Method for controlling a position of a movable object, position control system, and an exposure apparatus

Abstract

A method for controlling a position of a movable object, the method including: measuring a position of a sensor or sensor target on the movable object to obtain a position measurement signal, providing an error signal, providing a control signal on the basis of the error signal using a controller, providing a feed-forward signal on the basis of a set-point signal, actuating one or more actuators on the basis of the control signal and the feed-forward signal, and providing a compliance compensation signal, wherein the error signal is obtained by comparing a set-point position, the measured position of the position measurement, and the compliance compensation signal, and wherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.

Description

METHOD FOR CONTROLLING A POSITION OF A MOVABLE OBJECT. POSITION CONTROL SYSTEM. AND AN EXPOSURE APPARATUSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 719,561 which was filed on 12 November 2024 and which is incorporated herein in its entirety by referenceFIELD

[0002] The present description relates to a method for controlling a position of a movable object, a position control system, and an exposure apparatus.BACKGROUND

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

[0004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as ‘Moore’s law’. To keep up with Moore’s law the semiconductor industry is chasing technologies that enable to create increasingly smaller features. To project a pattern on a substrate an exposure apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. An exposure apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within a range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than an exposure apparatus which uses, for example, radiation with a wavelength of 193 nm.SUMMARY

[0005] In an exposure apparatus one or more positioning systems may be used to move movable objects along a trajectory. Such a positioning system may comprise a number of actuators to exert an actuation force on the movable object in an actuation direction, and a control system to provide an actuator input to the one or more actuators.

[0006] With an increasing demand on the throughput and overlay performance of an exposure apparatus, increased acceleration of a movable object, for example a short-stroke module of a patterning device support or a substrate support, is desirable.

[0007] It has been proposed to provide an actuator system for such short-stroke module comprising, to accelerate in a first direction, one or more first reluctance actuators arranged to exert a pulling force on the short-stroke module to accelerate the short-stroke module in the first direction, and to accelerate the short-stroke module in a second direction opposite to the first direction, one or more second reluctance actuators to exert a pulling force on the short-stroke module in the second direction opposite to the first direction. In addition to the force applied to the short stroke module for purpose of acceleration, a force may be maintained on all reluctance actuators to maintain a pre-tension on the short stroke module. Such pretension may improve controllability of the position of the short-stroke module.

[0008] This use of an actuator arrangement having one or more first reluctance motors and one or more second reluctance motors to exert pulling forces on the short-stroke module in acceleration directions, makes it possible to create large accelerations of the short-stroke module, but may also have a disadvantage of stretching of the short-stroke module. As a result of this stretching, the forces exerted on the short-stroke module for accurate positioning of the short-stroke module may be dependent on the direction in which the short-stroke module is accelerated. The stretching of the short-stroke module may thus cause inaccurate positioning of the short-stroke module.

[0009] It is an object to provide, for example, a method and / or a position control system for controlling a position of a movable object that facilitates high accelerations in combination with high positioning accuracy. It is an object to provide a method and / or a position control system for controlling a position of a movable object with high accelerations and high positioning accuracy, when using an actuator arrangement having reluctance motors arranged to exert simultaneously pulling forces on the movable object in opposite directions.

[0010] According to an aspect of the invention there is provided a method for controlling a position of a movable object, the method comprising:measuring a position of a sensor or sensor target on the movable object to obtain a position measurement signal,providing an error signal,providing a control signal on the basis of the error signal using a controller,providing a feed-forward signal on the basis of a set-point signal,actuating one or more actuators on the basis of the control signal and the feed-forward signal, andproviding a compliance compensation signal,wherein the error signal is obtained by comparing a set-point position, the measured position of the position measurement, and the compliance compensation signal, andwherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.

[0011] According to an aspect of the invention, there is provided a position control system forcontrolling the position of a movable object, the position control system comprising:a position measurement system configured to determine a position of a sensor or sensor target on the movable object,a comparator configured to provide an error signal,a controller for providing a control signal on the basis of the error signal,a feed-forward device for providing a feed-forward signal on the basis of a first signal related to the desired position, andone or more actuators configured to act on the movable object on the basis of the control signal and the feed-forward signal,wherein the position control system further comprises a compliance compensation device to provide a compliance compensation signal,wherein the error signal is based on a set-point position, the measured position, and the compliance compensation signal,wherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.

[0012] According to an aspect of the invention, there is provided an exposure apparatus comprising: an illumination system configured to condition a radiation beam;a patterning device support configured to support a patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam;a substrate support constructed to hold a substrate; anda projection system configured to project the patterned radiation beam onto a target portion of the substrate,wherein the lithographic apparatus further comprises the position control system as described herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:Figure 1 depicts a schematic overview of an exposure apparatus, the exposure apparatus being a lithographic apparatus;Figure 2 depicts a detailed view of a part of the lithographic apparatus of Figure 1 ;Figure 3 schematically depicts a position control system to control a position of a movable object;Figure 4 schematically depicts a positioning system comprising a long-stroke module, a shortstroke module and reluctance motors to move the short-stroke module with respect to the long-stroke module; andFigure 5 schematically depicts an algorithm to obtain a direction dependent compliancecompensation for the positioning system of Figure 4.DETAILED DESCRIPTION

[0014] 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).

[0015] The term “reticle”, “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective, binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array.

[0016] Figure 1 schematically depicts an exposure apparatus. The exposure apparatus is a lithographic apparatus LA. The lithographic apparatus LA includes an illumination system (also referred to as illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation or EUV radiation), a mask support (e.g., a mask table) MT constructed 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 constructed 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.

[0017] 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 may 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 may be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in its cross section at a plane of the patterning device MA.

[0018] 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 may be considered as synonymous with the more general term “projection system” PS.

[0019] The lithographic apparatus LA may be of a type wherein at least a portion of the substrate maybe covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system PS and the substrate W - which is also referred to as immersion lithography. More information on immersion techniques is given in United States Patent No. US 6952253, which is incorporated herein in its entirety by reference.

[0020] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also named “dual stage”). In such “multiple stage” machine, the substrate supports WT may be used in parallel, and / or steps in preparation of a subsequent exposure of the substrate W may be carried out on the substrate W located on one of the substrate support WT while another substrate W on the other substrate support WT is being used for exposing a pattern on the other substrate W.

[0021] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measurement stage. The measurement stage is arranged to hold a sensor and / or a cleaning device. The sensor may be arranged to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning device may be arranged to clean part of the lithographic apparatus, for example a part of the projection system PS or a part of a system that provides the immersion liquid. The measurement stage may move beneath the projection system PS when the substrate support WT is away from the projection system PS.

[0022] In operation, the radiation beam B is incident on the patterning device, e.g. mask, MA which is held on the mask support MT, and is patterned by the pattern (design layout) present on patterning device MA. Having traversed the patterning device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position measurement system PMS, the substrate support WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor (which is not explicitly depicted in Figure 1) may be used to accurately position the patterning device MA with respect to the path of the radiation beam B. Patterning device MA and substrate W may be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks P 1 , P2 as illustrated occupy dedicated target portions, they may be located in spaces between target portions. Substrate alignment marks P 1 , P2 are known as scribe-lane alignment marks when these are located between the target portions C.

[0023] To clarify embodiments of the invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axis, i.e., an x-axis, a y-axis and a z-axis. Each of the three axis is orthogonal to the other two axis. 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 about 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 is not limiting the invention and is used for clarification only. Instead, another coordinate system, such as a cylindrical coordinate system, may be used to clarify the invention. The orientation of the Cartesian coordinate system may be different, for example, such that the z-axishas a component along the horizontal plane.

[0024] Figure 2 shows a more detailed view of a part of the lithographic apparatus LA of Figure 1. The lithographic apparatus LA may 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. Additionally, the metrology frame MF may support a part of the position measurement system PMS. The metrology frame MF is supported by the base frame BF via the vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce vibrations from propagating from the base frame BF to the metrology frame MF.

[0025] The second positioner PW is arranged to accelerate the substrate support WT by providing a driving force between the substrate support WT and the balance mass BM. The driving force accelerates the substrate support WT in a desired direction. Due to the conservation of momentum, the driving force is also applied to the balance mass BM with equal magnitude, but at a direction opposite to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the masses of the moving part of the second positioner PW and the substrate support WT. A similar balance mass arrangement may be applied to the mask support MT.

[0026] In an embodiment, the second positioner PW is supported by the balance mass BM. For example, wherein 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, wherein the second positioner PW comprises a linear motor and wherein the second positioner PW comprises a bearing, like a gas bearing, to levitate the substrate support WT above the base frame BF.

[0027] The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the substrate support WT or mask support MT. The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the support WT or MT. The sensor may be an optical sensor such as an interferometer or an encoder. The position measurement system PMS may comprise a combined system of an interferometer and an encoder. The sensor may be another type of sensor, such as a magnetic sensor, a capacitive sensor or an inductive sensor. The position measurement system PMS may determine the position relative to a reference, for example the metrology frame MF or the projection system PS. The position measurement system PMS may determine the position of the substrate table WT and / or the mask support MT by measuring the position or by measuring a time derivative of the position, such as velocity or acceleration.

[0028] The position measurement system PMS may comprise an encoder system. An encoder system is known from for example, United States patent application publication no. US2007 / 0058173, which is incorporated herein in its entirety by reference. The encoder system comprises an encoder head, a grating and a sensor. The encoder system may receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam as well as the secondary radiation beam originate from the same radiation beam, i.e., the original radiation beam. At least one of the primary radiation beamand 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, +lstorder, -1storder, +2ndorder and -2ndorder. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. A sensor in the encoder head determines a phase or phase difference of the combined radiation beam. The sensor generates a signal based on the phase or 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 may be arranged on the support WT or MT. The other of the encoder head and the grating may be arranged on the metrology frame MF or the base frame BF. For example, a plurality of encoder heads are arranged on the metrology frame MF, whereas a grating is arranged on a top surface of the substrate support WT. In another example, a grating is arranged on a bottom surface of the substrate support WT, and an encoder head is arranged below the substrate support WT.

[0029] The position measurement system PMS may comprise an interferometer system. An interferometer system is known from, for example, United States patent no. US6,020,964, hereby incorporated in its entirety by reference. The interferometer system may comprise a beam splitter, a mirror, a reference mirror and a sensor. A beam of radiation 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 an embodiment, the mirror is connected to the support WT or MT. The reference mirror may be connected to the metrology frame MF. In an embodiment, the measurement beam and the reference beam are combined into a combined radiation beam by an additional optical component instead of the beam splitter.

[0030] The first positioner PM may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT relative to the long-stroke module with a high accuracy over a small range of movement. The long-stroke module is arranged to move the shortstroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. 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 relative to the projection system PS with a high accuracy over a large range of movement. Similarly, the second positioner PW may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT relative to the long-stroke module with a high accuracy over a small range of movement.The long-stroke module is arranged to move the short-stroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. 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 relative to the projection system PS with a high accuracy over a large range of movement.

[0031] The first positioner PM and the second positioner PW each are provided with an actuator to move respectively the mask support MT and the substrate support WT. The actuator may be a linear actuator to provide a driving force along a single axis, for example the y-axis. Multiple linear actuators may be applied to provide driving forces along multiple axis. The actuator may be a planar actuator to provide a driving force along multiple axes. For example, the planar actuator may be arranged to move the support WT or MT in 6 degrees of freedom. The actuator may be an electro-magnetic actuator comprising 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 electrical current to the at least one coil. The actuator may be a moving-magnet type actuator, which has the at least one magnet coupled to the respective support WT or MT. The actuator may be a moving-coil type actuator which has the at least one coil coupled to the respective support WT or MT. The actuator may be a voice-coil actuator, a reluctance actuator, a Lorentz-actuator or a piezo-actuator, or any other suitable actuator.

[0032] Figure 3 shows a control scheme of a position control system to control the position of a movable object P (such as support MT, support WT, a short stroke module associated with support MT or WT, etc.). The position control system is arranged to provide actuator inputs as input signals for one or more actuators ACT. The one or more actuators ACT will exert an actuation force on the movable object P corresponding to the respective actuator inputs resulting in an acceleration of the movable object P to a position related value, such as position, velocity and / or acceleration.

[0033] The position control system comprises a set-point generator SP, a feedforward controller FF, a feedback controller FB, a gain balancing and gain scheduling device GB and a compliance compensation device CC.

[0034] The set-point generator SP is arranged to provide a series of set-points to be followed by the controlled movable object P. The series of set-points may for instance comprise a series of positions, velocities and / or accelerations that represent an intended trajectory of the movable object P.

[0035] The feedforward controller FF may provide a feedforward control signal on the basis of the setpoint provided by the set-point generator SP. The feedback controller FB may provide a feedback control signal on the basis of a control error.

[0036] The gain balancing and gain scheduling device GB is arranged to carry out gain balancing and gain scheduling steps to provide a transformation of the control signal into the actuator inputs. The gain balancing and gain scheduling device GB may comprise a transformation matrix arranged to transform the control signal into actuation signals that are fed into the one or more actuators ACT in order to exert actuation forces on the movable object P in respective actuation directions.

[0037] The gain balancing and gain scheduling steps may for instance provide a transformation of thecontrol signal, e.g. the desired actuator forces, into the actuator input, e.g. current setpoints for the one or more actuators ACT, using a non-linear function of required force and actual actuator position.

[0038] The gain balancing and gain scheduling steps may apply a series of linear controllers, wherein each of the linear controllers is arranged to provide a specific control for a different operating point of the system, e.g. a position of the actuator ACT. On the basis of one or more scheduling variables, the actual operating region of the actuator ACT may be determined, and the associated linear controller may be selected to provide the respective actuator input.

[0039] The compliance compensation device CC is arranged to provide a compliance compensation signal which is subtracted from the measured position as measured by the position measurement system PMS. The compliance compensation device CC is configured to approximate the effect of internal deformation of the object P on the measured position. This approximation of the effect of internal deformation of the object P on the measured position is subtracted from the measured position to obtain the feedback signal which is fed back and subtracted from the position set-point signal. The resulting error signal can be used to decrease the effect of internal deformation as this effect is at least partially compensated by the subtraction of the compliance compensation signal.

[0040] The compliance compensation device CC calculates the compliance compensation signal on the basis of the feed-forward signal. Any other suitable signal may be used. The compliance compensation device comprises a compliance compensation gain. In the present embodiment this compliance compensation gain takes into account the direction of acceleration of the object P and the resulting effect on the position measurement by the position measurement system PMS.

[0041] Figure 4 shows an embodiment of a short-stroke module PM-SS of a positioner supporting a patterning device MA. The short-stroke module PM-SS may be supported by a long-stroke module PM-LS as described above. To accelerate the short-stroke module PM-SS in x-direction with respect to the long-stroke module PM-LS, one or more reluctance actuators are provided. An advantage of reluctance motors is that they can provide large forces to create large accelerations of the short-stroke module PM-SS. However, the reluctance actuators can only provide a pulling force.

[0042] In the embodiment of Figure 4, two first reluctance actuators RAC-1 are arranged to exert a first pulling force on the short-stroke module PM-SS in a first direction (positive x-direction) and two second reluctance actuators RAC -2 are arranged to exert a second pulling force on the short-stroke module PM-SS in a second direction opposite to the first direction (negative x-direction).

[0043] To accelerate the short-stroke module PM-SS in the first direction (positive x-direction) the two first reluctance actuators RAC-1 may exert a first pulling force on the short-stroke module PM-SS to accelerate the short-stroke module PM-SS in the first direction and the two second reluctance actuators RAC -2 may exert a second pulling force smaller than the first pulling force on the short-stroke module PM-SS in the second direction to create a pre-tensioning of the short-stroke module PM-SS. This pretensioning is applied to allow a feedback controller to maintain more accurate positioning of the shortstroke module PM-SS by providing corrective forces against external noise and disturbance forces. Inthis situation, the first pulling force may be relatively large compared to the second pulling force.

[0044] Similarly, to accelerate the short-stroke module PM-SS in the second direction (negative x-direction), the second reluctance actuators RAC -2 may exert a second pulling force on the short-stroke module PM-SS to accelerate the short-stroke module PM-SS in the second direction, while the first reluctance actuators RAC-1 are used to exert a first pulling force smaller than the second pulling force on the short-stroke module PM-SS in the first direction to allow pre-tensioning of the short-stroke module PM-SS for varying feedback controller force. In this situation, the second pulling force may be relatively large compared to the first pulling force.

[0045] Correspondingly, reluctance actuators may be provided to move the short-stroke module PM-SS in other directions, e.g. y-direction.

[0046] The use of one or more first reluctance motors RAC-1 and one or more second reluctance motors RAC -2 to exert simultaneously pulling forces on the short-stroke module PM-SS in opposite directions, for example positive and negative x-direction makes it possible to create large and controlled accelerations of the short-stroke module PM-SS, but may also have a disadvantage of stretching of the short-stroke module PM-SS as a result of pre-tensioning, i.e. exerting a pulling force in opposite directions and on opposite sides of the short-stroke module PM-SS. Due to this stretching, the resulting force exerted on the short-stroke module PM-SS is dependent on the direction in which the short-stroke module PM-SS is accelerated. This could possibly lead to acceleration direction dependent crosstalk, as the crosstalk is no longer constant with respect to the direction in which the short-stroke module PM-SS is accelerated.

[0047] The position of the short-stroke module PM-SS may be controlled with the control scheme of Figure 3. In this control scheme, the gain balancing and gain scheduling device GB and / or the compliance compensation device CO can be used to compensate for acceleration direction dependent crosstalk resulting from the use of the one or more first reluctance motors RAC-1 and the one or more second reluctance motors RAC-2 exerting pulling forces on the short-stroke module PM-SS in opposite directions.

[0048] The gain balancing and gain scheduling device GB comprises the transformation matrix arranged to transform the control signal into actuation signals that are fed into the one or more actuators ACT, for example the reluctance actuators RAC-1, RAC-2.

[0049] To determine gains of such a transformation matrix, it is proposed to use a frequency response function (FRF) system identification method. Such a FRF system identification method may for example comprise the following steps.

[0050] A multi-sine signal is constructed through the summation of sine waves across a user-defined excitation frequency grid. Subsequently, a crest-factor optimization may be performed on the phase of these sine waves for global amplitude reduction towards the effective signal value. The obtained multisine signals may then be injected into the actuators to measure transfers and perform frequency response function (FRF) system identification to determine the gains of the transformation matrix.

[0051] To perform decoupling of the actuators and compensate for direction dependent crosstalk, a frequency domain gain balancing calibration method may be used to determine an updated transformation matrix.

[0052] Similar to the method to obtain the gains of a transformation matrix of the gain balancing and gain scheduling device GB, a frequency response function (FRF) system identification method may be used to determine compliance compensation gains of the compliance compensation device CO.

[0053] Figure 5 schematically depicts a compliance compensation algorithm that can be used to determine the compliance compensation gains to be used in the compliance compensation device CO. This compliance compensation algorithm is designed such that it is a continuous calculation which does not contain hard switching. As an alternative, a method containing a hard switch could be applied.

[0054] The algorithm comprises three types of inputs: set-point signals SP, feed-forward signals FF and pretension signals PT. The set-point signals SP are guided into three compliance matrixes, a mean feedforward compliance matrix CC1, a direction dependent compliance matrix CC2 and a pretension compliance matrix PTC. The mean feedforward compliance matrix CC1 takes into account compliance compensation gains which are not dependent on the acceleration direction of the movable object P, e.g. the short-stroke module PM-SS. The direction dependent compliance matrix CC2 takes into account compliance compensation gains which are dependent on the acceleration direction of the movable object P, e.g. the short-stroke module PM-SS. And the pretension compliance matrix PTC defines the relationship between the set-point signals SP and the resulting effects in the pre-tensioning of the movable object P, e.g. the short-stroke module PM-SS.

[0055] The outputs of the mean feedforward compliance matrix CC1 and the direction dependent compliance matrix CC2 are, after being combined with feedforward signals FF, guided to a compliance delay matrix COD. Correspondingly, the output of the pretension compliance matrix PTC is, after being combined with the pretension signal PT guided to a pretension delay matrix PTD. The compliance delay matrix COD and the pretension delay matrix PTD define time delays within the system.

[0056] The FRF system identification method may be applied for multiple positions, wherein for each position an optimization criterium is used. This optimization criterium is for example a generalized least-squares approximation that is used to fit the mass and compliance parameters of the different matrices.

[0057] The mass, compliance parameters and time delays are thus calculated for the feedforward from the mean compliance matrix CC1, the direction dependent compliance matrix CC2, and the pretension compliance matrix PTC as well as the compliance delay matrix COD and the pretension delay matrix PTD. The new parameters obtained with the FRF system identification method may be used to overwrite the old parameters.

[0058] To evaluate the effect of the new parameters, scans may be performed to measure time domain control errors. The time domain control errors should decrease when the new parameters are implemented.

[0059] Hereinabove, a method using a gain balancing and gain scheduling device GB and / or a compliance compensation device CO to compensate for acceleration direction dependent crosstalk resulting from the use of the one or more first reluctance actuators RAC-1 and the one or more second reluctance actuators RAC-2 exerting pulling forces on the short-stroke module PM-SS in opposite direction is described. This method may also be used to compensate for acceleration direction dependent crosstalk in other movable objects, in particular movable objects that are negatively affected by acceleration direction dependent crosstalk, for example due to stretching or internal deformations of the movable object. Such a movable object may for example be a substrate support, in particular a shortstroke module of a substrate support.

[0060] Furthermore, the above embodiments describe the actuation of a short-stroke module of a support MT or WT using reluctance motors configured to exert a pulling force on the short-stroke module. In other embodiments, the actuators may be other actuators than reluctance motors, when used in a configuration in which at least one first actuator is arranged to pull the movable object in a first direction and at least one second actuator is arranged to pull the movable object in a second direction opposite to the first direction or in which at least one first actuator is arranged to push the movable object in a first direction and at least one second actuator is arranged to push the movable object in a second direction opposite to the first direction. Such a configuration could for example comprise pullpush Lorentz motors, which are arranged to only exert pulling forces or only exert pushing forces on the movable object in opposite directions to make acceleration in opposite directions possible.

[0061] The compliance compensation can be used to compensate for acceleration direction dependent crosstalk due to stretching or compression due to push or pull forces in opposite directions.

[0062] Although specific reference may be made in this text to the use of a lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquidcrystal displays (LCDs), thin-film magnetic heads, etc.

[0063] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non-vacuum) conditions.

[0064] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention, where the context allows, is not limited to optical lithography and may be used in other applications, for example imprint lithography.

[0065] Where the context allows, embodiments of the invention may be implemented in hardware,firmware, software, or any combination thereof. Embodiments of the invention 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 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, 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. and in doing that may cause actuators or other devices to interact with the physical world.

[0066] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

[0067] Embodiments include the following numbered clauses:1. A method for controlling a position of a movable object, the method comprising:measuring a position of a sensor or sensor target on the movable object to obtain a position measurement signal,providing an error signal,providing a control signal on the basis of the error signal using a controller,providing a feed-forward signal on the basis of a set-point signal,actuating one or more actuators on the basis of the control signal and the feed-forward signal, andproviding a compliance compensation signal,wherein the error signal is obtained by comparing a set-point position, the measured position of the position measurement, and the compliance compensation signal, andwherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.2. The method of clause 1, wherein actuating the one or more actuators comprises using at least one first actuator of the one or more actuators to pull or push the movable object in a first direction and using at least one second actuator of the one or more actuators to pull or push, respectively, the movable object in a second direction opposite to the first direction.3. The method of clause 2, comprising, during accelerating of the movable object in the first direction, using the at least one first actuator to exert a first pulling force on the movable object toaccelerate the movable object in the first direction and using the at least one second actuator to exert a second pulling force smaller than the first pulling force on the movable object in the second direction opposite to the first direction to create a pre-tensioning of the movable object.4. The method of clause 3, comprising, during accelerating of the movable object in the second direction, using the at least one second actuator to exert a second pulling force on the movable object to accelerate the movable object in the second direction and using the at least one first actuator to exert a first pulling force smaller than the second pulling force on the movable object in the first direction opposite to the second direction to create a pre-tensioning of the movable object.5. The method of any of clauses 1-4, wherein the one or more actuators comprises one or more reluctance motors.6. The method of any of clauses 1-5, wherein the movable object is a short-stroke module of a positioning system comprising a long-stroke module arranged to move the short-stroke module relative to a reference with a relatively low accuracy over a large range of movement, while the short-stroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.7. The method of any of clauses 1-6, wherein the direction dependent compliance compensation signal is configured to compensate stretching of the movable object caused by pulling forces exerted on the movable object by the one or more actuators or wherein the direction dependent compliance compensation signal is configured to compensate compression of the movable object caused by pushing forces exerted on the movable object by the one or more actuators.8. The method of any of clauses 1-7, further comprising using a direction dependent compliance compensation gain to obtain the compliance compensation signal.9. The method of clause 8, wherein the direction dependent compliance compensation gain is obtained by carrying out a system identification method, for example a frequency response system identification method, or by another parametrizing method based on a model.10. The method of clause 9, wherein the system identification method comprises fitting mass, compliance parameters and compliance time delays using a mean compliance matrix, a direction dependent compliance matrix and a pretension compliance matrix as well as a compliance delay matrix and a pretension delay matrix.11. A position control system for controlling the position of a movable object, the position control system comprising:a position measurement system configured to determine a position of a sensor or sensor target on the movable object,a comparator configured to provide an error signal,a controller configured to provide a control signal on the basis of the error signal, a feed-forward device configured to provide a feed-forward signal on the basis of a first signal related to the desired position,one or more actuators configured to act on the movable object on the basis of the control signal and the feed-forward signal, anda compliance compensation device to provide a compliance compensation signal, wherein the error signal is based on a set-point position, the measured position, and the compliance compensation signal, andwherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.12. The position control system of clause 11, wherein the one or more actuators comprise at least one first actuator to pull or push the movable object in a first direction and at least one second actuator to pull or push, respectively, the movable object in a second direction opposite to the first direction.13. The position control system of clause 12, wherein, to accelerate in a first direction, the at least one first actuator is configured to exert a first pulling force on the movable object to accelerate the movable object in the first direction and wherein the at least one second actuator is configured to exert a second pulling force smaller than the first pulling force on the movable object in the second direction opposite to the first direction to create a pre-tensioning of the movable object.14. The position control system of clause 13, wherein, to accelerate in the second direction, the at least one second actuator is configured to exert a second pulling force on the movable object to accelerate the movable object in the second direction and wherein the at least one first actuator is configured to exert a first pulling force smaller than the second pulling force on the movable object in the first direction opposite to the second direction to create a pre-tensioning of the movable object. 15. The position control system of any of clauses 11-14, wherein the one or more actuators comprises one or more reluctance motors.16. The position control system of any of clauses 11-15, wherein the movable object is a shortstroke module of a positioning system comprising a long-stroke module arranged to move the shortstroke module relative to a reference with a relatively low accuracy over a large range of movement, while the short-stroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.17. The position control system of any of clauses 11-16, wherein the direction dependent compliance compensation signal is configured to compensate stretching of the movable object caused by pulling forces exerted on the movable object by one or more actuators.18. The position control system of any of clauses 11-17, further configured to provide a direction dependent compliance compensation gain to obtain the compliance compensation signal.19. The position control system of clause 18, wherein the direction dependent compliance compensation gain is obtained by carrying out of a system identification method, for example a frequency response system identification method or by another parametrizing method based on a model.20. The position control system of clause 19, wherein the system identification method comprisesfitting mass, compliance parameters and compliance time delays using a mean compliance matrix, a direction dependent compliance matrix and a pretension compliance matrix.21. An exposure apparatus comprising:an illumination system configured to condition a radiation beam;a patterning device support configured to support a patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam; a substrate support constructed to hold a substrate;a projection system configured to project the patterned radiation beam onto a target portion of the substrate; andthe position control system of any of clauses 11-20.22. The exposure apparatus of clause 21, wherein the movable object is the substrate support and / or the patterning device support,wherein the movable object is for example a short-stroke module of a positioning system comprising a long-stroke module arranged to move the short-stroke module relative to a reference with a relatively low accuracy over a large range of movement, while the short-stroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.

Claims

CLAIMS1. A method for controlling a position of a movable object, the method comprising:measuring a position of a sensor or sensor target on the movable object to obtain a position measurement signal,providing an error signal,providing a control signal on the basis of the error signal using a controller,providing a feed-forward signal on the basis of a set-point signal,actuating one or more actuators on the basis of the control signal and the feed-forward signal, andproviding a compliance compensation signal,wherein the error signal is obtained by comparing a set-point position, the measured position of the position measurement, and the compliance compensation signal, andwherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.

2. The method of claim 1, wherein actuating the one or more actuators comprises using at least one first actuator of the one or more actuators to pull or push the movable object in a first direction and using at least one second actuator of the one or more actuators to pull or push, respectively, the movable object in a second direction opposite to the first direction.

3. The method of claim 2, comprising, during accelerating of the movable object in the first direction, using the at least one first actuator to exert a first pulling force on the movable object to accelerate the movable object in the first direction and using the at least one second actuator to exert a second pulling force smaller than the first pulling force on the movable object in the second direction opposite to the first direction to create a pre-tensioning of the movable object.

4. The method of claim 3, comprising, during accelerating of the movable object in the second direction, using the at least one second actuator to exert a second pulling force on the movable object to accelerate the movable object in the second direction and using the at least one first actuator to exert a first pulling force smaller than the second pulling force on the movable object in the first direction opposite to the second direction to create a pre -tensioning of the movable object.

5. The method of any of claims 1-4, wherein the one or more actuators comprises one or more reluctance motors.

6. The method of any of claims 1-5, wherein the movable object is a short-stroke module of a positioning system comprising a long-stroke module arranged to move the short-stroke module relative to a reference with a relatively low accuracy over a large range of movement, while the shortstroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.

7. The method of any of claims 1-6, wherein the direction dependent compliance compensation signal is configured to compensate stretching of the movable object caused by pulling forces exerted on the movable object by the one or more actuators or wherein the direction dependent compliance compensation signal is configured to compensate compression of the movable object caused by pushing forces exerted on the movable object by the one or more actuators.

8. The method of any of claims 1-7, further comprising using a direction dependent compliance compensation gain to obtain the compliance compensation signal.

9. The method of claim 8, wherein the direction dependent compliance compensation gain is obtained by carrying out a system identification method, for example a frequency response system identification method, or by another parametrizing method based on a model.

10. The method of claim 9, wherein the system identification method comprises fitting mass, compliance parameters and compliance time delays using a mean compliance matrix, a direction dependent compliance matrix and a pretension compliance matrix as well as a compliance delay matrix and a pretension delay matrix.

11. A position control system for controlling the position of a movable object, the position control system comprising:a position measurement system configured to determine a position of a sensor or sensor target on the movable object,a comparator configured to provide an error signal,a controller configured to provide a control signal on the basis of the error signal, a feed-forward device configured to provide a feed-forward signal on the basis of a first signal related to the desired position,one or more actuators configured to act on the movable object on the basis of the control signal and the feed-forward signal, anda compliance compensation device to provide a compliance compensation signal, wherein the error signal is based on a set-point position, the measured position, and the compliance compensation signal, andwherein the compliance compensation signal is a direction dependent compliance compensation signal, which direction dependent compliance compensation signal is dependent on a direction of acceleration of the movable object.

12. The position control system of claim 11, wherein the one or more actuators comprise at least one first actuator to pull or push the movable object in a first direction and at least one second actuator to pull or push, respectively, the movable object in a second direction opposite to the first direction.

13. The position control system of claim 12, wherein, to accelerate in a first direction, the at least one first actuator is configured to exert a first pulling force on the movable object to accelerate the movable object in the first direction and wherein the at least one second actuator is configured to exert a second pulling force smaller than the first pulling force on the movable object in the second direction opposite to the first direction to create a pre-tensioning of the movable object.

14. The position control system of claim 13, wherein, to accelerate in the second direction, the at least one second actuator is configured to exert a second pulling force on the movable object to accelerate the movable object in the second direction and wherein the at least one first actuator is configured to exert a first pulling force smaller than the second pulling force on the movable object in the first direction opposite to the second direction to create a pre-tensioning of the movable object.

15. The position control system of any of claims 11-14, wherein the one or more actuators comprises one or more reluctance motors.

16. The position control system of any of claims 11-15, wherein the movable object is a shortstroke module of a positioning system comprising a long-stroke module arranged to move the shortstroke module relative to a reference with a relatively low accuracy over a large range of movement, while the short-stroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.

17. The position control system of any of claims 11-16, wherein the direction dependent compliance compensation signal is configured to compensate stretching of the movable object caused by pulling forces exerted on the movable object by one or more actuators.

18. The position control system of any of claims 11-17, further configured to provide a direction dependent compliance compensation gain to obtain the compliance compensation signal.

19. The position control system of claim 18, wherein the direction dependent compliancecompensation gain is obtained by carrying out of a system identification method, for example a frequency response system identification method or by another parametrizing method based on a model.

20. The position control system of claim 19, wherein the system identification method comprises fitting mass, compliance parameters and compliance time delays using a mean compliance matrix, a direction dependent compliance matrix and a pretension compliance matrix.

21. An exposure apparatus comprising:an illumination system configured to condition a radiation beam;a patterning device support configured to support a patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam;a substrate support constructed to hold a substrate;a projection system configured to project the patterned radiation beam onto a target portion of the substrate; andthe position control system of any of claims 11-20.

22. The exposure apparatus of claim 21, wherein the movable object is the substrate support and / or the patterning device support,wherein the movable object is for example a short-stroke module of a positioning system comprising a long-stroke module arranged to move the short-stroke module relative to a reference with a relatively low accuracy over a large range of movement, while the short-stroke module is arranged to move relative to the long-stroke module with a high accuracy over a small range of movement.

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