high-precision magnetic levitation stage for photolithographyprecision engineering 69. stage can...

High-precision magneticlevitation stagefor photolithography

Won-jong Kim* and David L. Trumper†*SatCon Technology Corporation, Cambridge, MA and †MassachusettsInstitute of Technology, Cambridge, MA, USA

In this paper, we present a high-precision magnetic levitation (maglev)stage for photolithography in semiconductor manufacturing. This stage isthe world’s first maglev stage that provides fine six-degree-of-freedom mo-tion controls and realizes large (50 mm 3 50 mm) planar motions with onlya single magnetically levitated moving part. The key element of this stage isa linear motor capable of providing forces in both suspension and transla-tion without contact. The advantage of such a stage is that the mechanicaldesign is far simpler than competing conventional approaches and, thus,promises faster dynamic response and higher mechanical reliability. Thestage operates with a positioning noise as low as 5 nm rms in x and y, andacceleration capabilities in excess of 1 g (10 m/s2). We demonstrate theutility of this stage for next-generation photolithography or in other high-precision motion control applications. © 1998 Elsevier Science Inc.

Keywords: precision motion control; photolithography; magnetic levita-tion; mechatronics

Introduction

High-precision position control systems, such aswafer stepper stages for photolithography in semi-conductor manufacturing, must provide travelover relatively large displacements in a plane(hundreds of millimeters), small displacements(hundreds of micrometers) normal to the plane,and small rotational displacements (milliradians)around three orthogonal axes. Such a stage mustachieve position stability on the order of tens ofnanometers. There are significant advantages of asingle magnetically levitated moving part for thisapplication, because such a stage can provide allthe required motions. A literature review of theclass of conventional as well as levitated single-moving-part positioners can be found in Kim.1

The one moving part also has a simple mechanicalstructure that yields fast dynamics. These fast dy-namics are directly related to high throughput,which is an important design specification formanufacturing equipment.

Several design considerations were raised inthe course of discussing specifications and featuresneeded in photolithography. First, a one–moving-part design is more preferable because of manu-facturing simplicity and simple dynamics. Second,the motor magnets should be put on the platen toavoid thermal expansion and problematic umbili-cal cables. Third, a compact design leads to a lightmoving part; namely, the platen and a small foot-print. Fourth, to generate rotational motions, theactuators’ lines of force must not pass through theplaten’s center of mass. Fifth, the lens’ field ofview above the wafer area must be clear. Thus, weselected a moving magnet-stationary winding stagedriven by with four permanent magnet linear sus-pension motors for prototyping. Figure 1 is a per-spective view of the selected design concept. Thisdesign has the following advantages:

Address reprint requests to Dr. W.-J. Kim, SatCon TechnologyCorp., 161 1st St., Cambridge, MA 02142, USA. E-mail: [email protected]

Precision Engineering 22:66–77, 1998© 1998 Elsevier Science Inc. All rights reserved. 0141-6359/98/$–see front matter655 Avenue of the Americas, New York, NY 10010 PII S0141-6359(98)00009-9

Y no umbilical cables to the platen exceptfor the ground wire for the capacitive gapsensors;

Y symmetry in the x- and y-directions;Y no overhung steel targets for electromag-

nets or preload magnets; i.e., nothingabove the platen;

Y no heat dissipation on the platen (exceptfor negligible eddy current loss in the mag-nets) to minimize deformation caused bythermal expansion; and

Y heat generated by the stators easily removedto the mounting table by conduction.

We have designed a novel permanent magnetlinear motor to provide drive force as well as sus-pension force for a magnetically levitated wafer-stepper stage.1,2 The linear motors consist of Hal-bach-type3 magnet arrays attached to theunderside of the levitated puck and coil sets at-tached to the fixed machine platform. The platenis levitated without contact by four such perma-nent-magnet linear motors, which provide bothsuspension and drive forces. By coordinating theforces applied by each motor, the stage can beaccurately controlled in six degrees of freedom.The platen mass of 5.58 kg is supported againstgravity by the combined forces of the four motors.The present design has a travel of 50 mm in x andy, a travel of 400 mm in z, and is capable of milli-radian-scale rotations about each of these threeaxes. Detailed fabrication issues of the stage can befound in Kim1 and Kim et al.4 and are not re-peated here. The electromechanics and configu-ration based on our theory and design has alsobeen adopted in a scanning stage built by MikeHolmes at the University of North Carolina—Charlotte.5

This paper presents the working principles un-derlying the stage operation, and experimental datademonstrating the stage performance capabilities.In the following section, an overview of the mag-

netic levitation stage is given. The next section de-scribes the real-time control of the stage. Test re-sults are presented and discussed in the last section.

High-precision planar magnetic levitator

Figure 2 is a photograph of a prototype magneticlevitation stage designed and implemented by theauthors. The stage position in the plane is mea-sured with three laser interferometers with sub-nanometer resolution. The stage position out ofthe plane is measured by three capacitance gaugeswith nanometer resolution. At present, the stage isoperational with a positioning noise of 5 nm rmsin x and y, and is demonstrating acceleration ca-pabilities in excess of 1 g (10 m/s2).

Working principles

Figure 3 depicts the dynamic equilibrium aroundwhich the levitator operates and is stabilized. Thepeaks of idealized sinusoidal stator currents areshown as x into the page and z out of the page. Wealso show the associated north (N) and south (S)poles generated by these currents. At a fixed time,if we generate the current approximately by asinusoidal distribution in the y-direction, as illus-trated in Figure 3, there is a vertical repulsive forcebetween the same magnetic poles of the magnetarray and the current distribution (i.e., corre-sponding north to north and south to south). Thisvertical repulsive force lifts the platen against grav-ity. The vertical motions of the platen are stablebecause of a positive magnetic spring effect be-tween the magnet array and stator currents. Theincremental equation of motion in the verticaldirection is derived in Kim1 as follows:

5.58d2z̃dt2 1 13600z̃ 5 f̃z (1)

where z̃ and f̃z are incremental vertical positionand force, respectively. However, because thisequilibrium is unstable in the lateral direction (in

Figure 1 Perspective view of the magneticallylevitated stage; the motor forces acting on eachmagnet array are shown as arrows; the statorsare labeled I through IV

Kim and Trumper: High-precision magnetic levitation stage

67PRECISION ENGINEERING

the y-direction in the figure), we need active feed-back control to stabilize the motion of the platenaround this dynamic equilibrium. Conceptually,we can control the magnitude of the vertical forceby changing the magnitude of the stator currents,and control the lateral force by commutation. SeeKim,1 and Trumper et al.2 for more details. This

two-force linear levitation motor can be consid-ered as a technical building block that can beapplied to a wide range of new positioning sys-tems.

The four motors in Figure 1 collaborativelygenerate all six-degree-of-freedom motions forfocusing and alignment and large two-dimen-

Figure 2 Photograph of high-precision magnetic levitation stage for photolithography; the stage is drivenby the four stators attached to the optical table; the laser source and optics can be seen to the left and behindthe stage; the three laser paths reflect off the stick mirrors housed in the black assembly on top of the stage;the vertical posts act as mechanical stops

Figure 3 Suspension of the platen in dynamic equilibrium; the peaks of the stator currents are indicated asdots and crosses; the corresponding north and south poles are shown


68 APRIL 1998 VOL 22 NO 2

sional (2-D) step and scanning motions for suchhigh-precision positioners as a wafer stepperstage in semiconductor manufacturing. Two ofthe motors (I and III) drive the stage in thex-direction, and the other two (II and IV), in they-direction. The motor forces are coordinatedappropriately to control the remaining degreesof freedom.

Parameters and specifications

For our three-phase permanent magnet linear mo-tors, the parameters have the following values:magnet remanence, m0M0 5 1.29 T, pitch l 5 25.6mm, and the nominal motor air gap z0 5 250 mm.The magnet array thickness is D 5 l/4, and thewinding thickness is G 5 l/5.

To drive the motors, we implement lineartransconductance power amplifiers, with maxi-mum current and voltage ratings of 61.5 A at 622V.1 The nominal power dissipation per motor re-quired to carry the stage weight is 5.4 W at the0.5-A nominal peak phase current. The total sus-pension power coefficient of the stage is, thus, 7.2mW/N 2. The resistance and the self-inductance ofone phase winding are 14.4 V and 3.44 mH, re-spectively.

Instrumentation

Control algorithms are implemented digitally in aPentek 4284 board based on the Texas InstrumentTMS320C40 digital signal processor. A RadiSys80486-100 MHz VME PC takes care of the userinterface, such as monitoring levitator state vari-

ables and command interpretation. The PC andthe digital signal processor communicate witheach other over the VMEbus using dual-portshared RAM residing on the Pentek 4284 board.On the VMEbus exist three channels of Hewlett-Packard 10897A laser axis boards for horizontalmotions and a DATEL DVME-622 12-bit digital-to-analog (D/A) converter board. There is a MIXbuslocal to the digital signal processor connected to aPentek 4245 16-bit analog-to-digital (A/D) con-verter board.

We have three ADE 3800 systems includingthree ADE 2810 capacitance probes for verticalmotions. The output ranges of the ADE 3800systems are modified to be 67.5 V to match theinput voltage swing of Pentek 4245 A/D con-verter board. This maximizes the position sensi-tivity. The zero point of the gauging system is setat the 450-mm air gap between the top surfaces ofADE 2810 capacitance probes and the targets onthe bottom side of the platen. The scale factor(displacement-to-voltage ratio) is determined bythe sensing range that is 200 mm–700 mm. Theair gaps between the capacitance probes andtheir targets are nominally 500 mm. The air gapsbetween the stator windings and the magnet ar-rays are nominally 250 mm. Because the nominalsensor air gap subtracted by the motor air gap(250 mm) is larger than the minimum of thecapacitance probe sensing range (200 mm), thesystem metrology functions properly, even whenthe magnets on the platen are in contact with thestators, which is the case at start-up. Thus, the

Figure 4 Discrete-time lead-lag compensators with decoupling transformation



stage can properly levitate from a power-off con-dition, because the probe signals are “live” overthe whole allowed travel range. In the followingsection, we describe the real-time control of themagnetic levitator.

Real-time digital control

Initial testing procedure

Because vertical modes are stable at the opera-tion point we set, it is a proper approach toattempt to close the vertical control loop first.

We mechanically confine the unstable lateral mo-tions for the initial vertical motion testing. Thisconfinement is achieved with Mylar tapes to fixfour corners of the top surface of the platen withrespect to the eight bumper posts (visible in Fig-ure 2). Because the nominal lateral forces at theoperation point (a dynamic equilibrium) arezero, the tapes have only to withstand small per-turbation forces and lateral forces caused by mis-placement of the platen from the equilibriumpoint resulting from the tape compliance. Thethree-degree-of-freedom vertical modes are es-

Figure 5 5-mm step response in x without decoupling transformation



sentially free from constraint with this scheme.The dynamics attributable to Mylar tapes are veryslow and, thus, negligible. After closing the loopfor the vertical translational motion, the othertwo control loops for rotational motions c and uabout the x- and y-axes respectively, are closed.Finally, we close the other three degrees of free-dom, x, y, and f. In this paper, we follow the xyzconvention, which is commonly used in engi-neering applications, to define Euler angles.6 Forsmall angular motions in our levitator, the Eulerangles c, u, and f can be considered as rotationalangles around x, y, and z-axes, respectively.

Decoupled control

Figure 4 is a block diagram of the decoupled dis-crete-time lead-lag controllers for x and u with A 50.96300, B 5 0.68592, C 5 0.99624, and D 5 1.The gains K for the six axes x, y, z, c, u, and f are2.2261 3 106 N/m, 2.2261 3 106 N/m, 2.3141 3106 N/m, 2.2504 3 104 N/rad, 2.2504 3 104

N/rad, and 3.9804 3 104 N/rad, respectively. Be-cause of the geometric symmetry in x and y of thelevitation system, they have identical gains. Thesame is true for the controllers for c and u. Thesampling rate is 5 kHz.

Figure 6 5-mm step response in x with decoupling transformation



Figure 5 shows a 5-mm step response in x withthese lead-lag compensators without the decou-pling transformation denoted in Figure 4. All thesix-axis controllers are operational in this experi-ment. Note that the platen dynamics are coupledin six degrees of freedom. Because of this cou-pling nature of the platen, there are perturbedmotions in all the other five axes. The step re-sponse also shows that the system has only about20° phase margin as compared with a design valueof 45°, and this response shows correspondinglymore ringing compared with the computer simu-lation.

This phenomenon of the loss of phase marginoriginates from an unmodeled coupling effect. Spe-cifically, the center of mass of the platen is not onthe plane that encloses the actuation points offorces of the linear motors. Thus, any linear motionin the x-direction, for example, generates perturbedrotational motion around the y-axis. It is the reasonFigure 5 shows large angular position fluctuations inu, the rotation around the y-axis. We calculated thevertical offset of the platen center of the mass. It isabove the actuation plane by 33.4 mm. It is not easyto model these couplings exactly, but we can at leastcorrect this deterministic perturbation by subtract-

Figure 7 Positioning noise in all six axes



ing the erroneous torque around the y-axis that isthe linear force in the x-direction multiplied by the33.4-mm moment arm, as indicated in Figure 4. Theperturbed torque around the x-axis is correctedlikewise. Figure 6 shows another 5-mm step responsewith this decoupling transformation implementedwith the same lead-lag compensators above. We cansee that the perturbed motions in other axes andthe ringing are significantly decreased. It shows nowa typical step response of a second-order system withdamping ratio, z 5 0.5 as designed.

Test results

We provide test results of positioning noise, smallrepetitive steps, and fast large steps of the mag-netic levitation stage in this section.

Positioning noise

Figure 7 shows the position regulation result usingthe decoupled lead-lag controllers designedabove. The platen’s position is held at the origin inthe global coordinate frame. The positioningnoises in x- and y-axes are on the order of 5 nmrms. The positioning noise in f is 0.05 mrad rms.The vertical displacement z shows a 70-nm posi-tion error envelope, which is about 10-nm-orderrms positioning noise. The A/D converter elec-tronics noise is primarily responsible for the in-creased positioning noise in z, relative to x and y,which are measured with subnanometer resolu-

tion by means of our laser interferometer system.The A/D quantization levels of 7.6 nm per leastcount are visible in the z data. This is far coarserthan the interferometer channels’ least count of0.6 nm.

The test result in Figure 7 also has a domi-nant 120-Hz noise. Lab floor vibration caused bya large transformer in the lab, or heating, venti-lation, and air-conditioning (HVAC) equipmentlocated in the next room is believed to generatethis noise. Figure 8 shows a power spectrum of thefloor vibration effect as measured with an accel-erometer on the top surface of the optical tablevisible in Figure 2. The floor vibration of our labalso includes other lower frequency componentsat 7.5, 8, 15, and 28 Hz. A more detailed trace ofthis floor vibration can be found in Ludwick.7This vibration is attenuated by an air spring iso-lation system, but is still dominant in the errormotions.

50-nm repetitive steps

Figure 9 shows 50-nm repetitive steps in x. Thistest result clearly shows that the resolution of thestage is better than 10 nm. Thus, the resolutionversus the travel range is better than one part in5 million in the x-y plane. The stage shows nohysteretic error, because it is free from slidingfriction.

Figure 8 Power spectrum of the floor vibration effect as transmitted through the optical table



20-mm steps

To demonstrate our stage’s motion capability, wepresent double 20-mm steps in y in Figure 10. Weaccelerate the platen at 1 g (10 m/s2) until itsvelocity reaches the maximum slew rate of 200mm/s of the laser head we use. The platen movesat this constant velocity for 80 ms and is deceler-ated at 1 g. This motion trajectory is typically re-ferred to as a trapezoidal velocity profile. So, a20-mm step command completes in 120 ms.

Figure 10 also shows the dynamic couplingeffect to the other five degrees of freedom dur-ing the 20-mm steps in y. In the future, bettermodeling of the coupled dynamics with accurateestimations of the platen center of mass androtational inertias will be required to minimizeerroneous forces and torques in other axes. Twoerror motion profiles in each axis beginning atabout t 5 0 s and t 5 0.4 s are almost identical,as should be the case given the identical refer-ence changes at these two times. The small dif-ference between the two most likely originatesfrom the nonuniformity of the stator fabrication,because the platen has moved 20 mm betweenthe first and second stages.

Figure 11 shows details of the same data pre-sented in Figure 10 from t 5 0.6 s to t 5 1 s. Weagain observe the dominant 120-Hz noise compo-nent described earlier in this section. The presentlead-lag controllers need roughly 250 ms more tobring the errors in all six axes within their steady-state positioning noise level. This settling time canbe reduced by control design. First, move thedominant closed-loop pole more deeply into theleft half s-plane by sacrificing phase margin bymoving the lag zero to the left in the s-plane.Second, increase the whole closed-loop systembandwidth, which is limited by system structuralresonances. Fine-tuning of the controllers to opti-mize dynamic performance is another area forfollow-on work.

Demonstrations

We have also demonstrated that the stage cangenerate motions typical of a wafer stepper. Theplaten makes step-and-settle motions describedabove in the positive y-direction, steps over in thepositive x-direction, makes step-and-settle mo-tions in the negative y-direction, and so on. Theplaten can also follow a circle with 30-mm diam-

Figure 9 50-nm repetitive steps of stage in x-direction



eter in 1 second. The purpose of this demonstra-tion is to show this magnetic levitation system cangenerate user-specified 6-axis motions with pre-determined paths having large travel in theplane.

Conclusions

We have designed and implemented the world’sfirst flying puck, high-precision, six-degree-of-free-dom, magnetic levitator with large 2-D motioncapability for photolithography in semiconductormanufacturing. The magnetically levitated platen

generates all the required small motions for focus-ing and alignments, as well as large planar motionsfor wafer positioning. This magnetic levitationstage can be readily used in a clean room or avacuum chamber, because there is no wear parti-cle generation, and no lubrication is required.This design is also highly suitable for vacuum en-vironments, because the heat generated in themotors is in the fixed frame and, thus, can bereadily removed by material conduction.

Furthermore, there is no backlash, becausethe levitation system uses no intermediate power

Figure 10 20-mm steps in y on a trapezoidal velocity profile



transmission devices such as lead screws. Thanksto the lack of friction or stiction, the positionaccuracy depends primarily upon the fundamen-tal limits of metrology and control. Another ad-vantage is that no fine finishing of surfaces ofmechanical parts, such as for precision bearings, isnecessary. This simplifies the production processand reduces the manufacturing cost.

The magnetic levitation stage has been testedsuccessfully. We implemented decoupled lead-lagdigital controllers in a TMS320C40 digital signalprocessor. The sampling rate of the system is 5kHz. The control loop for the levitator has been

closed at a 50-Hz bandwidth. Important experi-mental achievements include 5-nm rms position-ing noise in x and y, 10-nm rms positioning noisein z, 20-mm steps following 120-ms references, and1-g acceleration. We, thus, have demonstrated thatthis magnetic levitator is a promising candidate asthe high-precision positioning stage in next-gen-eration semiconductor manufacturing.

Acknowledgments

Portions of this work are part of a thesis submittedby W.-J. Kim1 for the Ph.D. in electrical engineer-

Figure 11 Details of the 20-mm steps in y from 0.6 to 1 second to show the fine-settling behavior



ing and computer science at the MassachusettsInstitute of Technology, Cambridge, Massachu-setts. This work is supported in part by a contractfrom Sandia National Laboratories under subcon-tract no. AH-4243 and in part by a scholarshipfrom Korean Ministry of Education to W.-J. Kimand a National Science Foundation PresidentialYoung Investigator Award (DDM-9496102) toD. L. Trumper.

References1 Kim, W.-J. “High-precision planar magnetic levitation.”

Ph.D. thesis, Massachusetts Institute of Technology, Cam-bridge, MA, June 1997

2 Trumper, D. L., Kim, W.-J. and Williams, M. E. “Design andanalysis framework for linear permanent-magnet ma-chines,” IEEE Trans Ind Appl, 1996, 32, 371–379

3 Halbach, K. “Design of permanent multipole magnets withoriented rare earth cobalt material,” Nucl Instrum Meth,1980, 169, 1–10

4 Kim, W.-J., Trumper, D. L. and Bryan, J. B. “Linear-motor-levitated stage for photolithography,” Ann CIRP, 1997, 46,447–450

5 Holmes, M. L., Hocken, R. J. and Trumper, D. L. “A long-range scanning stage (the LORS project),” Proceedings of1997 ASPE annual meeting, October 1997

6 Goldstein, H. Classical Mechanics. Reading, MA: Addison-Wesley, 1980, chap. 4

7 Ludwick, S. J. “Modeling and control of a six degree offreedom magnetic/fluidic motion control stage.” Master’sthesis, Massachusetts Institute of Technology, Cambridge,MA, February 1996



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