MECHATRONICS SYSTEM CONTROL METHOD, LITHOGRAPHIC APPARATUS CONTROL METHOD, AND LITHOGRAPHIC APPARATUS

Abstract

A control method for controlling a mechatronic system includes: b) providing a model of the mechatronic system including a disturbance compensation parameter; and c) modifying the disturbance compensation parameter by obtaining a servo error of the mechatronic system, obtaining a set point of the mechatronic system, determining a predicted servo error of the mechatronic system based on the set point and the model of the mechatronic system including the disturbance compensation parameter, and modifying the disturbance compensation parameter based on a correlation between the servo error and the predicted servo error. The method further includes updating a feedforward transfer function of a feedforward structure of the mechatronic system based on the modified disturbance compensation parameter, and continuously determining a control signal for controlling the mechatronic system using the updated feedforward transfer function.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to European Application No. 22172302.6, filed May 9, 2022, which is incorporated by reference in its entirety into this specification.

[0002] The present invention relates to a control method for controlling a mechatronic system, a control method for a lithographic apparatus, and a lithographic apparatus. [Background technology]

[0003]

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

[0004]

[0004] As semiconductor manufacturing processes continue to improve, the dimensions of circuit elements have continued to shrink, while the amount of functional elements, such as transistors, per device has been steadily increasing for decades, following a trend commonly referred to as "Moore's Law". To keep up with Moore's Law, the semiconductor industry is pursuing technologies that allow for the creation of ever smaller features. When projecting a pattern onto a substrate, a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features that are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Lithographic apparatus using extreme ultraviolet (EUV) radiation with wavelengths in the range of 4 nm to 20 nm, e.g., 6.7 nm or 13.5 nm, can be used to form smaller features on a substrate than lithographic apparatus using radiation with a wavelength of, e.g., 193 nm.

[0005]

[0005] In lithographic apparatus, precise control of the mechatronic system is required. For example, the position of the wafer table needs to be precisely controlled in order to project a pattern at a desired location on the substrate. A control system incorporating a feedback controller and a feedforward controller may be used. The feedforward transfer function of the feedforward controller may take into account the expected characteristics of the mechatronic system. However, the characteristics of the mechatronic system may vary, for example over time or as a function of other variables such as the position of the wafer table. As a result of such variations, the feedforward transfer function of the feedforward controller may be less accurate. Summary of the Invention

[0006]

[0006] In view of the above, an object of the present invention is to provide accurate control of a mechatronics system.

[0007]

[0007] According to one embodiment of the present invention, there is provided a control method for controlling a mechatronic system, the method comprising: a) providing a model of a mechatronic system including disturbance compensation parameters; b) modifying disturbance compensation parameters, -Get servo errors in mechatronic systems, obtaining a set point for the mechatronic system and determining a predicted servo error for the mechatronic system based on the set point and a model of the mechatronic system including disturbance compensation parameters; Modifying disturbance compensation parameters based on the correlation between the servo error and the predicted servo error. By making the above correction, c) updating a feedforward transfer function of a feedforward structure of the mechatronic system based on the modified disturbance compensation parameters; and d) continuously determining a control signal for controlling the mechatronic system using the updated feedforward transfer function; Includes.

[0008] According to another embodiment of the present invention, there is provided a method for controlling a lithographic apparatus, the method comprising controlling a mechatronic system of the lithographic apparatus according to a method according to an embodiment of the present invention.

[0009]

[0009] According to yet another embodiment of the present invention, there is provided a lithographic apparatus including a control system configured to control a mechatronic system of the apparatus, the control system configured to control the mechatronic system in accordance with a control method according to one embodiment of the present invention. [Brief description of the drawings]

[0010]

[0010] Some embodiments of the present invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which: [Figure 1] 1 is a schematic overview of a lithographic apparatus that may be employed in accordance with an embodiment of the present invention; [Diagram 2] FIG. 2 illustrates a detailed view of a portion of the lithographic apparatus of FIG. 1; [Diagram 3] 2 illustrates generally a position control system as part of a positioning system that may be employed in accordance with an embodiment of the present invention; [Figure 4] FIG. 1 shows a schematic control block diagram on which a control method according to an embodiment is described. [Figure 5A] 1 shows a top view of a scan pattern of a lithographic apparatus; [Figure 5B] FIG. 2 illustrates a setpoint trajectory in the X direction versus time for a scan pattern of a lithographic apparatus. [Figure 5C] FIG. 2 illustrates a setpoint trajectory in the Y direction versus time for a scan pattern of a lithographic apparatus. [Figure 6]2 shows a flow diagram of a control method according to an embodiment of the present invention; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011]

[0011] In this specification, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet, e.g., having a wavelength in the range of about 5 to 100 nm).

[0012]

[0012] The terms "reticle", "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam according to the pattern to be created in a target portion of a substrate. In this context, the term "light valve" may also be used. In addition to traditional masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0013] 1 illustrates a lithographic apparatus LA, which includes an illumination system (also called illuminator) IL configured to condition a radiation beam B (e.g. UV, DUV or EUV radiation), a mask support (e.g. mask table) MT constructed to support a patterning device (e.g. mask) MA and coupled to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g. wafer table) WT constructed to hold a substrate (e.g. resist coated wafer) W and coupled to a second positioner PW configured to accurately position the substrate support according to certain parameters, and a projection system (e.g. refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0014]

[0014] In operation, the illumination system IL receives a radiation beam from the radiation source SO, for example via the 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 the radiation. The radiation beam B is conditioned by the illuminator IL so that it has a desired spatial and angular intensity distribution in its cross-section in the plane of the patterning device MA.

[0015]

[0015] The term "projection system" PS as used herein should be broadly interpreted to encompass various types of projection systems including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, appropriate for the exposure radiation being used and / or 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.

[0016]

[0016] The lithographic apparatus LA may be of a type in which 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 space between the projection system PS and the substrate W, which is also referred to as immersion lithography. More information about immersion techniques can be found in US Pat. No. 6,952,253, which is incorporated herein by reference.

[0017] The lithographic apparatus LA may be of a type equipped with two or more substrate supports WT (also referred to as "dual stage"). In such a "multi-stage" machine, the substrate supports WT can be used in parallel and / or a substrate W arranged on one substrate support WT can be prepared for a next exposure while another substrate W arranged on the other substrate support WT is used to expose a pattern onto this other substrate W.

[0018]

[0018] 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 a number of sensors. The cleaning device may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of a system for supplying immersion liquid. The measurement stage may be moved below the projection system PS when the substrate support WT is spaced apart from the projection system PS.

[0019]

[0019] In operation, a radiation beam B is incident on a patterning device (e.g. mask) MA held on a mask support MT and is patterned by a pattern (design layout) present on the patterning device MA. After passing through the patterning device MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. The substrate support WT can be accurately moved using a second positioner PW and a position measurement system IF to position different target portions C, for example, in aligned and focused positions in the path of the radiation beam B. Similarly, the patterning device MA can be accurately positioned relative to the path of the radiation beam B using a first positioner PM and possibly another position sensor (not explicitly shown in Figure 1). The patterning device MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 as illustrated occupy dedicated target portions, they may be located in spaces between the target portions. When they are located between target portions C, the substrate alignment marks P1, P2 are known as scribe-lane alignment marks.

[0020]

[0020] To clarify the invention, a Cartesian coordinate system is used. This Cartesian coordinate system has three axes: x, y, and z. Each of these three axes is orthogonal to the other two. Rotation about the x axis is called Rx rotation, rotation about the y axis is called Ry rotation, and rotation about the z axis is called Rz rotation. The x and y axes define a horizontal plane, while the z axis is vertical. This Cartesian coordinate system is not a limitation of the invention and is used only for clarity. Alternatively, another coordinate system, such as a cylindrical coordinate system, can be used to clarify the invention. The Cartesian coordinate system may be oriented differently, for example the z axis may have a component along the horizontal plane.

[0021]

[0021] Figure 2 shows a part of the lithographic apparatus LA of Figure 1 in more detail. 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. The metrology frame MF may also support 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 being transmitted from the base frame BF to the metrology frame MF.

[0022]

[0022] 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. This driving force accelerates the substrate support WT in a desired direction. Due to conservation of momentum, the driving force is also applied to the balance mass BM with the same magnitude, but in an opposite direction to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the moving parts of the second positioner PW and the mass of the substrate support WT.

[0023]

[0023] In one embodiment, the second positioner PW is supported by the balance mass BM. For example, the second positioner PW comprises a planar motor for levitating 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, the second positioner PW comprises a linear motor and the second positioner PW comprises a bearing (such as a gas bearing) for levitating the substrate support WT above the base frame BF.

[0024]

[0024] The position measurement system PMS may include any type of sensor suitable for determining the position of the substrate support WT. The position measurement system PMS may include any type of sensor suitable for determining the 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 include a combined interferometer and encoder system. The sensor may also be another type of sensor, such as a magnetic, capacitive or inductive sensor. The position measurement system PMS may determine a relative position of the metrology frame MF or the projection system PS, etc. with respect to a reference. The position determination of the substrate table WT and / or the mask support MT by the position measurement system PMS may be performed by measuring the position or by measuring a time derivative of the position, such as a velocity or an acceleration.

[0025]

[0025] The position measurement system PMS may include an encoder system. An encoder system is known, for example, from US patent application US2007 / 0058173A1, filed 7 September 2006, which is incorporated herein by reference. The encoder system comprises an encoder head, a diffraction grating and a sensor. The encoder system may receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam and the secondary radiation beam originate from the same radiation beam, i.e. the original radiation beam. At least one of the primary radiation beam and the secondary radiation beam is generated by diffracting the original radiation beam with a diffraction grating. If both the primary radiation beam and the secondary radiation beam are generated by diffracting the original radiation beam with a diffraction grating, the primary radiation beam should have a different diffraction order from the secondary radiation beam. The different diffraction orders can be, for example, +1, -1, +2 and -2. 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 the phase or phase difference of this composite radiation beam. Based on this phase or phase difference, the sensor generates a signal. This signal is indicative of the position of the encoder head relative to the diffraction grating. One of the encoder head and the diffraction grating may be disposed on the substrate structure WT. The other of the encoder head and the diffraction grating may be disposed on the metrology frame MF or the base frame BF. For example, the multiple encoder heads are disposed on the metrology frame MF, while the diffraction grating is disposed on a top surface of the substrate support WT. In another example, the diffraction grating is disposed on a bottom surface of the substrate support WT, and the encoder head is disposed below the substrate support WT.

[0026]

[0026] The position measurement system PMS may include an interferometer system. An interferometer system is known, for example, from US Pat. No. 6,020,964, filed 13 July 1998, which is incorporated herein by reference. The interferometer system may comprise a beam splitter, a mirror, a reference mirror and a sensor. The beam splitter splits the radiation beam 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 a sensor. The sensor determines the phase or frequency of the combined radiation beam. Based on this phase or frequency, the sensor generates a signal. This signal is representative of the displacement of the mirror. In an embodiment, the mirror is connected to the substrate support WT. The reference mirror may be connected to a metrology frame MF. In one embodiment, the measurement and reference beams are combined into a combined radiation beam by an additional optical component rather than a beam splitter.

[0027]

[0027] The first positioner PM may include a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT with high accuracy over a narrow range of movement relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module with high accuracy over a wide range of movement relative to the projection system PS with relatively low accuracy. By combining the long-stroke module and the short-stroke module, the first positioner PM can move the mask support MT with high accuracy over a wide range of movement relative to the projection system PS. Similarly, the second positioner PW may include a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT with high accuracy over a narrow range of movement relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module with high accuracy over a wide range of movement relative to the projection system PS with relatively low accuracy. By combining the long-stroke module and the short-stroke module, the second positioner PW can move the substrate support WT with high accuracy over a wide range of movement relative to the projection system PS.

[0028]

[0028] The first positioner PM and the second positioner PW are provided with actuators for moving the mask support MT and the substrate support WT, respectively. The actuators may be linear actuators providing a driving force along a single axis (e.g. the Y-axis). It is also possible to provide driving forces along multiple axes by applying multiple linear actuators. The actuators may be planar actuators providing driving forces along multiple axes. For example, such planar actuators may be arranged to move the substrate support WT with six degrees of freedom. The actuators may be electromagnetic actuators comprising at least one coil and at least one magnet. Such actuators are arranged to move the at least one coil relative to the at least one magnet by applying a current to the at least one coil. The actuators may be moving magnet type actuators having at least one magnet coupled to the substrate support WT and the mask support MT, respectively. The actuators may be moving coil type actuators having at least one coil coupled to the substrate support WT and the mask support MT, respectively. The actuators may be voice coil actuators, reluctance actuators, Lorentz actuators, or piezo actuators, or any other suitable actuators.

[0029]

[0029] The lithographic apparatus LA includes a position control system PCS as shown diagrammatically in Fig. 3. The position control system PCS includes a setpoint generator SP, a feedforward controller FF, and a feedback controller FB. The position control system PCS provides a drive signal to an actuator ACT, which may be an actuator of the first positioner PM or the second positioner PW. The actuator ACT drives a plant P, which may include a substrate support WT or a mask support MT. An output of the plant P is a position quantity, e.g. a position, a velocity, an acceleration, etc. The position quantity is measured by a position measurement system PMS. A signal generated by the position measurement system PMS is a position signal representative of the position quantity of the plant P. A signal generated by the setpoint generator SP 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. A difference between the reference signal and the position signal forms an input to a feedback controller FB. Based on this input, the feedback controller FB provides at least a part of the drive signal for the actuator ACT. The reference signal may form an input to a feedforward controller FF, based on which the feedforward controller FF provides at least a part of the drive signal for the actuator ACT. The feedforward FF may utilize information about the dynamic characteristics of the plant P, such as mass, stiffness, resonant modes, natural frequencies, etc.

[0030]

[0030] The servo performance of mechatronic systems in lithography apparatus, for example, in wafer stage (WS) or reticle stage (RS) of lithography apparatus, may depend on mechanical structure, actuation, and feedforward (FF) compensation of known disturbances. The main disturbance to the control loop may be excitation of mechanical structure by setpoint trajectory. Typical FF compensation of setpoint trajectory may include velocity compensation, acceleration compensation, jerk compensation, snap compensation, and compliance compensation. In addition, disturbance forces may be known, for example, from cable slab, eddy current damping and reluctance in long stroke (LoS), dynamic link and cooling water pressure pulse in short stroke (SS). Usually, most of the actuation forces come from FF and disturbance compensation, and only require minor adjustment by feedback (FB) control. Therefore, proper parameterization of compensation parameters may be desired to achieve accurate tracking performance.

[0031]

[0031] However, calibration of compensation parameters may not be straightforward. Manufacturing tolerances may cause machine-to-machine variations. For example, the stage may be subject to variations in motor constants caused by back iron saturation (current dependent), coil position relative to the magnet, magnet strength variations, magnet plate flatness, and amplifier nonlinearities. Temperature dependent magnetic field strength and amplifier components may also have an effect. Furthermore, the mass, inertia, and dynamics of the stage may be position dependent, for example due to cable slab roll-off. Different lithography applications may also cause significant variations in the mass of the wafer.

[0032]

[0032] Also, the actuators of the stage may not be located at the center of gravity (CoG) but distributed throughout the stage. Thus, applying a decoupling matrix allows the use of distributed control, i.e., six independent single-input single-output (SISO) controllers, one for each rigid body logical direction. By moving the stage within a fixed measurement system, the decoupling matrix may be position dependent. Furthermore, LoS planar actuators may use a commutation measurement system that is subject to sensor drift and slow thermal dynamics. It should be noted that the commutation of a three-phase motor may also cause force disturbances in the case of commutation offsets.

[0033]

[0033] Also, precise time alignment may be required between the control paths of FF and FB, as well as between peripherals such as LoS and SS, i.e., to compensate for amplifier, sensor and communication delays. Therefore, to meet the servo error specification, sub-sample time alignment may be required, which can be approximated by a compensation based on higher order time derivatives, i.e., a jerk FF that compensates for the time mismatch of acceleration FF compensation.

[0034]

[0034] In summary, due to position and load dependence, machine-to-machine variability, and time-varying effects, the calibration of FF and disturbance compensation parameters may not be straightforward. In known solutions, all compensation parameters may be calibrated and then kept constant during normal operation. The calibration method applied for the FF parameters may be based on a data-based calibration method. The separation parameters may require fine-tuning, which can be done by a data-based calibration method.

[0035]

[0035] In addition to accurate feedforward control, the system may require diagnostics to monitor system degradation during normal operation. Diagnostics may monitor the MA and MSD values ​​of servo errors. Methods that may improve servo performance may also be suitable for improving diagnostics, in that they can pinpoint the specific disturbance source that causes the servo error.

[0036]

[0036] Learning strategies have been the subject of investigation for many years. Because WS performs similar trajectories repeatedly, e.g. exposure scans, the focus is often on exploiting the repetitive nature of WS scans to employ optimization procedures in real time (i.e. while the machine is in operation).

[0037]

[0037] The concept of iterative learning control (ILC) can be applied to systems that repeat the same setpoint trajectory. The ILC approach generates force trajectories that can attempt to compensate for control errors based on an estimate of the controlled system. Thus, ILC relies on a description of the system and a fixed setpoint trajectory and may not utilize explicit knowledge of disturbance sources. An obstacle in applying an online ILC strategy can be robustness to setpoint variations, i.e., dealing with non-iterative (thermal) corrections applied to the setpoint of the exposure scan and alignment with other parts of the machine, such as the source, reticle, POB, etc.

[0038]

[0038] Conventional learning strategies may rely on repeated setpoint trajectories and may not be able to remove structured servo errors in the lithographic apparatus online while providing the necessary robustness against setpoint variations.

[0039]

[0039] Although very high servo performance may be achieved in lithographic apparatus, in other cases further improvement may be desired.

[0040]

[0040] The present invention aims to achieve further improvement of servo control performance (improved overlay or high acceleration setpoints) by enabling online adaptation of feedforward, disturbance compensation and decoupling parameters subject to time variations. Online adaptation is also called "learning". By utilizing the acceleration phase to learn locally optimal parameter settings, position-dependent parameters can be compensated by field-by-field optimization during constant velocity exposure scanning.

[0041]

[0041] Fig. 4 shows a block schematic diagram, according to which the updated disturbance compensation parameters are determined. A set point STP is input to the model MD. The set point may be a set point STP generated by a set point generator SP and provided to a control system (such as the control system according to Fig. 3). The model MD determines a servo error ESR predicted from the set point STP. The model MD may also include the inverse of the plant behavior as well as the characteristics of the feedback controller behavior, so that it is possible to predict the servo error of the mechatronic system based on the set point. Furthermore, the set point STP is provided to the control system, whereby a servo error SR is measured. The servo error SR is understood to be the input to the feedback controller FB, i.e. the difference between the set point STP and the feedback signal derived by the PMS from the output of the plant P. A correlation is then performed between the predicted servo error ESR and the measured servo error SR. This correlation can be performed as follows: The predicted servo error ESR and the measured servo error SR are multiplied by X as shown in Figure 4, and then the correlation is calculated, for example, over N consecutive time periods, where N is a natural number greater than 1. The following equation (1) can be used to determine this correlation:

[0042]

number

[0043]

[0043] where e represents the predicted servo error signal ESR derived using the model, and e represents the measured servo error signal SR. The variable C is a constant related to the magnitude of the predicted error, the horizontal line length, and the excitation characteristics of the setpoint. The variable C may be calibrated for a worst-case setpoint with a known maximum excitation.

[0044] As a result, the estimated value θ of the disturbance compensation parameter LS The estimate of the disturbance compensation parameter may include, for example, a least squares estimate. Then, in successive time steps, the estimate θ is obtained by converging to an optimal disturbance compensation parameter θ by a steepest descent optimization with a step size c, for example, using the following equation (2): LS From this, the disturbance compensation parameter θ can be determined.

[0045]

[0045] θ(t+1)=θ(t)−cθ LS (t) (2)

[0046]

[0046] In each iteration, the determined disturbance compensation parameter θ is used to update a feedforward transfer function of a feedforward structure of the mechatronic system, and the control signal is determined to control the mechatronic system using the updated feedforward transfer function. The feedforward transfer function of the feedforward structure of the mechatronic system may include reciprocal plant behaviors, such as the inverse mass and compliance of the mechatronic structure.

[0047] The modified disturbance compensation parameters are: obtaining a servo error of the mechatronic system; - obtaining a set point of the mechatronic system and determining a predicted servo error of the mechatronic system based on the set point and a model of the mechatronic system including disturbance compensation parameters; - modifying disturbance compensation parameters based on a correlation between the servo error and a predicted servo error; and updating a feedforward transfer function of a feedforward structure of the mechatronic system based on the modified disturbance compensation parameters; A control signal for controlling the mechatronic system is continuously determined using the iteratively updated feedforward transfer function. The model may be updated based on the modified disturbance compensation parameters, which may allow a more accurate determination of a predicted servo error and may facilitate convergence of the disturbance compensation parameters to an appropriate value.

[0048]

[0048] By using multiple iterations over the past N iterations (N is a natural number), the optimization can be performed, and thus the disturbance control parameters can be optimized over time. Assuming that the servo error depends linearly on the compensation parameters, the servo error and the predicted servo error can be combined using the least squares method to provide an analytical solution.

[0049]

[0049] The time scale of the past N iterations and / or the time scale of the update of the modified disturbance compensation parameters may be set to exceed the time scale of the repeating pattern at the setpoint and / or the time scale of the feedback controlled system (e.g., the time scale indicated by the bandwidth of the feedback controlled system). As a result, the optimization is performed over a time scale that is longer than the time scale of the repeating pattern at the setpoint and / or the time scale of the bandwidth of the feedback controlled system, which may avoid the optimization being hindered by the dynamics of the setpoint and / or the feedback controlled system.

[0050]

[0050] The disturbance control parameters may include any parameters that may exhibit change, variation, tolerance, etc. For example, the disturbance control parameters may include the mass of a mechatronic system.

[0051]

[0051] The control signal determined by the above-mentioned method may be a feedforward signal generated by a feedforward structure of a control system, such as, for example, the feedforward FF of the position control system described with reference to FIG. 3. The feedforward signal may represent a feedforward force of a mechatronic system. Thus, the feedforward signal can be accurately determined, taking into account changes, fluctuations, tolerances, etc. in the mechatronic system. Since the feedforward control may provide a relatively fast control, the accuracy of such a feedforward control can be increased by the above-mentioned recursive method. Thus, in addition to being relatively fast, the feedforward can also provide a relatively accurate control, taking into account the above-mentioned changes, fluctuations, tolerances, etc.

[0052]

[0052] The control signal determined by the above method may be a feedforward signal generated by a feedforward structure of the control system, which may provide a feedforward signal from a first mechatronic subsystem to a second mechatronic subsystem of the mechatronic system. For example, the first mechatronic subsystem may include a support (e.g. a support for a patterning device), while the second mechatronic subsystem may include a substrate table. Thus, the determination of the disturbance compensation parameters allows for accurate feedforward, whereby disturbances caused by the movement of the support relative to the positioning of the substrate table may be accurately controlled, in that the variations in disturbances caused by the support to the substrate table may be taken into account.

[0053]

[0053] The mechatronic system may comprise an actuator, such as an electromagnetic actuator. The disturbance compensation parameters may be used to take into account variations or tolerances, for example variations or position dependence of the force constant of the actuator, commutation position parameters between the magnet and the coil.

[0054]

[0054] The control methods described herein can be used to control mechatronic systems of a lithographic apparatus.

[0055]

[0055] For example, the control signal may comprise a feedforward signal of the lithographic apparatus. The disturbance parameter may be included in a feedforward structure that generates the feedforward signal. For example, the mechatronic system may comprise a substrate table of the lithographic apparatus, whereby the feedforward structure is configured to provide a feedforward signal representative of a feedforward force of the substrate table.

[0056]

[0056] As another example, the control signal determined by the above method may be a feedforward signal generated by a feedforward structure of a control system, which may provide a feedforward signal from a first mechatronic subsystem of the lithographic apparatus to a second mechatronic subsystem of the lithographic apparatus. For example, the first mechatronic subsystem may include a support for supporting a patterning device, and the second mechatronic subsystem may include a substrate table. Thus, the determination of the disturbance compensation parameters allows for an accurate feedforward signal, which allows for accurate control of the disturbance caused by the movement of the support relative to the positioning of the substrate table, in that the disturbance variations caused by the support to the substrate table may be taken into account.

[0057]

[0057] Other subsystems of a lithographic apparatus in which the present control methods may be used may include the positioning of optical elements, for example the position of an optical element such as a lens or a mirror may be controlled by the methods described herein.

[0058]

[0058] Essentially the control method can be applied to any disturbance compensation that uses a setpoint signal as input, for example friction, eddy current damping, reluctance, mass, jerk, snap, compliance, coolant pressure pulse, etc.

[0059]

[0059] In addition, in theory, the method can also be used for parameters in the feedback loop, such as the separated parameters in the GB matrix, etc. In this case, not only the parameters in the FF structure need to be updated, but also the parameters in the model that generates the servo error prediction need to be updated.

[0060]

[0060] The method according to the invention allows the control of the mechatronic system to be more accurate. Variable parameters in the mechatronic system can be taken into account, and thus the values ​​of the variable parameters are learned by comparison of the modeled servo error and the measured servo error. The correlation between the modeled servo error and the measured servo error is maximized in that the disturbance compensation parameters are learned to values ​​that maximize this correlation. The disturbance compensation parameters are used to control the mechatronic system and allow the variables of the mechatronic system to be taken into account, such as the variation or position dependence of the force constant of the actuator, or the variation of the mass. The correlation can be determined over a time range that exceeds the time range of the periodic movement of the mechatronic system, thus making it possible to determine appropriate values ​​of the disturbance compensation parameters for mechatronic systems that are subjected to movement periods such as acceleration, constant speed, deceleration, etc. The variation of the variable parameters over time may be taken into account. For example, in the case of position-dependent parameters, such as dependence on the stage position, the disturbance compensation parameters can be continuously adapted according to the control method to take into account the variation of the parameters with changes in position (e.g., the position of the stage). The inventive control may be particularly useful in feedforward in that it accounts for variable parameters in the mechatronic system, such as variable mass, position dependency, variable motor force constants, etc., so that accurate feedforward control can be determined. The variable parameters traditionally introduce inaccuracies into the feedforward signal, which can be reduced by the present invention. Disturbance compensation parameters are learned to account for the variable parameters, which may improve feedforward accuracy. As a result, feedback control corrective actions that may be required to compensate for variable parameters in the feedforward path may be reduced, allowing for more accurate mechatronic system control.

[0061]

[0061] Thus, a robust online learning may be obtained as described herein, for example as a result of using manipulated variables based on a model of the control system H' with suboptimal parameters θ'. This model may provide an estimate of the servo error signal e typical of an imperfect calibration of the parameters to be optimized based on the actual set point STP. A correlation between the measured servo error e and the predicted servo error e above shows that there is room for improvement. The correlation may be evaluated, for example, in a receding horizon manner over the past N steps. The latter is calculated as a least squares estimate θ of the parameter deviation from the optimum in the considered historical data. LS Then, the disturbance parameter θ may be updated at each time step, for example using steepest descent optimization with a step size c, to converge to an optimal value.

[0062] The above learning strategy can be implemented and experimentally verified to demonstrate its feasibility by simultaneously compensating the following six parameters during an exposure scan (see FIGS. 5A-5C): Mass (motor force constant) FF parameters in x and y directions Time alignment between FF and FB in x and y directions Position offset of planar actuator commutation in x and y directions

[0063]

[0063] Figure 5A shows a top view of the substrate table setpoint trajectory as the substrate table moves in a horizontal plane. Figures 5B and 5C show the x- and y-direction components of the setpoint trajectory of Figure 5A, respectively. In Figure 5A, the x-direction is represented on the horizontal axis and the y-component is represented on the vertical axis. After tilting the feedforward of the substrate table control, i.e., after determining the disturbance compensation parameters as described herein, the servo error in the x-direction and the servo error in the y-direction can be reduced.

[0064]

[0064] The above control method can be summarized as follows with reference to FIG.

[0065]

[0065] A control method for controlling a mechatronics system, comprising: a) providing (601) a model of a mechatronic system, including disturbance compensation parameters; b) modifying (602) disturbance compensation parameters, -Get servo error of mechatronics system (602A), - obtaining a set point for the mechatronic system (602B) and determining a predicted servo error for the mechatronic system based on the set point and a model of the mechatronic system including disturbance compensation parameters; - modifying (602C) disturbance compensation parameters based on the correlation between the servo error and the predicted servo error; By this, the disturbance compensation parameters are corrected; c) updating (603) a feedforward transfer function of a feedforward structure of the mechatronic system based on the modified disturbance compensation parameters; d) continuously determining (604) a control signal for controlling the mechatronic system using the updated feedforward transfer function; The method includes:

[0066]

[0066] Although specific reference is made in this specification to the use of lithographic apparatus in IC manufacture, it should be understood that the lithographic apparatus described herein may have other applications. Potential other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0067]

[0067] Although specific reference is made herein to embodiments of the invention in the context of lithographic apparatus, embodiments of the invention may also 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 objects such as wafers (or other substrates), masks (or other patterning devices), etc. These apparatus are commonly referred to as lithography tools. Such lithography tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0068]

[0068] Although specific reference has been made above to the use of embodiments of the present invention in the context of optical lithography, it will be appreciated that, where circumstances permit, the present invention is not limited to optical lithography and may also be used in other applications, such as imprint lithography.

[0069]

[0069] Where circumstances permit, embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention may also be implemented as instructions stored on a machine-readable medium and readable and executable 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 a read-only memory (ROM), a random access memory (RAM), a magnetic storage medium, an optical storage medium, a flash memory device, or an electrical, optical, acoustic, or other form of propagated signal (e.g., carrier wave, infrared signal, digital signal, etc.). Also, firmware, software, routines, instructions may be described herein as performing certain operations. However, it should be understood that such description is merely for convenience and that such operations are in fact due to a computing device, processor, controller, or other device executing the firmware, software, routines, instructions, etc., which may cause an actuator or other device to interact with the physical world.

[0070]

[0070] Although specific embodiments of the present invention have been described above, it is apparent that the present invention can be embodied in other ways than those described above. The above description is intended to be illustrative and not restrictive.

Claims

1. 1. A control method for controlling a mechatronics system, comprising: a) providing a model of the mechatronic system including disturbance compensation parameters; b) modifying the disturbance compensation parameters, - acquiring a servo error of said mechatronic system; - obtaining set points for the mechatronic system and determining a predicted servo error for the mechatronic system based on the set points and the model of the mechatronic system including the disturbance compensation parameters; - modifying the disturbance compensation parameters based on a correlation between the servo error and the predicted servo error; modifying the disturbance compensation parameter by c) updating a feedforward transfer function of a feedforward structure of the mechatronic system based on the modified disturbance compensation parameters; and d) continually determining a control signal for controlling the mechatronic system using the updated feedforward transfer function; A control method comprising:

2. 2. The control method of claim 1, further comprising repeating steps b) and c) to iteratively update the feedforward transfer function, and in step d), controlling the mechatronics system using the iteratively updated feedforward transfer function.

3. The method of claim 2 , wherein b) further comprises updating the model based on the modified disturbance compensation parameters.

4. The control method according to claim 2 or 3, wherein the disturbance compensation parameter is modified based on the correlation between the servo error and the predicted servo error in N previous iterations, where N is a natural number greater than 1.

5. The control method of claim 4 , wherein the correlation between the servo error and the predicted servo error in N previous iterations is synthesized using a least squares method.

6. A method according to any one of claims 2 to 5, wherein the time scale of the N previous repetitions is set to exceed the time scale of the repeating pattern at the setpoint.

7. The control method according to any one of claims 1 to 6, wherein the control signal is a feedforward signal representing a feedforward force of the mechatronic system generated by the feedforward structure, and the disturbance compensation parameter is included in the feedforward transfer function of the feedforward structure.

8. 7. The control method of claim 1, wherein the mechatronic system includes a dual mechatronic subsystem, the model of the mechatronic system includes the feedforward structure from one of the mechatronic subsystems to the other of the mechatronic subsystems, and the disturbance compensation parameters are included in the feedforward transfer function of the feedforward structure.

9. The method according to any one of the preceding claims, wherein the mechatronic system comprises an actuator, for example an electromagnetic actuator.

10. A method of controlling a lithographic apparatus, comprising controlling a mechatronic system of said lithographic apparatus according to a method according to any one of the preceding claims.

11. A lithographic apparatus comprising a control system configured to control a mechatronic system of the lithographic apparatus, the control system being configured to control the mechatronic system according to a control method according to any one of claims 1 to 9.

12. The lithographic apparatus of claim 11 , comprising a feedforward structure configured to provide a feedforward force, the disturbance compensation parameter being included in the feedforward structure.

13. The lithographic apparatus of claim 12 , wherein the mechatronic system comprises a substrate table configured to hold a substrate, and the feedforward structure is configured to provide the feedforward force to the substrate table.

14. 14. The lithographic apparatus of claim 11, wherein the mechatronic system comprises a dual mechatronic subsystem, and the lithographic apparatus comprises a feedforward structure from one of the mechatronic subsystems to the other of the mechatronic subsystems, the feedforward structure including the disturbance compensation parameters.

15. 15. A lithographic apparatus according to claim 14, comprising a substrate table configured to hold a substrate and a support for supporting a patterning device, the support being included in the one of the mechatronic subsystems and the substrate table being included in the other of the mechatronic subsystems.

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