NANO LETTERS
Piezoelectric Coefficient Measurements in Ferroelectric Single Crystals Using High Voltage Atomic Force Microscopy
2003 Vol. 3, No. 2 169-171
Alex G. Agronin, Yossi Rosenwaks,* and Gil I. Rosenman* Department of Electrical Engineering-Physical Electronics, Tel AViV UniVersity, Ramat-AViV, 69978, Israel Received November 13, 2002
ABSTRACT We report on the use of high voltage atomic force microscopy for direct measurements of the piezoelectric coefficient d33 of monodomain RbTiOPO4 ferroelectric crystal. The measurements are compared with the conventional ac voltage modulation atomic force microscopy based technique, which needs calibration of the measurement apparatus. The comparison of the two measurement methods with literature reported values is discussed.
Atomic force microscopy (AFM) has been successfully applied for imaging ferroelectric domain structures with nanometer resolution.1 The origin of the AFM domain contrast is based on both specific physical properties of the ferroelectrics and the employed AFM technique.2 Among the various imaging modes, the contact piezoresponse mode is the most promising for high-resolution domain imaging3,4 and piezoelectric coefficient measurements.5-7 Application of the piezoresponse AFM is based on the detection of the piezoelectric vibrations of the ferroelectric sample when a low ac voltage is applied across the AFM tip-sample system. The contrast between the differently oriented domains is due to variation in the piezoelectric coefficient. However, to extract the piezoelectric coefficient the inevitable electrostatic interaction generated between the tip and the ferroelectric surface must be considered. Moreover, this electrostatic interaction complicates the piezoelectric coefficient measurement. One possible solution was recently suggested2 where the contributions of both electromechanical and electrostatic interactions were calculated. The proposed theory was used to determine the real local value of the piezoelectric coefficient for tetragonal perovskite ferroelectric BaTiO3 containing 180° domain structure.2 Several works were performed to measure the d33 coefficient of the piezoelectric tensor of ferroelectric PZT thin films using AFM tip as a top electrode5,6 and applying ac bias in the contact mode. The piezoelectric coefficient d33 was measured5 and was found to be consistent with published macroscopic measurements. According to Zavala et al.,6 more accurate results can be obtained when using a top electrode sputtered on the ferro* Corresponding authors. Tel.: (972)-3-640-62-48. Fax: (972)-3-64235-08. E-mail:
[email protected];
[email protected]. 10.1021/nl0258933 CCC: $25.00 Published on Web 01/07/2003
© 2003 American Chemical Society
electric, which improves the electrical contact between the tip and the surface. Christman et al.7 have conducted piezoelectric coefficient measurements for X-cut single-crystal quartz and ZnO thin films. To reduce the electrostatic interaction, the conductive AFM diamond tip was grounded. The measurements of X-cut quartz yielded d11 ) 0.014-0.019 Å/V which is below the expected value d11 ) 0.023 Å/V. In this work we apply two different experimental methods for piezoelectric coefficient measurements in RTP single crystals. The first is the well-known ac low voltage modulation method mentioned above. Ferroelectric monodomain 1 mm thick RbTiOPO4 (RTP) crystals were measured. RTP crystals belong to the orthorhombic mm2 point group8 and possess spontaneous polarization Ps ∼ 32 µC/cm2 and a coercive field of around 35 kV/cm.9 To decrease the electrostatic contribution to the measured piezoresponse, the samples were coated with Ti (∼500 Å) deposited by RF sputtering on the top polar face of the ferroelectric sample, and the bottom surface was pasted using silver paint to the sample holder. The studies were conducted by using commercial AFM (Autoprobe CP, Veeco, Inc.). A heavily doped silicon cantilever with a spring constant of ∼3.2 N/m was used; the nominal radius of the tip apex was ∼10 nm. An ac voltage at a frequency f ) 3 kHz was applied to the tip; this frequency is far above the low-pass cutoff frequency of the AFM topography feedback loop. On the other hand, this frequency is far below the cantilever mechanical resonance frequency in a free vibrating state; thus no damage can be caused to the tip due to resonance oscillations. A lock-in amplifier demodulates the AFM photodetector signal amplitude, and the piezoelectric coefficient can be obtained from
Figure 1. High voltage atomic force microscope setup for piezoelectric coefficients measurements.
the measurements following calibration of the photodetector signal. The second method is based on high voltage atomic force microscopy (HVAFM), which was recently applied for tailoring submicrometer domain configurations in different ferroelectric crystals.10 The use of the HVAFM is required due to the following. The sensitivity of a typical AFM system in topography mode is limited to about 1 Å (noise level) in the vertical axis. Another practical limitation is that only several dozen volts can be applied to the tip of a conventional AFM. Thus, when measuring the piezoelectric coefficient of RTP crystal (d33 ≈ 10 pm/V),14 applying 50 V to the tip will result in a 5 Å surface deformation that is difficult to measure in topography mode. This implies that small piezoelectric coefficients of around 10 pm/V cannot be measured using this direct method. We have used our HVAFM in order to apply a dc voltage in the range (0-300) V to the sample electrodes as shown in Figure 1. The sample piezoelectric deformation was recorded by AFM in the contact topography mode and then used for calculating directly the piezoelectric coefficient. This method allows to measure low values of piezoelectric coefficients without the need for any calibration procedure. Two options were considered concerning the electrodetip-sample system. The first is to apply a high voltage between the conductive tip and the bottom sample electrode, similar to the ferroelectric nanodomain reversal setup.10 Applying the voltage via the AFM tip results in an inhomogeneous electric field throughout the crystal, which requires integration of the electric field in order to obtain a correct d33 value.11,12 Moreover, high voltage application in such a setup generates very high electric field at the AFM tip apex reaching ∼107 V/cm, which may result in a domain switching under the tip10 and obscure the original value of the piezoelectric coefficient. Consequently, plain conductive electrodes deposited on both polar faces of the ferroelectric sample can eliminate this problem. In this case the measurements are performed under homogeneous electric field allowing easy direct measurements and evaluation of the piezoelectric coefficient. Figure 2 shows the measured linear dependence between the applied voltage and the photodetector signal for singlecrystal RTP measured using the conventional ac method. The piezoelectric coefficient d33 can be found13 according to β ) Rd33, where β is the slope of a linear fit to the data of Figure 2, and R is a calibration constant of the photodetector sensitivity. The calculated piezoelectric coefficient d33 ≈ 2 × 10-12 pm/V is a factor of 5 smaller than that measured using conventional macroscopic techniques where d33 coef170
Figure 2. Measured piezoresponse as a function of the AC bias applied across the tip-sample system. The dashed line is a linear fit to the data used to extract β defined in the text.
Figure 3. (a) Topography image of RTP crystal subjected to voltage stresses between -300 V to +300 V as shown by the arrows. Bright (dark) regions correspond to +300 V(-300 V) voltage application. (b) Height profile of the surface topography along the line in (a).
ficient was calculated using experimentally measured material density, dielectric permeabilities, electromechanical coupling coefficients, etc.14 Several reasons can account for this discrepancy: the first is possible clamping of the piezoelectric response by the high pressure of the AFM tip and the surrounding surface;6 a second possibility could be the tip-surface electrostatic interaction. The third could be poor electrical contact between the tip and the sample. In addition, the conversion of the photodetector signal to displacement can give rise to additional error. Using the second method of the HVAFM, a voltage V ) (300 V was applied between the two sample electrodes and switched during scanning. The resulting homogeneous field was lower than the coercive field of the RTP crystals.9 Figure 3 shows the surface topography image measured during the high voltage application. The dark (bright) strips correspond to regions where a negative (positive) voltage was applied. Nano Lett., Vol. 3, No. 2, 2003
The height profile (Figure 3b) shows all the three levels of the deformed surface. Each level corresponds to a different voltage magnitude: 300 V, 0 V, or -300 V. It is observed that opposite voltage polarity causes extension or contraction of the sample due to the linearity of the piezoelectric effect. It should be emphasized that the optically polished sample is held (using a conductive paste) equally over the entire bottom sample surface; moreover, the sample edges were free to expand in the X-Y directions in accordance with the d31, d32 coefficients. Therefore, no sample bending was observed, in contrast to thin films measurements using optical methods.15 The measured topography changes were about ∆L ∼ 30 Å (for a voltage of (300 V), which correspond to d33 ) 30 Å/300 V ) 10 pm/V; this value of d33 is in good agreement with macroscopic measurements.14 Additionally, the fact that positive (negative) voltages cause the surface to contract (extend), indicates the piezoelectric origin of the measured topography changes.16 When applying high dc voltage for direct d33 measurements, a possible electrostriction contribution should also be considered. The total crystal deformation X is given by17 X ) Q(Ps + 0E)2 ) QPs2 + 20 QPsE + Q022E2
(1)
where Q is the electrostriction coefficient, Ps is the spontaneous polarization, QPs2 is the spontaneous strain, E is the applied electric field, and 0 and are the vacuum and relative permittivities, respectively. The piezoelectric coefficient is d ) 20QPs
(2)
According to eq 2, the electrostriction coefficient Q33 ≈ 0.11 C2/m2 was evaluated using d33 ) 11.34 pm/V, 33 ) 18 (ref 14), and Ps ) 0.32 C/m2 (ref 9). The strain caused by the electrostriction deformation was calculated according to Xel ) Q022E2 ≈ 2.54 × 10-10. This means that our 1 mm thick RTP sample elongates in the range of ∆L ) 2.54 × 10-10 × 10-3 ) 2.54 × 10-13 m due to ( 300 V application.
Nano Lett., Vol. 3, No. 2, 2003
This is negligible compared to the observed piezoelectric deformation ∆L ∼ 30 Å ) 3 × 10-9 m. Therefore, the piezoelectric coefficient evaluated above was not affected by the electrostriction deformation. In conclusion, we have demonstrated the use of HVAFM for piezoelectric coefficient measurements in single-crystal ferroelectrics. The measured d33 value was in a good agreement with literature reported values. Using the conventional ac voltage method, a d33 smaller by a factor of 5 was obtained. Thus we believe that the HVAFM can be a very useful tool for direct accurate measurements of low piezoelectric coefficients in ferroelectrics. References (1) Gruverman, A.; Auciello, O.; Tokumoto, H. Integr. Ferroelectr. 1998, 19, 49. (2) Kalinin, S. V.; Bonnell, D. A. Phys. ReV. B 2002, 65, 125408. (3) Gruverman, A.; Auciello, O.; Tokumoto, H. Annu. ReV. Mater. Sci. 1998, 28, 101. (4) Roelofs, A.; Bottger, U.; Wase, R.; Schlaphof, F.; Trogisch, S.; Eng, L. M. Appl. Phys. Lett. 2000, 77, 3444. (5) Gruverman, A.; Auciello, O.; Tokumoto, H. J. Vac. Sci. Technol. B 1996, 14, 602. (6) Zavala, G.; Fender, J. H.; Trolier-McKinstry, S. J. Appl. Phys. 1997, 81, 7480. (7) Christman, J. A.; Woolcott, R. R.; Kingon, A. I., Jr.; Nemanich, R. J. Appl. Phys. Lett. 1998, 73, 3851. (8) Cheng, L. K.; Bierlein, J. D. Ferroelectr. 1993, 142, 209. (9) Urenski, P.; Rosenman, G.; Molotskii, M. J. Mater. Res. 2001, 16, 1493. (10) Rosenman, G.; Urenski, P.; Agronin, A.; Rosenwaks, Y.; Molotski, M. Appl. Phys. Lett. 2002, Dec. 30. (11) Durkan, C.; Chu, D. P.; Migliorato, P.; Welland, M. E. Appl. Phys. Lett. 2000, 76, 366. (12) Hong, J. W.; Noh, K. H.; Sang-il Park, Kwun, S. I.; Khim, Z. G. Phys. ReV. B 1998, 58, 5078. (13) Harnagea, C.; Pignolet, A.; Alexe, M.; Hesse, D.; Go¨selle, U. Appl. Phys. A 2000, 70, 261. (14) Sil’vestrova, I. M.; Pisarevskii, Yu.; Voronkova, V. I.; Yanovski, K. SoV. Phys. Crystallogr. 1990, 35, 140. (15) Kholkin, A. L.; Wu¨tchrich, Ch.; Taylor, D. V.; Setter, N. ReV. Sci. Instrum. 1935, 67, 1935. (16) Wang, Y.; Kleemann, W.; Woike, T.; Pankrath, R. Phys. ReV. B 2000, 61, 3333. (17) Uchino, K. Ferroelectric deVices; Marcel Dekker Inc.: New York, 2000.
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