Setpoint generator, position control system, stage apparatus and exposure apparatus

Abstract

The invention provides a setpoint generator for a position control system of a positioner comprising a master module and a slave module, the positioner being configured to displace an object, the setpoint generator being configured to, during a displacement of the object: - determine a master setpoint trajectory for the master module; - determine a slave setpoint trajectory for the slave module by means of an optimization algorithm; the optimization algorithm using at least part of the master setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.

Description

SETPOINT GENERATOR, POSITION CONTROL SYSTEM, STAGE APPARATUS ANDEXPOSURE APPARATUSFIELD

[0001] The present invention relates to a setpoint generator for a position control system of a positioner which can be applied to position a substrate or a patterning device in an exposure apparatus relative to a projection system, in order to expose the substrate to a patterned radiation beam, a position control system, a stage apparatus and an exposure apparatus.BACKGROUND

[0002] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (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).

[0003] 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 a lithographic 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. A lithographic 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 a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[0004] In order to ensure an accurate projection of the pattern on the substrate use is made of a positioner to position the substrate relative to the patterning device. Typically, such a positioner comprises a short-stroke module which can achieve an accurate positioning of the substrate over comparatively short distances and a long-stroke module which can displace the substrate and the shortstroke module over comparatively long distances. Typically, the position of the short-stroke module and the long-stroke module is controlled by a master-slave controller, whereby the short-stroke module is considered the master, the long-stroke module serving as slave, following the short-stroke module.

[0005] Apart from an accurate positioning of the substrate relative to the radiation beam comprising the pattern, there is a continuous wish to improve or increase the throughput of lithographic apparatus, this often is requiring an increased power of the positioner to achieve higher accelerations and velocities. When the performance of a positioner with a master-slave configuration is to beincreased, it has been found that the application of the known master-slave control schemes imposes a limit to the improvements which can be achieved.SUMMARY

[0006] It is an objective of the present invention to enable an improved performance of a positioner having a master-slave configuration.

[0007] According to an aspect of the invention, there is provided a setpoint generator for a position control system of a positioner comprising a master module and a slave module, the positioner being configured to displace an object, the setpoint generator being configured to, during a displacement of the object: determine a master setpoint trajectory for the master module; determine a slave setpoint trajectory for the slave module by means of an optimization algorithm; the optimization algorithm using at least part of the master setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.

[0008] According to another aspect of the present invention, there is provide a position control system comprising a setpoint generator according to the invention.

[0009] According to another aspect of the present invention, there is provide a stage apparatus comprising a position control system according to the invention.

[0010] According to another aspect of the present invention, there is provide an exposure apparatus comprising a stage apparatus according to the invention.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] 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 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;Figure 4 depicts a process as can be performed by a setpoint generator according to the invention;Figures 5 and 6 schematically depict positioners according to embodiments of the present invention.Figure 7 schematically depicts a position control system according to the invention.Figures 8 and 9 schematically depict trajectories of modules of a positioner as can be applied in the present invention.Figures 10a and 10b schematically show locations of a set of alignment marks on a substrate and a routing along said set of alignment marks.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 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.

[0014] Figure 1 schematically depicts 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.

[0015] In an embodiment, the first positioner PM and / or the second positioner PW can be configured to be controlled by a position control system according to the invention.

[0016] 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.

[0017] 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.

[0018] The lithographic apparatus LA may be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a spacebetween the projection system PS and the substrate W - which is also referred to as immersion lithography. More information on immersion techniques is given in US6952253, which is incorporated herein by reference.

[0019] 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.

[0020] 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.

[0021] 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 IF, 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 Pl, P2 as illustrated occupy dedicated target portions, they may be located in spaces between target portions. Substrate alignment marks Pl, P2 are known as scribe-lane alignment marks when these are located between the target portions C.

[0022] To clarify 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-axis has a component along the horizontal plane.

[0023] 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.

[0024] 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.

[0025] 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.

[0026] The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the substrate support WT. The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the mask support 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.

[0027] The position measurement system PMS may comprise an encoder system. An encoder system is known from for example, United States patent application US2007 / 0058173A1, filed on September 7, 2006, hereby incorporated 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 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 theoriginal 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, + 1storder, -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 substrate structure WT. 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.

[0028] The position measurement system PMS may comprise an interferometer system. An interferometer system is known from, for example, United States patent US6,020,964, filed on July 13, 1998, hereby incorporated 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 substrate support WT. 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.

[0029] 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.

[0030] Within the meaning of the present invention, the short-stroke module of the first positioner PM can be considered an example of a master module of a positioner according to the invention and the long-stroke module of the first positioner PM can be considered an example of a slave module of a positioner according to the invention.

[0031] 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.

[0032] Within the meaning of the present invention, the short-stroke module of the second positioner PW can be considered an example of a master module of a positioner according to the invention and the long-stroke module of the second positioner PW can be considered an example of a slave module of a positioner according to the invention.

[0033] The first positioner PM and the second positioner PW each are provided with one or more actuators to move respectively the mask support MT and the substrate support WT. The one or more 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 axis. For example, the planar actuator may be arranged to move the substrate support WT 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 substrate support WT respectively to the mask support MT. The actuator may be a moving-coil type actuator which has the at least one coil coupled to the substrate support WT respectively to the mask support MT. The actuator may be a voice-coil actuator, a reluctance actuator, a Lorentz -actuator or any other suitable actuator.

[0034] The lithographic apparatus LA comprises a position control system PCS as schematically depicted in Figure 3. The position control system PCS comprises a setpoint generator SP, and a control unit or controller CU, said control unit comprising a feedforward controller FF and a feedback controller FB. The position control system PCS provides a drive signal to the actuator ACT. The actuator ACT may be the actuator of the first positioner PM or the second positioner PW. The actuator ACT drives the plant P, which may comprise the substrate support WT or the mask support MT. An output of the plant P is a position quantity such as position or velocity or acceleration. The position quantity is measured with the position measurement system PMS. The position measurement system PMS generates a signal, which is a position signal representative of the position quantity of the plant P. The setpoint generator SP generates a signal, which is a reference signal representative of a desired position quantity of the plant P. For example, the reference signal represents a desired trajectory of the substrate support WT. The position signal and the reference signal are applied as input to the control unit CU of the position control system PCS. A difference between the reference signal and the position signal formsan input for the feedback controller FB of the control unit or controller CU. Based on the input, the feedback controller FB provides at least part of the drive signal for the actuator ACT. The reference signal may form an input for the feedforward controller FF. Based on the input, the feedforward controller FF provides at least part of the drive signal for the actuator ACT. The feedforward FF may make use of information about dynamical characteristics of the plant P, such as mass, stiffness, resonance modes and eigenfrequencies.

[0035] In an embodiment, the position control system PCS comprises a position control system according to the invention, said position control system PCS comprising a setpoint generator SP according to the invention.

[0036] In accordance with an embodiment of the present invention, there is provided a setpoint generator which can provide a setpoint for a positioner having a master-slave configuration. Within the meaning of the present invention, a positioner having a master-slave configuration is a positioner which comprises multiple positioning modules which co-operate to achieve a positioning or displacement of an object.

[0037] As an example of such a positioner, the aforementioned first and second positioners PW and PM can be mentioned. Such positioners can e.g. have a short-stroke module for accurate positioning of an object table holding a patterning device or a substrate, and a long-stroke module for displacing the short-stroke module and the object table over comparatively large distances, with a more coarse accuracy.

[0038] As another example of such a positioner, a positioner having two long-stroke modules can be mentioned. Such a positioner can e.g. comprises a first long-stroke module, serving to position or displace an object along a desired trajectory, and a second long-stroke module, serving to follow the first long-stroke module, e.g. in substantially one degree of freedom. Such an arrangement can e.g. occur in case the first long-stroke module comprises an electromagnetic motor configured to displace an object in a plane, i.e. in two degrees of freedom. In such an arrangement, various cables and tubes may need to be connected to the mover of said long-stroke module, e.g. for powering and cooling. To facilitate the two-dimensional movement of the first long-stroke module, the second long-stroke module is provided, which holds the cables and tubes and follows the first long-stroke module, e.g. in one degree of freedom. More details on such an arrangement are described below.

[0039] In an embodiment, the present invention provides a setpoint generator for generating a setpoint for a positioner having a master-slave configuration, e.g. having a master module and one or more slave modules. Such a master-slave configuration thus implies that the positioner comprises multiple positioning modules. The setpoint generator according to the invention is configured to determine a distinct setpoint for each module of the multiple positioning modules, rather than copying the setpoint of one module and applying it to the other modules in order for the slave module or modules to substantially follow the master module.

[0040] The process as applied by the setpoint generator according to the present invention to arrive at the setpoint trajectories of the multiple positioning modules is schematically illustrated in Figure 4.

[0041] In accordance with the present invention, the setpoint generator is configured to, in a first step 410, determine a setpoint trajectory for the master module of the positioner. Such a setpoint trajectory for the master module may also be referred to as the master setpoint trajectory or in short the master setpoint or master trajectory. Such a master setpoint trajectory may e.g. indicate a desired position of the master module or the object that is to be displaced by the positioner, as a function of time. Such a trajectory can be expressed as a table or a mathematical function or the like. The setpoint trajectory can e.g. be expressed as a series or sequence of piece-wise polynomials. In an embodiment, the setpoint generator according to the present invention can determine the master setpoint trajectory based on a set of displacement parameters which in general define the displacement that needs to be made and any operational parameters or limits of the positioner that need to be taken into account. The set of displacement parameters relied on can thus comprise position information for the trajectory that needs to be performed and operational parameters of the positioner. In case the required displacement involves an exposure process of a substrate in an exposure apparatus, the position information can e.g. include position information of one or more fields on the substrate that need to be exposed during the exposure process. Such position information may e.g. include nominal positions of the fields that need to be exposed, the length of the fields, the number of fields, etc. The operational parameters can include limits of the positioner such as maximum velocity, maximum acceleration, maximum jerk, or maximum snap that need to be taken into account to determine the setpoint trajectory.

[0042] In accordance with the present invention, the setpoint generator is further configured to determine, in a second step 420, a setpoint trajectory for the slave module of the positioner by using an optimization algorithm. Such a setpoint trajectory for the slave module may also be referred to as the slave setpoint trajectory or in short the slave setpoint or slave trajectory. Such a slave setpoint trajectory may e.g. indicate a desired position of the slave module as a function of time. Such a trajectory can equally be expressed as a table or a mathematical function or the like. The setpoint trajectory can e.g. be expressed as a series or sequence of piece-wise polynomials.

[0043] In general, an optimization algorithm is an algorithm which aims to find a set of parameters which, when applied to a mathematical function or expression, results in an optimum value, either a maximum or a minimum, for said mathematical function or expression, taking account of one or more boundary conditions. The mathematical function or expression may also be referred to as an objective function.

[0044] Various methods or algorithms have been developed in the past decades to arrive at an optimum for an objective function. Such algorithms can e.g. make use of derivatives information in case derivatives can be obtained for the objective function.

[0045] In accordance with the present invention, an optimisation algorithm is applied to find a setpoint trajectory for a slave module of a positioner, based on a determined setpoint trajectory for themaster module of the positioner, which results in an optimal value for an objective function, the objective function describing a performance characteristic of the positioner, e.g. of the slave module of the positioner.

[0046] In accordance with the present invention, the objective function as applied by the optimisation algorithm is associated with a performance characteristic of the positioner. In particular, the objective function can e.g. comprise a mathematical expression which can relate to a certain behaviour of the positioner.

[0047] As a first example, the objective function can comprise a mathematical expression of the power consumption of the slave module of the positioner. For a given slave setpoint trajectory, the objective function derives the associated power consumption which would occur in case the slave module would be controlled, e.g. by a position control system, to follow the given slave setpoint trajectory. The power consumption associated with a displacement along the slave setpoint trajectory can e.g. be obtained using a mathematical model of the slave module, in particular of the motors or actuators of the slave module. Such a mathematical model may e.g. enable to determine an RMS value of a supply current of a motor or actuator of the slave module following the slave setpoint trajectory. Rather than a detailed motor model, similar results can be obtained by applying an objective function which expresses an RMS value of the acceleration occurring during the slave setpoint trajectory. In this respect, it can be noted that in general a supply current to a motor or actuator will be proportional to the generated force and thus the acceleration of an object onto which the force is exerted.

[0048] As a second example, the objective function can comprise a mathematical expression of a dynamic characteristic of the slave module. In such case, the objective function can e.g. comprise a mathematical function for an RMS value of a dynamic characteristic of a motor of the slave module when following the secondary setpoint trajectory. Examples of such a dynamic characteristic can e.g. be a velocity, acceleration, jerk or snap. With respect to the latter, it has been observed that a minimization of an objective function comprising an RMS value of the snap, the snap being the 4thtime- derivative of the position, provides a good trade-off between a minimization of the power consumption and a desired dynamic behavior. As another dynamic characteristic, a specific frequency spectrum, region or range can be mentioned. For a given slave setpoint trajectory, the frequency content of said trajectory can be determined and assessed or evaluated with respect to a required condition or objective function. As such, as an objective, a slave setpoint trajectory can be determined which e.g. avoid certain frequencies or a particular frequency region when applied. By doing so, certain vibrations or other dynamic disturbances can be avoided or mitigated.

[0049] In an embodiment of the present invention, the objective function that is optimized by the optimization algorithm as applied by the setpoint generator comprises a combination of objectives. In such an embodiment, the objective function can comprise a weighted combination of multiple objectives, e.g. a weighted combination of an RMS value of the acceleration and an RMS value of a positional difference between the master module and the slave module. This weighted combination canthen e.g. be minimized. The optimisation algorithm as applied in the setpoint generator according to the invention may further take into account one or more boundary conditions. As an example, a threshold of an allowable positional deviation between the master setpoint trajectory and the slave setpoint trajectory can be such a boundary condition. In an embodiment, such a threshold may also be applied to only certain portions of the trajectory. In case of an exposure process of a substrate, a maximum positional deviation between the master setpoint trajectory and the slave setpoint trajectory can be set during a scanning portion of the setpoint trajectory. Figures 8 and 9 describe this process in more detail. Operational parameters of the slave module may also serve as boundary conditions. Such parameters can e.g. be limits such as a maximum velocity, maximum acceleration or maximum jerk which the slave module can generate.

[0050] In an embodiment of the present invention, the setpoint generator is configured to perform at least part of the process as illustrated in Figure 4, i.e. the process of determining the setpoint trajectories for the positioning modules of the positioner, during operation of the positioner, e.g. during a displacement of the object. In advanced positioning processes, such as the positioning of a substrate during an exposure process in an exposure apparatus, the setpoint trajectory of the master module of the positioner, said module e.g. holding an object table holding the substrate, may be determined during the exposure process. In such case, the master setpoint trajectory that is to be followed may be known for only a certain period in advance, e.g. a few seconds. Said period, or part thereof, may then be used to determine the slave setpoint trajectory that is to be followed. More details on such a process will be provided below.

[0051] Figures 5 and 6 schematically show positioners which can be controlled using a setpoint generator according to the invention.

[0052] Figure 5 schematically shows a side view or front view of a first embodiment of a positioner 500 comprising multiple positioning modules for positioning an object. The positioner 500 comprises an object table 510 configured to hold an object 520, e.g. a substrate, a first positioning module 530 and a second positioning module 540. In the embodiment as shown, the first positioning module 530, which can be considered the master module, is connected to the object table 510, and is configured to position the object table 510. The first positioning module 530 as shown comprises a set of actuators 532 for positioning the object table 510. In an embodiment, the first positioning module 530 can comprises a set of actuators 532 which is configured to position the object table in 6 degrees of freedom (6 DOF), e.g. with a high accuracy, over comparatively short distances. In this respect, the first positioning module 530 can be considered an example of the short-stroke module as discussed above. The actuators 532 as shown can e.g. be electromagnetic actuators such as Lorentz actuators or reluctance actuators. Such actuators can e.g. each comprises a first member 532.1, e.g. a magnetic or ferromagnetic member, configured to co-operate with a second member 532.2, e.g. a coil member, in order to generate a force in a predetermined direction.

[0053] The second positioning module 540 of the positioner 500 as shown in Figure 5 comprises a mover 540.1 which can displace relative to a stator 540.2 of the second positioning module 540. The second positioning module 540 can e.g. comprises a linear motor or a planar motor. In such arrangement, the mover 540.1 can e.g. comprise an array of coils which can be supplied with a current, while the stator 540.2 can e.g. comprise an array of permanent magnets (or vice versa). The second positioning module 540 can e.g. be configured to displace the first positioning module 530 and the object table 510 over comparatively large distances. As such, the second positioning module 540 can be considered as an example of the long-stroke module as discussed above.

[0054] The positioner 500 further comprises a position control system PCS according to the invention, the position control system PCS being configured to generated position control signals 550 for controlling the positioning modules 530 and 540 of the positioner. In the embodiment as shown, the position control system PCS comprises a setpoint generator SG which is configured to generate setpoints or setpoint trajectories for the positioning modules 530 and 540 of the positioner 500. The position control system PCS can have a similar structure as the position control system PCS as shown in Figure 3, i.e. comprising a setpoint generator SG and a control unit CU. Note that both components, i.e. the setpoint generate SG and the control unit CU of a position control system according to the present invention need not be integrated in one module or structure. As an example, the setpoint generator can e.g. be part of a master control system which can be remote from the control unit CU of the position control system PCS. In such case, the setpoint trajectories as determined by the setpoint generator SG can be communicated to the control unit CU by any suitable means of communication, e.g. via a network.

[0055] Figure 6 schematically shows a top view of a second embodiment of a positioner 600 according to the present invention, the positioner 600 comprising a first positioning module 610 and a second positioning module 620 for displacing and positioning an object. In the embodiment as shown, the first positioning module 610 comprises a mover 610.1 which is configured to move an object table in a plane extending in the indicated X and Y directions. The object table can e.g. hold an object 630 such as a substrate. The mover 610.1 can be moved in the indicated XY plane by means of interaction with a stator 610.2 of the first positioning module 610. The first positioning module 610 can e.g. be an electromagnetic planar motor whereby the mover 610.1 comprises one or more arrays of coils which can be supplied with currents and whereby the stator 610.2 comprises a two-dimensional spatially alternating pattern of permanent magnets. In an alternative embodiment the mover 610.1 comprises permanent magnets and the stator 610.2 comprises an array of coils which, in use, forms a two- dimensional spatially alternating magnetic field. In the embodiment as shown, the second positioning module 620 comprises a mover 620.1 which can move relative to a stator 620.2 along the indicated Y- direction. The second positioning module 620 can e.g. comprises a linear motor, e.g. a linear electromagnetic motor. In the arrangement as shown, both the first positioning module 610 and the second positioning module 620 can be considered examples of long-stroke modules.

[0056] In the embodiment as shown, the purpose of the second positioning module 620 is to displace a cable assembly 640 of the positioner 600. The cable assembly 640, which is connected between the mover 610.1 of the first positioning module 610 and the mover 620.1 of the second positioning module 620, can e.g. comprise cables for providing a supply current to the mover 610.1. The cable assembly 640 can also comprise one or more tubes to supply a cooling fluid to the mover 610.1, e.g. to cool the mover and / or the object table holding the object 630. The second positioning module 620 can also be referred to as a follower stage and facilitates the movement of the first positioning module 610 which holds the object 630. During operation, the second positioning module 620 will typically follow the movements of the first positioning module 610 along the Y-direction. In known arrangements of a positioner 600, the second positioning module 620 thus applies the Y-direction setpoint or setpoint trajectory of the first positioning module 610. In accordance with the present invention however, the position of the second positioning module 620 is controlled by a position control system PCS having a setpoint generator SG according to the present invention. The setpoint generator SG according to the invention can thus determine a setpoint trajectory for both the first positioning module 610 and the second positioning module 620. In particular, the setpoint generator SG may determine a first setpoint trajectory for the first positioning module 610, said module serving as the master module, and a second setpoint trajectory for the second positioning module 620, serving as the slave module, whereby the second setpoint trajectory is determined by means of an optimisation algorithm, as mentioned above.

[0057] As a third embodiment of a positioner according to the present invention, a combination of the positioner 500 and 600 can be considered. In such a combined positioner, a positioner is obtained which comprises: a first positioning module, which is a short-stroke module similar to the short-stroke module 530 of Figure 5, said module serving as a master module, a second positioning module, which is a long-stroke module similar to the long-stroke module 540 of Figure 5 or the long-stroke module 610 of Figure 6, a third positioning module, which is also a long-stroke module similar to the long-stroke module 620 of Figure 6 and which serves as a follower stage to the second positioning module.In such an arrangement, both the second positioning module and the third positioning module can be considered slave modules of the first positioning module. As such, in an embodiment, the setpoint trajectories for the second positioning module and the third positioning module can be determined by a setpoint generator according to the invention, by means of an optimization algorithm. In such embodiment, the optimization algorithm can apply at least part of the master setpoint trajectory, i.e. the setpoint trajectory for the first positioning module, one or more boundary conditions and a first objective function to determine the setpoint trajectory for the second positioning module. Further, the optimization algorithm can apply at least part of the master setpoint trajectory, i.e. the setpoint trajectory for the first positioning module, one or more boundary conditions and a second objective function to determine the setpoint trajectory for the third positioning module. Note that in such arrangement, theoptimization algorithm as applied may also be different for determining the setpoint trajectory for the second positioning module and the setpoint trajectory for the third positioning module.Alternatively, in such an arrangement having three positioning modules, the second positioning module can be a slave module with respect to the first positioning module and can be a master module with respect to the third positioning module. In such arrangement, the setpoint trajectory for the second positioning module will thus be based on the setpoint trajectory for the first positioning module, whereas the setpoint trajectory for the third positioning module will be based on the setpoint trajectory for the second positioning module. A setpoint generator which is structured in this manner is schematically illustrated in Figure 7 which will be detailed below.

[0058] In yet another embodiment, the positioner according to the invention comprises more than 3 modules, e.g. 4 modules. In general, the present invention, can be implemented in positioner comprising multiple modules which co-operate together to move a particular object or object table. Referring to the embodiment as shown in Figure 6, the stator 610.2 of the first positioning module 610 may be a balance mass, rather than a stationary structure. In such arrangement, the position of the stator 610.2 may need to be controlled as well, e.g. by means of one or more actuators arranged to position the stator 610.2. In such arrangement, these one or more actuators may receive a setpoint or setpoint trajectory as well, which can e.g. be derived using a setpoint generator according to the invention.

[0059] Figure 7 schematically illustrates a position control system PCS including a setpoint generator according to the present invention, whereby the setpoint generator SG is configured to determine setpoint trajectories for 3 positioning modules of a positioner, these modules co-operating to displace an object. In Figure 7, the generation of the 3 setpoint trajectories STI, ST2 and ST3 is performed by modules or routines SGI, OA1 and OA2 of the setpoint generator SG.

[0060] The position control system PCS as shown in Figure 7 comprises a setpoint generator SG and a control unit or controller CU which applies the setpoint trajectories STI, ST2 and ST3 of the setpoint generator SG to generate control signals CS to control the positioner.

[0061] The setpoint generator SG as shown in Figure 7 is configured to determine a first setpoint trajectory STI, which is a setpoint trajectory for the master module of the positioner. Such a master module can e.g. correspond to a short-stroke module similar to the short-stroke module 530 of Figure 5. In the embodiment as shown, the generation of the setpoint trajectory STI by module or routine SGI of the setpoint generator SG is based on a set of input parameters which can e.g. include the aforementioned displacement parameters. Such parameters may in general define the displacement that needs to be made and any operational parameters or limits of the positioner that need to be taken into account. The set of displacement parameters relied on can thus comprise position information for the trajectory that needs to be performed and operational parameters of the positioner.

[0062] The setpoint generator SG as shown is further configured to determine, using an optimization algorithm indicated by OA1, a setpoint trajectory ST2 for a slave module of the positioner. Such a slave module can e.g. correspond to a long-stroke module similar to the long-stroke module 540of Figure 5. In the embodiment as shown, the generation of the setpoint trajectory ST2 by the optimization algorithm OA1 of the setpoint generator SG is based on the setpoint trajectory STI of the master module and takes account one or more boundary conditions, indicated by boundary conditions 1 in Figure 7. These boundary conditions 1 can e.g. express limits of operational parameters of the slave module and / or limits with respect to the positional relation between the master module and the slave module.

[0063] The setpoint generator SG as shown is further configured to determine, using an optimization algorithm indicated by OA2, a setpoint trajectory ST3 for a further slave module of the positioner. This further slave module can e.g. correspond to a long-stroke module similar to the long- stroke module 620 of Figure 6. In the embodiment as shown, the generation of the setpoint trajectory ST3 by the optimization algorithm OA2 of the setpoint generator SG is based on the setpoint trajectory ST2 of the slave module and takes into account one or more boundary conditions, indicated by boundary conditions 2 in Figure 7. These boundary conditions 2 can e.g. express limits of operational parameters of the further slave module and / or limits with respect to the positional relation between the slave module and the further slave module.

[0064] As mentioned above, the setpoint trajectories, e.g. trajectories STI, ST2 and ST3 of the setpoint generator SG according to the invention can be expressed as a table or a mathematical function or the like. The setpoint trajectory or trajectories can e.g. be expressed as a series or sequence of piece- wise polynomials. In case a more suitable format would be required for the control unit of the position control system according to the invention, a conversion to such formal can be implemented in the setpoint generator SG or in the control unit CU.

[0065] The setpoint generator according to the invention may advantageously be applied in a position control system of a positioner positioning a substrate table, such as positioner PW positioning substrate table WT as discussed above, in a lithographic apparatus or exposure apparatus. In particular, the substrate, which comprises a plurality of fields that need to be exposed to a radiation beam with a patterned cross-section, needs to be accurately positioned relative to a projection system of the apparatus, in order to project the pattern onto the substrate. Typically, the substrate table, e.g. table WT, holding the substrate W follows a meandering pattern to expose the various field to the radiation beam. The setpoint generator according to the present invention may also be applied, in a substantially similar manner, to determine a setpoint trajectory for other processes that are performed in a lithographic apparatus. Such processes e.g. including the position measurement or position determination of a plurality of marks on the substrate. Such a position measurement of a plurality of marks on a substrate, e.g. alignment marks, may require the substrate to follow a similar trajectory which requires the substrate to be positioned at different locations, in order to perform the position measurement of the marks.

[0066] Figure 8 schematically shows a possible trajectory, in an XY-plane, that is to be followed by a substrate table, during an exposure process, when exposing three consecutive fields on thesubstrate. As can be seen, the meandering trajectory that is to be followed comprises an alternating sequence of straight moves 810 in the horizontal direction of the drawing and curves 820. The arrows in the trajectory indicating the direction of movement of the substrate / substrate table. During the straight moves 810, which can also be referred to as scan moves or scan trajectories, a field on the substrate is exposed to the radiation beam having the pattern, whereas during the curves 820, which can also be referred to as preparation moves or preparation trajectories, the substrate is displaced in order to start the scanning of the next field. Typically, the scan trajectories are trajectories during which the substrate is moved at a substantially constant speed, e.g. in Y or -Y direction. During the preparation move or trajectory, the substrate is displaced to start a next scan, of a next field on the substrate.

[0067] Typically, a known setpoint generator will determine such a trajectory which is to be followed and provide it to a control unit of a position control system, e.g. to control the positioning of a short-stroke module, thereby providing an accurate positioning of the substrate along the trajectory as depicted. In a known setpoint generator, the same setpoint trajectory may then also be applied to control the position of a long-stroke module that is configured to displace the short-stroke module and the substrate table holding the substrate. In such arrangement, the long-stroke module would thus follow the exact same trajectory as the short-stroke module.

[0068] In accordance with an embodiment of the present invention, a setpoint generator is provided which determines an alternative setpoint trajectory for a slave module of the positioner positioning the substrate. This alternative setpoint trajectory is determined by means of an optimization algorithm which uses at least part of the determined setpoint trajectory for the master module or shortstroke module. In general, a setpoint generator for an exposure process of a semiconductor substrate will not determine a setpoint trajectory for an entire substrate in one go. Rather, the setpoint generator will ensure that the setpoint or setpoint trajectory that needs to be followed is known a few, e.g. 5 fields ahead or upfront. By doing so, the setpoint generator can still make adjustments to the setpoint trajectory during the exposure process itself. With respect to the determination of the setpoint trajectory for the slave module, or the long-stroke module, e.g. module 540 in Figure 5, it can also be pointed out that this setpoint trajectory can be determined, using the optimization algorithm, based on information of only part of the master setpoint trajectory. In particular, it has been devised by the inventors that the slave setpoint trajectory of a particular field on a substrate can be determined in case the master setpoint trajectory for said field and for a consecutive field have been determined. Note that a setpoint trajectory for a field on the substrate can be considered a combination of a preparation trajectory and a scan trajectory.

[0069] Figure 9 schematically illustrates the process of determining the setpoint trajectories in more detail. Figure 9 schematically shows a similar master setpoint trajectory as shown in Figure 8, whereby: move P(N) corresponds to the preparation trajectory for field N, move S(N) corresponds the scan trajectory for field N,move P(N+1) corresponds to the preparation trajectory for field N+l move S(N+1) corresponds the scan trajectory for field N+l, move P(N+2) corresponds to the preparation trajectory for field N+2, and move S(N+2) corresponds the scan trajectory for field N+2.In case the master setpoint trajectory as indicated is known, the setpoint generator according to the invention can determined the slave setpoint trajectory for field N, i.e. the moves for the slave module which are to be followed when the master module executes moves P(N) and S(N), based on the moves or trajectories P(N), S(N), P(N+1) and S(N+1).

[0070] Similarly , the setpoint generator according to the invention can determine the slave setpoint trajectory for field N+l, i.e. the moves for the slave module which are to be followed when the master module executes moves P(N+1) and S(N+1), based on the moves or trajectories P(N+1), S(N+1), P(N+2) and S(N+2).

[0071] Once both the master setpoint trajectory and slave setpoint trajectory for a field are known, the exposure process for said field can be executed.

[0072] By means of the optimization algorithm as applied by the setpoint generator according to the invention, a more advantageous setpoint trajectory for the slave module of the positioner can be obtained, e.g. more advantageous w.r.t. power dissipation or dynamic behavior. Merely as an illustration, Figure 9 further shows a possible slave setpoint trajectory 900 which can be followed by a slave module when the trajectory P(N) - S(N) - P(N+1) - ... - S(N+2) is performed. The slave setpoint trajectory is assumed to start from the same initial position (Xi, Yi) as the master setpoint trajectory. Note that, in the example given, the slave module following the slave setpoint trajectory 900 follows a shorter trajectory. It can also be pointed out that during the scan trajectories S(N), S(N+1) and S(N+2), the slave module also makes a displacement in the X-direction.

[0073] By optimizing the trajectory of the slave module of the positioner positioning the object, it may occur that the slave module is no longer the limiting factor in the performance of the positioner. As a result, the improved performance of the positioner as a whole can be obtained when using the setpoint generator according to the invention. Alternatively or in addition, the optimization of the trajectory that is to be followed by the slave module may create a design freedom for the slave module which can be used to e.g. reduce the required power rating of the module, or may be used to reduce the weight or volume or costs of the module.

[0074] In an embodiment of the present invention, an optimization algorithm may also be applied to determine a setpoint trajectory of a master module of a positioner. In general, the optimization algorithm can also be applied in case such a master module is the only positioning module of the positioner. In particular, the optimization algorithm has been found to be advantageous to determine the preparatory trajectories of an exposure process of multiple fields or a measurement process of multiple marks such as alignment marks.

[0075] In such embodiment, the setpoint generator as applied may perform an initial step of determining a setpoint trajectory for the master module or the sole positioning module in a conventional manner, e.g. resulting in a table or set of polynomials describing the initial setpoint trajectory to be followed as a function of time. In case of an exposure process, such a trajectory may be similar to the trajectory as shown in Figure 8. In case of an alignment measurement process, the position of a plurality of alignment marks, which are distributed over the surface of the substrate, may need to be determined. Figure 10a schematically shows locations of such a plurality of alignment marks 1010 on a substrate 1000. Figure 10b schematically shows a routing 1020, i.e. a trajectory that is to be followed by the substrate, in order to bring each of the alignment marks close to the alignment position measurement tool. The required trajectory to be followed to measure the position of the multiple alignment marks can be considered to have similar characteristics as an exposure process trajectory. In this respect, it can be pointed out that the position measurement of an alignment mark may require that the stage holding the substrate moves at a comparatively slow speed or is halted when the alignment mark is in a capturing range of the measurement tool. In between the measurement of two marks, the stage is then accelerated and decelerated in order to perform the measurement sequence as quickly as possible. Such a trajectory that is to be performed in between two consecutive measurements of alignment marks can thus be considered a preparation trajectory as well. As such, an alignment measurement process may also be considered an alternating sequence of preparation trajectories and scanning trajectories. It may also be understood by the skilled person that the overall power consumption and dynamic excitations caused by the stage will be predominantly occur during the execution of the preparation trajectories and not during the scan trajectories which would typically occur at a low or zero acceleration or deceleration. As such, in order to focus on optimizing a certain behavior of the stage, an optimization of the preparation trajectories of a process, e.g. an exposure process or an alignment measurement process, can be considered.In an embodiment, the present invention therefore provides a setpoint generator for a position control system of a positioning module of a positioner, whereby the setpoint generator is configured to: determine an initial setpoint trajectory for the positioning module of the positioner; determine a modified setpoint trajectory for the positioning module of the positioner by means of an optimization algorithm; the optimization algorithm using at least part of the initial setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.

[0076] In a similar manner as discussed above, the setpoint generator can, in an embodiment, be configured to determine the initial setpoint trajectory and / or the modified setpoint trajectory during the execution of the process. In such case, the initial setpoint trajectory can be calculated for a number of fields, e.g. fields to be exposed, or a number of locations which needs to be accessed to measure an alignment mark. When the initial setpoint trajectory is determined, e.g. for 5 to 10 fields or locations, amodified setpoint trajectory can be determined, based on the initial setpoint trajectory, or part thereof, by means of the optimization algorithm. Once the modified setpoint trajectory is known for one or more fields or locations, the process can commence, i.e. the modified setpoint trajectory can be executed by the positioner. During the positioning, the initial setpoint trajectory will then be extended to further fields or locations, as well as the modified setpoint trajectory, such that the desired setpoint may be provided to the position control system when needed.

[0077] Such a setpoint generator may e.g. be applied in a positioner for positioning a substrate in a lithographic apparatus, whereby the positioner is configured to displace the substrate in order to execute various processes on the substrate. As mentioned, such processes can e.g. include an exposure process, whereby various fields on the substrate are exposed to a patterned radiation beam, or an alignment measurement process, whereby the position of various alignment marks on the substrate needs to be determined.

[0078] In an embodiment, the step of determining the initial setpoint trajectory can comprise: obtaining operational parameters of the positioner such as maximum velocity, maximum acceleration or maximum jerk; obtaining position information of one or more locations or fields on the substrate to which the process needs to be applied; determining the initial setpoint trajectory for the positioning module based on the operational parameters and the position information.

[0079] In such embodiment, the initial setpoint trajectory may thus take account of basic limitations of the positioner. In accordance with an embodiment of the present invention, said initial setpoint trajectory may further be optimized to a modified setpoint trajectory, using an optimization algorithm, in a similar manner as discussed above. For the lithographic processes as described, i.e. the exposure process and the alignment measurement process, the setpoint trajectory that is to be followed will typically span, for each of the one or more locations or fields on the substrate, a preparation trajectory and a scan trajectory. Of these two trajectory components, the preparation trajectory correlates most to the positioner performance, e.g. the dynamic behavior or the power consumption. As such, in an embodiment, the optimization of the setpoint trajectory is only performed on the preparation trajectory. Therefore, in an embodiment, the setpoint generator according to the invention is configured to determine a modified setpoint trajectory of the preparatory trajectory for the positioning module of the positioner by means of an optimization algorithm determining a modified setpoint trajectory of the preparation trajectory for the one or more locations or fields.

[0080] In an embodiment of the present invention, the setpoint trajectory of the positioning module or the slave module can be considered to be known as a substantially continuous function, i.e. the required displacement of the module, e.g. in the XY -plane as a function of time is known as a continuous function. This facilitates and enables that the time-derivatives of this function can be determined. Examples which are already mentioned above are the velocity (first time-derivative of the position), theacceleration (second time-derivative of the position), the jerk (third time-derivative of the position) and the snap (fourth time-derivative of the position).

[0081] As a result, the objective function may also be expressed as a substantially continuous function of which the derivatives can be determined. This may facilitate the optimization process to arrive at an optimal value of the objective function. In particular, in an embodiment of the present invention, the optimization process makes use of quadratic programming to arrive at an optimal value of the objective function.

[0082] In an embodiment, the setpoint generator according to the invention, is applied in a position control system according to the invention, said position control system can e.g. be used to control a positioner having multiple positioning modules.

[0083] In an embodiment, a stage apparatus is provided, the stage apparatus comprising a position control system according to the invention, and a positioner. In such embodiment, the positioner can e.g. comprise a short-stroke module as the master module and a long-stroke module as the slave module. In such embodiment, the stage apparatus can further comprise an object table for holding a substrate, whereby the short-stroke module is configured to position the object table.

[0084] In an embodiment, the present invention further provides an exposure apparatus comprising a stage apparatus according to the invention.

[0085] 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.

[0086] 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.

[0087] 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.

[0088] 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, amachine -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.

[0089] 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. Other aspects of the invention are set-out as in the following numbered clauses.1. A setpoint generator for a position control system of a positioner comprising a master module and a slave module, the positioner being configured to displace an object, the setpoint generator being configured to, during a displacement of the object: determine a master setpoint trajectory for the master module; determine a slave setpoint trajectory for the slave module by means of an optimization algorithm; the optimization algorithm using at least part of the master setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.2. The setpoint generator according to clause 1, wherein the performance characteristic of the positioner comprises a power consumption of the positioner and / or a dynamic characteristic of the positioner.3. The setpoint generator according to any of the preceding clauses, wherein the master setpoint trajectory comprises a sequence of piecewise polynomials.4. The setpoint generator according to any of the preceding clauses, wherein the optimization algorithm is configured to determine the slave setpoint trajectory which minimizes the objective function, within the one or more boundary conditions.5. The setpoint generator according to clause 4, wherein the one or more boundary conditions comprises a threshold of an allowable deviation between the master setpoint trajectory and the slave setpoint trajectory.6. The setpoint generator according to any of the clauses 4 to 5, wherein the slave setpoint trajectory is determined by means of quadratic programming.7. The setpoint generator according to any of the preceding clauses 4 to 6, wherein the objective function comprises a mathematical expression of the power consumption of the master module as function of the slave setpoint trajectory.8. The setpoint generator according to any of the clauses 4-6, wherein the objective function comprises a mathematical expression associated with an RMS value of an acceleration of the master module when following the secondary setpoint trajectory.9. The setpoint generator according to any of the clauses 4-6, wherein the objective function comprises a mathematical expression associated with an RMS value of a dynamic characteristic of a motor of the master module following the secondary setpoint trajectory, the dynamic characteristic comprising at least one of a velocity, acceleration, jerk or snap.10. The setpoint generator according to any of the preceding clauses, wherein the object is a substrate and wherein the displacement of the substrate is part of an exposure process or an inspection process of the substrate.11. The setpoint generator according to clause 10, wherein determining the master setpoint trajectory comprises: obtaining operational parameters of the positioner such as maximum velocity, maximum acceleration or maximum jerk; obtaining position information of one or more fields on the substrate that need to be exposed during the exposure process or inspected during the inspection process; determining the primary setpoint trajectory for the one or more fields or a subset thereof, based on the operational parameters and the position information.12. The setpoint generator according to clause 10 or 11, wherein the primary setpoint trajectory spans, for each of the one or more fields on the substrate, a preparation trajectory and a scan trajectory.13. The setpoint generator according to clause 11 or 12, wherein the setpoint generator is configured to determine the master setpoint trajectory during the exposure process.14. The setpoint generator according to clause 13, wherein the setpoint generator is configured to determine a slave setpoint trajectory for an exposure of a field N based on a master setpoint trajectory for an exposure of the field N and a field N+l.15. A position control system comprising a setpoint generator according to any of the clauses 1 to 14.16. A stage apparatus comprising a position control system according to clause 15, the stage apparatus comprising a short-stroke module as the master module and a long-stroke module as the slave module.17. The stage apparatus according to clause 16, further comprising an object table for holding a substrate, the short-stroke module being configured to position the object table.18. An exposure apparatus comprising a stage apparatus according to clause 16 or 17.19. A setpoint generator for a position control system of a positioning module of a positioner, whereby the setpoint generator is configured to: determine an initial setpoint trajectory for the positioning module of the positioner;determine a modified setpoint trajectory for the positioning module of the positioner by means of an optimization algorithm; the optimization algorithm using at least part of the initial setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner. The setpoint generator according to clause 19, wherein the object is a substrate and wherein the displacement of the substrate is part of a process applied to the substrate. The setpoint generator according to clause 19 or 20, wherein determining the initial setpoint trajectory comprises: obtaining operational parameters of the positioner such as maximum velocity, maximum acceleration or maximum jerk; obtaining position information of one or more locations or fields on the substrate to which the process needs to be applied; determining the initial setpoint trajectory for the positioning module based on the operational parameters and the position information. The setpoint generator according to clause 21, wherein the initial setpoint trajectory spans, for each of the one or more locations or fields on the substrate, a preparation trajectory and a scan trajectory. The setpoint generator according to clause 22, wherein determining a modified setpoint trajectory for the positioning module of the positioner by means of an optimization algorithm comprises determining a modified setpoint trajectory of the preparation trajectory for the one or more locations or fields. The setpoint generator according to clause 21, wherein the process is an exposure process an alignment measurement or an inspection process. A position control system comprising a setpoint generator according to any of the clauses 19 to 24. A stage apparatus comprising a position control system according to clause 25, the stage apparatus comprising a short-stroke module as the positioning module and a long-stroke module as a slave module.

Claims

CLAIMS1. A setpoint generator for a position control system of a positioner comprising a master module and a slave module, the positioner being configured to displace an object, the setpoint generator being configured to, during a displacement of the object: determine a master setpoint trajectory for the master module; determine a slave setpoint trajectory for the slave module by means of an optimization algorithm; the optimization algorithm using at least part of the master setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.

2. The setpoint generator according to claim 1, wherein the performance characteristic of the positioner comprises a power consumption of the positioner and / or a dynamic characteristic of the positioner.

3. The setpoint generator according to any of the preceding claims, wherein the master setpoint trajectory comprises a sequence of piecewise polynomials.

4. The setpoint generator according to any of the preceding claims, wherein the optimization algorithm is configured to determine the slave setpoint trajectory which minimizes the objective function, within the one or more boundary conditions.

5. The setpoint generator according to claim 4, wherein the one or more boundary conditions comprises a threshold of an allowable deviation between the master setpoint trajectory and the slave setpoint trajectory.

6. The setpoint generator according to any of the claims 4 to 5, wherein the slave setpoint trajectory is determined by means of quadratic programming.

7. The setpoint generator according to any of the preceding claims 4 to 6, wherein the objective function comprises a mathematical expression of the power consumption of the master module as function of the slave setpoint trajectory.

8. The setpoint generator according to any of the claims 4-6, wherein the objective function comprises a mathematical expression associated with an RMS value of an acceleration of the master module when following the secondary setpoint trajectory.

9. The setpoint generator according to any of the claims 4-6, wherein the objective function comprises a mathematical expression associated with an RMS value of a dynamic characteristic of a motor of the master module following the secondary setpoint trajectory, the dynamic characteristic comprising at least one of a velocity, acceleration, jerk or snap.

10. The setpoint generator according to any of the preceding claims, wherein the object is a substrate and wherein the displacement of the substrate is part of an exposure process or an inspection process of the substrate.

11. The setpoint generator according to claim 10, wherein determining the master setpoint trajectory comprises: obtaining operational parameters of the positioner such as maximum velocity, maximum acceleration or maximum jerk; obtaining position information of one or more fields on the substrate that need to be exposed during the exposure process or inspected during the inspection process; determining the primary setpoint trajectory for the one or more fields or a subset thereof, based on the operational parameters and the position information.

12. The setpoint generator according to claim 10 or 11, wherein the primary setpoint trajectory spans, for each of the one or more fields on the substrate, a preparation trajectory and a scan trajectory.

13. A position control system comprising a setpoint generator according to any of the claims 1 to 12.

14. A stage apparatus comprising a position control system according to claim 13, the stage apparatus comprising a short-stroke module as the master module and a long-stroke module as the slave module.

15. The stage apparatus according to claim 14, further comprising an object table for holding a substrate, the short-stroke module being configured to position the object table.

16. An exposure apparatus comprising a stage apparatus according to claim 14 or 15.

17. A setpoint generator for a position control system of a positioning module of a positioner, whereby the setpoint generator is configured to: determine an initial setpoint trajectory for the positioning module of the positioner;determine a modified setpoint trajectory for the positioning module of the positioner by means of an optimization algorithm; the optimization algorithm using at least part of the initial setpoint trajectory, one or more boundary conditions and an objective function, the objection function being associated with a performance characteristic of the positioner.

18. The setpoint generator according to claim 17, wherein the object is a substrate and wherein the displacement of the substrate is part of a process applied to the substrate.

19. The setpoint generator according to claim 17 or 18, wherein determining the initial setpoint trajectory comprises: obtaining operational parameters of the positioner such as maximum velocity, maximum acceleration or maximum jerk; obtaining position information of one or more locations or fields on the substrate to which the process needs to be applied; - determining the initial setpoint trajectory for the positioning module based on the operational parameters and the position information.

20. A position control system comprising a setpoint generator according to any of the claims 17 to 19.

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