Levitation Linear Motors for Precision Positioning

Extended Summary 本文は pp.1345–1351

David L. Trumper Non-member (Massachusetts Institute of Technology, [email protected])

Keywords: magnetic levitation, linear motor, precision positioning

The author has been active in the development of levitation de- actuators typically control six degrees of freedom of a suspended vices for precision positioning during the last 18 years. Principal short-stroke fine positioning platform. In the lithography applica- among the techniques studied has been the use of two-force or levi- tion, the platform payload may be a semiconductor wafer or a reticle tation linear motors. By the term levitation linear motor we mean a bearing the master pattern to be imaged. motor which is capable of creating forces which can be used to in- Long-stroke levitation linear motors typically use periodic mag- dependently control translation in two orthogonal directions. These netic structures. The configuration of such motors is most com- motors have been designed into stages for precision positioning in monly an iron-free permanent magnet array in the Halbach con- lithography, scanned probe microscopy, and other precision mea- figuration which is driven by an iron-free multiphase coil set. By surement systems. In such devices, the use of levitation linear mo- properly choosing the phase drive currents, forces in levitation and tors allows the control of six stage degrees of freedom to nanometer translation can be controlled. The key physical insight in the design resolution with a single moving part. of such levitation linear motors is that coil currents can be located This paper presents an overview of the operating principles, elec- in the spatially varying field of a magnet array so as to provide inde- tromagnetic configurations, and system level performance of levi- pendently controllable levitation and translation forces. While there tation linear motors for precision applications, with connections to are a number of possible magnet array configurations, the four-block the large body of literature in this research area. We classify motion Halbach array mounted to a nonmagnetic backing plate is most com- systems with travel under about 10 mm as short-stroke, and devices monly used. with travel larger than about 10 mm as long-stroke. Short-stroke The paper presents the governing physics of such levitation lin- multiaxis drives typically use single-pole magnetics, whereas long- ear motors, and shows their use in a number of example systems. stroke devices typically use multipole periodic magnetic structures. We also present configurations of levitation linear motors for low The reason for this is that the magnetic flux return structures for stray field environments such as electron beam lithography. The single-pole devices become prohibitively large as the stroke length usual planar configuration can also be repackaged in a tubular de- increases. The paper discusses both classes of levitation systems. sign. Related stages use levitation linear motors in association with There are a number of physical principles by which levitation a checkerboard magnet array. Here the levitated stage carries 4 sets motors can operate. These include the main machine types of vari- of three phase coils which are used to move in the vicinity of an able reluctance, electromagnetic induction, and permanent magnet. x-y checkerboard magnet array. The 4 sets of coils are used to pro- Of these, for precision positioning, the bulk of practice has utilized duce 8 controllable forces to thereby control the six stage degrees of permanent magnet devices, with many of these being air-core (pure freedom. Lorentz-type) actuators. Some reasons for this preference for per- In summary, the paper provides a historical overview of the de- manent magnet devices are presented. Given this predominance, the velopment of magnetically levitated precision positioners, with a paper focuses on levitation linear motors of the permanent magnet focus on those using levitation linear motors. As of 1990 this was type. a relatively new approach for the precision engineering community, Short-stroke levitation linear positioners generally use sets of but these types of magnetic suspensions have begun to see wider ap- single-force Lorentz actuators (voice coils) configured so as to ac- plication. There is a parallel history in the use of linear motors: as tuate in multiple degrees of freedom. A ubiquitous example is the little as two decades ago, linear motors were a specialty item, but in compound focus/track actuator for the lens in CD and DVD drives. the intervening years, their use has become routine. This has been The actuator for this compound motion is typically a pancake type facilitated by advances in capability and by cost reductions in mate- coil in which the main voice coil used for focus has smaller coils rials and electronics. We can forsee a similar curve coming into play glued onto it which are used for track following. Related short- for the application of magnetic levitation techniques, and in partic- stroke devices have also been used in robotics and in semiconduc- ular the use of linear motors to both translate and levitate a moving tor lithography. In these applications, six independent voice coil platform.

–13– Paper

Levitation Linear Motors for Precision Positioning

∗ David L. Trumper Non-member

The author has been active in the development of levitation devices for precision positioning during the last 18 years. Principal among the techniques studied has been the use of two-force or levitation linear motors. These motors have been designed into stages for precision positioning in lithography, scanned probe microscopy, and other precision measurement systems. In such devices, the use of levitation linear motors allows the control of six stage degrees of freedom to nanometer resolution with a single moving part. This paper presents an overview of the operating principles, electromagnetic configurations, and system level performance of levitation linear motors for precision applications. The configuration of such motors is most commonly an iron-free permanent magnet array in the Halbach configuration which is driven by an iron-free multiphase coil set. By properly choosing the phase drive currents, forces in levitation and translation can be controlled. This opens possibilities for novel positioning system configurations and performance capabilities.

Keywords: magnetic levitation, linear motor, precision positioning

alternative, electromagnetic induction devices, of necessity 1. Introduction dissipate power on the moving platform, which is disadvanta- This paper gives an introduction to levitation linear mo- geous in a precision machine. Further, it is difficult to control tors and their application for precision positioning systems. an induction machine to achieve accurately-controlled forces By the term levitation linear motor we mean a motor which as a function of time, since the machine inherently operates is capable of creating forces which can be used to indepen- with an AC drive signal on its multiple phases. Balanced ma- dently control translation in two orthogonal directions. chine operation can minimize but not eliminate this AC force While there are configurations for capacitive linear motors, signature associated with induction machines. For these rea- the focus of this paper is on magnetic linear devices. The reasons this paper concentrates on permanent magnet machines. son for this is that the capacitive duals of magnetic drives are For other applications, such as transportation or general of much lower force density and so are not of direct inter- manufacturing processes, the alternate motor types are of est for most macroscopic applications; magnetic drives dom- greater interest. The main type of levitation which has been inate at the macro-scale. However, capacitive levitation mo- researched for maglev trains is based upon magnetic induc- tors may be of greater interest in microscale devices. tion caused by train-borne superconducting magnets acting In this paper, we classify motion systems with travel un- upon fixed coils in the track. The most significant current der about 10 mm as short-stroke, and devices with travel development of this technology is in Japan, at the Yamanashi larger than about 10 mm as long-stroke. Short-stroke mul- maglev test track which operates full-size train sets (9) capable tiaxis drives typically use single-pole magnetics, whereas of carrying passengers. The Yamanashi test track is the ba- long-stroke devices typically use multipole periodic mag- sis for plans for commercializing this technology in revenue netic structures. The reason for this is that the magnetic flux service, perhaps within the next decade. In this maglev de- return structures for single-pole devices become prohibitively sign, the superconducting magnets also provide field excita- large as the stroke length increases. The paper discusses both tion for the linear synchronous motor which drives the train. classes of levitation systems. Permanent magnets cannot achieve the high fields at large There are a number of physical principles by which lev- air gaps associated with superconducting magnets and thus itation motors can operate. These include the main ma- are not competitive for induced levitation for trains. How- chine types of variable reluctance, electromagnetic induction, ever, such levitation designs for transportation represent their and permanent magnet. Of these, for precision positioning, own specialty, with requirements quite distinct from those for the bulk of practice has utilized permanent magnet devices, nanometer-level motion control, and so we do not consider with many of these being air-core (pure Lorentz-type) actua- these types of motors further in this paper. tors. Variable reluctance devices tend to have large attraction Variable reluctance based linear motors have advantages forces in the axis perpendicular to the main axis of travel. of simplicity and ruggedness of construction and have often These large spurious forces make levitation problematic and been used in general motion systems, typically in association also make it difficult to achieve accurate control along with with air bearing support. Levitated versions of such machines vibration minimization in a precision machine. The second can be designed to simultaneously control short-stroke levitation along with long-stroke positioning. A good example ∗ Massachusetts Institute of Technology Cambridge, MA, 02139, U.S.A. is the linear levitated variable reluctance stage designed by [email protected] Higuchi (11). However, the large gap-normal forces and small

電学論 D，126 巻 10 号，2006 年 1345 air gaps associated with levitated variable reluctance motors lead to fast unstable dynamics in the gap-normal direction and thus they are difficult to precisely control as levitation devices. Variable reluctance levitation, with integral linear motor drives, is used in the Transrapid maglev train (10) designed in Germany. Here, there is a tradeoff between small gaps which are good for levitation efficiency and associated tight track alignment tolerances, which may lead to expensive mainte- nance of the guideway. A maglev train using this technology is now operational at the Shanghai airport in China. The sub-class of permanent magnet flux-steering linear Fig. 1. Two-force linear actuator for CD lens focus and (7) motors referred to as Sawyer motors can be loosely clas- track-following. The main drive coil (focus) is labeled sified with the pure variable-reluctance devices. These mo- 5, and the pancake coils (track following) are labeled 6. tors have been used with air bearings in earlier stages for Figure taken from (1) semiconductor photolithography and in manufacturing applications (8), for example by the Xynetics corporation, but are not well suited to levitation without air bearing support. The Sawyer motors are also challenging to use for highly precise positioning due to the large offset forces which have high spatial frequencies as the stage is scanned, and so are not considered further herein. The main sections of this paper now focus on short-stroke and long-stroke levitation linear motors for precision positioning, with the largest emphasis on the long-stroke devices. Fig. 2. Six axis positioner developed by Hollis for use ff 2. Short-stroke Levitation Linear Motors as a robotic end e ector. Figure taken from (2) Short-stroke levitation linear positioners generally use sets of single-force Lorentz actuators (voice coils) configured so as to actuate in multiple degrees of freedom. A ubiquitous example is the compound focus/track actuator for the lens in CD and DVD drives. The actuator for this compound motion is typically a pancake type coil in which the main voice coil used for focus has smaller coils glued onto it which are used for track following. An example of this configuration can be seen in the patent (1). The configuration of the coil is shown in an image from this patent in Figure 1. Current into plane; arrows show force acting on wire; equal and opposite force on magnet array An innovative 6-axis positioner was developed by Hollis at IBM (2); an image from his patent is shown in Figure 2. Hollis Fig. 3. Forces on currents into the page resulting from interaction with fields from a Halbach array referred to this device as the “Magic Wrist”, and designed it for use as a six-axis robotic end effector. As can be seen in the figure, the wrist consists of six voice-coil actuators con- below, with some sections adapted directly from (14). figured to control the six suspended degrees of freedom. 3.1 Levitation Linear Motor Physics The key phys- Related devices were pioneered for lithography by Dan ical insight in the design of levitation linear motors is that Galburt (3) (4). These designs use voice-coil type actuators to coil currents can be located in the spatially varying field of levitate in six degrees of freedom a platform carrying a semi- a magnet array so as to provide independently controllable conductor wafer. The devices are used to position the wafer levitation and translation forces. For example, consider the during exposure in a lithography machine. four currents (directed into the page) shown below a Halbach array in Figure 3. 3. Long-stroke Levitation Linear Motors While we have shown one particular magnet array in Fig- For long-travel levitation linear motion applications, peri- ure 3, there are a number of magnet array possibilities. Four odic magnetic structures are the norm. Such ideas are de- of these possibilities are shown in Figure 4. In the IAS pa- veloped in the author’s Doctoral thesis research (12) utilizing per (14) we show that the ideal Halbach array is stronger than conventional magnetic arrays interacting with an ironless set the sinusoidal vertical array by a factor of 2, and has zero of stator coils, and first presented in (13). Based upon a sug- magnetic field on the back side of the array. Further, the gestion of the late Dr. Klaus Halbach, the inventor of the Hal- more readily fabricated four block Halbach array has a field bach array, the motor performance was improved by adopting within 90% of the ideal Halbach array. For this reason, we the use of Halbach magnet arrays (5) (6). The physics of these have chosen to work with the four block Halbach configura- arrays and their use in levitation linear motors is presented tion in the levitation linear motors that we’ve designed. It is in (14). Some key results from this paper are summarized also possible to consider more broadly the possible Halbach

1346 IEEJ Trans. IA, Vol.126, No.10, 2006 Levitation Linear Motors for Precision Positioning

component. We further deﬁne γn ≡ |kn|. The stator layer is of thickness Γ, and within this layer the current density is represented by the Fourier series ∞ − jknz J = J˜niye ······························(2) n=−∞

th Fig. 4. Four possible magnet array topologies for use in Here Jñ is the complex amplitude of the n current density levitation linear motors component. The details of the motor fields and forces are developed in (14). A key result from that paper, summarized below, is the motor forces as they depend upon the stator current density. To derive this result, we assume that the stator currents are sinusoidally distributed with a fundamental period of l Fig. 5. Linear levitation motor configuration and thus that Jñ is equal to zero for n ±1. Specifically, we let J˜1 = Ja + jJb,andJ˜−1 = Ja − jJb.Thatis,2Ja is the peak phase A current density and 2Jb is the peak phase B current density. We also assume that the magnet array is a four-block Halbach array of the form C in Figure 4 and that permanent magnets have a uniform magnetization of M0. Under these assumptions, the forces acting on one spatial period of the magnet array can be shown to be λ − γ γ Fx −γ1 xo sin 1zo cos 1zo Ja = µo MoGe Fzλ cos γ1zo sin γ1zo Jb ···················· (3) Fig. 6. Idealized linear levitation motor geometry for analysis where Fxλ and Fzλ are the x-directed and z-directed forces per spatial wavelength, respectively. Here µo Mo is the rema- nence of the permanent magnets ( 1.2 T for neodymium- configurations with varying horizontal and vertical propor- iron-boron). The constant tions vis-a-vis conventional iron-based magnet arrays. This √ is a main subject of the Ph.D. thesis of John Ofori (22);his 2 2wl −γ Γ −γ ∆ ffi G = (1 − e 1 )(1 − e 1 ) ················(4) design interest therein is power e cient motors for electric π2 vehicle propulsion. With this perspective in hand, the configuration of a pos- contains the effects of the motor geometry. The x0 and z0 de- sible levitation linear motor might be as shown in Figure 5. pendencies have been explicitly retained since these variables Here a four block Halbach array is levitated above a multi- represent motion of the magnet array relative to the stator. phase set of stator coils. For the purposes of control, the motor commutation laws This motor configuration can be represented by an ideal- can then be derived by inverting (3) to yield ized geometry, as shown in Figure 6, which is suitable for γ 1 xo − γ γ analytical derivation of the motor fields and forces. Here Jas = e sin 1zo cos 1zo Fxd µ γ γ the motor is assumed to have a depth of w into the paper Jbs o MoGNm cos 1zo sin 1zo Fzd and to extend indefinitely in the ±z direction. Edge effects ···················· (5) in the y-direction are ignored in this analysis so that a two- dimensional model is applicable. The stator is fixed in the where Nm is the number of spatial periods l of the magnet ar- laboratory frame x, y, z (Y-slide motions are ignored herein). ray which interact with the stator. Here Fxd and Fzd are sig- The primed coordinate frame x, y, z is fixed in the layer of nals that exist within the controller and represent the forces magnetization, and is displaced from the unprimed frame by the controller is requesting to act on the entire motor in the x and z directions respectively. The signals Jas and Jbs are the the vector (x0 +Γ)ix + z0iz. Here vector quantities are represented by an overbar. current densities which are calculated to achieve the desired The magnetization layer is of thickness ∆, and within this forces. If the analytical model (3) is accurate, then the com- layer the magnetization is represented by the Fourier series mutation laws (5) linearize and decouple the plant. The paper also presents results for power-optimization of ∞ − jk z the motor parameters. This paper serves as the analytical M = M˜ v i + M˜ i e n ················· n x hn z (1) foundation for many of the motor designs presented below. =−∞ n To put levitated stages in context, it is also instructive to study th Here M˜ vn and M˜ hn are the complex amplitudes of the n linear motor driven stages supported on air bearings such as vertical and horizontal Fourier magnetization components, those presented by Gao (39) (40) along with novel two dimen- respectively. Assuming that the spatial period of the array sional surface encoders (41) (42) which are used to measure the th is l,thenkn = 2πn/l is the wavenumber of the n Fourier stage position.

電学論 D，126 巻 10 号，2006 年 1347 Fig. 7. Flying puck stage designed by Kim. Four levitation linear motors control all six degrees of freedom

3.2 The Flying Puck Stage The author worked with Doctoral student Won-jong Kim (30)–(33) on the design of linear motor levitated stages for photolithography. The designed stage is referred to as the Flying Puck, since it consists of a Fig. 8. The Long-Range Scanning Stage (LORS) de- single-part levitated stage, reminiscent of a hockey puck, as signed by Michael Holmes in his Doctoral thesis, shown in Figure 7. This moving stage has four Halbach ar- later rechristened the Sub-Atomic Measuring Machine rays mounted on its bottom surface. Each of these arrays has (SAMM) as new measurement probes were added by an associated stator coil set mounted in the fixed frame; each Chunhai Wang stator/magnet array set is capable of producing levitation and translation forces as indicated by the arrows in the figure. All bottom of the chamber as shown in the figure. These four levitation forces point in the vertical (z) direction; two of the motors drive four corresponding magnet arrays on the lev- motor translation forces point in the x-direction, and two of itated stage, utilizing the same physics, and essentially the these forces point in the y-direction. This arrangement yields same configuration as in Kim’s stage discussed above. Thus a set of 8 forces which can be coordinated to control all 6 there are 8 forces to control the six stage degrees of freedom. stage degrees of freedom. The stage motion is measured in 3 The advantage of floating the stage in oil is to minimize rel- degrees of freedom (z, θx,andθy) by capacitance gages and ative vibration between the stage and housing, and to reduce in 3 degrees of freedom (x, y,andθz) by laser interferometer. the power consumption of the linear motors by offloading the More recently, Kim has continued to study magnetically platen weight. This configuration is ideally suited to the slow levitated six-axis positioners. The short-stroke devices re- scanning motions of the SAMM stage. ported in (34), (35) use six Lorentz actuators with the coils With the linear motor drives, the stage has a working vol- in the fixed frame and the magnets mounted on the moving umeof50mmby50mminthe x-y plane, and travel out of stage. the plane of 100 µm. This makes the stage well-suited to ac- 3.3 The Sub-Atomic Measuring Machine (SAMM) curate measurements of samples located on the stage. In the At UNC-Charlotte, Michael Holmes worked with the au- first implementation, Holmes used a scanning tunneling mi- thor (23), developing an instrument which was called the croscope for sample feature measurement. Angstrom Machine. This device used magnetic suspension Follow-on work by Dr. Chunhai Wang (29) and Prof. Robert to move a platen floated in fluid at neutral bouyancy to pro- Hocken replaced the scanning tunneling microscope with vide travel in a cube of 100 µm, with an ultimate positioning a confocal microscope specialized for the measurement of noise floor on the order of 50 pm RMS. This stage was used cross-shaped artifacts on a photomask, and this sample was to move a sample under the probe of a scanning tunnelling used for intercomparison with measurements taken at the microscope, and thereby to achieve atomic-resolution images German national standards laboratory (PTB), achieving an with the stage in suspension (24)–(26). agreement on the order of 25 nm. We expect that better agree- This Master’s thesis work demonstrated the utility of com- ment can be achieved in the future, with one of the main bined magnetic/fluid suspension, and led (27) to the design of a challenges being standardizing measuring techniques at such longer-range stage which might be used for precision dimen- high accuracy requirements. sional measurement of objects such as integrated circuits and The SAMM stage continues to be operated by Prof. Robert photomasks (28). The stage which was developed is shown in Hocken and his staff at UNC-Charlotte. We are currently an exploded view in Figure 8. This stage is floated in flu- planning a refurbishment of the system along with a con- orosilicone oil as was used in the Angstrom Stage, but the troller upgrade to replace the original digital signal pro- stage drives are four levitation linear motors located at the cessing board and interferometer interpolation electronics

1348 IEEJ Trans. IA, Vol.126, No.10, 2006 Levitation Linear Motors for Precision Positioning

Fig. 9. Magnetically levitated stage designed by Williams for EUVL; figure taken from (18) Fig. 10. Linear motor levitated stage; bottom view showing magnet arrays. Figure taken from (19) designed by Mike Holmes. 3.4 Levitation Stage Using Checkerboard Magnet Ar- ray Another type of levitation linear motor capable of 6 degree of freedom positioning was developed by John Compter (43). In this work the levitated stage carries 4 sets of three phase coils which are used to move in the vicinity of an x-y checkerboard magnet array. The 4 sets of coils are used to produce 8 controllable forces to thereby control the six stage degrees of freedom. This paper is the first which identifies the parasitic torques associated with the levitation linear motor topology. That is, as the motor is levitated and positioned during a scanning motion, the required levitation currents also can produce torques about vectors lying in the plane of the motor. These undesired torques become important in a device intended for rapid positioning and settling tasks, as they form a disturbance on the stage angular po- Fig. 11. Linear motor levitated stage stator with stage removed. This view shows the five liquid-cooled stators sition; the larger the drive forces, the larger these torques which drive the magnet arrays. Figure taken from (19) become. The use of such stages in manufacturing and photolithography applications is presented in the patent (44). 3.5 Extreme UV Lithography Stage Dr. Mark and a Halbach magnet array fixed to the bottom of the stage. Williams started working with the author at UNC-Charlotte, Although this motor in the EUVL stage is capable of levita- moved with the author to MIT, and completed his Doctorate tion forces, since levitation is handled by conventional vari- at MIT in 1998 (15). His thesis considered the design of preci- able reluctance magnetic bearings, the motor is driven for sion stages for photolithography (16), including the use of Hal- pure tanslation forces by choice of the commutation laws. bach array based motors of designs such as those discussed The cable feed 34 to the levitated stage is managed by a sec- above. An example of the types of stages he designed can be ondary carriage which rides on linear guides 32. The sec- found in the patent (17). ondary carriage has its own magnet array which is driven by Following the completion of his Ph.D., Dr. Williams began separately controlling sections of the linear motor coils 22. working on a stage for use in vacuum for motions of the wafer A purely linear motor levitated stage designed by Dr. and reticle in Extreme Ultraviolet Lithography (EUVL). The Williams is described in the patent (19). The stage and sta- stage design which was used in the EUVL system is docu- tor assembly for this machine are shown in Figures 10 and mented in (18); a drawing from this patent is shown in Fig- 11. As shown in Figure 10, the bottom of the stage has three ure 9. In this figure, the lower stage 10 is of a conventional magnet array sets 36 a,b,c. Further the sides of the stage design driven by a ball screw 28 and motor 78. The stage each have corresponding magnet array sets 36 d,e. Each of rides on four rolling-element linear guides to effect motion in these magnet arrays interacts with a corresponding linear mo- the x-direction. This lower stage is in the shape of a beam tor stator 70 a, b, c, d, e to provide scanning and levitation oriented in the y-direction. The cable feeds to the lower stage forces. Taken in sets, the linear motors all contribute to the can be seen as the loop at the left end of the beam. The upper x-directed main scanning motion, and to the control of the (y-travel) stage is magnetically levitated off this beam with other 5 degrees of freedom of the levitated stage. The stators variable reluctance actuators mounted on the towers seen de- have provisions electrical connections and for water cooling, scending at the corners of the stage. The steel rails for these via the connectors shown at the end of each stator. magnetic levitation actuators are mounted in the slots visi- 3.6 Low Stray-field Levitation Linear Motors Paul ble on the near edge of the beam, and in similar slots on the Konkola’s Master’s thesis work (36)–(38) focused on the principle far edge of the beam. The upper stage is driven in the y- that since the motor far-field magnetic stray is dominated by direction by a linear motor with coils 22 fixed in the beam, the lowest order multipole in the array field expansion, low

電学論 D，126 巻 10 号，2006 年 1349 3.7 Tubular Linear Motors Halbach arrays can also be configured as a cylinder, as shown in Figure 13 which is taken from (14). A tubular linear motor utilizing such a cylindrical Halbach array was developed by Berhan in his Mas- ter’s thesis (20) and further reported in (21). This tubular motor utilized annular coils in the fixed frame wound on an alu- minum cylinder, and an interior Halbach cylindrical magnet array moving on the driven stage. It is also possible to design a levitation linear motor in this configuration where the stator coils are broken up into three circumferential segments and are thereby capable of providing forces in the two lateral dimensions in addition to the main axial thrust. 4. Conclusions This paper has provided a historical overview of the development of a number of magnetically levitated precision Fig. 12. Low stray field magnet array topology devel- positioners, with a focus on those using levitation linear mo- oped by Konkola for use in applications such as e-beam lithography requiring low stray fields. Arrows show mag- tors. As of 1990 this was a new approach for the precision netization direction in permanent magnet blocks engineering community, but these types of magnetic suspensions have begun to see wider application. There is a parallel history in the use of linear motors: as little as two decades ago, linear motors were a specialty item, but in the intervening years, their use has become routine. This has been facilitated by advances in capability and by cost reductions in materials and electronics. One can forsee a similar curve coming into play for the application of magnetic levitation techniques, and in particular the use of linear motors to both translate and levitate a moving platform. Acknowledgment First, my thanks to the many students who have con- tributed to the work discussed above; space limitations pre- clude mentioning them all. Thanks also to Prof. Robert Hocken of UNC-Charlotte who collaborated on a number of these projects. Portions of this work were supported by the Fig. 13. Concept for a cylindrical Halbach array which U.S. National Science Foundation under several contracts, by can be used in a tubular linear motor the U.S. Government, Sematech, the Geophysical Corpora- tion of America (GCA), Integrated Solutions, Inc. (ISI), E- stray fields at a given distance are best achieved by eliminat- Tech Corp., and by internal MIT funds. ing the lowest-order multipoles from the array field. Such (Manuscript received Nov. 29, 2005, cancellation was achieved by superposition of multipoles in revised May 17, 2006) successive segments of the magnetic array. The resulting magnet array appears as shown in Figure 12. Because rare earth permanent magnets with magnetization References density M can be modeled as an equivalent lateral surface 6 ( 1 ) H. Kano: “Optical Pickup Apparatus of Thin Type with Magnetic Circuit”, current on the order of 10 A/mviaJeq = ∇×M,theyare U.S. Patent #6,285,644 (2001) far more important in a stray field sense than typical air core ( 2 ) R.L. Hollis, Jr.: “Magnetically Levitated Fine Motion Wrist with Pro- motor windings, which might have an equivalent surface cur- grammable Compliance”, U.S. Patent #4,874,998 (1989) rent an order of magnitude or more smaller. Nonetheless, the ( 3 ) D.N. Galburt: “Microlithographic Apparatus”, U.S. Patent #4,952,858 (1990) stray field from the stator coils needs to be considered as part ( 4 ) D.N. Galburt and G. O’Connor: “Wafer Stage with Reference Surface”, U.S. of minimizing the total motor stray flux. Konkola’s motor de- Patent #5,285,142 (1994) sign terminated the stator with half current-density windings ( 5 ) K. Halbach: “Design of Permanent Multipole Magnets with Oriented Rare at each end in order to reduce the far-field effect. Earth Cobalt Material”, Nuclear Instruments and Methods, 169, pp.1–10 (1980) Konkola’s design calculations indicate that it should be ( 6 ) K. Halbach: “Physical and Optical Properties of Rare Earth Cobalt Magnets”, −7 possible to achieve lower than 2 × 10 T stray field at a dis- Nuclear Instruments and Methods, 187, pp.109–117 (1981) tance of 150 mm from the motor air-gap plane. This stray ( 7 ) B.A. Sawyer: “Magnetic Positioning Device”, U.S. Patent #3,457,482 (1969) field would be compatible with electron beam lithography re- ( 8 ) E.R. Pelta: “Two-Axis Sawyer Motor for Motion Systems”, IEEE Control Systems Magazine (1987-10) quirements. Experimentally-measured stray fields are about ( 9 ) M. Ono, S. Koga, and H. Ohtsuki: “Japan’s Superconducting Maglev Train”, a factor of 10 larger; this discrepancy is believed to be primar- IEEE Instrumentation and Measurement Magazine, pp.9–15 (2002-3) ily due to dimensional and magnetization angle tolerances in (10) P. Holmer: “Faster than a speeding bullet train”, IEEE Spectrum,Vol.40, the permanent magnet blocks. No.8, pp.30–34 (2003-8)

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(11) T. Higuchi: “Linear Stepping Motor”, U.S. Patent #4,689,529 (1987) (32) W.-J. Kim and D.L. Trumper: “High-Precision Magnetic Levitation Stage for (12) D.L. Trumper: “Magnetic Suspension Techniques for Precision Motion Con- Photolithography”, Precision Engineering, Vol.22, No.2, pp.66–77 (1998-4) trol”, Ph.D. Thesis, Electrical Engineering and Computer Science, MIT (33) W.-J. Kim, D.L. Trumper, and J.H. Lang: “Modeling and Vector Control of (1990) a Planar Magnetic Levitator”, IEEE Transactions on Industry Applications, (13) D.L. Trumper and M.A. Queen: “Precision Magnetic Suspension Linear Vol.34, No.6, pp.1254–1262 (1998-11/12) Bearing”, NASA Int. Symp. on Mag. Susp. Tech., Hampton, VA, (1991-8) (34) S. Verma, W.-J. Kim, and J. Gu: “Six-axis nanopositioning device with preci- (14) D.L. Trumper, M.E. Williams, and T.H. Nguyen: “Magnet Arrays for Syn- sion magnetic levitation technology”, IEEE/ASME Transactions on Mecha- chronous Machines”, IEEE Industry Applications Society Annual Confer- tronics, Vol.9, No.2, pp.384–391 (2004-6) ence, Toronto, Canada (1993-10) (35) S. Verma, W.-J. Kim, and H. Shakir: “Multi-axis maglev nanopositioner for (15) M.E. Williams: “Precision Six Degree of Freedom Magnetically-Levitated precision manufacturing and manipulation applications”, IEEE Transactions Photolithography Stage”, Ph.D. Thesis, Mechanical Engineering, MIT on Industry Applications, Vol.41, No.5, pp.1159–1167 (2005-9/10) (1998) (36) P. Konkola: “Magnetic Bearing Stages for Electron-Beam Lithography”, (16) M.E. Williams and D.L. Trumper: “Magnetic Bearing Stage for Photolithog- M.S. Thesis, Mechanical Engineering, MIT (1998) raphy”, CIRP Annals, Vol.42, No.1, pp.607–610 (1993) (37) P. Konkola and D.L. Trumper: “Electromagnetic Design of a Low-Fringing- (17) D.L. Trumper and M.E. Williams: “Positioner With Long Travel in Two Di- Field Magnetic Bearing Stage for Electron Beam Lithography”, JSME Inter- mensions”, U.S. Patent #5,699,621 (1997) national Journal, Special Issue on Magnetic Bearings, Series C, Vol.46, No.2 (18) M.E. Williams: “Extreme-UV Scanning Wafer and Reticle Stages”, U.S. (2003-6) Patent #6,353,271 (2002) (38) P. Konkola and D.L. Trumper: “Methods and Apparatus Involving Selec- (19) M.E. Williams: “Magnetic Levitation Stage Apparatus and Method”, U.S. tively Tailored Electromagnetic Fields”, U.S. Patent #6,316,849 (2001) Patent #6,777,833 (2004) (39) S. Dejima, W. Gao, K. Katakura, S. Kiyono, and Y. Tomita: “Dynamic mod- (20) M.T. Berhan, “Implementation of a Halbach Array in a Tubular Linear Mo- eling, controller design and experimental validation of a planar motion stage tor”, M.S. Thesis, Mechanical Engineering, MIT (1996) for precision positioning”, Precision Engineering, Vol.29, Issue 3, pp.263– (21) W.-J. Kim, M.T. Berhan, D.L. Trumper, and J.H. Lang: “Analysis and Imple- 271 (2005-7) mentation of a Tubular Motor with Halbach Magnet Array”, 1996 IEEE-IAS (40) W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita: “A Annual Meeting, San Diego, CA (1996-10) surface motor-driven planar motion stage integrated with an XYθZ surface (22) J. Ofori-Tenkorang: “Permanent-magnet synchronous motors and associated encoder for precision positioning”, Precision Engineering, Vol.28, Issue 3, power electronics for direct-drive vehicle propulsion”, Ph.D. Thesis, Electri- pp.329–337 (2004-7) cal Engineering, MIT (1996) (41) W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka: “Precision (23) M.L. Holmes: “Analysis and Design of a Magnetically-Suspended Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a Motion Control Stage”, M.S. Thesis, Electrical Engineering, UNC-Charlotte surface encoder”, Precision Engineering, Vol.27, Issue 3, pp.289–298 (2003- (1994) 7) (24) M.L. Holmes and D.L. Trumper: “Magnetic/Fluid Bearing Stage for Atomic- (42) W. Gao, S. Dejima, Y. Shimizu, and S. Kiyono: “Precision measaurement of Scale Motion Control”, Precision Engineering, Vol.18, No.1, pp.38–49 two-axis positions and tilt motions using a surface encoder”, CIRP Annals, (1996-1) Vol.52, No.1, pp.435–8 (2003) (25) S.J. Ludwick, D.L. Trumper, and M.L. Holmes: “Modeling and Control of (43) J.C. Compter: “Electro-dynamic planar motor”, Precision Engineering, a Six Degree of Freedom Magnetic/Fluidic Motion Control Stage”, IEEE Vol.28, Issue 2, pp.171–180 (2004-4) Transactions on Control Systems Technology, Special Issue on Magnetic (44) P.C.M. Frissen, J.C. Compter, A.T.A. Peijnenburg, and E.R. Loopstra: “Dis- Bearing Control, Vol.4, No.5, pp.553–564 (1996-9) placement Device”, U.S. Patent #6,879,063 (2005) (26) S.J. Ludwick: “Modeling and Control of a Six Degree of Freedom Mag- netic/Fluidic Motion Control Stage”, M.S. Thesis, Mechanical Engineering, MIT (1996) (27) M. Holmes: “Long-Range Scanning Stage”, Ph.D. Thesis, Electrical Engi- neering, UNC-Charlotte (1998) (28) M.L. Holmes, D.L. Trumper, and R.J. Hocken: “Atomic-Scale Precision David L. Trumper (Non-member) joined the MIT Department of Motion Control Stage (The Angstrom Stage)”, CIRP Annals, Vol.44, No.1, Mechanical Engineering in August 1993, and holds pp.455–460 (1995) the rank of Professor. He received the B.S., M.S., (29) C.-H. Wang, R.J. Hocken, and D.L. Trumper: “Dynamics and Control of the and Ph.D. degrees from MIT in Electrical Engineer- UNCC/MIT Subatomic Measuring Machine”, CIRP Annals, Vol.50, No.1, ing and Computer Science, in 1980, 1984, and 1990, pp.373–376 (2001) respectively. He is a member of the IEEE, ASME, (30) W.-J. Kim: “High-Precision Planar Magnetic Levitation”, Ph.D. Thesis, and ASPE (currently serving as President of ASPE), Electrical Engineering and Computer Science, MIT (1997) is an Associate Editor of Precision Engineering, and (31) W.-J. Kim, D.L. Trumper, and J. Bryan: “Linear Motor Levitated Stage for is a Corresponding Member of CIRP. Photolithography”, CIRP Annals, Vol.46, No.1, pp.447–450 (1997)

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