APPLIED PHYSICS LETTERS VOLUME 80, NUMBER 8 25 FEBRUARY 2002 Effect of cantilever–sample interaction on piezoelectric force microscopy Seungbum Honga) and Hyunjung Shin Storage Lab, Samsung Advanced Institute of Technology, Suwon 440-600, Korea Jungwon Woo and Kwangsoo No Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, Korea 共Received 9 October 2001; accepted for publication 17 December 2001兲 We report on the evidence for the cantilever–sample 共CS兲 capacitive force contribution to the piezoelectric force microscopy 共PFM兲. In addition, we present that positioning of the tip near the edge of the sample surface can significantly reduce this spurious contribution for any combinations of tip cantilever and film. As proof of both the existence of CS interaction and its reduction, the domains formed by the application of voltage pulses through the tip are observed by PFM at two different positions, i.e., sample center and edge. In accordance with the model that a piezoresponse consists of a piezoelectric vibration of the film and an electrostatic force induced vibration of cantilever, the domain contrasts are characterized by dot structure in the amplitude and negligible contrast in the phase images when the tip is placed in the center of the sample surface. However, reducing the CS interaction by placing the tip near the sample edge yields domain contrasts showing ring structure in the amplitude and a clear 180° phase shift in the phase images. Accompanying resolution enhancement in phase images results in smaller size of domains 共bits兲 produced by identical voltage pulses as is evidenced from bit size estimation. Additional evidence for reduction of CS interaction is obtained from piezoresponse hysteresis measurement. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1454219兴 Ferroelectric domain imaging using contact mode atomic force microscopy, often called piezoelectric force microscopy 共PFM兲, is widely used as a nondestructive probe to observe the domain configuration and dynamics.1– 4 However, the probing mechanism and resulting domain contrasts were not clearly understood due to the competitive contributions, to tip vibration signal, from electrostatic and piezoelectric forces between tip and sample, and capacitive force between cantilever and sample. Regarding the tip–sample interaction, many researchers believe that piezoelectric vibration under the tip yields the domain contrast.1– 4 However, it is clear that electrostatic force effect exists and can be the dominant factor when converse piezoelectric effect is small.5 Regardless of the origin of whether the domain contrast comes from either piezoelectricity or electrostatic force effect or their combination, there is a consensus of the fact that the contrast represents the ferroelectric domain, thereby enabling us to measure domain size and determine projected polarization direction. Many researchers calculated the cantilever–sample 共CS兲 capacitive force and its contribution to electrostatic force microscopy,4,6,7 and concluded that it does not have a significant effect on the obtained domain contrast. This is true for noncontact imaging when the tip–sample distance is small, and for contact imaging when the tip height is large or the spring constant of the cantilever is high. However, in case one uses a low-aspect ratio tip with a soft cantilever, CS interaction strongly interferes with the domain signal. Specific quantitative description of the aforementioned condition can be obtained when the information on the sample piezoa兲 Electronic mail: [email protected] electric coefficient, applied field, tip height, tip radius, spring constant of the cantilever, and Young’s modulus of the sample surface are available. For the combination of tips 共UL06A or B, Park Scientific Instruments兲 and films used in our laboratory, it was clear that the CS interaction was nonnegligible, and often contributed to the blurred phase images.8 Using a stiff cantilever can certainly reduce this artifact, but there are some drawbacks. The tip can damage the surface of the films by scratching. Also, there are some materials that need a soft cantilever such as polymer ferroelectric films. We previously explored the tip–sample and cantilever– sample interactions to clarify each contribution and their origins.8 In this letter, we present further evidence of CS interaction affecting the PFM images and piezoresponse hysteresis measurement. Then, we present a method that can effectively reduce the spurious effect from the cantilever and can be applied to virtually any combinations of tip– cantilever system and films. We used a commercial atomic force microscope 共Autoprobe M5, Park Scientific Instruments兲 and a lock-in amplifier 共SR830, Standford Research Systems兲 for topography and domain image acquisition. Detailed descriptions of the equipment can be found in a previous publication.9 The tip 共UL06B兲 was positioned at the center 共‘‘C’’ position兲 and near the edge 共E position兲共⬃40 ␮m distance from the sample edge兲 of the sample. 17 kHz ac voltage of 1 Vpp 共peak to peak兲 was applied to the tip while the bottom electrode was grounded. The scan frequency was 0.5 Hz, and the scan size was 2.5 ␮m⫻2.5 ␮m. Initially, the domains were oriented from bottom to top by applying ⫹20 V to the bottom electrode over the scan 0003-6951/2002/80(8)/1453/3/$19.00 1453 © 2002 American Institute of Physics Downloaded 12 Jan 2004 to 143.248.115.81. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp 1454 Hong et al. Appl. Phys. Lett., Vol. 80, No. 8, 25 February 2002 FIG. 1. Topography 关共a兲 and 共d兲兴, amplitude 关共b兲 and 共e兲兴, and phase 关共c兲 and 共f兲兴 images of reversed domains 共bits兲 for C 关共a兲–共c兲兴 and E 关共d兲–共f兲兴 positions. The bits were formed by applying ⫺18 V pulses of 33, 8.25, 1.65. and 0.66 ms to bottom electrode. The white bars in 共a兲 and 共d兲 represent 500 nm. area of 5⫻5 ␮m2 共which is referred to as back poling兲. After the back poling process, series of ⫺18 V pulses with pulse widths of 33, 8.25, 1.65, and 0.66 ms were applied to the bottom electrode over the scan area of 2.5⫻2.5 ␮ m2 inside the back poled area 共Fig. 1兲. Round-shaped bright dots 共top to bottom oriented domains兲 were formed and observed in amplitude 共A兲 for C position 关Fig. 1共b兲兴 and in phase 共␾兲 images for E position 关Fig. 1共f兲兴. Dark ring structure or dots were found in an amplitude image for the E position 关Fig. 1共e兲兴. No distinct features were found in phase image for the C position 关Fig. 1共c兲兴. Our observation in Fig. 1 supports the CS capacitive force contribution in C position to the tip vibration signal, because it matches the situation where CS interaction acts as an additional offset in piezoresponse. The following equation describes the piezoresponse, A cos ⌽, in terms of tip–sample and cantilever–sample interactions. A cos ⌽ ⫽ 再冋冋 d 33⫺ 册 2K⌫ lever 共 V dc⫹V c 兲 V ac k lever ⫺d 33⫺ for ↓domain 2K⌫ lever 共 V dc⫹V c 兲 V ac for k lever ↑domain, 册共1兲 where all of the parameters are defined in Ref. 8. The first term of each of the right-hand sides of Eq. 共1兲 is the piezoelectric contribution of the film, whereas the second term is the capacitive contribution of the cantilever. For domain imaging V dc equals 0, and the second term in Eq. 共1兲 becomes positive in our case because ⌫ lever⬍0 and V c ⫽0.3– 0.7 V for p-type Si tips and Pt bottom electrode. FIG. 2. Expected piezoresponse 关共a兲 and 共d兲兴, amplitude 关共b兲 and 共e兲兴 and phase 关共c兲 and 共f兲兴 signals and accompanying images of a reversed domain for C 关共a兲–共c兲兴 and E 关共d兲–共f兲兴 positions. Since the curves obtained by letting A cos ⌽⫽0 in Eq. 共1兲 serve as asymptotes for the hysteresis loop,8 it is clear that CS interaction also leads to a horizontal shift of the loop. This reasoning explains both the positive vertical shifts of the piezoresponse in Fig. 2共a兲 and the constant phase value in Fig. 2共c兲. On the other hand, when CS interaction does not exist, one can put ⌫ lever⫽0 so that the second term in the bracket vanishes. Then, the piezoresponse represents the piezoelectric coefficient multiplied by V ac . This can explain the drop in the amplitude signal at the domain boundary by competitive contribution of positive 共⫺d 33兲 and negative 共⫹d 33兲 domains in Fig. 2共e兲. Figures 2共a兲–2共c兲 illustrate the resulting piezoresponse, amplitude, phase signals and accompanying images when CS capacitive force is present. Its contribution is marked as an arrow in Fig. 2共a兲. Dot structure10 in amplitude 关cf. Figs. 1共b兲 and 2共b兲兴, and no significant features in phase 关cf. Figs. 1共c兲 and 2共c兲兴 images can be explained by Eq. 共1兲. Positioning the tip near the edge of the sample 共E position兲 can significantly reduce CS interaction due to the small capacitive coupling between the cantilever and bottom electrode. The expected piezoresponse, amplitude and phase signals, and accompanying images in the absence of CS interaction are depicted in Figs. 2共d兲–2共f兲. Ring structure in amplitude 关Fig. 2共e兲兴 and dot structure in phase 关Fig. 2共f兲兴 images are expected for fully penetrating domains of opposite polarity to that of the matrix. This is in good agreement with the results shown in Figs. 1共e兲共white dotted area兲 and Downloaded 12 Jan 2004 to 143.248.115.81. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp Hong et al. Appl. Phys. Lett., Vol. 80, No. 8, 25 February 2002 1455 FIG. 3. Dependence of bit size 共reversed domain size兲 on voltage pulse width for C and E positions. 1共f兲. Detailed analysis of the evolution from ring to dot structure in amplitude image 关Fig. 1共e兲兴 is published in our previous publication,9 which is related to a different domain boundary effect for fully and nonfully penetrating domains in thickness direction. The presence of CS interaction broadens the boundary width between the domains of opposite polarity. It is clear that the broadening effect is more prominent if the domain size reduces. The broadening is expected to be proportional to the areal ratio of the bit to the cantilever. Figure 3 was obtained by measuring the diameter of dot-shaped domains in Figs. 1共b兲 and 1共f兲. The diameter was measured from the line profile of each opposite domain 共defined by ‘‘bit’’兲 where full width half maximum 共FWHM兲 was the criterion for the size measurement. As can be seen in Fig. 3, the bit size varied almost linearly with logarithmic value of pulse width for both C and E positions, of which the origin can be understood by the coercive field contour and its dependence on pulse width.9 The bit size measured from Fig. 1共b兲 showed a larger value than that from Fig. 1共f兲. Also, the difference between the bit sizes measured at different positions came closer to each other as the pulse width increased. This phenomenon is likely to originate from the broadening effect of CS interaction on the bit boundaries that has a decreasing tendency with bit size 共or pulse width兲. Also, it strongly supports the argument that removing spurious CS interaction can further enhance the resolution of domain images. Furthermore, the piezoresponse hysteresis curves were collected from position C and E as shown in Fig. 4. The vertical shift of the loop, which is defined by 冋册 p r,max⫹p r,min 2 ⫻100共 % 兲 , 共 p r,max⫺p r,min兲共2兲共where p r represents remnant piezoresponse兲 changed from ⫹55% to ⫺10% as the tip moved from C to E position. The latter value is closer to the vertical shift 共⫺1.4%兲 of polarization electric field 共PE兲 hysteresis curve measured by RT66A on Pt top electrode region.11 The horizontal shift 共defined in the same way as for vertical shift兲 changed from FIG. 4. Piezoresponse hysteresis curve measurement for 共a兲 C and 共b兲 E positions. ⫺57% to ⫹16%, which is in good agreement with⫹12% of PE curve. The coercive voltages from PE measurement were ⫺1.5 and 2.4 V, which are in better agreement with those from E position 共⫺1.2 and 2.3 V兲 than C position 共⫺1.6 and ⫺0.1 V兲. The slope of the curve 共defined as (p s,max ⫺ p s,min)/20, where p s is spontaneous piezoresponse兲, which is proportional to ⌫ lever in Eq. 共1兲, reduced from 60 to 7. This suggests that significant portion of CS interaction was removed by placing the tip near the edge of the sample. Dr. C. J. Kim is gratefully acknowledged for supplying the piezoelectric transducer sample. A. Gruverman and M. Tanaka, J. Appl. Phys. 89, 1836 共2001兲. E. Z. Luo, Z. Xie, J. B. Xu, I. H. Wilson, and L. H. Zhao, Phys. Rev. B 61, 203 共2000兲. 3 L. M. Eng, M. Abplanalop, and P. Guenter, Appl. Phys. A: Mater. Sci. Process. 66, S679 共1998兲. 4 S. V. Kalinin, and D. A. Bonnell, Phys. Rev. B 63, 125411 共2001兲. 5 J. W. Hong, G. H. Noh, S. -I. Park, S. I. Kwun, and Z. G. Kim, Phys. Rev. B 58, 5078 共1998兲. 6 T. Hochwitz, A. K. Henning, C. Levey, C. Daghlian, and J. Slinkman, J. Vac. Sci. Technol. B 14, 457 共1996兲. 7 S. Belaidi, P. Girard, and G. Leveque, J. Appl. Phys. 81, 1023 共1997兲. 8 S. Hong, J. Woo, H. Shin, J. U. Jeon, Y. E. Pak, E. L. Colla, N. Setter, E. Kim, and K. No, J. Appl. Phys. 89, 1377 共2001兲. 9 J. Woo, S. Hong, N. Setter, H. Shin, J.-U. Jeon, Y. E. Pak, and K. No, J. Vac. Sci. Technol. B 19, 818 共2001兲. 10 P. Paruch, T. Tybell, and J. -M. Triscone, Appl. Phys. Lett. 79, 530 共2001兲. 11 However, the reason for decrease in absolute value of p r in the E position down to 1/4 of that in the C position is not clearly understood. It is under further investigation using high aspect ratio tip and will be presented in a future publication. 1 2 Downloaded 12 Jan 2004 to 143.248.115.81. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp