Vibration control of structural element of exposure apparatus

Abstract

A method of controlling vibration of a structural element of an exposure apparatus includes: receiving position data of the structural element; determining a position error signal based at least in part on the position data of the structural element and the specified position; determining a force command to damp a specified vibration mode frequency based at least in part on the position error signal and the specified vibration mode frequency of the structural element; and transmitting a force command to the actuator such that the actuator applies a force to the structural element and dampens vibrations of the structural element at least at a specified vibration mode frequency of the structural element.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 393,161, filed on July 28, 2022, which is incorporated herein by reference in its entirety. Technical Field

[0003] The present disclosure relates to systems and methods for controlling and / or reducing vibrations of structural elements in precision systems such as lithographic exposure equipment. Background Art

[0004] Exposure equipment is used in photolithography processes for manufacturing microelectronic devices (e.g., liquid crystal display devices or semiconductor devices (e.g., integrated circuits)) that transfers a predetermined pattern on a photomask or reticle to a substrate (e.g., a photosensitive glass plate or wafer) by exposing the substrate to illumination light (e.g., an energy beam) through a projection optical system (e.g., including multiple lenses). In such systems, the reticle and substrate must be precisely aligned so that the substrate is exposed and the desired features are formed, which may be several nanometers in size. However, vibrations of the support structure of the exposure equipment and its various subsystems may cause the reticle, projection optical system, and / or substrate to move relative to each other during exposure, which may negatively affect the formation of each feature on the substrate. Vibrations of the support structure at relatively low frequencies may be particularly problematic. Passive mass dampers on such structures require cumbersome manual adjustments, and the effectiveness of passive mass dampers is often limited by space constraints within the machine. Therefore, there is a need for improved systems for controlling vibrations of support structures in photolithography exposure equipment. Summary of the invention

[0005] Certain embodiments of the present disclosure relate to systems and methods for controlling or reducing vibrations of a structural member or assembly of a precision system such as a lithographic exposure apparatus. In a representative embodiment, a method includes: receiving position data of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and a specified position of the structural element; determining a force command based at least in part on the position error signal and a specified vibration mode frequency of the structural element to damp the specified vibration mode frequency; and transmitting the force command to an actuator so that the actuator applies a force to the structural element and damps the vibration of the structural element at least at the specified vibration mode frequency of the structural element.

[0006] In any or all of the disclosed embodiments, determining the force command further comprises applying a phase correction to the position error signal.

[0007] In any or all of the disclosed embodiments, determining the force command further comprises filtering the position error signal using a low pass filter.

[0008] In any or all of the disclosed embodiments, the low pass filter comprises a derivative control.

[0009] In any or all of the disclosed embodiments, the phase correction is applied using the low pass filter.

[0010] In any or all of the disclosed embodiments, determining the force command further comprises filtering the position error signal using a bandpass filter.

[0011] In any or all of the disclosed embodiments, determining the force command further comprises filtering the position error signal using a notch filter.

[0012] In any or all of the disclosed embodiments, data of the position of the structural element is received from a sensor coupled to the structural element at a location distal to the actuator.

[0013] In any or all of the disclosed embodiments, the specified vibration mode frequency is 2 Hz to 10 kHz, 2 Hz to 5 kHz, 2 Hz to 1 kHz, 2 Hz to 500 Hz, 2 Hz to 300 Hz, 2 Hz to 200 Hz, or 2 Hz to 100 Hz.

[0014] In any or all of the disclosed embodiments, the designated vibration frequency is lower than a vibration mode frequency of the actuator.

[0015] In any or all of the disclosed embodiments, determining the force command further comprises determining the force command to damp a plurality of specified vibration mode frequencies of the structural element.

[0016] In any or all of the disclosed embodiments, the structural element is an optical surface plate, a substrate table or a mask table of the exposure apparatus.

[0017] In another representative embodiment, a system includes: an exposure device including a structural element; an actuator system coupled to the structural element, the actuator system including an actuator and a sensor; and a control system configured to: receive position data of the structural element from the sensor; determine a position error signal based at least in part on the position data and a specified position of the structural element; determine a force command based at least in part on the position error signal and a specified vibration mode frequency of the structural element to damp the specified vibration mode frequency; and transmit the force command to the actuator so that the actuator applies a force to the structural element and damps vibration of the structural element at least at the specified vibration mode frequency of the structural element.

[0018] In any or all of the disclosed embodiments, the control system is further configured to apply a phase correction to the position error signal.

[0019] In any or all of the disclosed embodiments, the control system is further configured to filter the position error signal using a low pass filter.

[0020] In any or all of the disclosed embodiments, the low pass filter comprises a derivative control.

[0021] In any or all of the disclosed embodiments, the phase correction is applied through the low pass filter.

[0022] In any or all of the disclosed embodiments, the control system is further configured to filter the position error signal using a bandpass filter.

[0023] In any or all of the disclosed embodiments, the control system is further configured to filter the position error signal using a notch filter.

[0024] In any or all of the disclosed embodiments, the sensor is spaced apart from the actuator on the structural element.

[0025] In any or all of the disclosed embodiments, the specified vibration mode frequency is 2 Hz to 10 kHz, 2 Hz to 5 kHz, 2 Hz to 1 kHz, 2 Hz to 500 Hz, 2 Hz to 300 Hz, 2 Hz to 200 Hz, or 2 Hz to 100 Hz.

[0026] In any or all of the disclosed embodiments, the structural element is an optical surface plate, a substrate table or a mask table of the exposure apparatus.

[0027] In another representative embodiment, a method includes: receiving position data of a structural element of an exposure device; determining a position error signal based at least in part on the position data and a specified position of the structural element; filtering the position error signal using a low-pass filter including a derivative control; applying a phase correction to the position error signal using the low-pass filter; determining a force command based at least in part on the filtered, phase-corrected position error signal to damp a specified vibration mode frequency of the structural element; and transmitting the force command to an actuator coupled to the structural element so that the actuator applies a force to the structural element and damps vibrations of the structural element at least at the specified vibration mode frequency of the structural element.

[0028] The foregoing and other objects, features and advantages of the disclosed technology will become more apparent from the following detailed description made with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a view schematically showing the structure of a liquid crystal exposure apparatus according to the first embodiment.

[0030] Figure 2 It is shown Figure 1 A view of a substrate stage device included in a liquid crystal exposure apparatus.

[0031] Figure 3 yes Figure 1 Schematic diagram of a substrate measurement system of a liquid crystal exposure device in FIG.

[0032] Figure 4 is a view (No. 1) for explaining the operation of the substrate stage apparatus.

[0033] Figure 5 is a view (No. 2) for explaining the operation of the substrate stage apparatus.

[0034] Figure 6 : is a block diagram showing the input / output relationship of a main controller which mainly constitutes the control system of the liquid crystal exposure apparatus.

[0035] Figure 7 is a schematic side elevation view of an actuator system coupled to a structural element according to one embodiment.

[0036] Figure 8 is a schematic diagram showing structural elements and an actuator system represented as a mass-spring-damper system.

[0037] Fig. 9 and Fig.10 It is shown Figure 8Bode plot of the open-loop frequency response of the mass-spring-damper system shown to various excitation forces.

[0038] Fig.11 is a schematic block diagram of a control system for controlling vibration of a structural element at a vibration mode frequency according to one embodiment.

[0039] Fig.12 is a process flow diagram illustrating a representative method of controlling structural mode vibrations of a structural element according to one embodiment.

[0040] Fig.13 is a schematic block diagram of a control system for controlling vibration of a structural element at multiple vibration mode frequencies according to one embodiment.

[0041] Fig.14 is a top plan view of an actuator system coupled to a plate member according to one embodiment.

[0042] Fig.15 According to one embodiment, Fig.14 A schematic block diagram of a control system for controlling the vibration of a plate member at two vibration mode frequencies is shown.

[0043] FIG. 16A to FIG. 16C It shows that when the impulse force acts on Fig.14 Graphs of acceleration versus time and acceleration versus frequency on the plate member shown.

[0044] Fig.17 ] are Bode plots showing the magnitude and phase of the frequency response of the system without feedback control, with damping control for the first vibration mode, and with damping control for both the first and second modes.

[0045] Fig.18 is a side elevation view of another experimental system including a beam member supported by two support members and having an actuator system mounted on the beam member.

[0046] Fig.19 Schematically shows Fig.18 The first vibration mode and the second vibration mode of the beam member are shown.

[0047] Fig. 20 7 is a Bode plot showing the magnitude and phase of the open loop frequency response of the system 700 as measured by the two accelerometers of the actuator system.

[0048] Fig.21 is a Bode plot showing the open loop frequency response of system 700 and the frequency response of Fig.18 The accelerometers co-located in the actuator derive position data and the frequency response of the applied control.

[0049] FIG. 22A to FIG. 22B Includes a graph of acceleration versus time and a Fast Fourier Transform (FFT) showing the open loop impulse response of the system ( Fig.22A ) and use from Fig.18 The first accelerometer-derived position data is used to apply the impulse response of the system to control ( Fig. 22B ).

[0050] Fig.23 is a Bode plot showing Fig.18 The open loop frequency response of the system is shown, as is the frequency response of control applied using position data derived from a second accelerometer.

[0051] Fig.24A and Fig. 24B Includes a graph of acceleration versus time and a fast Fourier transform showing Fig.18 The open-loop pulse response of the system shown ( Fig.24A ) and applying control using position data derived from a second accelerometer Fig.18 The impulse response of the system shown ( Fig. 24B ).

[0052] Fig.25 is a side elevation view of another embodiment of the experimental structural system.

[0053] Figure 26 to Figure 28 It is shown Fig.25 Bode plots of the three structural vibration modes of the system shown.

[0054] Fig.29 is a schematic block diagram illustrating a control system configured to implement a peaking filter control channel in parallel with a damping filter control channel according to another embodiment.

[0055] Fig.30 and Fig.31 yes Fig.25 The system shown is Fig.29 The Bode diagram of the dynamic response of the control system shown in Figure 1 is shown in Figure 2.

[0056] Fig.32 include Fig.25 The system shown is Fig.29 The acceleration versus time and acceleration versus frequency curves are shown when the system is controlled.

[0057] Fig.33 is a top plan view of another embodiment of a structural system including a rectangular plate member and an actuator and a plurality of accelerometer sensors coupled to the plate member.

[0058] Fig.34Another embodiment of a control system including two control loops is shown, wherein the two control loops are configured to Fig.33 The four modes of vibration of the structure shown are controlled.

[0059] Fig.35 yes Fig.33 Bode plot of the open-loop frequency response of the system shown when excited by a pulse.

[0060] Fig.36 Based on Fig.34 Bode plots of the frequency response of the system showing the force commands of the control system while applying control to four vibration modes.

[0061] FIG. 37A to FIG. 37B include Fig.33 Plots of acceleration versus time and acceleration versus frequency for the system shown.

[0062] Fig.38 is a top plan view of another configuration of four accelerometers, actuators, and vibrators on a plate member.

[0063] Fig.39 Another embodiment of a control system including two control loops is shown, wherein the two control loops are configured to Fig.38 The four modes of vibration of the structure shown are controlled.

[0064] Fig.40 Surface deformation of a rectangular plate at nine vibration modes of the plate based on a finite element analysis model of the plate is shown.

[0065] Figure 41 to Figure 44 The input coordinates and output coordinates of the modal space model of the structural element under various vibration modes are schematically shown.

[0066] Fig.45 is a schematic diagram of an immersion microlithography system, which is another example of a sophisticated system that includes the platform assembly described herein.

[0067] Fig.46 is a schematic diagram of an extreme ultraviolet (UV) microlithography system, which is another example of a sophisticated system that includes the platform assembly described herein.

[0068] Fig.47 is a process flow diagram illustrating exemplary steps associated with a process for fabricating a semiconductor device.

[0069] Fig.48 It is shown that, for example, Fig.47 00106] A process flow diagram of exemplary steps associated with processing a substrate (eg, a wafer) performed in a process shown in FIG.

[0070] Fig.49 is a schematic diagram of a microlithography system as an exemplary precision system, the microlithography system including a platform assembly disclosed herein, the platform assembly including at least one holding device.

[0071] Fig.50 is a schematic block diagram illustrating a representative computer control system for implementing the disclosed systems and methods. DETAILED DESCRIPTION

[0072] Certain embodiments of the present disclosure relate to actuator systems and associated control systems and methods that can be used to control / reduce / attenuate vibrations of structural elements in precision systems such as lithography exposure equipment. In certain embodiments, the actuators and control systems described herein can be tuned to attenuate relatively low frequency vibrations (e.g., resonant modes of structures excited by reaction forces applied by moving components of the system (e.g., substrate stages, mask stages, etc.), but the control system can be configured to detect and attenuate structural mode vibrations having frequencies of any magnitude (e.g., 2 Hz to 10 kHz) within the sampling rate frequency range of the system and / or the amplifier bandwidth of the actuator.

[0073] In some embodiments, the actuator system may include an actuator (e.g., a voice coil motor) and one or more motion sensors (e.g., an accelerometer), although other types of actuators and / or sensors may be used. The actuator and sensor may be positioned at the same location or at different locations on the structural element. In some embodiments, the location of the actuator and sensor may be selected so that the sensor detects a relatively large displacement of the structural element associated with one or more specified vibration modes and / or so that the force applied to the structural element by the actuator causes a relatively large displacement of the structural element and thus increases the damping effect.

[0074] In some embodiments, the control system described herein may be configured to compensate for phase lags in the system associated with one or more of sensor position (e.g., because it relates to the vibration mode shape of the structural element), sensor bandwidth, and / or time delays associated with signal processing and digital control. In some embodiments, the control system may implement a combination of a low-pass filter, a band-pass filter, and / or one or more notch filters. In some embodiments, one or more of the filters (e.g., a low-pass filter) may include derivative control. In some embodiments, one or more of the filters (e.g., a low-pass filter) may be configured to apply phase correction to the position error signal received in the feedback control loop to compensate for the above-mentioned phase lag. In some embodiments, the control system may include multiple control elements implemented in parallel, wherein each control element includes a combination of filters described herein and is configured to generate force commands to attenuate the vibration of the structural element at a specified vibration mode frequency while reducing coupling between the modes. Therefore, the control system described herein may be configured to attenuate the vibration of the structural element under one or more vibration modes (e.g., two modes, three modes, four modes, etc.). In certain embodiments, the control system may also be configured such that the actuator system may damp modal frequencies of the structural element that are lower than modal frequencies of the actuator-structure interaction, for example using a peak filter.

[0075] In the case of implementing the control method described herein, the actuator system and control system of the present disclosure can significantly reduce the vibration magnitude of structural elements excited by the reaction force of the relative motion of other structures in the precision system. The actuator system and control system can also significantly reduce the stabilization time of such structural elements, which can significantly improve the substrate positioning accuracy and throughput of, for example, lithography exposure equipment.

[0076] Example 1: Photolithography exposure equipment

[0077] Will use Figures 1 to 6 A representative embodiment of the first embodiment will be described.

[0078] Figure 1 The structure of an exposure device (here, a liquid crystal exposure device 10) according to one embodiment is schematically shown. The liquid crystal exposure device 10 is a projection exposure device of a step-and-scan method or a so-called scanner, and its exposure target is an object (here, a glass substrate P). The glass substrate P (hereinafter simply referred to as "substrate P") is formed in a rectangular shape (e.g., a square shape) in a plan view and can be used in a liquid crystal display device (flat panel display) and the like.

[0079] The liquid crystal exposure apparatus 10 has an illumination system 12, a mask stage device 14 for holding a mask M on which a circuit pattern and the like are formed, a projection optical system 16, an apparatus main section 18, a substrate stage device 20 for holding a substrate P, a control system for these components, and the like. Figure 1 The surface in the +Z direction in the projection optical system 16) is coated with a resist (e.g., a photosensitive agent). In the following, the direction in which the mask M and the substrate P are scanned relative to each other with respect to the projection optical system 16 during exposure will be described as the X-axis direction, the direction orthogonal to the X-axis direction in the horizontal plane will be described as the Y-axis direction, the direction orthogonal to the X-axis and the Y-axis will be described as the Z-axis direction (a direction parallel to the optical axis direction of the projection optical system 16), and the rotation directions around the X-axis, Y-axis, and Z-axis will be described as the θx direction, the θy direction, and the θz direction, respectively. In addition, the positions in the X-axis direction, the Y-axis direction, and the Z-axis direction will be described as the X position, the Y position, and the Z position, respectively.

[0080] In some embodiments, the illumination system 12 may be constructed in a manner similar to the illumination systems disclosed in U.S. Pat. No. 5,729,331 and similar U.S. Pat. Nos., and may irradiate the mask M using light emitted from a light source (e.g., a mercury lamp or a laser diode) serving as exposure illumination light (illumination light) IL via a reflecting mirror, a dichroic mirror, a shutter, a wavelength selective filter, various kinds of lenses, and similar components. As the illumination light IL, light such as an i-line (wavelength 365 nm), a g-line (wavelength 436 nm), or an h-line (wavelength 405 nm) (or a composite light of the above i-line, g-line, and h-line) may be used.

[0081] As the mask M held by the mask stage device 14, a transmission type photomask is used. Figure 1 The mask M is moved in the scanning direction (X-axis direction) with a predetermined long stroke, and is also appropriately finely moved in the Y-axis direction and the θz direction by the main controller 100 via the mask driving system 102, which includes a linear motor, an actuator such as a ball screw device, and the like (see Figure 6 The position information of the mask M in the XY plane (including the rotation amount information in the θz direction; the same applies below) can be obtained by the main controller 100 via the mask measurement system 104, which includes an encoder system or a measurement system such as an interferometer system.

[0082] The projection optical system 16 is arranged below the mask stage device 14. The projection optical system 16 is a so-called multi-lens projection optical system, and may have a structure similar to that of the projection optical system disclosed in U.S. Patent No. 6,552,775 and similar U.S. Patents, and is equipped with a plurality of lens modules that form an erect normal image using a double telecentric equal magnifying system.

[0083] In the liquid crystal exposure apparatus 10, when the illumination light IL illuminates the illumination area on the mask M, the illumination light IL passes through (transmits) the mask M to form a projection image (partial erect image) of the circuit pattern of the mask M in the illumination area on the irradiation area (exposure area) conjugated with the illumination area on the substrate P via the projection optical system 16. Then, scanning exposure of one shot area (shot area) on the substrate P is performed by relatively moving the mask M in the scanning direction with respect to the illumination area (illumination light IL) and relatively moving the substrate P in the scanning direction with respect to the exposure area (illumination light IL), and the pattern formed on the mask M is transferred to the shot area.

[0084] The apparatus main section 18 supports the mask stage device 14 and the projection optical system 16, and is installed on the floor F in the clean room via a vibration isolation device 19. The apparatus main section 18 may be constructed in a manner similar to the apparatus main section disclosed in U.S. Patent Application Publication No. 2008 / 0030702, and has an upper mounting section 18a, a pair of intermediate mounting sections 18b, and a lower mounting section 18c. Since the upper mounting section 18a is a member that supports the projection optical system 16, hereinafter, in the embodiment, the upper mounting section 18a will be referred to and explained as an "optical surface plate 18a". Here, in the scanning exposure operation using the liquid crystal exposure apparatus 10 in the embodiment, since the position control of the substrate P is performed with respect to the illumination light IL irradiated via the projection optical system 16, the optical surface plate 18a that supports the projection optical system 16 is used as a reference member when the position control of the substrate P is performed.

[0085] The substrate stage device 20 is a device for carrying out position control of the substrate P with high precision relative to the projection optical system 16 (illumination light IL), the projection optical system 16 moves the substrate P along the horizontal plane (X-axis direction and Y-axis direction) with a predetermined long stroke, and also finely moves the substrate P in directions with six degrees of freedom. Although the structure of the substrate stage device used in the liquid crystal exposure apparatus 10 is not particularly limited, in the illustrated embodiment, a substrate stage device 20 of a so-called coarse / fine movement structure is used as an example, and the substrate stage device 20 includes a gate-type two-dimensional coarse movement stage and a fine movement stage that performs fine movement relative to the two-dimensional coarse movement stage, as disclosed in U.S. Patent Application Publication No. 2012 / 0057140 and similar U.S. Patent Application Publications.

[0086] The substrate stage device 20 is equipped with a fine moving stage 22, a Y coarse moving stage 24, an X coarse moving stage 26, a supporting section (here, a weight compensation device 28), a pair of base frames 30 (one base frame 30 of the pair of base frames 30 is in the Figure 1 Not shown, refer to Figure 4 ), a substrate drive system 60 for moving each component of the substrate stage device 20 (refer to Figure 6 ), a substrate measurement system 70 (refer to Figure 6 ) and similar systems.

[0087] like Figure 2 As shown in FIG. 1 , the fine movement stage 22 is equipped with a substrate holder 32 and a stage main section 34. The substrate holder 32 is formed into a plate shape (or box shape) having a rectangular shape in a plan view (refer to FIG. 1 ). Figure 4 ), the substrate P is mounted on the upper surface (substrate mounting surface) of the substrate holder 32. The size of the upper surface of the substrate holder 32 in the X-axis direction and the Y-axis direction is set to be approximately the same size as the substrate P (actually slightly shorter than the substrate P). By holding the substrate P by the substrate holder 32 by vacuum suction in a state mounted on the upper surface of the substrate holder 32, the flatness of the substrate P is corrected almost entirely (over the entire surface) along the upper surface of the substrate holder 32. The stage main section 34 includes a plate-shaped (or box-shaped) member having a rectangular shape in a plan view, the size of which is shorter than the substrate holder 32 in the X-axis direction and the Y-axis direction and is integrally connected to the lower surface of the substrate holder 32.

[0088] Return to reference Figure 1 The Y coarse moving stage 24 is located below the fine moving stage 22 (located on the -Z side of the fine moving stage 22) and is arranged on the pair of base frames 30. Figure 4As shown in , the Y rough moving stage 24 has a pair of X beams 36. The pair of X beams 36 are arranged parallel to the Y axis direction at a predetermined interval. The pair of X beams 36 are mounted on the pair of base frames 30 via a mechanical linear guide device and can freely move in the Y axis direction on the pair of base frames 30.

[0089] Return to reference Figure 1 , the X coarse moving stage 26 is located above the Y coarse moving stage 24 (located on the +Z side of the Y coarse moving stage 24) and is arranged below the fine moving stage 22 (arranged between the fine moving stage 22 and the Y coarse moving stage 24). The X coarse moving stage 26 is a plate-shaped member having a rectangular shape in a plan view, and the stage is connected to the Y coarse moving stage 24 via a plurality of mechanical linear guide devices 38 (refer to Figure 2 ) is mounted on the pair of X beams 36 (refer to Figure 4 ) on the Y coarse movement stage 24, and the stage freely moves in the X-axis direction relative to the Y coarse movement stage 24 while moving integrally with the Y coarse movement stage 24 in the Y-axis direction.

[0090] like Figure 6 As shown in FIG. 1 , the substrate drive system 60 is equipped with: a first drive system 62 for finely moving the fine moving stage 22 in the directions of six degrees of freedom (each of the X-axis direction, the Y-axis direction, the Z-axis direction, the θx direction, the θy direction, and the θz direction) relative to the optical surface plate 18 a; and a second drive system 64 for moving the Y coarse moving stage 24 in the Y-axis direction with a long stroke on the base frame 30 (each referring to FIG. 1 ). Figure 1 ); and a third drive system 66 for moving the X coarse moving stage 26 in the X-axis direction with a long stroke on the Y coarse moving stage 24 (each referring to Figure 1 Although the type of actuator constituting the second drive system 64 and the third drive system 66 is not particularly limited, a linear motor, a ball screw drive, or the like may be used as an example ( Figure 1 and similar figures showing linear motors).

[0091] Although the type of actuator constituting the first drive system 62 is not particularly limited, Figure 2 In the figures and the like, a plurality of linear motors (voice coil motors) 40 ( Figure 1 and Figure 24. The X linear motors 40 are not shown in the figure). Each linear motor 40 has a stator attached to the X coarse moving stage 26, and also has a mover attached to the stage main section 34 of the fine moving stage 22, and for the fine moving stage 22, thrust is given in directions of six degrees of freedom relative to the X coarse moving stage 26 via each linear motor 40. As an example, the detailed structure of each of the first drive system 62, the second drive system 64, and the third drive system 66 is disclosed in U.S. Patent Application Publication No. 2010 / 0018950.

[0092] The main controller 100 uses the first drive system 62 to provide a thrust to the fine moving stage 22, so that the fine moving stage 22 and the X coarse moving stage 26 (each referred to as Figure 1 ) are maintained within a predetermined range in the X-axis direction and the Y-axis direction. Here, when the fine moving stage 22 is moved with a long stroke in the X-axis direction or the Y-axis direction, “the position is maintained within a predetermined range” is used only to imply that the X coarse moving stage 26 (the X coarse moving stage 26 and the Y coarse moving stage 24 when the fine moving stage 22 moves in the Y-axis direction) and the fine moving stage 22 move in the same direction at almost the same speed, and the fine moving stage 22 and the X coarse moving stage 26 do not have to move strictly synchronously, and a predetermined relative movement (relative position displacement) is allowed.

[0093] Return to reference Figure 2 The weight canceling device 28 is provided with a weight canceling device 42 for supporting the weight of the fine moving stage 22 from below and a Y stepping guide 44 for supporting the weight canceling device 42 from below.

[0094] The weight canceling device 42 (also referred to as a center column) is inserted into an open section formed in the X rough moving stage 26, and is mechanically connected to the X rough moving stage 26 at the height of the center of gravity position via a plurality of connecting members 46 (also referred to as a bending device). The X rough moving stage 26 and the weight canceling device 42 are connected by the plurality of connecting members 46 in a state of vibration (physical) separation in the Z-axis direction, the θx direction, and the θy direction. The weight canceling device 42 moves in the X-axis direction and / or the Y-axis direction integrally with the X rough moving stage 26 by being pulled by the X rough moving stage 26.

[0095] The weight canceling device 42 supports the weight of the fine moving stage 22 from below in a non-contact manner via a pseudo-spherical bearing device called a leveling device 48. This allows the fine moving stage 22 to move relative to the weight canceling device 42 in the X-axis direction, the Y-axis direction, and the θz direction and to oscillate relative to the horizontal plane (relative movement in the θx direction and the θy direction). Regarding the structure and function of the weight canceling device 42 and the leveling device 48, an example is disclosed in U.S. Patent Application Publication No. 2010 / 0018950.

[0096] The Y step guide 44 includes a member extending parallel to the X axis and is arranged between the pair of X beams 36 of the Y rough moving stage 24 (see Figure 4 ). The upper surface of the Y stepping guide 44 is set to be parallel to the XY plane (horizontal plane), and the weight compensation device 42 is mounted on the Y stepping guide 44 in a non-contact manner via an air bearing 50. When the weight compensation device 42 (i.e., the fine moving stage 22 and the substrate P) moves in the X-axis direction (scanning direction), the Y stepping guide 44 serves as a surface plate. The Y stepping guide 44 is mounted on the lower mounting section 18c via a mechanical linear guide device 52, and is restricted in relative movement in the X-axis direction while freely moving in the Y-axis direction relative to the lower mounting section 18c.

[0097] The Y step guide 44 is mechanically connected via a plurality of connecting members 54 at the height of the center of gravity (see Figure 4 ) to the Y rough moving stage 24 (the pair of X beams 36). The connecting member 54 is a bending device similar to the above-mentioned connecting member 46, which connects the Y rough moving stage 24 and the Y stepping guide 44 in the state of the vibration (solid) direction of five degrees of freedom; not including the Y axis direction in the direction of six degrees of freedom. The Y stepping guide 44 moves integrally with the Y rough moving stage by being pulled by the Y rough moving stage 24.

[0098] like Figure 4 As shown in FIG. 1 , the pair of base frames 30 are each composed of a member extending parallel to the Y axis and are installed on the floor F in parallel with each other (refer to FIG. 1 ). Figure 1 The base frame 30 is physically (or vibrationally) separated from the main section 18 of the apparatus.

[0099] Next, a substrate measurement system 70 for obtaining position information of a substrate P (actually, a fine moving stage 22 for holding the substrate P) in directions of six degrees of freedom will be described.

[0100] Figure 3 Schematic diagram of substrate measurement system 70 is shown. Substrate measurement system 70 is equipped with: a first measurement system (here, a fine moving stage measurement system 76 (refer to Figure 6 )), including a first scale (here, upward scale 72) possessed by the Y coarse stage 24 (associated with the Y coarse stage 24) and a first head (here, downward X head 74x and downward Y head 74y) possessed by the fine stage 22; and a second measurement system (here, coarse stage measurement system 82 (refer to Figure 6 )), including an optical surface plate 18a (refer to Figure 2 ) has a second scale (here, downward scale 78) and a second head (here, upward X head 80x and upward Y head 80y) of the Y coarse moving stage 24. It should be noted that Figure 3 2 shows a fine moving stage 22, which is modeled as a member for holding the substrate P. In addition, the spacing (pitch) between the gratings in the diffraction gratings possessed by each of the scales 72 and 78 is shown to be much wider than the actual spacing. The same applies to other drawings. In addition, since the distance between each head and each scale is much shorter than the distance between the laser light source and the strip mirror of the conventional optical interferometer system, the influence of air fluctuations is less than that of the optical interferometer system, which allows the position control of the substrate P with high precision, so that the exposure accuracy can be improved.

[0101] The upward scale 72 is fixed to the upper surface of the scale base 84. The scale base 84 is as shown in FIG. Figure 4 As shown in FIG. 1 , one is located on the +Y side of the fine moving stage 22 and one is located on the -Y side. Figure 2 As shown in FIG. 1 , the scale base 84 is fixed to the X beam 36 of the Y rough moving stage 24 via an arm member 86 formed into an L shape when viewed from the X-axis direction. Therefore, the scale base 84 (and the upward scale 72) can be moved in the Y-axis direction with a predetermined long stroke integrally with the Y rough moving stage 24. Regarding the arm member 86, as shown in FIG. Figure 4 As shown in FIG. 1 , although two arm members 86 are separately arranged in the X-axis direction for one X beam 36 , the number of arm members 86 is not limited thereto and may be appropriately increased or decreased.

[0102] The scale base 84 is a member extending parallel to the X-axis, and the length in the X-axis direction is set to be equal to the length of the substrate holder 32 (ie, the substrate P ( Figure 4 The ruler base 84 is preferably formed of a material that hardly generates thermal deformation (e.g., ceramic and the like). The same applies to other components to be described later; the ruler base 92 and the head bases 88 and 96.

[0103] The upward scale 72 is a plate-shaped (strip-shaped) member extending in the X-axis direction and has a reflective two-dimensional grating (so-called grating) formed on its upper surface (the surface facing the +Z side (upper side)), wherein the periodic directions of the reflective two-dimensional grating are two-axis directions orthogonal to each other (the X-axis direction and the Y-axis direction in the present embodiment).

[0104] The head base 88 is fixed to each of the central sections of the side surfaces on the +Y side and the -Y side of the substrate holder 32 via an arm member 90 corresponding to the above-mentioned scale base 84 (refer to Figure 2 Each downward header 74x and 74y (see Figure 3 ) is fixed to the lower surface of the header base 88.

[0105] In the fine mobile stage measurement system 76 (refer to Figure 6 ), such as Figure 3 As shown in FIG. 1 , for one head base 88, two downward X heads 74x are arranged separately in the X-axis direction, and two downward Y heads 74y are arranged separately in the X-axis direction. Each of the heads 74x and 74y irradiates the corresponding upward scale 72 with a measuring beam, and also receives light (here, diffracted light) from the upward scale 72. The light from the upward scale 72 is supplied to a detector, and the output of the detector is supplied to the main controller 100 (refer to FIG. 1 ). Figure 6 ). The main controller 100 obtains the relative movement amount of each of the headers 74x and 74y with respect to the scale 72 based on the output of the detector. It should be noted that in the description, "header" simply means a section that emits a measuring beam onto the diffraction grating and a section onto which light from the diffraction grating is incident, and the header itself shown in each of the drawings does not necessarily have a light source and a detector.

[0106] As described above, the fine mobile stage measurement system 76 (refer to Figure 6 ), four X linear encoder systems are constructed using a total of four (two each on the +Y side and -Y side of the substrate P) downward X heads 74x and corresponding upward scales 72, and four Y linear encoder systems are constructed using a total of four (two each on the +Y side and -Y side of the substrate P) downward Y heads 74y and corresponding upward scales 72. The main controller 100 (refer to Figure 6 ) The position information (hereinafter referred to as “first information”) of the fine moving stage 22 (substrate P) in the X-axis direction, the Y-axis direction and the θz direction is obtained by using the outputs of the above-mentioned four X linear encoder systems and the four Y linear encoder systems.

[0107] Here, in the case of using the upward scale 72, the measurable distance in the X-axis direction is set to be longer than the measurable distance in the Y-axis direction. Figure 4As shown in , the length of the upward scale 72 in the X-axis direction is approximately the same as the length of the scale base 84 and is substantially set to a length that can cover the movable range of the fine moving stage 22 in the X-axis direction. At the same time, the size of the upward scale 72 in the width direction (Y-axis direction) (and the interval between a pair of heads 74x and 74y adjacent in the Y-axis direction) is set to approximately a length so that even when the fine moving stage 22 performs fine movement in the Y-axis direction relative to the upward scale 72, the measurement beam from each of the heads 74x and 74y does not move away from the grating surface (surface to be measured) of the corresponding upward scale 72.

[0108] Next, we will use Figure 4 and Figure 5 Describe the fine mobile stage measurement system 76 (refer to Figure 6 ) operation. Figure 4 and Figure 5 The substrate stage device 20 is shown before and after the fine movement stage 22 is moved with a long stroke in the X-axis direction and the Y-axis direction. Figure 4 The fine movement stage 22 is shown in a state where it is positioned almost at the center of the movable range in the X-axis direction and the Y-axis direction, and Figure 5 The fine movement stage 22 is shown in a state where it is positioned at the +X side stroke end of the movable range in the X-axis direction and also positioned at the −Y side stroke end in the Y-axis direction.

[0109] from Figure 4 and Figure 5 It can be seen that the measurement beam from each of the heads 74x and 74y attached to the fine moving stage 22 does not move away from the grating surface of the upward scale 72 regardless of the position of the fine moving stage 22 in the Y-axis direction, including the case when the fine moving stage 22 performs fine movement in the Y-axis direction. In addition, when the fine moving stage 22 also moves with a long stroke in the X-axis direction, the measurement beam from each of the downward heads 74x and 74y does not move away from the grating surface of the upward scale 72.

[0110] Next, the rough mobile station measurement system 82 (see Figure 6 ).from Figure 1 and Figure 4 It can be seen that the rough moving stage measurement system 82 of this embodiment has two downward scales 78 (that is, a total of four downward scales 78), which are separately arranged on the +Y side and the -Y side of the projection optical system 16 in the X-axis direction (refer to Figure 1 ). The downward scale 78 passes through the scale base 92 (refer to Figure 2 ) is fixed to the lower surface of the optical surface plate 18a. The scale base 92 is a plate-like member extending in the Y-axis direction, and the length in the Y-axis direction is set to be equal to the fine moving stage 22 (that is, the substrate P ( Figure 4 (not shown)) the movable distance in the Y-axis direction is approximately the same (actually slightly longer).

[0111] Similar to the upward scale 72 described above, the downward scale 78 is a plate-like (strip-like) member extending in the Y-axis direction and a reflective two-dimensional grating (so-called grating) is formed on the lower surface (surface facing the Z side (lower side)) of the downward scale 78, and the periodic directions of the reflective two-dimensional grating are two-axis directions orthogonal to each other (in this embodiment, the X-axis direction and the Y-axis direction). It should be noted that the grating pitch of the diffraction grating of the downward scale 78 may be the same as or different from the grating pitch of the diffraction grating of the upward scale 72.

[0112] like Figure 2 As shown in FIG. 1 , the head base 96 is fixed to each of the pair of scale bases 84 that the Y rough moving stage 24 has via an arm member 94 formed into an L shape when viewed from the X-axis direction. Figure 4 As shown in FIG, the head base 96 is arranged near the ends on the +X side and the -X side of the scale base 84. Figure 3 As shown in FIG. 1 , each of the upward heads 80x and 80y is fixed to the upper surface of the header base 96. Therefore, a total of four header bases 96 (and the upward heads 80x and 80y) can be moved in the Y-axis direction integrally with the Y coarse moving stage 24.

[0113] In using the rough mobile stage measurement system 82 (refer to Figure 6 ), if Figure 3 As shown in FIG. 1 , for one head base 96, two upward X heads 80x and two upward Y heads 80y are separately arranged in the Y-axis direction. Each of the heads 80x and 80y irradiates the corresponding downward scale 78 with a measuring beam, and also receives light (here, diffracted light) from the downward scale 78. The light from the downward scale 78 is supplied to a detector not shown, and the output of the detector is supplied to the main controller 100 (refer to FIG. 1 ). Figure 6 ). The main controller 100 obtains the relative movement amount of each of the heads 80x and 80y with respect to the scale 78 based on the output of the detector. As described above, in the coarse stage measurement system 82 of the present embodiment, eight X linear encoder systems are constructed using a total of eight upward X heads 80x and corresponding downward scales 78, and eight Y linear encoder systems are also constructed using a total of eight upward Y heads 80y and corresponding downward scales 78. The main controller 100 (refer to Figure 6 ) obtains position information (hereinafter referred to as “second information”) about the Y coarse moving stage 24 in the X-axis direction, the Y-axis direction, and the θz direction by appropriately using the outputs of the above-mentioned eight X linear encoder systems and the eight Y linear encoder systems.

[0114] In addition, each of the upward scale 72 fixed on the scale base 84 and the upward heads 80x and 80y integrally fixed to the scale base 84 via the head base 96 is arranged so that their mutual positional relationship does not change and the positional relationship is known. Hereinafter, information related to the relative positional relationship between the upward scale 72 and each of the upward heads 80x and 80y integrally fixed to the upward scale 72 will be referred to as "third information". It should be noted that although in the description, the upward scale 72 and the upward heads 80x and 80y are described as being arranged so that their positional relationship does not change, the liquid crystal exposure apparatus 10 may be equipped with a measurement system for measuring the positional relationship between the upward scale 72 and the upward heads 80x and 80y. The same applies to each embodiment to be described below.

[0115] Main controller 100 (see Figure 6 ) obtains position information about the fine moving stage 22 (substrate P) in the XY plane based on the above-mentioned first information to third information with the optical surface plate 18a (projection optical system 16) as a reference, and uses the above-mentioned substrate driving system 60 (refer to Figure 6 ) implements position control of the substrate P relative to the projection optical system 16 (illumination light IL).

[0116] As described above, in the substrate measurement system 70 of the present embodiment, position information about the Y coarse moving stage 24 moving with a long stroke in the Y-axis direction is obtained by the coarse moving stage measurement system 82, which includes the downward scale 78 whose measurable distance in the Y-axis direction is longer than that of the downward scale 78 in the X-axis direction (the Y-axis direction is used as the main measurement direction), and position information about the fine moving stage 22 moving with a long stroke in the X-axis direction is also obtained by the fine moving stage measurement system 76, which includes the upward scale 72 whose measurable distance in the X-axis direction is longer than that of the upward scale 72 in the Y-axis direction (the X-axis direction is used as the main measurement direction). That is, in the coarse moving stage measurement system 82 and the fine moving stage measurement system 76, the moving direction of each encoder head (74x, 74y, 80x, and 80y) coincides with the main measurement direction of the corresponding scale (72 and 78).

[0117] In addition, the main controller 100 uses the Z tilt position measurement system 98 (each referring to Figure 6) obtains position information about the fine moving stage 22 (substrate P) in each of the Z-axis direction, the θx direction, and the θy direction (hereinafter referred to as the “Z tilt direction”). Although the structure of the Z tilt position measurement system 98 is not particularly limited, a measurement system using a displacement sensor attached to the fine moving stage 22 may be used as an example, as disclosed in U.S. Patent Application Publication No. 2010 / 0018950 and similar U.S. Patent Application Publications.

[0118] It should be noted that, although not shown, the substrate measurement system 70 also has a measurement system for obtaining position information about the X coarse moving stage 26. In the embodiment, since the position information about the fine moving stage 22 (substrate P) in the X-axis direction is obtained via the Y coarse moving stage 24 with the optical surface plate 18a as a reference, the measurement accuracy of the X coarse moving stage 26 itself is not necessarily at the same level as that of the fine moving stage 22. The position measurement of the X coarse moving stage 26 may be performed based on the output of the above-mentioned fine moving stage measurement system 76 and the output of a measurement system (not shown) that measures the relative position between the X coarse moving stage 26 and the fine moving stage 22, or the position measurement of the X coarse moving stage 26 may be performed using an independent measurement system.

[0119] In the liquid crystal exposure device 10 (refer to Figure 1 ), in the main controller 100 (refer to Figure 6 ), the mask M is loaded onto the mask stage device 14 by a mask loader (not shown), and the substrate P is loaded onto the substrate holder 32 by a substrate loader (not shown). Then, alignment measurement is performed by the main controller 100 using an alignment detection system (not shown), and after the alignment measurement has been completed, an exposure operation of the step-and-scan method is sequentially performed on a plurality of shot areas on the substrate P. In the alignment measurement operation and the exposure operation of the step-and-scan method, the substrate measurement system 70 measures position information about the fine moving stage 22.

[0120] In the case of using the liquid crystal exposure device 10 of the above-mentioned embodiment, since the position of the fine moving stage 22 (substrate P) is measured using a substrate measurement system 70 including an encoder system, the influence of air fluctuations is smaller than that of conventional measurements using an optical interferometer system, which allows the position of the substrate P to be controlled with high precision, thereby improving the exposure accuracy.

[0121] In addition, since the substrate measurement system 70 performs position measurement of the substrate P with the downward scale 78 fixed to the optical surface plate 18a (the apparatus main section 18) as a reference (via the upward scale 72), the position measurement of the substrate P can be performed with the projection optical system 16 substantially as a reference. This allows the position control of the substrate P to be performed with the illumination light IL as a reference, which can improve the exposure accuracy.

[0122] It should be noted that the structure of the above-described substrate measurement system 70 may be appropriately changed as long as position information on the fine movement stage 22 (substrate P) can be obtained with desired accuracy within the movable range of the fine movement stage 22 .

[0123] That is, although a long scale having a length approximately the same as that of the scale base 84 is used as the upward scale 72 in the above embodiment, the scale is not limited thereto, and a scale having a shorter length in the X-axis direction may be arranged at a predetermined interval in the X-axis direction, similar to the encoder system disclosed in International Publication WO 2015 / 147319. In this case, since a gap is formed between a pair of scales adjacent in the X-axis direction, one of the headers 74x and one of the headers 74y adjacent in the X-axis direction should always face the scale by making the interval in the X-axis direction of each of the pair of headers 74x and 74y adjacent in the X-axis direction wider than the above gap. The same applies to the relationship between the downward scale 78 and the upward headers 80x and 80y.

[0124] In addition, although the upward scale 72 is arranged on the +Y side and the -Y side of the fine moving stage 22, the arrangement is not limited thereto, and the scale may be arranged only on one side (the +Y side or the -Y side). In the case where only one upward scale 72 is arranged and a plurality of scales are arranged at a predetermined pitch (a gap between scales) in the X-axis direction as described above, the number and arrangement of each of the heads 74x and 74y should be set so that at least two downward X heads 74x (or downward Y heads 74y) always face the scales to allow position measurement of the fine moving stage 22 to be always performed in the θz direction. The same applies to the downward scale 78, and the number and arrangement of the downward scale 78 and the upward heads 80x and 80y may be appropriately changed as long as position measurement of the Y coarse moving stage 24 in the X-axis direction, the Y-axis direction, and the θz direction can be always performed.

[0125] In addition, although the two-dimensional diffraction gratings whose periodic directions are in the X-axis direction and the Y-axis direction are formed on the upward scale 72 and the downward scale 78, the X diffraction grating whose periodic direction is in the X-axis direction and the Y diffraction grating whose periodic direction is in the Y-axis direction may be separately formed on the scales 72 and 78. In addition, although the two-dimensional diffraction grating in the embodiment has periodic directions in the X-axis direction and the Y-axis direction, the periodic direction of the diffraction grating is not limited thereto and may be appropriately changed if the position measurement of the substrate P in the XY plane can be performed with desired accuracy.

[0126] In addition, Z tilt position information about the substrate P can be measured by attaching a downward displacement sensor to the head base 88 and also using a sensor having the scale base 84 (or the reflective surface of the upward scale 72) as a reference. In addition, at least three of the plurality of downward heads 74x and 74y can be used as a two-dimensional head (so-called XZ head or YZ head), which can perform measurement in the vertical direction and position measurement in a direction parallel to the horizontal plane, and Z tilt position information about the substrate P can be obtained by using the grating surface of the upward scale 72 through the two-dimensional head. Similarly, Z tilt position information about the Y coarse moving stage 24 can be measured using the scale base 92 (or the downward scale 78) as a reference. As the XZ head or YZ head, an encoder head of a structure similar to the displacement sensor head disclosed in, for example, U.S. Patent No. 7,561,280 can be used.

[0127] More details regarding the liquid crystal exposure apparatus 10 may be found in US Pat. No. 10,670,977, which is incorporated herein by reference.

[0128] Example 2: Actuator system and control method for active vibration damping

[0129] As the various stage assemblies of the exposure apparatus 10 (e.g., such as the mask stage apparatus 14 and / or the substrate stage apparatus 20) move in the step-and-scan operation described above, reaction forces formed by the various linear motors or other stage drives may be transmitted to fixed structural elements of the apparatus. These reaction forces may cause structural elements of the apparatus to vibrate, and in some cases may excite vibrations at resonant mode frequencies of the structural elements. In some embodiments, such vibrations may have a frequency of 2 Hz to 10 kHz, such as 5 Hz to 10 kHz, 100 Hz to 10 kHz, 100 Hz to 5 kHz, 10 kHz or less, 5 kHz or less, 3 kHz or less, 2 kHz or less, 1 kHz or less, 500 Hz or less, 300 Hz or less, 200 Hz or less, or 100 Hz or less. Such vibrations, particularly lower frequency vibrations (e.g., 500 Hz or less), can be particularly problematic on structural elements that support components or instruments that must be precisely aligned with the substrate P and / or on structural elements that serve as positional references for various stage assemblies, because the amplitudes of such vibrations tend to be relatively large.

[0130] One such structural element of the exposure apparatus 10 is the optical surface plate 18a, which, as described above, supports the projection optical system 16 and also serves as a reference for a substrate measurement system 70 for effecting position control of the substrate p. In certain embodiments, an actuator system may be employed to actively damp / reduce / control vibrations of structural elements such as the optical surface plate 18a. In certain embodiments, the actuator system may include one or more actuators, one or more sensors, and a controller or control system (e.g., a main controller 100 or another system) that controls the operation of the actuators based on data from the sensors to damp vibrations of the structural elements.

[0131] For example, Figure 7 A representative example of an actuator system 200 is shown, which includes an actuator 202 mounted or coupled to a structural element 204 (also referred to as a structural member). The actuator system 200 may also include a plurality of sensors. A first sensor 206A is shown as being co-located with the actuator 202 (e.g., mounted to the actuator 202), and a second sensor 206B is shown as being located distal to the actuator 202 and coupled to the structural element 204. Depending on, for example, the shape of the structural element, the size of the structural element, the vibration mode of the structural element to be damped, etc., the system may include any number of actuators and any number of sensors. The actuators and / or sensors may also be positioned at any location on the structural element (e.g., the upper or lower surface of the structural element, the side surface, etc.) or may be incorporated into the body of the structural element.

[0132] In some embodiments, the actuator 202 may be any type of electric actuator with a suitably fast response time, such as a voice coil motor (VCM), a piezoelectric actuator, a linear motor, a reluctance actuator, etc.

[0133] In some embodiments, the sensors 206A and 206B may be acceleration sensors such as accelerometers or vibration sensors, velocity sensors such as moving coils or piezoelectric velocity receivers, position sensors such as linear potentiometers, capacitive sensors, linear encoders, interferometers, or combinations thereof. In the following examples, the sensors are configured as accelerometers, but other types of sensors may also be used.

[0134] Figure 8 300 and an actuator system 302, represented as a mass-spring-damper system. The structural element 300 is shown coupled to an absolute reference (e.g., the ground) 304 via a spring 306 and a damper 308. Figure 8 For purposes of the present invention, actuator system 302 represents an actuator and a co-located accelerometer sensor and is coupled to structural element 300 through spring 310 and damper 312. The motion of structural element 300 relative to ground 304 can be determined by the mass of the structural element, the spring constant of spring 306, and the damping coefficient of damper 308. The mass of structural element 300 and the spring constant of spring 306 can determine the vibration mode frequency of structural element 300. In the example of an exposure apparatus, structural element 300 can be similar to an optical surface plate, a substrate stage, a mask stage, or other structures in a machine coupled to actuator system 302.

[0135] The motion of the actuator system 302 relative to the structural element 300 may be determined by the mass of the actuator system elements, the spring constant of the spring 310, and the damping coefficient of the damper 312. The mass of the actuator system 302 and the spring constant of the spring 310 may determine the vibration mode frequency of the actuator system 302. In certain embodiments, the vibration mode frequency of the actuator system may be the frequency at which the actuator or actuator system vibrates relative to the structural element while the actuator is operating. In certain embodiments, designing the system such that the mode frequency of the actuator system 302 is less than the mode frequency of the structural element 300 may allow the actuator system 302 to more effectively damp the structural mode vibrations of the structural element 302, but as shown in subsequent examples herein, this is not required.

[0136] When an actuator of the actuator system 302 applies a force to the structural element 300, the actuator pushes the actuator system 302 and a reaction force acts on the structural element 300. The double arrow 314 indicates the relative movement of the actuator system 302 and the structural element 300 when the actuator is activated. Fig. 9 When the actuator system 302 applies a disturbance force Figure 8 The open loop frequency response of the mass-spring-damper system is shown. The structural modal vibrations of the structural element 300 can be seen between 30 Hz and 40 Hz, and the modal vibrations of the actuator system 302 can be seen between 20 Hz and 30 Hz. Each mode can have a phase drop of 180°.

[0137] Fig.10 304 and 306. The diagram shows the effect of a disturbance force (e.g., an impulse) applied to the structural element 300 (e.g., a vibrator device separate from the actuator system and positioned between the ground 304 and the structural element 300) on the structural element 300. Figure 8 The open loop frequency response of the system is shown. The force applied by the vibrator device is given by Figure 8 Indicated by arrow 316 in FIG. Fig.10 The vibration mode frequencies of the actuator system are not shown.

[0138] In certain embodiments, vibrations of the structural element 300 due to disturbance forces may be damped by operating the actuator system 302 according to a control scheme that is based on one or more vibration frequencies of the structural element to be damped and includes phase correction to compensate for one or more of amplifier bandwidth, sensor signal conditioning, and / or digital control time delays in the control system.

[0139] exist Fig.11 A representative embodiment of a feedback control system 400 is shown in FIG. A mass-spring-damper system of the ground, structural elements, and actuator system is represented at box 402 and is referred to as the structural system hereinafter. The control system 400 may also include an integration element 404 (also referred to as an integration and filtering tool or module) and a filter controller or filter control element 406. A disturbance force d is shown acting on the structural system 402, which causes the structural system 402 to accelerate and move (e.g., vibrate). In certain embodiments, the dynamic response (e.g., facility response) of the structural system 402 may be given by the transfer function P(s) in the following equation 1, where m is the inertia of the vibration mode to be controlled, d r is the damping ratio, and ω r is the specified vibration frequency to be damped.

[0140]

[0141] When the structural system 402 is disturbed by the disturbance force d, the acceleration of the actuator can be determined by the co-located accelerometer sensor, and at block 404, the acceleration signal can be provided to the integration element. In some embodiments, the integration element 404 can integrate the acceleration signal received from the accelerometer sensor to obtain the position signal (for example, the integration element can integrate the accelerometer sensor signal twice). The integration element 404 can also filter the accelerometer signal using one or more filters to select a specific frequency or frequency band. For example, in some embodiments, the integration element 404 can filter the signal using a high-pass filter, which can reduce the low-frequency drift of the signal from the accelerometer sensor. A representative transfer function H of the integration element 404 representing the integral combination of the accelerometer signal and the high-pass filter is given below in Equation 2: a2p (s), where d a is the damping ratio, and ω a is the cutoff frequency of the high-pass filter.

[0142]

[0143] The resulting position signal (also referred to as position data) may then be subtracted from a position command signal x(s) representing a specified position of the structural system 402 at a summing junction 408. In certain embodiments, the position command x(s) (e.g., a specified position of a structural element) may be zero in the event that vibration / motion of the structural system 402 is undesirable. Subtracting the position signal from the position command signal x(s) may result in a position error signal, which may be provided to the filter control element 406.

[0144] The filter control element 406 may determine a force command u, which may be transmitted to an actuator of the actuator system to cause the actuator to apply a force to the structural element. In the following discussion, u is referred to as a force command, but may also be a current command. Fig.11 , a force command u is shown as being transmitted from the filter control element 406 and acting on the structural system 402 to damp vibrations of the structural system.

[0145] In certain embodiments, the filter control element 406 may apply one or more of a low-pass filter, a band-pass filter, a notch filter, and / or a high-pass filter to the position error signal to generate the force command u. In a particular embodiment, the filter control element 406 may apply a combination of a derivative-controlled low-pass filter (hereinafter referred to as a damping filter), a band-pass filter, and a notch filter. A representative transfer function C(s) of the filter control element 406 is given below in Equation 3, where H damp(s) is the transfer function of the damping filter, H bandpass (s) is the transfer function of the bandpass filter, and H notch (s) is the transfer function of the notch filter. The filters may be applied to the input signal sequentially (e.g., serially). The respective transfer functions of the damping filter, the bandpass filter, and the notch filter are multiplied in Equation 3. It should be noted that the order of the filters in Equation 3 is only an example, and the filters may be applied to the input signal in any order.

[0146] C(s)=H damp (s)·H bandPass (s)·H notch (s) Equation 3

[0147] In some embodiments, the damping filter may include a derivative control term (also referred to as a damping control term or a velocity control term) and a low-pass filter term. For example, in some embodiments, the transfer function H of the damping filter may be given by the following equation 4: damp (s), where k d is the damping gain, k d ω r s is the derivative control term of the transfer function (also called the damping coefficient), and the expression is the low-pass filter term.

[0148]

[0149] In some embodiments, depending on the specific requirements of the system, the low pass filter may be underdamped (e.g., d r <1), critically damped (e.g., d r = 1) or overdamped (e.g., d r >1). In some embodiments, the damping ratio d r It can be 0.05 to 10. In some embodiments, a larger damping ratio may make the control frequency range wider, but it may also be associated with coupling between modes. In some embodiments, the damping gain k of the derivative control term of the damping filter can be d Changes are made to tune the gains of the control system.

[0150] In some embodiments, the transfer function of the notch filter can be given by Equation 5, where d1 and d2 are the damping ratios, and ω n is the target frequency of the notch filter.

[0151]

[0152] In some embodiments, the target frequency ω of the notch filter ncan be the target mode frequency ω of the structural element r Another vibration mode of a different type. For example, the frequency ω of the notch filter n It may also be another vibration mode of the structure that is excited in response to the force command u of the actuator, but not necessarily a resonant mode frequency of the structural element.

[0153] In some embodiments, the transfer function of the bandpass filter can be given by Equation 6, where d bp is the damping ratio.

[0154]

[0155] In some embodiments, the phase of the damping control force command u may be aligned at the target resonant frequency of the structural element to be damped. In some embodiments, a damping filter may be used to achieve phase alignment. For example, in some embodiments, the structural system transfer function P(s), the integrating element transfer function H a2p The sum of the phase angles of (s) and the filter control element transfer function C(s) can be set to zero as shown in Equation 7 below.

[0156] ∠P(jω r )+∠H a2p (jω r )+∠C(jω r )=0Equation 7

[0157] In some embodiments, the phase angle of the filter control element transfer function may be the phase angle ∠H of the damping filter transfer function. damp (jω r ), the phase angle ∠H of the bandpass filter transfer function bandPass (jω r ) and the phase angle ∠H of the notch filter transfer function notch (jω r In some embodiments, the phase angle ∠H of the bandpass filter transfer function bandPass (jω r ) can be zero.

[0158] In some embodiments, the phase lag θ of the system can be defined as the phase angle ∠P(jω) of the structural system transfer function. r ), the phase angle ∠H of the transfer function of the integrating element a2p (jω r ) and the phase angle ∠H of the notch filter transfer function notch (jω r ) as given in Equation 8 below.

[0159] θ=∠P(jω r)+∠H a2p (jω r )+∠H notch (jω r ) Equation 8

[0160] In some embodiments, the damping filter transfer function can be obtained by setting the phase angle ∠H damp (jω r ) is set equal to -θ in the following equation 9 to tune the damping filter to compensate for the phase lag θ of the system.

[0161] ∠H damp (jω r )=-θEquation 9

[0162] In the case of applying Euler's Formula, phase correction can be applied to the transfer function H of the damping filter using one of the two equations in the system of equations 10 below: damp (s).

[0163]

[0164] The damped filter transfer function H is given in Equation 11 below damp (s) (Equation 4) multiplied by the result of each of the two equations in the system of equations 10. In certain embodiments, in the damping filter transfer function H damp When the phase angle of (s) is equal to -θ in Equation 9, the second equation in the system of equations 11 below can avoid the generation of direct current (DC) terms. In certain embodiments, avoiding DC terms can be advantageous because the DC terms can cause the actuator to apply a constant position and / or a constant force to the structural element, which can hinder vibration damping.

[0165]

[0166] The phase correction may also be applied in the manner described above using a bandpass filter or using a notch filter.Depending on the specific characteristics of the system, the total amount of phase correction may also be distributed among the damping filter, the bandpass filter and / or the notch filter.

[0167] Therefore, the filter control element 406 can be controlled by using a phase-corrected damping filter H damp (s) filtering the position error signal received from summing junction 408 (e.g., applying a phase-corrected low-pass filter with derivative control), using a bandpass filter H bandpass(s) Filtering the phase-corrected signal output of the damping filter and using a notch filter H notch (s) The output of the bandpass filter is filtered to determine a force command u. The resulting force command u can then be transmitted to the actuator.

[0168] In certain embodiments, the control systems described herein may be configured to control / reduce vibrations of a structural element having any frequency within the control sampling rate limits of the system and / or the amplifier bandwidth of the actuator. Thus, in certain embodiments, the specified frequency or target frequency ω of the damping filter r It may be 2 Hz to 10 kHz, for example 5 Hz to 10 kHz, 100 Hz to 10 kHz, 100 Hz to 5 kHz, 10 kHz or less than 10 kHz, 5 kHz or less than 5 kHz, 3 kHz or less than 3 kHz, 2 kHz or less than 2 kHz, 1 kHz or less than 1 kHz, 500 Hz or less than 500 Hz, 300 Hz or less than 300 Hz, 200 Hz or less than 200 Hz, or 100 Hz or less than 100 Hz.

[0169] In other embodiments, the filter control element may implement other types of control, such as proportional control and / or integral control, instead of or in addition to derivative control. For example, since the damping force is the damping ratio of the system multiplied by the velocity, proportional control of velocity, integral control of acceleration, or derivative control of position may be used to damp the system.

[0170] Fig.12A representative method for reducing vibration of a structural element using the actuator system and control system described herein is shown. At process block 420, position data (e.g., position signal) of a structural element of an exposure device may be received (e.g., received from an integrating element after integrating and filtering an accelerometer signal). At process block 422, a position error signal may be determined relative to a specified position (or trajectory), for example, by subtracting the position data / signal from the specified position. At process block 424, a force command may be determined based at least in part on a specified vibration mode frequency of the structural element to be damped and the position error signal. In some embodiments, determining the force command may include filtering the position error signal using a low pass filter (e.g., including a derivative controlled low pass filter), filtering the position error signal using a band pass filter, and / or filtering the position error signal using a notch filter as described herein. The above operations may be performed in any combination and in any order. In some embodiments, determining the force command may include, for example, applying a phase correction to the position error signal using a low pass filter. At process block 426 , the resulting force command may be communicated to an actuator such that the actuator applies a force to the structural element and dampens vibrations of the structural element at least at a specified vibration mode frequency of the structural element.

[0171] Example 3: Control system and method for damping multiple vibration mode frequencies

[0172] In certain examples, the control methods described above may be adapted to control / damp vibrations of a structural element at multiple frequencies (eg, multiple resonant mode frequencies of the structural element). Fig.13 Another embodiment of a feedback control system 500 is shown in which control of multiple frequencies / vibration modes is implemented in parallel. Fig.13 The feedback control system 500 shown in FIG. 5 has a block 502 representing the plant dynamics of the mass-spring-damper system to be controlled, which may represent the response to the disturbance force d given by the transfer function P(s) in Equation 1 above. The control system 500 may also include an integrating element 504, which may be as described above with reference to Fig.11 and the transfer function H given in Equation 2 a2p(s) is described above. After the position signal obtained by the integrating element 504 is subtracted from the position command signal x(s), the resulting position error signal can be provided to a plurality of filter control elements 506 implemented in parallel. In some embodiments, the number of filter control elements 506 can correspond to the number of vibration frequencies of the structural element to be controlled using the actuator system. For example, in some embodiments, each filter control element 506 can implement a combination of the phase-corrected damping filter control, bandpass filter control, and notch filter control described above. Each filter control element 506 can be tuned to attenuate a specific target frequency (e.g., a specific vibration mode frequency of the structural element).

[0173] The outputs of the filter control elements 506 may be summed at summing point 508 to yield a force command u that is transmitted to the actuator system described above. The transfer function C(s) of the combined outputs of the filter control elements 506 may be defined as the sum of the transfer functions of each individual filter control element, as given below in Equation 12, where N is the total number of filter control elements 506, and therefore the number of controlled vibration modes.

[0174]

[0175] In some embodiments, each filter control element 506 may apply one or more notch filters to avoid exciting other vibration frequencies. r , the transfer function of the notch filter may be substantially as given in Equation 5 above. In some embodiments, the notch filter transfer functions may be multiplied together so that the transfer function C of each filter control element 506 is k (s) can be given by Equation 13, where the transfer function of the damping filter H damp (s) is substantially the same as the transfer function given above in Equation 4, and the transfer function H of the bandpass filter is bandpass (s) is essentially the same as the transfer function given above in Equation 6.

[0176]

[0177] In some embodiments, since the control of different vibration modes at the frequencies of interest can be achieved by adding a transfer function C i (s) (e.g., where i = 1 ... N and i ≠ k) in ω k The notch filter is used to decouple the filter, so the filter control element output C i (jω k ) can be approximately equal to C k (jω k ), as given below in Equation 14.

[0178]

[0179] In some embodiments, the phase correction of the damped filter output of each filter control element may also be decoupled (eg, determined independently of the other filter control elements). For example, since C(jω k ) is approximately equal to C given in Equation 14 above k (jω k ), so for the target frequency ω r For the kth filter control element below, the sum of the phase angles in Equation 7 can be expressed as the sum of the phase angles given in the following Equation 15.

[0180] ∠P(jω r,k )+∠H a2p (jω r,k )+∠C k (jω r,k )=0Equation 15

[0181] Therefore, the phase lag θ of the kth filter control element is k can be expressed as a phase lag given in Equation 16 below.

[0182]

[0183] Where phase correction is applied according to the second equation in the system of Equation 10 above, the phase-corrected transfer function of the damping filter of the kth filter control element may be expressed as the transfer function given in Equation 17 below.

[0184]

[0185] The control systems and methods described above can significantly reduce the vibration magnitude of one or more vibration modes of the structure when a disturbing force is applied to the structure. The control systems and methods described above can also significantly reduce the settling time of the system compared to an undamped response. For example, the control systems and methods described herein can be applied to a structure subjected to a disturbing force applied to the structure. Fig.14 The experimental system 600 shown in FIG. 6 is used to control / damp vibrations excited by pulses. Fig.14 6 is a top plan view of a system 600 including a rectangular metal plate member 602 supported at three corners and an actuator system 604 mounted to a top surface of the plate member 602 at the unsupported corners. The actuator system 604 includes an actuator configured as a voice coil motor (VCM) 606 and a sensor configured as an accelerometer 608 mounted atop (e.g., co-located with) the VCM 606.

[0186] The actuator system 604 is composed of Fig.15 The control system 610 shown in FIG. 6 is controlled by the control system 610 according to the above reference Fig.13 The control system 610 is configured according to the principles described in the control system shown. The control system 610 includes two filter control elements 612A and 612B, which are implemented in parallel and are configured to provide damping control of two vibration modes of the plate member 602. The control system 610 also includes a system block 614 representing the dynamic response of the mass-spring-damper model of the system and an integrating element 616 configured in a manner similar to the integrating element described above. Each filter control element 612A and 612B implements a corresponding filter control scheme C1(s) and C2(s), and the filter control schemes C1(s) and C2(s) include the above-mentioned phase-corrected damping filters (e.g., phase-corrected low-pass filters including derivative control), bandpass filters, and one or more notch filters.

[0187] FIG. 16A to FIG. 16C The upper graph in shows the acceleration measured by the accelerometer 608 when the system 600 is excited by a pulse formed by striking the plate member 602 . FIG. 16A to FIG. 16C The lower graph in shows the acceleration versus frequency of the system 600. The undamped / uncontrolled response of the system ( Fig.16A ), and the system response when the control system 610 operates to damp the first vibration mode (e.g., using the filter control element 612A) ( Fig. 16B ), and the response when the control system operates to damp both the first vibration mode and the second vibration mode (e.g., using both filter control elements 612A and 612B) ( Fig. 16C ). Fig.17 is a Bode plot showing the magnitude and phase of the frequency response of a system without feedback control, with damping control for the first vibration mode, and with damping control for both the first and second modes. FIG. 16A to FIG. 16C and Fig.17 As can be seen in FIG. 6 , the control system 610 reduces the acceleration of the plate member vibration to nearly 0 m / s in approximately 0.1 second. 2 , and significantly reduces the peak magnitude of vibration by approximately 20 dB for the first mode and approximately 10 dB for the second mode.

[0188] The control systems and methods described herein may also be configured to operate using sensor feedback from one or more accelerometer sensors located remotely from the actuator. In other words, the one or more accelerometers of the system need not be co-located with the actuator. In such a configuration, the phase correction applied by the filter control element operating on the signal from the remote accelerometer may be adjusted accordingly to account for, for example, phase angle differences caused by the distance between the accelerometer and the actuator and / or phase differences associated with modal deformations of the structure at different vibration modes.

[0189] For example, Fig.18 is a side elevation view showing another experimental system 700 that includes a metal beam member 702 of rectangular cross-section that is clamped to two support members 704 and 706 that are spaced apart from each other along the length of the beam member 702. The system 700 also includes an actuator system, generally indicated at 708, mounted to the top surface of the beam member 702 between the support members 704 and 706. The actuator system 708 includes an actuator configured as a VCM 710 and two accelerometer sensors 712 and 714. The accelerometer sensor 712 is mounted on top of the VCM 710, and the other accelerometer sensor 714 is mounted directly to the beam member 702 at a location spaced apart from the VCM 710. The actuator system 708 is composed of an actuator and a plurality of accelerometer sensors. Fig.15 The control system 610 shown in FIG. 1 is similar to the control system 610 shown in FIG. 1 .

[0190] Fig.19 The first vibration mode and the second vibration mode of the beam member 702 and the relative positions of the two accelerometer sensors 712 and 714 are schematically shown. Fig.19 It can be seen that in the first mode, the two sensors 712 and 714 are in phase, and in the second mode, the two sensors are 180° out of phase. Therefore, the damping filter of each filter control element is configured to apply a phase correction based on the associated accelerometer signal so that the VCM acts in the correct direction to damp the vibration of the beam member in both the first vibration mode and the second vibration mode.

[0191] Fig. 20 7 is a Bode plot showing the magnitude and phase of the open loop frequency response of system 700 as measured by accelerometers 712 and 714. A peak corresponding to the first beam vibration mode can be seen at approximately 80 Hz, and a peak corresponding to the second beam vibration mode can be seen at approximately 210 Hz. It can be seen in the phase plot that the two accelerometer signals are in phase at the first mode frequency and 180° at the second mode frequency.

[0192] Fig.21 7 is a Bode plot showing the open loop frequency response of the system 700 and the frequency response of control applied using position data derived from the first accelerometer 712 co-located with the VCM 710 . Fig.22A and Fig. 22B Includes a graph of acceleration versus time and a fast Fourier transform (FFT) showing the open loop impulse response of the system ( Fig.22A ) and an impulse response of a system to which control is applied using position data derived from the first accelerometer 712 ( Fig. 22B ). The two graphs show relatively rapid damping of the oscillations and relatively low peak magnitudes of the first and second mode frequencies when damping is performed using the actuator system.

[0193] Fig.23 7 is a Bode plot showing the open loop frequency response of the system 700 and the frequency response of control applied using position data derived from a second accelerometer 714 located remote from the VCM 710 . Fig.24A and Fig. 24B Includes a plot of acceleration versus time and the Fast Fourier Transform, which shows the open loop impulse response of the system ( Fig.24A ) and the impulse response of the system to which control is applied using position data derived from the second accelerometer 714 ( Fig. 24B ). Fig.23 and FIG. 24A to FIG. 24B Also shown is the relatively rapid damping of the oscillations and the relatively low peak magnitudes of the first and second mode frequencies when damped using the actuator system. Based on the phase lag information from the Bode plot, the phase correction term of the damping filter of each filter control element can be tuned to control the actuator system using the first accelerometer 712, the second accelerometer 714, or both. Thus, control can be implemented using data from sensors that are co-located with the actuator or located elsewhere in the system remote from the actuator to tune the filters of the various filter control elements.

[0194] Example 4: Control for damping vibration mode frequencies lower than the vibration mode frequency of an actuator system System and method

[0195] In certain embodiments, using the filters and phase correction methods described herein, the disclosed control system can also be configured to damp structural vibration modes that have frequencies lower than the vibration mode frequencies of the actuator system (e.g., the frequencies at which the actuator vibrates relative to the structural element to which it is mounted when the actuator is active). For example, Fig.25 An experimental structural system 800 is shown, which uses Fig.15The control system 610 is similarly configured to be controlled by a control system. The structural system 800 includes a T-shaped metal member 802, which is supported at both ends by curved members 804 and 806. The T-shaped metal member 802 includes a first main portion 808 and a second portion 810, the second portion 810 is located at or near the center of the main portion 808 and extends downwardly from the main portion 808 and perpendicular to the main portion 808. The curved members 804 and 806 are coupled to a base member 812, which is coupled to a bench member 814 (e.g., an optical bench). The curved members 804 and 806 suspend the T-shaped metal member 802 above the base member 812.

[0196] An actuator system 816 including a VCM 818 and an accelerometer 820 is coupled to the second portion 810 of the T-shaped metal member 802 and is configured to act in the x-direction. The accelerometer 820 is coupled to the housing of the VCM 818 (in other words, the accelerometer is co-located with the VCM). A vibrator in the form of a VCM 822 is positioned between the second portion 810 of the T-shaped metal member 802 and a bracing member 824 fixed to the base member 812. The vibrator VCM 822 is configured to apply an impulse disturbance force to the system 800. The vibration mode frequency of the system is changed by adding a weight 826 to the T-shaped metal member 802.

[0197] In one configuration, the system 800 is configured to vibrate at a resonant mode of 15.7 Hz. The system also exhibits several other vibration mode frequencies below 100 Hz, including vibration mode frequencies at 21.7 Hz, 22.8 Hz, 30.5 Hz, and 44 Hz. The vibration mode frequency of the actuator system 816 relative to the T-shaped metal member 802 is 22.2 Hz. Therefore, the 15.7 Hz mode and the 21.7 Hz mode of the structure are below the mode frequencies of the actuator system 816, and the 22.8 Hz mode is only slightly above the actuator system mode frequency. Figure 26 to Figure 28 Bode plots of the damped and undamped frequency responses of system 800 are presented in FIG. 8 , respectively, showing the 15.7 Hz mode, the 21.7 Hz mode, and the 22.8 Hz mode of the system. Fig. 27 and Fig.28 The damping gain k is given in d The control results of different values ​​of . Figure 26 to Figure 28 It can be seen that by adjusting the damping gain k of the damping filter d By adjusting (Equation 17), the control system can be tuned to effectively damp the modal frequencies of the structural system below the vibration modal frequencies of the actuator system 816. Specifically, compared to the open loop response, a k of 75d The value reduces the peak magnitude of the 15.7 Hz mode by approximately 20 dB, and reduces the magnitude of the 21.7 Hz mode by 10 to 15 dB. d The value reduces the peak magnitude of the 22.8 Hz mode by approximately 15 dB. The settling time of each vibration mode is also reduced to 0.2 seconds or less, compared to up to 5 seconds for the 15.7 Hz mode in an undamped system.

[0198] Example 5: Control system using peak filter control to damp vibration mode frequencies from external sources System and Method

[0199] In certain embodiments, the control systems described herein may also be configured to damp / control vibrations transmitted from the remote disturbing force to the structural system. For example, in certain embodiments, one or more of the filter control elements of the system may include a peak filter (e.g., a bandpass filter) instead of or in addition to the damping filter described above. For example, in certain embodiments, one or more of the filter control elements of the control system may implement the damping filter control described above, and one or more of the filter control elements may be configured to implement the peak filter control described below.

[0200] In some embodiments, the peak filter may be tuned to pass the target vibration frequency or the frequency to be damped. In some embodiments, the peak filter may be configured to apply the above-mentioned phase correction to phase lags associated with, for example, remote positioning of the accelerometer sensor, time delays of the actuator amplifier, signal conditioning, and / or time delays of the digital control. In some embodiments, as described above, the phase correction may also enable the peak filter to damp vibrations of the structural system below the modal frequency of the actuator system. In some embodiments, the peak filter described herein may have less impact on higher frequency dynamics than the damping filter control, and therefore may be implemented in conjunction with the damping filter to control lower frequency modes with limited coupling between damped vibration modes.

[0201] For example, Fig.29An embodiment of a control system 900 is shown, which is configured to implement a peak filter control channel in parallel with a damping filter control channel. The control system 900 includes a system block 902, which is configured to represent the dynamic response of the structural system to be controlled, an integrating element 904, and two filter control elements 906 and 908 implemented in parallel. The system block 902 is configured to represent the dynamic response of the structural system to be controlled, and the integrating element 904 is configured similarly to the above-mentioned integrating elements. The filter control element 906 can implement a phase-corrected damping filter control C1 (s) based on the transfer function of equation 17 above, for example. The filter control element 908 can implement a combination of phase-corrected peak filter control, bandpass filter control, and notch filter control based on the transfer function C2 (s) in equation 18 below.

[0202]

[0203] In some embodiments, the transfer function H of the peak filter is peak (s) can be given by the following equation 19, where k a is the damping gain, d p is the damping ratio, and ω p is the target frequency of the peaking filter.

[0204]

[0205] In some embodiments, the transfer function H of the bandpass filter control bandpass (s) can be similar to the above equation 6, and the transfer function H of the notch filter notch (s) may be similar to Equation 5 above. The phase lag θ of the system may be determined according to Equation 16 above. The number of notch filters included may depend on the number of vibration modes of the structural element to be damped, and both the resonant frequency of the structure and / or the vibration modes of the structure excited by the actuator may be considered when damping other modes. In certain embodiments, the peak filter may include derivative control, proportional control, and / or integral control similar to the damping filter described above.

[0206] In the representative working example, when the vibrator VCM 828 shown in dashed lines applies an impulse force to the support member 814, Fig.29 The control system 900 is used to Fig.25 The vibration of the structural system 800 is controlled / damped. In the present working example, the VCM 822 is removed from the system. The VCM 828 is relatively close to the structural system 800 along the z-axis (e.g., before entering the Fig.25The impulse disturbance force applied by VCM 828 to support member 814 induces a 19.5 Hz vibration mode of support member 814 and a 45 Hz vibration mode of structural system 800. The 45 Hz vibration mode of structural system 800 is damped using filter control element 906 implementing phase-corrected damping filter control, and the 19.5 Hz vibration mode of the optical support is damped using filter control element 908 implementing phase-corrected peak filter control.

[0207] exist Fig.30 and Fig.31 The frequency response of system 800 when controlled by control system 900 is shown in the Bode plot in FIG. Fig.30 The frequency response of system 800 when excited by a current command from an actuator is shown. Fig.31 The frequency response of the system 800 when excited by a vibrator VCM 828 coupled to the support member 814 is shown. Fig.30 and Fig.31 The open loop response of the system, the response when feedback control is applied through the damping filter control element 906, and the response with both the damping filter control channel 906 and the peaking filter control element 908 applied are shown. Figure 30 to Figure 32 The line labeled "Feedback 1" in is the response of the system, where the peak filter is tuned so that k a = 160, and is tuned in line "Feedback 2" so that k a =300. Fig.30 and Fig.31 It can be seen that compared with the undamped system, the filter control elements 906 and 908 have a The peak magnitudes of the support component modes and the structural system modes will be significantly reduced at this value. Fig.32 , the two control schemes also reduce the measured accelerations associated with the two modes and reduce the settling time of the structural system 800 to less than 0.3 seconds.

[0208] Example 6: Control system and method using multiple remote sensors

[0209] In certain embodiments, the actuator system may include multiple sensors located at different locations on the structural system to be controlled, and data from multiple such sensors may be used in multiple control loops to damp multiple vibration modes of the structure. A control system for such a structure may include multiple control loops including filter control elements with feedback from different sensors in the structural system. In certain embodiments, the outputs of the various control loops may be summed to produce a force command for the actuator system.

[0210] For example, Fig.33 A top plan view of a structural system 1000 is shown, which includes a rectangular plate member 1002 and an actuator system generally indicated at 1004. The actuator system 1004 includes a VCM 1006 and a plurality of accelerometer sensors 1008, 1010, 1012, 1014, and 1016. In the configuration shown, the accelerometer sensor 1008 is co-located with the VCM 1006, and the remaining sensors are arranged around the edges of the plate member 1002. Fig.33 1002 is coupled to and suspended above an optical mount or another support by three support members 1018A to 1018C in the triangular arrangement shown. A vibrator configured as a VCM 1020 is positioned along the middle of the right edge of the plate member between support members 1018A and 1018B.

[0211] In some embodiments, depending on the placement of the accelerometer sensor, the accelerometer sensor may sense one or more specific vibration modes of the structural system while not sensing other vibration modes, depending on whether the location of the sensor coincides with the nodes of one or more vibration modes. For example, when excited by an impulse disturbance force from the actuator VCM 1006 and / or from the vibrator VCM 1020, such as Fig.33 The plate member 1002 configured in FIG. 1006 shows four relatively low frequency vibration modes. The first mode is at 61 Hz, the second mode is at 96 Hz, the third mode is at 165 Hz, and the fourth mode is at 282 Hz. The accelerometer 1008 positioned atop the VCM 1006 detects the second, third, and fourth modes well, but does not have a strong signal from the first mode. The accelerometer 1014 provides a clear signal for the first vibration mode.

[0212] Various vibration modes in such a structural system can be controlled using a control system that implements the damping filter control architecture and / or peak filter control architecture described herein in multiple parallel control loops, wherein each control loop is configured to damp vibrations in one or more modes based on feedback from sensors positioned to sense vibrations of the structure in one or more target modes of the control loop. For example, Fig.34 A representative control system 1030 is shown including two control loops (also referred to as control channels) that can be used to control Fig.33The four modes of vibration of the structure 1000 shown. The first control loop is generally indicated at 1032, and the second control loop is generally indicated at 1034. The control system includes a system block 1036 representing the dynamic response of the structural system 1000. The first control loop 1032 also includes an integrating element 1038 and three filter control elements 1040, 1042 and 1044 implemented in parallel. The position signal output from the integrating element 1038 is subtracted from the position command signal x(s) to obtain a position error signal, which is input to the filter control elements 1040 to 1044. The filter control elements 1040 to 1044 can be configured to implement filter control based on transfer functions C1(s), C2(s) and C3(s). The filter control elements can be configured to implement the phase-corrected damping filter control described above with reference to equations 13 to 17 and / or the phase-corrected peak filter control described above with reference to equations 18 and 19. The filter control elements 1040-1044 may be tuned for a particular target mode frequency of the structural system 1000. In a particular embodiment, the filter control elements 1040-1044 are configured to control the second mode, the third mode, and the fourth mode of the structural system 1000, respectively.

[0213] The second control loop 1034 may also include an integrating element 1048 and a summing junction 1050, which outputs a position error signal to a filter control element 1052 after the position signal of the integrating element is subtracted from the position command signal x(s). The filter control element 1052 may implement a filter control based on the transfer function C4(s), which may include a phase-corrected damping filter control similar to Equations 13 to 17 above or a phase-corrected peaking filter control as described with reference to Equations 18 and 19, and is tuned for a specific target mode frequency of the structural system 1000. In a particular embodiment, the filter control element 1048 of the second control loop is tuned to attenuate a first vibration mode of the structural system 1000.

[0214] The outputs of the filter control elements 1040 to 1044 of the first control loop 1032 and the output of the filter control element 1052 of the second control loop 1034 may be summed at a summing point 1054 to provide a command signal u, which is provided to the actuator system. Before the command signal is provided to the structural system block 1036, the disturbance force d u is shown combined with the force command signal at summing junction 1056 .

[0215] In use Fig.33When vibration of the structural system 1000 is attenuated, the first control loop 1032 can operate using acceleration data obtained from the accelerometer 1008 co-located with the VCM 1006, and can be configured to control the second vibration mode, the third vibration mode, and the fourth vibration mode of the plate member 1002. The second control loop 1034 can be configured to control the first vibration mode of the plate member 1002 using the acceleration data obtained from the accelerometer 1014. Therefore, in the illustrated embodiment, the first accelerometer signal acc1 from the accelerometer 1008 is transmitted to the integration element 1038 of the first control loop 1032. The integration element 1038 outputs a position signal pos1 to the summing junction 1046, and the position signal pos1 is subtracted from the position command signal x(s) to obtain a position error signal provided to the filter control elements 1040 to 1044. The equation for the first accelerometer signal acc1 is given below in Equation 20, where and

[0216]

[0217] For the second control loop 1034, the second accelerometer signal acc2 from the accelerometer 1014 is transmitted to the integrating element 1048 of the second control loop. The integrating element 1048 outputs the position signal pos2 to the summing junction 1050, where the position signal pos2 is subtracted from the position command signal x(s) to obtain the position error signal. The position error signal is provided to the filter control element 1052. The equation for the second accelerometer signal acc2 is given below in Equation 21, where and

[0218]

[0219] Equations 20 and 21 relate to how the feedback filter controller and the sensor are coupled in a closed loop system. In certain embodiments, Equations 20 and 21 can be used for offline control design synthesis and simulation in the frequency domain before actually implementing the control system.

[0220] Fig.35 Show Fig.33 The Bode plot of the open loop frequency response of the system 1000 when excited by a pulse from the vibrator VCM 1020 is shown. Peaks can be seen in the 61 Hz mode, the 96 Hz mode, the 165 Hz mode, and the 282 Hz mode. Fig.35 As indicated in , accelerometer 1014 provides a clear signal in the 61 Hz mode, while accelerometer 1008 provides a clear signal in the second mode, the third mode, and the fourth mode. Fig.36 Based on Fig.34 Bode plots of the frequency response of the system using the actuator system to apply all four modes of control while controlling the force command of the control system 1030 are shown. Fig.36 For each vibration mode in the image, a significant reduction in peak magnitude can be seen.

[0221] Fig.37A and Fig.37B Graphs of acceleration versus time (top) and acceleration versus frequency (bottom) for system 1000 are shown in FIG. Fig.37A and Fig.37B It can be seen that when using Fig.34 In the case of the actuator system 1004 controlled by the control system shown, each of the four controlled vibration modes of the structural system 1000 is almost completely damped at 0.2 seconds after the impulse excitation. This is a significant improvement over an undamped system, in which the vibrations last for a second or longer. Thus, the disclosed control system can be used to significantly reduce the settling time of multiple vibration modes of a structural system and vibrations at frequencies below 300 Hz, such as, in particular, below 100 Hz.

[0222] The control loop of the control system 1030 may be configured in a variety of ways depending on factors such as the shape, size, etc. of the structural system, the positioning of the accelerometer sensors 1010-1016, the location of the actuator 1006, the location of the vibrator VCM, and the like. Fig.38 Another arrangement of four accelerometers 1010 to 1016, an actuator VCM 1006, and a vibrator VCM 1020 on a plate member 1002 is shown. The accelerometer 1008 is shown removed from the actuator VCM 1006. Fig.38 The configuration shown in the figure shows that the panel member 1002 is similar to the above reference Fig.33 In some embodiments, the accelerometer 1014 provides clear signals for the first and third vibration modes, and the accelerometer 1010 provides clear signals for the second and fourth modes. Fig.39 Rearrange as shown in Fig.34The control system shown in the figure enables the signal acc1 from the accelerometer 1010 to be fed back to the filter control elements 1040 and 1044, which are arranged in parallel in the first control loop 1032 and are configured to generate control signals to attenuate the vibrations in the first mode and the third mode. The signal acc2 from the accelerometer 1014 is fed back to the filter control elements 1042 and 1052, which are arranged in parallel in the second control loop 1034 and are configured to generate control signals to attenuate the second mode and the fourth mode. Therefore, the control system described herein may include any number of control loops, which implement any number of filter control elements depending on the number of vibration modes to be controlled, the number and positioning of accelerometers that detect the target mode of the system, etc.

[0223] Example 7: Structural system dynamics model and placement of sensors and actuators

[0224] In certain embodiments, the magnitude of the force command for suppressing / controlling the vibration of the structural system at a specific vibration mode frequency may be estimated based on the magnitude of the vibration at the mode frequency. In certain embodiments, the magnitude of the vibration of a specific mode may be measured experimentally and / or determined using any of various models of the system and its frequency response (e.g., finite element analysis (FEA) models, state space models, and the like). In certain embodiments, the displacement of the structural system at a first location may be determined from such a system model in response to a force applied to the structural system at a second location. Information from such models and / or measurements of the system may be used to select the location of the actuator and / or the location of one or more accelerometer sensors to effectively damp one or more selected vibration modes of the structure.

[0225] For example, in a representative example, e.g. Fig.38 The dynamics of a structural system such as the plate member 1002 shown can be transformed into a decoupled modal coordinate space. The dynamics of the structural system can be given by the expression in Equation 22 below, where M is the mass matrix of the FEA model, K is the stiffness matrix of the FEA model, and v is the displacement vector.

[0226]

[0227] Solving the eigenvalue expression in Equation 23 below yields and φ k , where ω 2 is the eigenvalue and φ is the eigenvector, is the square of the natural frequency of the kth mode (scalar), φ kis a vector representing the mode shape of the kth mode, where k=1,…N and N is three times the number of nodes in the three-dimensional FEA model.

[0228] The mode shape matrix M of the FEA model can be given in Equation 23 below modal , where Φ=[Φ1…φ N ] and m k is the model quality of the kth mode.

[0229]

[0230] The modal stiffness matrix K of the FEA model can be given in Equation 24 below modal , where the modal stiffness of the kth mode is

[0231]

[0232] The identity can be used The mode shape matrix φ is scaled to give the expression in Equation 25 below.

[0233]

[0234] The modal mass matrix can be normalized to Φ T MΦ=I,where m k = 1 is the modal mass of the kth mode.

[0235] The modal stiffness matrix can be normalized to yield the following expression in Equation 26, where is the modal mass of the kth mode.

[0236]

[0237] This results in a mass-normalized mode shape equation which is the displacement v of the structural system at the first position j according to the expression in Equation 27 below: j The force u applied at the second position i i ratio.

[0238]

[0239] In Equation 27, φ k is the vector representation of the mode shape of the kth mode of the structural system given by Equation 28 below, and ξ k is the damping ratio.

[0240]

[0241] In some embodiments, the facility model of the flexible mode dynamics of a structural system can be represented as a second-order transfer function, such as the one given in Equation 29 below.

[0242]

[0243] The transfer function of Equation 29 can be transformed into modal coordinates using the relation v = Φq to obtain the expression in Equation 30.

[0244]

[0245] The modal mass matrix term Φ T MΦ can be the modal mass matrix term given in Equation 23 above, and the modal stiffness matrix Φ T KΦ can be the modal stiffness matrix given in Equation 26 above. The damping matrix term Φ T DΦ can be approximated as Equation 31 below.

[0246]

[0247] The relation v = Φq can be written as Equation 32 below, where N is the number of modes.

[0248]

[0249] The reduced-order model of the system can be given in Equation 33 below, where n < N, and the term E j,i is the DC approximation of the higher-order dynamics that are ignored, given in Equation 34.

[0250]

[0251] Fig.40 Shows a simulation of the shape of the top surface of the plate member 1002 according to the above FEA model when the plate member is supported at three locations. Fig.38 as shown. Fig.40 Shows the displacement patterns associated with nine vibration modes of the plate member 1002.

[0252] In some embodiments, accelerometer sensors can be placed on the structural system at locations where the displacement is maximum with respect to one or more vibration modes. For example, referring to Fig.40 , in the first mode and the second mode, the displacement of the top surface of the plate member 1002 in the z direction (e.g., the plane out of the page) is maximum at the lower left corner and the lower right corner. Therefore, accelerometers located at these corners will provide a clear signal of the acceleration / displacement of the plate member surface associated with the first and second vibration modes. In Fig.40It can also be seen in Figure 1 that an accelerometer located at or near the center of the plate member 1002 can provide a clear signal of the displacement associated with the third vibration mode. Therefore, for the selected vibration mode to be controlled, the accelerometer can be arranged at a location that coincides with a large displacement of the plate surface. FEA models of the dynamics of the structural system can help determine the placement of accelerometers and / or actuators, especially when the environment and / or constraints of the structural system in its intended application cannot be easily reproduced by experiment.

[0253] In some embodiments, using various accelerometers to swap the position of the actuator VCM (effectively changing the input position and output position of the system) can cause similar vibration responses of the structural system. For example, placing the actuator VCM 1006 at Fig.38 At the location of the accelerometer 1010 in , and vice versa, a similar vibration profile can be formed in response to the disturbance force from the actuator VCM.

[0254] Example 8: Estimation of control force

[0255] In some embodiments, the magnitude of the force command sufficient to damp the vibration at the selected modal frequency may be estimated using a structural system dynamics model such as that described herein (optionally in conjunction with the magnitude of the vibration measured at the selected frequency to be damped). In some embodiments, modal decomposition techniques may be used to model the rigid body modes (and / or flexible modes) of the structural element. For example, in some instances, Fig.38 The displacement at position j on a plate member similar to the plate member 1002 shown may be given by Equation 35 below.

[0256]

[0257] In Equation 35, the structural system facility dynamics P j,i (s) can be determined according to the above equation 33. Perturbation Dynamics Model D j,l (s) may be given by Equation 36 below, but may require experimental verification in certain embodiments.

[0258]

[0259] In some embodiments, when no control is applied (e.g., u i =0), the magnitude of the displacement of the plate member at position j due to the vibration in the target mode k can be v j The absolute value of |v j (jω k )|. Therefore, the magnitude of the force command to damp the vibration at position j due to mode k vibration can be given by the following Equation 37.

[0260]

[0261] In certain embodiments, the structural system dynamics model in modal space may consider rigid body vibration modes of the structural system. Fig.41 Schematically showing an unconstrained structural element 1100 having a length L and indicating the length of the structural element 1100 when a force u is applied. i (e.g., by an actuator of an actuator system) i And the member 1100 responds to the force u i The displacement v j The x-coordinate of j In some embodiments, for the first mode φ1, where ω1=0, φ 1i and φ 1j can be equal to the value given in Equation 38 below This relationship is also Fig.42 It is shown in Fig.42 Show Fig.41 An exemplary first rigid body mode of a beam member is shown.

[0262]

[0263] for Fig.43 The second rigid body mode φ2 of the beam member shown in FIG, where ω2 = 0, φ 2,i can be expressed as given in Equation 39 below and φ 2,j It can be expressed as given in Equation 40 below, where I zz is the moment of inertia of the structural element about the z-axis when the structural element 1100 rotates about the z-axis.

[0264]

[0265] By substituting the expression in Equation 38 above into Equation 40, the expression given in Equation 27 above can be rewritten and simplified according to the following Equation 41: ratio.

[0266]

[0267] When considering the two rigid body modes φ1 and φ2, Equation 41 states that for the two rigid body modes, the input force u i How does the dynamics of affect the output position v j A similar formulation can be extended to the flexible modes of structural elements.

[0268] An example of a rotation mode about the z-axis is Fig.44 It is shown in and can be expressed according to the following equation 42.

[0269]

[0270] Substituting φ in equations 39 and 40 above 2,i and φ 2,j Substituting into the above expression we can get Fig.44 The rotation mode θ around the z-axis is shown in z A series of equivalent expressions in the following equation 43.

[0271]

[0272] In certain embodiments, positioning the actuator at a location on the structural system that causes a relatively large mode shape displacement in response to the application / input of a force can improve controllability. A larger moment arm of the actuator (e.g., the magnitude of the mode shape displacement at the force application point or sensor measurement point) can result in a larger moment constant, which is the product of the actuator force constant and the moment arm at the actuator point. In certain embodiments, positioning the accelerometer sensor at a location with a relatively large mode shape displacement for a selected vibration mode can improve the ability of the accelerometer sensor to sense the displacement of the structural element associated with the selected mode. Therefore, in certain embodiments, it can be beneficial to position the actuator and / or sensor at a location with a relatively large mode shape displacement associated with a particular vibration mode to be damped.

[0273] In certain embodiments, the dynamic response of the structural system may also be formulated as a state-space model. can be expressed as the following equation 44, where v j is the displacement at j, u i is the force at location i, and N is the number of vibration modes in the model.

[0274]

[0275] The following equation 45 provides an example of a single-input single output (SISO) system, which is equivalent to the equation 44: The expression of q k is the displacement of the structural element in the kth mode.

[0276]

[0277] In certain embodiments, the SISO system may include a term representing the residual elasticity associated with omitted higher order modes, which may be similar to Equation 34 above.

[0278] Equation 46 provides an exemplary multiple-input multiple-output (MIMO) system.

[0279]

[0280] Equation 46 can be expanded into an equivalent system of equations given in Equation 47.

[0281]

[0282] In some embodiments, a SISO state-space model and / or a MIMO state-space model of the structural system can be used to represent the system dynamics decoupled in terms of modal coordinates and more convenient in simulation than a transfer function model. In some embodiments, since the actuators and sensors described above are related to the mode shapes, the parameter φ in Eq. 44 and Eq. 46 can be used. k,j and φ k,i To determine the placement of actuators and sensors.

[0283] One or more of the actuator systems, control systems, and / or control methods described herein may provide significant advantages over known systems and methods for vibrations of structures in precision systems, such as lithography systems. For example, the actuator systems described herein may effectively attenuate vibrations of various structures in a lithography system. For example, the systems described herein may attenuate relatively low frequency vibrations, such as frequencies of 500 Hz or less (e.g., 300 Hz or less, 200 Hz or less, or 100 Hz or less) or higher frequency vibrations up to about 10 kHz (or the sampling and bandwidth limitations of the system), thereby reducing or eliminating the need for passive dampers for this purpose. The disclosed systems and methods may also significantly reduce the magnitude of vibration peaks of a structural element associated with one or more vibration modes of the structural element. This may reduce relative motion of different structures in a precision system, such as an optical surface plate, a substrate stage, and / or a mask stage in a lithography exposure apparatus. Where one structural element serves as a position reference for another structural element, this can significantly improve positioning accuracy by reducing the amplitude of structural mode vibrations, which can be relatively large without damping.

[0284] The systems and methods described herein can also significantly reduce the stabilization time of a structural system after being excited by a disturbing force. Such systems can be implemented, for example, to reduce vibrations caused by the movement of a substrate stage and / or a mask stage in an exposure apparatus. As described above, certain configurations of the systems described herein can reduce the stabilization time of a structural system similar to an optical surface plate from one second or more to 0.2 seconds or less. This can significantly increase the throughput of an exposure apparatus by reducing the time required for vibrations between exposures to naturally dissipate or to dissipate under the influence of a passive damper.

[0285] The systems and methods described herein may also be adapted for use on various structural elements and in various configurations. For example, in the context of an exposure apparatus, the actuator systems and control methods described herein may be configured for use on an optical surface plate, a substrate stage, a mask stage, or any other structure of an exposure apparatus in which damping of structural vibrations may be indicated. The control system may be configured to attenuate one, two, three, four, five or more vibration modes of the structural system and vibrations excited by control of other modes. The control system may also be configured to utilize feedback from sensors located at the location of the actuator and / or at the far end of the actuator by implementing the phase correction methods described herein. The phase correction methods described herein may also be used to damp vibration modes of the structure (the vibration modes have frequencies lower than the mode frequencies of the actuator-structure interaction) and higher frequency modes of the structure.

[0286] Example 9: Exemplary Precision System

[0287] The methods and apparatus disclosed above can be used in conjunction with various precision systems, such as various types of photolithography systems and other wafer processing systems and methods, including the above-mentioned photolithography exposure system. The control system and method can also be used in conjunction with the following reference Figure 45 to Figure 49 Any of the described precision system embodiments and methods and / or the structural elements or subsystems associated therewith may be used in combination. Fig.45, showing certain features of an immersion lithography system (an exemplary precision system), namely, a light source 1340, an illumination optical system 1342, a reticle stage 1344, a projection optical system 1346, and a wafer (substrate) stage 1348, all of which are arranged along an optical axis A. The light source 1340 is configured to generate a pulsed beam of illumination light, such as 248 nm DUV light generated by a KrF excimer laser, 193 nm DUV light generated by an ArF excimer laser, or 157 nm DUV light generated by an F2 excimer laser. The illumination optical system 1342 includes an optical integrator and at least one lens that conditions and shapes the illumination beam for illuminating a specific area on a patterned reticle 1350 mounted to the reticle stage 1344. The pattern defined on the reticle 1350 corresponds to a pattern to be photolithographically transferred to a wafer 1352 held on the wafer stage 1348. Lithographic transfer in this system is performed by projecting an aerial image of the pattern from the mask 1350 onto the wafer 1352 using a projection optical system 1346. The projection optical system 1346 typically includes a number of individual optical elements (not shown in detail) that project the image onto the wafer 1352 at a specific reduction ratio (e.g., 1 / 4 or 1 / 5). To be imprintable, the wafer surface is coated with a layer of a suitable exposure-sensitive material (called a "resist").

[0288] The mask stage 1344 is configured to move the mask 1350 in the X direction, the Y direction and rotate about the Z axis. To this end, the mask stage is equipped with one or more linear motors with cooling coils as described herein. The two-dimensional position and orientation of the mask 1350 on the mask stage 1344 are detected in real time by a laser interferometer (not shown), and the positioning of the mask 1350 is achieved by the main control unit based on the detection performed in this way.

[0289] Wafer 1352 is held by a wafer holder ("chuck", not shown) on wafer stage 1348. Wafer stage 1348 includes mechanisms (not shown) for controlling and adjusting the focus position (along the Z axis) and the tilt angle of wafer 1352 as desired. Wafer stage 1348 also includes electromagnetic actuators (e.g., linear motors or planar motors, or both) for moving the wafer in an XY plane substantially parallel to the image forming surface of projection optical system 1346. These actuators desirably include linear motors, one or more planar motors, or both.

[0290] The wafer stage 1348 also includes a mechanism for adjusting the tilt angle of the wafer 1352 by an autofocus and autoleveling method. Therefore, the wafer stage is used to align the wafer surface with the image surface of the projection optical system. The two-dimensional position and orientation of the wafer are monitored in real time by another laser interferometer (not shown). Control data based on this monitoring result is transmitted from the main control unit to the drive circuit for driving the wafer stage. During exposure, the light passing through the projection optical system is moved from one position on the wafer to another position in a sequential manner in a step-and-repeat or step-and-scan manner according to the pattern on the mask.

[0291] The projection optical system 1346 typically includes a number of lens elements that work together to form an exposure image on the resist-coated surface of the wafer 1352. For convenience, the farthest optical element (i.e., closest to the wafer surface) is the objective lens 1353. Since the system shown is an immersion lithography system, the system includes an immersion liquid 1354 located between the objective lens 1353 and the surface of the wafer 1352. As discussed above, the immersion liquid 1354 is of a specific type. The immersion liquid is present at least when the pattern image of the mask is exposed onto the wafer.

[0292] Immersion liquid 1354 is provided by a liquid supply unit 1356, which may include a container, a pump, and a temperature regulator (not shown separately). Liquid 1354 is slowly discharged into the gap between objective lens 1353 and the wafer surface by a nozzle mechanism 1355. A liquid recovery system 1358 includes a recovery nozzle 1357, which removes liquid from the gap as fresh liquid 1354 is provided by supply source 1356. Thus, a substantially constant volume of continuously replaced immersion liquid 1354 is provided between objective lens 1353 and the wafer surface. The temperature of the liquid is adjusted to be approximately the same as the temperature within the chamber in which the lithography system itself is provided.

[0293] Also shown is a sensor window 1360 that extends across a recess 1362 defined in the wafer stage 1348 in which the sensor 1364 is located. Thus, the window 1360 isolates the sensor 1364 in the recess 1362. As the immersion fluid 1354 is continuously replaced, moving the wafer stage 1348 to place the window 1360 below the objective lens 1353 allows the beam passing through the projection optical system 1346 to be transmitted through the immersion fluid and the window 1360 to the sensor 1364.

[0294] A probe beam source 1380 is positioned to direct a probe beam 1381 to the reticle 1350, and a detection system 1382 is configured to detect the portion of the probe beam modulated by the reticle 1350. As described above, the detected beam can be used to assess reticle distortion so that appropriate system adjustments can be made to correct, prevent, or at least partially compensate for the distortion.

[0295] Now refer to Fig.46 , an alternative embodiment of a precision system that may include one or more electromagnetic actuators with active cooling coils as described herein is EUVL system 1400, shown as a representative precision system incorporating electromagnetic actuators as described herein. The illustrated system 1400 includes a vacuum chamber 1402, which includes vacuum pumps 1406a, 1406b, which are arranged so that a desired vacuum level can be established and maintained within respective chambers 1408a, 1408b of the vacuum chamber 1402. For example, vacuum pump 1406a maintains a vacuum level of approximately 50 mTorr in the upper chamber (mask chamber) 1408a, and vacuum pump 1406b maintains a vacuum level of less than approximately 1 mTorr in the lower chamber (optical chamber) 1408b. The two chambers 1408a, 1408b are separated from each other by a barrier wall 1420. For ease of discussion, various components of the EUVL system 1400 are not shown, but it is understood that the EUVL system 1400 may include components such as a reaction frame, a vibration isolation mechanism, various actuators, and various controllers.

[0296] EUV reticle 1416 is held by reticle chuck 1414 coupled to reticle stage 1410. Reticle stage 1410 holds reticle 1416 and allows the reticle to be moved laterally in a scanning manner, such as during lithography exposure using the reticle. A shielding device is provided between reticle 1416 and barrier wall 1420. Illumination source 1424 generates EUV illumination beam 1426, which enters optical chamber 1408b and reflects from one or more mirrors 1428 and passes through illumination optical system 1422 to illuminate desired locations on reticle 1416. When illumination beam 1426 reflects from reticle 1416, the beam is "patterned" with portions of the pattern that actually illuminate the reticle. Barrier wall 1420 acts as a pressure differential barrier and can be used as a reticle shield to protect reticle 1416 from particle contamination during use. Barrier wall 1420 defines an opening 1434 through which an illumination beam 1426 can illuminate a desired area of ​​reticle 1416. Incident illumination beam 1426 on reticle 1416 is patterned by interaction with pattern-defining elements on the reticle, and the resulting patterned beam 1430 is typically propagated downward through projection optics 1438 to reach the surface of wafer 1432 held by wafer chuck 1436 on wafer stage 1440, which effects a scanning motion of the wafer during exposure. Thus, an image of the reticle pattern is projected onto wafer 1432.

[0297] The wafer stage 1440 may include (not shown in detail) a positioning stage and a wafer tablet, which may be driven by, for example, a planar motor or one or more linear motors, and the wafer tablet is magnetically coupled to the positioning stage using, for example, an EI core actuator. The wafer chuck 1436 is coupled to the wafer table and may be suspended relative to the wafer table by, for example, one or more voice coil motors. If the positioning stage is driven by a planar motor, the planar motor typically utilizes corresponding electromagnetic forces generated by magnets and corresponding armature coils arranged in a two-dimensional manner. The positioning stage is configured to move in multiple degrees of freedom of motion (e.g., three to six degrees of freedom) to allow the wafer 1432 to be positioned in a desired position and orientation relative to the projection optical system 1438 and the mask 1416.

[0298] The EUVL system including the above-described EUV source and illumination optical system can be constructed by assembling various assemblies and subsystems in a manner to ensure that the specified standards of mechanical accuracy, electrical accuracy, and optical accuracy are met and maintained. In order to establish these standards before, during, and after assembly, the various subsystems (especially the illumination optical system 1422 and the projection optical system 1438) are evaluated and adjusted as needed to achieve the specified accuracy standards. Similar evaluations and adjustments are performed according to the requirements of the mechanical and electrical subsystems and assemblies. Assembling the various subsystems and assemblies includes creating the required optical and mechanical interfaces, electrical interconnects, and plumbing interconnects between the assemblies and subsystems. After the EUVL system is assembled, further evaluations, calibrations, and adjustments are performed as needed to ensure that the specified system accuracy and operating precision are achieved. In order to maintain cleanliness standards and avoid contamination, the EUVL system (and certain subsystems and assemblies of the system) are assembled in a clean chamber or similar chamber where particulate contamination, temperature, and humidity are controlled.

[0299] like Fig.46 , a probe beam source 1450 may be positioned to direct a probe beam 1451 to a reticle 1416. A detection system 1452 is positioned to receive at least a portion of the probe beam that has been reflected, refracted, diffracted, phase shifted, or otherwise modulated by interaction with the reticle 1416. Based on a detector signal response to this beam portion, reticle distortion may be assessed in the detection system as described above.

[0300] A semiconductor device can be fabricated by a process including a microlithography step performed using the above-described microlithography system. Fig.47 In step 1501, the functional and performance characteristics of the semiconductor device are designed. In step 1502, a mask ("mask") that defines the desired pattern is designed and produced according to the previous design step. At the same time, in step 1503, a substrate (wafer) is produced and coated with a suitable resist. In step 1504 ("wafer processing"), the mask pattern designed in step 1502 is exposed to the surface of the substrate using a microlithography system. In step 1510, the mask distortion can be estimated during the above exposure. In step 1505, the semiconductor device is assembled (including "cutting" to cut individual devices or "chips" from the wafer, "bonding" to bond the wiring to specific locations on the chip, and "packaging" to enclose the device in a suitable package for use). In step 1506, the assembled device is tested and inspected.

[0301] exist Fig.4816 shows representative details of a wafer processing process including microlithography steps. In step 1611 ("oxidation"), the wafer surface is oxidized. In step 1612 ("chemical vapor deposition (CVD)"), an insulating layer is formed on the wafer surface by chemical vapor deposition. In step 1613 (electrode formation), electrodes are formed on the wafer surface, for example by vapor deposition. In step 1614 ("ion implantation"), ions are implanted into the wafer surface. These steps 1611 to 1614 constitute representative "pre-processing" steps for the wafer and are selected at each step according to the processing requirements.

[0302] At each stage of wafer processing, when the pre-processing steps have been completed, the following "post-processing" steps are implemented. The first post-processing step is step 1615 ("photoresist formation"), in which a suitable resist is applied to the surface of the wafer. Next, in step 1616 ("exposure"), the pattern is photolithographically transferred from the mask to the resist layer on the wafer using the above-mentioned microlithography system. Mask distortion can be compensated during the pattern transfer. In step 1617 ("development"), the exposed resist on the wafer is developed to form a usable mask pattern corresponding to the resist pattern in the resist on the wafer. In step 1618 ("etching"), the area not covered by the developed resist (i.e., the exposed material surface) is etched to a controlled depth. In step 1619 ("photoresist removal"), the residual developed resist is removed ("stripped") from the wafer.

[0303] By repeating the pre-processing step and the post-processing step as needed, a plurality of interconnected circuit pattern layers are formed on the wafer. Generally speaking, a set of pre-processing steps and post-processing steps are performed to form each layer.

[0304] Included in the present disclosure are any of a variety of precision systems that include a stage or similar device for holding a workpiece or other item useful in manufacturing. An example of a precision system is a microlithography system or exposure "tool" used to manufacture semiconductor devices. Fig.4917 is a schematic diagram of an exemplary microlithography system 1710 that includes features of the technology described herein. System 1710 includes a system frame 1712, an illumination system 1714, an imaging optical system 1716, a reticle stage assembly 1718A-1718B, a substrate stage assembly 1720A-1720B, a positioning system 1722A-1722D, and a system controller 1724. The configuration of the components of system 1710 is particularly useful for transferring a pattern of an integrated circuit (not shown) from a reticle 1726 to a semiconductor wafer 1728. System 1710 is mounted to a mounting base 1730 (e.g., a ground, base, or floor) or other support structure. The system also includes a measurement system that measures the position of a lithographic substrate (as an exemplary workpiece) along an axis (e.g., a z-axis or optical axis) with increased accuracy and precision. In system 1710, the reticle stage assembly and / or the substrate stage assembly 1720 includes the multi-blade holding device described in the above representative embodiments.

[0305] In some examples, the specified vibration mode frequency may be 5Hz to 10kHz, 5Hz to 5kHz, 5Hz to 1kHz, 5Hz to 500Hz, 5Hz to 300Hz, 5Hz to 200Hz, 5Hz to 100Hz, 2Hz to 10kHz, 2Hz to 5kHz, 2Hz to 1kHz, 2Hz to 500Hz, 2Hz to 300Hz, 2Hz to 200Hz, 2Hz to 100Hz, 1Hz to 10kHz, 1Hz to 5kHz, 1Hz to 1kHz, 1Hz to 500Hz, 1Hz to 300Hz, 1Hz to 200Hz, 1Hz to 100Hz, or any range between any of the frequencies described herein. The specified vibration mode frequency may also be less than 1Hz.

[0306] Example 10: Representative computing environment

[0307] Fig.50 A general example of a computing environment 1800 in which the software and control algorithms of the described embodiments may be implemented is shown. For example, the software and / or hardware used to implement the various control systems, filters, and phase correction methods described herein may be configured similarly to the computing environment 1800, and may be a local computing system integrated as part of the exposure apparatus assembly, or may be a remote computing system as described herein.

[0308] Since the technology can be implemented in various general-purpose computing environments or special-purpose computing environments, computing environment 1800 is not intended to impose any limitations on the scope of use or functionality of the technology. For example, the disclosed technology can be implemented using other computer system configurations, including programmable automation controllers, programmable logic controllers, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), handheld devices, multiprocessor systems, programmable consumer electronics, network PCs, minicomputers, and similar systems. The disclosed control method can also be implemented in a distributed computing environment, where tasks are performed by remote processing devices linked through a communication network. In a distributed computing environment, program modules can be located in both local memory storage devices and remote memory storage devices.

[0309] Reference Fig.50 , the computing environment 1800 includes at least one processing unit 1810 and a memory 1820. Fig.50 , this most basic configuration 1830 is included within the dashed line. Processing unit 1810 executes computer executable instructions and can be a real processor or a virtual processor. In a multi-processing system, multiple processing units execute computer executable instructions to increase processing power, and in this way, multiple processors can run simultaneously. Memory 1820 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory, etc.) or can be some combination of the two. Memory 1820 stores software 1880, which can, for example, implement the techniques described herein. The computing environment can have additional features. For example, computing environment 1800 includes storage 1840, one or more input devices 1850, one or more output devices 1860, and one or more communication connections 1870. An interconnection mechanism (not shown), such as a bus, controller, or network, interconnects the components of the computing environment 1800. Typically, operating system software (not shown) provides an operating environment for other software executed in the computing environment 1800 and coordinates the activities of the components of the computing environment 1800.

[0310] Storage device 1840 may be removable or non-removable and include non-volatile solid-state memory, disks, or any other medium that can be used to store information and that can be accessed within computing environment 1800. Storage device 1840 stores instructions, plug-in data, and messages that can be used to implement software 1880 of the techniques described herein.

[0311] The input device 1850 may be, for example, an accelerometer, a position sensor such as an optical time-of-flight sensor, a temperature sensor, a position encoder, or a touch input device such as a keyboard, a keypad, a mouse, a touch screen display, a stylus or a trackball, a voice input device, a scanning device, or another device that provides input to the computing environment 1800. The output device 1860 may be a wired or wireless signal transmitter, a display, or another device that provides output from the computing environment 1800.

[0312] The communication connection 1870 enables communication with a device or computing entity through a communication medium (e.g., a connection network). The communication medium conveys information, such as control signals, computer executable instructions, sensor input or output, or other data in a modulated data signal. The communication connection 1870 is not limited to wired connections (e.g., megabit or gigabit Ethernet, wireless broadband, fiber channel via electrical or optical connections), but also includes wireless technologies (e.g., RF connections via Bluetooth, wireless fidelity (WiFi) (Institute of Electrical and Electronics Engineers, IEEE) 802.11a / b / n), World Interoperability for Microwave Access (WiMax), cellular, satellite, laser, infrared) and other suitable communication connections for providing network connectivity for the disclosed controlled devices.

[0313] Some embodiments of the disclosed methods may be implemented using computer executable instructions that implement all or part of the disclosed techniques in a computing cloud 1890 or other remote computing system. For example, the disclosed methods may be executed on a processing unit 1810 located in a computing environment 1830, or the disclosed methods may be executed on a server located in a computing cloud 1890.

[0314] Computer-readable media are any available media that can be accessed within the computing environment 1800. As an example and not limitation, in the case of using the computing environment 1800, computer-readable media include memory 1820 and / or storage device 1840. It is readily understood that the term computer-readable storage media includes media used for data storage (such as memory 1820 and storage device 1840) and does not include transmission media (such as modulated data signals).

[0315] Explanation of terminology

[0316] For the purpose of this description, certain aspects, advantages and novel features of embodiments of the present disclosure are set forth herein. The disclosed methods, apparatuses and systems are not limited in any way. On the contrary, the present disclosure relates to all novel features and aspects of the various disclosed embodiments in individual form and in various combinations and sub-combinations with each other. The methods, apparatuses and systems are not limited to any particular aspect or feature or combination thereof, and the disclosed embodiments do not require the presence of any one or more specific advantages or problems to be solved. Unless not physically present, the scope of the present disclosure includes any feature disclosed herein in combination with any other feature disclosed herein.

[0317] Although the operations of some of the disclosed embodiments are described in a particular sequential order for ease of presentation, it should be understood that unless a particular statement set forth herein requires a particular order, such an illustrative approach encompasses rearrangement. For example, the operations described sequentially may be rearranged or performed simultaneously in some cases. In addition, for simplicity, the figures may not illustrate the various ways in which the disclosed components may be used in conjunction with other components.

[0318] As used in the present disclosure and claims, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. In addition, the term "includes" means "comprises." Furthermore, the terms "coupled" and "associated" generally mean electrically coupled or linked, electromagnetically coupled or linked, and / or physically (e.g., mechanically or chemically) coupled or linked, and do not exclude the presence of intervening elements between coupled or associated items in the absence of specific language to the contrary.

[0319] In some instances, values, procedures, or devices may be referred to as "lowest," "optimal," "minimum," or similar expressions. Such descriptions are intended to indicate that a selection may be made among a number of alternatives, and that such a selection is not necessarily better, lesser, or more preferred over other selections.

[0320] In the description, specific terms such as "up", "down", "upper", "lower", "horizontal", "vertical", "left", "right" and the like may be used. These terms are used where appropriate to provide some clarity when dealing with relative relationships. However, these terms are not intended to imply absolute relationships, positions and / or orientations. For example, the "upper" surface of an object may become the "lower" surface simply by turning the object over. Despite this, the object is still the same object.

[0321] Unless otherwise indicated, all numbers used in the specification or claims to express frequency, material quantity, angle, pressure, molecular weight, percentage, temperature, time, etc. should be understood to be modified by the term "about". Therefore, unless otherwise indicated, numerical parameters implicitly or explicitly stated are approximate values, which may depend on the desired properties sought and / or the detection limits under test conditions / methods familiar to those of ordinary skill in the art. When directly and clearly distinguishing an embodiment from the discussed prior art, the embodiment numbers are not approximate values ​​unless the word "about" is quoted. In addition, all alternatives listed herein are not equivalent.

[0322] Although there are alternatives to the various components, parameters, operating conditions, etc. described herein, this does not mean that those alternatives are necessarily equivalent and / or perform equally well. Unless otherwise stated, it is not intended that the alternatives are listed in a preferred order.

[0323] In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the embodiments shown are merely examples and should not be considered as limiting the scope of the present disclosure. Rather, the scope of the present disclosure is at least as broad as the following claims and their equivalents. Therefore, all that is within the scope and spirit of these claims is claimed herein.

Claims

1. A method comprising: receiving data on the position of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and a specified position of the structural element; determining a force command to damp the specified vibration mode frequency based at least in part on the position error signal and the specified vibration mode frequency of the structural element; as well as The force command is transmitted to an actuator so that the actuator applies a force to the structural element and damps vibrations of the structural element at least at the specified vibration mode frequency of the structural element. 2 . The method of claim 1 , wherein determining the force command further comprises applying a phase correction to the position error signal. 3 . The method of claim 2 , wherein determining the force command further comprises filtering the position error signal using a low pass filter. The method of claim 3 , wherein the low pass filter comprises a derivative control.

5. A method according to claim 3 or 4, wherein the phase correction is applied using the low pass filter.

6. The method of any preceding claim, wherein determining the force command further comprises filtering the position error signal using a bandpass filter.

7. The method of any preceding claim, wherein determining the force command further comprises filtering the position error signal using a notch filter.

8. A method according to any preceding claim, wherein data of the position of the structural element is received from a sensor coupled to the structural element at a location distal to the actuator.

9. A method according to any preceding claim, wherein the specified vibration mode frequency is 2 Hz to 10 kHz, 2 Hz to 5 kHz, 2 Hz to 1 kHz, 2 Hz to 500 Hz, 2 Hz to 300 Hz, 2 Hz to 200 Hz or 2 Hz to 100 Hz.

10. A method according to any preceding claim, wherein the prescribed vibration frequency is below a vibration mode frequency of the actuator.

11. The method of any preceding claim, wherein determining the force commands further comprises determining the force commands to damp a plurality of specified vibration mode frequencies of the structural element.

12. The method according to claim 11, wherein the structural element is an optical surface plate, a substrate stage or a mask stage of the exposure apparatus.

13. A system comprising: Exposure equipment, including structural elements; an actuator system coupled to the structural element, the actuator system comprising an actuator and a sensor; as well as The control system is configured to: receiving data from the sensor regarding the position of the structural element; determining a position error signal based at least in part on the position data and a specified position of the structural element; determining a force command to damp the specified vibration mode frequency based at least in part on the position error signal and the specified vibration mode frequency of the structural element; as well as The force command is transmitted to the actuator so that the actuator applies a force to the structural element and damps vibrations of the structural element at least at the specified vibration mode frequency of the structural element.

14. The system of claim 13, wherein the control system is further configured to apply a phase correction to the position error signal.

15. The system of claim 14, wherein the control system is further configured to filter the position error signal using a low pass filter.

16. The system of claim 15, wherein the low pass filter includes a derivative control.

17. The system of any one of claims 15 or 16, wherein the phase correction is applied via the low pass filter.

18. The system of any one of claims 13 to 17, wherein the control system is further configured to filter the position error signal using a bandpass filter.

19. The system of any one of claims 13 to 18, wherein the control system is further configured to filter the position error signal using a notch filter.

20. The system of any one of claims 13 to 19, wherein the sensor is spaced apart from the actuator on the structural element.

21. The system of any one of claims 13 to 20, wherein the specified vibration mode frequency is 2 Hz to 10 kHz, 2 Hz to 5 kHz, 2 Hz to 1 kHz, 2 Hz to 500 Hz, 2 Hz to 300 Hz, 2 Hz to 200 Hz, or 2 Hz to 100 Hz.

22. The system according to any one of claims 13 to 21, wherein the structural element is an optical surface plate, a substrate table or a mask table of the exposure apparatus.

23. A method comprising: receiving data on the position of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and a specified position of the structural element; filtering the position error signal using a low pass filter including a derivative control; applying a phase correction to the position error signal using the low pass filter; determining a force command to damp a specified vibration mode frequency of the structural element based at least in part on the filtered, phase-corrected position error signal; as well as The force command is transmitted to an actuator coupled to the structural element so that the actuator applies a force to the structural element and damps vibrations of the structural element at least at the specified vibration mode frequency of the structural element.

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