phys. 1994, 33, 3775.
S0743-7463(97)00061-9 CCC: $14.00
Figure 1. Schematic of the cantilever and scanning mechanism showing the location of the electromagnet inside the piezotube assembly. The conventional topography and the stiffness image can be measured simultaneously. The deflection of the cantilever is measured with a two-segment photodetector.
properties from the sample deformation during AFM scans by vibrating the sample or the cantilever at high frequencies.4-7 These results suggest that force modulation imaging can be used in a wide range of applications including identifying and mapping differences in stiffness or elasticity, and evaluating materials’ homogeneities. Although the indirect force modulation technique in which the sample position is modulated has been successfully used, there are four problems. First, the cantilever stiffness has to be chosen according to the material’s stiffness (see eq 5 given later). Second, indentation amplitude cannot be measured directly. © 1997 American Chemical Society
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Figure 2. Scanning electron micrograph of an AFM cantilever with a piece of SmCo magnet.
Third, the vertical displacement of the sample causes lateral motion of the cantilever, since the indirect force technique requires a large amplitude of displacement for obtaining appreciable signals. Fourth, the vibration amplitude of the cantilever does not reflect the stiffness of the sample surface correctly, because the buckling of the cantilever is sometimes caused in the case of indirect force modulation. On the contrary, the direct force modulation technique has several advantages overcoming these problems: the cantilever stiffness has nothing to do with the materials stiffness, the depth of surface deformation can be measured directly, the lateral forces effect can be minimized, and the contrast of the stiffness image does not invert. In this paper we showed that direct force modulation can detect the difference of poly(ethylene oxide) (PEO) and mica using a faint force without modified polymer.
Yamamoto and Yamada Cantilever deflection is measured using an optical lever method.16 Prior to the measurement, the deflection of the cantilever was calibrated by lifting up the sample by 10 nm and measuring the signal change of the photodetector. Samples are mounted on a piezoelectric tube scanner (20 × 20 µm2), inside of which a coil for an electromagnet is fixed. The coil is suspended by an aluminum holder so as to touch neither the piezotube nor the backside of the sample, which is necessary to avoid mechanical vibrations of the coil. The coil consists of 1000 turns with a core diameter of 3 mm and an inductance of 5 mH. All experiments were carried out in an ambient air atmosphere. 2.2. Processes of Magnetized Cantilevers. The tip is a pyramid with an apex radius of less than 20 nm microfabricated on the cantilevers. For the present experiment, two different cantilevers with spring constants of 0.68 N/m (Olympus Opt. Inc.) were used. First a large SmCo magnet was crushed, and a piece of SmCo magnet (less than 15 µm in diameter) was glued at the end of the backside of a microfabricated cantilever with epoxy resin using a three-way micromanipulator under an optical microscope. The scanning electron microscopy (SEM) picture of the cantilever is shown in Figure 2. 2.3. Direct Force Modulation Technique. With the direct force modulation technique, the sample assembly is scanned while a modulating force is applied directly to the tip using a magnetic field. The modulation frequency (5 kHz) is higher than the bandwidth of the feedback loop of 0.5 kHz. The response of the cantilever to this oscillation is detected with a lock-in amplifier and is used to obtain images related to local elastic properties of the sample surface. When the tip is brought into contact with a sample, the vibration amplitude is reduced. The oscillation amplitude is larger on the soft area than on the hard area with direct force modulation while the response becomes smaller on the soft area with indirect force modulation, as shown in Figure 3. Then the contrast of the stiffness images between the direct and indirect force modulation methods is reversed. A topographic image is also measured simultaneously with the force modulation data. 2.4. Sample Preparation. To compare the sensitivities of direct force modulation and indirect force modulation, the poly(ethylene oxide) (PEO) sample was prepared by dissolving it in benzene. The PEO sample was then spin-coated on fleshly cleaved mica substrates at 2000 rpm for 60 s to make uniform 10 nm thick films (2 wt % concentration) before annealing at 170 °C for 24 h under vacuum. The molecular weight of PEO is 100 000.
2. Experimental Section 2.1. AFM Apparatus Using a Coil. The experimental setup for the force modulation measurement is shown in Figure 1.
(16) Meyer, G.; Amer, N. Appl. Phys. Lett. 1988, 53, 1045. (17) Nielsen, L. E. Mechanical Properties of Polymers; Reinhold: New York, 1967.
Figure 3. Schematics of the elastic measurement with AFM. (a) The forced oscillation of the tip leads to a measured amplitude of the cantilever. The amplitude of the response is a function of the elasticity; the oscillations have a smaller amplitude over a harder area on the sample than that over a soft area. (b) The oscillation of the sample height leads to the amplitude of the cantilever. Under the applied force with indirect force modulation, the cantilever amplitude is larger in a harder area on the sample than it is on a soft area.
Direct and Indirect Force Modulation Methods
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Figure 4. Topographic (a) and stiffness (b) images of poly(ethylene oxide) on mica obtained simultaneously in an area of 4 × 3 µm2. Topography and stiffness (c) images also obtained simultaneously, with a cantilever of 0.68 N/m spring constant at a repulsive force of 1.0 nN. The topography in part a shows films with thicknesses about 10 nm and with islands of diameters of 0.5-2.0 µm. The data in part b are the response of the cantilever for the forced oscillation of the tip, which is applied directly at 5 kHz with about 0.9 nN. The data in part c are the response of the cantilever for the oscillation of the sample height at 5 kHz with a peak-to-peak amplitude of about 1.3 nm.
3. Results We measured the stiffness of PEO on mica to compare the sensitivities of direct force modulation and indirect force modulation methods using a cantilever of 0.68 N/m. Parts a and b of Figure 4 show a typical AFM topographic image and a simultaneously recorded stiffness image of PEO on mica with direct force modulation, respectively. Figure 4c is an image corresponding to Figure 4b measured by indirect force modulation. In the topographic image in Figure 4a, there appear islands with a diameter of 0.52.0 µm and a height of about 10 nm. Therefore we found that the bright area in image b corresponds to the PEO films and that the dark area corresponds to the mica. As expected, the amplitude of the cantilever’s motion is large when the tip is on the PEO with direct force modulation. The contrast of a stiffness image with indirect force modulation is reversed, as in shown part c. From Figure 4b we found that the ratio of the difference between the amplitudes of the cantilever on the PEO and on the mica to the amplitude of the cantilever on the PEO was 87.0%. In the case of Figure 4c, the ratio of the difference between the amplitudes of the cantilever on the PEO and on the mica to the amplitude of the cantilever on the mica was found to be 3.6%. Note that the contrast ratio of stiffness for these two cases, shown in Figure 4b and c, is about 24.2. This means that the sensitivity is
increased by as much as a factor of 24 over that of the conventional sample oscillation method with the cantilever of 0.68 N/m. 4. Discussion The PEO films and mica can be detected using the direct force modulation technique at high sensitivities. The contrast of the stiffness image corresponds to the difference of the cantilever amplitudes on the two phases. Here we defined the difference |∆x| ) xpeo - xmica, where xpeo and xmica are the cantilever amplitudes on the PEO and the mica, respectively. In the case of direct force modulation, |∆x| is given by
|∆x| ) xpeo - xmica ) F/(k + Speo) - F/(k + Smica) (1) Here F, k, Speo, and Smica denote the small modulation of force which is applied by the magnetic force, the spring constant of the cantilever, the tip-PEO stiffness, and the tip-mica stiffness, respectively. When the spring constant k approachs zero, |∆x| becomes a maximum value
|∆x| ) xpeo - xmica ) F/Speo - F/Smica
(2)
This means that the high sensitivity could be realized for any samples, when the soft cantilever is used.
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The response of direct force modulation is directly related to the sample stiffness, S, by
S ) (F/x) - k
(3)
A quantitative analysis using eq 3 revealed effective stiffnesses of the PEO film of 5.3 N/m and of mica of 82.1 N/m from Figure 4b. In the case of indirect force modulation, |∆x| can be written as follows:
|∆x| ) xpeo - xmica ) {[Speo/(k + Speo)] - [Smica/(k + Smica)]}X0 (4) Here X0 denotes the driving oscillation amplitude of the sample. |∆x| has its maximum value when the spring constant k is given by
k ) (SpeoSmica)1/2
(5)
The difference between the tip amplitudes on the samples can be calculated as a function of the cantilever stiffness and is shown in Figure 5. The data in Figure 5a correspond to the difference between tip amplitudes with indirect force modulation. The absolute value of |∆x| could be increased by increasing the spring constant k in the range less than 20 N/m. The spring constant of 20 N/m gives us high contrast when the samples are PEO and mica. It is clear that the cantilever stiffness has to be chosen according to the material’s stiffness, and the maximum sensitivity of contrast varies with the material’s stiffness. If a high-stiffness cantilever is used and the same area on the sample is scanned several times, polymer films are undoubtedly modified. In contrast, |∆x| could be increased by decreasing the spring constant, as shown in Figure 5b using direct force modulation. Then it is convenient to use the direct force modulation method for any samples because the cantilever stiffness does not need to be chosen according to the material’s stiffness. Conclusions We succeeded in taking a stiffness image of the distribution of PEO films with a weak force and no modified
Figure 5. Simulation of the calculated difference between the amplitudes of the cantilever on the PEO and the mica, |∆x|, as a function of the stiffness of the cantilever. (a) indirect force modulation; (b) direct force modulation.
sample surface using direct force modulation. Direct force modulation ensures a higher contrast stiffness image using a soft cantilever than indirect force modulation. Especially when we take the stiffness image of unknown soft materials, direct force modulation is useful. Acknowledgment. This work was partly supported by the National Research Laboratory of Metrology. The authors would like to thank Dr. Motomatsu for the preparation of the samples. LA970061J
