Evaluation of Hysteresis Property of Piezo Actuator by Moire Interference Method

Hiroyuki Masuda

Corrosion Analysis Group , National Institute for Metals Science

1-2-1 Sengen Tukba Ibaraki Japan 305

Abstract
The scanning prove microscopes (SPM) are now commonly used in studying micro-structures and micro-processing. The SPM can be used not only to observe the surface of materials but also to fabricate very small structures. However the accuracy of the SPM image is usually unknown around the range between 50 and 500 nm, because no proper standard material exists to get the hysteresis property of the piezo actuator. When we observe the automically flat surface by SPM, we can often find noise-like pattern around the scanning range of 50 to 200 nm. This pattern is moire pattern produced by atoms or molecular. We applied this moire pattern to the measurement of the hysteresis property of the piezo actuator around the range between 50 and 500 nm. The results show that this method is very accurate and useful to measure the hysteresis property of the piezo actuator.

Keywords: Hysteresis Property, Piezo Actuator , Moire Interference Method, Mica, SPM

Introduction
The scanning prove microscopes (SPM), such as the scanning tunneling microscope (STM) and the atomic force microscope (AFM), are now commonly used in studying micro-structures and micro-processing. The SPM can be used not only to observe the surface of materials but also to fabricate very small structures. However the accuracy of the SPM image is usually unknown around the range between 50 and 500 nm, because no proper standard material exists to get the hysteresis property of the piezo actuator. Moire interference method is often used to measure the strain distribution, because the strain change can be measured more accurately than the direct measurement method. When we observe the automically flat surface by SPM, we can often find noise-like pattern around the scanning range of 50 to 200 nm. This pattern is moire pattern produced by atoms or molecular. We discuss the application of this moire pattern to the measurement of the hysteresis property of the piezo actuator around the range between 50 and 500 nm.

Principle
Figure 1 shows the principle of moire interference method. Moire interference method can be used for atoms and molecular arranged regularly. Moire pattern usually appear when the sampling distance is nearly equal to the period of atoms or molecular. Two types of Moire pattern is considered. One is that moire pattern produced when the sampling distance is smaller than the period of atoms or molecular Pf, and the other is that moire pattern produced when the sampling distance is bigger than the period of atoms or molecular. We call the former moire pattern positive moire pattern and the later negative moire pattern. The relation between moire pattern spacing d and the sampling distance Pc is written as:

for positive moire pattern 1/d = 1/Pc - 1/(1 + e)Pf (1)
for negative moire pattern 1/d = 1/(1 + e)Pf - 1/Pc (2)

where e is the strain.
We can determine the hysteresis property by these equations.

Experiment
The specimen used was mica (15 x 15 x 0.5 mm). The AFM used was SP7000(SEIKO). Test was performed at 23C in air with scanning range of 15 to 200 nm, scanning speed of 2 mm/s, sampling data of 256 x 256 and tip-force of 0.2 nN.

Results and Discussion
We first took the AFM image of mica molecular with scanning range of 15 nm. Figs. 2(a) and 2(b) show the AFM image of mica molecular with and without FFT treatment. The period of molecular at horizontal direction is found about 0.55 nm. Moire pattern appears when the sampling distance is nearly equal to the period of molecular, that is, 0.55 x 256 = 140.8 nm. Figs. 3(a) - 3(g) show moire patterns observed in various scan range. As we expected, the moire pattern spacing is the biggest at the scan range of 140 nm. Moire patterns produced at the scan range smaller than 140 nm correspond to positive moire pattern and produced at the scan range bigger than 140 nm correspond to negative moire pattern. Fig. 4 shows the relation between the moire pattern spacing and the sampling distance, where the moire pattern spacing was obtained from the averaging the image data at the center part (100 pixels). The broken line shows the theoretical curves expressed as equations (1) and (2). It is clear that the observed moire pattern spacing coincides with the theoretical curves. However, the moire pattern spacing as shown in Figs. 3 should be the same in whole scanned area if no hysteresis exists in the piezo actuator. The change of the moire pattern spacing is caused by the hysteresis property of the piezo actuator. Calibration of the hysteresis property was done by using Fig. 3(e). Fig. 5 shows the calibration of the hysteresis by both the moire interference method and the conventional method (estimated from the large standard sample). The difference of strain accuracy exceeds more than 4%. If we use the horizontal sampling data of 512, we can observe the moire pattern around the scan range of 280 nm in this material. In this way, we can calibrate the wider range of hysteresis on the piezo actuator.

Conclusion
Moire interference method is very convienient to calibrate the hysteresis property of piezo actuator. Mica or graphite is standard material to calibrate the SPM accuracy and easy to get. Using this method, we can get more accurate image around 50 to 500 nm.