Electromagnetic motor and method for determining position-dependent motor constant of electromagnetic motor

Abstract

The invention provides a method of determining a position dependent motor constant of an electromagnetic motor, the electromagnetic motor comprising a magnet assembly and a coil assembly configured to be displaced relative to each other in a direction of movement, the method comprises: displacing the magnet assembly along a predetermined trajectory of interest in the direction of movement at a substantially constant speed relative to the coil assembly; applying a disturbance having a predetermined frequency to the electromagnetic motor during the displacement of the magnet assembly relative to the coil assembly; determining a position error and an electromagnetic motor force of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest; a position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest is determined based on the determined position error and the electromagnetic motor force.

Description

Cross Reference to Related Applications

[0001] This application claims priority from EP application 23166250.3 filed on 31 March 2023, the contents of which are incorporated herein by reference in their entirety. TECHNICAL FIELD

[0002] The present invention relates to an electromagnetic motor, in particular an electromagnetic motor that can be applied in a lithographic apparatus, for example for displacing or positioning a patterning device or a substrate. BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. The lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). It can project a pattern (which can also be referred to as a design layout or design) from a patterning device (for example a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (for example a wafer).

[0004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have continually decreased while the amount of functional elements (such as transistors) incorporated into a chip has increased, following a trend commonly referred to as Moore's law. To keep up with Moore's law, the industry continues to develop new tools and techniques to create increasingly smaller features. To project a pattern on a substrate, a lithographic apparatus can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which can be formed on the substrate. More advanced lithographic apparatuses can use a deeper ultraviolet (DUV) radiation, having a wavelength of 13.5 nm or even extreme ultraviolet (EUV) radiation, having a wavelength of 13.5 nm or even 6.7 nm. In order to project a pattern on a substrate a lithographic apparatus can use a radiation beam to project a pattern on a substrate.

[0005] To form a pattern of a patterning device onto a substrate, a scanning process is typically applied, whereby both the patterning device and the substrate are displaced relative to the applied radiation beam. Typically, electromagnetic motors and actuators are applied to realize this displacement. To ensure accurate positioning of the pattern of the patterning device on the substrate, it is important to accurately control the motors and actuators involved in the positioning. Typically, the response of known actuators or motors to a specific control signal can be unknown to some extent for various reasons. In particular, the known motor constant indicating the force generated per unit of current is not constant over the displacement range of the motor or actuator. To account for this, methods have been developed to determine the motor constant in order to improve the positioning of the motor or actuator. It has been found that known methods to determine the motor constant are rather time consuming or lack resolution. SUMMARY

[0006] It is an object of the present invention to provide a method of determining position dependent motor constants of an electromagnetic motor that at least alleviates the above-mentioned problems of known methods.

[0007] According to an aspect of the present invention, there is provided an electromagnetic motor comprising: a magnet assembly configured to generate a magnetic field; a coil assembly comprising at least one coil; the coil assembly being configured to cooperate with the magnet assembly to cause the magnet assembly to move relative to the coil assembly in a movement direction; a power supply configured to supply power to the coil assembly during use; a control unit configured to: control the power supply to supply a current to the coil assembly so as to displace the magnet assembly relative to the coil assembly along a predetermined trajectory of interest in the movement direction at a substantially constant speed; apply an interference to the electromagnetic motor having a predetermined frequency during displacement of the magnet assembly relative to the coil assembly; determine a position of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest and an electromagnetic motor force; determine a position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position and the electromagnetic motor force.

[0008] According to another aspect, there is provided a stage apparatus for use in a lithographic apparatus, the stage comprising an electromagnetic motor according to the present invention. The stage apparatus can for example be configured to hold a patterning device or a substrate.

[0009] According to yet another aspect, there is provided a lithographic apparatus comprising a stage apparatus according to the present invention.

[0010] According to yet another aspect of the present invention, there is provided a method of determining position dependent motor constants of an electromagnetic motor, the electromagnetic motor comprising a magnet assembly and a coil assembly, the magnet assembly and the coil assembly being configured to displace relative to each other in a movement direction, the method comprising: displacing the magnet assembly relative to the coil assembly along a predetermined trajectory of interest in the movement direction at a substantially constant speed; applying an interference to the electromagnetic motor having a predetermined frequency during displacement of the magnet assembly relative to the coil assembly; determining a position error of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest and an electromagnetic motor force; determining a position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force. BRIEF DESCRIPTION OF DRAWINGS

[0011] Embodiments of the application will now be described, by way of example only, with reference to the accompanying drawings: Figure 1 A schematic illustration of a lithographic apparatus is shown; Figure 2 A detailed view of a part of the lithographic apparatus of Figure 1 Figure 3 A position control system is schematically illustrated; Figure 4 A first electromagnetic motor according to the application is shown; Figure 5 A second electromagnetic motor according to the application is shown; Figure 6 The variation of the motor constant along the trajectory Y1-Y2 is schematically illustrated; Figure 7 A position control system applicable to the application is schematically illustrated; Figure 8 A flow chart of a method according to the application is schematically illustrated; Figure 9 A position control system applicable to the application is schematically illustrated, including possible positions of an inserted disturbance; Figure 10 Various ways of determining the amplitude of the alternating signal are schematically illustrated. DETAILED DESCRIPTION

[0012] In the present document, the terms“radiation” and“beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[0013] The term“reticle”,“mask” or“patterning device” as used herein can be broadly interpreted to refer to a generic patterning device that can be used in processes of patterning a beam of radiation, so as to impinge a patterned cross-section on a target portion of a substrate. The term“light valve” can also be used in this document. Besides the traditional mask (transmissive or reflective, binary, phase-shift, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array.

[0014] Figure 1 ​An lithographic apparatus LA is schematically illustrated. The lithographic apparatus LA includes an illumination system (also referred to as illuminator) IL configured to condition radiation B (e.g., UV, DUV or EUV radiation), a mask support (e.g., a mask table) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA in accordance with certain parameters, a substrate support (e.g., a wafer table) WT configured to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support in accordance with certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0015] In operation, the illumination system IL receives a radiation beam from a radiation source SO, e.g., via a beam delivery system BD. The illumination system IL can include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and / or other types of optical components, or any combination thereof, for directing, shaping, and / or controlling radiation. The illuminator IL can be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in its plane of

[0016] The term “projection system” PS used herein should be broadly interpreted as encompassing various types of projection system, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, and / or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein can be considered as synonymous with the more general term “projection system” PS.

[0017] The lithographic apparatus LA can be of a type that includes a liquid supply system to supply a liquid to a space between the projection system PS and the substrate W, e.g., to fill a gap, and / or to fill a space that would otherwise be filled with air. The liquid supply system can supply liquid such as water (and possibly also other liquids such as an immersion fluid) to the space. The liquid can be supplied along the entire surface of the gap, or only along parts of the gap. The liquid can be retained in the gap with liquid retention means, for example a fluid retention frame, disposed in the gap, and / or a fluid retention frame disposed above the projection system PS. A liquid can be used to fill the space between the projection system PS and the substrate W, e.g., for effecting immersion lithography. The use of liquid enables improved resolution of the lithography process. More information on liquid immersion can be found in US 6952253, which is incorporated herein by reference.

[0018] The lithographic apparatus LA can also be of a type that includes two or more substrate supports WT (also referred to as “dual stage”).

[0019] In addition to the substrate support WT, the lithography apparatus LA can include a measurement table. The measurement table is arranged to hold a sensor and / or a cleaning device. The sensor can be arranged to measure a characteristic of the projection system PS or a characteristic of the radiation beam B. The measurement table can hold a plurality of sensors. The cleaning device can be arranged to clean a part of the lithography apparatus, for example a part of the projection system PS or a part of the system that provides the immersion liquid. The measurement table can be movable under the projection system PS when the substrate support WT is distanced from the projection system PS.

[0020] In operation, the radiation beam B is incident on a patterning device (for example a mask MA) held by the mask support MT and forms an image of the pattern (design layout) present on the patterning device MA. After passing through the patterning device MA, the radiation beam B passes through the projection system PS which projects the beam onto a target portion C of the substrate W. By means of the second positioner PW and the position measurement system IF, the substrate support WT can be accurately moved, for example, so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and possibly another position sensor (not explicitly shown in Figure 1 The patterning device MA and the substrate W can be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the shown substrate alignment marks Pl, P2 occupy a dedicated target portion, they can be located in a space between target portions. When the substrate alignment marks Pl, P2 are located between target portions C, they are referred to as scribe-lane alignment marks.

[0021] For the sake of clarity, a Cartesian coordinate system is used to elucidate the present invention. The Cartesian coordinate system has three axes, namely an x-axis, a y-axis and a z-axis. Each of the three axes is orthogonal to the other two axes. A rotation around the x-axis is referred to as an Rx rotation. A rotation around the y-axis is referred to as an Ry rotation. A rotation around the z-axis is referred to as an Rz rotation. The x-axis and the y-axis define a horizontal plane, whereas the z-axis is in a vertical direction. The Cartesian coordinate system does not limit the present invention and is only used for clarity. Instead, another coordinate system (for example a cylindrical coordinate system) can be used to elucidate the present invention. The orientation of the Cartesian coordinate system can be different, for example, such that the z-axis has a component along the horizontal plane.

[0022] Figure 2 A more detailed view of a part of the lithography apparatus LA of Figure 1 is shown. The lithography apparatus LA can be provided with a base frame BF, a balance mass BM, a metrology frame MF and a vibration isolation system IS. The metrology frame MF supports the projection system PS. In addition, the metrology frame MF can support Figure 1The position measurement system PMS is part of a lithographic apparatus LA. The metrology frame MF is supported by a base frame BF via a vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce propagation of vibrations from the base frame BF to the metrology frame MF.

[0023] The second positioner PW is arranged to accelerate the substrate support WT by providing a drive force between the substrate support WT and the balance mass BM. The drive force accelerates the substrate support WT in a desired direction. Due to conservation of momentum, the drive force is also applied to the balance mass BM with an equal magnitude but in a direction opposite to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the mass of the moving parts of the second positioner PW and the substrate support WT.

[0024] In one embodiment, the second positioner PW is supported by the balance mass BM. For example, where the second positioner PW comprises a planar motor to levitate the substrate support WT above the balance mass BM. In another embodiment, the second positioner PW is supported by the base frame BF. For example, where the second positioner PW comprises a linear motor and where the second positioner PW comprises a bearing, such as a gas bearing, to levitate the substrate support WT above the base frame BF.

[0025] The position measurement system PMS can comprise any type of sensor suitable to determine the position of the substrate support WT. The position measurement system PMS can comprise any type of sensor suitable to determine the position of the mask support MT. The sensor can be an optical sensor, such as an interferometer or an encoder. The position measurement system PMS can comprise a combination of an interferometer and an encoder. The sensor can be another type of sensor, such as a magnetic sensor, a capacitive sensor or an inductive sensor. The position measurement system PMS can determine the position relative to a reference, for example the metrology frame MF or the projection system PS. The position measurement system PMS can determine the position of the substrate table WT and / or the mask support MT by measuring the position or by measuring the time derivative of the position, for example the velocity or the acceleration.

[0026] The position measurement system PMS can comprise an encoder system. The encoder system is known from, for example, US patent application US 2007 / 0058173 Al filed on September 7, 2006, which is incorporated herein by reference. The encoder system comprises an encoder head, a grating, and a sensor. The encoder system can receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam and the secondary radiation beam originate from the same radiation beam, i.e., an original radiation beam. At least one of the primary radiation beam and the secondary radiation beam is created by diffracting the original radiation beam with the grating. If both the primary radiation beam and the secondary radiation beam are created by diffracting the original radiation beam with the grating, the primary radiation beam needs to have a different diffraction order than the secondary radiation beam. Different diffraction orders are, for example, +1 order, -1 order, +2 order, and -2 order. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. The sensor in the encoder head determines a phase or a phase difference of the combined radiation beam. The sensor generates a signal based on the phase or the phase difference. The signal is representative of a position of the encoder head relative to the grating. One of the encoder head and the grating can be arranged on the substrate structure WT. The other one of the encoder head and the grating can be arranged on the metrology frame MF or the base frame BF. For example, multiple encoder heads are arranged on the metrology frame MF, while the grating is arranged on a top surface of the substrate support WT. In another example, the grating is arranged on a bottom surface of the substrate support WT, and the encoder head is arranged below the substrate support WT.

[0027] The position measurement system PMS can comprise an interferometer system. The interferometer system is known from, for example, US patent US 6,020,964 filed on July 13, 1998, which is incorporated herein by reference. The interferometer system can comprise a beam splitter, a mirror, a reference mirror, and a sensor. A radiation beam is split by the beam splitter into a reference beam and a measurement beam. The measurement beam propagates to the mirror and is reflected by the mirror back to the beam splitter. The reference beam propagates to the reference mirror and is reflected by the reference mirror back to the beam splitter. At the beam splitter, the measurement beam and the reference beam are combined into a combined radiation beam. The combined radiation beam is incident on the sensor. The sensor determines a phase or a frequency of the combined radiation beam. The sensor generates a signal based on the phase or the frequency. The signal is representative of a displacement of the mirror. In one embodiment, the mirror is connected to the substrate support WT. The reference mirror can be connected to the metrology frame MF. In one embodiment, the measurement beam and the reference beam are combined into the combined radiation beam by additional optical components instead of the beam splitter.

[0028] The first positioner PM can include a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT with high precision within a small range of movement relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module with relatively low precision within a large range of movement relative to the projection system PS. With the combination of the long-stroke module and the short-stroke module, the first positioner PM is able to move the mask support MT with high precision relative to the projection system PS within a large range of movement. Similarly, the second positioner PW can include a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT with high precision within a small range of movement relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module with relatively low precision within a large range of movement relative to the projection system PS. With the combination of the long-stroke module and the short-stroke module, the second positioner PW is able to move the substrate support WT with high precision relative to the projection system PS within a large range of movement.

[0029] The first positioner PM and the second positioner PW are each provided with an electromagnetic motor to move the mask support MT and the substrate support WT, respectively. The electromagnetic motor can be a linear motor to provide a driving force along a single axis, e.g., the y-axis. Multiple linear motors can be applied to provide driving forces along multiple axes. The motor can be a planar motor to provide a driving force along multiple axes. For example, a planar motor can be arranged to move the substrate support WT with 6 degrees of freedom. The electromagnetic motor can be an electromagnetic actuator including at least one coil and at least one magnet. The actuator is arranged to move the at least one coil relative to the at least one magnet by applying an electric current to the at least one coil. The actuator can be a moving-magnet type actuator having the at least one magnet coupled to the substrate support WT and the mask support MT, respectively. The actuator can be a moving-coil type actuator having the at least one coil coupled to the substrate support WT and the mask support MT, respectively. The electromagnetic actuator can be a voice coil actuator, a magneto-resistive actuator, a Lorentz actuator, or a piezoelectric actuator, or any other suitable actuator.

[0030] The lithographic apparatus LA includes as Figure 3A position control system PCS is schematically shown. The position control system PCS comprises a setpoint generator SP, a feedforward controller FF and a feedback controller FB. The position control system PCS provides a drive signal to a device / motor combination P-EM / P. The device / motor combination comprises an electromagnetic motor EM, which can be a motor of a first positioner PM or a second positioner PW. The motor EM of the device / motor combination P-EM drives a device P, which can comprise a substrate support WT or a mask support MT. The device P can also be referred to as a motor driven load. The output of the device / motor combination P-EM is a position quantity, such as a position or a velocity or an acceleration of the device. The position quantity is measured with a position measurement system PMS. The position measurement system PMS generates a signal, which is a position signal representing the position quantity of the device P. The setpoint generator SP generates a signal, which is a reference signal representing a desired position quantity of the device P. For example, the reference signal represents a desired trajectory of the substrate support WT. The difference between the reference signal and the position signal forms an input to the feedback controller FB. Based on this input, the feedback controller FB provides at least part of the drive signal to the electromagnetic motor EM of the device / motor combination P-EM. The reference signal can form an input to the feedforward controller FF. Based on this input, the feedforward controller FF provides at least part of the drive signal to the motor EM of the device / motor combination. The feedforward FF can make use of information about the dynamic properties of the device P, such as mass, stiffness, resonance modes and eigenfrequencies.

[0031] The present invention aims to improve the performance of electromagnetic motors or actuators applied in a lithographic apparatus, for example the motors applied in the long stroke or short stroke modules described above.

[0032] Figure 4 A first example of an electromagnetic motor 400 according to the present invention is schematically shown. In the embodiment shown, the electromagnetic motor 400 comprises a magnet assembly 410 and a coil assembly 420. The magnet assembly 410 as shown comprises two magnet yokes 410.1 provided with permanent magnets 410.2. The coil assembly 420 as shown comprises a single coil, which can carry an electric current in a direction perpendicular to the plane of the drawing. When supplied with such a current, a force will be generated between the magnet assembly 410 and the coil assembly 420, which force acts in the indicated X direction. Said force can cause a movement of the coil assembly 410 relative to the magnet assembly 420 in said direction, which direction is therefore also referred to as the direction of movement of the electromagnetic actuator 400. Typically, the coil assembly 420 can also have multiple coils.

[0033] According to the present application, the electromagnetic motor 400 further comprises a power supply 430 for powering the coil assembly. The power supply 430 can for example be configured to supply a current indicated by the dashed line 430.1 to one or more coils of the coil assembly 410 of the electromagnetic motor 400. The electromagnetic motor 400 further comprises a control unit 440 configured to control the power supply 430 of the electromagnetic motor 400. In particular, according to the present application, the control unit is configured to control the electromagnetic motor in a specific way in order to determine a position dependent motor constant of the electromagnetic motor along a trajectory of interest in the direction of motion. The trajectory of interest can for example correspond to a specific stroke of the electromagnetic motor as shown in the figure.

[0034] In one embodiment, the control unit of the electromagnetic motor according to the present application can comprise a position control system as shown in Figure 3 Generally, the control unit 440 of the electromagnetic motor according to the present application can be configured to receive one or more input signals, such as position measurement signals or setpoint signals, and can be configured to output one or more control signals to control the electromagnetic motor. In order to determine the position dependent motor constant, the control unit 440 of the electromagnetic motor according to the present application is configured to perform the following actions.

[0035] In a first step, the control unit 440 of the electromagnetic motor 400 is configured to control the power supply 430 indicated by the control signal 440.1 to supply a current to the coil assembly 410 in order to displace the magnet assembly relative to the coil assembly in the direction of motion along a predetermined trajectory of interest at a substantially constant speed. To this end, the control unit 440 can be configured to generate the required position setpoint to achieve the displacement. As such, the control unit 440 can comprise a setpoint generator similar to the setpoint generator SP as described above. Alternatively, the control unit 440 can receive a setpoint signal 440.2 from an external setpoint generator.

[0036] In a second step, the control unit 440 is configured to apply a disturbance to the electromagnetic motor 400 having a predetermined frequency during the displacement of the magnet assembly relative to the coil assembly. As will be explained in more detail below, there are various ways to apply a disturbance to the electromagnetic motor, for example by injecting a disturbance force in the control scheme applied by the control unit, or by applying an actual disturbance force to the electromagnetic actuator.

[0037] In a third step, the control unit 440 is configured to determine the position of the magnet assembly relative to the coil assembly along the trajectory of interest and the electromagnetic motor force. In one embodiment, the control unit 440 can be connected to a position measurement system, for example Figure 3 as shown in the figure PMS, which can be configured to measure the position of the coil assembly 420 and / or the magnet assembly 410 in order to obtain a position measurement signal of the coil assembly and / or the magnet assembly.

[0038] In a fourth step, the control unit is configured to determine a position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position and the electromagnetic motor force.

[0039] As a result, a motor constant of the electromagnetic motor along the predetermined trajectory of interest is obtained. When this position dependent motor constant is implemented in the control unit of the electromagnetic motor subsequently, a more accurate position control of the load driven by the motor can be obtained.

[0040] Figure 4 The exemplary electromagnetic motor 400 shown in Fig. 4 can also be referred to as an electromagnetic actuator or linear actuator or Lorentz actuator. Such electromagnetic motors or actuators typically have a relatively small stroke. In case a load or device is to be moved over a considerable distance, an electromagnetic motor can be used, for example, having a coil assembly with an array of coils and a magnet assembly with an array of magnets.

[0041] Figure 5 An electromagnetic motor 500 according to the present application is schematically shown, which is capable of having a relatively large displacement of the coil assembly with respect to the magnet assembly. Figure 5 (a) shows a cross section of the motor 500 schematically, which shows a magnet assembly 510 comprising an array of magnets 510.1 (e.g. permanent magnets) arranged on a magnet yoke 510.2 (e.g. a ferromagnetic yoke or the like). The motor 500 further comprises a coil assembly 520 comprising an array of coils 520.2 arranged along the indicated Y direction and mounted to a holder 520.1. In the arrangement as shown, the array of magnets 510.1 is configured to generate a spatially alternating magnetic field along the indicated Y direction during use, which Y direction can also be referred to as the direction of movement, since during use, when a suitable set of currents is supplied to the array of coils 520.2 of the coil assembly 520, movement of the coil assembly 520 with respect to the magnet assembly 510 in the direction of movement can be established. Note that in a similar way as discussed with respect to Figure 4 The electromagnetic motor 500 further comprises a power supply and control unit for powering and controlling the coil assembly 520 of the electromagnetic motor 500. These components are not shown in Fig. 5. Figure 5 (a). Figure 5 (b) and 5 (c) show the electromagnetic motor 500 schematically for two different positions of the coil assembly 520 of the motor with respect to the magnet assembly 510. In Figure 5 (b), the coil assembly 520 is in a leftmost position with respect to the magnet assembly 510 along the direction of movement, while in Figure 5In (c), the coil assembly 520 is positioned at the rightmost position relative to the magnet assembly 510 along the direction of movement. Therefore, the range of strokes Y1 to Y2 can be considered as the useful operating range of the motor, or the trajectory of interest in the direction of movement. Note that positioning the coil assembly beyond the range Y1 to Y2 relative to the magnet assembly will result in a reduction in the interaction between the coil assembly and the magnet assembly, which will lead to a significant reduction in the motor constant (i.e., the amount of force generated per unit current supplied to the coil assembly).

[0042] For illustrative purposes only, Figure 6 The diagram schematically illustrates the motor constant K as a function of the relative position (Y) between the coil assembly and the magnet assembly of a motor such as electromagnetic motor 500. Note that the motor constant K(y) can vary along the range Y1 to Y2 between values ​​Kmin and Kmax, and the range Y1 to Y2 can be related to... Figure 5 The range shown is similar to the range shown. Typically, perceived variations in motor constants can have various causes, such as manufacturing tolerances of the magnet assembly, the applied magnet, the coils in the coil array, and the coil assembly itself. Perceived variations in motor constants will also typically include a periodic component, which can be associated, for example, with the magnet pitch of the magnet array in the motor's magnet assembly.

[0043] Reference Figure 7-8 The method for obtaining position-dependent motor constants according to the present invention will be explained in more detail.

[0044] Figure 7 A more detailed position control scheme is schematically illustrated, which can be used to control the electromagnetic motor according to the invention, for example, to control a stage device in a lithography apparatus. The control scheme, particularly the position control scheme PCS, can be implemented, for example, in the control unit of the electromagnetic motor according to the invention. In addition to the following, Figure 7 The control scheme shown is similar to Figure 3 The control scheme. In Figure 7 The control scheme further details the P-EM(y) assembly of the equipment motors to illustrate that the electromagnetic motors used in the equipment motor assembly can have position-dependent motor constants, i.e., motor constants that depend on the y-position of the equipment motor assembly. From a control perspective, the equipment motor assembly can be considered as a system or component that converts force into acceleration, which then causes displacement along the direction of movement. In this case, the equipment motor assembly can be defined by the nominal motor constant Km. nom This is characterized by singular values. Due to the aforementioned effects, the actual motor constant will not be constant, but rather a function of the position y in the direction of movement. This is in Figure 7 The detailed equipment / motor combination is represented as Km(y) in the P-EM. Therefore, Figure 7The output of block Km(y) in the diagram represents the actual force generated by the motor, which is used to accelerate the load, represented by the mass m. The output of the P-EM(y) block thus corresponds to the displacement y of the driven device or load.

[0045] As mentioned above, the output of the position control system PCS corresponds to the drive signal for the P-EM(y) combination. In the illustrated PCS system, the drive signal is a combination of the output of the feedforward controller FF and the feedback controller FB. In general, the drive signal, indicated by reference numeral 710, will be considered as the desired drive force or desired motor force for driving the device to the desired position indicated by the setpoint generator. This drive signal will not result in the desired acceleration or displacement of the device in view of the position dependent motor constant Km(y). In case the position dependent motor constant Km(y) is known in advance, a correction can be applied to the drive signal in such a way that the desired control of the device is obtained. In Figure 7 In the diagram, the correction is indicated as K rcp (y), which is thus a position dependent correction or adjustment that can be applied to the generated drive signal 710. As a result of the correction or adjustment, an adjusted drive signal 720 can thus be obtained, which takes into account the position dependent motor constant Km(y). In the present invention, a method is disclosed that enables the determination of the position dependent motor constant Km(y), and thus the determination of the required correction or adjustment K rcp (y) to take into account the position dependence. In Figure 8 The method of determining the position dependent motor constant is schematically illustrated in the flowchart, which can also be considered as a kind of calibration method for the electromagnetic motor.

[0046] As Figure 8 illustrated, the method of determining the position dependent motor constant according to the present invention comprises a first step 810 of displacing a magnet assembly of the electromagnetic motor with respect to a coil assembly of the electromagnetic motor along a predetermined trajectory of interest in a direction of motion at a substantially constant speed. In one embodiment, the first step can be implemented in practice, for example, by a control unit of the electromagnetic motor, which is configured to control a power supply of the electromagnetic motor, as for example described above with reference to Figure 4 The trajectory of interest can for example be the range of motion of the electromagnetic motor, for example the range Y1 to Y2 as illustrated in Figure 5 and Figure 6

[0047] The method of determining the position dependent motor constant according to the present invention further comprises a second step 820 of applying a disturbance with a predetermined frequency to the electromagnetic motor during the displacement of the magnet assembly with respect to the coil assembly, which disturbance exposes the mass behavior of the device. In other words, the frequency of the disturbance should be in the range where the device or load shows mass behavior, i.e. 1 / ms 2 ​with a slope of -2. Various ways of implementing such a disturbance will be described in detail below.

[0048] The method of determining position dependent motor constants according to the present application further comprises a third step 830 of determining the position of the magnet assembly relative to the coil assembly and the electromagnetic motor force along the predetermined trajectory of interest. With reference to the control scheme of Figure 7 , the position of the magnet assembly relative to the coil assembly can be determined, for example, using a position measurement system such as the PMS system indicated.

[0049] The method of determining position dependent motor constants according to the present application further comprises a fourth step 840 of determining the position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force. With reference to the control scheme of Figure 7 , in embodiments of the present application, the electromagnetic motor force can be equivalent to the drive signal 710 generated by the position control system PCS.

[0050] With regard to the implementation of step 820 of the method according to the present application, the following approach can be applied.

[0051] In a first embodiment, the disturbance referred to in step 820 of the method of determining position dependent motor constants according to the present application can be implemented in the position control system or control unit for controlling the electromagnetic motor for which the motor constant is to be determined. This is shown in Figure 9 . Figure 9 A position control scheme similar to the scheme of Figure 7 is schematically shown, except for the position dependent correction or adjustment Krcp(y) to be determined.

[0052] As a first example, the disturbance of step 820 of the method according to the present application can be injected or superimposed to the drive signal generated by the position control system PCS. In Figure 9 , this is indicated by arrow 910. In the embodiment shown, the drive signal (i.e. the combination of the outputs of the feed forward controller FF and the feedback controller FB representing the desired drive force or desired motor force) is combined with the disturbance indicated by arrow 910. In this example, the disturbance can thus be considered as a disturbance force or force component added to the drive signal output by the PCS. This disturbance force is further referred to as disturbance force F_dist(y).

[0053] As a second example, the disturbance of step 820 of the method according to the present application can be injected or superimposed to the set point used by the PCS. In Figure 9In this case, the setpoint generator SP can be configured to generate setpoints to perform displacements along a predetermined trajectory of interest mentioned in step 810 of the method according to the application. The disturbance indicated by arrow 920 can thus be added to the setpoints. In this example, the disturbance can thus be considered as a position disturbance added to the setpoints.

[0054] As a third example, the disturbance of step 820 of the method according to the application can be injected or superimposed to the position error determined by the PCS. In this case, the position error is obtained by the difference between the setpoints of the setpoint generator SP and the y-positions determined by the position measurement system PMS. The position error is input into the feedback controller FB. The disturbance indicated by arrow 930 can be injected or superimposed to the position error. In this example, the disturbance can thus be considered as a position disturbance added to the position error. The position error is further referred to as e(y). Figure 9

[0055] In a second embodiment, the disturbance of step 820 of the method according to the application can be implemented as an actual disturbance force applied to the calibrated electromagnetic motor. This can be done for example by applying a disturbance force to the stator or to the mover of the electromagnetic motor in case both are movable. In case the stator is mounted to a rigid construction, the disturbance force can be applied to the mover. In the context of a lithographic apparatus, the electromagnetic motor (e.g. the motor shown in Fig. 1) can be applied in a long stroke module, e.g. as described above. Such a long stroke module can further comprise a short stroke module, e.g. comprising one or more actuators configured to position an object table. In an embodiment, one or more of the actuators of the short stroke module can be used to induce a disturbance force on the electromagnetic motor of the long stroke module. Figure 5

[0056] In embodiments of the application, the applied disturbance is a substantially sinusoidal disturbance with a predetermined frequency.

[0057] The method of determining a position dependent motor constant according to the application, in particular step 840 of the method, can be implemented as follows.

[0058] As shown in Fig. 2, the electromagnetic motor for driving an apparatus or object, such as an object table, will have a position dependent motor constant which can be described by Km(y). Alternatively, Km(y) can be expressed as: Figure 9 (1)

[0059] In order to compensate for the position dependent effect of the motor constant, the correction Krcp(y) should be such that: (2) where c is a constant. ​​​Thus, when [1 + k(y)] or Km(y) is known, the K rcp (y) can be determined. In addition to the constant gain, the position dependent motor constant can also be determined by determining Figure 7 and Figure 9 the transfer function P-EM(y) as shown in Fig. 2. From this, the compensation can be determined.

[0060] According to the method of the present application, this is done as follows: For determining the position dependent motor constant, the electromagnet motor is moved along a predetermined trajectory of interest at a substantially constant velocity along the trajectory. During said displacement, a disturbance of a predetermined frequency, e.g. a sinusoidally varying disturbance, is applied to the motor. During said displacement, various characteristics can be tracked. In particular, the position of the magnet assembly relative to the coil assembly and the electromagnetic motor force F_act(y) will be tracked as a function of the displacement, i.e. along the trajectory of interest. Other variables that can be tracked during the displacement along the trajectory of interest are the position error e and the applied disturbance, e.g. the disturbance force F_dist(y). Due to the nature of the applied disturbance, the electromagnetic motor force and the error e as well as the disturbance force are alternating signals or traces. For determining the transfer function P-EM(y), only the amplitudes of said tracked variables are required.

[0061] Using this tracked data, the transfer function P-EM(y) can be determined as follows: Based on the process sensitivity PS(y) and the sensitivity S(y) of the process, the transfer function P-EM(y) is determined. In particular: (3) wherein: is the amplitude of the position error e along the predetermined trajectory, is the amplitude of the disturbance force applied during the displacement along the predetermined trajectory, and is the amplitude of the actuator force applied during the displacement along the predetermined trajectory. (4) (5) In view of equation (5), the transfer function P-EM(y) and thus the position dependent motor constant as given by equation (1) for example, can be derived from the position error e and from the actuator force .

[0062] Note that the position error e can be easily obtained as the difference between the actual position y measured by the PMS system as shown in Fig. 1 and the setpoint obtained from the setpoint generator SP. Figure 7 and Figure 9 Fig. 2.

[0063] It can also be noted that, as mentioned above, the electromagnetic motor force may be equivalent to the driving signal 710 generated by the position control system PCS as indicated. Figure 7 and Figure 9

[0064] As mentioned above, the position error, the disturbance force and the electromagnetic motor force are typically alternating signals. The amplitude of such signals can be determined, for example, using a fitting algorithm or similar method. Reference is made to Figure 10 Such a method is schematically explained.

[0065] Figure 10 A signal S is schematically shown, which may, for example, correspond to the actual position y measured along the trajectory of interest, the position error e, the disturbance force or the electromagnetic motor force. It is noted that the indicated signal S also corresponds to the signal obtained over time, i.e. during the constant speed displacement, assuming that the displacement along the trajectory of interest is a displacement at substantially constant speed. It is noted that the signal S is a periodic signal, i.e. it has a period T.

[0066] A first method to derive the amplitude of the signal S is to perform a fit of the signal to a sinusoidal signal spanning one or more periods of the signal S. It is noted that the period of the signal S is known, since it will correspond to the period of the disturbance force having a predetermined frequency. In Figure 10 the window 1000 spans 3 periods of the signal S. To determine the amplitude of the signal S over said window, the signal S can be fitted to a sinusoidal signal M(y) spanning the same period as the window 1000.

[0067] The signal M(y) can be considered to be a sinusoidal signal having an unknown amplitude and phase, optionally a sinusoidal signal having an unknown offset and an unknown slope. The general expression for M(y) will thus be: M(y) = A1*sin(2π *y+ A2) + A3*y +A4 (6)

[0068] Using known fitting techniques, for example least square fitting, the parameters A1-A4 can be obtained, from which it can then be considered that A1 corresponds to the amplitude of the signal S over the window 1000. The procedure can then be repeated for adjacent windows until the amplitude of the signal S is obtained over the desired trajectory of interest. It is noted that by the first method shown, one value of the amplitude of the signal S over the window 1000 will be obtained. To obtain a more dense or more detailed dataset of the amplitude of the signal S, the window 1000 can be made narrower, for example spanning only one period. Alternatively or in addition, the sequence of applied windows can be overlapping.

[0069] A second method to derive the amplitude of the signal S is to determine the maximum and minimum values of the signal S. For a portion of the signal S, these maximum and minimum values are indicated by Figure 10 ​the corresponding MAX and MIN indications in the signal S. To obtain the amplitude of the signal S, one can then consider fitting a polynomial to the maxima and minima, etc., resulting in polynomials Pmax and Pmin. Subtracting Pmin from Pmax will yield the amplitude of the signal S.

[0070] On the right side of Figure 10 a third method of obtaining the amplitude of the signal S is shown, which can be considered a simplified version of the second method. To obtain the amplitude value of the signal S, a line L is constructed between two adjacent maxima of the signal. Then, the amplitude of the signal S at the minimum between the two adjacent maxima can be interpreted as the distance D between said minimum and the line.

[0071] Irrespective of the method applied, it can be noted that a sufficiently high interference frequency and / or a sufficiently low substantially constant velocity of displacement is preferably chosen to ensure that the available amplitude data is sufficient to accurately assess motor constant variations of the electromagnetic motor. In this regard, it is recommended to ensure that at least 5 data points are available within the magnet pitch of the electromagnetic motor.

[0072] Once the amplitudes of the required signals are obtained, the transfer function P-EM(y) as well as the correction K rcp (y) can be determined. When the correction K rcp (y) is subsequently implemented in the position control system or control unit of the electromagnetic motor, a more accurate positioning or displacement of the load or device driven by the motor can be obtained.

[0073] As mentioned above, the electromagnetic motor according to the present application can advantageously be used to drive a stage of a lithographic apparatus. As will be appreciated by the skilled person, the electromagnetic motor according to the present application can also be used to drive other components in a lithographic apparatus, for example a reticle mask device. Advantageously, the electromagnetic motor according to the present application can also be applied outside the field of lithography.

[0074] Although specific reference can be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein can have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc.

[0075] Although specific reference can be made in this text to embodiments of the application in the context of lithography apparatus, embodiments of the application can be used in other apparatus. For example, embodiments of the application can be used in a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or another substrate) or a mask (or another patterning device). These apparatus can generally be referred to as lithographic tools. Such lithographic tools can use vacuum conditions or environmental (non-vacuum) conditions.

[0076] Although specific reference can have been made above to the use of embodiments of the application in the context of optical lithography, it will be appreciated that embodiments of the application can be used in other applications, for example, imprint lithography, where the context allows.

[0077] RAMEmbodiments of the application can be implemented in hardware, firmware, software, or any combination thereof, to the extent that the context allows. Embodiments of the application can also be implemented as instructions stored on a machine-readable medium, which can be read and executed by one or more processors. A machine-readable medium can 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 can include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other form of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions can 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 processing of the firmware, software, routines, instructions, etc. by the computing device, processor, controller or other devices, and that the firmware, software, routines, instructions, etc. can not produce further tangible objects or be stored on storage media apart from the machine-readable medium.

[0078] While specific embodiments of the application have been described above, it will be appreciated that the application can be practiced otherwise than as described. The description is intended to be illustrative, not restrictive. It will be apparent to those skilled in the art that modifications, changes and substitutions can be made by men of ordinary skill in the art without departing from the scope of the claims as set forth below. Other aspects of the application are set forth in the following numbered clauses. 1. An electromagnetic motor comprising: a magnet assembly configured to generate a magnetic field; a coil assembly comprising at least one coil; the coil assembly being configured to cooperate with the magnet assembly so as to cause the magnet assembly to move in a direction of movement relative to the coil assembly; a power supply configured to supply power to the coil assembly during use; a control unit configured to: control the power supply to supply a current to the coil assembly so as to displace the magnet assembly in the direction of movement relative to the coil assembly along a predetermined trajectory of interest at a substantially constant velocity; apply an interference having a predetermined frequency to the electromagnetic motor during displacement of the magnet assembly relative to the coil assembly; determine a position of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest and an electromagnetic motor force; determine a position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position and the electromagnetic motor force. 2. The electromagnetic motor according to aspect 1, wherein the magnet assembly comprises an array of magnets to generate a spatially alternating magnetic field in the direction of movement during use, and wherein the coil assembly comprises an array of coils arranged in the direction of movement. 3. The electromagnetic motor according to aspect 1 or 2, wherein the disturbance is a substantially sinusoidal disturbance. 4. The electromagnetic motor according to any one of the preceding aspects, wherein the control unit is configured to receive or generate a position setpoint of the electromagnetic motor to cause the displacement, and to receive a position signal representative of a position of the electromagnetic motor. 5. The electromagnetic motor according to aspect 4, wherein the control unit is configured to determine a position error along the trajectory of interest based on the position signal and the position setpoint, and to determine the position dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force. 6. The electromagnetic motor according to aspect 4 or 5, wherein the control unit is configured to determine a desired motor force during the displacement based on the position setpoint and the position signal. 7. The electromagnetic motor according to aspect 6, wherein the disturbance is a disturbance force, and wherein the control unit is configured to superimpose the disturbance force to the desired motor force. 8. The electromagnetic motor according to any one of aspects 4 to 7, wherein the disturbance is a position disturbance, and wherein the control unit is configured to superimpose the position disturbance to the position setpoint or to a difference between the position setpoint and the position signal. 9. The electromagnetic motor according to any one of aspects 4 to 7, wherein the electromagnetic motor further comprises an actuator, and wherein the control unit is configured to control operation of the actuator so as to cause the disturbance. 10. The electromagnetic motor according to any one of the preceding aspects, wherein determining the position of the magnet assembly relative to the coil assembly and the electromagnetic motor force comprises determining an amplitude of the electromagnetic motor force and the position along the predetermined trajectory of interest. 11. The electromagnetic motor according to any one of the preceding aspects with reference to aspect 2, wherein the predetermined frequency and substantially constant velocity are selected to have multiple periods of the disturbance during displacement of the magnet assembly relative to the coil assembly across a magnet pitch of the array of magnets. 12. A stage apparatus for use in a lithographic apparatus, the stage comprising an electromagnetic motor according to any of the preceding aspects. 13. The stage apparatus according to aspect 12, wherein the stage is configured to hold a patterning device or a substrate. 14. A lithographic apparatus comprising a stage apparatus according to aspect 12 or 13. 15. A method of determining position dependent motor constants of an electromagnetic motor, the electromagnetic motor comprising a magnet assembly and a coil assembly, the magnet assembly and the coil assembly being configured to be displaced relative to each other in a direction of movement, the method comprising: - displacing the magnet assembly relative to the coil assembly along a predetermined trajectory of interest in the direction of movement at a substantially constant velocity; - applying a disturbance to the electromagnetic motor having a predetermined frequency during displacement of the magnet assembly relative to the coil assembly; - determining a position error and an electromagnetic motor force of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest; - determining position dependent motor constants of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force. 16. The method according to aspect 15, further comprising: - receiving or generating a position setpoint of the electromagnetic motor to cause the displacement and receiving a position signal indicative of a position of the electromagnetic motor. 17. The method according to aspect 16, further comprising: - determining a desired motor force during the displacement based on the position setpoint and the position signal. 18. The method according to aspect 17, wherein the disturbance is a disturbance force, and wherein applying the disturbance comprises superimposing the disturbance force to the desired motor force.

Claims

1. An electromagnetic motor, comprising: a magnet assembly configured to generate a magnetic field; a coil assembly comprising at least one coil; the coil assembly being configured to cooperate with the magnet assembly to cause the magnet assembly to move relative to the coil assembly in a movement direction; a power supply configured to supply power to the coil assembly during use; a control unit configured to: control the power supply to supply a current to the coil assembly so as to displace the magnet assembly relative to the coil assembly along a predetermined trajectory of interest at a substantially constant speed; apply an interference having a predetermined frequency to the electromagnetic motor during displacement of the magnet assembly relative to the coil assembly; determine a position of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest and an electromagnetic motor force; determine a position-dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position and the electromagnetic motor force.

2. The electromagnetic motor of claim 1, wherein the magnet assembly comprises an array of magnets for generating a spatially alternating magnetic field in the movement direction during use, and wherein the coil assembly comprises an array of coils arranged in the movement direction.

3. The electromagnetic motor of claim 1 or 2, wherein, the interference is a substantially sinusoidal interference.

4. The electromagnetic motor of any one of the preceding claims, wherein the control unit is configured to receive or generate a position setpoint of the electromagnetic motor to cause the displacement, and is configured to receive a position signal representative of a position of the electromagnetic motor.

5. The electromagnetic motor of claim 4, wherein the control unit is configured to determine a position error along the predetermined trajectory of interest based on the position signal and the position setpoint, and is configured to determine the position-dependent motor constant of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force.

6. The electromagnetic motor of claim 4 or 5, wherein the control unit is configured to determine a desired motor force during the displacement based on the position setpoint and the position signal.

7. The electromagnetic motor of any one of claims 4 to 6, wherein, the interference is a position interference, and wherein the control unit is configured to superimpose the position interference to the position setpoint or to a difference between the position setpoint and the position signal.

8. The electromagnetic motor of any one of claims 4 to 6, wherein the electromagnetic motor further comprises an actuator, and wherein the control unit is configured to control operation of the actuator so as to cause the interference.

9. The electromagnetic motor of any one of the preceding claims, wherein determining the position of the magnet assembly relative to the coil assembly and the electromagnetic motor force comprises determining a magnitude of the electromagnetic motor force and the position along the predetermined trajectory of interest.

10. The electromagnetic motor according to any of the preceding claims when dependent on claim 2, wherein, the predetermined frequency and the substantially constant speed are selected to have a plurality of periods of the interference during displacement of the magnet assembly relative to the coil assembly across a magnet pitch of the array of magnets.

11. A stage apparatus for use in a lithographic apparatus, the stage comprising an electromagnetic motor according to any one of the preceding claims.

12. The stage apparatus according to claim 11, wherein the stage is configured to hold a patterning device or a substrate.

13. A lithographic apparatus comprising a stage apparatus according to claim 11 or 12.

14. A method of determining position dependent motor constants of an electromagnetic motor, the electromagnetic motor comprising a magnet assembly and a coil assembly, the magnet assembly and the coil assembly being configured to be displaced relative to each other in a movement direction, the method comprising: displacing the magnet assembly relative to the coil assembly along a predetermined trajectory of interest in the movement direction at a substantially constant velocity; applying a disturbance to the electromagnetic motor having a predetermined frequency during the displacement of the magnet assembly relative to the coil assembly; determining a position error and an electromagnetic motor force of the magnet assembly relative to the coil assembly along the predetermined trajectory of interest; determining position dependent motor constants of the electromagnetic motor along the predetermined trajectory of interest based on the determined position error and the electromagnetic motor force.

15. The method according to claim 14, further comprising: receiving or generating a position setpoint of the electromagnetic motor to cause the displacement, and receiving a position signal indicative of a position of the electromagnetic motor.

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