Methods and Systems

Abstract

A method for controlling vibration of a structural element of an exposure apparatus includes receiving data on 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 for damping a specified vibration mode frequency of the structural element based at least in part on the position error signal and the specified vibration mode frequency, and sending the force command to an actuator such that the actuator applies a force to the structural element to damp vibration of the structural element at least at the specified vibration mode frequency of the structural element.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims the benefits of U.S. Provisional Application No. 63 / 393,161, filed on 28 July 2022, which is incorporated herein by reference in its entirety.

[0002] This disclosure relates to a system and method for controlling and / or reducing vibrations of structural elements in precision systems such as lithography exposure apparatus. [Background technology]

[0003] In photolithography processes for manufacturing microelectronic devices such as liquid crystal displays and semiconductor devices (such as integrated circuits), exposure equipment is used to transfer a predetermined pattern on a photomask or reticle onto a substrate such as a photosensitive glass plate or wafer by irradiating the substrate with illumination light (e.g., an energy beam) via a projection optical system (e.g., including multiple lenses). In such systems, the reticle and substrate must be precisely aligned in order to expose the substrate and form desired features of a size of several nanometers. However, vibrations of the support structure of the exposure equipment and its various subsystems can cause the reticle, projection optical system, and / or substrate to move relative to each other during exposure, potentially adversely affecting the formation of features on the substrate. Vibrations of the support structure at relatively low frequencies can be particularly problematic. Passive mass dampers on such structures require cumbersome manual adjustment, and their effectiveness is often limited by space constraints within the machine. Therefore, improvements to systems for controlling vibrations of the support structure in lithography exposure equipment are needed. [Overview of the project]

[0004] Specific embodiments of the present disclosure relate to systems and methods for controlling or reducing vibrations of structural members or assemblies of precision systems such as lithography exposure apparatus. In a typical embodiment, the method includes receiving position data of a structural element of an exposure apparatus; determining a position error signal based at least partially on the position data and a specified position of the structural element; determining a force command to attenuate the specified vibration mode frequency of the structural element based at least partially on the position error signal and a specified vibration mode frequency; and transmitting the force command to an actuator so that the actuator applies force to the structural element and at least attenuates the vibration of the structural element at the specified vibration mode frequency.

[0005] In any or all of the disclosed embodiments, determining the force command further includes applying a phase correction to the position error signal.

[0006] In any or all of the disclosed embodiments, determining the force command further includes filtering the position error signal using a low-pass filter.

[0007] In any or all of the disclosed embodiments, the low-pass filter includes differential control.

[0008] In any or all of the disclosed embodiments, the phase correction is applied using the low-pass filter.

[0009] In any or all of the disclosed embodiments, determining the force command further includes filtering the position error signal using a bandpass filter.

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

[0011] In any or all of the disclosed embodiments, the positional data of the structural element is received from a sensor connected to the structural element at a location away from the actuator.

[0012] In any or all of the disclosed embodiments, the designated vibration mode frequencies are 2Hz to 10kHz, 2Hz to 5kHz, 2Hz to 1kHz, 2Hz to 500Hz, 2Hz to 300Hz, 2Hz to 200Hz, or 2Hz to 100Hz.

[0013] In any or all of the disclosed embodiments, the designated vibration frequency is lower than the vibration mode frequency of the actuator.

[0014] In any or all of the disclosed embodiments, determining the force command further includes determining the force command to attenuate a plurality of specified vibration mode frequencies of the structural element.

[0015] In any or all of the disclosed embodiments, the structural element is an optical platen, substrate stage, or mask stage of the exposure apparatus.

[0016] In another representative embodiment, the system comprises an exposure apparatus including a structural element, an actuator system connected to the structural element, the actuator system comprising an actuator and a sensor, and a control system that receives position data of the structural element from the sensor, determines a position error signal based at least partially on the position data and a specified position of the structural element, determines a force command to attenuate the specified vibration mode frequency based at least partially on the position error signal and a specified vibration mode frequency of the structural element, and transmits the force command to the actuator so that the actuator applies force to the structural element and at least attenuates the vibration of the structural element at the specified vibration mode frequency.

[0017] In any or all of the disclosed embodiments, the control system applies phase correction to the position error signal.

[0018] In any or all of the disclosed embodiments, the control system filters the position error signal using a low-pass filter.

[0019] In any or all of the disclosed embodiments, the low-pass filter includes differential control.

[0020] In any or all of the disclosed embodiments, the phase correction is applied by the low-pass filter.

[0021] In any or all of the disclosed embodiments, the control system filters the position error signal using a bandpass filter.

[0022] In any or all of the disclosed embodiments, the control system filters the position error signal using a notch filter.

[0023] In any or all of the disclosed embodiments, the sensor is spaced apart from the actuator on the structural element.

[0024] In any or all of the disclosed embodiments, the designated vibration mode frequencies are 2Hz to 10kHz, 2Hz to 5kHz, 2Hz to 1kHz, 2Hz to 500Hz, 2Hz to 300Hz, 2Hz to 200Hz, or 2Hz to 100Hz.

[0025] In any or all of the disclosed embodiments, the structural element is an optical platen, substrate stage, or mask stage of the exposure apparatus.

[0026] In another representative embodiment, the method includes receiving position data of a structural element of an exposure apparatus; determining a position error signal based at least partially on the position data and a specified position of the structural element; filtering the position error signal using a low-pass filter including differential control; applying phase correction to the position error signal using the low-pass filter; determining a force command to attenuate a specified vibration mode frequency of the structural element based at least partially on the filtered and phase-corrected position error signal; and transmitting the force command to an actuator connected to the structural element so that the actuator applies force to the structural element and attenuates the vibration of the structural element at least at the specified vibration mode frequency of the structural element.

[0027] The above and other purposes, features, and advantages of the disclosed technology will become more apparent from the following detailed description, which will proceed with reference to the attached drawings. [Brief explanation of the drawing]

[0028] [Figure 1] Figure 1 is a schematic diagram showing the configuration of a liquid crystal exposure apparatus according to the first embodiment. [Figure 2] Figure 2 shows the substrate stage device of the liquid crystal exposure apparatus shown in Figure 1. [Figure 3] Figure 3 is a schematic diagram of the substrate measurement system included in the liquid crystal exposure apparatus shown in Figure 1. [Figure 4] Figure 4 is a diagram (part 1) illustrating the operation of the substrate stage device. [Figure 5] Figure 5 is a diagram (part 2) illustrating the operation of the substrate stage device. [Figure 6] Figure 6 is a block diagram showing the input / output relationships of the main control unit, which is the main component of the control system for a liquid crystal exposure apparatus. [Figure 7] Figure 7 is a schematic side elevation view of an actuator system connected to a structural element according to one embodiment. [Figure 8]Figure 8 is a schematic diagram showing the structural elements and actuator system represented as a mass-spring-damper system. [Figure 9] Figures 9 and 10 are Bode plots showing the open-loop frequency response of the mass-spring-damper system of Figure 8 for various excitation forces. [Figure 10] Figures 9 and 10 are Bode plots showing the open-loop frequency response of the mass-spring-damper system of Figure 8 for various excitation forces. [Figure 11] Figure 11 is a schematic block diagram of a control system for controlling vibrations of a structural element at vibration mode frequencies according to one embodiment. [Figure 12] Figure 12 is a process flow diagram showing a typical method for controlling structural mode vibrations of a structural element according to one embodiment. [Figure 13] Figure 13 is a schematic block diagram of a control system for controlling vibrations of a structural element at multiple vibration mode frequencies according to one embodiment. [Figure 14] Figure 14 is a top view of an actuator system connected to a plate member according to one embodiment. [Figure 15] Figure 15 is a schematic block diagram of a control system for controlling the vibration of the plate member shown in Figure 14 at two vibration mode frequencies, according to one embodiment. [Figure 16A] Figures 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force is applied to the plate member shown in Figure 14. [Figure 16B] Figures 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force is applied to the plate member shown in Figure 14. [Figure 16C] Figures 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force is applied to the plate member shown in Figure 14. [Figure 17]Figure 17 shows Bode plots illustrating the amplitude and phase of the system's frequency response when no feedback control is used, when damping control of the first vibration mode is used, and when damping control of both the first and second modes is used. [Figure 18] Figure 18 is a side elevation view of another experimental system, which includes a beam member supported by two support members, with an actuator system attached to the beam member. [Figure 19] Figure 19 schematically shows the first and second vibration modes of the beam member in Figure 18. [Figure 20] Figure 20 is a Bode plot showing the amplitude and phase of the open-loop frequency response of system 700 as measured by two accelerometers of the actuator system. [Figure 21] Figure 21 is a Bode plot showing the open-loop frequency response of system 700 and the frequency response for control using position data derived from an accelerometer located in the same place as the actuator in Figure 18. [Figure 22A] Figures 22A and 22B include acceleration-versus-time and Fast Fourier Transform (FFT) plots showing the open-loop impulse response of the system (Figure 22A) and the impulse response of the system performing control using the position data derived from the first accelerometer in Figure 18 (Figure 22B). [Figure 22B] Figures 22A and 22B include acceleration-versus-time plots and Fast Fourier Transform (FFT) plots showing the open-loop impulse response of the system (Figure 22A) and the impulse response of the system to which control using position data derived from the first accelerometer in Figure 18 is applied (Figure 22B). [Figure 23] Figure 23 is a Bode plot showing the open-loop frequency response of the system in Figure 18 and the frequency response when control is performed using position data derived from the second accelerometer. [Figure 24A]Figures 24A and 24B include acceleration-versus-time plots and fast Fourier transform plots showing the open-loop impulse response of the system in Figure 18 (Figure 24A) and the impulse response of the system in Figure 18 when control is performed using position data derived from a second accelerometer (Figure 24B). [Figure 24B] Figures 24A and 24B include acceleration-versus-time plots and fast Fourier transform plots showing the open-loop impulse response of the system in Figure 18 (Figure 24A) and the impulse response of the system in Figure 18 when control is performed using position data derived from a second accelerometer (Figure 24B). [Figure 25] Figure 25 is a side elevation view of another embodiment of the experimental structural system. [Figure 26] Figures 26 to 28 are Bode plots showing the three structural vibration modes of the system in Figure 25. [Figure 27] Figures 26-28 are 8-bode plots showing the three structural vibration modes of the system in Figure 25. [Figure 28] Figures 26 to 28 are Bode plots showing the three structural vibration modes of the system in Figure 25. [Figure 29] Figure 29 is a schematic block diagram showing a control system configured to implement a peak filter control channel in parallel with an attenuation filter control channel, according to another embodiment. [Figure 30] Figures 30 and 31 are Bode plots of the dynamic response of the system in Figure 25 when controlled by the control system in Figure 29. [Figure 31] Figures 30 and 31 are Bode plots of the dynamic response of the system in Figure 25 when controlled by the control system in Figure 29. [Figure 32] Figure 32 includes graphs of acceleration vs. time and acceleration vs. frequency for the system in Figure 25 when controlled by the system in Figure 29. [Figure 33] Figure 33 is a top view of another embodiment of a structural system including a rectangular plate member and actuators and multiple accelerometer sensors connected to the plate member. [Figure 34] Figure 34 shows another embodiment of a control system that includes two control loops configured to control the four modes of oscillation of the structure in Figure 33. [Figure 35] Figure 35 is the Bode plot of the open-loop frequency response of the system in Figure 33 when excited by an impulse. [Figure 36] Figure 36 is a Bode plot of the frequency response of a system that controls four vibration modes based on force commands from the control system in Figure 34. [Figure 37A] Figures 37A and 37B include plots of acceleration versus time and acceleration versus frequency for the system shown in Figure 33. [Figure 37B] Figures 37A and 37B include plots of acceleration versus time and acceleration versus frequency for the system shown in Figure 33. [Figure 38] Figure 38 is a top-down plan view of another configuration of four accelerometers, actuators, and a vibrator on a plate member. [Figure 39] Figure 39 shows another embodiment of a control system that includes two control loops configured to control the four modes of oscillation of the structure in Figure 38. [Figure 40] Figure 40 shows the surface deformation of a rectangular plate in nine vibration modes, based on a finite element analysis model of the plate. [Figure 41] Figures 41 to 44 schematically show the input and output coordinates of the modal space model of structural elements in various vibration modes. [Figure 42] Figures 41 to 44 schematically show the input and output coordinates of the modal space model of structural elements in various vibration modes. [Figure 43] Figures 41 to 44 schematically show the input and output coordinates of the modal space model of structural elements in various vibration modes. [Figure 44] Figures 41 to 44 schematically show the input and output coordinates of the modal space model of structural elements in various vibration modes. [Figure 45]Figure 45 is a schematic diagram of an immersion microlithography system, which is another example of a precision system including a stage assembly as described herein. [Figure 46] Figure 46 is a schematic diagram of an extreme ultraviolet microlithography system, which is another example of a precision system including the stage assembly described herein. [Figure 47] Figure 47 is a process flow diagram illustrating exemplary steps related to the process for manufacturing semiconductor devices. [Figure 48] Figure 48 is a process flow diagram illustrating exemplary steps related to the processing of a substrate (e.g., a wafer), such as those performed in the process shown in Figure 47. [Figure 49] Figure 49 is a schematic diagram of a microlithography system as an exemplary precision system, comprising a stage assembly disclosed herein, including at least one holding device. [Figure 50] Figure 50 is a schematic block diagram showing a typical computer-controlled system for implementing the disclosed system and method. [Modes for carrying out the invention]

[0029] Specific embodiments of this disclosure relate to actuator systems and related control systems and methods that can be used to control / reduce / attenuate vibrations of structural elements in precision systems such as lithography exposure apparatus. In specific embodiments, the actuators and control systems described herein can be tuned to attenuate relatively low-frequency vibrations, such as resonant modes of structures excited by reaction forces applied by moving components of the system, such as substrate stages and mask stages. However, the control system can be configured to detect and attenuate structural mode vibrations having any frequency within the system's sampling rate frequency range and / or the actuator's amplifier bandwidth, such as 2 Hz to 10 kHz.

[0030] In certain embodiments, the actuator system may comprise an actuator, such as a voice coil motor, and one or more motion sensors, such as accelerometers, although other types of actuators and / or sensors may also be used. The actuators and sensors may be positioned at the same or different locations on the structural element. In certain embodiments, the positions of the actuators and sensors may be selected so that the sensors detect relatively large displacements of the structural element related to a particular vibration mode, and / or so that the force applied to the structural element by the actuator results in relatively large displacements of the structural element and thus increases the damping effect.

[0031] In certain embodiments, the control system described herein may be configured to compensate for phase delays in the system related to one or more of the following: sensor position (e.g., related to the vibration mode shape of the structural element), sensor bandwidth, and / or time delays related to signal processing and digital control. In certain embodiments, the control system may implement a combination of low-pass filters, band-pass filters, and / or one or more notch filters. In certain embodiments, one or more of the filters, such as low-pass filters, may include differential control. In certain embodiments, one or more of the filters, such as low-pass filters, may be configured to compensate for the aforementioned phase delays by applying phase correction to the position error signal received in a feedback control loop. In certain embodiments, the control system may include a plurality of control elements implemented in parallel, each control element comprising a combination of the filters described herein and configured to generate force commands to attenuate vibrations of a structural element at a specific vibration mode frequency while reducing coupling between modes. Thus, the control system described herein may be configured to attenuate vibrations of a structural element in one or more vibration modes, such as two-mode, three-mode, or four-mode. In certain embodiments, the control system may also be configured so that the actuator system can attenuate the mode frequencies of structural elements that are lower than the mode frequencies of the actuator-structure interaction, using a peak filter or the like.

[0032] By implementing the control methods described herein, the actuator systems and control systems of this disclosure can significantly reduce the amplitude of vibrations of structural elements excited by reaction forces from the relative motion of other structures in a precision system. The actuator systems and control systems can also significantly shorten the settling time of such structural elements, thereby significantly improving, for example, the substrate positioning accuracy and throughput of a lithography exposure apparatus.

[0033] Example 1: Lithography exposure apparatus

[0034] A typical embodiment of the first embodiment will be described using Figures 1 to 6.

[0035] Figure 1 schematically shows the structure of an exposure apparatus (here, a liquid crystal exposure apparatus 10) according to one embodiment. The liquid crystal exposure apparatus 10 is a step-and-scan type projection exposure apparatus, a so-called scanner, where the 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 (for example, a square shape) in plan view and can be used in liquid crystal display devices (flat panel displays), etc.

[0036] The liquid crystal exposure apparatus 10 includes an illumination system 12, a mask stage device 14 that holds a mask M on which a circuit pattern is formed, a projection optical system 16, the main body of the apparatus 18, a substrate stage device 20 that holds a substrate P on which a resist (for example, a photosensitive agent) is coated on its surface (the surface facing the +Z direction in Figure 1), and control systems for these. Hereinafter, the direction in which the mask M and substrate P are scanned relative to the projection optical system 16 during exposure will be described as the X-axis direction, the direction perpendicular to the X-axis direction in the horizontal plane will be described as the Y-axis direction, the direction perpendicular to the X and Y axes 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, Y and Z axes will be described as the θx direction, θy direction, and θz direction, respectively. Furthermore, the positions in the X, Y and Z axis directions will be described as the X position, Y position, and Z position, respectively.

[0037] In certain embodiments, the illumination system 12 is configured similarly to illumination systems disclosed, for example, in U.S. Patent No. 5,729,331, and can irradiate the mask M with exposure illumination light (illumination light) IL by emitting light from a light source (mercury lamp, laser diode, etc.) via a reflective mirror, dichroic mirror, shutter, wavelength-selective filter, and various lenses. As illumination light IL, for example, i-line (wavelength 365 nm), g-line (wavelength 436 nm), or h-line (wavelength 405 nm) light (or a composite light of i-line, g-line, and h-line) can be used.

[0038] A transmissive photomask is used as the mask M held by the mask stage device 14. A predetermined circuit pattern is formed on the lower surface of the mask M (the surface facing the -Z direction in Figure 1). The mask M is moved by the main control device 100 via a mask drive system 102 including actuators such as a linear motor and a ball screw device, with a predetermined long stroke in the scanning direction (X-axis direction), and is also finely moved as appropriate in the Y-axis direction and θz direction (see Figure 6). Position information of the mask M in the XY plane (including rotation amount information in the θz direction; the same applies hereinafter) can be acquired by the main control device 100 via a mask measurement system 104 including a measurement system such as an encoder system and an interferometer system.

[0039] The projection optical system 16 is located below the mask stage device 14. The projection optical system 16 is a so-called multi-lens projection optical system and can have a configuration similar to that of projection optical systems disclosed in U.S. Patent No. 6,552,775, etc., and comprises multiple lens modules that form an erect image in a bilateral telecentric 1:1 system.

[0040] In the liquid crystal exposure apparatus 10, when illumination light IL illuminates the illumination area on the mask M, the illumination light IL passes through (transmits) the mask M and, via the projection optical system 16, forms a projected image (partially erect image) of the circuit pattern of the mask M within the illumination area on the illuminated area (exposure area) on the substrate P which is conjugate to the illumination area. Then, as the mask M moves relative to the illumination area (illumination light IL) in the scanning direction, and the substrate P moves relative to the exposure area (illumination light IL) in the scanning direction, one shot area on the substrate P is scanned and exposed, and the pattern formed on the mask M is transferred to the shot area.

[0041] The main body 18 of the apparatus supports the mask stage apparatus 14 and the projection optical system 16 and is installed on the floor F in the cleanroom via a vibration isolation device 19. The main body 18 of the apparatus can be configured similarly to the main body of the apparatus disclosed in U.S. Patent Application Publication No. 2008 / 0030702 and has an upper mount portion 18a, a pair of intermediate mount portions 18b, and a lower mount portion 18c. Since the upper mount portion 18a is a member that supports the projection optical system 16, in this embodiment, the upper mount portion 18a will be referred to as the optical base plate 18a. In the scanning exposure operation using the liquid crystal exposure apparatus 10 in this embodiment, the position of the substrate P is controlled with respect to the illumination light IL irradiated via the projection optical system 16, so the optical base plate 18a that supports the projection optical system 16 functions as a reference member when controlling the position of the substrate P.

[0042] The substrate stage device 20 is used to precisely control the position of the substrate P relative to the projection optical system 16 (illumination light IL), and moves the substrate P along the horizontal plane (X-axis and Y-axis directions) with a predetermined long stroke, and also moves the substrate P minutely in the six degrees of freedom directions. The structure of the substrate stage device used in the liquid crystal exposure apparatus 10 is not particularly limited, but in the illustrated embodiment, as an example, a substrate stage device 20 with a so-called coarse-fine movement structure is used, which includes a gantry-type two-dimensional coarse-movement stage and a fine-movement stage that is moved minutely relative to the two-dimensional coarse-movement stage, as disclosed in U.S. Patent Application Publication No. 2012 / 0057140, etc.

[0043] The substrate stage apparatus 20 includes a fine adjustment stage 22, a Y coarse adjustment stage 24, an X coarse adjustment stage 26, and a support section (here, a weight cancellation device 28). 、 The system includes a pair of base frames 30 (one of the pair is not shown in Figure 1; see Figure 4), a substrate drive system 60 used to move each component of the substrate stage device 20 (see Figure 6), and a substrate measurement system 70 used to measure the positional information of each component (see Figure 6).

[0044] As shown in Figure 2, the fine-adjustment stage 22 comprises a substrate holder 32 and a stage body 34. The substrate holder 32 is formed in the shape of a rectangular plate (or box) in plan view (see Figure 4), and the substrate P is placed on its upper surface (substrate mounting surface). The dimensions of the upper surface of the substrate holder 32 in the X and Y axes are set to be approximately the same as the dimensions of the substrate P (actually slightly shorter). The substrate P is held by vacuum suction on the upper surface of the substrate holder 32 while it is placed on the upper surface of the substrate holder 32, thereby correcting its flatness almost entirely along the upper surface of the substrate holder 32 (overall). The stage body 34 comprises a rectangular plate (or box) member in plan view whose dimensions in the X and Y axes are shorter than those of the substrate holder 32, and is integrally connected to the lower surface of the substrate holder 32.

[0045] Returning to Figure 1, the Y coarse adjustment stage 24 is located below (-Z side) the fine adjustment stage 22 and is positioned on a pair of base frames 30. The Y coarse adjustment stage 24 has a pair of X beams 36, as shown in Figure 4. The pair of X beams 36 are positioned parallel to the Y axis at a predetermined distance apart. The pair of X beams 36 are mounted on the pair of base frames 30 via a mechanical linear guide device and are movable on the pair of base frames 30 in the Y axis direction.

[0046] Returning to Figure 1, the X-coarse adjustment stage 26 is located above (+Z side) the Y-coarse adjustment stage 24 and below the fine adjustment stage 22 (between the fine adjustment stage 22 and the Y-coarse adjustment stage 24). The X-coarse adjustment stage 26 is a rectangular plate-shaped member in plan view and is mounted on a pair of X-beams 36 (see Figure 4) of the Y-coarse adjustment stage 24 via a plurality of mechanical linear guide devices 38 (see Figure 2). It is movable in the X-axis direction relative to the Y-coarse adjustment stage 24 and moves integrally with the Y-coarse adjustment stage 24 in the Y-axis direction.

[0047] As shown in Figure 6, the substrate drive system 60 includes a first drive system 62 for finely moving the fine-adjustment stage 22 relative to the optical base plate 18a in six degrees of freedom directions (X-axis, Y-axis, Z-axis, θx, θy, and θz directions), a second drive system 64 for moving the Y-coarse-adjustment stage 24 on the base frame 30 (see Figure 1 for each) in a long stroke in the Y-axis direction, and a third drive system 66 for moving the X-coarse-adjustment stage 26 on the Y-coarse-adjustment stage 24 (see Figure 1 for each) in a long stroke in the X-axis direction. The types of actuators constituting the second drive system 64 and the third drive system 66 are not particularly limited, but as an example, linear motors and ball screw drivers can be used (a linear motor is shown in Figure 1, etc.).

[0048] The types of actuators constituting the first drive system 62 are not particularly limited, but as an example, Figure 2 shows a plurality of linear motors (voice coil motors) 40 that generate thrust in the X-axis, Y-axis, and Z-axis directions (the X linear motor is not shown in Figures 1 and 2). Each linear motor 40 has a stator attached to the X coarse-motion stage 26 and a movable part attached to the stage body 34 of the fine-motion stage 22, and the fine-motion stage 22 is supplied with thrust in six degrees of freedom directions to the X coarse-motion stage 26 via each linear motor 40. The detailed configurations of the first to third drive systems 62, 64, and 66 are disclosed as an example in U.S. Patent Application Publication No. 2010 / 0018950.

[0049] The main control device 100 applies thrust to the fine-motion stage 22 using the first drive system 62 so that the relative positions of the fine-motion stage 22 and the X-coarse-motion stage 26 (see Figure 1 for each) remain within a predetermined range in the X-axis and Y-axis directions. Here, when moving the fine-motion stage 22 with a long stroke in the X-axis or Y-axis direction, "remaining within a predetermined range of relative position" means that the X-coarse-motion stage 26 (or the X-coarse-motion stage 26 and Y-coarse-motion stage 24 when moving the fine-motion stage 22 in the Y-axis direction) and the fine-motion stage 22 move in the same direction at approximately the same speed. It is not necessary for the fine-motion stage 22 and the X-coarse-motion stage 26 to move in strict synchronization, and a predetermined relative movement (relative positional misalignment) is permitted.

[0050] Returning to Figure 2, the weight cancellation device 28 includes a weight cancellation device 42 that supports the weight of the fine-movement stage 22 from below, and a Y-step guide 44 that supports the weight cancellation device 42 from below.

[0051] The weight cancellation device 42 (also called the center pillar) is inserted into an opening formed in the X coarse-motion stage 26 and is mechanically connected to the X coarse-motion stage 26 at the height of the center of gravity via a plurality of connecting members 46 (also called the flexure device). The X coarse-motion stage 26 and the weight cancellation device 42 are connected by the plurality of connecting members 46 in a state of vibrational (physical) separation in the Z-axis direction, θx direction, and θy direction. The weight cancellation device 42 moves integrally with the X coarse-motion stage 26 in the X-axis and / or Y-axis direction by being pulled by the X coarse-motion stage 26.

[0052] The weight cancellation device 42 non-contactively supports the weight of the micro-movement stage 22 from below via a pseudo-spherical bearing device called a leveling device 48. This allows the micro-movement stage 22 to move relative to the weight cancellation device 42 in the X, Y, and θz directions, and to swing relative to the horizontal plane (relative movement in the θx and θy directions). The structure and function of the weight cancellation device 42 and the leveling device 48 are disclosed, for example, in U.S. Patent Application Publication No. 2010 / 0018950.

[0053] The Y-step guide 44 comprises a member extending parallel to the X-axis and is positioned between a pair of X-beams 36 of the Y-coarse stage 24 (see Figure 4). The upper surface of the Y-step guide 44 is set parallel to the XY plane (horizontal plane), and a weight cancellation device 42 is mounted on the Y-step guide 44 non-contact via an air bearing 50. The Y-step guide 44 functions as a base plate when the weight cancellation device 42 (i.e., the fine stage 22 and the substrate P) moves in the X-axis direction (scanning direction). The Y-step guide 44 is mounted on the lower mount portion 18c via a mechanical linear guide device 52, and is movable in the Y-axis direction relative to the lower mount portion 18c, while relative movement in the X-axis direction is restricted.

[0054] The Y-step guide 44 is mechanically connected to the Y-coarse stage 24 (a pair of X-beams 36) via a plurality of connecting members 54 at the height of its center of gravity (see Figure 4). The connecting members 54, like the connecting members 46 described above, are flexure devices that connect the Y-coarse stage 24 and the Y-step guide 44 in vibration (physical) directions of 5 of the 6 degrees of freedom, excluding the Y-axis direction. The Y-step guide 44 moves integrally with the Y-coarse stage 24 by being pulled by the Y-coarse stage 24.

[0055] As shown in Figure 4, the pair of base frames 30 each have members extending parallel to the Y-axis and are installed parallel to each other on the floor F (see Figure 1). The base frames 30 are physically (or vibratively) separated from the main body 18 of the device.

[0056] Next, we will describe the substrate measurement system 70 for acquiring positional information in the six degrees of freedom directions of the substrate P (actually the micro-movement stage 22 that holds the substrate P).

[0057] Figure 3 shows a schematic diagram of the substrate measurement system 70. The substrate measurement system 70 comprises a first measurement system (here, a fine-motion stage measurement system 76 (see Figure 6)) which includes a first scale (here, an upward scale 72) on the Y coarse-motion stage 24 (associated with the Y coarse-motion stage 24) and a first head (here, a downward X head 74x and a downward Y head 74y) on the fine-motion stage 22, and a second measurement system (here, a coarse-motion stage measurement system 82 (see Figure 6)) which includes a second scale (here, a downward scale 78) on the optical table 18a (see Figure 2) and a second head (here, an upward X head 80x and an upward Y head 80y) on the Y coarse-motion stage 24. Note that in Figure 3, the fine-motion stage 22 is modeled as a member that holds the substrate P. Also, the grating spacing (pitch) of the diffraction gratings on scales 72 and 78, respectively, is shown to be significantly wider than in reality. The same applies to the other figures. Furthermore, since the distance between each head and each scale is significantly shorter than the distance between the laser light source and the bar mirror in conventional optical interferometer systems, the effect of air fluctuations is smaller than in optical interferometer systems, allowing for highly accurate position control of the substrate P and improving exposure accuracy.

[0058] The upward scale 72 is fixed to the upper surface of the scale base 84. As shown in Figure 4, one scale base 84 is positioned on each of the +Y and -Y sides of the fine adjustment stage 22. As shown in Figure 2, the scale base 84 is fixed to the X-beam 36 of the Y-coarse adjustment stage 24 via an L-shaped arm member 86 when viewed from the X-axis direction. Therefore, the scale base 84 (and the upward scale 72) can move integrally with the Y-coarse adjustment stage 24 in the Y-axis direction with a predetermined long stroke. As shown in Figure 4, two arm members 86 are provided spaced apart in the X-axis direction for one X-beam 36, but the number of arm members 86 is not limited to this and can be increased or decreased as appropriate.

[0059] The scale base 84 is a member that extends parallel to the X-axis, and its length in the X-axis direction is set to be about twice the length in the X-axis direction of the substrate holder 32 (i.e., the substrate P (not shown in Figure 4)) (similar to that of the Y-step guide 44). The scale base 84 is preferably made of a material that is resistant to thermal deformation, such as ceramics. The same applies to the scale base 92 and head bases 88 and 96, which will be described later.

[0060] The upward-facing scale 72 is a plate-shaped (strip-shaped) member extending in the X-axis direction, and a reflective two-dimensional grid (a so-called grating) is formed on its upper surface (the surface facing the +Z side (upward side)) with two mutually orthogonal axis directions (in this embodiment, the X-axis and Y-axis directions) as periodic directions.

[0061] The head base 88 is fixed to the center of the +Y and -Y sides of the substrate holder 32 via arm members 90 corresponding to the scale base 84 described above (see Figure 2). The downward-facing heads 74x and 74y (see Figure 3) are fixed to the lower surface of the head base 88, respectively.

[0062] In the micro-movement stage measurement system 76 of this embodiment (see Figure 6), as shown in Figure 3, two downward-facing X-heads 74x and two downward-facing Y-heads 74y are arranged spaced apart in the X-axis direction on a single head base 88. Each of the heads 74x and 74y irradiates the corresponding upward-facing scale 72 with measurement light and receives light (diffracted light in this case) from the upward-facing scale 72. The light from the upward-facing scale 72 is supplied to a detector, and the output of the detector is supplied to the main control device 100 (see Figure 6). The main control device 100 determines the relative movement of each head 74x and 74y with respect to the scale 72 based on the output of the detector. In this specification, "head" refers to the part that irradiates the diffraction grating with measurement light and the part into which light from the diffraction grating is incident, and the head itself shown in each figure does not need to have a light source or detector.

[0063] As described above, in the micro-movement stage measurement system 76 of this embodiment (see Figure 6), four X linear encoder systems are configured by a total of four downward X heads 74x (two each on the +Y side and -Y side of the substrate P) and corresponding upward scales 72, and four Y linear encoder systems are configured by a total of four downward Y heads 74y (two each on the +Y side and -Y side of the substrate P) and corresponding upward scales 72. The main control device 100 (see Figure 6) uses the outputs of the four X linear encoder systems and the four Y linear encoder systems described above to acquire position information (hereinafter referred to as "first information") of the micro-movement stage 22 (substrate P) in the X-axis direction, Y-axis direction, and θz direction.

[0064] Here, the upward scale 72 is set so that the measurable distance in the X-axis direction is longer than the measurable distance in the Y-axis direction. Specifically, as shown in Figure 4, the length of the upward scale 72 in the X-axis direction is about the same as the length of the scale base 84, and is set to be long enough to cover the movable range of the micro-movement stage 22 in the X-axis direction. On the other hand, the width dimension (Y-axis direction) of the upward scale 72 (and the distance between a pair of adjacent heads 74x, 74y in the Y-axis direction) is set to be long enough so that even when the micro-movement stage 22 is moved in the Y-axis direction relative to the upward scale 72, the measurement light from each head 74x, 74y does not deviate from the corresponding grid plane (measurement target surface) of the upward scale 72.

[0065] Next, the operation of the micro-movement stage measurement system 76 (see Figure 6) will be explained using Figures 4 and 5. Figures 4 and 5 show the substrate stage device 20 before and after the micro-movement stage 22 moves in a long stroke in the X-axis and Y-axis directions. Figure 4 shows the micro-movement stage 22 positioned approximately in the center of the movable range in the X-axis and Y-axis directions, while Figure 5 shows the micro-movement stage 22 positioned at the +X-side stroke end of the movable range in the X-axis direction and at the -Y-side stroke end in the Y-axis direction.

[0066] As can be seen from Figures 4 and 5, regardless of the position of the micro-movement stage 22 in the Y-axis direction, the measurement light from the heads 74x and 74y attached to the micro-movement stage 22 will never deviate from the grid plane of the upward scale 72, even when the micro-movement stage 22 is moved in the Y-axis direction. Furthermore, when the micro-movement stage 22 moves in a long stroke in the X-axis direction, the measurement light from each of the downward heads 74x and 74y will never deviate from the grid plane of the upward scale 72.

[0067] Next, the coarse stage measurement system 82 (see Figure 6) will be described. As can be seen from Figures 1 and 4, the coarse stage measurement system 82 of this embodiment has two downward scales 78 (i.e., a total of four downward scales 78) arranged spaced apart in the X-axis direction on the +Y side and -Y side of the projection optical system 16 (see Figure 1). The downward scales 78 are fixed to the lower surface of the optical platen 18a via a scale base 92 (see Figure 2). The scale base 92 is a plate-shaped member extending in the Y-axis direction, and its length in the Y-axis direction is set to be approximately the same as (actually slightly longer than) the movable distance in the Y-axis direction of the fine stage 22 (i.e., the substrate P (not shown in Figure 4)).

[0068] The downward scale 78 is a plate-shaped (strip-shaped) member extending in the Y-axis direction, and on its lower surface (the surface facing the -Z side (downward side)), a reflective two-dimensional grating (a so-called grating) is formed with two mutually orthogonal axes (in this embodiment, the X-axis and Y-axis directions) as the periodic directions, similar to the upward scale 72 described above. The grating pitch of the diffraction grating on the downward scale 78 may be the same as or different from the grating pitch of the diffraction grating on the upward scale 72.

[0069] As shown in Figure 2, a head base 96 is fixed to each of the pair of scale bases 84 of the Y coarse adjustment stage 24 via an L-shaped arm member 94 when viewed from the X-axis direction. The head bases 96 are positioned near the +X and -X ends of the scale bases 84, respectively, as shown in Figure 4. Each upward-facing head 80x, 80y is fixed to the upper surface of the head base 96, as shown in Figure 3. Thus, a total of four head bases 96 (and upward-facing heads 80x, 80y) are movable in the Y-axis direction integrally with the Y coarse adjustment stage 24.

[0070] In the coarse stage measurement system 82 of this embodiment (see Figure 6), as shown in Figure 3, two upward X heads 80x and two upward Y heads 80y are arranged spaced apart in the Y-axis direction on a single head base 96. Each of the heads 80x and 80y irradiates a corresponding downward scale 78 with measurement light and receives light (diffracted light in this case) 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 control device 100 (see Figure 6). Based on the output of the detector, the main control device 100 obtains the relative movement of each head 80x and 80y with respect to the scale 78. As described above, in the coarse stage measurement system 82 of this embodiment, eight X linear encoder systems are configured by a total of eight upward X heads 80x and their corresponding downward scales 78, and eight Y linear encoder systems are configured by a total of eight upward Y heads 80y and their corresponding downward scales 78. The main control unit 100 (see Figure 6) appropriately uses the outputs of the eight X linear encoder systems and eight Y linear encoder systems described above to acquire position information (hereinafter referred to as "second information") of the Y coarse motion stage 24 in the X-axis direction, Y-axis direction, and θz direction.

[0071] Furthermore, the upward-facing scale 72 fixed on the scale base 84 and the upward-facing heads 80x and 80y, which are integrally fixed to the scale base 84 via the head base 96, are arranged such that their relative positions are constant and known. Hereinafter, information regarding the relative positional relationship between the upward-facing scale 72 and the upward-facing heads 80x and 80y integrally fixed thereto will be referred to as "third information". In this specification, the upward-facing scale 72 and the upward-facing heads 80x and 80y have been described as being arranged such that their relative positions are constant, but the liquid crystal exposure apparatus 10 may be equipped with a measurement system for measuring the relative positions of the two. The same applies to each embodiment described below.

[0072] Based on the first to third pieces of information described above, the main control device 100 (see Figure 6) acquires positional information of the micro-movement stage 22 (substrate P) in the XY plane with respect to the optical platen 18a (projection optical system 16), and uses the substrate driving system 60 (see Figure 6) described above to control the position of the substrate P relative to the projection optical system 16 (illumination light IL).

[0073] Thus, in the substrate measurement system 70 of this embodiment, the position information of the Y coarse motion stage 24, which moves with a long stroke in the Y-axis direction, is acquired by the coarse motion stage measurement system 82, which includes a downward scale 78 that has a longer measurable distance in the Y-axis direction than in the X-axis direction (the Y-axis direction is the main measurement direction). Similarly, the position information of the fine motion stage 22, which moves with a long stroke in the X-axis direction, is acquired by the fine motion stage measurement system 76, which includes an upward scale 72 that has a longer measurable distance in the X-axis direction than in the Y-axis direction (the X-axis direction is the main measurement direction). In other words, in the coarse motion stage measurement system 82 and the fine motion stage measurement system 76, the direction of movement of each encoder head (74x, 74y, 80x, 80y) coincides with the main measurement direction of the corresponding scale (72, 78).

[0074] Furthermore, the main control device 100 uses the Z-tilt position measurement system 98 (see Figure 6) to acquire position information for the Z-axis, θx, and θy directions (hereinafter referred to as the "Z-tilt direction") of the micro-movement stage 22 (substrate P). The configuration of the Z-tilt position measurement system 98 is not particularly limited, but as an example, a measurement system using a displacement sensor attached to the micro-movement stage 22, as disclosed in U.S. Patent Application Publication No. 2010 / 0018950, can be used.

[0075] Although not shown in the diagram, the substrate measurement system 70 also has a measurement system for acquiring position information of the X coarse adjustment stage 26. In this embodiment, the position information of the fine adjustment stage 22 (substrate P) in the X-axis direction is acquired via the Y coarse adjustment stage 24 with the optical base plate 18a as the reference, so the measurement accuracy of the X coarse adjustment stage 26 itself does not need to be the same as that of the fine adjustment stage 22. The position measurement of the X coarse adjustment stage 26 may be performed based on the output of the fine adjustment stage measurement system 76 described above and the output of a measurement system (not shown) that measures the relative position between the X coarse adjustment stage 26 and the fine adjustment stage 22, or it may be performed using an independent measurement system.

[0076] In the liquid crystal exposure apparatus 10 configured as described above (see Figure 1), under the control of the main control device 100 (see 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, the main control device 100 performs alignment measurement using an alignment detection system (not shown), and after the alignment measurement is completed, step-and-scan exposure operations are sequentially performed on multiple shot areas set on the substrate P. During the alignment measurement operation and the step-and-scan exposure operation, the position information of the micro-movement stage 22 is measured by the substrate measurement system 70.

[0077] According to the liquid crystal exposure apparatus 10 of this embodiment described above, the position of the micro-movement stage 22 (substrate P) is measured using a substrate measurement system 70 including an encoder system. Compared to conventional measurements using an optical interferometer system, the influence of air fluctuations is reduced, allowing for high-precision position control of the substrate P and improving exposure accuracy.

[0078] Furthermore, since the substrate measurement system 70 measures the position of the substrate P using a downward scale 78 fixed to the optical table 18a (main body of the device 18) as a reference (via an upward scale 72), the position of the substrate P can be measured using the projection optical system 16 as a substantially reference. This allows for position control of the substrate P using the illumination light IL as a reference, thereby improving exposure accuracy.

[0079] Furthermore, the configuration of the substrate measurement system 70 described above can be modified as appropriate, as long as the positional information of the micro-movement stage 22 (substrate P) can be acquired with the desired accuracy within the movable range of the micro-movement stage 22.

[0080] In other words, in the above embodiment, a long scale having a length similar to that of the scale base 84 was used as the upward scale 72, but the scale is not limited to this, and scales with a shorter length in the X-axis direction may be arranged at predetermined intervals in the X-axis direction, similar to the encoder system disclosed in International Publication No. 2015 / 147319. In this case, a gap is formed between a pair of adjacent scales in the X-axis direction, so by making the distance in the X-axis direction between each of a pair of adjacent heads 74x and 74y wider than the gap, one of the heads 74x and one of the heads 74y can always face the scale. The relationship between the downward scale 78 and the upward heads 80x and 80y is similar.

[0081] Furthermore, while the upward scale 72 is positioned on both the +Y and -Y sides of the fine-adjustment stage 22, the scale is not limited to this arrangement and may be positioned on only one side (either the +Y or -Y side). As mentioned above, if only one upward scale 72 is provided and multiple scales are positioned at predetermined intervals (gap between scales) in the X-axis direction, the number and arrangement of each head 74x, 74y should be set so that at least two downward X-heads 74x (or downward Y-heads 74y) are always facing the scale, enabling constant position measurement of the fine-adjustment stage 22 in the θz direction. The same applies to the downward scale 78; the number and arrangement of the downward scale 78 and upward heads 80x, 80y can be changed as appropriate, as long as constant position measurement of the Y-coarse-adjustment stage 24 in the X-axis, Y-axis, and θz directions is possible.

[0082] Furthermore, while the upward scale 72 and downward scale 78 have two-dimensional diffraction gratings formed with the X-axis and Y-axis directions as periodic directions, an X-diffraction grating with the X-axis direction as periodic and a Y-diffraction grating with the Y-axis direction as periodic may be formed separately on scales 72 and 78. Also, although the two-dimensional diffraction grating in this embodiment has the X-axis and Y-axis directions as periodic directions, the periodic directions of the diffraction grating are not limited to these and can be changed as appropriate, as long as the position measurement of the substrate P in the XY plane can be performed with the desired accuracy.

[0083] Alternatively, a downward-facing displacement sensor may be attached to the head base 88, and this sensor may be used to measure the Z-tilt position information of the substrate P with respect to the scale base 84 (or the reflective surface of the upward-facing scale 72). Furthermore, at least three of the multiple downward-facing heads 74x, 74y may be configured as two-dimensional heads (so-called XZ heads or YZ heads) capable of measuring both the position parallel to the horizontal plane and the vertical direction, and the Z-tilt position information of the substrate P may be acquired using the two-dimensional heads with respect to the grid surface of the upward-facing scale 72. Similarly, the Z-tilt position information of the Y-coarse adjustment stage 24 may be measured with respect to the scale base 92 (or the downward-facing scale 78). As the XZ head or YZ head, for example, an encoder head with a configuration similar to the displacement sensor head disclosed in U.S. Patent No. 7,561,280 can be used.

[0084] Further details relating to the liquid crystal exposure apparatus 10 are described in U.S. Patent No. 10,670,977, which is incorporated herein by reference.

[0085] Example 2: Active vibration damping actuator system and control method

[0086] As the various stage assemblies of the exposure apparatus 10 (e.g., the mask stage apparatus 14 and / or the substrate stage apparatus 20) move in the step-and-scan operation described above, reaction forces generated by various linear motors or other stage drivers may be transmitted to the fixed structural elements of the apparatus. These reaction forces may cause the structural elements of the apparatus to vibrate, and in certain situations, may excite vibrations at the resonant mode frequencies of the structural elements. In certain embodiments, such vibrations may have frequencies of 2 Hz to 10 kHz, e.g., 5 Hz to 10 kHz, 100 Hz to 10 kHz, 100 Hz to 5 kHz, less than 10 kHz, less than 5 kHz, less than 3 kHz, less than 2 kHz, less than 1 kHz, less than 500 Hz, less than 300 Hz, less than 200 Hz, or less than 100 Hz. Such vibrations, especially low-frequency vibrations (e.g., less than 500 Hz), can be particularly problematic for structural elements that support components or equipment that must be precisely aligned with the substrate P, and / or structural elements that serve as positional references for various stage assemblies, because the amplitude of such vibrations tends to be relatively large.

[0087] One such structural element of the exposure apparatus 10 is the optical platen 18a, as described above, which supports the projection optical system 16 and also functions as a reference for the substrate measurement system 70 used to control the position of the substrate P. In certain embodiments, an actuator system can be used to actively dampen / reduce / control vibrations of structural elements such as the optical platen 18a. In certain embodiments, the actuator system may comprise one or more actuators, one or more sensors, and a controller or control system (e.g., a main control unit 100 or another system) that controls the operation of the actuators to dampen vibrations of the structural elements based on data from the sensors.

[0088] For example, Figure 7 shows a typical example of an actuator system 200 comprising an actuator 202 attached to or connected to a structural element 204 (also called a structural member). The actuator system 200 may further comprise several sensors. A first sensor 206A is positioned in the same location as the actuator 202 (e.g., attached to the actuator 202), and a second sensor 206B is shown spaced apart from the actuator 202 and connected to the structural element 204. The system may comprise any number of actuators and any number of sensors, depending, 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 actuators and / or sensors may be positioned at any location on the structural element, such as the top or bottom surface, the side surface, or they may be incorporated into the body of the structural element.

[0089] In certain embodiments, the actuator 202 may be any type of electric actuator having a sufficiently fast response time, such as a voice coil motor (VCM), piezo actuator, linear motor, or reluctance actuator.

[0090] In certain embodiments, sensors 206A and 206B may be acceleration or vibration sensors such as accelerometers, 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 example, the sensor is configured as an accelerometer, but other types of sensors may also be used.

[0091] Figure 8 is a schematic diagram showing a structural element 300 to be controlled / damped together with an actuator system 302 represented as a mass-spring-damper system. The structural element 300 is shown connected to an absolute reference (e.g., the ground) 304 by a spring 306 and a damper 308. In Figure 8, the actuator system 302, representing the actuator and an accelerometer sensor located at the same position, is connected to the structural element 300 by a spring 310 and a damper 312. The motion of the structural element 300 relative to the ground 304 can be determined by the mass of the structural element, the spring constant of the spring 306, and the damping coefficient of the damper 308. The mass of the structural element 300 and the spring constant of the spring 306 can determine the vibration mode frequency of the structural element 300. In the example of an exposure apparatus, the structural element 300 can be analogous to an optical platen, a substrate stage, a mask stage, or other structure in the machine to which the actuator system 302 is connected.

[0092] The motion of the actuator system 302 relative to the structural element 300 can 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 can 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 the actuator system vibrates relative to the structural element while the actuator is operating. In certain embodiments, the system can be designed such that the mode frequency of the actuator system 302 is smaller than the mode frequency of the structural element 300, thereby allowing the actuator system 302 to vibrate relative to the structural element. 300 This allows for more efficient damping of structural mode vibrations, although this is not essential, as will be demonstrated in subsequent examples herein.

[0093] When the 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-headed arrow 314 indicates the relative motion between the actuator system 302 and the structural element 300 when the actuator is activated. Figure 9 shows the open-loop frequency response of the mass-spring-damper system of Figure 8 when a disturbance force is applied by the actuator system 302. Structural mode vibrations of the structural element 300 are observed between 30 Hz and 40 Hz, and mode vibrations of the actuator system 302 are observed between 20 Hz and 30 Hz. A phase drop of 180° is observed for each mode.

[0094] Figure 10 shows the open-loop frequency response of the system in Figure 8 when an external disturbance force (e.g., an impulse) is applied to the structural element 300 by an exciter placed between the ground 304 and the structural element 300, separate from the actuator system. The force applied by the exciter is represented by arrow 316 in Figure 8. The vibration mode frequencies of the actuator system are not visible in Figure 10.

[0095] In certain embodiments, vibrations of the structural element 300 caused by disturbance forces can be attenuated by operating the actuator system 302 according to a control scheme that includes the vibration frequency of the structural element to be attenuated or phase correction to compensate for one or more of the following in the control system: amplifier bandwidth, sensor signal adjustment, and / or digital control time delay.

[0096] A typical embodiment of the feedback control system 400 is shown in Figure 11. The ground, structural elements, and the mass-spring-damper system of the actuator system are represented by box 402, which will be referred to as the structural system below. The control system 400 may further include an integral element 404 (also called an integral and filter tool or module) and a filter controller or filter control element 406. The figure shows how a disturbance force d acts on the structural system 402, resulting in acceleration and motion (e.g., vibration) of the structural system 402. In a particular embodiment, the dynamic response of the structural system 402 (e.g., plant response) can be given by the transfer function P(s) of Equation 1 below, where m is the inertia of the vibration mode of the controlled system, and d r ω is the damping ratio, r is the specific vibration frequency to be damped.

number

[0097] When the structural system 402 is disturbed by an external disturbance force d, the acceleration of the actuator can be determined by an accelerometer sensor located in the same place, and the acceleration signal can be provided to the integrating element in block 404. In certain embodiments, the integrating element 404 can integrate the acceleration signal received from the accelerometer sensor to obtain a position signal (for example, the accelerometer signal can be integrated twice by the integrating element). The integrating element 404 can also filter the accelerometer signal with one or more filters to select a specific frequency or frequency band. For example, in certain embodiments, the integrating element 404 can filter the signal with a high-pass filter, thereby reducing low-frequency drift of the signal from the accelerometer sensor. A typical transfer function H of the integrating element 404 representing the combination of integration of the accelerometer signal and high-pass filtering. a2p (s) is given by the following equation 2. Here, d a ω is the damping ratio, a This is the cutoff frequency of the high-pass filter.

number

[0098] The obtained position signal (also called position data) can be subtracted in the summing junction 408 from a position command signal x(s) representing a specified position of the structural system 402. In certain embodiments, the position command x(s) (e.g., a specified position of a structural element) may be zero if vibration / motion of the structural system 402 is undesirable. By subtracting the position signal from the position command signal x(s), a position error signal can be obtained, which can be supplied to the filter control element 406.

[0099] The filter control element 406 can determine a force command u, which is transmitted to the actuator of the actuator system, causing the actuator to apply force to the structural element. In the following description, u is referred to as a force command, but it may also be a current command. In Figure 11, the force command u is shown to be transmitted from the filter control element 406 and act on the structural system 402 to dampen vibrations of the structural system.

[0100] 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 a force command u. In certain embodiments, the filter control element 406 may apply a combination of a low-pass filter, a band-pass filter, and a notch filter, including differential control referred to below as a damping filter. A typical transfer function C(s) of the filter control element 406 is given by the following equation 3, where H damp (s) is the transfer function of the attenuation filter, and H bandpass (s) is the transfer function of the bandpass filter, and H notch(s) is the transfer function of the notch filter. The filter can be applied sequentially (e.g., in series) to the input signal. The transfer functions of the attenuation filter, the band-pass filter, and the notch filter are multiplied in Equation 3. The order of the filters in Equation 3 is only an example, and the filters can be applied to the input signal in any order.

Number

[0101] In certain embodiments, the attenuation filter can include a derivative control term (also called an attenuation control term or a velocity control term) and a low-pass filter term. For example, in certain embodiments, the transfer function H damp (s) of the attenuation filter can be given by Equation 4 below. Here, k d is the attenuation gain, k d ω r s is the derivative control term (also called the attenuation coefficient) of the transfer function, and the equation

Number

Number

[0102] In certain embodiments, the low-pass filter can be under-damped (e.g., d r < 1), critically damped (e.g., d r = 1), or over-damped (e.g., d r > 1) according to the specific requirements of the system. In certain embodiments, the damping ratio d r can be set to 0.05 to 10 according to the frequency of the controlled object. In certain embodiments, increasing the damping ratio broadens the control frequency range but may also be related to the coupling between modes. In certain embodiments, the gain of the control system can be adjusted by changing the attenuation gain k d of the derivative control term of the attenuation filter.

[0103] In a particular embodiment, the transfer function of the notch filter may be given by Equation 5, where d1 and d2 are the attenuation ratios, and ω n This is the target frequency for the notch filter.

number

[0104] In certain embodiments, the target frequency ω of the notch filter n The target mode frequency is ω r It may be a different vibration mode of a different structural element. For example, the frequency ω of a notch filter. n This could be another vibration mode of the structure excited in response to the force command u of the actuator, but it does not necessarily have to be the resonant mode frequency of the structural element.

[0105] In a particular embodiment, the transfer function of the bandpass filter is given by Equation 6, where d bp This is the damping ratio.

number

[0106] In certain embodiments, the phase of the damping control force command u can be aligned with the target resonant frequency of the structural element being damped. In certain embodiments, phase alignment can be achieved using a damping filter. For example, in certain embodiments, the structural system transfer function P(s) and the integral 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.

number

[0107] In a particular embodiment, the phase angle ∠C(jω) of the filter control element transfer function r ) is the phase angle ∠H of the attenuation 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 ) can be the sum of ). In certain embodiments, the phase angle ∠H of the bandpass filter transfer function bandPass (jω r ) can be zero.

[0108] In a particular embodiment, the phase lag θ of the system is the phase angle ∠P(jω) of the structural transfer function, as shown in Equation 8 below. r ), the phase angle ∠H of the integral element transfer function a2p (jω r ), and the phase angle ∠H of the notch filter transfer function notch (jω r It can be defined as the sum of ).

number

[0109] In certain embodiments, the phase angle ∠H of the attenuation filter transfer function damp (jω r By setting ) to equal to -θ as shown in Equation 9 below, it is possible to adjust the attenuation filter to compensate for the phase lag θ of the system.

number

[0110] Applying Euler's formula, the transfer function H of the damping filter can be obtained by using one of the two equations in the system of Equation 10 below. damp Phase correction can be applied to (s).

number

[0111] Attenuation filter transfer function H dampThe result of multiplying (s)(Equation 4) by each of the two equations in the system of Equation 10 is given by the following Equation 11. In a particular embodiment, the damping filter transfer function H damp If the phase angle of (s) is equal to -θ as in Equation 9, then the second equation of the system in Equation 11 below can avoid the generation of a DC term. Avoiding the generation of a DC term may be advantageous in certain embodiments, as the DC term results in the application of a constant position and / or constant force to the structural element by the actuator, which can hinder vibration damping.

number

[0112] Phase correction can also be performed using a bandpass filter or a notch filter in the manner described above. The total amount of phase correction can also be distributed among attenuation filters, bandpass filters, and / or notch filters, depending on the specific characteristics of the system.

[0113] Therefore, the filter control element 406 applies a phase-corrected attenuation filter H to the position error signal received from the summing junction 408. damp The signal is filtered using (s) (for example, by applying a phase-compensated low-pass filter with differential control), and the phase-compensated signal output of the attenuation filter is filtered through a band-pass filter H bandpass Filtered with (s), the output of the bandpass filter is notch filter H notch The force command u can be determined by filtering by (s). The resulting force command u is then sent to the actuator.

[0114] In certain embodiments, the control system described herein may be configured to control / reduce vibrations of structural elements having any frequency within the control sampling rate limit of the system and / or within the amplifier bandwidth of the actuator. Thus, in certain embodiments, the damping filter or target frequency ω may be specified. rThis can be 2Hz to 10kHz, for example, 5Hz to 10kHz, 100Hz to 10kHz, 100Hz to 5kHz, 10kHz or less, 5kHz or less, 3kHz or less, 2kHz or less, 1kHz or less, 500Hz or less, 300Hz or less, 200Hz or less, or 100Hz or less.

[0115] 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 differential control. For example, since the damping force is the damping ratio of the system multiplied by the velocity, the system can be damped using proportional control of velocity, integral control of acceleration, or differential control of position.

[0116] Figure 12 shows a typical method for reducing vibration of a structural element using the actuator and control systems described herein. In process block 420, position data (e.g., position signal) of the structural element of the exposure apparatus can be received (e.g., from an integrating element after integrating and filtering the accelerometer signal). In process block 422, a position error signal can be determined for a specified position (or trajectory), for example, by subtracting position data / signal from a specified position. In process block 424, a force command can be determined at least in part based on a specified vibration mode frequency of the structural element to be damped and the position error signal. In certain embodiments, determining the force command may include filtering the position error signal using a low-pass filter (e.g., a low-pass filter with differential control), 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 can be performed in any combination and in any order. In certain embodiments, determining the force command may include applying phase correction to the position error signal using a low-pass filter, for example. In process block 426, the resulting force command can be transmitted to the actuator so that the actuator applies force to the structural element and dampens the vibration of the structural element at least at a specified vibration mode frequency of the structural element.

[0117] Example 3: Control system and method for attenuating multiple vibration mode frequencies

[0118] In certain cases, the control method described above can be adapted to control / dampend vibrations of structural elements at multiple frequencies, such as multiple resonant mode frequencies of the structural elements. Figure 13 shows another embodiment of a feedback control system 500 in which control of multiple frequency / vibration modes is performed in parallel. The feedback control system 500 shown in Figure 13 has a block 502 representing the plant dynamics of the controlled mass-spring-damper system, which can show the response to a disturbance force d given by the transfer function P(s) of Equation 1 above. The control system 500 has a transfer function H given in Figure 11 and Equation 2 a2p The system may further include an integral element 504 that can operate as described above with reference to (s). After the position signal obtained by the integral 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 that are implemented in parallel. In certain embodiments, the number of filter control elements 506 can correspond to the number of vibration frequencies of the structural element controlled by the actuator system. For example, in certain embodiments, each filter control element 506 can perform a combination of phase-compensated damping filter control, bandpass filter control, and notch filter control, as described above. Each filter control element 506 can be tuned to dampen a specific target frequency, such as a specific vibration mode frequency of the structural element.

[0119] The outputs of the filter control elements 506 are added at the summing junction 508, resulting in a force command u that is transmitted to the actuator system as described above. The transfer function C(s) of the combined output of the filter control elements 506 can be defined as the sum of the individual transfer functions of the individual filter control elements, as shown in Equation 12 below, where N is the total number of filter control elements 506 and the number of vibration modes being controlled.

number

[0120] In certain embodiments, one or more notch filters can be applied by each filter control element 506 to avoid excitation of other vibration frequencies. The transfer function of the notch filter is for each target frequency ω r For this, it is substantially the same as the one given by equation 5 above. In a particular embodiment, the notch filter transfer function is the transfer function C of each filter control element 506. k (s) may be multiplied together as given by Equation 13, and the transfer function H of the damping filter damp (s) is substantially the same as that given in equation 4 above, and is the transfer function H of the bandpass filter. bandpass (s) is essentially the same as the one given in equation 6 above.

number

[0121] In a specific embodiment, the filter control element output C i (jω k The sum of ) is as shown in equation 14 below: C k (jω k This can be made approximately equal to the transfer function C. i (s) ω k The use of a notch filter allows for the isolation of control over different vibration modes at the relevant frequencies, for example, where i=1···N and i≠k.

number

[0122] In certain embodiments, the phase correction of the attenuation filter output of each filter control element can also be isolated (for example, it can be determined independently of other filter control elements). For example, C(jω k ) is given by equation 14 above, C k (jω k Since it is approximately equal to ), the target frequency ω rThe sum of the phase angles in Equation 7 for the k-th filter control element in can be expressed as shown in Equation 15 below.

number

[0123] Phase delay θ of the k-th filter control element k Therefore, it can be expressed as shown in equation 16 below.

number

[0124] When phase correction is applied according to the second equation in the system of equation 10 above, the phase-corrected transfer function of the attenuation filter of the k-th filter control element can be expressed as shown in equation 17 below.

number

[0125] The control systems and methods described above can significantly reduce the amplitude of vibrations in one or more vibration modes of a structure when a disturbance force is applied to the structure. The control systems and methods can also significantly shorten the settling time of the system compared to an undamped response. For example, the control systems and methods described herein were applied to control / dampend vibrations excited by an impulse applied to an experimental system 600 shown in Figure 14. Figure 14 is a top view of the system 600, which includes a rectangular metal plate member 602 supported at three corners and an actuator system 604 attached to the upper surface of the plate member 602 at the unsupported corners. The actuator system 604 included an actuator configured as a voice coil motor (VCM) 606 and a sensor configured as an accelerometer 608 mounted on top of the VCM 606 (for example, located in the same position as the VCM).

[0126] The actuator system 604 was controlled by the control system 610 shown in Figure 15, configured according to the principles described above with reference to the control system in Figure 13. The control system 610 included two filter control elements 612A and 612B, which were mounted in parallel and configured to provide damping control for two vibration modes of the plate member 602. The control system 610 further included a system block 614 representing the dynamic response of the mass-spring-damper model of the system, and an integral element 616 configured similarly to those described above. Each filter control element 612A and 612B implemented their respective filter control schemes C1(s) and C2(s), which included a phase-compensated damping filter (e.g., a phase-compensated low-pass filter with differential control as described above), a band-pass filter, and one or more notch filters, as described above.

[0127] The upper graphs in Figures 16A to 16C show the acceleration measured by the accelerometer 608 when the system 600 is excited by an impulse generated by striking the plate member 602. The lower graphs in Figures 16A to 16C show the acceleration versus frequency of the system 600. The undamped / uncontrolled response of the system (Figure 16A) is shown along with the system's response (Figure 16B) when the control system 610 is operated to dampen the first vibration mode (e.g., using filter control element 612A), and the response (Figure 16C) when the control system is operated to dampen both the first and second vibration modes (e.g., using both filter control elements 612A and 612B). Figure 17 is a Bode plot showing the amplitude and phase of the system's frequency response when no feedback control is performed, when damping control is performed on the first vibration mode, and when damping control is performed on both the first and second modes. As can be seen from Figures 16A to 16C and Figure 17, the control system 610 reduces the acceleration of the plate member vibration to approximately 0 m / s² within about 0.1 seconds. 2 This reduced the noise level significantly, lowering the maximum amplitude to approximately 20 dB in the first mode and approximately 10 dB in the second mode.

[0128] The control systems and methods described herein can also be configured to operate using sensor feedback from one or more accelerometer sensors located away from the actuator. In other words, one or more accelerometers in the system do not need to be located in the same place as the actuator. In such a configuration, the phase correction performed by the filter control element acting on the signal from the remote accelerometer can be appropriately adjusted to take into account, for example, the difference in phase angle arising from the distance between the accelerometer and the actuator, and / or the phase difference associated with the modal deformation of the structure in different vibration modes.

[0129] For example, Figure 18 is a side elevation view showing another experimental system 700, which included a rectangular cross-section metal beam member 702 clamped to two support members 704 and 706 spaced apart from each other along the length of the beam member 702. System 700 further included an actuator system, generally indicated as 708, mounted on the upper surface of the beam member 702 between the support members 704 and 706. Actuator system 708 included an actuator configured as a VCM 710 and two accelerometer sensors 712 and 714. Accelerometer sensor 712 was mounted on top of the VCM 710, while the other accelerometer sensor 714 was mounted directly to the beam member 702 at a position spaced apart from the VCM 710. Actuator system 708 was controlled by a control system similar to the control system 610 shown in Figure 15.

[0130] Figure 19 schematically shows the first and second vibration modes of the beam member 702, as well as the relative positions of the two accelerometer sensors 712 and 714. As can be seen from Figure 19, 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 filters of each filter control element were configured to apply phase correction based on the relevant accelerometer signals so that the VCM acts in the correct direction to dampen the vibration of the beam member in both the first and second vibration modes.

[0131] Figure 20 is a Bode plot showing the amplitude and phase of the open-loop frequency response of system 700 as measured by accelerometers 712 and 714. The peak corresponding to the first beam oscillation mode is observed at approximately 80 Hz, and the peak corresponding to the second beam mode is observed at approximately 210 Hz. As can be seen in the phase plot, the two accelerometer signals are in phase at the first mode frequency and 180° apart at the second mode frequency.

[0132] Figure 21 is a Bode plot showing the open-loop frequency response of system 700 and the frequency response when control is performed using position data derived from the first accelerometer 712 located in the same position as the VCM 710. Figures 22A and 22B include acceleration-versus-time and fast Fourier transform (FFT) plots showing the open-loop impulse response of the system (Figure 22A) and the impulse response of the system when control is performed using position data derived from the first accelerometer 712 (Figure 22B). Both plots show that when damped using the actuator system, the vibration damping is relatively fast and the maximum amplitude of the first and second modes of frequency is relatively low.

[0133] Figure 23 is a Bode plot showing the open-loop frequency response of system 700 and the frequency response when control is performed using position data obtained from a second accelerometer 714 located away from VCM 710. Figures 24A and 24B include acceleration-versus-time plots and fast Fourier transform plots showing the open-loop impulse response of the system (Figure 24A) and the impulse response of the system when control is performed using position data derived from the second accelerometer 714 (Figure 24B). Figures 23 and 24A-24B also show that when damped using the actuator system, the vibrations dampen relatively quickly and the maximum amplitudes of the first and second modes are relatively low. Based on the phase lag information from the Bode plots, the phase correction term of the damping filter of each filter control element can be adjusted to control the actuator system using either the first accelerometer 712, the second accelerometer 714, or both. Thus, control can be performed using data from sensors located in the same location as the actuator, or from sensors located elsewhere in the system away from the actuator, and the filters of various filter control elements can be adjusted.

[0134] Example 4: Control system and method for attenuating vibration mode frequencies lower than the vibration mode frequency of an actuator system

[0135] In certain embodiments, using the filters and phase correction methods described herein, the disclosed control system may also be configured to attenuate structural vibration modes having 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, Figure 25 shows an experimental structural system 800 controlled using a control system configured similarly to the control system 610 of Figure 15. The structural system 800 included a T-shaped metal member 802 supported at both ends by flexure members 804 and 806. The T-shaped metal member 802 included a first main portion 808 and a second portion 810 located at or near the center of the main portion 808 and extending downward from the main portion 808 and perpendicular to the main portion 808. The flexure members 804 and 806 were connected to a base member 812 connected to a bench member 814 (e.g., an optical bench). The flexure members 804 and 806 suspended the T-shaped metal member 802 on the base member 812.

[0136] An actuator system 816, including a VCM818 and an accelerometer 820, was connected to a second portion 810 of a T-shaped metal member 802 and configured to act in the x-direction. The accelerometer 820 was connected to the housing of the VCM818 (in other words, the accelerometer was located in the same place as the VCM). An exciter in the form of a VCM822 was positioned between the second portion 810 of the T-shaped metal member 802 and a bracing member 824 fixed to a base member 812. The exciter VCM822 was configured to impart an impulsive disturbance force to the system 800. The vibration mode frequency of the system was changed by adding a weight 826 to the T-shaped metal member 802.

[0137] In one configuration, system 800 was configured to vibrate in a resonant mode of 15.7 Hz. The system also exhibited several other vibration mode frequencies below 100 Hz, including 21.7 Hz, 22.8 Hz, 30.5 Hz, and 44 Hz. The vibration mode frequency of actuator system 816 relative to the T-shaped metal member 802 was 22.2 Hz. Thus, the 15.7 Hz and 21.7 Hz modes of the structure were below the mode frequencies of actuator system 816, and the 22.8 Hz mode was only slightly above the mode frequency of the actuator system. Bode plots of the damped and undamped frequency responses of system 800 showing the 15.7 Hz, 21.7 Hz, and 22.8 Hz modes of the system are shown in Figures 26 to 28, respectively. Damping gain k d The results of controlling the value by changing the value are shown in Figures 27 and 28. As can be seen from Figures 26 to 28, the damping gain k of the damping filter d By adjusting (Equation 17), the control system can be adjusted to effectively attenuate the mode frequencies of the structural system that are lower than the vibration mode frequencies of the actuator system 816. In particular, k d When the value of k was set to 75, the maximum amplitude of the 15.7 Hz mode decreased by approximately 20 dB and the amplitude of the 21.7 Hz mode decreased by 10-15 dB compared to the open-loop response. d Setting the value to 412 reduced the maximum amplitude of the 22.8Hz mode by approximately 15dB. The settling time for each vibration mode also decreased to less than 0.2 seconds, compared to a maximum of 5 seconds for the 15.7Hz mode in the undamped system.

[0138] Example 5: Control system and method for attenuating vibration mode frequencies from an external source using peak filter control

[0139] In certain embodiments, the control systems described herein may also be configured to dampen / control vibrations transmitted to the structural system from remote disturbance forces. For example, in certain embodiments, one or more 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 filter control elements of the control system may be configured to perform the damping filter control described above, and one or more filter control elements may be configured to perform the peak filter control described below.

[0140] In certain embodiments, the peak filter can be tuned to allow one or more target vibration frequencies to be attenuated to pass through. In certain embodiments, the peak filter can be configured to perform phase compensation as described above to compensate for phase delays associated with, for example, remote positioning of accelerometer sensors, time delays of actuator amplifiers, signal conditioning, and / or time delays of digital controls. In certain embodiments, the phase compensation can enable the peak filter to attenuate vibrations of the structural system that are lower than the mode frequencies of the actuator system, as described above. In certain embodiments, the peak filter described herein has less impact on high-frequency dynamics than attenuation filter control and can therefore be implemented in combination with an attenuation filter to control low-frequency modes while limiting the coupling between attenuated vibration modes.

[0141] For example, Figure 29 shows an embodiment of a control system 900 configured to implement a peak filter control channel in parallel with an attenuation filter control channel. The control system 900 includes a system block 902 configured to represent the dynamic response of the structural system under control, an integral element 904 configured similarly to those described above, and two filter control elements 906 and 908 implemented in parallel. The filter control element 906 can implement, for example, a phase-compensated attenuation filter control C1(s) based on the transfer function of Equation 17 above. The filter control element 908 can implement a combination of phase-compensated peak filter control, bandpass filter control, and notch filter control based on the transfer function C2(s) of Equation 18 below.

number

[0142] In a particular embodiment, the transfer function H of the peak filter peak (s) can be given by the following equation 19, where k a is the damping gain, and d p ω is the damping ratio, p This is the target frequency for the peak filter.

number

[0143] In a particular embodiment, the transfer function H of the bandpass filter control bandpass (s) is the same as in equation 6 above, and the transfer function H of the notch filter notch (s) can be the same as in Equation 5 above. The phase lag θ of the system can be determined according to Equation 16 above. The number of notch filters included depends on the number of vibration modes of the structural element to be damped, and when damping other modes, both the resonant frequency of the structure and / or the vibration modes of the structure excited by the actuator can be taken into consideration. In certain embodiments, the peak filter may include differential control, proportional control, and / or integral control, similar to the damping filter described above.

[0144] In a typical embodiment, the control system 900 in Figure 29 was used to control / dampe the vibration of the structural system 800 in Figure 25 when an impulse force was applied to the bench member 814 by the exciter VCM828, shown by the dashed line. In this embodiment, VCM822 was removed from the system. VCM828 was offset from the structural system 800 along the z-axis (for example, in the direction toward the plane of the paper in Figure 25). The impulse disturbance force applied to the bench member 814 by VCM828 resulted in a 19.5 Hz vibration mode for the bench member 814 and a 45 Hz vibration mode for the structural system 800. The 45 Hz vibration mode of the structural system 800 was attenuated using a filter control element 906 that performed phase-corrected damping filter control, and the 19.5 Hz vibration mode of the optical bench was attenuated using a filter control element 908 that performed phase-corrected peak filter control.

[0145] The frequency response of system 800 when controlled by control system 900 is shown in the Bode plots of Figures 30 and 31. Figure 30 shows the frequency response of system 800 when excited by a current command from an actuator. Figure 31 shows the frequency response of system 800 when excited by an exciter VCM828 connected to bench member 814. Figures 30 and 31 show the open-loop response of the system, the response when feedback control is applied via damping filter control element 906, and the damping filter control element The response when both 906 and the peak filter control element 908 are applied is shown. In Figures 30 to 32, the line labeled "Feedback 1" indicates that the peak filter is k a The system response is adjusted to be =160, and on the line "Feedback 2", k a =300. As can be seen from Figures 30 and 31, filter control elements 906 and 908 are both k aIn terms of values, the maximum amplitudes of the bench member mode and the structural system mode were significantly reduced compared to the non-damped system. Referring to Figure 32, both control methods also reduced the measured acceleration associated with both modes, reducing the settling time of the structural system 800 to less than 0.3 seconds.

[0146] Example 6: Control system and method using multiple spaced-apart sensors

[0147] In certain embodiments, the actuator system may include a plurality of sensors positioned at different locations on the structural system under control, and data from a plurality of such sensors can be used in a plurality of control loops to dampen a plurality of vibration modes of the structure. The control system for such a structure may include a plurality of control loops that include a filter control element with feedback from different sensors within the structural system. In certain embodiments, the outputs of the various control loops can be summed to generate a force command for the actuator system.

[0148] For example, Figure 33 shows a top-down plan view of a structural system 1000, which includes a rectangular plate member 1002 and an actuator system collectively shown as 1004. The actuator system 1004 included a VCM 1006 and several accelerometer sensors 1008, 1010, 1012, 1014, and 1016. In the illustrated configuration, accelerometer sensor 1008 was located in the same place as the VCM 1006, and the remaining sensors were arranged around the edge of the plate member 1002. In Figure 33, accelerometer 1010 was located near the center of the upper end of the plate member, and accelerometer 1016 was located near the center of the lower end of the plate member. Accelerometer 1012 was located in the upper left corner, and accelerometer 1014 was located in the lower left corner. The plate member 1002 was suspended above an optical bench or another support, connected by three support members 1018A-1018C in the illustrated triangular arrangement. The vibrator, configured as VCM1020, was positioned along the center of the right edge of the plate member between support members 1018A and 1018B.

[0149] In certain embodiments, depending on the placement of the accelerometer sensors, the accelerometer sensors may be able to sense specific vibration modes of the structural system and may not sense other vibration modes depending on whether the sensor's position coincides with the node of the vibration mode. For example, a plate member 1002 configured as shown in Figure 33 exhibited four relatively low-frequency vibration modes when excited by impulse disturbance forces from actuator VCM1006 and / or exciter VCM1020. The first mode was 61 Hz, the second mode was 96 Hz, the third mode was 165 Hz, and the fourth mode was 282 Hz. Accelerometer 1008, placed on VCM1006, detected the second, third, and fourth modes well, but did not obtain a strong signal from the first mode. Accelerometer 1014 provided a clear signal for the first vibration mode.

[0150] Various vibration modes in such a structural system can be controlled using a control system that implements the damping filter and / or peak filter control architecture described herein in multiple parallel control loops, each control loop being configured to dampen 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, Figure 34 shows a typical control system 1030 that includes two control loops (also called control channels) that can be used to control four modes of vibration of the structure 1000 of Figure 33. The first control loop is typically indicated by 1032, and the second control loop is typically indicated by 1034. The control system includes a system block 1036 that represents the dynamic response of the structural system 1000. The first control loop 1032 further includes an integral element 1038 and three filter control elements 1040, 1042, and 1044 implemented in parallel. The position signal output from the integral element 1038 is subtracted from the position command signal x(s) to obtain a position error signal, which is then input to the filter control elements 1040-1044. The filter control elements 1040-1044 can be configured to perform filter control based on the transfer functions C1(s), C2(s), and C3(s). The filter control elements can be configured to perform phase-compensated attenuation filter control as described above with reference to equations 13-17, and / or phase-compensated peak filter control as described above with reference to equations 18 and 19. The filter control elements 1040-1044 can be tuned to specific target mode frequencies of the structural system 1000. In certain embodiments, the filter control elements 1040-1044 are configured to control the second, third, and fourth modes of the structural system 1000, respectively.

[0151] The second control loop 1034 may also include an integral element 1048 and an additive junction 1050 that outputs a position error signal to the filter control element 1052 after subtracting the position signal of the integral element from the position command signal x(s). The filter control element 1052 can perform filter control based on the transfer function C4(s), which may include phase-compensated attenuation filter control similar to equations 13-17 above, or phase-compensated peak filter control as described with reference to equations 18 and 19, and is tuned to a specific target mode frequency of the structural system 1000. In certain embodiments, the filter control element of the second control loop 1052 It was adjusted to dampen the first vibration mode of the structural system 1000.

[0152] The outputs of the filter control elements 1040-1044 of the first control loop 1032 are added together with the output of the filter control element 1052 of the second control loop 1034 at the summing junction 1054 to provide a command signal u to the actuator system. (Disturbance force d) u This is represented as being combined with a force command signal at the add junction 1056 before the command signal is provided to the structural system block 1036.

[0153] When used to dampen vibrations of the structural system 1000 in Figure 33, the first control loop 1032 can operate using acceleration data acquired from an accelerometer 1008 located in the same place as the VCM 1006, and can be configured to control the second, third, and fourth vibration modes of the plate member 1002. The second control loop 1034 can utilize acceleration data acquired from an accelerometer 1014 to control the first vibration mode of the plate member 1002. Thus, in the illustrated embodiment, the first accelerometer signal acc1 from the accelerometer 1008 is transmitted to the integral element 1038 of the first control loop 1032. The integral element 1038 outputs a position signal pos1 to the summing junction 1046, which is subtracted from the position command signal x(s) to obtain a position error signal provided to the filter control elements 1040-1044. The equation for the first accelerometer signal acc1 is given by the following equation 20, where,

number

number

number

[0154] With respect to the second control loop 1034, the second accelerometer signal acc2 from accelerometer 1014 is transmitted to the integral element 1048 of the second control loop. The integral element 1048 outputs the position signal pos2 to the summing junction 1050, where it 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 by the following equation 21, where,

number

number

number

[0155] Equations 20 and 21 relate to how the feedback filter controller and sensor are coupled in a closed-loop system. In certain embodiments, equations 20 and 21 can be used in offline control design synthesis and simulation in the frequency domain before the control system is actually implemented.

[0156] Figure 35 shows the Bode plot of the open-loop frequency response of system 1000 in Figure 33 when excited by an impulse from the vibrator VCM1020. Peaks are observed in the 61Hz, 96Hz, 165Hz, and 282Hz modes. As shown in Figure 35, accelerometer 1014 provided a clear signal for the 61Hz mode, and accelerometer 1008 provided clear signals for the second, third, and fourth modes. Figure 36 is the Bode plot of the frequency response of the system performing control of all four modes using the actuator system based on force commands from the control system 1030 in Figure 34. In Figure 36, it can be seen that the maximum amplitude is significantly reduced for each vibration mode.

[0157] Plots of acceleration versus time (top) and acceleration versus frequency (bottom) for system 1000 are shown in Figures 37A and 37B. As seen in Figures 37A and 37B, using actuator system 1004 controlled according to the control system in Figure 34, each of the four controlled vibration modes of structural system 1000 is almost completely damped within 0.2 seconds after impulse excitation. This is a significant improvement over undamped systems where vibrations persist for more than 1 second. Thus, the disclosed control system can be used to significantly reduce the settling time of multiple vibration modes of structural systems and vibrations at frequencies such as below 300 Hz, and especially below 100 Hz.

[0158] The control loop of the control system 1030 can be configured in various ways depending on factors such as the shape and size of the structural system, the positioning of the accelerometer sensors 1010-1016, the position of the actuator 1006, and the position of the vibrator VCM. Figure 38 shows another arrangement of four accelerometers 1010-1016, actuator VCM 1006, and vibrator VCM 1020 on the plate member 1002. Accelerometer 1008 is removed from actuator VCM 1006. The configuration in Figure 38 shows four vibration modes of the plate member 1002, similar to those described above with reference to Figure 33. In a particular embodiment, accelerometer 1014 provides clear signals for the first and third vibration modes, and accelerometer 1010 provides clear signals for the second and fourth modes. Therefore, the control system in Figure 34 can be rearranged as shown in Figure 39 so that the signal acc1 from accelerometer 1010 is fed back to filter control elements 1040 and 1044, which are arranged in parallel within a first control loop 1032 and configured to generate control signals for attenuating vibrations in the first and third modes. The signal acc2 from accelerometer 1014 is fed back to filter control elements 1042 and 1052, which are arranged in parallel within a second control loop 1034 and configured to generate control signals for attenuating the second and fourth modes. Thus, the control system described herein may include any number of control loops implementing any number of filter control elements, depending on the number of vibration modes to be controlled, the number and location of accelerometers detecting the target modes of the system, etc.

[0159] Example 7: Structural system dynamic model and arrangement of sensors and actuators

[0160] In certain embodiments, the amplitude of a force command for suppressing / controlling vibrations of a structural system at a specific vibration mode frequency can be estimated based on the amplitude of vibration at that mode frequency. In certain embodiments, the amplitude of vibrations in a particular mode can be determined experimentally by measurement and / or using any of various models of the system and its frequency response, such as finite element analysis (FEA) models or state-space models. In certain embodiments, the displacement of the structural system at a first position in response to a force applied to the structural system at a second position can be determined from such a system model. Information from such a model of the system and / or measurements can be used to select the positions of actuators and / or one or more accelerometer sensors to effectively dampen one or more selected vibration modes of the structure.

[0161] For example, in a typical case, the dynamics of a structural system such as the plate member 1002 in Figure 38 can be transformed into a separated mode coordinate space. The dynamics of the structural system can be given by the following equation 22, 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.

number

[0162] The solution to the eigenvalue equation is given by equation 23 below. Here, ω 2 is an eigenvalue, φ is an eigenvector, and ω k 2 φ is the square of the natural frequency of the k-th mode (a scalar quantity), and k is a vector representing the mode shape of the k-th mode, where k=1, ...N, and N is three times the number of nodes in the 3D FEA model.

[0163] The mode shape matrix M of the FEA model modal This can be given by the following equation 23, where,

number

Number

[0164] The mode stiffness matrix K of the FEA model modal can be given by the following Equation 24, where the mode stiffness of the k-th mode is k k = m k ω k 2 is.

Number

[0165] The mode shape matrix Φ is scaled using the identity

Number

Number

[0166] The mode mass matrix can be normalized to MΦ = I, where m T = 1 is the mode mass of the k-th mode. k = 1 is the mode mass of the k-th mode.

[0167] The mode stiffness matrix can be normalized to result in the following Equation 26, where ω k 2 is the mode mass of the k-th mode.

Number

[0168] This is the displacement v of the structural system at the first position j j and the force u applied at the second position ii results in a mass-normalized mode shape equation, which is a ratio with

Number

[0169] In Equation 27, φ k is the vector representation of the mode shape of the structural system for the k-th mode given by Equation 28 below, and ξ k is the damping ratio.

Number

[0170] In a particular embodiment, the plant model of the flexible mode dynamics of the structural system can be represented as a second-order transfer function as shown in Equation 29 below.

Number

[0171] The transfer function of Equation 29 can be transformed into mode coordinates using the relationship v = Φq, and Equation 30 is obtained.

Number

[0172] The mode mass matrix term Φ T MΦ can be given by Equation 23 above, and the mode stiffness matrix Φ T KΦ can be given by Equation 26 above. The damping matrix term Φ T DΦ can be approximated as shown in Equation 31 below.

Number

[0173] The relationship v = Φq can be written as shown in Equation 32 below, where N is the number of modes.

Number

[0174] The reduced-order model of a system where n < N can be given by the following Equation 33, where the term E j,i is the DC approximation of the neglected high-order dynamics given by Equation 34.

Number

Number

[0175] FIG. 40 is a diagram showing a simulation of the shape of the upper surface of the plate member 1002 of FIG. 38 according to the above-described FEA model when the plate member is supported at three locations. In FIG. 40, displacement patterns related to nine vibration modes of the plate member 1002 are shown.

[0176] In a particular embodiment, the accelerometer sensor can be placed at a position on the structural system where the displacement from one or more vibration modes is maximum. For example, referring to FIG. 40, the displacement in the z-direction (e.g., the direction out of the plane of the paper) of the upper surface of the plate member 1002 is maximum at the lower left and lower right corners in the first mode, as well as in the second mode. Thus, accelerometers placed at these corners provide a clear signal of the acceleration / displacement of the plate member surface related to the first and second vibration modes. As can also be seen from FIG. 40, an accelerometer placed at or near the center of the plate member 1002 can provide a clear signal of the displacement related to the third vibration mode. Thus, the accelerometer can be placed at a position that coincides with the large displacement of the plate surface for the selected vibration mode of the controlled object. The FEA model of the dynamics of the structural system can assist in determining the placement of accelerometers and / or actuators, particularly in situations where the environment and / or constraints of the structural system in its intended application cannot be easily reproduced experimentally.

[0177] In certain embodiments, similar vibration responses from the structural system can be obtained by swapping the positions of the actuator VCM with various accelerometers, or in fact by changing the input and output positions of the system. For example, placing actuator VCM 1006 in the position of accelerometer 1010 in Figure 38, and vice versa, can produce similar vibration profiles in response to disturbance forces from the actuator VCM.

[0178] Example 8: Estimation of control force amplitude

[0179] In certain embodiments, a model of structural system dynamics, such as those described herein, can be optionally used in combination with the measured amplitude of vibrations at a selected frequency to be damped to estimate the amplitude of a force command sufficient to dampen vibrations at a selected modal frequency. In certain embodiments, the rigid modes (and / or flexible modes) of a structural element can be modeled using modal decomposition techniques. For example, in a particular example, the displacement at position j on a plate member similar to the plate member 1002 in Figure 38 is given by the following equation 35.

number

[0180] In Equation 35, the structural system plant dynamics P j,i (s) can be determined according to equation 33 above. Disturbance dynamics model D j,l (s) can be given by equation 36 below, although certain implementations may require experimental verification.

number

[0181] In certain embodiments, the magnitude of the displacement of the plate member at position j due to vibration in the target mode k is not subject to control (e.g., u i When v = 0, j The absolute value of, for example, |v j(jω k )| can be expressed as follows. Therefore, the magnitude of the force command required to dampen the vibration at position j due to the vibration of mode k can be given by the following equation 37.

number

[0182] In certain embodiments, the model of structural system dynamics in modal space can take into account rigid vibration modes of the structural system. Figure 41 shows a force u having length L. i The x coordinate x is applied (for example, by the actuator of an actuator system). i to, force u i Displacement v of member 1100 in response to j x coordinate x j A schematic diagram of the unconstrained structural element 1100 is shown along with it. In a particular embodiment, for the first mode φ1, when ω1=0, φ 1,i and φ 1,j As given in Equation 38 below,

number

number

[0183] For the second rigid body mode φ2 of the beam member shown in Figure 43, if ω2 = 0, then φ 2,i It can be expressed as given by the following equation 39, φ 2,j It can be expressed as given by the following equation 40, and I zz This is the moment of inertia of structural element 1100 about the z-axis when the structural element is rotated about the z-axis.

number

number

[0184] By substituting equations 38 to 40 above, the result is obtained in equation 27 above.

number

number

[0185] When two rigid body modes φ1 and φ2 are considered, equation 41 is given by the input force u i The dynamics from these two rigid body modes determine the output position v j This describes how it contributes to [the system]. A similar formulation can be extended to the flexible modes of structural elements.

[0186] An example of a rotation mode around the z-axis is shown in Figure 44 and can be expressed according to the following equation 42.

number

[0187] The φ of formulas 39 and 40 above 2,i and φ 2,j By substituting the formula, the rotation mode θ around the z-axis shown in Figure 44 can be obtained. z Regarding this, we can obtain a series of equivalent equations shown in Equation 43 below.

number

[0188] In certain embodiments, controllability can be improved by positioning the actuator at a location on the structural system that results in a relatively large mode shape displacement in response to the application / input of force. The larger the moment arm of the actuator (e.g., the magnitude of the mode shape displacement at the force application point or sensor measurement point), the larger the moment constant, which is the product of the actuator force constant and the moment arm at the actuator point. In certain embodiments, the ability of the accelerometer sensor to sense the displacement of structural elements associated with a selected vibration mode can be improved by positioning the accelerometer sensor at a location that has a relatively large mode shape displacement for a selected vibration mode. Therefore, in certain embodiments, it is beneficial to position the actuator and / or sensor at a location that has a relatively large mode shape displacement associated with a specified vibration mode to be damped.

[0189] In certain embodiments, the dynamic response of a structural system can also be formulated as a state-space model.

number

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[0190] Equation 45 below is the same as in Equation 44.

number

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[0191] 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.

[0192] Equation 46 provides an exemplary multiple-input multiple-output (MIMO) system.

number

[0193] Equation 46 can be expanded into an equivalent system of equations given in Equation 47.

number

[0194] In certain embodiments, a SISO and / or MIMO state-space model of the structural system can be used to represent the system dynamics separated according to modal coordinates, which is more convenient in simulation than a transfer function model. In certain embodiments, the parameter φ in equations 44 and 46 is used. k,j and φ k,i Since these relate to the mode shape, they can be used to determine the placement of actuators and sensors as described above.

[0195] One or more of the actuator systems, control systems, and / or control methods described herein can offer significant advantages over known systems and methods for controlling structural vibrations in precision systems such as lithography systems. For example, the actuator systems described herein can effectively dampen vibrations of various structures within a lithography system. For instance, the systems described herein can dampen relatively low-frequency vibrations (e.g., frequencies below 500 Hz, such as below 300 Hz, below 200 Hz, or below 100 Hz) or higher-frequency vibrations up to about 10 kHz (or the sampling and bandwidth limits of the system), thereby reducing or eliminating the need for passive dampers for such purposes. The disclosed systems and methods can also significantly reduce the maximum amplitude of vibrations of structural elements related to one or more vibration modes of the structural element. This can reduce the relative motion of different structures within precision systems such as optical plates, substrate stages, and / or mask stages in a lithography exposure apparatus. When one structural element functions 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 if not damped.

[0196] The systems and methods described herein can also significantly reduce the settling time of a structural system after excitation by disturbance forces. Such systems can be implemented, for example, to reduce vibrations in an exposure apparatus caused by the movement of the substrate stage and / or mask stage. As described above, certain configurations of the systems described herein can reduce the settling time of a structural system similar to an optical platen from more than 1 second to less than 0.2 seconds. This can significantly improve the throughput of the exposure apparatus by reducing the time required between exposures for vibrations to subside naturally or under the influence of passive dampers.

[0197] The systems and methods described herein can 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 can be configured for use on an optical platen, substrate stage, mask stage, or any other structure of the exposure apparatus in which damping of structural vibrations can be demonstrated. The control system can be configured to dampen one, two, three, four, five, or more vibration modes of the structural system, as well as vibrations excited by the control of other modes. The control system can also be configured to utilize feedback from sensors located at the actuator's position and / or from sensors located away from the actuator by implementing the phase compensation method described herein. The phase compensation method described herein can also be used to dampen vibration modes of the structure having frequencies lower than the mode frequencies of the actuator-structure interaction, as well as higher frequency modes of the structure.

[0198] Example 9: Exemplary Precision System

[0199] The methods and apparatus described above can be used with various precision systems, including various types of lithography systems and other wafer processing systems and methods, including the lithography exposure system described above. The control systems and methods can also be used in combination with any of the embodiments and methods of precision systems, and / or their associated structural elements or subsystems, described below with reference to Figures 45 to 49. Referring to Figure 45, specific features of an immersion lithography system (an exemplary precision system) are shown, 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 the optical axis A. The light source 1340 is configured to generate a pulsed beam of illumination light, such as 248 nm DUV light produced by a KrF excimer laser, 193 nm DUV light produced by an ArF excimer laser, or 157 nm DUV light produced by an F2 excimer laser. The illumination optical system 1342 includes an optical integrator and at least one lens that adjusts and shapes the illumination beam to illuminate a specific area of ​​the reticle 1350 on which a pattern is formed, which is placed on the reticle stage 1344. The pattern defined on the reticle 1350 corresponds to a pattern that is lithographically transferred onto a wafer 1352 held on the wafer stage 1348. Lithographic transfer in this system is performed by projecting a spatial image of the pattern from the reticle 1350 onto the wafer 1352 using a projection optical system 1346. The projection optical system 1346 typically comprises many individual optical elements (not shown in detail) that project the image onto the wafer 1352 at a specified reduction ratio (e.g., 1 / 4 or 1 / 5). To be imprintable, the wafer surface is coated with a layer of appropriate exposure-sensitive material called a "resist".

[0200] The reticle stage 1344 is configured to move the reticle 1350 in rotational directions about the X, Y, and Z axes. For this purpose, the reticle stage comprises one or more linear motors having cooling coils as described herein. The two-dimensional position and orientation of the reticle 1350 on the reticle stage 1344 are detected in real time by a laser interferometer (not shown), and the reticle 1350 is positioned by the main control unit based on this detection.

[0201] The wafer 1352 is held by a wafer holder ("chuck," not shown) on a wafer stage 1348. The wafer stage 1348 includes a mechanism (not shown) for controlling and adjusting the focus position (along the Z axis) and tilt angle of the wafer 1352 as needed. The wafer stage 1348 also includes electromagnetic actuators (e.g., linear motors, planar motors, or both) for moving the wafer in an XY plane substantially parallel to the imaging plane of the projection optical system 1346. These actuators preferably include linear motors, one or more planar motors, or both.

[0202] Furthermore, the wafer stage 1348 is equipped with a mechanism to adjust the tilt angle of the wafer 1352 using an autofocus and auto-leveling method. In this way, the wafer stage plays a role in aligning the wafer surface with the image plane 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 that drives the wafer stage. During exposure, the light passing through the projection optical system is moved sequentially from one position to another on the wafer according to a pattern on the reticle, using a step-and-repeat or step-and-scan method.

[0203] The projection optical system 1346 typically has multiple lens elements that work together to form an exposure image on the resist-coated surface of the wafer 1352. For convenience, the most distal (i.e., closest to the wafer surface) optical element is the objective lens 1353. Since the illustrated system is an immersion lithography system, it includes an immersion liquid 1354 located between the objective lens 1353 and the surface of the wafer 1352. As described above, the immersion liquid 1354 is of the specified type. The immersion liquid is present at least while the reticle pattern image is exposed on the wafer.

[0204] The immersion fluid 1354 is supplied from a liquid supply unit 1356, which may include a tank, a pump, and a temperature controller (not shown individually). The fluid 1354 is slowly discharged by a nozzle mechanism 1355 into the gap between the objective lens 1353 and the wafer surface. The fluid recovery system 1358 includes a recovery nozzle 1357 that removes the fluid from the gap as the supply unit 1356 supplies new fluid 1354. As a result, a substantially constant volume of continuously replaced immersion fluid 1354 is provided between the objective lens 1353 and the wafer surface. The temperature of the fluid is adjusted to be approximately the same as the temperature in the chamber in which the lithography system itself is located.

[0205] Also shown is a sensor window 1360 extending across a recess 1362 defined within the wafer stage 1348 where the sensor 1364 is positioned. Thus, the window 1360 isolates the sensor 1364 within the recess 1362. By moving the wafer stage 1348 so that the window 1360 is positioned below the objective lens 1353 while continuously replacing the immersion liquid 1354, the light beam passing through the projection optical system 1346 passes through the immersion liquid and the window 1360 to reach the sensor 1364.

[0206] The interlogging beam source 1380 is positioned to direct the interlogging light beam 1381 toward the reticle 1350, and the detection system 1382 is configured to detect a portion of the interlogging beam modulated by the reticle 1350. The detected beam can be used to evaluate the distortion of the reticle, as described above, and appropriate system adjustments can be made to correct, prevent, or at least partially compensate for the distortion.

[0207] Referring here to Figure 46, an alternative embodiment of a precision system that may include one or more electromagnetic actuators having actively cooled coils as described herein is the EUVL system 1400 as a typical precision system incorporating electromagnetic actuators as described herein. The illustrated system 1400 comprises a vacuum chamber 1402 including vacuum pumps 1406a, 1406b arranged to enable the establishment and maintenance of desired vacuum levels in each of the chambers 1408a, 1408b of the vacuum chamber 1402. For example, vacuum pump 1406a maintains a vacuum level of about 50 mTorr in the upper chamber (reticle chamber) 1408a, and vacuum pump 1406b maintains a vacuum level of less than about 1 mTorr in the lower chamber (optical chamber) 1408b. The two chambers 1408a, 1408b are separated from each other by a partition wall 1420. Although various components of the EUVL system 1400 are not shown in the diagram for the sake of clarity, it will be understood that the EUVL system 1400 may include components such as a reaction frame, vibration isolation mechanisms, various actuators, and various controllers.

[0208] The EUV reticle 1416 is held by a reticle chuck 1414 connected to a reticle stage 1410. The reticle stage 1410 holds the reticle 1416 and can move the reticle to scan laterally while it is being used, for example, for lithography exposure. A blind device is located between the reticle 1416 and the partition wall 1420. An illumination source 1424 is incident on the optical chamber 1408b, reflected by one or more mirrors 1428, and generates an EUV illumination beam 1426 that illuminates a desired position on the reticle 1416 via the illumination optics 1422. As the illumination beam 1426 is reflected from the reticle 1416, the beam is "patterned" by the pattern portion on the reticle that is actually being illuminated. The partition wall 1420 can function as a differential pressure barrier and as a reticle shield to protect the reticle 1416 from particle contamination during use. The partition 1420 defines an aperture 1434 from which the illumination beam 1426 can illuminate a desired area of ​​the reticle 1416. The incident illumination beam 1426 on the reticle 1416 is patterned by interaction with the pattern-defining elements on the reticle, and the resulting patterned beam 1430 propagates generally downward and reaches the surface of the wafer 1432 held by the wafer chuck 1436 on the wafer stage 1440, which performs scanning motion of the wafer during exposure, via the projection optical system 1438. This projects an image of the reticle pattern onto the wafer 1432.

[0209] The wafer stage 1440 may include a positioning stage that can be driven, for example, by a planar motor or one or more linear motors, and a wafer table that is magnetically connected to the positioning stage using, for example, an EI core actuator (details omitted). The wafer chuck 1436 is connected to the wafer table and may be levitated relative to the wafer table by, for example, one or more voice coil motors. When the positioning stage is driven by a planar motor, the planar motor typically utilizes the electromagnetic forces generated by magnets and corresponding armature coils arranged in two dimensions. The positioning stage is configured to be movable with multiple degrees of freedom, for example, 3 to 6 degrees of freedom, so that the wafer 1432 can be positioned in a desired position and orientation relative to the projection optical system 1438 and the reticle 1416.

[0210] The EUVL system, including the EUV source and illumination optics system described above, can be constructed by assembling various assemblies and subsystems to ensure that specified standards of mechanical, electrical, and optical precision are met and maintained. Various subsystems (particularly the illumination optics 1422 and projection optics 1438) are evaluated and adjusted as necessary to achieve the specified precision standards before, during, and after assembly to establish these standards. Similar evaluations and adjustments are made to mechanical and electrical subsystems and assemblies as needed. The assembly of various subsystems and assemblies involves creating optical and mechanical interfaces, electrical interconnections, and piping interconnections between assemblies and subsystems as required. After the EUVL system is assembled, further evaluations, calibrations, and adjustments are made as necessary to ensure that the specified system accuracy and operational precision are achieved. To maintain certain standards of cleanliness and contamination avoidance, the EUVL system (and specific subsystems and assemblies of the system) is assembled in a cleanroom or similar environment where particulate contamination, temperature, and humidity are controlled.

[0211] As shown in Figure 46, the interlogging beam source 1450 can be positioned to direct the interlogging light beam 1451 toward the reticle 1416. The detection system 1452 is positioned to receive at least a portion of the interlogging beam that has been reflected, refracted, diffracted, phase-shifted, or otherwise modulated by its interaction with the reticle 1416. Based on the detector signal response to this beam portion, the distortion of the reticle can be evaluated in the detection system as described above.

[0212] Semiconductor devices can be manufactured by a process that includes microlithography steps performed using a microlithography system, as described above. Referring to Figure 47, in step 1501, the functional and performance characteristics of the semiconductor device are designed. In step 1502, a reticle ("mask") defining the desired pattern is designed and fabricated according to the previous design step. Meanwhile, in step 1503, a substrate (wafer) is fabricated and coated with a suitable resist. In step 1504 ("wafer processing"), the reticle pattern designed in step 1502 is exposed onto the surface of the substrate using a microlithography system. In step 1510, as described above, the distortion of the reticle during exposure can be estimated. In step 1505, the semiconductor device is assembled (including "dicing," where individual devices or "chips" are cut from the wafer; "bonding," where wires are joined to specific locations on the chip; and "packaging," where the device is enclosed in a suitable package for use). In step 1506, the assembled device is tested and inspected.

[0213] Figure 48 shows typical details of a wafer processing process including a microlithography step. In step 1611 ("oxidation"), the wafer surface is oxidized. In step 1612 ("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 on the wafer surface. These steps 1611 to 1614 constitute typical "pre-treatment" steps for the wafer, and each step is selected according to processing requirements.

[0214] At each stage of wafer processing, once the pre-processing steps are completed, the following "post-processing" steps are performed. The first post-processing step is step 1615 ("photoresist formation"), where a suitable resist is applied to the surface of the wafer. Next, in step 1616 ("exposure"), the pattern is lithographically transferred from the reticle to the resist layer on the wafer using the microlithography system described above. Reticle distortion can be compensated for during pattern transfer. In step 1617 ("development"), the exposed resist on the wafer is developed to form a usable mask pattern on the resist on the wafer that corresponds to the resist pattern. In step 1618 ("etching"), areas not covered by the developed resist (i.e., exposed material surfaces) are etched away to a controlled depth. In step 1619 ("photoresist removal"), the residual developed resist is removed ("exfoliated") from the wafer.

[0215] By repeating pre-processing and post-processing steps as needed, multiple interconnection layers of circuit patterns can be formed on a wafer. Generally, one set of pre-processing and post-processing steps is performed to form each layer.

[0216] This disclosure includes any of a variety of precision systems, including stages for holding workpieces or other articles useful for manufacturing. An example of a precision system is a microlithography system or exposure “tool” used to manufacture semiconductor devices. A schematic diagram of an exemplary microlithography system 1710 having the technical features described herein is shown in Figure 49. System 1710 includes a system frame 1712, an illumination system 1714, an imaging optics system 1716, reticle stage assemblies 1718A-1718B, substrate stage assemblies 1720A-1720B, positioning systems 1722A-1722D, and a system controller 1724. The configuration of the components of system 1710 is particularly useful for transferring integrated circuit patterns (not shown) from a reticle 1726 onto a semiconductor wafer 1728. System 1710 is mounted on a mounting base 1730, for example, the ground, a base, a floor, or other support structure. The system also includes a measurement system for measuring the position of a lithography substrate (as an exemplary workpiece) along an axis (e.g., the z-axis or optical axis) with improved accuracy and precision. In system 1710, the reticle stage assembly and / or substrate stage assembly 1720 include a multi-blade holder as described in the representative embodiment above.

[0217] In certain examples, the specified vibration mode frequency may be any range between 5Hz and 10kHz, 5Hz and 5kHz, 5Hz and 1kHz, 5Hz and 500Hz, 5Hz and 300Hz, 5Hz and 200Hz, 5Hz and 100Hz, 2Hz and 10kHz, 2Hz and 5kHz, 2Hz and 1kHz, 2Hz and 500Hz, 2Hz and 300Hz, 2Hz and 200Hz, 2Hz and 100Hz, 1Hz and 10kHz, 1Hz and 5kHz, 1Hz and 1kHz, 1Hz and 500Hz, 1Hz and 300Hz, 1Hz and 200Hz, 1Hz and 100Hz, or any of the frequencies listed herein. The specified vibration mode frequency may also be less than 1Hz.

[0218] Example 10: Typical Computing Environment

[0219] Figure 50 shows a generalized example of a computing environment 1800 in which the software and control algorithms for the embodiments described herein may be implemented. For example, the software and / or hardware for implementing 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 an exposure apparatus assembly, or a remote computing system as described herein.

[0220] Computing environment 1800 is not intended to imply any limitation on the scope of use or functionality of the technology, and the technology may be implemented in a variety of general-purpose or dedicated computing environments. For example, the disclosed technology may be implemented in 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, and minicomputers. The disclosed control method may be implemented in a distributed computing environment in which tasks are performed by remote processing units linked over a communication network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0221] Referring to Figure 50, the computing environment 1800 includes at least one processing unit 1810 and memory 1820. In Figure 50, this most basic configuration 1830 is enclosed within the dashed line. The processing unit 1810 executes computer executable instructions and may be a real processor or a virtual processor. In a multiprocessing system, multiple processing units execute computer executable instructions to increase processing power, and thus multiple processors can operate simultaneously. The memory 1820 may be volatile memory (e.g., registers, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or a combination thereof. The memory 1820 stores, for example, software 1880 that can implement the techniques described herein. The computing environment may have additional features. For example, the computing environment 1800 may include storage 1840, one or more input devices 1850, one or more output devices 1860, and one or more communication connections 1870. Interconnection mechanisms (not shown), such as buses, controllers, or networks, interconnect the components of the computing environment 1800. Typically, operating system software (not shown) provides an operating environment for other software running within the computing environment 1800 and coordinates the activity of the components of the computing environment 1800.

[0222] The storage 1840 may be removable or non-removable and may include non-volatile solid-state memory, magnetic disks, or any other medium that can be used to store information and can be accessed within the computing environment 1800. The storage 1840 stores instructions, plug-in data, and messages for software 1880 that may be used to implement the technology described herein.

[0223] 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, keypad, mouse, touchscreen display, pen, or trackball, an audio 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.

[0224] The communication connection 1870 enables communication to a device or computing entity via a communication medium (e.g., a connected network). The communication medium transmits information such as control signals, computer executable instructions, sensor inputs or outputs, or other data in modulated data signals. The communication connection 1870 is not limited to wired connections (e.g., megabit or gigabit Ethernet, InfiniBand, Fibre Channel via electrical or optical fiber connections), but also includes wireless technologies (e.g., Bluetooth). (Registered trademark) This also includes WiFi (IEEE 802.11a / b / n), WiMAX, cellular, satellite, laser, infrared RF connectivity, and other suitable communication connections for providing network connectivity to the disclosed controlled device.

[0225] Some embodiments of the disclosed method can be executed using computer executable instructions that implement all or part of the disclosed technology in a computing cloud 1890 or other remote computing system. For example, the disclosed method can be executed on a processing unit 1810 located within a computing environment 1830, or the disclosed method can be executed on a server located within a computing cloud 1890.

[0226] Computer-readable media are any available media accessible within the computing environment 1800. For example, and not limited to, in the computing environment 1800, computer-readable media include memory 1820 and / or storage 1840. For ease of understanding, the term computer-readable storage media includes media for data storage, such as memory 1820 and storage 1840, but does not include transmission media, such as modulated data signals.

[0227] Explanation of terms

[0228] For the purposes of this description, certain aspects, advantages, and novel features of the embodiments of the Disclosure are described herein. The disclosed methods, apparatus, and systems are not limited in any way. Rather, the Disclosure covers all novel features and aspects of the various disclosed embodiments, both individually and in various combinations and partial combinations with one another. The methods, apparatus, and systems are not limited to any particular aspect or feature or combination thereof, and the disclosed embodiments do not require that any one or more particular advantages exist or problems are solved. The scope of the Disclosure includes any features disclosed herein that can be combined with any other features disclosed herein, unless it is physically impossible.

[0229] Some operations of the disclosed embodiments are described in a specific sequential order for convenience of presentation; however, it should be understood that this method of description is inclusive of reordering unless a specific order is required by the specific language used herein. For example, operations described sequentially may, in some cases, be performed in a different order or simultaneously. Furthermore, for the sake of simplification, the accompanying drawings may not show all the different ways in which the disclosed components may be used with other components.

[0230] As used in this disclosure and claims, the singular forms “a,” “an,” and “the” include the plural form unless the context makes it clear otherwise. Furthermore, the term “includes” means “equipped with.” Furthermore, the terms “connected” and “related” generally mean being connected or linked electrically, electromagnetically, and / or physically (e.g., mechanically or chemically), and do not preclude the existence of intermediate elements between connected or related elements unless there is a specific opposite term.

[0231] In some examples, values, procedures, or devices may be referred to as "lowest," "best," or "minimum." Such descriptions are intended to indicate that a choice is possible from among many alternatives, and such a choice does not necessarily have to be better, smaller, or preferable to other choices.

[0232] In the specification, certain terms such as “top,” “bottom,” “upper side,” “lower side,” “horizontal,” “vertical,” “left,” and “right” may be used. These terms are used to clarify descriptions to some extent when dealing with relative relationships, where applicable. However, these terms are not intended to imply absolute relationships, positions, and / or orientations. For example, with respect to an object, the “top” surface can simply become the “bottom” surface by turning the object upside down. Nevertheless, they are still the same thing.

[0233] Unless otherwise specified, all figures used herein or in the claims, representing frequencies, material quantities, angles, pressures, molecular weights, percentages, temperatures, times, etc., should be understood to be modified by the term "approximately." Therefore, unless implicitly or explicitly indicated otherwise, the numerical parameters described are approximations that may depend on the desired properties and / or detection limits obtained under test conditions / methods well known to those skilled in the art. Where embodiments are directly and explicitly distinguished from the prior art discussed, the figures in embodiments are not approximations unless the word "approximately" is stated. Furthermore, not all alternatives described herein are equivalents.

[0234] While there are alternatives to the various components, parameters, and operating conditions described herein, this does not necessarily mean that these alternatives are equivalent and / or perform equally well. Nor does it mean that the alternatives are listed in preferred order unless otherwise specified.

[0235] Given the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are merely examples and should not be construed as limiting the scope of this disclosure. Rather, the scope of this disclosure is at least as broad as the following claims and their equivalents. Accordingly, we assert all that is contained within the scope and spirit of these claims.

Claims

1. Receiving data on the position of structural elements of the exposure apparatus, The position error signal is determined based at least partially on the position data and the specified position of the structural element. Applying phase correction to the aforementioned position error signal, Determining a force command to attenuate the specified vibration mode frequency of the structural element, at least partially based on the position error signal to which the phase correction has been applied and the specified vibration mode frequency, The actuator applies force to the structural element and transmits the force command to the actuator so as to dampen the vibration of the structural element at least at the specified vibration mode frequency of the structural element. A method that includes this.

2. The method according to claim 1, further comprising obtaining the position data by integrating an acceleration signal received from a sensor.

3. The method according to claim 2, further comprising determining the force command by filtering the position error signal using a low-pass filter.

4. The method according to claim 3, wherein the low-pass filter includes differential control.

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

6. The method according to any one of claims 1 to 4, wherein determining the force command further comprises filtering the position error signal using a bandpass filter.

7. The method according to any one of claims 1 to 4, further comprising determining the force command by filtering the position error signal using a notch filter.

8. The method according to any one of claims 1 to 4, wherein the position data of the structural element is obtained based on a signal received from a sensor connected to the structural element at a position away from the actuator.

9. The method according to any one of claims 1 to 4, 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. The method according to any one of claims 1 to 4, wherein the specified vibration mode frequency is lower than the vibration mode frequency of the actuator.

11. The method according to any one of claims 1 to 4, wherein determining the force command further comprises determining the force command to attenuate 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 platen, a substrate stage, or a mask stage of the exposure apparatus.

13. An exposure apparatus including structural elements, An actuator system connected to the aforementioned structural element, comprising an actuator and a sensor, The data of the position of the structural element is received, A position error signal is determined based at least partially on the position data and the specified position of the structural element. Applying phase correction to the aforementioned position error signal, Based at least partially on the position error signal to which the phase correction has been applied and the specified vibration mode frequency of the structural element, a force command to attenuate the specified vibration mode frequency is determined. The actuator applies force to the structural element and transmits the force command to the actuator so as to attenuate the vibration of the structural element at least at the specified vibration mode frequency of the structural element. Control system and, A system equipped with these features.

14. The control system obtains the position data by integrating the acceleration signal received from the sensor, according to claim 13.

15. The control system filters the position error signal using a low-pass filter, according to claim 14.

16. The system according to claim 15, wherein the low-pass filter includes differential control.

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

18. The control system according to any one of claims 13 to 16, wherein the control system filters the position error signal using a bandpass filter.

19. The control system filters the position error signal using a notch filter. The system according to any one of claims 13 to 16.

20. The system according to any one of claims 13 to 16, wherein the sensor is spaced apart from the actuator on the structural element.

21. The system according to any one of claims 13 to 16, 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 16, wherein the structural element is an optical platen, a substrate stage, or a mask stage of the exposure apparatus.

23. Receiving data on the position of structural elements of the exposure apparatus, Determining a position error signal based at least partially on the position data and the specified position of the structural element, Filtering the position error signal using a low-pass filter that includes differential control, Applying phase correction to the position error signal using the low-pass filter, Determining a force command to attenuate a specified vibration mode frequency of the structural element, based at least partially on the filtered and phase-corrected position error signal, The actuator connected to the structural element applies force to the structural element and transmits the force command to the actuator so as to attenuate the vibration of the structural element at least at the specified vibration mode frequency of the structural element. A method that includes this.

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