Systems and methods for magnetically levitated object stages

Abstract

A transport system includes an object stage, two opposing pairs of linear motors, and a controller. The two opposing pairs of linear motors accelerate the object stage along a longitudinal axis and maintain a vertical gap between the object stage and the two opposing pairs of linear motors along a vertical axis. The controller is coupled to the two opposing pairs of linear motors and controls movement of the object stage and the vertical gap. The transport system can include reluctance actuators coupled to the object stage to maintain the vertical gap and a horizontal gap between the object stage and the reluctance actuators by counter-balancing forces generated by the controller. Advantageously the transport system can reduce contamination (avoids gas bearings), reduce parasitic normal forces, reduce cogging, provide low negative stiffness, maintain precise linear control of the object stage, and maintain equal gaps around the object stage during high acceleration.

Description

SYSTEMS AND METHODS FOR MAGNETICALLY LEVITATED OBJECT STAGESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 537,247 which was filed on 8 September 2023 and which is incorporated herein in its entirety by reference.FIELD

[0002] The present disclosure relates to transport apparatuses, systems, and methods, for example, magnetically levitated transport systems and linear motors for lithographic apparatuses and systems.BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern of a patterning device (e.g., a mask, a reticle) onto a layer of radiation-sensitive material (resist) provided on a substrate.

[0004] To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which can be formed on the substrate. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, deep ultraviolet (DUV) radiation with a wavelength of 157 nm or 193 nm or 248 nm.

[0005] Linear motors with gas bearings have been used to control an object stage, but are difficult to implement and can generate contaminant particles in the lithographic apparatus. Further, the complexity of gas bearing solutions is very high and object stage designs using gas bearings in vacuum suffer from stiffness issues. Linear motors based on magnetic levitation avoid the need for gas bearings, provide a low negative stiffness, and support an object stage by magnetic forces without any mechanical contact, thus limiting the generation of contaminant particles.

[0006] However, magnetic levitation systems can suffer from parasitic normal forces, cogging, and instability. At high accelerations, it can become difficult to maintain a correct gap or distance between the object stage and the linear motor. Further, magnetic levitation systems can be unstable due to very large negative stiffness that can cause the system to move sufficiently off center and spontaneously slide or flip.SUMMARY

[0007] Accordingly, there is a need to provide a linear motor transport system based on magnetic levitation to avoid gas bearings, reduce contamination, reduce parasitic normal forces, reduce cogging,provide low negative stiffness, maintain precise linear control and stability of an object stage (e.g., reticle stage), and maintain equal gaps around the object stage during high acceleration.

[0008] In some aspects, a transport system can include an object stage, two opposing pairs of linear motors, and a controller. In some aspects, the object stage can have a longitudinal axis, a transverse axis, and a vertical axis. In some aspects, the two opposing pairs of linear motors can be configured to accelerate the object stage along the longitudinal axis. In some aspects, the two opposing pairs of linear motors can be configured to maintain a vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis. In some aspects, the two opposing pairs of linear motors can include a first pair of linear motors and a second pair of linear motors. In some aspects, the first pair of linear motors can include a first upper linear motor coupled to a top surface of the object stage and a first lower linear motor coupled to a bottom surface of the object stage. In some aspects, the second pair of linear motors can include a second upper linear motor coupled to the top surface of the object stage and a second lower linear motor coupled to the bottom surface of the object stage. In some aspects, the first and second pairs of linear motors can be symmetric about the vertical axis. In some aspects, the controller can be coupled (e.g., electrically) to the two opposing pairs of linear motors. In some aspects, the controller can be configured to control movement of the object stage along the longitudinal axis and control the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis.

[0009] In some aspects, the first upper and lower linear motors are symmetric about the longitudinal axis. In some aspects, the second upper and lower linear motors are symmetric about the longitudinal axis. In some aspects, the first upper and lower linear motors are symmetric about an axis substantially parallel to the longitudinal axis. In some aspects, the second upper and lower linear motors are symmetric about the axis substantially parallel to the longitudinal axis.

[0010] In some aspects, the first upper and lower linear motors are symmetric about a center of mass of the object stage, and the second upper and lower linear motors are symmetric about the center of mass of the object stage. In some aspects, the first upper and lower linear motors are symmetric about a center of gravity of the object stage, and the second upper and lower linear motors are symmetric about the center of gravity of the object stage.

[0011] In some aspects, the controller can be configured to maintain a horizontal gap between the object stage and the two opposing pairs of linear motors along the transverse axis. In some aspects, the first and second pairs of linear motors can extend along the longitudinal axis and can be coupled to transverse distal ends of the object stage. In some aspects, the transverse distal ends of the object stage can have a symmetric shape. In some aspects, the symmetric shape can include an opening angle of about 90 degrees. In some aspects, the symmetric shape can be a right triangle. In some aspects, the object stage can have a hexagonal cross-section along the transverse axis.

[0012] In some aspects, the controller can be configured to control movement of the object stage along the longitudinal axis with a first control loop. In some aspects, the controller can be configured to controlthe vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis with a second control loop. In some aspects, the second control loop can be superimposed on the first control loop.

[0013] In some aspects, the second control loop can be applied when variable magnets of the two opposing pairs of linear motors are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors. In some aspects, the second control loop can be applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.

[0014] In some aspects, the first and second control loops can be configured to operate in a three-phase control scheme. In some aspects, the first and second control loops can be configured to operate in a four-phase control scheme. In some aspects, the first and second control loops can be configured to operate in a five-phase control scheme. In some aspects, the first and second control loops can be configured to operate in a six-phase control scheme. In some aspects, the first and second control loops can be configured to operate in a nine-phase control scheme.

[0015] In some aspects, the transport system can further include a plurality of reluctance actuators. In some aspects, the plurality of reluctance actuators can be coupled (e.g., magnetically) to the object stage. In some aspects, the plurality of reluctance actuators can be configured to maintain the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis. In some aspects, the plurality of reluctance actuators can be configured to apply counter-balancing forces along the vertical axis relative to forces applied along the vertical axis by the controller. In some aspects, the plurality of reluctance actuators can be symmetric about the vertical axis. In some aspects, the plurality of reluctance actuators can be configured to maintain a horizontal gap between the object stage and the plurality of reluctance actuators. In some aspects, the plurality of reluctance actuators can be configured to apply counter-balancing forces along the transverse axis relative to forces applied along the transverse axis by the controller.

[0016] In some aspects, the plurality of reluctance actuators can extend along the longitudinal axis. In some aspects, the plurality of reluctance actuators can be coupled (e.g., magnetically) to transverse distal ends of the object stage. In some aspects, the transverse distal ends of the object stage can have a symmetric shape. In some aspects, the symmetric shape can include an opening angle of about 90 degrees. In some aspects, the symmetric shape can be a right triangle. In some aspects, the object stage can have a hexagonal cross-section along the transverse axis. In some aspects, the transverse distal ends of the object stage can include a soft magnetic material.

[0017] In some aspects, the first upper linear motor can be configured to maintain a first upper vertical gap between the top surface of the object stage and the first upper linear motor. In some aspects, the first lower linear motor can be configured to maintain a first lower vertical gap between the bottom surface of the object stage and the first lower linear motor. In some aspects, the second upper linear motor can be configured to maintain a second upper vertical gap between the top surface of the objectstage and the second upper linear motor. In some aspects, the second lower linear motor can be configured to maintain a second lower vertical gap between the bottom surface of the object stage and the second lower linear motor. In some aspects, the controller can be configured to adjust the first upper and lower linear motors so that the first upper and lower vertical gaps are equal. In some aspects, the controller can be configured to adjust the second upper and lower linear motors so that the second upper and lower vertical gaps are equal.

[0018] In some aspects, forces between the first upper and lower linear motors of the first pair of linear motors can be equal and opposite. In some aspects, forces between the second upper and lower linear motors of the second pair of linear motors can be equal and opposite. In some aspects, a spatial arrangement of the two opposing pairs of linear motors surrounding the object stage can be configured to reduce parasitic normal forces in the first and second pairs of linear motors.

[0019] In some aspects, a linear motor can include a first component, a second component, and a controller. In some aspects, the first component can include an armature having a plurality of magnetic cores surrounded by respective coil windings thereby forming a plurality of variable magnets (e.g., electromagnets). In some aspects, the second component can include a plurality of permanent magnets having alternating polarity. In some aspects, the first and second components can be opposing. In some aspects, the first and second components can be configured to translate relative to one another along a longitudinal axis of the linear motor. In some aspects, the first and second components can be configured to maintain a vertical gap between the first and second components. In some aspects, the controller can be configured to control the vertical gap between the first and second components.

[0020] In some aspects, the controller can be configured to control translation along the longitudinal axis with a first control loop. In some aspects, the controller can be configured to control the vertical gap between the first and second components with a second control loop. In some aspects, the second control loop can be superimposed on the first control loop.

[0021] In some aspects, the second control loop can be applied when variable magnets of the first component are aligned spatially with opposing permanent magnets of the second component. In some aspects, the second control loop can be applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.

[0022] In some aspects, the first and second control loops can be configured to operate in a three-phase control scheme. In some aspects, the first and second control loops can be configured to operate in a four-phase control scheme, a five-phase control scheme, a six-phase control scheme, or a nine -phase control scheme.

[0023] In some aspects, the plurality of magnetic cores can be spaced apart by a magnetic core pitch and the plurality of permanent magnets can be spaced apart by a permanent magnet pitch. In some aspects, a ratio of the magnetic core pitch to the permanent magnet pitch is 1.33 (e.g., three-phase control). In some aspects, the ratio of the magnetic core pitch to the permanent magnet pitch is 1.25(e.g., four-phase control). In some aspects, the ratio of the magnetic core pitch to the permanent magnet pitch is 1.2 (e.g., five -phase control). In some aspects, the ratio of the magnetic core pitch to the permanent magnet pitch is 1.16 (e.g., six-phase control). In some aspects, the ratio of the magnetic core pitch to the permanent magnet pitch is 1.11 (e.g., nine-phase control).

[0024] In some aspects, the plurality of magnetic cores can include a soft magnetic material. In some aspects, the plurality of permanent magnets can be arranged in a Halbach array.

[0025] In some aspects, a lithographic apparatus can include an illumination system, a projection system, a reticle stage, and a transport system. In some aspects, the illumination system can be configured to illuminate a patterning device. In some aspects, the projection system can be configured to project an image of the patterning device onto a patterning substrate. In some aspects, the reticle stage can be configured to support the patterning device. In some aspects, the reticle stage can include a longitudinal axis, a transverse axis, and a vertical axis. In some aspects, the transport system can be configured to translate the reticle stage. In some aspects, the transport system can include two opposing pairs of linear motors and a controller. In some aspects, the two opposing pairs of linear motors can be configured to translate the reticle stage along the longitudinal axis and maintain a vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis. In some aspects, the controller can be coupled (e.g., electrically) to the two opposing pairs of linear motors and configured to control translation of the reticle stage along the longitudinal axis and control the vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis.

[0026] In some aspects, the controller can be configured to control translation of the reticle stage along the longitudinal axis with a first control loop, and control the vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis with a second control loop. In some aspects, the second control loop can be applied when variable magnets of the two opposing pairs of linear motors are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors. In some aspects, the second control loop can be applied to variable magnets in a sequence S„ = 3 / z + l where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.

[0027] In some aspects, a method can include applying a first control loop to two opposing pairs of linear motors to accelerate an object stage along a longitudinal axis of the object stage. In some aspects, the method can further include applying a second control loop to the two opposing pairs of linear motors to maintain a vertical gap between the object stage and the two opposing pairs of linear motors along a vertical axis of the object stage. In some aspects, the second control loop can be superimposed on the first control loop.

[0028] In some aspects, the applying the second control loop can include activating variable magnets of the two opposing pairs of linear motors when variable magnets are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors. In some aspects, the activating variable magnets can include activating variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., suchthat a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.

[0029] In some aspects, the method can further include applying a third control loop to a plurality of reluctance actuators to maintain the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis and to counter-balance forces along the vertical axis from the second control loop. In some aspects, the third control loop can be configured to maintain a horizontal gap between the object stage and the plurality of reluctance actuators. In some aspects, the plurality of reluctance actuators can extend along the longitudinal axis and can be coupled to transverse distal ends of the object stage.

[0030] Implementations of any of the techniques described above may include an EUV light source, a DUV light source, a system, a method, a process, a device, and / or an apparatus. The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.

[0031] Further features and exemplary aspects of the aspects, as well as the structure and operation of various aspects, are described in detail below with reference to the accompanying drawings. It is noted that the aspects are not limited to the specific aspects described herein. Such aspects are presented herein for illustrative purposes only. Additional aspects will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein.BRIEF DESCRIPTION OF THE DRAWINGS / FIGURES

[0032] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the aspects and, together with the description, further serve to explain the principles of the aspects and to enable a person skilled in the relevant art(s) to make and use the aspects.

[0033] FIG. 1 is a schematic illustration of a lithographic apparatus, according to an exemplary aspect.

[0034] FIG. 2 is a schematic cross-sectional illustration of a linear motor, according to an exemplary aspect.

[0035] FIG. 3 is a schematic cross-sectional illustration of a pair of linear motors utilizing the linear motor shown in FIG. 2, according to an exemplary aspect.

[0036] FIG. 4 is a schematic front perspective illustration of a transport system utilizing the pair of linear motors shown in FIG. 3, according to an exemplary aspect.

[0037] FIG. 5 is a schematic front illustration of the transport system shown in FIG. 4.

[0038] FIG. 5A is a schematic front illustration of an alternative transport system utilizing the pair of linear motors shown in FIG. 3, according to an exemplary aspect.

[0039] FIG. 5B is a schematic front illustration of an alternative transport system utilizing angled pairs of linear motors, according to an exemplary aspect.

[0040] FIG. 6 is a schematic diagram of a three-phase control scheme for one or more linear motors, according to an exemplary aspect.

[0041] FIG. 7 is a schematic diagram of a four-phase control scheme for one or more linear motors, according to an exemplary aspect.

[0042] FIG. 8 illustrates a control flow diagram for a three-phase control scheme for one or more linear motors, according to an exemplary aspect.

[0043] FIG. 9 illustrates a control flow diagram for a four-phase control scheme for one or more linear motors, according to an exemplary aspect.

[0044] FIG. 10 illustrates a control flow diagram for the transport system shown in FIGS. 4 and 5, according to an exemplary aspect.

[0045] The features and exemplary aspects of the aspects will become more apparent from the detailed description set forth below when taken in conjunction with the drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and / or structurally similar elements. Additionally, generally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears. Unless otherwise indicated, the drawings provided throughout the disclosure should not be interpreted as to-scale drawings.DETAILED DESCRIPTION

[0046] This specification discloses one or more aspects that incorporate the features of this present invention. The disclosed aspect(s) merely exemplify the present invention. The scope of the invention is not limited to the disclosed aspect(s). The present invention is defined by the claims appended hereto.

[0047] The aspect(s) described, and references in the specification to “one aspect,” “an aspect,” “an example aspect,” “an exemplary aspect,” etc., indicate that the aspect(s) described may include a particular feature, structure, or characteristic, but every aspect may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same aspect. Further, when a particular feature, structure, or characteristic is described in connection with an aspect, it is understood that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other aspects whether or not explicitly described.

[0048] Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “on,” “upper” and the like, may be used herein for ease of description to describe one element or feature’s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly.

[0049] The term “about” or “substantially” or “approximately” as used herein indicates the value of a given quantity that can vary based on a particular technology. Based on the particular technology, the term “about” or “substantially” or “approximately” can indicate a value of a given quantity that varies within, for example, 1-15% of the value (e.g., ±1%, ±2%, ±5%, ±10%, or ±15% of the value).

[0050] The term “movement” or “move” as used herein indicates changing a physical location or spatial position of an object in three-dimensions, for example, an object stage (e.g., object stage 320). In some aspects, the term “movement” or “move” includes translation of an object along an axis or parallel to an axis, for example, a transverse axis (e.g., X-axis), a longitudinal axis (e.g., Y-axis), and / or a vertical axis (e.g., Z-axis). In some aspects, the term “movement” or “move” includes translation by acceleration, deceleration, and / or constant velocity.

[0051] The term “center of mass” or “COM” as used herein indicates a point at which the distribution of mass of an object (e.g., an object stage) is equal in all directions and does not depend on a gravitational field (e.g., Earth’s gravitational field).

[0052] The term “center of gravity” or “COG” as used herein indicates a point at which the distribution of weight of an object (e.g., an object stage) is equal in all directions and does depend on a gravitational field (e.g., Earth’s gravitational field).

[0053] Aspects of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Aspects of the disclosure may also be implemented as instructions stored on a machine -readable medium, which may be read and executed by one or more processors. A machine- readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, and / or instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[0054] Before describing such aspects in more detail, however, it is instructive to present an example environment in which aspects of the present disclosure may be implemented.

[0055] Exemplary Lithographic System

[0056] FIG. 1 shows a lithographic system comprising a radiation source SO and a lithographic apparatus FA. The radiation source SO is configured to generate an EUV and / or a DUV radiation beam B and to supply the EUV and / or DUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT (e.g., a mask table, a reticle table, a reticle stage) configured to support a patterning device MA (e.g., a mask, a reticle), a projection system PS, and a substrate table WT configured to support a substrate W.

[0057] The illumination system IL is configured to condition the EUV and / or DUV radiation beam B before the EUV and / or DUV radiation beam B is incident upon the patterning device MA. Thereto, the illumination system IL may include a faceted field mirror device 10 and a faceted pupil mirror device 11. The faceted field mirror device 10 and faceted pupil mirror device 11 together provide the EUVand / or DUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to, or instead of, the faceted field mirror device 10 and faceted pupil mirror device 11.

[0058] After being thus conditioned, the EUV and / or DUV radiation beam B interacts with the patterning device MA. This interaction may be reflective (as shown), which may be preferred for EUV radiation. This interaction may be transmissive, which may be preferred for DUV radiation. As a result of this interaction, a patterned EUV and / or DUV radiation beam B’ is generated. The projection system PS is configured to project the patterned EUV and / or DUV radiation beam B’ onto the substrate W. For that purpose, the projection system PS may comprise a plurality of mirrors 13, 14 which are configured to project the patterned EUV and / or DUV radiation beam B’ onto the substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV and / or DUV radiation beam B ’ , thus forming an image with features that are smaller than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated as having only two mirrors 13, 14 in FIG. 1, the projection system PS may include a different number of mirrors (e.g. six or eight mirrors).

[0059] The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus LA aligns the image, formed by the patterned EUV and / or DUV radiation beam B’, with a pattern previously formed on the substrate W.

[0060] Exemplary Linear Motor

[0061] As discussed above, linear motors based on gas bearings have been used to control an object stage (e.g., a reticle stage), for example, to position a patterning device in a lithographic apparatus. However, gas bearings (e.g., air bearings) are difficult to implement, especially in vacuum (e.g., EUV lithography) due to pump seals, and can generate contaminant particles in the lithographic apparatus. Linear motors based on magnetic levitation (e.g., linear induction motors, Lorentz motors, linear synchronous motors, etc.) can avoid gas bearings, provide a low negative stiffness, and perform magnetic levitation of an object stage simply by adjusting the load angle as a phase offset in the commutation (e.g., three-phase control).

[0062] However, magnetic levitation systems can suffer from cogging (e.g., resistance to preferred positions of magnetic core design) and instability. At high accelerations, it can become difficult to maintain a correct gap or distance between the object stage and the linear motor. Further, magnetic levitation systems can be unstable due to very large negative stiffness (e.g., due to permanent magnets on object stage) that can cause the system to move sufficiently off center and spontaneously slide or flip. Stable magnetic levitation can be achieved by using a feedback loop (e.g., via a controller) that periodically or continuously adjusts one or more electromagnets to correct motion of the object stage (e.g., a servomechanism).

[0063] Aspects of linear motor apparatuses, systems, and methods as discussed below can avoid gas bearings, utilize magnetic levitation, reduce contamination, reduce cogging, provide low negativestiffness, maintain precise linear control and stability of an object stage (e.g., reticle stage), and maintain an equal gap (e.g., vertical gap) of the object stage during high acceleration.

[0064] FIG. 2 illustrates linear motor 200, according to various exemplary aspects. FIG. 2 is a schematic cross-sectional illustration of linear motor 200, according to an exemplary aspect. Linear motor 200 can be configured to maintain precise linear control and stability of an object stage (e.g., object stage 320) coupled to linear motor 200 (e.g., coupled to second component 240). Linear motor200 can be further configured to maintain an equal gap (e.g., vertical gap 210) of an object stage (e.g., object stage 320) coupled to linear motor 200 (e.g., coupled to second component 240).

[0065] Although linear motor 200 is shown in FIG. 2 as a stand-alone apparatus and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, patterning device MA, pair of linear motors 300, transport system 400, alternative transport system 400', alternative transport system 400", three- phase control scheme 600, four-phase control scheme 700, control flow diagram 800, control flow diagram 900, and / or control flow diagram 1000. In some aspects, linear motor 200 can be part of a lithography apparatus, for example, lithographic apparatus LA. In some aspects, linear motor 200 can be part of a support structure, for example, support structure MT for patterning device MA. In some aspects, linear motor 200 can be part of a pair of linear motors, for example, pair of linear motors 300. In some aspects, linear motor 200 can be part of a transport system, for example, transport system 400.

[0066] As shown in FIG. 2, linear motor 200 can include first section 201, second section 201', third section 201", longitudinal axis 202 (e.g., Y-axis), transverse axis 204 (e.g., X-axis), vertical axis 206 (e.g., Z-axis), vertical gap 210, first component 220, second component 240, and controller 260. In some aspects, linear motor 200 can be configured to accelerate object stage 320 along longitudinal axis 202 (e.g., Y-axis). In some aspects, linear motor 200 can be configured to maintain vertical gap 210 between first component 220 and second component 240 along vertical axis 206 (e.g., Z-axis).

[0067] In some aspects, linear motor 200 can include one or more repeating sections or repeating units, for example, first section 201, second section 201', third section 201", etc., whose operation and functionality are the same and can be extended (repeated) indefinitely to any specific length of linear motor 200 (e.g., along longitudinal axis 202). For example, as shown in FIG. 2, first section 201, second section 201', and third section 201" can be arranged sequentially along longitudinal axis 202 for a three- phase control scheme (e.g., three-phase control scheme 600 shown in FIG. 6), such that each section contains three variable magnets 230a-230c, 230a'-230c', 230a"-230c", etc. The aspects of first section201 of linear motor 200 shown in FIG. 2, for example, and the aspects of second section 201', third section 201", etc. of linear motor 200 shown in FIG. 2 may be similar. Similar reference numbers are used to indicate features of the aspects of first section 201 of linear motor 200 shown in FIG. 2 and the similar features of the aspects of second section 201', third section 201", etc. of linear motor 200 shown in FIG. 2.

[0068] First component 220 can be configured to form a plurality of variable magnets 230a-230c, 230a'-230c', etc. (e.g., electromagnets) to move second component 240 relative to first component 220. First component 220 can be further configured to apply magnetic forces (e.g., periodically, sequentially, continuously) to second component 240 to move (e.g., translate) second component 240 along longitudinal axis 202 (e.g., Y-axis). First component 220 can be further configured to apply magnetic forces (e.g., periodically, sequentially, continuously) to second component 240 to move (e.g., translate) second component 240 along vertical axis 206 (e.g., Z-axis) to maintain vertical gap 210 between first and second components 220, 240.

[0069] As shown in FIG. 2, first component 220 can include armature 222, magnetic cores 224a-224c, 224a'-224c', etc. (e.g., teeth), and coil windings 228a-228c, 228a'-228c', etc. Magnetic cores 224a-224c, 224a'-224c', etc. can be surrounded by respective coil windings 228a-228c, 228a'-228c', etc. that are coupled (e.g., electrically) to controller 260 to form variable magnets 230a-230c, 230a'-230c', etc. (e.g., electromagnets), respectively. Variable magnets 230a-230c, 230a'-230c', etc. can be configured to have a variable or transient polarity (e.g., ]., ) that can be adjusted and changed by controller 260 over time (e.g., via adjustment of magnitude and direction of coil currents to coil windings 228a-228c, 228a'- 228c', etc.). In some aspects, a magnitude and a direction of each variable magnet 230a-230c, 230a'- 230c', etc. can be adjusted via controller 260.

[0070] In some aspects, a magnitude and a direction (e.g., polarity) of certain variable magnets 230a- 230c, 230a'-230c', etc. of first component 220 can be adjusted (e.g., ]., j ) when directly aligned to an opposing polarity (e.g., j ) of corresponding permanent magnets 244a-244d, 244a'-244d', etc. of second component 240, such that the applied magnetic forces will only result in changes along vertical axis 206 (e.g., Z-axis). For example, as shown in FIG. 2, variable magnets 230a, 230a', 230a" can have opposite polarity, J, (S), when directly aligned to corresponding permanent magnets 244a, 244a', 244a" of opposing polarity, (N), thereby adjusting (e.g., decreasing) vertical gap 210 along vertical axis 206 (e.g., Z-axis) due to magnetic attraction forces, and the magnitude (e.g., via coil current amplitude) can be increased or decreased to thereby increase or decrease the magnetic attraction forces. For example, conversely, as shown in FIG. 2, variable magnets 230a, 230a', 230a" can have matching polarity, (N), when directly aligned to corresponding permanent magnets 244a, 244a', 244a" of opposing polarity, (N), thereby adjusting (e.g., increasing) vertical gap 210 along vertical axis 206 (e.g., Z-axis) due to magnetic repulsion forces, and the magnitude (e.g., via coil current amplitude) can be increased or decreased to thereby increase or decrease the magnetic repulsion forces.

[0071] In some aspects, magnetic cores 224a-224c, 224a'-224c', etc. can include iron. In some aspects, magnetic cores 224a-224c, 224a'-224c', etc. can include a soft magnetic material, for example, ironsilicon alloys, iron-nickel alloys, iron-cobalt alloys, cobalt amorphous alloys, iron nanocrystalline alloys, laminated iron, powdered iron, ferrite, or a combination thereof. In some aspects, magnetic cores 224a-224c, 224a'-224c', etc. can be part of armature 222. In some aspects, magnetic cores 224a-224c,224a'-224c', etc. and armature 222 can include the same material (e.g., iron). In some aspects, magnetic cores 224a-224c, 224a'-224c', etc. and armature 222 can include different materials.

[0072] In some aspects, magnetic cores 224a-224c, 224a'-224c', etc. can be spaced apart by a magnetic core pitch. For example, as shown in FIG. 2, magnetic cores 224a-224c, 224a'-224c' can be spaced apart from each other along longitudinal axis 202 (e.g., Y-axis) by magnetic core pitch 226. In some aspects, magnetic core pitch 226 can be in a range of about 1 mm to about 50 mm. For example, magnetic core pitch 226 can be about 25 mm. In some aspects, a depth of magnetic cores 224a-224c, 224a'-224c', etc. relative to armature 222 can be in a range of about 50 mm to about 250 mm. For example, the depth of magnetic cores 224a-224c, 224a'-224c' relative to armature 222 can be about 150 mm.

[0073] In some aspects, variable magnets 230a-230c, 230a'-230c', etc. of first component 220 can be skewed. For example, magnetic cores 224a-224c, 224a'-224c' (e.g., teeth) can be skewed (e.g., tilted or oblique magnetic pole) along longitudinal axis 202 (e.g., Y-axis), for example, in the shape of an oblique parallelepiped, to influence interaction between variable magnets 230a-230d, 230a'-230d' and permanent magnets 244a-244d, 244a'-244d', for example, to reduce cogging.

[0074] In some aspects, first component 220 can be coupled to a balance mass configured to mimic coarse movements, dampen, and return first component 220 to an equilibrium position. For example, as shown in FIG. 2, armature 222 can be attached (e.g., secured) to balance mass 390. In some aspects, first component 220 can be stationary (e.g., fixed to balance mass 390) and second component 240 can move relative to first component 220. In some aspects, first component 220 and second component 240 can be opposing. For example, as shown in FIG. 2, first component 220 and second component 240 can be opposing along vertical axis 206 (e.g., Z-axis).

[0075] In some aspects, linear motor 200 can include one or more sensors to monitor relative motion of first and second components 220, 240. For example, as shown in FIG. 2, first component 220 can include sensors 232, 232' to monitor vertical gaps 210 between first and second components 220, 240 in first and second sections 201, 201', respectively. In some aspects, sensors 232, 232' can include any distance sensor and / or proximity sensor, for example, but not limited to, a light sensor (e.g., laser, infrared, LED, VCSEL, etc.), an ultrasonic sensor, a LIDAR sensor, a range sensor, a time-of-flight sensor, a photoelectric sensor, a capacitive sensor, an inductive sensor, an electromagnetic sensor (e.g., magnetic, flux, RF, etc.), or a combination thereof.

[0076] In some aspects, sensors 232, 232' can be coupled (e.g., electronically, wirelessly, etc.) to controller 260 and send distance data and / or proximity data to controller 260. For example, sensors 232, 232' can monitor vertical gap 210 and send distance data to controller 260 as part of a feedback loop with controller 260 so that controller 260 can dynamically adjust (e.g., periodically, continuously) one or more variable magnets 230a-230c, 230a'-230c' of first component 220 to correct motion of second component 240 (e.g., object stage 320), thereby forming a servomechanism. In some aspects, sensors 232, 232', variable magnets 230a-230c, 230a'-230c', and controller 260 can form a servomechanism to automatically adjust vertical gap 210 between first and second components 220, 240 based on error-sensing negative feedback from sensors 232, 232', for example, to reduce deviations of second component 240 along vertical axis 206 (e.g., Z-axis) from a preset vertical gap 210 (e.g., 1 mm) during movement along longitudinal axis 202 (e.g., Y-axis).

[0077] Second component 240 can be configured to provide a plurality of permanent magnets 244a- 244d, 244a'-244d', etc. having alternating polarity (e.g., , ]., , ]., ...). Second component 240 can be further configured to be coupled to an object stage (e.g., object stage 320) and move relative to first component 220 via magnetic forces. As shown in FIG. 2, second component 240 can include backing magnetic layer 242, permanent magnets 244a-244d, 244a'-244d', etc., and / or supporting permanent magnets 248a-248d, 248a'-248d', etc. In some aspects, second component 240 can be coupled to an object stage. For example, as shown in FIG. 2, backing magnetic layer 242 can be attached (e.g., secured) to a portion of object stage 320.

[0078] In some aspects, backing magnetic layer 242 can include iron. In some aspects, backing magnetic layer 242 can include a soft magnetic material, for example, iron-silicon alloys, iron-nickel alloys, iron-cobalt alloys, cobalt amorphous alloys, iron nanocrystalline alloys, laminated iron, powdered iron, ferrite, or a combination thereof. In some aspects, permanent magnets 244a-244d, 244a'- 244d', etc. can include a permanent magnetic material, for example, iron, neodymium, cobalt, gadolinium, samarium, dysprosium, nickel, samarium-cobalt alloys, neodymium-iron-boron (NIB), or a combination thereof. In some aspects, supporting permanent magnets 248a-248d, 248a'-248d', etc can include a permanent magnetic material, for example, iron, neodymium, cobalt, gadolinium, samarium, dysprosium, nickel, samarium-cobalt alloys, NIB, or a combination thereof.

[0079] In some aspects, backing magnetic layer 242 can support permanent magnets 244a-244d, 244a'- 244d', etc. and supporting permanent magnets 248a-248d, 248a'-248d', etc. For example, as shown in FIG. 2, backing magnetic layer 242 can support permanent magnets 244a-244d, 244a'-244d' of alternating polarity interspersed with corresponding supporting permanent magnets 248a-248d, 248a'- 248d'. In some aspects, supporting permanent magnets 248a-248d, 248a'-248d', etc. can be interspersed between permanent magnets 244a-244d, 244a'-244d', etc. of alternating polarity to augment the magnetic field of second component 240 (e.g., Halbach array). In some aspects, supporting permanent magnets 248a-248d, 248a'-248d', etc. can be omitted or replaced with non-magnetic spacers.

[0080] In some aspects, second component 240 can include a spatially rotating pattern of magnetization. For example, as shown in FIG. 2, permanent magnets 244a-244d, 244a'-244d' and supporting permanent magnets 248a-248d, 248a'-248d' can have a rotating magnetization (e.g.,]., ...) along longitudinal axis 202 (e.g., Y-axis), such that the magnetic field opposing first component 220 (strong side) is enhanced while the magnetic field opposing backing magnetic layer 242 (weak side) is canceled (e.g., field near zero). In some aspects, permanent magnets 244a-244d, 244a'- 244d', etc. and supporting permanent magnets 248a-248d, 248a'-248d', etc. can be arranged in a Halbach array. For example, as shown in FIG. 2, permanent magnets 244a-244d, 244a'-244d' and supportingpermanent magnets 248a-248d, 248a'-248d' can have a rotating magnetization ( , J,, ...) along longitudinal axis 202 (e.g., Y-axis).

[0081] In some aspects, permanent magnets 244a-244d, 244a'-244d', etc. can have alternating polarity (e.g., T, ],, T, and include one additional permanent magnet (e.g., permanent magnet 244d) relative to the number of corresponding variable magnets 230a-230c, 230a'-230c', etc. of first component 220. For example, as shown in FIG. 2, first section 201 can include three variable magnets 230a-230c and four permanent magnets 244a-244d of alternating polarity ( , ]., , ],). In some aspects, a width of permanent magnets 244a-244d, 244a'-244d', etc., along longitudinal axis 202 (e.g., Y-axis), can be equal to a width of magnetic cores 224a-224c, 224a'-224c', etc. (e.g., teeth) along longitudinal axis 202 (e.g., Y-axis). For example, the width can be in a range of about 1 mm to about 30 mm, for example, about 15 mm.

[0082] In some aspects, permanent magnets 244a-244d, 244a'-244d' can be spaced apart by a permanent magnet pitch. For example, as shown in FIG. 2, permanent magnets 244a-244d, 244a'-244d' can be spaced apart from each other along longitudinal axis 202 (e.g., Y-axis) by permanent magnet pitch 246. In some aspects, permanent magnet pitch 246 can be in a range of about 1 mm to about 50 mm. For example, permanent magnet pitch 246 can be about 20 mm.

[0083] In some aspects, magnetic cores 224a-224c, 224a'-224c' can be spaced apart by magnetic core pitch 226 and permanent magnets 244a-244d, 244a'-244d' can be spaced apart by permanent magnet pitch 246. In some aspects, a ratio of magnetic core pitch 226 to permanent magnet pitch 246 is 1.33 (e.g., for three-phase control). In some aspects, the ratio of magnetic core pitch 226 to permanent magnet pitch 246 is 1.25 (e.g., for four-phase control). In some aspects, the ratio of magnetic core pitch 226 to permanent magnet pitch 246 is 1.2 (e.g., for five-phase control). In some aspects, the ratio of magnetic core pitch 226 to permanent magnet pitch 246 is 1.16 (e.g., for six-phase control). In some aspects, the ratio of magnetic core pitch 226 to permanent magnet pitch 246 is 1.11 (e.g., for nine -phase control).

[0084] In some aspects, permanent magnets 244a-244d, 244a' -244d', etc. and / or supporting permanent magnets 248a-248d, 248a'-248d', etc. of second component 240 can be skewed. For example, permanent magnets 244a-244d, 244a'-244d' can be skewed (e.g., tilted or oblique magnetic pole) along longitudinal axis 202 (e.g., Y-axis), for example, in the shape of an oblique parallelepiped, to influence interaction between permanent magnets 244a-244d, 244a'-244d' and variable magnets 230a-230d, 230a'-230d', for example, to reduce cogging.

[0085] Controller 260 can be configured to control movement (e.g., translation) of second component 240 relative to first component 220 along longitudinal axis 202 (e.g., Y-axis) with first control loop 262. Controller 260 can be further configured to control vertical gap 210 between first and second components 220, 240 with second control loop 264. As shown in FIG. 2, controller 260 can be coupled (e.g., electronically) to first component 220 via coil windings 228a-228c, 228a'-228c' and include first control loop 262 and second control loop 264. In some aspects, controller 260 can adjust a magnitude and a direction of coil currents to coil windings 228a-228c, 228a'-228c', to thereby adjust a magneticfield strength and a polarity (e.g., J,, T) of each variable magnet 230a-230c, 230a'-230c'. In some aspects, controller 260 can include one or more controllers, for example, one controller to implement first control loop 262 (e.g., Y-axis control) and one controller to implement second control loop 264 (e.g., Z-axis control).

[0086] First control loop 262 can be configured to accelerate second component 240 along longitudinal axis 202 (e.g., Y-axis). In some aspects, for example, first control loop 262 can include a three-phase control scheme (U, V, W), where each coil current has a phase offset of 120 degrees to adjust the load angle of second component 240.

[0087] Second control loop 264 can be configured to adjust second component 240 along vertical axis 206 (e.g., Z-axis) to maintain and / or adjust vertical gap 210. Second control loop 264 can be further configured to reduce negative stiffness of second component 240 (e.g., object stage 320). In some aspects, second control loop 264 can include a three-phase control scheme (U, V, W), where each coil current has a phase offset of 120 degrees and a magnitude and a polarity (e.g., ]., j ) of certain variable magnets 230a-230c, 230a'-230c', etc. are adjusted to increase, decrease, and / or maintain vertical gap 210.

[0088] In some aspects, first and second control loops 262, 264 can operate on the same control scheme, for example, a three-phase control scheme (U, V, W). In some aspects, first and second control loops 262, 264 can operate on different control schemes, for example, second control loop 264 can operate on a three-phase control scheme (U, V, W) while first control loop 262 can operate on a six- phase control scheme (A, B, C, D, E, F).

[0089] In some aspects, second control loop 264 can be superimposed on first control loop 262. For example, first and second control loops 262, 264 can be combined such that the coil current signal (e.g., magnitude and direction) of second control loop 264 is overlaid on the coil current signal (e.g., magnitude and direction) of first control loop 262, thereby forming a resultant coil current waveform having both Y-axis and Z-axis control. In some aspects, first and second control loops 262, 264 can be in phase (e.g., three-phase control) such that the coil current signal (e.g., magnitude and direction) of second control loop 264 is combined (e.g., added or subtracted) with the coil current signal (e.g., magnitude and direction) of first control loop 262, thereby forming a resultant coil current waveform of greater or lower magnitude having both Y-axis and Z-axis control.

[0090] In some aspects, controller 260 can apply second control loop 264 to specific coil windings 228a, 228a', 228a", etc. (e.g., in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . .) at specific times (e.g., when variable magnets 230a, 230a', 230a", etc. are directly aligned with opposing permanent magnets 244a, 244a', 244a", etc.), thereby adjusting second component 240 along vertical axis 206 (e.g., Z-axis control). In some aspects, controller 260 can implement first and second control loops 262, 264 with the same amplifiers and coil windings 228a-228c, 228a'-228c', etc. In some aspects, controller 260 can implement second control loop 264 (e.g., Z-axis control) with different amplifiers and coil windings 228a-228c, 228a'-228c', etc. than first control loop 262 (e.g., Y-axis control).

[0091] In some aspects, second control loop 264 can be applied when variable magnets 230a-230c, 230a'-230c', etc. of first component 220 are aligned spatially with opposing permanent magnets 244a- 244d, 244a'-244d', etc. of second component 240. For example, as shown in FIG. 2, variable magnets 230a, 230a', 230a", etc. can be activated via second control loop 264 (e.g., Z-axis control) when directly over corresponding permanent magnets 244a, 244a', 244a", etc. to control vertical gap 210.

[0092] In some aspects, second control loop 264 can be applied to variable magnets 230a-230c, 230a'- 230c', etc. in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along vertical axis 206 (e.g., Z-axis) is applied from variable magnets 230a-230c, 230a'-230c', etc. in the sequence Snto maintain vertical gap 210. For example, as shown in FIGS. 2 and 6, second control loop 264 can be applied to variable magnets 230a, 230a', 230a", etc. in sequence Sn250, that is directly over corresponding permanent magnets 244a, 244a', 244a", etc., such that a magnetic force (e.g., attraction and / or repulsion magnetic force) along vertical axis 206 (e.g., Z-axis) is applied between variable magnets 230a, 230a', 230a", etc. in sequence Sn250 to corresponding permanent magnets 244a, 244a', 244a", etc. to adjust and / or maintain vertical gap 210.

[0093] In some aspects, second control loop 264 (e.g., Z-axis control) can be applied in sequence Sn250 sequentially to adjacent groups of variable magnets 230a-230c, 230a'-230c', etc. to control vertical gap 210, for example, in a three-phase control scheme, while second component 240 is moving (e.g., translating) along longitudinal axis 202 (e.g., Y-axis). For example, as shown in FIGS. 2 and 6, second control loop 264 (e.g., Z-axis control) can be applied in three-phase control scheme 600 to adjust and / or maintain vertical gap 210 periodically as second component 240 moves along longitudinal axis 202 (e.g., +Y-axis) with first configuration 60 (e.g., first phase) activating variable magnets 230a, 230a', 230a", etc. in sequence Sn250, second configuration 62 (e.g., second phase) activating variable magnets 230b, 230b', 230b", etc. in sequence Sn250, and third configuration 64 (e.g., third phase) activating variable magnets 230c, 230c', 230c", etc. in sequence Sn250.

[0094] In some aspects, variable magnets 230a-230c, 230a'-230c', etc. of first component 220 can be skewed (e.g., tilted or oblique magnetic pole) and controller 260 can implement second control loop 264 (e.g., Z-axis control) when corresponding permanent magnets 244a-244d, 244a'-244d', etc. are crossed, for example, within a certain tolerance level. For example, second control loop 264 (e.g., Z- axis control) can be applied when permanent magnets 244a, 244a', 244a", etc. cross corresponding variable magnets 230a, 230a', 230a", etc. within a tolerance of magnetic core pitch 226, for example, within about 15% of magnetic core pitch 226.

[0095] In some aspects, permanent magnets 244a-244d, 244a'-244d', etc. of second component 240 can be skewed (e.g., tilted or oblique magnetic pole) and controller 260 can implement second control loop 264 (e.g., Z-axis control) when corresponding variable magnets 230a-230d, 230a'-230d', etc. are crossed, for example, within a certain tolerance level. For example, second control loop 264 (e.g., Z- axis control) can be applied when variable magnets 230a, 230a', 230a", etc. cross correspondingpermanent magnets 244a, 244a', 244a", etc. within a tolerance of permanent magnet pitch 246, for example, within about 15% of permanent magnet pitch 246.

[0096] In some aspects, variable magnets 230a-230d, 230a'-230d', etc. of first component 220 can be skewed and / or permanent magnets 244a-244d, 244a'-244d', etc. of second component 240 can be skewed to reduce cogging along vertical axis 206 (e.g., Z-axis). For example, cogging of linear motor 200 along vertical axis 206 (e.g., Z-axis) can be reduced by at least about 5%, for example, about 10%.

[0097] In some aspects, first and second control loops 262, 264 can be configured to operate in a three- phase control scheme. For example, as shown in FIG. 6, second control loop 264 can operate in three- phase control scheme 600. In some aspects, first and second control loops 262, 264 can be configured to operate in a four-phase control scheme. For example, as shown in FIG. 7, second control loop 264 can operate in four-phase control scheme 700. In some aspects, first and second control loops 262, 264 can be configured to operate in a five-phase control scheme. In some aspects, first and second control loops 262, 264 can be configured to operate in a six-phase control scheme. In some aspects, first and second control loops 262, 264 can be configured to operate in a nine-phase control scheme.

[0098] In some aspects, first section 201, second section 201', third section 201", etc. of linear motor 200 can be arranged sequentially along longitudinal axis 202 for a four-phase control scheme (e.g., four-phase control scheme 700 shown in FIG. 7), such that each section contains four variable magnets 230a-230d, 230a'-230d', etc. In some aspects, first section 201, second section 201', third section 201", etc. of linear motor 200 can be arranged sequentially along longitudinal axis 202 for a five-phase control scheme, such that each section contains five variable magnets. In some aspects, first section 201, second section 201', third section 201", etc. of linear motor 200 can be arranged sequentially along longitudinal axis 202 for a six-phase control scheme, such that each section contains six variable magnets. In some aspects, first section 201, second section 201', third section 201", etc. of linear motor 200 can be arranged sequentially along longitudinal axis 202 for a nine-phase control scheme, such that each section contains nine variable magnets.

[0099] Exemplary Pair of Linear Motors

[0100] FIG. 3 illustrates pair of linear motors 300, according to various exemplary aspects. FIG. 3 is a schematic cross-sectional illustration of pair of linear motors 300 utilizing linear motor 200 shown in FIG. 2, according to an exemplary aspect. Pair of linear motors 300 can be configured to maintain precise linear control and stability of object stage 320 coupled to pair of linear motors 300 (e.g., coupled to upper and lower linear motors 200a, 200b). Pair of linear motors 300 can be further configured to maintain equal gaps (e.g., upper vertical gap 210a, lower vertical gap 210b) of object stage 320 coupled to pair of linear motors 300.

[0101] Although pair of linear motors 300 is shown in FIG. 3 as a stand-alone apparatus and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, patterning device MA, linear motor 200, transport system 400, alternative transport system 400', alternative transport system 400", three-phase control scheme 600, four-phase control scheme 700, control flow diagram 800, control flow diagram 900, and / or control flow diagram 1000. In some aspects, pair of linear motors 300 can be part of a lithography apparatus, for example, lithographic apparatus LA. In some aspects, pair of linear motors 300 can be part of a support structure, for example, support structure MT for patterning device MA. In some aspects, pair of linear motors 300 can be part of a transport system, for example, transport system 400.

[0102] The aspects of linear motor 200 shown in FIG. 2, for example, and the aspects of upper linear motor 200a and lower linear motor 200b of pair of linear motors 300 shown in FIG. 3 may be similar. Similar reference numbers are used to indicate features of the aspects of linear motor 200 shown in FIG. 2 and the similar features of the aspects of upper linear motor 200a and lower linear motor 200b of pair of linear motors 300 shown in FIG. 3. One difference between the aspects of linear motor 200 shown in FIG. 2 and the aspects of upper linear motor 200a and lower linear motor 200a of pair of linear motors 300 shown in FIG. 3 is that pair of linear motors 300 includes two opposing upper and lower linear motors 200a, 200b along vertical axis 326 (e.g., Z-axis) of object stage 320, mirrored about line of symmetry 301 and longitudinal axis 322 (e.g., Y-axis) of object stage 320, rather than just a single linear motor 200 as shown in FIG. 2. In some aspects, upper linear motor 200a shown in FIG. 3 can include linear motor 200 shown in FIG. 2. In some aspects, lower linear motor 200b shown in FIG. 3 can include linear motor 200 shown in FIG. 2.

[0103] As shown in FIG. 3, pair of linear motors 300 can include line of symmetry 301, upper linear motor 200a, lower linear motor 200b, upper vertical gap 210a, lower vertical gap 210b, and object stage 320. Upper linear motor 200a is similar to linear motor 200 shown in FIG. 2 and similar reference numbers are used to indicate the similar features of linear motor 200 shown in FIG. 2 and upper linear motor 200a shown in FIG. 3. Lower linear motor 200b is similar to linear motor 200 shown in FIG. 2 and similar reference numbers are used to indicate the similar features of linear motor 200 shown in FIG. 2 and lower linear motor 200b shown in FIG. 3. Discussion of upper and lower linear motors 200a, 200b is not duplicated here for brevity, but the aspects and features of each are similar to linear motor 200 described above.

[0104] In some aspects, pair of linear motors 300 can be configured to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis). In some aspects, pair of linear motors 300 can be configured to maintain upper vertical gap 210a and lower vertical gap 210b between object stage 320 and pair of linear motors 300 along vertical axis 326 (e.g., Z-axis). For example, pair of linear motors 300 can control upper and lower vertical gaps 210a, 210b to be equal. In some aspects, pair of linear motors 300 can be configured to reduce parasitic normal forces due to the pairing of upper and lower linear motors 200a, 200b. For example, as shown in FIG. 3, pair of linear motors 300 can include opposing upper and lower linear motors 200a, 200b that balance parasitic normal forces, since magnetic forces (e.g., attractive magnetic forces) trying to close upper vertical gap 210a in upper linear motor 200a are equaland opposite to magnetic forces (e.g., attractive magnetic forces) trying to close lower vertical gap 210b in lower linear motor 200b.

[0105] Object stage 320 can be configured to move relative to pair of linear motors 300. Object stage 320 can be further configured to support an object, for example, a patterning device. As shown in FIG. 3, object stage 320 can include longitudinal axis 322 (e.g., Y-axis), transverse axis 324 (e.g., X-axis), vertical axis 326 (e.g., Z-axis), front surface 330, back surface 332, top surface 334, bottom surface 336, side surfaces 338a, 338b, and transverse distal ends 340a, 340b. In some aspects, object stage 320 can be a moving magnet stage with one or more permanent magnets attached to a portion of object stage 320. For example, as shown in FIG. 3, second component 240 of upper linear motor 200a can be attached (e.g., secured) to a portion of top surface 334 of object stage 320 and second component 240 of lower linear motor 200b can be attached (e.g., secured) to a portion of bottom surface 336 of object stage 320.

[0106] Controller(s) 260 can be configured to control movement (e.g., translation) of object stage 320 relative to upper and lower linear motors 200a, 200b along longitudinal axis 322 (e.g., Y-axis) with first control loop 262. Controller(s) 260 can be further configured to control upper vertical gap 210a of upper linear motor 200a and lower vertical gap 210b of lower linear motor 210b with second control loop 264. As shown in FIG. 3, controller(s) 260 can be coupled (e.g., electronically) to upper and lower linear motors 200a, 200b and include first control loop 262 (e.g., Y-axis control) and second control loop 264 (e.g., Z-axis control). In some aspects, controller(s) 260 can adjust a magnetic field strength and a polarity (e.g., ].,of each variable magnet 230a-230c, 230a'-230c', etc. of upper and lower linear motors 200a, 200b. In some aspects, controller(s) 260 can operate and control upper and lower linear motors 200a, 200b synchronously. In some aspects, controllers 260 of upper and lower linear motors 200a, 200b can be combined into a single (master) controller 260.

[0107] Exemplary Transport System

[0108] As discussed above, the complexity of gas bearing solutions (e.g., air bearings) is very high and object stage designs using gas bearings in vacuum suffer (e.g., EUV lithography) from stiffness issues and particle contamination. Magnetic levitation transport systems, where the object stage is supported by magnetic forces without any mechanical contact, provide the advantages of frictionless motion, vacuum compatibility, and contamination-free operation.

[0109] However, magnetic levitation systems can suffer from parasitic normal forces, cogging (e.g., resistance to preferred positions of iron core design), and instability. At high accelerations (e.g., along a longitudinal axis), it can become difficult to maintain correct gaps or distances around the object stage (e.g., vertical gaps, horizontal gaps) relative to one or more linear motors that are accelerating the object stage. Further, magnetic levitation systems can be unstable due to very large negative stiffness (e.g., due to permanent magnets on object stage) that can cause the system to move sufficiently off center and spontaneously slide or flip. Stable magnetic levitation can be achieved by using one or more feedbackloops (e.g., via one or more controllers) that periodically or continuously adjusts one or more electromagnets to correct motion of the object stage (e.g., a servomechanism).

[0110] Aspects of transport apparatuses, systems, and methods as discussed below can avoid gas bearings, utilize magnetic levitation, reduce contamination, reduce parasitic normal forces, reduce cogging, provide low negative stiffness, maintain precise linear control and stability of an object stage (e.g., reticle stage), and maintain equal gaps (e.g., vertical and horizontal gaps) around the object stage during high acceleration.

[0111] FIGS. 4 and 5 illustrate transport system 400, according to various exemplary aspects. FIG. 4 is a schematic front perspective illustration of transport system 400 utilizing pair of linear motors 300 shown in FIG. 3, according to an exemplary aspect. FIG. 5 is a schematic front illustration of transport system 400 shown in FIG. 4. Transport system 400 can be configured to maintain precise linear control and stability of object stage 320 coupled to opposing first and second pairs of linear motors 300a, 300b. Transport system 400 can be further configured to maintain equal gaps (e.g., upper vertical gap 210a, lower vertical gap 210b, first horizontal gap 350a, second horizontal gap 350b) around object stage 320 coupled to transport system 400 during high acceleration.

[0112] Although transport system 400 is shown in FIGS. 4 and 5 as a stand-alone apparatus and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, patterning device MA, linear motor 200, pair of linear motors 300, three-phase control scheme 600, four-phase control scheme 700, control flow diagram 800, control flow diagram 900, and / or control flow diagram 1000. In some aspects, transport system 400 can be part of a lithography apparatus, for example, lithographic apparatus LA. In some aspects, transport system 400 can be part of a support structure, for example, support structure MT for patterning device MA. In some aspects, transport system 400 can include two opposing pairs of linear motors, for example, two pairs of linear motors 300.

[0113] The aspects of pair of linear motors 300 shown in FIG. 3, for example, and the aspects of first pair of linear motors 300a and second pair of linear motors 300b of transport system 400 shown in FIGS. 4 and 5 may be similar. Similar reference numbers are used to indicate features of the aspects of pair of linear motors 300 shown in FIG. 3 and the similar features of the aspects of first pair of linear motors 300a and second pair of linear motors 300b of transport system 400 shown in FIGS. 4 and 5. One difference between the aspects of pair of linear motors 300 shown in FIG. 3 and the aspects of first pair of linear motors 300a and second pair of linear motors 300b of transport system 400 shown in FIGS. 4 and 5 is that transport system 400 includes two opposing first and second pairs of linear motors 300a, 300b along transverse axis 324 (e.g., X-axis) of object stage 320, symmetric about vertical axis 326 (e.g., Z-axis) of object stage 320, rather than just a single pair of linear motors 300 as shown in FIG. 3. In some aspects, first pair of linear motors 300a shown in FIGS. 4 and 5 can include pair of linear motors 300 shown in FIG. 3. In some aspects, second pair of linear motors 300b shown in FIGS. 4 and 5 can include pair of linear motors 300 shown in FIG. 3.

[0114] As shown in FIGS. 4 and 5, transport system 400 can include first pair of linear motors 300a, second pair of linear motors 300b, upper vertical gap 210a, lower vertical gap 210b, object stage 320, first horizontal gap 350a, second horizontal gap 350b, first pair controller 360a, second pair controller 360b, first reluctance motor 370a, second reluctance motor 370b, first reluctance controller 380a, and second reluctance controller 380b. First pair of linear motors 300a is similar to pair of linear motors 300 shown in FIG. 3 and similar reference numbers are used to indicate the similar features of pair of linear motors 300 shown in FIG. 3 and first pair of linear motors 300a shown in FIGS. 4 and 5. Second pair of linear motors 300b is similar to pair of linear motors 300 shown in FIG. 3 and similar reference numbers are used to indicate the similar features of pair of linear motors 300 shown in FIG. 3 and second pair of linear motors 300b shown in FIGS. 4 and 5. Discussion of first and second pairs of linear motors 300a, 300b is not duplicated here for brevity, but the aspects and features of each are similar to pair of linear motors 300 described above.

[0115] In some aspects, transport system 400 can be configured to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis), for example, via first control loop (e.g., Y-axis control). In some aspects, transport system 400 can be configured to maintain upper vertical gap 210a and lower vertical gap 210b between object stage 320 and first and second pairs of linear motors 300a, 300b, respectively, along vertical axis 326 (e.g., Z-axis). For example, first and second pairs of linear motors 300a, 300b can control upper and lower vertical gaps 210a, 210b to be equal, for example, via second control loop 264 (e.g., Z-axis control). In some aspects, transport system 400 can be further configured to maintain first horizontal gap 350a and second horizontal gap 350b between object stage 320 and first and second reluctance actuators 370a, 370b, respectively, along transverse axis 324 (e.g., X-axis). For example, first and second reluctance actuators 370a, 370b can control first and second horizontal gaps 350a, 350b to be equal, for example, via third control loop 382 (e.g., X-axis control).

[0116] In some aspects, transport system 400 can be configured to reduce parasitic normal forces due to first and second pairs of linear motors 300a, 300b each having opposing upper and lower linear motors 200a, 200b that balance parasitic normal forces. In some aspects, transport system 400 can be configured to reduce negative stiffness of object stage 320 due to first and second pairs of linear motors 300a, 300b being arranged symmetrically about object stage 320. For example, as shown in FIG. 4, first and second pairs of linear motors 300a, 300b can be opposing along transverse axis 324 (e.g., X-axis) and mirror symmetric about the longitudinal axis 322 and vertical axis 326 plane (e.g., YZ-plane).

[0117] In some aspects, for example, as shown in FIG. 4, first pair of linear motors 300a can include upper linear motor 200a coupled to a portion of top surface 334 of object stage 320 (e.g., right side) and lower linear motor 200b coupled to a portion of bottom surface 336 of object stage 320 (e.g., right side), such that upper and lower linear motors 200a, 200b are mirror symmetric about the transverse axis 324 and longitudinal axis 322 plane (e.g., XY-plane). In some aspects, for example, as shown in FIG. 4, second pair of linear motors 300b can include upper linear motor 200a coupled to a portion of top surface 334 of object stage 320 (e.g., left side) and lower linear motor 200b coupled to a portion ofbottom surface 336 of object stage 320 (e.g., left side), such that upper and lower linear motors 200a, 200b are mirror symmetric about the transverse axis 324 and longitudinal axis 322 plane (e.g., XY- plane). In some aspects, magnetic forces between upper and lower linear motors 200a, 200b of first pair of linear motors 300a can be equal and opposite. In some aspects, magnetic forces between upper and lower linear motors 200a, 200b of second pair of linear motors 300b can be equal and opposite.

[0118] In some aspects, upper linear motor 200a of first pair of linear motors 300a can be configured to maintain upper vertical gap 210a between a portion of top surface 334 of object stage 320 (e.g., right side) and upper linear motor 200a, and lower linear motor 200b of first pair of linear motors 300a can be configured to maintain lower vertical gap 210b between a portion of bottom surface 336 of object stage 320 (e.g., right side) and lower linear motor 200b, for example, via second control loop 264 (e.g., Z-axis control). In some aspects, upper linear motor 200a of second pair of linear motors 300b can be configured to maintain upper vertical gap 210a between a portion of top surface 334 of object stage 320 (e.g. , left side) and upper linear motor 200a, and lower linear motor 200b of second pair of linear motors 300b can be configured to maintain lower vertical gap 210b between a portion of bottom surface 336 of object stage 320 (e.g., left side) and lower linear motor 200b, for example, via second control loop 264 (e.g., Z-axis control).

[0119] Object stage 320 can be configured to move relative to first and second pairs of linear motors 300a, 300b. Object stage 320 can be further configured to support an object, for example, a patterning device. As shown in FIGS. 4 and 5, object stage 320 can include longitudinal axis 322 (e.g., Y-axis), center of mass (COM) 323, center of gravity (COG) 323a, transverse axis 324 (e.g., X-axis), vertical axis 326 (e.g., Z-axis), front surface 330, back surface 332, top surface 334, bottom surface 336, side surfaces 338a, 338b, and transverse distal ends 340a, 340b. In some aspects, object stage 320 can be a moving magnet stage with one or more permanent magnets attached to a portion of object stage 320. For example, as shown in FIGS. 4 and 5, upper linear motors 200a of first and second pairs of linear motors 300a, 300b can each be attached (e.g., secured) to portions of top surface 334 of object stage 320 and lower linear motors 200b of first and second pairs of linear motors 300a, 300b can each be attached (e.g., secured) to portions of bottom surface 336 of object stage 320.

[0120] In some aspects, first and second pairs of linear motors 300a, 300b can be arranged symmetrically about longitudinal axis 322 (e.g., Y-axis) of object stage 320. In some aspects, first and second pairs of linear motors 300a, 300b can be arranged symmetrically about an axis substantially parallel to longitudinal axis 322 (e.g., Y-axis) of object stage 320. For example, as shown in FIG. 5A, first and second pairs of linear motors 300a, 300b can be arranged symmetrically about parallel longitudinal axis 322a (e.g., orthogonal to XZ-plane) of asymmetric object stage 320'. In some aspects, first and second pairs of linear motors 300a, 300b can be arranged symmetrically about COM 323 of object stage 320. In some aspects, first and second pairs of linear motors 300a, 300b can be arranged symmetrically about COG 323a of object stage 320.

[0121] In some aspects, transverse distal ends 340a, 340b of object stage 320 can have a symmetric shape. For example, as shown in FIG. 5, transverse distal ends 340a, 340b can have a triangular shape, for example, a right triangle. In some aspects, transverse distal ends 340a, 340b of object stage 320 can have a symmetric shape with an opening angle. For example, as shown in FIG. 5, the opening angle can be about 90 degrees. In some aspects, for example, as shown in FIG. 5, object stage 320 can have a hexagonal cross-section along the transverse axis 324 and vertical axis 326 plane (e.g., XZ-plane). In some aspects, transverse distal ends 340a, 340b of object stage 320 can include a soft magnetic material, for example, iron-silicon alloys, iron-nickel alloys, iron-cobalt alloys, cobalt amorphous alloys, iron nanocrystalline alloys, laminated iron, powdered iron, ferrite, or a combination thereof.

[0122] First and second pair controllers 360a, 360b can be configured to control movement (e.g., translation) of object stage 320 relative to first and second pairs of linear motors 300a, 300b, respectively, along longitudinal axis 322 (e.g., Y-axis) with first control loop 262. First and second pair controllers 360a, 360b can be further configured to control upper vertical gap 210a of upper linear motors 200a and lower vertical gap 210b of lower linear motors 210b, respectively, with second control loop 264. As shown in FIGS. 4 and 5, first and second pair controllers 360a, 360b can be coupled (e.g., electronically) to upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b, respectively, and include first control loop 262 (e.g., Y-axis control) and second control loop 264 (e.g., Z-axis control).

[0123] In some aspects, first and second pair controllers 360a, 360b can adjust a magnetic field strength and a polarity (e.g., 1, j ) of each variable magnet 230a-230c, 230a'-230c', etc. of upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b, respectively. In some aspects, first and second pair controllers 360a, 360b can operate and control first and second pairs of linear motors 300a, 300b synchronously. In some aspects, first and second pair controllers 360a, 360b of first and second pairs of linear motors 300a, 300b can be combined into a single (master) controller.

[0124] In some aspects, first pair controller 360a can be configured to adjust upper and lower linear motors 200a, 200b of first pair of linear motors 300a so that upper and lower vertical gaps 210a, 210b of first pair of linear motors 300a are equal, for example, via second control loop 264 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop). In some aspects, second pair controller 360b can be configured to adjust upper and lower linear motors 200a, 200b of second pair of linear motors 300b so that upper and lower vertical gaps 210a, 210b of second pair of linear motors 300b are equal, for example, via second control loop 264 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop). In some aspects, first and second pair controllers 360a, 360b can be configured to adjust upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b, respectively, so that upper and lower vertical gaps 210a, 210b of both first and second pairs of linear motors 300a, 300b are all equal, for example, via second control loop 264 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop).

[0125] First and second reluctance motors 370a, 370b can be configured to maintain upper and lower vertical gaps 210a, 210b of first and second pairs of linear motors 300a, 300b, respectively, along vertical axis 326 (e.g., Z-axis). First and second reluctance motors 370a, 370b can be further configured to maintain first and second horizontal gaps 350a, 350b between object stage 320 and first and second reluctance motors 370a, 370b, respectively, along transverse axis 324 (e.g., X-axis). As shown in FIGS. 4 and 5, first and second reluctance motors 370a, 370b can be coupled (e.g., magnetically) to object stage 320 and include first and second reluctance actuators 372a, 372b, respectively. In some aspects, first and second reluctance motors 370a, 370b can extend along longitudinal axis 322 (e.g., Y-axis) adjacent transverse distal ends 340a, 340b (e.g., soft magnetic material) of object stage 320 and separated by first and second horizontal gaps 350a, 350b, respectively.

[0126] In some aspects, for example, as shown in FIG. 4, first reluctance motor 370a can include a plurality of first reluctance actuators 372a coupled (e.g., magnetically) to transverse distal end 340a (e.g., soft magnetic material) and extending along side surface 338a of object stage 320 (e.g., right side), such that first reluctance actuators 372a are mirror symmetric about the transverse axis 324 and longitudinal axis 322 plane (e.g., XY-plane). In some aspects, for example, as shown in FIG. 4, second reluctance motor 370b can include a plurality of second reluctance actuators 372b coupled (e.g., magnetically) to transverse distal end 340b (e.g., soft magnetic material) and extending along side surface 338b of object stage 320 (e.g., left side), such that second reluctance actuators 372b are mirror symmetric about the transverse axis 324 and longitudinal axis 322 plane (e.g., XY-plane). In some aspects, first and second reluctance motors 370a, 370b can be arranged symmetrically about object stage 320. For example, as shown in FIG. 4, first and second reluctance motors 370a, 370b can extend along longitudinal axis 322 (e.g., Y-axis), be opposing along transverse axis 324 (e.g., X-axis), and be mirror symmetric about the longitudinal axis 322 and vertical axis 326 plane (e.g., YZ-plane).

[0127] In some aspects, first and second reluctance motors 370a, 370b can be configured to apply counter-balancing forces along vertical axis 326 (e.g., Z-axis) relative to forces applied along vertical axis 326 (e.g., Z-axis) by first and second pairs of linear motors 300a, 300b, respectively. For example, as shown in FIG. 4, first and second reluctance motors 370a, 370b can be configured to assist (e.g., correct) first and second pairs of linear motors 300a, 300b when applying second control loop 264 (e.g., Z-axis control) to increase stability of object stage 320, for example, if object stage 320 goes sufficiently off center to cause second control loop 264 to become unstable.

[0128] In some aspects, first and second reluctance motors 370a, 370b can be configured to apply counter-balancing forces along transverse axis 324 (e.g., X-axis) relative to forces applied along transverse axis 324 (e.g., X-axis) by first and second pairs of linear motors 300a, 300b, respectively. For example, as shown in FIG. 4, first and second reluctance motors 370a, 370b can be configured to assist (e.g., correct) first and second pairs of linear motors 300a, 300b when applying first control loop 262 (e.g., Y-axis control) and / or second control loop 264 (e.g., Z-axis control) to increase stability ofobject stage 320, for example, if object stage 320 goes sufficiently off center to cause first control loop 262 and / or second control loop 264 to become unstable.

[0129] First and second reluctance actuators 372a, 372b can be configured to act as a safety circuit and reduce instability of object stage 320 (e.g., deviations from center) during movement (e.g., high acceleration). First and second reluctance actuators 372a, 372b can be configured to exert magnetic attraction forces on object stage 320 through magnetic transverse distal ends 340a, 340b (e.g., soft magnetic material) to adjust and / or maintain upper and lower vertical gaps 210a, 210b and / or first and second horizontal gaps 350a, 350b. In some aspects, first and second reluctance actuators 372a, 372b can utilize C-core reluctance actuators. For example, as shown in FIG. 4, first and second reluctance actuators 372a, 372b can include C-core reluctance actuators 373 (e.g., C-shaped ferromagnetic armature magnetized by a coil winding) paired to magnetic transverse distal ends 340a, 340b (e.g., soft magnetic material) of object stage 320. In some aspects, first and second reluctance actuators 372a, 372b can be oriented at an angle to magnetic transverse distal ends 340a, 340b (e.g., soft magnetic material) of object stage 320. For example, as shown in FIGS. 4 and 5, first and second reluctance actuators 372a, 372b can be oriented at about 45 degrees to transverse axis 324 (e.g., X-axis), for example, perpendicular to side surfaces 338a, 338b of object stage 320.

[0130] In some aspects, first and second reluctance actuators 372a, 372b can be replaced by other actuators and / or guide bearings, for example, including but not limited to, Lorentz actuators, gas bearings (e.g., air bearings), rollers (e.g., nylon rollers, silicone rollers, polyurethane rollers, etc.), skids (e.g., nylon skids, silicone skids, polyurethane skids, etc.), runners (e.g., nylon runners, silicone runners, polyurethane runners, etc.), rails (e.g., nylon rails, silicone rails, polyurethane rails, etc.), or a combination thereof for added safety and supplemental guidance. In some aspects, first and second reluctance actuators 372a, 372b can include Lorentz actuators. In some aspects, first and second reluctance actuators 372a, 372b can include gas bearings (e.g., air bearings). In some aspects, first and second reluctance actuators 372a, 372b can include guide bearings or guide rollers (e.g., rollers, skids, runners, rails, etc.).

[0131] First and second reluctance controllers 380a, 380b can be configured to control (e.g., correct) movement of object stage 320 along vertical axis 326 (e.g., Z-axis) and transverse axis 324 (e.g., X- axis) with third control loop 382, for example, in response to movement of object stage 320 from first and second pair controllers 360a, 360b. As shown in FIGS. 4 and 5, first and second reluctance controllers 380a, 380b can be coupled (e.g., electronically) to first and second reluctance motors 370a, 370b, respectively, and include third control loop 382 (e.g., XZ-plane control).

[0132] In some aspects, first and second reluctance controllers 380a, 380b can adjust a magnetic field strength and a polarity (e.g., 1, j ) of each reluctance actuator 372a, 372b of first and second reluctance motors 370a, 370b, respectively. In some aspects, first and second reluctance controllers 380a, 380b can operate and control first and second reluctance motors 370a, 370b synchronously. In some aspects, first and second reluctance controllers 380a, 380b of first and second reluctance motors 370a, 370b canbe combined into a single (master) controller. In some aspects, first and second pair controllers 360a, 360b for first and second pairs of linear motors 300a, 300b and first and second reluctance controllers 380a, 380b for first and second reluctance motors 370a, 370b of transport system 400 can be combined into a single (master) controller.

[0133] In some aspects, first reluctance controller 380a can be configured to adjust first reluctance actuators 372a (e.g., C-core) of first reluctance motor 370a so that upper and lower vertical gaps 210a, 210b of first pair of linear motors 300a are equal, for example, via third control loop 382 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop). In some aspects, second reluctance controller 380a can be configured to adjust second reluctance actuators 372b (e.g., C-core) of second reluctance motor 370b so that upper and lower vertical gaps 210a, 210b of second pair of linear motors 300b are equal, for example, via third control loop 382 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop). In some aspects, first and second reluctance controllers 380a, 380b can be configured to adjust first and second reluctance actuators 372a, 372b of first and second reluctance motors 370a, 370b, respectively, so that upper and lower vertical gaps 210a, 210b of both first and second pairs of linear motors 300a, 300b are all equal, for example, via third control loop 382 (e.g., Z-axis control) and sensors 232a, 232b, 232a', 232b' (e.g., negative feedback loop). In some aspects, third control loop 382 (e.g., Z-axis control) is applied by first and second reluctance controllers 380a, 380b to first and second reluctance motors 370a, 370b, respectively, when upper and lower vertical gaps 210a, 210b of both first and second pairs of linear motors 300a, 300b exceed a threshold value, for example, about 2 mm.

[0134] In some aspects, first reluctance controller 380a can be configured to adjust first reluctance actuators 372a (e.g., C-core) of first reluctance motor 370a so that first horizontal gap 350a is within a preset value (e.g., about 1 mm), for example, via third control loop 382 (e.g., X-axis control) and horizontal sensor 374a (e.g., negative feedback loop). In some aspects, second reluctance controller 380b can be configured to adjust second reluctance actuators 372b (e.g., C-core) of second reluctance motor 370b so that second horizontal gap 350b is within a preset value (e.g., about 1 mm), for example, via third control loop 382 (e.g., X-axis control) and horizontal sensor 374b (e.g., negative feedback loop). In some aspects, first and second reluctance controllers 380a, 380b can be configured to adjust first and second reluctance actuators 372a, 372b (e.g., C-core) of first and second reluctance motors 370a, 370b, respectively, so that first and second horizontal gaps 350a, 350b between object stage 320 and first and second reluctance motors 370a, 370b are equal, for example, via third control loop 382 (e.g., X-axis control) and horizontal sensors 374a, 374b (e.g., negative feedback loop). In some aspects, third control loop 382 (e.g., X-axis control) is applied by first and second reluctance controllers 380a, 380b to first and second reluctance motors 370a, 370b, respectively, when first and second horizontal gaps 350a, 350b exceed a threshold value, for example, about 1 mm.

[0135] Third control loop 382 can be configured to adjust object stage 320 along transverse axis 324 (e.g., X-axis) to maintain and / or adjust first and second horizontal gaps 350a, 350b. Third control loop382 can be further configured to act as a safety circuit and reduce instability of object stage 320 (e.g., deviations from center) during movement (e.g., high acceleration), for example, by providing assistance to second control loop 264 (e.g., Z-axis control). In some aspects, if first and second reluctance motors 370a, 370b adjust upper and lower vertical gaps 210a, 210b and first and second horizontal gaps 350a, 350b of object stage 320 correctly within a certain tolerance level (e.g., deviation less than 10% from a preset gap value of 1 mm) via third control loop 382 (e.g., XZ-plane control), then second control loop 264 (e.g., Z-axis control) can be omitted since magnetic forces applied by first and second reluctance motors 370a, 370b affect both X-axis control and Z-axis control of object stage 320 (e.g., FR = Fx+ Fz= IFRICOS(O) + IFRlsin(O), where FR is the magnetic force applied by the reluctance actuator and 0 is the orientation angle of the reluctance actuator relative to transverse axis 324, for example, 0 = 45 degrees).

[0136] In some aspects, third control loop 382 can include a three-phase control scheme (U, V, W), where each reluctance actuator 372a, 372b (e.g., C-core coil current) has a phase offset of 120 degrees (e.g., switched or variable reluctance actuator), and a magnitude and a polarity (e.g., 1,of certain reluctance actuator 372a, 372b are adjusted to increase, decrease, and / or maintain upper and lower vertical gaps 210a, 210b and / or first and second horizontal gaps 350a, 350b, respectively.

[0137] In some aspects, first and second reluctance motors 370a, 370b can include one or more sensors to monitor relative motion of object stage 320. For example, as shown in FIGS. 4 and 5, first and second reluctance motors 370a, 370b can include horizontal sensors 374a, 374b to monitor first and second horizontal gaps 350a, 350b between transverse distal ends 340a, 340b of object stage 320 and first and second reluctance motors 370a, 370b, respectively. In some aspects, horizontal sensors 374a, 374b can include any distance sensor and / or proximity sensor, for example, but not limited to, a light sensor (e.g., laser, infrared, LED, VCSEL, etc.), an ultrasonic sensor, a LIDAR sensor, a range sensor, a time-of- flight sensor, a photoelectric sensor, a capacitive sensor, an inductive sensor, an electromagnetic sensor (e.g., magnetic, flux, RF, etc.), or a combination thereof.

[0138] In some aspects, horizontal sensors 374a, 374b can be coupled (e.g., electronically, wirelessly, etc.) to first and second reluctance controllers 380a, 380b and send distance data and / or proximity data to first and second reluctance controllers 380a, 380b, respectively. For example, horizontal sensors 374a, 374b can monitor first and second horizontal gaps 350a, 350b and send distance data to first and second reluctance controllers 380a, 380b as part of a feedback loop with first and second reluctance controllers 380a, 380b, so that first and second reluctance controllers 380a, 380b can dynamically adjust (e.g., periodically, continuously) one or more reluctance actuators 372a, 372b of first and second reluctance motors 370a, 370b to correct motion of object stage 320, thereby forming a servomechanism, respectively.

[0139] In some aspects, sensors 232a, 232b, 232a', 232b', horizontal sensors 374a, 374b, first and second reluctance actuators 372a, 372b, and first and second reluctance controllers 380a, 380b can form a servomechanism to automatically adjust upper and lower vertical gaps 210a, 210b and first and secondhorizontal gaps 350a, 350b around object stage 320 based on error-sensing negative feedback from sensors 232a, 232b, 232a', 232b' and horizontal sensors 374a, 374b, respectively. For example, the servomechanism can reduce deviations of object stage 320 along vertical axis 326 (e.g., Z-axis) from preset upper and lower vertical gaps 210a, 210b (e.g., 1 mm) and along transverse axis 324 (e.g., X- axis) from preset first and second horizontal gaps 350a, 350b (e.g., 1 mm) during movement along longitudinal axis 202 (e.g., Y-axis).

[0140] In some aspects, first and second reluctance motors 370a, 370b can be coupled to a balance mass configured to mimic coarse movements, dampen, and return first and second reluctance motors 370a, 370b to an equilibrium position. For example, as shown in FIG. 5, first and second reluctance actuators 372a, 372b can be attached (e.g., secured) to balance mass 390. In some aspects, first and second reluctance motors 370a, 370b can be stationary (e.g., fixed to balance mass 390).

[0141] Exemplary Alternative Transport Systems

[0142] FIGS. 5A and 5B illustrate alternative transport systems 400', 400", according to various exemplary aspects. FIG. 5A is a schematic front illustration of alternative transport system 400' utilizing first and second pairs of linear motors 300a, 300b, according to an exemplary aspect. Alternative transport system 400' can be configured to maintain precise linear control and stability of asymmetric object stage 320' coupled to opposing first and second pairs of linear motors 300a, 300b. Alternative transport system 400' can be further configured to maintain equal gaps (e.g., upper vertical gap 210a, lower vertical gap 210b, first horizontal gap 350a, second horizontal gap 350b) around asymmetric object stage 320' coupled to alternative transport system 400' during high acceleration.

[0143] Although alternative transport system 400' is shown in FIG. 5A as a stand-alone apparatus and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, patterning device MA, linear motor 200, pair of linear motors 300, three-phase control scheme 600, four-phase control scheme 700, control flow diagram 800, control flow diagram 900, and / or control flow diagram 1000. In some aspects, alternative transport system 400' can be part of a lithography apparatus, for example, lithographic apparatus LA. In some aspects, alternative transport system 400' can be part of a support structure, for example, support structure MT for patterning device MA. In some aspects, alternative transport system 400' can include two opposing pairs of linear motors, for example, two pairs of linear motors 300.

[0144] The aspects of transport system 400 shown in FIGS. 4 and 5, for example, and the aspects of alternative transport system 400' shown in FIG. 5A may be similar. Similar reference numbers are used to indicate features of the aspects of transport system 400 shown in FIGS. 4 and 5 and the similar features of the aspects of alternative transport system 400' shown in FIG. 5A. One difference between the aspects of transport system 400 shown in FIGS. 4 and 5 and the aspects of alternative transport system 400' shown in FIG. 5A is that alternative transport system 400' includes asymmetric object stage 320' that includes parallel longitudinal axis 322a, COM 323, and COG 323a, for example, that areshifted down vertically (e.g., Z-axis), and first and second pairs of linear motors 300a, 300b that are arranged symmetrically about parallel longitudinal axis 322a, rather than object stage 320 and first and second pairs of linear motors 300a, 300b arranged symmetrically about longitudinal axis 322.

[0145] As shown in FIG. 5A, alternative transport system 400' can include first pair of linear motors 300a, second pair of linear motors 300b, upper vertical gap 210a, lower vertical gap 210b, asymmetric object stage 320', first horizontal gap 350a, second horizontal gap 350b, first pair controller 360a, second pair controller 360b, first reluctance motor 370a, second reluctance motor 370b, first reluctance controller 380a, and second reluctance controller 380b. Alternative transport system 400' is similar to transport system 400 shown in FIGS. 4 and 5 and similar reference numbers are used to indicate the similar features of transport system 400 shown in FIGS. 4 and 5 and alternative transport system 400' shown in FIG. 5A. Discussion of transport system 400 components and / or functionality (e.g., first and second pairs of linear motors 300a, 300b) is not duplicated here for brevity, but the aspects and features of each are similar to transport system 400 described above.

[0146] FIG. 5B is a schematic front illustration of alternative transport system 400" utilizing first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b'. Alternative transport system 400" can be configured to maintain precise linear control (e.g., 6DOF) and stability of extended object stage 320" (e.g., extended side surfaces 338a, 338b) coupled to opposing first and second angled (e.g., XZ- plane) pairs of linear motors 300a', 300b'. Alternative transport system 400" can be further configured to maintain equal gaps (e.g., upper horizontal and vertical gap 210a', lower horizontal and vertical gap 210b') around extended object stage 320" coupled to alternative transport system 400" during high acceleration.

[0147] Although alternative transport system 400" is shown in FIG. 5B as a stand-alone apparatus and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, patterning device MA, linear motor 200, pair of linear motors 300, three-phase control scheme 600, four-phase control scheme 700, control flow diagram 800, control flow diagram 900, and / or control flow diagram 1000. In some aspects, alternative transport system 400" can be part of a lithography apparatus, for example, lithographic apparatus LA. In some aspects, alternative transport system 400" can be part of a support structure, for example, support structure MT for patterning device MA. In some aspects, alternative transport system 400" can include two opposing angled pairs of linear motors, for example, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b'.

[0148] The aspects of transport system 400 shown in FIGS. 4 and 5, for example, and the aspects of alternative transport system 400" shown in FIG. 5B may be similar. Similar reference numbers are used to indicate features of the aspects of transport system 400 shown in FIGS. 4 and 5 and the similar features of the aspects of alternative transport system 400" shown in FIG. 5B. One difference between the aspects of transport system 400 shown in FIGS. 4 and 5 and the aspects of alternative transport system 400" shown in FIG. 5B is that alternative transport system 400" includes extended object stage320" and first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' coupled to side surfaces 338a, 338b of extended object stage 320" to maintain upper and lower horizontal and vertical gaps 210a', 210b' (e.g., XZ-gaps) around extended object stage 320" during high acceleration (e.g., along Y-axis), rather than transport system 400 with first and second pairs of linear motors 300a, 300b coupled to top and bottom surfaces 334, 336 of object stage 320 to maintain upper and lower vertical gaps 210a, 210b and first and second reluctance motors 370a, 370b coupled to side surfaces 338a, 338b to maintain first and second horizontal gaps 350a, 350b.

[0149] As shown in FIG. 5B, alternative transport system 400" can include first angled (e.g., XZ-plane) pair of linear motors 300a', second angled (e.g., XZ-plane) pair of linear motors 300b', upper horizontal and vertical gap 210a', lower horizontal and vertical gap 210b', extended object stage 320", first pair controller 360a, and second pair controller 360b. Alternative transport system 400" is similar to transport system 400 shown in FIGS. 4 and 5 and similar reference numbers are used to indicate the similar features of transport system 400 shown in FIGS. 4 and 5 and alternative transport system 400" shown in FIG. 5B. Discussion of transport system 400 components and / or functionality (e.g., first and second pairs of linear motors 300a, 300b) is not duplicated here for brevity, but the aspects and features of each are similar to transport system 400 described above.

[0150] First angled (e.g., XZ-plane) pair of linear motors 300a' is similar to first pair of linear motors 300a shown in FIGS. 4 and 5 except first angled (e.g., XZ-plane) pair of linear motors 300a' is rotated in the XZ-plane (e.g., upper linear motor 200a is at an angle between -X-axis and +Z-axis, lower linear motor 200b is at an angle between -X-axis and -Z-axis) and coupled to side surface 338a (e.g., arranged perpendicular to side surface 338a), and similar reference numbers are used to indicate the similar features of first pair of linear motors 300a shown in FIGS. 4 and 5 and first angled (e.g., XZ-plane) pair of linear motors 300a' shown in FIG. 5B. Second angled (e.g., XZ-plane) pair of linear motors 300b' is similar to second pair of linear motors 300b shown in FIGS. 4 and 5 except second angled (e.g., XZ- plane) pair of linear motors 300b' is rotated in the XZ-plane (e.g., upper linear motor 200a is at an angle between -i-X-axis and +Z-axis, lower linear motor 200b is at an angle between -i-X-axis and -Z-axis) and coupled to side surface 338b (e.g., arranged perpendicular to side surface 338b), and similar reference numbers are used to indicate the similar features of second pair of linear motors 300b shown in FIGS. 4 and 5 and second angled (e.g., XZ-plane) pair of linear motors 300b' shown in FIG. 5B. Discussion of first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' is not duplicated here for brevity, but the aspects and features of each are similar to first and second pairs of linear motors 300a, 300b described above.

[0151] In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can be arranged symmetrically about longitudinal axis 322 (e.g., Y-axis) of extended object stage 320". In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can be arranged symmetrically about COM 323 of extended object stage 320". In some aspects, first and secondangled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can be arranged symmetrically about COG 323a of extended object stage 320".

[0152] In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can be replaced by other actuators and / or motors, for example, including but not limited to, Lorentz actuators, gas bearings (e.g., air bearings), rollers (e.g., nylon rollers, silicone rollers, polyurethane rollers, etc.), or a combination thereof. In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can include Lorentz actuators. In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can include gas bearings (e.g., air bearings). In some aspects, first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b' can include guide bearings or guide rollers.

[0153] In some aspects, alternative transport system 400" can further include additional actuators and / or guide bearings, for example, including but not limited to, reluctance actuators (e.g., first and second reluctance actuators 372a, 372b shown in FIGS. 4 and 5), gas bearings (e.g., air bearings), rollers (e.g., nylon rollers, silicone rollers, polyurethane rollers, etc.), skids (e.g., nylon skids, silicone skids, polyurethane skids, etc.), runners (e.g., nylon runners, silicone runners, polyurethane runners, etc.), rails (e.g., nylon rails, silicone rails, polyurethane rails, etc.), or a combination thereof, in addition to first and second angled (e.g., XZ-plane) pairs of linear motors 300a', 300b', for added safety and supplemental guidance.

[0154] Exemplary Control Schemes

[0155] FIGS. 6 and 7 illustrate control schemes for linear motor 200, pair of linear motors 300, and transport system 400, according to various exemplary aspects. FIG. 6 is a schematic diagram of three- phase control scheme 600, according to an exemplary aspect. Three-phase control scheme 600 can be configured to maintain precise linear control and stability of object stage 320 along vertical axis 326 (e.g., Z-axis) and adjust and / or maintain equal upper and lower vertical gaps 210a, 210b. Three-phase control scheme 600 shall be described with reference to FIGS. 2-5. However, three-phase control scheme 600 is not limited to those example aspects.

[0156] Although three-phase control scheme 600 is shown in FIG. 6 as a stand-alone control scheme and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, linear motor 200, second control loop 264, pair of linear motors 300, transport system 400, alternative transport system 400', alternative transport system 400", control flow diagram 800, and / or control flow diagram 1000. In some aspects, three-phase control scheme 600 can be utilized in linear motor 200, for example, in first and second components 220, 240 via controller 260. In some aspects, three-phase control scheme 600 can be utilized in pair of linear motors 300, for example, in upper and lower linear motors 200a, 200b via controllers 260. In some aspects, three-phase control scheme 600 can be utilized in transport system 400, for example, in first and second pairs of linear motors 300a, 300b via first and second pair controllers 360a, 360b.

[0157] As shown in FIG. 6, in first configuration 60 (e.g., first phase), variable magnets 230a, 230a', 230a", etc. in sequence Sn250 (e.g., Sn= 3n + 1 where n = 0, 1, 2, 3, ...) are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control). In second configuration 62 (e.g., second phase), variable magnets 230b, 230b', 230b", etc. in sequence Sn250, adjacent to first configuration 60 along a direction of travel of object stage 320 (e.g., +Y-axis), are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control). In third configuration 64 (e.g., third phase), variable magnets 230c, 230c', 230c", etc. in sequence Sn250, adjacent to second configuration 62 along a direction of travel of object stage 320 (e.g., +Y-axis), are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control).

[0158] In some aspects, three-phase control scheme 600 can be utilized in second control loop 264 (e.g., Z-axis control), for example, via controller 260 in linear motor 200, via controllers 260 in pair of linear motors 300, or via first and second pair controllers 360a, 360b of transport system 400. In some aspects, three-phase control scheme 600 can be utilized to adjust upper and lower vertical gaps 210a, 210b (e.g., Z-axis control) along a direction of travel of object stage 320 (e.g., Y-axis). For example, as shown in FIG. 6, three-phase control scheme 600 with first configuration 60, second configuration 62, and third configuration 64 can be applied sequentially as object stage 320 translates along the positive longitudinal axis 322 (e.g., +Y-axis). In some aspects, three-phase control scheme 600 can be reversed for bi-directional control of object stage 320. For example, three-phase control scheme 600 order can be reversed so that third configuration 64, second configuration 62, and first configuration 60 are applied sequentially as object stage 320 translates along the negative longitudinal axis 322 (e.g., -Y- axis).

[0159] FIG. 7 is a schematic diagram of four-phase control scheme 700, according to an exemplary aspect. Four-phase control scheme 700 can be configured to maintain precise linear control and stability of object stage 320 along vertical axis 326 (e.g., Z-axis) and adjust and / or maintain equal upper and lower vertical gaps 210a, 210b. Four-phase control scheme 700 shall be described with reference to FIGS. 2-5. However, four-phase control scheme 700 is not limited to those example aspects.

[0160] Although four-phase control scheme 700 is shown in FIG. 7 as a stand-alone control scheme and / or system, the aspects of this disclosure can be used with other apparatuses, systems, and / or methods, such as, but not limited to, lithographic apparatus LA, support structure MT, linear motor 200, second control loop 264, pair of linear motors 300, transport system 400, alternative transport system 400', alternative transport system 400", control flow diagram 900, and / or control flow diagram 1000. In some aspects, four-phase control scheme 700 can be utilized in linear motor 200, for example, in first and second components 220, 240 via controller 260. In some aspects, four-phase control scheme 700 can be utilized in pair of linear motors 300, for example, in upper and lower linear motors 200a, 200bvia controllers 260. In some aspects, four-phase control scheme 700 can be utilized in transport system 400, for example, in first and second pairs of linear motors 300a, 300b via first and second pair controllers 360a, 360b.

[0161] As shown in FIG. 7, in first configuration 70 (e.g., first phase), variable magnets 230a, 230a', 230a", etc. in sequence Sn250 (e.g., Sn= 4n + 1 where n = 0, 1, 2, 3, ...) are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control). In second configuration 72 (e.g., second phase), variable magnets 230b, 230b', 230b", etc. in sequence Sn250, adjacent to first configuration 70 along a direction of travel of object stage 320 (e.g., +Y-axis), are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control). In third configuration 74 (e.g., third phase), variable magnets 230c, 230c', 230c", etc. in sequence Sn250, adjacent to second configuration 72 along a direction of travel of object stage 320 (e.g., +Y-axis), are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control). In fourth configuration 76 (e.g., fourth phase), variable magnets 230d, 230d', 230d", etc. in sequence Sn250, adjacent to third configuration 74 along a direction of travel of object stage 320 (e.g., +Y-axis), are activated to adjust upper and lower vertical gaps 210a, 210b and move object stage 320 along vertical axis 326 (e.g., Z-axis), for example, by second control loop 264 (e.g., Z-axis control).

[0162] In some aspects, four-phase control scheme 700 can be utilized in second control loop 264 (e.g., Z-axis control), for example, via controller 260 in linear motor 200, via controllers 260 in pair of linear motors 300, or via first and second pair controllers 360a, 360b of transport system 400. In some aspects, four-phase control scheme 700 can be utilized to adjust upper and lower vertical gaps 210a, 210b (e.g., Z-axis control) along a direction of travel of object stage 320 (e.g., Y-axis). For example, as shown in FIG. 7, four-phase control scheme 700 with first configuration 70, second configuration 72, third configuration 74, and fourth configuration 76 can be applied sequentially as object stage 320 translates along the positive longitudinal axis 322 (e.g., +Y-axis). In some aspects, four-phase control scheme 700 can be reversed for bi-directional control of object stage 320. For example, four-phase control scheme 700 order can be reversed so that fourth configuration 76, third configuration 74, second configuration 72, and first configuration 70 are applied sequentially as object stage 320 translates along the negative longitudinal axis 322 (e.g., -Y-axis).

[0163] Exemplary Control Flow Diagrams

[0164] FIGS. 8-10 illustrate control flow diagrams for linear motor 200, pair of linear motors 300, and transport system 400, according to various exemplary aspects. FIG. 8 illustrates control flow diagram 800 for a three-phase control scheme (e.g., three-phase control scheme 600) for linear motor 200, pair of linear motors 300, and / or transport system 400, according to an exemplary aspect. It is to be appreciated that not all steps in FIG. 8 are needed to perform the disclosure provided herein. Further,some of the steps may be performed simultaneously, sequentially, and / or in a different order than shown in FIG. 8. Control flow diagram 800 shall be described with reference to FIGS. 2-6. However, control flow diagram 800 is not limited to those example aspects.

[0165] In step 802, as shown in the example of FIGS. 2-6, first control loop 262 (e.g., Y-axis control) can be applied to first component 220 of linear motor 200 to accelerate second component 240, opposing first component 220, along longitudinal axis 202 (e.g., Y-axis) of linear motor 200. In some aspects, for example, as shown in FIG. 3, first control loop 262 (e.g., Y-axis control) can be applied to pair of linear motors 300 to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis) of object stage 320. In some aspects, for example, as shown in FIGS. 4 and 5, first control loop 262 (e.g., Y-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis) of object stage 320.

[0166] In step 804, as shown in the example of FIGS. 2-6, second control loop 264 (e.g., Z-axis control) can be applied to first component 220 of linear motor 200 to maintain vertical gap 210 between first and second components 220, 240 along vertical axis 206 (e.g., Z-axis) of linear motor 200. In some aspects, for example, as shown in FIG. 3, second control loop 264 (e.g., Z-axis control) can be applied to pair of linear motors 300 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and pair of linear motors 300 along vertical axis 326 (e.g., Z-axis) of object stage 320. In some aspects, for example, as shown in FIGS. 4 and 5, second control loop 264 (e.g., Z-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and first and second pairs of linear motors 300a, 300b along vertical axis 326 (e.g., Z-axis) of object stage 320.

[0167] In step 806, as shown in the example of FIGS. 2-6, variable magnets 230a-230c, 230a'-230c', etc. of first component 220 in sequence Sn250 (e.g., three-phase sequence Sn= 3n + 1 where n = 0, 1, 2, 3, ...) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'- 244d', etc. of second component 240 to adjust and / or maintain vertical gap 210. In some aspects, variable magnets 230a-230c, 230a'-230c', etc. of upper and lower linear motors 200a, 200b of pair of linear motors 300 in sequence Sn250 (e.g., three-phase sequence Sn= 3n + 1 where n = 0, 1, 2, 3, ...) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'-244d', etc. of upper and lower linear motors 200a, 200b of pair of linear motors 300, respectively, to adjust and / or maintain upper and lower vertical gaps 210a, 210b. In some aspects, variable magnets 230a-230c, 230a'- 230c', etc. of upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b of transport system 400 in sequence Sn250 (e.g., three-phase sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . .) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'- 244d', etc. of upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b of transport system 400, respectively, to adjust and / or maintain upper and lower vertical gaps 210a, 210b.

[0168] FIG. 9 illustrates control flow diagram 900 for a four-phase control scheme (e.g., four-phase control scheme 700) for linear motor 200, pair of linear motors 300, and / or transport system 400, according to an exemplary aspect. It is to be appreciated that not all steps in FIG. 9 are needed to perform the disclosure provided herein. Further, some of the steps may be performed simultaneously, sequentially, and / or in a different order than shown in FIG. 9. Control flow diagram 900 shall be described with reference to FIGS. 2-5 and 7. However, control flow diagram 900 is not limited to those example aspects.

[0169] In step 902, as shown in the example of FIGS. 2-5 and 7, first control loop 262 (e.g., Y-axis control) can be applied to first component 220 of linear motor 200 to accelerate second component 240, opposing first component 220, along longitudinal axis 202 (e.g., Y-axis) of linear motor 200. In some aspects, first control loop 262 (e.g., Y-axis control) can be applied to pair of linear motors 300 to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis) of object stage 320. In some aspects, first control loop 262 (e.g., Y-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis) of object stage 320.

[0170] In step 904, as shown in the example of FIGS. 2-5 and 7, second control loop 264 (e.g., Z-axis control) can be applied to first component 220 of linear motor 200 to maintain vertical gap 210 between first and second components 220, 240 along vertical axis 206 (e.g., Z-axis) of linear motor 200. In some aspects, second control loop 264 (e.g., Z-axis control) can be applied to pair of linear motors 300 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and pair of linear motors 300 along vertical axis 326 (e.g., Z-axis) of object stage 320. In some aspects, second control loop 264 (e.g., Z-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and first and second pairs of linear motors 300a, 300b along vertical axis 326 (e.g., Z-axis) of object stage 320.

[0171] In step 906, as shown in the example of FIGS. 2-5 and 7, variable magnets 230a-230d, 230a'- 230d', etc. of first component 220 in sequence S„ 250 (e.g., four-phase sequence .S'„ = 4 / z + I where n = 0, 1, 2, 3, ...) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'-244d', etc. of second component 240 to adjust and / or maintain vertical gap 210. In some aspects, variable magnets 230a-230d, 230a'-230d', etc. of upper and lower linear motors 200a, 200b of pair of linear motors 300 in sequence Sn250 (e.g., four-phase sequence .S'„ = 4 / z + I where n = 0, 1, 2, 3, ...) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'-244d', etc. of upper and lower linear motors 200a, 200b of pair of linear motors 300, respectively, to adjust and / or maintain upper and lower vertical gaps 210a, 210b. In some aspects, variable magnets 230a-230d, 230a'- 230d', etc. of upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a, 300b of transport system 400 in sequence Sn250 (e.g., four-phase sequence .S'„ = 4 / z + I where n = 0, 1, 2, 3, ...) can be activated when aligned spatially with opposing permanent magnets 244a-244d, 244a'- 244d', etc. of upper and lower linear motors 200a, 200b of first and second pairs of linear motors 300a,300b of transport system 400, respectively, to adjust and / or maintain upper and lower vertical gaps 210a, 210b.

[0172] FIG. 10 illustrates control flow diagram 1000 for transport system 400, according to an exemplary aspect. It is to be appreciated that not all steps in FIG. 10 are needed to perform the disclosure provided herein. Further, some of the steps may be performed simultaneously, sequentially, and / or in a different order than shown in FIG. 10. Control flow diagram 1000 shall be described with reference to FIGS. 2-7. However, control flow diagram 1000 is not limited to those example aspects.

[0173] In step 1002, as shown in the example of FIGS. 2-7, first control loop 262 (e.g., Y-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to accelerate object stage 320 along longitudinal axis 322 (e.g., Y-axis) of object stage 320.

[0174] In step 1004, as shown in the example of FIGS. 2-7, second control loop 264 (e.g., Z-axis control) can be applied to first and second pairs of linear motors 300a, 300b of transport system 400 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and first and second pairs of linear motors 300a, 300b along vertical axis 326 (e.g., Z-axis) of object stage 320.

[0175] In step 1006, optionally, as shown in the example of FIGS. 2-7, third control loop 382 (e.g., XZ-plane control) can be applied to first and second reluctance motors 370a, 370b of transport system 400 to maintain upper and lower vertical gaps 210a, 210b between object stage 320 and first and second pairs of linear motors 300a, 300b along vertical axis 326 (e.g., Z-axis) of object stage 320. In some aspects, third control loop 382 (e.g., XZ-plane control) can counter-balance forces along vertical axis 326 (e.g., Z-axis) generated from second control loop 264 (e.g., Z-axis control) in first and second pairs of linear motors 300a, 300b. In some aspects, third control loop 382 (e.g., XZ-plane control) can be applied to first and second reluctance motors 370a, 370b of transport system 400 to maintain first and second horizontal gaps 350a, 350b between object stage 320 and first and second reluctance motors 370a, 370b along transverse axis 324 (e.g., X-axis) of object stage 320.

[0176] Various embodiments of the present apparatuses, systems and methods are disclosed in the subsequent list of numbered clauses:1. A transport system comprising: an object stage having a longitudinal axis, a transverse axis, and a vertical axis; two opposing pairs of linear motors configured to accelerate the object stage along the longitudinal axis and maintain a vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis, the two opposing pairs of linear motors comprising: a first pair of linear motors comprising a first upper linear motor coupled to a top surface of the object stage and a first lower linear motor coupled to a bottom surface of the object stage; and a second pair of linear motors comprising a second upper linear motor coupled to the top surface of the object stage and a second lower linear motor coupled to the bottom surface of the object stage,wherein the first and second pairs of linear motors are symmetric about the vertical axis; and a controller coupled to the two opposing pairs of linear motors and configured to control movement of the object stage along the longitudinal axis and control the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis.2. The transport system of clause 1, wherein: the first upper and lower linear motors are symmetric about the longitudinal axis, and the second upper and lower linear motors are symmetric about the longitudinal axis.3. The transport system of clause 1, wherein: the first upper and lower linear motors are symmetric about an axis substantially parallel to the longitudinal axis, and the second upper and lower linear motors are symmetric about the axis substantially parallel to the longitudinal axis.4. The transport system of clause 1, wherein: the first upper and lower linear motors are symmetric about a center of mass of the object stage, and the second upper and lower linear motors are symmetric about the center of mass of the object stage.5. The transport system of clause 1, wherein: the first upper and lower linear motors are symmetric about a center of gravity of the object stage, and the second upper and lower linear motors are symmetric about the center of gravity of the object stage.6. The transport system of clause 1 , wherein the controller is configured to maintain a horizontal gap between the object stage and the two opposing pairs of linear motors along the transverse axis.7. The transport system of clause 6, wherein the first and second pairs of linear motors extend along the longitudinal axis and are coupled to transverse distal ends of the object stage.8. The transport system of clause 7, wherein the transverse distal ends of the object stage have a symmetric shape.9. The transport system of clause 8, wherein the symmetric shape comprises an opening angle of about 90 degrees.10. The transport system of clause 8, wherein the symmetric shape is a right triangle.11. The transport system of clause 8, wherein the object stage has a hexagonal cross-section along the transverse axis.12. The transport system of clause 1, wherein the controller is configured to: control movement of the object stage along the longitudinal axis with a first control loop, and control the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis with a second control loop.13. The transport system of clause 12, wherein the second control loop is superimposed on the first control loop.14. The transport system of clause 12, wherein the second control loop is applied when variable magnets of the two opposing pairs of linear motors are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors.15. The transport system of clause 14, wherein the second control loop is applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.16. The transport system of clause 12, wherein the first and second control loops are configured to operate in a three-phase control scheme.17. The transport system of clause 12, wherein the first and second control loops are configured to operate in a four-phase control scheme, a five-phase control scheme, a six-phase control scheme, or a nine-phase control scheme.18. The transport system of clause 11 , further comprising a plurality of reluctance actuators coupled to the object stage and configured to maintain the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis.19. The transport system of clause 18, wherein the plurality of reluctance actuators are configured to apply counter-balancing forces along the vertical axis relative to forces applied along the vertical axis by the controller.20. The transport system of clause 18, wherein the plurality of reluctance actuators are symmetric about the vertical axis and configured to maintain a horizontal gap between the object stage and the plurality of reluctance actuators.21. The transport system of clause 18, wherein the plurality of reluctance actuators extend along the longitudinal axis and are coupled to transverse distal ends of the object stage.22. The transport system of clause 21, wherein the transverse distal ends of the object stage have a symmetric shape.23. The transport system of clause 22, wherein the symmetric shape comprises an opening angle of about 90 degrees.24. The transport system of clause 22, wherein the symmetric shape is a right triangle.25. The transport system of clause 22, wherein the object stage has a hexagonal cross-section along the transverse axis.26. The transport system of clause 21, wherein the transverse distal ends of the object stage comprise a soft magnetic material.27. The transport system of clause 1, wherein: the first upper linear motor is configured to maintain a first upper vertical gap between the top surface of the object stage and the first upper linear motor,the first lower linear motor is configured to maintain a first lower vertical gap between the bottom surface of the object stage and the first lower linear motor, the second upper linear motor is configured to maintain a second upper vertical gap between the top surface of the object stage and the second upper linear motor, and the second lower linear motor is configured to maintain a second lower vertical gap between the bottom surface of the object stage and the second lower linear motor.28. The transport system of clause 27, wherein the controller is configured to: adjust the first upper and lower linear motors so that the first upper and lower vertical gaps are equal, and adjust the second upper and lower linear motors so that the second upper and lower vertical gaps are equal.29. The transport system of clause 1, wherein: forces between the first upper and lower linear motors of the first pair of linear motors are equal and opposite, and forces between the second upper and lower linear motors of the second pair of linear motors are equal and opposite.30. The transport system of clause 1 , wherein a spatial arrangement of the two opposing pairs of linear motors surrounding the object stage is configured to reduce parasitic normal forces in the first and second pairs of linear motors.31. A linear motor comprising: a first component comprising an armature having a plurality of magnetic cores surrounded by respective coil windings thereby forming a plurality of variable magnets; a second component comprising a plurality of permanent magnets having alternating polarity, wherein the first and second components are opposing and configured to translate relative to one another along a longitudinal axis of the linear motor and maintain a vertical gap between the first and second components; and a controller coupled to the first component and configured to control translation along the longitudinal axis and control the vertical gap between the first and second components.32. The linear motor of clause 31 , wherein the controller is configured to: control translation along the longitudinal axis with a first control loop, and control the vertical gap between the first and second components with a second control loop.33. The linear motor of clause 32, wherein the second control loop is superimposed on the first control loop.34. The linear motor of clause 32, wherein the second control loop is applied when variable magnets of the first component are aligned spatially with opposing permanent magnets of the second component.35. The linear motor of clause 34, wherein the second control loop is applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.36. The linear motor of clause 32, wherein the first and second control loops are configured to operate in a three-phase control scheme.37. The linear motor of clause 32, wherein the first and second control loops are configured to operate in a four-phase control scheme, a five-phase control scheme, a six-phase control scheme, or a nine-phase control scheme.38. The linear motor of clause 32, wherein: the plurality of magnetic cores are spaced apart by a magnetic core pitch and the plurality of permanent magnets are spaced apart by a permanent magnet pitch, and wherein a ratio of the magnetic core pitch to the permanent magnet pitch is 1.33.39. The linear motor of clause 31 , wherein the plurality of magnetic cores comprise a soft magnetic material.40. The linear motor of clause 31, wherein the plurality of permanent magnets are arranged in a Halbach array.41. A lithographic apparatus comprising: an illumination system configured to illuminate a patterning device; a projection system configured to project an image of the patterning device onto a patterning substrate; a reticle stage configured to support the patterning device and comprising a longitudinal axis, a transverse axis, and a vertical axis; and a transport system configured to translate the reticle stage, the transport system comprising: two opposing pairs of linear motors configured to translate the reticle stage along the longitudinal axis and maintain a vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis; and a controller coupled to the two opposing pairs of linear motors and configured to control translation of the reticle stage along the longitudinal axis and control the vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis.42. The lithographic apparatus of clause 41, wherein the controller is configured to: control translation of the reticle stage along the longitudinal axis with a first control loop, and control the vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis with a second control loop.43. The lithographic apparatus of clause 42, wherein the second control loop is applied when variable magnets of the two opposing pairs of linear motors are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors.44. The lithographic apparatus of clause 43, wherein the second control loop is applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.45. A method comprising: applying a first control loop to two opposing pairs of linear motors to accelerate an object stage along a longitudinal axis of the object stage; and applying a second control loop to the two opposing pairs of linear motors to maintain a vertical gap between the object stage and the two opposing pairs of linear motors along a vertical axis of the object stage, wherein the second control loop is superimposed on the first control loop.46. The method of clause 45, wherein the applying the second control loop comprises activating variable magnets of the two opposing pairs of linear motors when variable magnets are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors.47. The method of clause 46, wherein the activating variable magnets comprises activating variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.48. The method of clause 45, further comprising applying a third control loop to a plurality of reluctance actuators to maintain the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis and to counter-balance forces along the vertical axis from the second control loop.49. The method of clause 48, wherein the third control loop is configured to maintain a horizontal gap between the object stage and the plurality of reluctance actuators.50. The method of clause 49, wherein the plurality of reluctance actuators extend along the longitudinal axis and are coupled to transverse distal ends of the object stage.

[0177] Although specific reference may be made in this text to the use of the apparatus, system, and / or lithographic apparatus in the manufacture of ICs, it should be explicitly understood that such an apparatus, system, and / or lithographic apparatus described herein may have other possible applications, for example, it can be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, LCD panels, thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle,” “wafer,” or “die” herein may be considered as synonymous with the more general terms “mask,” “substrate,” and “target portion”, respectively.

[0178] Although specific reference may have been made above to the use of aspects in the context of optical lithography, it will be appreciated that aspects may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substratewhereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

[0179] It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by those skilled in relevant art(s) in light of the teachings herein.

[0180] The term “substrate” as used herein describes a material onto which material layers are added. In some aspects, the substrate itself may be patterned and materials added on top of it may also be patterned, or may remain without patterning. The substrate referred to herein may be processed, before or after exposure, for example, in a track unit (e.g., a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology unit, and / or an inspection unit. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example, to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0181] The following examples are illustrative, but not limiting, of the aspects of this disclosure. Other suitable modifications and adaptations of the variety of conditions and parameters normally encountered in the field, and which would be apparent to those skilled in the relevant art(s), are within the spirit and scope of the disclosure.

[0182] While specific aspects have been described above, it will be appreciated that the aspects may be practiced otherwise than as described. The description is not intended to limit the scope of the claims.

[0183] It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary aspects as contemplated by the inventor(s), and thus, are not intended to limit the aspects and the appended claims in any way.

[0184] The aspects have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed.

[0185] The foregoing description of the specific aspects will so fully reveal the general nature of the aspects that others can, by applying knowledge within the skill of the art, readily modify and / or adapt for various applications such specific aspects, without undue experimentation, without departing from the general concept of the aspects. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed aspects, based on the teaching and guidance presented herein.

[0186] The breadth and scope of the aspects should not be limited by any of the above-described exemplary aspects, but should be defined only in accordance with the following claims and their equivalents.

Claims

CLAIMS1. A transport system comprising: an object stage having a longitudinal axis, a transverse axis, and a vertical axis; two opposing pairs of linear motors configured to accelerate the object stage along the longitudinal axis and maintain a vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis, the two opposing pairs of linear motors comprising: a first pair of linear motors comprising a first upper linear motor coupled to a top surface of the object stage and a first lower linear motor coupled to a bottom surface of the object stage; and a second pair of linear motors comprising a second upper linear motor coupled to the top surface of the object stage and a second lower linear motor coupled to the bottom surface of the object stage, wherein the first and second pairs of linear motors are symmetric about the vertical axis; and a controller coupled to the two opposing pairs of linear motors and configured to control movement of the object stage along the longitudinal axis and control the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis.

2. The transport system of claim 1, wherein: the first upper and lower linear motors are symmetric about the longitudinal axis and the second upper and lower linear motors are symmetric about the longitudinal axis; or the first upper and lower linear motors are symmetric about an axis substantially parallel to the longitudinal axis and the second upper and lower linear motors are symmetric about the axis substantially parallel to the longitudinal axis.

3. The transport system of claim 1, wherein: the first upper and lower linear motors are symmetric about a center of mass of the object stage and the second upper and lower linear motors are symmetric about the center of mass of the object stage; or the first upper and lower linear motors are symmetric about a center of gravity of the object stage and the second upper and lower linear motors are symmetric about the center of gravity of the object stage.

4. The transport system of claim 1, wherein: the controller is configured to maintain a horizontal gap between the object stage and the two opposing pairs of linear motors along the transverse axis;the first and second pairs of linear motors extend along the longitudinal axis and are coupled to transverse distal ends of the object stage; the transverse distal ends of the object stage have a symmetric shape; the symmetric shape comprises an opening angle of about 90 degrees; the symmetric shape is a right triangle; and the object stage has a hexagonal cross-section along the transverse axis.

5. The transport system of claim 1, wherein the controller is configured to: control movement of the object stage along the longitudinal axis with a first control loop, and control the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis with a second control loop.

6. The transport system of claim 5, wherein: the second control loop is superimposed on the first control loop; the second control loop is applied when variable magnets of the two opposing pairs of linear motors are aligned spatially with opposing permanent magnets of the two opposing pairs of linear motors; the second control loop is applied to variable magnets in a sequence Sn= 3n + 1 where n = 0, 1, 2, 3, . . ., such that a force along the vertical axis is applied from variable magnets in the sequence Snto maintain the vertical gap.

7. The transport system of claim 5, wherein the first and second control loops are configured to operate in a three-phase control scheme, a four-phase control scheme, a five -phase control scheme, a six-phase control scheme, or a nine -phase control scheme.

8. The transport system of claim 1, further comprising a plurality of reluctance actuators coupled to the object stage and configured to maintain the vertical gap between the object stage and the two opposing pairs of linear motors along the vertical axis, wherein: the plurality of reluctance actuators are configured to apply counter-balancing forces along the vertical axis relative to forces applied along the vertical axis by the controller; the plurality of reluctance actuators are symmetric about the vertical axis and configured to maintain a horizontal gap between the object stage and the plurality of reluctance actuators; and the plurality of reluctance actuators extend along the longitudinal axis and are coupled to transverse distal ends of the object stage.

9. The transport system of claim 8, wherein: the transverse distal ends of the object stage have a symmetric shape;the symmetric shape comprises an opening angle of about 90 degrees; the symmetric shape is a right triangle; the object stage has a hexagonal cross-section along the transverse axis; and the transverse distal ends of the object stage comprise a soft magnetic material.

10. The transport system of claim 1, wherein: the first upper linear motor is configured to maintain a first upper vertical gap between the top surface of the object stage and the first upper linear motor; the first lower linear motor is configured to maintain a first lower vertical gap between the bottom surface of the object stage and the first lower linear motor; the second upper linear motor is configured to maintain a second upper vertical gap between the top surface of the object stage and the second upper linear motor; and the second lower linear motor is configured to maintain a second lower vertical gap between the bottom surface of the object stage and the second lower linear motor.

11. The transport system of claim 10, wherein the controller is configured to: adjust the first upper and lower linear motors so that the first upper and lower vertical gaps are equal, and adjust the second upper and lower linear motors so that the second upper and lower vertical gaps are equal.

12. The transport system of claim 1, wherein: forces between the first upper and lower linear motors of the first pair of linear motors are equal and opposite, and forces between the second upper and lower linear motors of the second pair of linear motors are equal and opposite.

13. The transport system of claim 1, wherein a spatial arrangement of the two opposing pairs of linear motors surrounding the object stage is configured to reduce parasitic normal forces in the first and second pairs of linear motors.

14. A linear motor comprising: a first component comprising an armature having a plurality of magnetic cores surrounded by respective coil windings thereby forming a plurality of variable magnets; a second component comprising a plurality of permanent magnets having alternating polarity,wherein the first and second components are opposing and configured to translate relative to one another along a longitudinal axis of the linear motor and maintain a vertical gap between the first and second components; and a controller coupled to the first component and configured to control translation along the longitudinal axis and control the vertical gap between the first and second components.

15. A lithographic apparatus comprising: an illumination system configured to illuminate a patterning device; a projection system configured to project an image of the patterning device onto a patterning substrate; a reticle stage configured to support the patterning device and comprising a longitudinal axis, a transverse axis, and a vertical axis; and a transport system configured to translate the reticle stage, the transport system comprising: two opposing pairs of linear motors configured to translate the reticle stage along the longitudinal axis and maintain a vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis; and a controller coupled to the two opposing pairs of linear motors and configured to control translation of the reticle stage along the longitudinal axis and control the vertical gap between the reticle stage and the two opposing pairs of linear motors along the vertical axis.

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