Piezo-driven metrological multiaxis nanopositioner - Semantic Scholar

REVIEW OF SCIENTIFIC INSTRUMENTS

VOLUME 72, NUMBER 11

NOVEMBER 2001

Piezo-driven metrological multiaxis nanopositioner Jong-Youp Shima) and Dae-Gab Gweon Nano Opto-Mechatronics Laboratory, Department of Mechanical Engineering, Korea Advanced Institute of Science & Technology, 373-1 Kusong-Dong, Yusong-Gu, ME3265, Taejon 305-701, Korea

共Received 3 January 2001; accepted for publication 12 August 2001兲 We report on the development of a metrological multiaxis nanopositioning device, which is operated by the piezo-based inertial method, as a sample stage for scanning probe microscopy. It has long moving range, unlimited in principle, and nanometer 共microradian兲 resolution. Two operation methods, inertial sliding and inertial walking, can be applied to the stage and the inertial operating method can make the stage have a simple and compact structure. By the structure and operation method high positioning stability can be obtained which is an important requirement for scanning probe microscopy. For a metrological nanopositioner, a three axes laser interferometric sensing scheme is adopted for planar motion and a 15 channel high voltage amplifier is designed and computer based digital-to-analog conversion is adopted. Therefore the nanopositioner can be feedback controlled with many choices of voltage wave forms and control methods. Design of the nanopositioner and piezo-driver and experimental results are presented. The device provides step sizes of 0.016 –10 ␮m at frequency up to about 7 kHz. The rotational range is limited by the interferometer alignment, 0.2°, and the step size is 0.17–103 arcsec. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1408932兴

I. INTRODUCTION

as conventional operation except for the complexity of the actuation, and the inertial walking method is the new one of which a cycle is composed of the actuation of three tube PZTs with expansion and contraction. The body is on the base by the supporting rod. The second method can eliminate PZT drift and driver voltage noise problems, therefore more position stability can be obtained.

A positioning device with both long moving range and nanometer resolution is more and more required in many surface inspection devices such as a scanning probe microscope 共SPM兲, scanning tunneling microscope 共STM兲, and scanning electron microscope 共SEM兲 as a sample stage. The stage requirements for these applications are high resolution, multiaxis movements, high positioning stability, and a compact and simple structure. Furthermore, with the standardization of the surface scanning devices there is also a need for a metrological sample stage. Since the development of scanning microscopes, piezo-driven translation devices for sample or probe manipulation in single, two, or three degrees of freedom have been reported.1– 6 These devices use either an Inchworm-like clamping mechanism or the inertial sliding principle. In this article a metrological multiaxis nanopositioning device is developed which is operated in two ways, inertial sliding and inertial walking, with three laser interferometers as the position sensing method for planar motion. It is a derivative of the Besocke design.2 It consists of three tube piezoelectric transducers 共PZTs兲 and three supporting rods, which are attached to a moving body 共sapphire ball at the one end of each tube兲, base with mirror polished surface, 15 channel high speed digital-to-analog converter 共DAC兲, and a 15 channel high voltage amplifier. Therefore the device can have three to six degree-of-freedom 共DOF兲 motion. The three planar motions (X,Y ,⌰) have unlimited motion range and nanometer 共micoradian兲 resolution and in the other three DOF motion travel range is limited by the expansion of tube PZTs. Inertial sliding operation is the one which is the same

II. MECHANICAL DESIGN AND OPERATING PRINCIPLE

Three four-segmented piezoelectric tubes 共outer diameter 6.35 mm, inner diameter 5.15 mm, length 30 mm兲 are attached to the moving body 共Fig. 1兲. An optically polished sapphire ball 共diameter 6 mm兲 is glued to one end of the tube. For the positioning stability7 and adequate operation of inertial motion, a high hardness material, sapphire ball, is used. The three tubes are located, respectively, at the vertex of an equilateral triangle of which the center coincides with the center point of the moving body. Similarly, three supporting rods 共diameter 6 mm, aluminum兲 are fixed to the moving body. A polished stainless steel ball 共diameter 6 mm兲 is fixed tight to one end of the rod. Similar to the case of the tube, the locations of the three rods are at the vertex of the equilateral triangle. The base plate is made of stainless steel and the body-contacting surface is plated with hard chrome. Finally the coated surface is polished to be smooth for good performance. Figure 2 shows the principle of operation methods. Inertial slider motion includes only deflection of the piezoelectric tube and the moving body is supported by the sapphire of the tube. By the rapid deflection of the second phase, large inertia force makes the body at rest and sliding at the contact point of the ball occurs. The next sequence is at moderate

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FIG. 1. The cut-view of the multiaxis nanopositioner with base plate is shown, therefore only two rods and a tube PZT are shown. To make the inside-body view other components 共two tube PZTs and a rod兲 are omitted 共refer to Fig. 3兲. In the real case three piezoelectric tubes with a sapphire ball at each end and three rods with a stainless steel ball at each end are attached to the moving body. To make a smooth surface the contact surface of the base is polished. Size of the moving body is 50⫻50 mm2 and that of base surface is 120⫻120 mm2.

operation speed and a single movement is accomplished with no sliding. Inertial walker motion includes deflection, contraction, and expansion of the tube and the moving body is supported by the ball of the rods when it is at rest. In the second phase, expansion of the tube lifts the body up and in the third phase deflection of the tube occurs and the body can move one small step. Finally, the fourth step, restoring its original tube shape, is a rapid phase. At this phase, contraction and deflection of the tube exist and sliding occurs at the contact point of the ball and surface by the inertia effects. Therefore when the body is at rest, it is supported by the ball

J.-Y. Shim and D.-G. Gweon

FIG. 3. Actuation direction of each tube to move the device. The component numbered 1 is a piezoelectric tube and that numbered 2 is a supporting rod. The direction of the arrow is determined by the input voltages, that is the deflection direction of each tube and the movement of each tube is realized by either operation methods.

of the rods. In the inertial walking method the difference between the two methods makes the positioning stability higher because the inertial slider method can have piezoelectric drift by itself and by the input voltage.8 Considering the inertial walker method, the device is supported by the stainless steel ball of the rods therefore undesirable effects are relatively decreased. For surface scanning microscopes the long-term stability of the device is an important factor since it can induce distortion of the scanning results. Figure 3 shows the PZT tube actuating directions in order to make a translational or rotational motion in the case of x translation and ␪ rotation, however, the y translation case is not shown. To make a y-direction translation simply make the deflection of the tube PZTs be in the y direction similar to the x-translation case. The deflection direction of each tube PZT can be determined by adjusting input voltages of PZT electrodes. To roughly estimate the operating conditions and performance some theoretical background is needed. At first the common acceleration condition of the tube end point, that is, moving body mass center, is examined. If mass of the body is m, gravitational acceleration g, and ␮ s is static friction, the sliding condition is

␮ s mg⬍m ␣

d 2V . dt 2

共1兲

In the above equation the acceleration term is represented as voltage input terms and ␣ is constant. From the relation equation between deflection and input voltage,9 ⌬x⫽

2&d 31L 2 V, ␲ Dt

共2兲

d 31 is the piezoelectric coefficient, D is the inner diameter of the tube, t is the thickness of the wall, and L is the length of the tube. Therefore

␣⫽ FIG. 2. Principle of one cycle operation: inertial slider and inertial walker. In the case of the inertial slider, sequence 햳 is the phase of rapid motion. In case of the inertial walker, sequence 햵 is the phase of rapid motion. Rapid motion means sliding occurs at the contact point by the inertia effects. The motion can be made by deflection, expansion, and contraction of piezoelectric tubes. The dotted line indicates the amount of movement.

2&d 31L 2 . ␲ Dt

共3兲

Finally the acceleration condition is as follows,

␮ s g ␲ Dt d 2V ⬎ , dt 2 2&d 31L 2

共4兲



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FIG. 4. 400 V–20 kHz sinewave following a single channel piezo-driver circuit. The driver is composed of a preamplifier and power amplifier that are all operational amplifiers. The design considerations are bandwidth, output power, and capacitive load. The preamp has unity gain, 1.6 MHz cutoff frequency, and voltage offset adjuster.

with s 11 the compliance coefficient, the first deflection resonant frequency of the single piezoelectric tube is9 f 1⫽

冉冊冑 1.88 L

2

D 2 ␳ s 11

,

共5兲

where ␳ is 7.8 g/cm3 and s 11 is 12.4⫻10⫺12 m2/N for PZT material,10 f 1 is 7.32 kHz for a single tube PZT. Assuming that maximum acceleration of tube end point by deflection motion is roughly defined by f 1 and voltage input is sinusoidal, Eq. 共4兲 becomes ¯V ⬎

␮ s g ␲ Dt

1 , 2 共 2␲ f 兲2 1 2&d 31L

共6兲

with d 31⫽⫺140⫻10⫺12 m/V and ␮ s ⫽0.3, the minimum voltage amplitude ¯V is 38 mV and the deflection of the tube is 0.76 nm. However, Eq. 共4兲 does not contain mass of the body, therefore the weight effect of the device on the operation cannot be examined. That effect can be estimated by the friction force and stiffness relation. The large mass will generate high friction force at the contact points and if the piezoelectric tube does not generate enough force to get over friction resistance, sliding cannot occur and movement cannot be accomplished adequately. Considering that piezoelectric material converts the electric force 共voltage兲 to mechanical force which causes strain in the material, the amount of deflection due to the friction force can be a measure of force comparison. Roughly the piezoelectric tube can be thought of as a simple beam, therefore using the deflection equation of the tube by friction force, the following equation is obtained: m

␦

⫽

9EI . ␮ S gL 3

共7兲

In the above equation, E is the elastic modulus, I is the area moment of inertia, and ␦ is the deflection. Calculating the equation with 0.2 kg mass, the value of ␦ is 0.485 ␮m. Therefore the minimum attainable motion of the device is determined by the weight effects and the minimum movement is about 0.485 ␮m. Considering the epoxy bonding, which is used for fixing the piezoelectric tube and ball, af-

fects on the stiffness and effective length of the tube and also the simple beam assumption make the piezoelectric tube more flexible, the value is actually somewhat lowered. The experimental real value is about 0.1 ␮m and that is lowered to 0.01 ␮m order by the adaptation of the actuation method which is discussed later.

III. ELECTRICAL DESIGN AND EXPERIMENTAL SETUP

A high speed, high voltage piezo-driver is designed. To follow arbitrary voltage input with low wave form distortion, a power operational amplifier is used.11 The design considerations are bandwidth, output power, and capacitive load. The bandwidth of the driver is about 20 kHz with 400 V amplitude. The preamp has unity gain, 1.6 MHz cutoff frequency, and a voltage offset adjuster. A quarter section of the outer electrode of the piezoelectric tube has 2 nF capacitance and the current passing through that section is proportional to the time derivative of voltage input. Therefore the higher and faster the voltage input is, the more current flows. The power amplifier must be able to source that amount of current at high voltage, that is, high power. X C⫽

1 . 2␲ f CL

共8兲

X c is the impedance of the tube at frequency f when tube has C L capacitance. With that impedance the current passing is calculated when the voltage output is maximum, I⫽

V max . XC

共9兲

When V max is 400 V and f is 7 kHz the current passing through the quarter section is 35.2 mA. The small signal stability considering capacitive load of the driver is also important because instability means that the driver has small oscillations and this affects the piezoelectric tube motion. There is a RC network circuit connecting pin number 4 and 5 of the power amplifier 共not shown in Fig. 4兲 and it provides the amplifier with phase compensation. Simple calculation gives the driver stability a 50° phase margin.


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FIG. 5. Schematic construction of the laser interferometer. B.B. is beam bender, B.S. is beam splitter, and I denotes interferometer component. A high performance laser interferometer is used for the planar motion sensor, that is X, Y, ⌰. Resolution of the interferometer is 5 nm and it has about a 200 kHz data update rate. Dielectric mirrors, which reflect light at about 633 nm, are attached to three sides of the nanopositioner.

In order to closed-loop control the nanopositioner, a numerical controller 共high performance computer兲, arbitrary wave form generator 共high speed DAC兲 and sensing scheme 共laser interferometer兲 are required. Two 12-bit eight-channel DACs12 are adopted and it has memory to store the wave form and can generate it at a speed of 1 Msamples/s. A high performance laser interferometer is used for a planar motion sensor, that is X, Y, ⌰. Resolution of the interferometer is 5 nm and it has about 200 kHz data update rate. Dielectric mirrors, which reflect light at about 633 nm, are attached to three mutually orthogonal sides of the device. The device is manufactured with flatness and parallelism of its sides being good enough to align a three axes interferometer laser beam. Figure 5 shows the interferometer setup schematic. The x direction has two interferometers and it can provide ␪ motion data. From x 1 and x 2 displacement data rotational motion ␪ can be obtained with the value of d, sensing the position distances of x 1 and x 2 .

␪⫽

x 1 ⫹x 2 . d

共10兲

x and y translation and ␪ rotation are obtained from x 1 , x 2 , and y data with simple mathematical equations. The rotational range is limited by the interferometer alignment, 0.2°. IV. EXPERIMENTAL RESULTS

To examine the performance of the device, a simple sawtooth wave is applied to the piezoelectric tube. Figures 6 and 7 show the results of the operation with inertial slider principle. The motion is to the direction of positive y. The sawtooth wave input voltage is applied to the electrode of the direction of positive y and the driving frequency is 700 Hz and the voltage amplitude is 50 V. The sawtooth steps are repeated 80 times. The total y displacement of the device is about 0.1 mm with 0.1 s and the speed can be improved with higher driving frequency and voltage amplitude. As shown in the Fig. 6共a兲 the speed 共mm/s兲 of the device is almost a constant value when the input voltage frequency and amplitude is fixed. The two x-axis displacements are also recorded

FIG. 6. Experimental results. Sawtooth wave input voltage is applied to the electrode of the direction of positive y, and the driving frequency is 700 Hz and voltage amplitude is 50 V. The waveform is repeated 80 times. 共a兲 y direction 共b兲 x 1 direction 共coupled motion by y-direction motion兲.

by the interferometer and shown in Figs. 6共b兲 and 7. These displacements are due to the couple by the y-axis motion and this coupling among three axes is caused by many uncertainties in the device setup and physical properties. First, setup errors of the tube PZTs can cause cross couple among the axes. These setup errors include tube PZT position error from the exact triangular vertex position, tube PZT electrode direction alignment error which can cause directly tube PZT deflection direction error, and finally each of three tube PZTs may not have the same piezoelectric constant. Second, the contact surface condition between the polished base surface and sapphire ball at tube PZT end. Though base surface condition and hardness quality of the sapphire ball are made good to decrease these contact surface problems, the friction coefficient at each contact surface is different from one another. Even though there exists small error by friction variation it can cause large motion couples considering operating principle. The movement of the device is composed of many



FIG. 7. This experiment shows the result of the x 2 共coupled motion by y-direction motion兲 direction. The oscillations in the figures of x-axis displacement are caused by sawtooth voltage input and the there exist 80 oscillatory wave forms.

small steps and even a small error can be integrated into a large motion error. From the experimental data in Figs. 6共b兲 and 7 roughly calculated coupled x-direction movements are about 6 ␮m, that is below 10% of the y direction movement and coupled ␪ rotation is about 0.1°. The oscillations in the figures of coupled x-axes displacements are caused by sawtooth voltage input in itself, therefore there exist 80 oscillatory wave forms. Figure 8 shows the smallest step that the device can make by the inertial slider operation and it is about 16 nm. As is predicted in the above theoretical considerations, movement of the device is not achieved clearly when the step size is below 0.1 ␮m. A simple adaptation to the operation makes the device have a resolution of 16 nm. That limitation is caused by the mass of the device, and if the dynamic inertia force is applied to the device against gravity, the effective mass will be reduced. The contraction of the tube is added in the sliding phase. V. DISCUSSION

A metrological multiaxis nanopositioning device, which is operated by the piezo-based inertial method as a sample stage for scanning microscopes, is developed. It has long moving range, unlimited in principle, and nanometer 共microradian兲 resolution. Two operation methods, inertial sliding

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FIG. 8. Result shows the smallest steps that the device can make with inertial slider operation. Displacement resolution of the device is about 16 nm. The contraction of the tube is added in the sliding phase.

and inertial walking, can be applied to the stage. Mechanical and electrical design procedure is presented. The experimental results show that resolution of the device is 16 nm 共0.64 ␮rad兲 and it can move at 1 mm/s speed, however, its final speed can be measured when it is closed loop controlled. The nanopositioner will be eventually closed loop controlled using interferometer sensors. Further research includes inertial walking operation, dynamic modeling of mechanical components of the positioner, device characteristics experiment, PZT tube input voltage wave form optimization, and control scheme development. And finally the nanopositioner will be applied to scanning tunneling microscopy, which is a laboratory-built device. D. W. Pohl, Rev. Sci. Instrum. 58, 54 共1987兲. K. Besocke, Surf. Sci. 181, 145 共1987兲. 3 J. W. Lyding, S. Skala, J. S. Hubacek, R. Brockenbrough, and G. Gammie, Rev. Sci. Instrum. 59, 1897 共1988兲. 4 Ch. Renner, Ph. Niedermann, A. D. Kent, and O. Fisher, J. Vac. Sci. Technol. A 8, 330 共1990兲. 5 L. Libioulle, A. Ronda, I. Derycke, J. P. Vigneron, and J. M. Gillis, Rev. Sci. Instrum. 64, 1489 共1993兲. 6 R. Erlandsson and L. Olsson, Rev. Sci. Instrum. 67, 1472 共1996兲. 7 H. van der Wulp and P. V. Pistecky, J. Vac. Sci. Technol. B 15, 566 共1997兲. 8 H. Jung, J.-Y. Shim, and D.-G. Gweon, Rev. Sci. Instrum. 71, 3436 共2000兲. 9 M. E. Taylor, Rev. Sci. Instrum. 64, 154 共1993兲. 10 Physik Instrumente Ceramic, Germany. 11 Apex Microtechnology, Tucson, AZ. 12 National Instruments, Austin, TX. 1 2
