Electromechanical system control method, lithographic equipment control method and lithographic equipment

Abstract

A control method for controlling an electromechanical system, comprising: providing a model of the electromechanical system, the model comprising disturbance compensation parameters; b) modifying the disturbance compensation parameter by: obtaining a servo error of the electromechanical system; -obtaining a setpoint of the electromechanical system and determining a predicted servo error of the electromechanical system based on the model of the electromechanical system comprising a disturbance compensation parameter and the setpoint,-modifying the disturbance compensation parameter based on a correlation between the servo error and the predicted servo error. The method also includes updating a feed-forward transfer function of the electromechanical system based on the modified disturbance compensation parameter, and continuously determining a control signal to control the electromechanical system using the updated feed-forward transfer function.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European application 22172302.6 filed on May 9, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to a control method for controlling an electromechanical system, a control method for a lithography device, and a lithography device. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern to a substrate. For example, a lithographic apparatus may be used in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as a "design layout" or "design") of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (e.g., a wafer).

[0005] As semiconductor manufacturing processes continue to advance, the number of functional elements (such as transistors) per device has been steadily increasing for decades while the size of circuit elements has been continuously reduced, following a trend commonly referred to as "Moore's law". In order to keep up with Moore's law, the semiconductor industry is seeking technologies that can produce smaller and smaller features. In order to project a pattern onto a substrate, a lithographic apparatus can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features patterned on the substrate. Typical wavelengths currently used are 365nm (i-line), 248nm, 193nm, and 13.5nm. A lithographic apparatus using extreme ultraviolet (EUV) radiation (having a wavelength in the range of 4nm to 20nm, such as 6.7nm or 13.5nm) can be used to form smaller features on a substrate than a lithographic apparatus using, for example, radiation having a wavelength of 193nm.

[0006] Accurate control of electromechanical systems is required in lithographic equipment. For example, the position of the wafer stage is to be accurately controlled so that a pattern is projected at a desired location on the substrate. A control system comprising a feedback controller and a feedforward controller can be used. The feedforward transfer function of the feedforward controller can take into account the expected properties of the electromechanical system. However, the properties of the electromechanical system can vary, such as over time or with other variables (such as the position of the wafer stage, etc.). As a result of such variations, the accuracy of the feedforward transfer function of the feedforward controller may be low. Summary of the invention

[0007] In view of the foregoing, it is an object of the present invention to provide accurate control of an electromechanical system.

[0008] According to an embodiment of the present invention, a control method for controlling an electromechanical system is provided, the method comprising:

[0009] a) providing a model of the electromechanical system, the model including disturbance compensation parameters;

[0010] b) modifying the disturbance compensation parameters by:

[0011] - obtaining a servo error of the electromechanical system;

[0012] - obtaining a set point for the electromechanical system and determining a predicted servo error for the electromechanical system based on a model of the electromechanical system including disturbance compensation parameters and the set point,

[0013] - modifying the disturbance compensation parameters based on a correlation between the servo error and the predicted servo error,

[0014] c) updating a feedforward transfer function of a feedforward structure of the electromechanical system based on the modified disturbance compensation parameters, and

[0015] d) continuously determining a control signal to control the electromechanical system using the updated feed-forward transfer function.

[0016] According to another embodiment of the present invention, a method for controlling a lithographic device is provided, comprising controlling a mechatronic system of the lithographic device according to a method according to an embodiment of the present invention.

[0017] According to another embodiment of the present invention, a lithography device is provided, comprising a control system, wherein the control system is configured to control an electromechanical system of the lithography device, and the control system is configured to control the electromechanical system according to a control method according to an embodiment of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0019] - Figure 1 depicts a schematic overview of a lithographic apparatus that may be employed in accordance with an embodiment of the present invention;

[0020] - Figure 2 Depiction Figure 1 a detailed view of a portion of a lithographic apparatus;

[0021] - Figure 3 schematically depicts a position control system as part of a positioning system that may be employed in accordance with an embodiment of the present invention;

[0022] - Figure 4depicts a schematic control block diagram on the basis of which a control method according to an embodiment will be explained;

[0023] - FIG. 5A to FIG. 5C A top view of a lithographic apparatus scanning a pattern, a plot of x-direction setpoint trajectory versus time, and a plot of y-direction setpoint trajectory versus time are depicted respectively; and

[0024] - Figure 6 A flow chart of a control method according to an embodiment of the present invention is depicted. DETAILED DESCRIPTION

[0025] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365nm, 248nm, 193nm, 157nm or 126nm) and EUV radiation (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5nm to 100nm).

[0026] The terms "reticle", "mask" or "patterning device" as used in the present invention may be broadly interpreted to refer to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam that corresponds to the pattern to be produced in a target portion of the substrate. In this context, the term "light valve" may also be used. In addition to classical masks (transmissive or reflective, binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0027] Figure 1 A lithographic apparatus LA is schematically depicted. The lithographic apparatus LA comprises an illumination system (also referred to as an 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 stage) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g., a wafer stage) WT configured to hold a substrate (e.g., a wafer coated with resist) W, connected to a second positioner PW configured to accurately position the substrate support according to 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 the patterning device MA onto a target portion C of the substrate W (e.g., a portion comprising one or more dies).

[0028] In operation, the illumination system IL receives a radiation beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various types of optical components for directing, shaping and / or controlling the radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof. 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 the plane of the patterning device MA.

[0029] The term "projection system" PS as used in the present invention should be interpreted broadly to cover various types of projection systems suitable for the exposure radiation used and / or for other factors such as the use of immersion liquid or the use of vacuum, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems or any combination thereof. Any term "projection lens" used herein may be considered synonymous with the more general term "projection system" PS.

[0030] The lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by an immersion liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system PS and the substrate W - this is also known as immersion lithography. More information on immersion techniques is given in US 6952253, which is incorporated herein by reference.

[0031] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as a "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel and / or a substrate W on one of the substrate supports WT may be used to expose a pattern on another substrate W while a step of preparing the substrate W for subsequent exposure is being performed on the substrate W on another substrate support WT.

[0032] In addition to the substrate support WT, the lithographic apparatus LA may also comprise a measurement platform. The measurement platform is arranged to hold sensors and / or cleaning means. The sensors may be arranged to measure properties of the projection system PS or properties of the radiation beam B. The measurement platform may hold a plurality of sensors. The cleaning means may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of the system providing immersion liquid. The measurement platform may be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0033] In operation, the radiation beam B is incident on the patterning device (e.g. mask) MA held on the mask support MT and is patterned by a pattern (design layout) present on the 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 the position measurement system IF, the substrate support WT can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B in a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor (in Figure 1 The patterning device MA (not explicitly depicted in the figure) can be used to accurately position the patterning device MA relative to the path of the radiation beam B. The patterning device MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 occupy dedicated target portions as illustrated, the marks can be located in the space between target portions. When the substrate alignment marks P1, P2 are located between the target portions C, these substrate alignment marks are called scribe line alignment marks.

[0034] In order to illustrate the present invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, namely the x-axis, the y-axis and the z-axis. Each of the three axes is orthogonal to the other two axes. The rotation around the x-axis is called the Rx rotation. The rotation around the y-axis is called the Ry rotation. The rotation around the z-axis is called the Rz rotation. The x-axis and the y-axis define a horizontal plane, while the z-axis is in the vertical direction. The Cartesian coordinate system is not limited to the present invention and is only used for illustration. As an alternative, another coordinate system (such as a cylindrical coordinate system) can be used to illustrate the present invention. The direction of the Cartesian coordinate system can be different, for example, so that the z-axis has a component along the horizontal plane.

[0035] Figure 2 Show Figure 1 A more detailed view of a part of the lithographic apparatus LA. The lithographic apparatus LA may be provided with a base frame, a balancing mass BM, a metrology frame MF and a vibration isolation system IS. The metrology frame MF supports a projection system PS. In addition, the metrology frame MF may support a part of the position measurement system PMS. The metrology frame MF is supported by the base frame via the vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce vibrations from the base frame being propagated to the metrology frame MF.

[0036] The second positioner PW is arranged to accelerate the substrate support WT by providing a driving force between the substrate support WT and the balancing mass BM. The driving force accelerates the substrate support WT in a desired direction. Due to conservation of momentum, the driving force is also applied to the balancing mass BM in an equal amount but in a direction opposite to the desired direction. Typically, the mass of the balancing mass BM is significantly greater than the mass of the moving parts of the second positioner PW and the substrate support WT.

[0037] In an embodiment, the second positioner PW is supported by the balancing mass BM. For example, wherein the second positioner PW comprises a planar motor for suspending the substrate support WT on the balancing 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 (such as a gas bearing) for suspending the substrate support WT on the base frame.

[0038] The position measurement system PMS may comprise any type of sensor suitable for determining the position of the substrate support WT. The position measurement system PMS may comprise 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 comprise a combined system with 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, such as the measurement 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 the time derivative of the position, such as a velocity or an acceleration.

[0039] The position measurement system PMS may include an encoder system. The encoder system is known, for example, from US patent application US2007 / 0058173A1 filed on September 7, 2006, which is 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 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 using the grating. If both the primary radiation beam and the secondary radiation beam are generated by diffracting the original radiation beam with the grating, the primary radiation beam needs to have a different diffraction order from the secondary radiation beam. Different diffraction orders are, for example, +1 order, -1 order, +2 order and -2 order. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. The sensor in the encoder head determines the phase or phase difference of the combined radiation beam. The sensor generates a signal based on the phase or phase difference. The signal represents the 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 measurement frame MF or the base frame. For example, a plurality of encoder heads are arranged on the measurement frame MF, whereby the grating is arranged on the top surface of the substrate support WT. In another example, the grating is arranged on the bottom surface of the substrate support WT, and the encoder head is arranged below the substrate support WT.

[0040] The position measurement system PMS may include an interferometer system. Encoder systems are known, for example, from U.S. Pat. No. 6,020,964 filed on July 13, 1998, which is hereby incorporated by reference. The interferometer system may include a beam splitter, a reflector, a reference reflector and a sensor. The radiation beam is split into a reference beam and a measurement beam by the beam splitter. The measurement beam propagates to the reflector and is reflected back to the beam splitter by the reflector. The reference beam propagates to the reference reflector and is reflected back to the beam splitter by the reference reflector. 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 the phase or frequency of the combined radiation beam. The sensor generates a signal based on the phase or frequency. The signal represents the displacement of the reflector. In an embodiment, the reflector is connected to the substrate support WT. The reference reflector may be connected to the measurement frame MF. In an embodiment, the measurement beam and the reference beam are combined into a combined radiation beam by an additional optical component replacing the beam splitter.

[0041] 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 relative to the long-stroke module over a small range of movement with high accuracy. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS over a large range of movement with relatively low accuracy. 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 over a large range of movement with high accuracy. 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 relative to the long-stroke module over a small range of movement with high accuracy. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS over a large range of movement with relatively low accuracy. 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 over a large range of movement with high accuracy.

[0042] The first positioner PM and the second positioner PW are each provided with an actuator for moving the mask support MT and the substrate support WT, respectively. The actuator may be a linear actuator for providing a driving force along a single axis (e.g., y-axis). A plurality of linear actuators may be applied to provide a driving force along a plurality of axes. The actuator may be a planar actuator for providing a driving force along a plurality of axes. For example, the planar actuator may be arranged to move the substrate support WT with 6 degrees of freedom. The actuator may be an electromagnetic 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 electric current to the at least one coil. The actuator may be a moving magnetic type actuator having the at least one magnet respectively coupled to the substrate support WT and the mask support MT. The actuator may be a moving coil type actuator having the at least one coil respectively coupled to the substrate support WT and the mask support MT. The actuator may be a voice coil actuator, a magnetoresistive actuator, a Lorentz actuator or a piezoelectric actuator, or any other suitable actuator.

[0043] The lithographic apparatus LA comprises a position control system PCS such as Figure 3Schematically depicted in . The position control system PCS includes a set point generator SP, 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 can be an actuator of the first positioner PM or the second positioner PW. The actuator ACT drives a facility P, which can include the substrate support WT or the mask support MT. The output of the facility P is a position quantity, such as position or speed or acceleration. The position quantity is measured using the position measurement system PMS. The position measurement system PMS generates a signal as a position signal representing the position quantity of the facility P. The set point generator SP generates a signal as a reference signal representing the desired position quantity of the facility P. For example, the reference signal represents the desired trajectory of the substrate support WT. The difference between the reference signal and the position signal forms the input of the feedback controller FB. Based on the input, the feedback controller FB provides at least a portion of the drive signal to the actuator ACT. The reference signal can form the input of the feedforward controller FF. Based on the input, the feedforward controller FF provides at least a portion of the drive signal to the actuator ACT.The feedforward FF may utilize information about the dynamic properties of the plant P, such as mass, stiffness, resonant modes and eigenfrequencies.

[0044] The servo performance of the electromechanical system in the lithographic apparatus (e.g., the wafer stage WS and the mask stage RS of the lithographic apparatus) can rely on the feedforward FF, compensation of the mechanical structure, actuation, and known disturbances. The main disturbance to the control loop can be the excitation of the mechanical structure by the set point trajectory. Typical FF compensations for the set point trajectory can include velocity, acceleration, jerk, snap, and compliance compensation. In addition, for example, the disturbance force of the cable board, the eddy current damping and magnetic resistance in the long stroke LoS, and the dynamic link and cooling water pressure pulse in the short stroke SS can be known. Typically, most of the actuation force comes from the FF and disturbance compensation, so only minor adjustments need to be made through feedback FB control. Therefore, appropriate parameterization of the compensation parameters may be expected to achieve accurate tracking performance.

[0045] However, calibration of the compensation parameters may not be straightforward or simple. Production tolerances may result in differences from machine to machine. For example, the platform may suffer from variations in motor constants caused by factors such as saturation of the back iron (current dependent, i.e., current related), coil position relative to the magnet, variations in magnet strength, magnet plate flatness, and nonlinearities in the amplifier. Temperature dependent, i.e., temperature related, magnetic field strength, and amplifier components may also play a role. In addition, platform mass, inertia, and dynamics may depend on position, for example, due to roll-off of cable boards. Different lithography applications may result in significant variations in wafer quality.

[0046] Furthermore, the actuators of the platform may not be located in the center of gravity CoG, but distributed above the platform. Therefore, a decoupling matrix may be applied to enable the use of non-centralized control, i.e. decentralized control, i.e. the ability to employ 6 independent single-input single-output SISO controllers, one for each rigid body logical direction. Due to the movement of the platform in the fixed measurement system, the decoupling matrix may become position dependent, i.e. position-dependent. Furthermore, LoS planar actuators may use commutation measurement systems that may be prone to sensor drift and slow thermal dynamics. Note that in the case of commutation offset, the 3-phase motor commutation may also generate force disturbances.

[0047] Furthermore, accurate time alignment between the FF and FB control paths, and peripherals such as LoS and SS, may be required, i.e., to compensate for delays in amplifiers, sensors, and communications. Thus, sub-sampled time alignment may be required to meet servo error specifications, which can be approximated by compensation based on higher order time derivatives (i.e., jerk FF) to compensate for time mismatches in acceleration FF compensation.

[0048] In summary, due to position and load dependencies, i.e. correlations, machine-to-machine variations, and time-varying effects, calibration of disturbance compensation parameters and FFs may not be straightforward. In known schemes, all compensation parameters may be calibrated and then kept constant during normal operation. The applied calibration method for FF parameters may be based on: a data-based calibration method. The decoupling parameters may require fine-tuning, which may be accomplished by a data-based calibration method.

[0049] In addition to accurate feedforward control, the system may require diagnostic functions to monitor system degradation during normal operation. The diagnostic functions may monitor the servo error MA and MSD values. Methods that can improve servo performance may also be suitable for improving diagnostics by being able to accurately point to the specific source of disturbance causing the servo error.

[0050] Learning strategies have been the subject of research for many years.Since WS iteratively performs similar trajectories, such as exposure scans, the focus can be optimized in real time (ie, during machine operation) by exploiting the iterative nature of the WS scans.

[0051] The concept of iterative learning control (ILC) can be applied to systems that repeat the same set point trajectory. The ILC method produces a force trajectory that can attempt to compensate for the control error based on an estimate of the controlled system. Therefore, ILC can rely on the system description and a fixed set point trajectory and may not exploit explicit knowledge of the source of disturbances. An obstacle to the application of online ILC strategies may be robustness to set point changes, i.e., to handle non-repetitive (thermal) corrections applied to the exposure scan set point and alignment with other parts of the machine (such as source, mask and POB).

[0052] Prior art learning strategies may rely on repeated set-point trajectories and may not be able to remove structured servo errors in a lithographic apparatus inline while providing the required robustness to set-point variations.

[0053] Although very high servo performance can be achieved in lithographic apparatus, further improvements may be desired.

[0054] The object of the present invention is to achieve further improvements in servo control performance (improved overlap or higher acceleration set points) by being able to adapt feedforward, disturbance compensation and decoupling parameters that are subject to time variations on-line. On-line adaptation is also referred to as "learning". Position-dependent parameters, i.e. position-dependent parameters, can be compensated by field-to-field optimization during constant velocity exposure scans by learning locally optimal parameter settings using an acceleration phase.

[0055] Figure 4 A schematic block diagram is depicted on which the determination of updated disturbance compensation parameters is based. 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 the control system, such as according to Figure 3 control system. The model MD determines the predicted servo error ESR from the set point STP. The model MD may include characteristics of the feedback controller behavior, as well as the inverse of the device behavior, thus making it possible to predict the servo error of the electromechanical system based on the set point. Furthermore, the set point STP is provided to the control system, whereby the servo error SR is measured. The servo error SR is to be understood as the difference between the input to the feedback controller FB, i.e. the set point STP, and the feedback signal as derived by the PMS from the output of the device P. The predicted servo error ESR is then associated with the measured servo error SR, which may be performed as follows: the predicted servo error ESR and the measured servo error SR are multiplied, as Figure 4 denoted by X in , the correlation is then calculated, for example, at N consecutive moments, where N is a natural number of N>1. When determining the correlation, the following formula (1) may be used:

[0056]

[0057] in represents the predicted servo error signal ESR as 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, horizontal length, and excitation properties of the set point. The variable C can be calibrated for the worst case set point with a known maximum excitation.

[0058] As a result, the disturbance compensation parameter θ is obtained LS The estimation of the disturbance compensation parameters may, for example, include a least squares estimation. Then, for example, a steepest descent optimization with a step size c may be used to estimate θ from LS The disturbance compensation parameter θ is determined at successive time steps to converge to the optimal disturbance compensation parameter θ using the following formula (2):

[0059] θ(t+1)=θ(t)–cθLS(t) (2)

[0060] In each iteration, the feedforward transfer function of the feedforward structure of the electromechanical system is updated using the determined disturbance compensation parameter θ, and a control signal is determined to control the electromechanical system using the updated feedforward transfer function. The feedforward transfer function of the feedforward structure of the electromechanical system may include an inverse of device behavior, such as an inverse mass and compliance of the electromechanical structure.

[0061] The modified disturbance compensation parameters may be repeatedly determined by repeating the following steps:

[0062] - obtaining a servo error of the electromechanical system;

[0063] - obtaining a set point of the electromechanical system and determining a predicted servo error of the electromechanical system based on the set point and a model of the electromechanical system including the disturbance compensation parameters,

[0064] - modifying the disturbance compensation parameters based on a correlation between the servo error and a predicted servo error, and

[0065] The feedforward transfer function of the feedforward structure of the electromechanical system is updated based on the modified disturbance compensation parameters.

[0066] A control signal for controlling the electromechanical system is continuously determined using the repeatedly updated feedforward transfer function. The model may be updated based on the modified disturbance compensation parameters, thereby enabling a more accurate determination of predicted servo error, which may facilitate convergence towards suitable values ​​of the disturbance compensation parameters.

[0067] In the case of N previous repetitions (N is a natural number), optimization can be performed using multiple iterations to optimize the disturbance control parameters over time. When assuming that the servo error depends linearly on the compensation parameters, the servo error and the predicted servo error can be combined using a least squares method to provide an analytical solution.

[0068] The time scale of the N previous repetitions and / or the time scale of the update to the modified disturbance compensation parameters can be set to exceed the time scale of the repetitive pattern in the set point and / or the time scale of the feedback control system, for example, a time scale indicated by the bandwidth of the feedback control system. As a result, the optimization can be performed on a time scale that is longer relative to the bandwidth of the system under feedback control and / or the time scale of the repetitive pattern in the set point, which can avoid that the dynamics of the system under feedback control and / or the set point will disturb the optimization.

[0069] A disturbance control parameter may include any parameter that may exhibit variations, fluctuations, tolerances, etc. For example, the disturbance control parameter may include the mass of the electromechanical system.

[0070] The control signal determined by the above method may be a feedforward signal generated by a feedforward structure of the control system, such as a reference signal. Figure 3 The feedforward FF of the position control system described above. The feedforward signal may represent the feedforward force of the electromechanical system. Therefore, the feedforward signal may be accurately determined taking into account variations, fluctuations, tolerances, etc. in the electromechanical system. Since the feedforward control may provide relatively fast control, the accuracy of the feedforward control may be improved by the recursive method described above. Therefore, in addition to relatively fast feedforward, the feedforward may also provide relatively accurate control taking into account the variations, fluctuations, tolerances, etc. mentioned.

[0071] The control signal as determined by the method described above may be a feedforward signal generated by a feedforward structure of the control system, the feedforward structure providing a feedforward signal from a first electromechanical subsystem to a second electromechanical subsystem of the electromechanical system. For example, the first electromechanical subsystem may comprise the support, such as a support of the patterning device, and the second electromechanical subsystem may comprise the substrate table. Thus, disturbances caused by movement of the support positioned on the substrate table may be accurately controlled, since the determination of the disturbance compensation parameters may enable an accurate feedforward, thereby taking into account changes in disturbances caused by the support on the substrate table.

[0072] The electromechanical system may include an actuator, such as an electromagnetic actuator.The disturbance compensation parameters may be used to account for fluctuations or tolerances, such as varying or position-dependent (ie position-dependent) actuator force constants, and commutation position parameters between magnets and coils.

[0073] The control method as described in this document may be used to control an electromechanical system of a lithographic apparatus.

[0074] For example, the control signal may include 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 electromechanical system may include 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.

[0075] As a further example, the control signal as determined by the method described above may be a feedforward signal generated by a feedforward structure of the control system, the feedforward structure providing a feedforward signal from a first electromechanical subsystem of the lithographic apparatus to a second electromechanical subsystem of the lithographic apparatus. For example, the first electromechanical subsystem may include a support supporting the pattern forming device, and the second electromechanical subsystem may include the substrate table. Thus, disturbances caused by movement of the support positioned on the substrate table may be accurately controlled, as the determination of the disturbance compensation parameters may enable an accurate feedforward signal, thereby taking into account changes in disturbances caused by the support on the substrate table.

[0076] Other subsystems of the lithographic apparatus that may use the present control method may include 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.

[0077] Basically, the control method can be applied to all disturbance compensations using a set point signal as input, such as for example friction, eddy current damping, reluctance, mass, jerk, snap, compliance, pressure pulses of cooling water, etc.

[0078] Furthermore, the method can theoretically also be applied to the parameters in the feedback loop, such as the decoupling parameters in the GB matrix. This would require updating not only the parameters in the FF structure, but also the parameters in the model that generates the servo error prediction.

[0079] By means of the method according to the invention, the electromechanical system can be controlled more accurately. Variable parameters in the electromechanical system can be taken into account, whereby the values ​​of the variable parameters are learned by comparing the modeled servo error with the measured servo error. The correlation between the modeled servo error and the measured servo error is maximized because the disturbance compensation parameter is learned to a value that maximizes the correlation. The use of the disturbance compensation parameter in the control of the electromechanical system enables variables in the electromechanical system, such as variable or position-dependent, i.e. position-dependent actuator force constants, variable masses, etc. to be taken into account. The correlation can be determined over a time span exceeding the time span of the periodic movement of the electromechanical system, thereby enabling the determination of suitable values ​​of the disturbance compensation parameter when the electromechanical system is subjected to a movement cycle such as, for example, acceleration, constant speed, deceleration, etc. The change of the variable parameter over time can be taken into account. For example, in the case of position-dependent, i.e. position-dependent parameters (such as platform position-dependent, i.e. platform position-dependent), the disturbance compensation parameter can be continuously adapted according to the control method to take into account the change of the parameter as the position (e.g., the position of the platform) changes. The control according to the invention may be particularly useful in feedforward, since accurate feedforward control may be determined, since variable parameters in the electromechanical system, such as variable mass, position dependency, variable motor force constants, etc., are taken into account. The variable parameters will normally result in inaccuracies in the feedforward signal, which may be reduced by the invention. The accuracy of the feedforward may be improved by learning the disturbance compensation parameters to take into account the variable parameters. Thus, corrective actions by the feedback control, which may otherwise be required to compensate for the variable parameters included in the feedforward path, may be reduced, thereby enabling the accuracy of the control of the electromechanical system to be improved.

[0080] Therefore, based on the Control system A model of, for example, by using instrumental variables, can produce robust online learning as described. This model can provide a servo error signal based on the actual setting value STP, typically for an imperfect calibration of the parameters subject to optimization. The measured servo error e and this predicted servo error The correlation between indicates that there is room for improvement. The correlation can be evaluated in a backward level manner, for example at the last time step. The latter can be considered equivalent to providing a least squares estimate θ for the parameter deviation resulting from the optimization of the past data under consideration LS The perturbation parameter θ may then be updated at each time step using, for example, steepest descent optimization with a step size c to converge to an optimal value.

[0081] A learning strategy can be implemented and experimentally validated to demonstrate the potential by compensating for 6 parameters simultaneously during the exposure scan, see FIG. 5A to FIG. 5C ,Right now:

[0082] Mass (motor force constant) FF parameters in x and y directions

[0083] Time alignment between FF and FB in x and y directions

[0084] • Position offset of planar actuator commutation in x and y directions.

[0085] Figure 5A A top view of a substrate table setpoint trajectory is depicted, whereby the substrate table moves in a horizontal plane. Figure 5B and Figure 5C Depicted separately Figure 5A The x- and y-components of the set point trajectory. Figure 5A In , the x direction is represented by the horizontal axis and the y component is represented by the vertical axis. After learning the feedforward for the substrate table control, ie after determining the disturbance compensation parameters as described in this document, the servo error in the x direction and the servo error in the y direction can be reduced.

[0086] refer to Figure 6 , the control method can be summarized as follows:

[0087] A control method for controlling an electromechanical system, the method comprising:

[0088] a) 601, providing a model of the electromechanical system, the model including disturbance compensation parameters;

[0089] b) 602, modifying the disturbance compensation parameter in the following manner:

[0090] -602A, obtaining a servo error of the electromechanical system;

[0091] - 602B, obtaining a set point for the electromechanical system and determining a predicted servo error for the electromechanical system based on a model of the electromechanical system including the disturbance compensation parameter and the set point,

[0092] - based on the correlation between the servo error and the predicted servo error, 602C, modifying the disturbance compensation parameter,

[0093] c) updating a feedforward transfer function of a feedforward structure of the electromechanical system based on the modified disturbance compensation parameters, 603, and

[0094] d) continuously determining, 604, a control signal to control the electromechanical system using the updated feed-forward transfer function.

[0095] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, 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, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0096] Although specific reference is made herein to embodiments of the invention in the context of lithographic equipment, embodiments of the invention may be used in other equipment. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus for measuring or processing an object such as a wafer (or other substrate) or a mask (or other pattern forming device). These apparatus may generally be referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0097] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention is not limited to optical lithography and may be used in other applications, such as imprint lithography, where the context permits.

[0098] Where context permits, 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 that can 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 that can be read by a machine (e.g., a computing device). For example, a machine-readable magnetic storage 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; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, herein, firmware, software, routines, instructions may be described as performing certain actions. However, it should be understood that such descriptions are for convenience only, and that these actions are actually generated by a computing device, a processor, a controller, or other device that executes firmware, software, routines, instructions, etc., and in doing so may cause an actuator or other device to interact with the physical world.

[0099] Although specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced in other ways than as described. The above description is intended to be illustrative rather than restrictive.

Claims

1. A control method for controlling an electromechanical system, the method comprising: a) providing a model of the electromechanical system, the model including disturbance compensation parameters; b) modifying the disturbance compensation parameters by: obtaining a servo error of the electromechanical system; obtaining a set point for the electromechanical system and determining a predicted servo error for the electromechanical system based on the model of the electromechanical system including disturbance compensation parameters and the set point, modifying the disturbance compensation parameter based on a correlation between the servo error and the predicted servo error, c) updating a feedforward transfer function of a feedforward structure of the electromechanical system based on the modified disturbance compensation parameters, and d) continuously determining a control signal to control the electromechanical system using the updated feed-forward transfer function.

2. The control method according to claim 1, wherein: b) and c) are repeated to repeatedly update the feedforward transfer function, and wherein, in d), the electromechanical system is controlled using the repeatedly updated feedforward transfer function.

3. The method according to claim 2, wherein: b) further comprising 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 a correlation between the servo error and the predicted servo error at N previous repetitions, N being a natural number greater than one.

5. The control method according to claim 4, wherein: The correlations between the servo errors at N previous repetitions and the predicted servo error are combined using a least squares method.

6. The control 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 repetition pattern in the set point.

7. A control method according to any one of the preceding claims, wherein: The control signal is a feedforward signal generated by the feedforward structure and representative of a feedforward force of the electromechanical system, and wherein the disturbance compensation parameter is included in the feedforward transfer function of the feedforward structure.

8. The control method according to any one of claims 1 to 6, wherein: The electromechanical system comprises a dual electromechanical subsystem, wherein the model of the electromechanical system comprises a feedforward structure from one of the electromechanical subsystems to another of the electromechanical subsystems, and wherein the disturbance compensation parameter is included in the feedforward transfer function of the feedforward structure.

9. A control method according to any one of the preceding claims, wherein: The electromechanical system includes an actuator, such as an electromagnetic actuator.

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

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

12. The lithographic apparatus of claim 11, comprising a feed-forward structure configured to provide a feed-forward force, and wherein the disturbance compensation parameter is included in the feed-forward structure.

13. The lithographic apparatus according to claim 12, wherein: The electromechanical system comprises a substrate table configured to hold a substrate, and the feed-forward structure is configured to provide the feed-forward force on the substrate table.

14. The lithographic apparatus according to any one of claims 11 to 13, wherein: The electromechanical system comprises a dual electromechanical sub-system, the lithographic apparatus comprises a feed-forward structure from one of the electromechanical sub-systems to another of the electromechanical sub-systems, and wherein the disturbance compensation parameter is included in the feed-forward structure.

15. The lithographic apparatus of claim 14, comprising a substrate table configured to hold a substrate and a support for supporting a pattern forming device, wherein one of the mechatronic subsystems comprises the support and another of the mechatronic subsystems comprises the substrate table.

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