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 TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 63 / 393,161, filed July 28, 2022, which is incorporated herein by reference in its entirety.

[0002] The present disclosure relates to systems and methods for controlling and / or reducing vibrations of structural elements in precision systems, such as lithographic exposure apparatus. [Background technology]

[0003] Photolithography processes for manufacturing microelectronic devices such as liquid crystal displays and semiconductor devices (e.g., integrated circuits) use exposure apparatuses 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) through a projection optical system (e.g., including multiple lenses). In such systems, the reticle and substrate must be precisely aligned to expose the substrate and form desired features on the order of a few nanometers in size. However, vibrations in the exposure apparatus's support structure and its various subsystems can cause the reticle, projection optical system, and / or substrate to move relative to one another during exposure, 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 tedious manual adjustment, and their effectiveness is often limited by space constraints within the machine. Therefore, improved systems for controlling vibrations of support structures in lithography exposure apparatuses are needed. Summary of the Invention

[0004] Certain 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 apparatuses. In an exemplary embodiment, a method includes receiving data of a position of a structural element of an exposure apparatus, determining a position error signal based at least in part on the position data and a specified position of the structural element, determining a force command for damping the specified vibration mode frequency of the structural element based at least in part on the position error signal and a 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 vibrations of the structural element at least at the specified vibration mode frequency of the structural element.

[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 with a low pass filter.

[0007] In any or all of the disclosed embodiments, the low pass filter includes a derivative 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 with a bandpass filter.

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

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

[0012] In any or all of the disclosed embodiments, the specified vibrational 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.

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

[0014] In any or all of the disclosed embodiments, determining the force commands further includes determining the force commands for damping a plurality of specified vibrational mode frequencies of the structural element.

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

[0016] In another exemplary embodiment, a system includes an exposure apparatus including a structural element; an actuator system coupled 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 in part on the position data and a specified position of the structural element, determines a force command for damping the specified vibration mode frequency based at least in part on the position error signal and a specified vibration mode frequency of the structural element, and sends the force command to the 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.

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

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

[0019] In any or all of the disclosed embodiments, the low pass filter includes a derivative 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 with 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 specified vibrational 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.

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

[0026] In another exemplary embodiment, a method includes receiving position data of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and a specified position of the structural element; filtering the position error signal with a low pass filter including a derivative control; applying a phase correction to the position error signal with the low pass filter; determining a force command for damping a specified vibration mode frequency of the structural element based at least in part on the filtered, phase corrected position error signal; and transmitting the force command to an actuator coupled to the structural element 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.

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

[0028] [Figure 1] FIG. 1 is a diagram schematically showing the configuration of a liquid crystal exposure apparatus according to the first embodiment. [Figure 2] FIG. 2 is a diagram showing a substrate stage device that the liquid crystal exposure apparatus of FIG. [Figure 3] FIG. 3 is a schematic diagram of a substrate measurement system provided in the liquid crystal exposure apparatus of FIG. [Figure 4] FIG. 4 is a diagram (part 1) for explaining the operation of the substrate stage device. [Figure 5] FIG. 5 is a diagram (part 2) for explaining the operation of the substrate stage device. [Figure 6] FIG. 6 is a block diagram showing the input / output relationship of the main control device that mainly constitutes the control system of the liquid crystal exposure device. [Figure 7] FIG. 7 is a schematic side elevation view of an actuator system coupled to a structural element, according to one embodiment. [Figure 8]FIG. 8 is a schematic diagram showing the structural elements and actuator system represented as a mass-spring-damper system. [Figure 9] 9 and 10 are Bode plots showing the open-loop frequency response of the mass-spring-damper system of FIG. 8 to various excitation forces. [Figure 10] 9 and 10 are Bode plots showing the open-loop frequency response of the mass-spring-damper system of FIG. 8 to various excitation forces. [Figure 11] FIG. 11 is a schematic block diagram of a control system for controlling vibration at vibration mode frequencies of a structural element, according to one embodiment. [Figure 12] FIG. 12 is a process flow diagram illustrating an exemplary method for controlling structural mode vibration of a structural element, according to one embodiment. [Figure 13] FIG. 13 is a schematic block diagram of a control system for controlling vibration of a structural element at multiple vibration mode frequencies, according to one embodiment. [Figure 14] FIG. 14 is a top plan view of an actuator system coupled to a plate member according to one embodiment. [Figure 15] FIG. 15 is a schematic block diagram of a control system for controlling vibration of the plate member of FIG. 14 at two vibration mode frequencies, according to one embodiment. [Figure 16A] 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force acts on the plate member of FIG. [Figure 16B] 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force acts on the plate member of FIG. [Figure 16C] 16A to 16C show graphs of acceleration versus time and acceleration versus frequency when an impulse force acts on the plate member of FIG. [Figure 17]FIG. 17 is a Bode plot showing the magnitude and phase of the frequency response of the system without feedback control, with damping control of the first vibration mode, and with damping control of both the first and second modes. [Figure 18] FIG. 18 is a side elevation view of another experimental system including a beam member supported by two support members, with an actuator system attached to the beam member. [Figure 19] FIG. 19 is a diagram schematically showing the first and second vibration modes of the beam member of FIG. [Figure 20] FIG. 20 is a Bode plot showing the magnitude and phase of the open loop frequency response of the system 700 as measured by the two accelerometers of the actuator system. [Figure 21] FIG. 21 is a Bode plot illustrating the open loop frequency response of the system 700 and implementing control using position data derived from accelerometers co-located with the actuators of FIG. [Figure 22A] 22A-22B include plots of acceleration versus time and fast Fourier transform (FFT) illustrating the open-loop impulse response of the system (FIG. 22A) and the impulse response of the system implementing control using position data derived from the first accelerometer of FIG. 18 (FIG. 22B). [Figure 22B] 22A-22B include plots of acceleration versus time and fast Fourier transform (FFT) plots showing the open-loop impulse response of the system (FIG. 22A) and the impulse response of the system applying control using position data derived from the first accelerometer of FIG. 18 (FIG. 22B). [Figure 23] FIG. 23 is a Bode plot illustrating the open loop frequency response of the system of FIG. 18 and implementing control using position data derived from the second accelerometer. [Figure 24A]24A and 24B include plots of acceleration versus time and fast Fourier transforms showing the open-loop impulse response of the system of FIG. 18 (FIG. 24A) and the impulse response of the system of FIG. 18 implementing control using position data derived from a second accelerometer (FIG. 24B). [Figure 24B] 24A and 24B include plots of acceleration versus time and fast Fourier transforms showing the open-loop impulse response of the system of FIG. 18 (FIG. 24A) and the impulse response of the system of FIG. 18 implementing control using position data derived from a second accelerometer (FIG. 24B). [Figure 25] FIG. 25 is a side elevation view of another embodiment of the experimental construction system. [Figure 26] 26 to 28 are Bode diagrams showing three structural vibration modes of the system of FIG. [Figure 27] 26 to 28 are 8-Bode diagrams showing the three structural vibration modes of the system of FIG. [Figure 28] 26 to 28 are Bode diagrams showing three structural vibration modes of the system of FIG. [Figure 29] FIG. 29 is a schematic block diagram illustrating 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] 30 and 31 are Bode plots of the dynamic response of the system of FIG. 25 when controlled by the control system of FIG. [Figure 31] 30 and 31 are Bode plots of the dynamic response of the system of FIG. 25 when controlled by the control system of FIG. [Figure 32] FIG. 32 contains graphs of acceleration versus time and acceleration versus frequency for the system of FIG. 25 when controlled by the system of FIG. [Figure 33] FIG. 33 is a top plan view of another embodiment of a structural system including a rectangular plate member and an actuator and a plurality of accelerometer sensors coupled to the plate member. [Figure 34] FIG. 34 shows another embodiment of a control system including two control loops configured to control four modes of vibration of the structure of FIG. [Figure 35] FIG. 35 is a Bode plot of the open-loop frequency response of the system of FIG. 33 when excited by an impulse. [Figure 36] FIG. 36 is a Bode plot of the frequency response of a system that implements control of four vibration modes based on force commands from the control system of FIG. [Figure 37A] 37A-37B include plots of acceleration versus time and acceleration versus frequency for the system of FIG. [Figure 37B] 37A-37B include plots of acceleration versus time and acceleration versus frequency for the system of FIG. [Figure 38] FIG. 38 is a top plan view of another arrangement of four accelerometers, actuators, and vibrators on a plate member. [Figure 39] FIG. 39 shows another embodiment of a control system including two control loops configured to control four modes of vibration of the structure of FIG. [Figure 40] Figure 40 shows the surface deformation of a plate in nine vibration modes of the plate based on a finite element analysis model of a rectangular plate. [Figure 41] 41 to 44 show schematic diagrams of input and output coordinates of a modal space model of a structural element in various vibration modes. [Figure 42] 41 to 44 show schematic diagrams of input and output coordinates of a modal space model of a structural element in various vibration modes. [Figure 43] 41 to 44 show schematic diagrams of input and output coordinates of a modal space model of a structural element in various vibration modes. [Figure 44] 41 to 44 show schematic diagrams of input and output coordinates of a modal space model of a structural element in various vibration modes. [Figure 45]FIG. 45 is a schematic diagram of an immersion microlithography system, which is another example of a precision system that includes the stage assemblies described herein. [Figure 46] FIG. 46 is a schematic diagram of an extreme ultraviolet microlithography system, which is another example of a precision system that includes the stage assemblies described herein. [Figure 47] FIG. 47 is a process flow diagram illustrating exemplary steps associated with a process for manufacturing a semiconductor device. [Figure 48] FIG. 48 is a process flow diagram illustrating exemplary steps associated with processing a substrate (eg, a wafer), such as may be performed in the process shown in FIG. [Figure 49] FIG. 49 is a schematic diagram of an exemplary precision system, a microlithography system, including a stage assembly as disclosed herein that includes at least one holding device. [Figure 50] FIG. 50 is a schematic block diagram illustrating a representative computer control system for implementing the disclosed systems and methods. DETAILED DESCRIPTION OF THE INVENTION

[0029] Certain embodiments of the present disclosure relate to actuator systems and associated control systems and methods that can be used to control / reduce / dampen vibrations of structural elements in precision systems such as lithography exposure apparatus. In certain embodiments, the actuators and control systems described herein can be tuned to damp relatively low frequency vibrations, such as resonant modes of a structure excited by reaction forces exerted by moving components of the system, such as a substrate stage, a mask stage, etc. However, the control system can be configured to detect and damp structural mode vibrations having any frequency within the sampling rate frequency range of the system and / or the amplifier bandwidth of the actuator, such as between 2 Hz and 10 kHz.

[0030] In certain embodiments, the actuator system can include an actuator, such as a voice coil motor, and one or more motion sensors, such as an accelerometer, although other types of actuators and / or sensors can be used. The actuators and sensors can be located at the same or different locations on the structural element. In certain embodiments, the locations of the actuators and sensors can be selected so that the sensors detect relatively large displacements of the structural element associated with particular vibration modes and / or so that forces applied to the structural element by the actuators result in relatively large displacements of the structural element, thus increasing the damping effect.

[0031] In certain embodiments, the control systems described herein can be configured to compensate for phase lags in the system associated with one or more of the sensor position (e.g., related to the vibration mode shape of the structural element), the sensor bandwidth, and / or time delays associated with signal processing and digital control. In certain embodiments, the control system can 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 the low-pass filters, can include derivative control. In certain embodiments, one or more of the filters, such as the low-pass filters, can be configured to apply a phase correction to a received position error signal in a feedback control loop to compensate for the aforementioned phase lag. In certain embodiments, the control system can include multiple control elements implemented in parallel, each comprising a combination of filters described herein and configured to generate force commands to damp vibrations at specific vibration mode frequencies of the structural element while reducing inter-modal coupling. Thus, the control systems described herein can be configured to damp vibrations at one or more vibration modes of the structural element, such as two modes, three modes, four modes, etc. In certain embodiments, the control system may also be configured to enable the actuator system to damp modal frequencies of the structural element that are lower than the modal frequencies of the actuator-structure interaction, such as by using a peak filter.

[0032] By implementing the control methods described herein, the actuator and control systems of the present 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 and control systems can also significantly reduce the settling time of such structural elements, thereby significantly improving substrate positioning accuracy and throughput of, for example, a lithography exposure apparatus.

[0033] Example 1: Lithography exposure apparatus

[0034] A representative embodiment of the first embodiment will be described with reference to FIGS.

[0035] Figure 1 shows a schematic diagram of 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 projection exposure apparatus, or so-called scanner, in which the object to be exposed is a glass substrate P. The glass substrate P (hereinafter simply referred to as substrate P) is formed in a rectangular shape (e.g., a square shape) in plan view, and can be used for liquid crystal display devices (flat panel displays) and the like.

[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 or the like is formed, a projection optical system 16, an apparatus main body 18, a substrate stage device 20 that holds a substrate P whose surface (the surface facing the +Z direction in FIG. 1 ) is coated with a resist (e.g., a photosensitive agent), and control systems for these components. Hereinafter, the direction in which the mask M and substrate P are scanned relative to the projection optical system 16 during exposure will be referred to as the X-axis direction, the direction perpendicular to the X-axis direction in the horizontal plane as the Y-axis direction, the direction perpendicular to the X-axis and Y-axis as the Z-axis direction (the direction parallel to the optical axis of the projection optical system 16), and the directions of rotation about the X-axis, Y-axis, and Z-axis as the θx direction, θy direction, and θz direction, respectively. Furthermore, positions in the X-axis, Y-axis, and Z-axis directions will be referred to as the X-position, Y-position, and Z-position, respectively.

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

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

[0039] The projection optical system 16 is disposed 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 the projection optical system disclosed in U.S. Pat. No. 6,552,775 and the like, and is equipped with multiple lens modules that form an erect, normal image in a double-telecentric, life-size system.

[0040] In the liquid crystal exposure apparatus 10, when the illumination light IL illuminates the illumination area on the mask M, the illumination light IL passes through (transmits) the mask M and, via the projection optical system 16, forms a projected image (partial erect image) of the circuit pattern of the mask M in the illumination area in an irradiation area (exposure area) on the substrate P that is conjugate with 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 apparatus main body 18 supports the mask stage device 14 and the projection optical system 16 and is installed on the floor F in the clean room via a vibration isolation device 19. The apparatus main body 18 can be configured similarly to the apparatus main body disclosed in U.S. Patent Application Publication No. 2008 / 0030702, and includes an upper mount 18a, a pair of intermediate mounts 18b, and a lower mount 18c. Because the upper mount 18a is a member that supports the projection optical system 16, in the following description of this embodiment, the upper mount 18a will be referred to as the optical surface plate 18a. Hereinafter, in the scanning exposure operation using the liquid crystal exposure apparatus 10 of this embodiment, the position of the substrate P is controlled relative to the illumination light IL irradiated via the projection optical system 16, and therefore the optical surface plate 18a that supports the projection optical system 16 functions as a reference member when controlling the position of the substrate P.

[0042] Substrate stage device 20 is a device used to perform highly accurate positional control of substrate P relative to projection optical system 16 (illumination light IL), and moves substrate P over a predetermined long stroke along the horizontal plane (X-axis direction and Y-axis direction), while also moving substrate P minutely in six degrees of freedom. The structure of the substrate stage device used in 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 finely moved relative to the two-dimensional coarse movement stage, as disclosed in U.S. Patent Application Publication No. 2012 / 0057140, etc.

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

[0044] As shown in FIG. 2, the fine movement stage 22 includes a substrate holder 32 and a stage main body 34. The substrate holder 32 is formed in the shape of a rectangular plate (or box) in plan view (see FIG. 4), and the substrate P is placed on its upper surface (substrate placement surface). The dimensions of the upper surface of the substrate holder 32 in the X-axis and Y-axis directions are set to be approximately the same as those of the substrate P (actually slightly shorter). The substrate P is held by vacuum suction to the substrate holder 32 while placed on the upper surface of the substrate holder 32, thereby correcting the flatness of the substrate P over almost the entire surface (entire surface) along the upper surface of the substrate holder 32. The stage main body 34 includes a rectangular plate (or box) member in plan view whose dimensions in the X-axis and Y-axis directions 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 FIG. 1, Y coarse movement stage 24 is disposed below (on the -Z side of) fine movement stage 22 and on a pair of base frames 30. As shown in FIG. 4, Y coarse movement stage 24 has a pair of X beams 36. The pair of X beams 36 are disposed parallel to the Y-axis direction at a predetermined interval. The pair of X beams 36 are attached to the pair of base frames 30 via mechanical linear guide devices and are movable on the pair of base frames 30 in the Y-axis direction.

[0046] 1, X coarse movement stage 26 is disposed above Y coarse movement stage 24 (on the +Z side) and below fine movement stage 22 (between fine movement stage 22 and Y coarse movement stage 24). X coarse movement stage 26 is a plate-like member that is rectangular in plan view, and is mounted on a pair of X beams 36 (see FIG. 4) that Y coarse movement stage 24 has, via multiple mechanical linear guide devices 38 (see FIG. 2). X coarse movement stage 26 is movable in the X-axis direction relative to Y coarse movement stage 24, and also moves integrally with Y coarse movement stage 24 in the Y-axis direction.

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

[0048] The type of actuator constituting first drive system 62 is not particularly limited, but FIG. 2 and other figures show, as an example, a plurality of linear motors (voice coil motors) 40 that generate thrust in the X-axis, Y-axis, and Z-axis directions, respectively (the X linear motors are not shown in FIGS. 1 and 2). Each linear motor 40 has a stator attached to X coarse movement stage 26 and a mover attached to stage main body 34 of fine movement stage 22, and thrust in six degrees of freedom is applied to X coarse movement stage 26 via each linear motor 40. The detailed configuration of first to third drive systems 62, 64, 66 is disclosed, for example, in U.S. Patent Application Publication No. 2010 / 0018950.

[0049] Main controller 100 applies a thrust to fine movement stage 22 using first drive system 62 so that the relative position between fine movement stage 22 and X coarse movement stage 26 (see FIG. 1 for each) remains within a predetermined range in the X-axis and Y-axis directions. Here, when fine movement stage 22 is moved over a long stroke in the X-axis direction or Y-axis direction, "the relative position remains within a predetermined range" means that X coarse movement stage 26 (X coarse movement stage 26 and Y coarse movement stage 24 when fine movement stage 22 is moved in the Y-axis direction) and fine movement stage 22 move at approximately the same speed in the same direction; fine movement stage 22 and X coarse movement stage 26 do not necessarily need to move in strict synchronization, and a predetermined relative movement (relative positional deviation) is allowed.

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

[0051] Weight cancellation device 42 (also called a center pillar) is inserted into an opening formed in X coarse movement stage 26 and is mechanically connected to X coarse movement stage 26 at the height of the center of gravity via multiple connecting members 46 (also called flexure devices). X coarse movement stage 26 and weight cancellation device 42 are connected by multiple connecting members 46 in a state where they are vibrationally (physically) separated in the Z axis direction, the θx direction, and the θy direction. Weight cancellation device 42 is pulled by X coarse movement stage 26, and thereby moves integrally with X coarse movement stage 26 in the X axis and / or Y axis directions.

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

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

[0054] Y step guide 44 is mechanically connected to Y coarse movement stage 24 (pair of X beams 36) at the height of its center of gravity via multiple connecting members 54 (see FIG. 4). Similar to connecting member 46 described above, connecting member 54 is a flexure device that connects Y coarse movement stage 24 and Y step guide 44 in a state of vibration (physical) directions with five degrees of freedom among the six degrees of freedom, excluding the Y-axis direction. Y step guide 44 moves integrally with the Y coarse movement stage 24 by being pulled by Y coarse movement stage 24.

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

[0056] Next, a substrate measurement system 70 for acquiring position information in six degrees of freedom of the substrate P (actually, the fine movement stage 22 that holds the substrate P) will be described.

[0057] FIG. 3 shows a schematic diagram of a substrate measurement system 70. The substrate measurement system 70 includes a first measurement system (here, fine movement stage measurement system 76 (see FIG. 6 )) including a first scale (here, upward scale 72) possessed by the Y coarse movement stage 24 (associated with the Y coarse movement stage 24) and a first head (here, downward X head 74x and downward Y head 74y) possessed by the fine movement stage 22, and a second measurement system (here, coarse movement stage measurement system 82 (see FIG. 6 )) including a second scale (here, downward scale 78) possessed by the optical surface plate 18a (see FIG. 2 ) and a second head (here, upward X head 80x and upward Y head 80y) possessed by the Y coarse movement stage 24. Note that in FIG. 3 , the fine movement stage 22 is modeled as a member that holds the substrate P. Furthermore, the grating interval (pitch) of the diffraction gratings possessed by each of the scales 72 and 78 is illustrated as being much wider than it actually is. 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 a conventional optical interferometer system, the influence of air fluctuations is smaller than in an optical interferometer system, and the position of the substrate P can be controlled with high precision, thereby improving exposure precision.

[0058] The upward scale 72 is fixed to the upper surface of a scale base 84. As shown in FIG. 4, one scale base 84 is arranged on each of the +Y and -Y sides of the fine movement stage 22. As shown in FIG. 2, the scale base 84 is fixed to the X beam 36 of the Y coarse movement stage 24 via an arm member 86 that is L-shaped when viewed from the X-axis direction. Therefore, the scale base 84 (and the upward scale 72) can move integrally with the Y coarse movement stage 24 in the Y-axis direction over a predetermined long stroke. As shown in FIG. 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] Scale base 84 is a member extending parallel to the X-axis, and its length in the X-axis direction is set to about twice the length of substrate holder 32 (i.e., substrate P (not shown in FIG. 4)) in the X-axis direction (about the same as Y step guide 44). Scale base 84 is preferably made of a material that is resistant to thermal deformation, such as ceramics. The same applies to scale base 92 and head bases 88 and 96, which will be described later.

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

[0061] Head bases 88 are fixed to the centers of the +Y and -Y side surfaces of substrate holder 32 via arm members 90 corresponding to the scale base 84 described above (see FIG. 2). Downward heads 74x and 74y (see FIG. 3) are fixed to the underside of head base 88, respectively.

[0062] In fine movement stage measurement system 76 of this embodiment (see FIG. 6), as shown in FIG. 3, two downward X heads 74x are arranged spaced apart in the X-axis direction and two downward Y heads 74y are arranged spaced apart in the X-axis direction relative to one head base 88. Each of heads 74x and 74y irradiates corresponding upward scale 72 with measurement light and receives light (here, diffracted light) from upward scale 72. The light from upward scale 72 is supplied to a detector, and the detector output is supplied to main controller 100 (see FIG. 6). Main controller 100 determines the relative movement amount of each head 74x and 74y with respect to scale 72 based on the detector output. Note that in this specification, the term "head" refers to the portion that irradiates measurement light onto a diffraction grating and the portion onto which light from the diffraction grating is incident; the heads shown in the figures do not themselves need to have a light source or detector.

[0063] As explained above, in fine movement stage measurement system 76 (see FIG. 6) of the present embodiment, four X linear encoder systems are made up of a total of four downward X heads 74x (two each on the +Y side and the -Y side of substrate P) and corresponding upward scales 72, and four Y linear encoder systems are made up of a total of four downward Y heads 74y (two each on the +Y side and the -Y side of substrate P) and corresponding upward scales 72. Main controller 100 (see FIG. 6) uses the outputs of the four X linear encoder systems and four Y linear encoder systems described above to acquire position information (hereinafter referred to as "first information") in the X-axis direction, Y-axis direction, and θz direction of fine movement stage 22 (substrate P).

[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 Fig. 4, the length of the upward scale 72 in the X-axis direction is approximately the same as that of the scale base 84, and is set so that it can cover the movable range of the fine movement stage 22 in the X-axis direction. On the other hand, the dimension in the width direction (Y-axis direction) of the upward scale 72 (and the distance between a pair of heads 74x, 74y adjacent in the Y-axis direction) is set so that the measurement light from each head 74x, 74y does not deviate from the corresponding grating surface (surface to be measured) of the upward scale 72, even when the fine movement stage 22 is finely moved in the Y-axis direction relative to the upward scale 72.

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

[0066] 4 and 5, regardless of the position of the fine movement stage 22 in the Y-axis direction, the measurement light from each of the heads 74x and 74y attached to the fine movement stage 22 does not deviate from the grating surface of the upward scale 72, even when the fine movement stage 22 moves finely in the Y-axis direction. Furthermore, when the fine movement stage 22 moves with a long stroke in the X-axis direction, the measurement light from each of the downward heads 74x and 74y does not deviate from the grating surface of the upward scale 72.

[0067] Next, the coarse movement stage measurement system 82 (see FIG. 6) will be described. As can be seen from FIGS. 1 and 4, the coarse movement 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 the -Y side of the projection optical system 16 (see FIG. 1). The downward scales 78 are fixed to the underside of the optical surface plate 18a via a scale base 92 (see FIG. 2). The scale base 92 is a plate-like 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 movement stage 22 (i.e., the substrate P (not shown in FIG. 4)).

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

[0069] As shown in Fig. 2, a head base 96 is fixed to each of a pair of scale bases 84 of Y coarse movement stage 24 via arm members 94 that are L-shaped when viewed in the X-axis direction. As shown in Fig. 4, head bases 96 are respectively disposed near the ends of scale base 84 on the +X side and -X side. As shown in Fig. 3, each of upward heads 80x, 80y is fixed to the upper surface of head base 96. Therefore, a total of four head bases 96 (and upward heads 80x, 80y) can move in the Y-axis direction integrally with Y coarse movement stage 24.

[0070] In coarse movement stage measurement system 82 of the present embodiment (see FIG. 6), as shown in FIG. 3, two upward-facing X heads 80x and two upward-facing Y heads 80y are arranged spaced apart in the Y-axis direction with respect to one head base 96. Each of heads 80x, 80y irradiates measurement light onto the corresponding downward-facing scale 78 and receives light (here, diffracted light) from downward-facing scale 78. The light from downward-facing scale 78 is supplied to a detector (not shown), and the output of the detector is supplied to main controller 100 (see FIG. 6). Main controller 100 obtains the amount of relative movement of each of heads 80x, 80y with respect to scale 78 based on the output of the detector. As described above, in coarse movement stage measurement system 82 of the present embodiment, a total of eight upward-facing X heads 80x and the corresponding downward-facing scales 78 constitute eight X linear encoder systems, and a total of eight upward-facing Y heads 80y and the corresponding downward-facing scales 78 constitute eight Y linear encoder systems. Main control device 100 (see FIG. 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") in the X-axis direction, Y-axis direction, and θz direction of Y coarse movement stage 24.

[0071] Furthermore, the upward scale 72 fixed on the scale base 84 and the upward heads 80x, 80y fixed integrally to the scale base 84 via the head base 96 are arranged so that their positional relationship is constant and known. Hereinafter, information regarding the relative positional relationship between the upward scale 72 and the upward heads 80x, 80y fixed integrally thereto will be referred to as "third information." Note that, although this specification has been described assuming that the upward scale 72 and the upward heads 80x and 80y are arranged so that their positional relationship is constant, the liquid crystal exposure apparatus 10 may also be provided with a measurement system that measures the positional relationship between them. This also applies to each of the embodiments described below.

[0072] Based on the first to third information described above, the main control device 100 (see Figure 6) acquires position information in the XY plane of the fine movement stage 22 (substrate P) relative to the optical surface plate 18a (projection optical system 16), and controls the position of the substrate P relative to the projection optical system 16 (illumination light IL) using the substrate drive system 60 described above (see Figure 6).

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

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

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

[0076] In the liquid crystal exposure apparatus 10 (see FIG. 1) configured as described above, under the control of the main controller 100 (see FIG. 6), a mask loader (not shown) loads the mask M onto the mask stage device 14, and a substrate loader (not shown) loads the substrate P onto the substrate holder 32. Then, the main controller 100 performs alignment measurement using an alignment detection system (not shown), and after the alignment measurement is completed, step-and-scan exposure operations are performed sequentially for multiple shot areas set on the substrate P. During the alignment measurement operation and step-and-scan exposure operation, the position information of the fine 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 fine movement stage 22 (substrate P) is measured using a substrate measurement system 70 including an encoder system, so that the influence of air fluctuations is less than in conventional measurements using an optical interferometer system, and the position of the substrate P can be controlled with high precision, thereby improving exposure precision.

[0078] Furthermore, the substrate measurement system 70 measures the position of the substrate P using the downward scale 78 fixed to the optical surface plate 18a (apparatus main body 18) as a reference (via the upward scale 72), and therefore can measure the position of the substrate P substantially using the projection optical system 16 as a reference. This makes it possible to control the position of the substrate P using the illumination light IL as a reference, thereby improving exposure accuracy.

[0079] The configuration of the substrate measurement system 70 described so far can be modified as appropriate as long as the position information of the fine movement stage 22 can be obtained with the desired accuracy within the movable range of the fine movement stage 22 (substrate P).

[0080] That is, in the above embodiment, a long scale having a length approximately equal to that of the scale base 84 is used as the upward scale 72, but the scale is not limited to this, and scales having a short length in the X-axis direction may be arranged at a predetermined interval in the X-axis direction, as in the encoder system disclosed in WO 2015 / 147319. In this case, a gap is formed between a pair of scales adjacent in the X-axis direction, so by making the interval in the X-axis direction between each pair of heads 74x, 74y adjacent in the X-axis direction wider than the gap, one of the heads 74x and one of the heads 74y can always face the scale. The same applies to the relationship between the downward scale 78 and the upward heads 80x, 80y.

[0081] Furthermore, although upward scale 72 is disposed on the +Y side and the -Y side of fine movement stage 22, this is not limiting and a scale may be disposed on only one side (the +Y side or the -Y side). Note that, as described above, when only one upward scale 72 is provided and multiple scales are disposed at predetermined intervals (gaps between scales) in the X-axis direction, the number and arrangement of heads 74x, 74y can be set so that at least two downward X heads 74x (or downward Y heads 74y) always face a scale so that position measurement in the θz direction of fine movement stage 22 can always be performed. The same applies to downward scale 78; the number and arrangement of downward scales 78 and upward heads 80x, 80y can be changed as appropriate as long as position measurement in the X-axis, Y-axis, and θz directions of Y coarse movement stage 24 can always be performed.

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

[0083] Alternatively, a downward-facing displacement sensor may be attached to head base 88, and this sensor may measure Z tilt position information of substrate P using scale base 84 (or the reflecting surface of upward scale 72) as a reference. At least three of the multiple downward heads 74x, 74y may be two-dimensional heads (so-called XZ heads or YZ heads) that can measure positions in directions parallel to the horizontal plane as well as in the vertical direction, and the grating surface of upward scale 72 may be used to acquire Z tilt position information of substrate P by the two-dimensional heads. Similarly, Z tilt position information of Y coarse movement stage 24 may be measured using scale base 92 (or downward scale 78) as a reference. For example, an encoder head having a configuration similar to that of the displacement sensor head disclosed in U.S. Pat. No. 7,561,280 may be used as the XZ head or YZ head.

[0084] Further details regarding the liquid crystal exposure apparatus 10 are described in US Pat. No. 10,670,977, which is incorporated herein by reference.

[0085] Example 2: Actuator system for active vibration suppression and control method

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

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

[0088] For example, FIG. 7 shows a representative example of an actuator system 200 including an actuator 202 attached to or coupled to a structural element 204 (also referred to as a structural member). The actuator system 200 can further include multiple sensors. A first sensor 206A is illustrated as being co-located with (e.g., attached to) the actuator 202, and a second sensor 206B is illustrated as being spaced apart from the actuator 202 and coupled to the structural element 204. The system can include any number of actuators and any number of sensors, depending, for example, on 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 can be located anywhere on the structural element, such as on the top or bottom surface, sides, etc., of the structural element, or can be integrated into the body of the structural element.

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

[0090] In particular embodiments, sensors 206A and 206B can be acceleration or vibration sensors such as accelerometers, velocity sensors such as moving coil or piezoelectric velocity receivers, position sensors such as linear potentiometers, capacitive sensors, linear encoders, interferometers, or combinations thereof. In the examples below, the sensors are configured as accelerometers, although other types of sensors can also be used.

[0091] FIG. 8 is a schematic diagram of a structural element 300 to be controlled / damped, along 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. The actuator system 302, which in FIG. 8 represents an actuator and a co-located accelerometer sensor, 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 vibrational mode frequencies of the structural element 300. In the example of an exposure apparatus, the structural element 300 could resemble an optical table, a substrate stage, a mask stage, or other structure within a machine to which the actuator system 302 is connected.

[0092] The motion of the actuator system 302 relative to the structural element 300 may be determined by the mass of the actuator system elements, the spring constant of the spring 310, and the damping coefficient of the damper 312. The mass of the actuator system 302 and the spring constant of the spring 310 may determine the vibration mode frequencies of the actuator system 302. In certain embodiments, the vibration mode frequencies of the actuator system may be the frequencies at which the actuator or actuator system vibrates relative to the structural element while the actuator is operating. In certain embodiments, designing the system so that the modal frequencies of the actuator system 302 are less than the modal frequencies of the structural element 300 allows the actuator system 302 to more efficiently damp the structural mode vibrations of the structural element 302, although this is not required, as demonstrated in subsequent examples herein.

[0093] When the actuator of actuator system 302 applies a force to structural element 300, the actuator pushes on actuator system 302, and a reaction force acts on structural element 300. Double-headed arrow 314 indicates the relative motion between actuator system 302 and structural element 300 when the actuator is actuated. Figure 9 shows the open-loop frequency response of the mass-spring-damper system of Figure 8 when a disturbance force is applied by actuator system 302. The structural mode vibration of structural element 300 is observed between 30 Hz and 40 Hz, and the mode vibration of actuator system 302 is 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 of Figure 8 when subjected to a disturbance force (e.g., an impulse) applied to the structural element 300 by a vibration exciter separate from the actuator system, such as by a vibration exciter positioned between the ground 304 and the structural element 300. The force applied by the vibration 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 due to disturbance forces can be damped by operating the actuator system 302 according to a control scheme that includes phase correction to compensate for one or more of amplifier bandwidth, sensor signal conditioning, and / or digital control time delays in the control system based on the vibration frequency or frequencies of the structural element to be damped.

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

number

[0097] Upon disturbance of the structural system 402 by a disturbance force d, the acceleration of the actuator may be determined by a co-located accelerometer sensor, and an acceleration signal may be provided to an integrating element in block 404. In certain embodiments, the integrating element 404 may integrate the acceleration signal received from the accelerometer sensor to obtain a position signal (e.g., the accelerometer signal may be integrated twice by the integrating element). The integrating element 404 may also filter the acceleration sensor signal with one or more filters to select specific frequencies or frequency bands. For example, in certain embodiments, the integrating element 404 may filter the signal with a high-pass filter, which may reduce low-frequency drift in the signal from the accelerometer sensor. A representative transfer function H of the integrating element 404, which represents the combination of the integration and high-pass filtering of the accelerometer signal, is a2p (s) is given by the following equation 2, where d a is the damping ratio, and ω a is the cutoff frequency of the high-pass filter.

number

[0098] The resulting position signal (also referred to as position data) may be subtracted at summing junction 408 from a position command signal x(s), which represents a desired position of the structural system 402. In certain embodiments, the position command x(s) (e.g., a desired position of a structural element) may be zero if no vibration / motion of the structural system 402 is desired. By subtracting the position signal from the position command signal x(s), a position error signal may be obtained, which may be provided to filter control element 406.

[0099] The filter control element 406 can determine a force command u that can be transmitted to an actuator of the actuator system to cause the actuator to apply a force to the structural element. In the following description, u will be referred to as a force command, but it may also be a current command. In FIG. 11, the force command u is shown transmitted from the filter control element 406 and acting on the structural system 402 to damp vibrations of the structural system.

[0100] In certain embodiments, the filter control element 406 can apply one or more of a low-pass filter, a band-pass filter, a notch filter, and / or a high-pass filter to the position error signal to generate the force command u. In certain embodiments, the filter control element 406 can apply a combination of a low-pass filter, a band-pass filter, and a notch filter including a derivative control, hereinafter referred to as a damping filter. A representative transfer function C(s) of the filter control element 406 is given by Equation 3 below, 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 filters can be applied sequentially (e.g., serially) to the input signal. The transfer functions of the attenuation filter, bandpass filter, and 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 damping filter may include a derivative control term (also referred to as a damping control term or a velocity control term) and a low-pass filter term. For example, in certain embodiments, the damping filter transfer function H damp (s) can be given by the following equation 4: where k d is the attenuation gain, and k d ω r s is the differential control term of the transfer function (also called the damping coefficient), and the formula

number

number

[0102] In certain embodiments, the low pass filter may be underdamped (e.g., d r <1), critical damping (e.g., d r =1), or overdamping (e.g., d r In certain embodiments, the damping ratio d r can be between 0.05 and 10, depending on the frequency of the controlled object. In certain embodiments, increasing the damping ratio increases the control frequency range, but may also be related to coupling between modes. In certain embodiments, the gain of the control system is determined by the damping gain k of the differential control term of the damping filter. d can be adjusted by changing

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

number

[0104] In certain embodiments, the target frequency ω of the notch filter n is the target modal frequency ω r For example, the frequency ω of the notch filter may be different from that of the structural element. n may be another vibration mode of the structure excited in response to the actuator force command u, but not necessarily a 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 is the damping ratio.

number

[0106] In certain embodiments, the phase of the damping control force command u can be aligned to 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), the integral element transfer function H a2p (s), and the sum of the phase angles of the filter control element transfer function C(s) can be set equal to zero, as shown in Equation 7 below.

number

[0107] In certain embodiments, the phase angle ∠C(jω 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 ) In certain embodiments, the phase angle ∠H of the bandpass filter transfer function bandPass (jω r ) may be zero.

[0108] In certain embodiments, the phase delay θ of the system is determined by the phase angle ∠P(jω 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 ) 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 It is possible to adjust the damping filter to compensate for the phase lag θ of the system by setting θ = −θ, as in Equation 9 below:

number

[0110] Applying Euler's formula, the transfer function H of the damping filter can be calculated by using one of the two equations in the system of Equation 10: damp A 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 Equation 11 below. 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, the second equation in the system of Equation 11 below can avoid the generation of a direct current (DC) term. Avoiding the generation of a DC term can be advantageous in certain embodiments because the DC term can result 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 be performed using bandpass filters in the manner described above, or using notch filters. 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] Thus, the filter control element 406 filters the position error signal received from the summing junction 408 through a phase corrected attenuation filter H damp (s) (e.g., by applying a phase-compensated low-pass filter with derivative control) and then pass the phase-compensated signal output of the attenuation filter through a band-pass filter H bandpass (s), and the output of the bandpass filter is passed through a notch filter H notch By filtering with (s), the force command u can be determined. The resulting force command u is then sent to the actuator.

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

[0115] In other embodiments, the filter control element may implement other types of control, such as proportional and / or integral control, instead of or in addition to derivative control. For example, since the damping force is the damping ratio of the system multiplied by the velocity, the system may be damped using proportional control of velocity, integral control of acceleration, or derivative control of position.

[0116] FIG. 12 illustrates an exemplary method for reducing vibration of a structural element using the actuator system and control system described herein. At process block 420, position data (e.g., a position signal) of a structural element of an exposure apparatus can be received (e.g., from an integrating element after integrating and filtering an accelerometer signal). At process block 422, a position error signal can be determined for a specified position (or trajectory), such as by subtracting the position data / signal from the specified position. At process block 424, a force command can be determined based at least in part on a specified vibration mode frequency of the structural element to be damped and the position error signal. In certain embodiments, determining the force command can include one or more of filtering the position error signal with a low-pass filter (e.g., a low-pass filter including a derivative control), filtering the position error signal with a band-pass filter, and / or filtering the position error signal with 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 can include applying a phase correction to the position error signal, such as with a low-pass filter. At process block 426, the resulting force command may be sent 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 frequencies of the structural element.

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

[0118] In certain examples, the control methods described above can be adapted to control / damping vibration of a structural element at multiple frequencies, such as multiple resonant mode frequencies of the structural element. FIG. 13 illustrates another embodiment of a feedback control system 500 in which control of multiple frequencies / vibration modes is performed in parallel. The feedback control system 500 shown in FIG. 13 has a block 502 representing the plant dynamics of the mass-spring-damper system to be controlled, which can show the response to a disturbance force d given by the transfer function P(s) in Equation 1 above. The control system 500 is controlled by the transfer function H(s) given in FIG. 11 and Equation 2. a2p The actuator system may further include an integrating element 504 that can operate as described above with reference to position command signal x(s). After the position signal obtained by the integrating element 504 is subtracted from the position command signal x(s), the resulting position error signal may be provided to multiple filter control elements 506 implemented in parallel. In certain embodiments, the number of filter control elements 506 may 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 may implement a combination of phase-corrected damping filter control, bandpass filter control, and notch filter control, as described above. Each filter control element 506 may be tuned to damp 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 summed at summing junction 508, resulting in a force command u that is sent to the actuator system as described above. The transfer function C(s) of the composite output of the filter control elements 506 can be defined as the sum of the transfer functions of each 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, to avoid exciting other vibration frequencies, one or more notch filters may be applied by each filter control element 506. The transfer function of the notch filters is r , is substantially the same as that given in Equation 5 above. In a particular embodiment, the notch filter transfer function is the transfer function C k (s) may be multiplied together as given by Equation 13, and the transfer function H damp (s) is essentially the same as that given in Equation 4 above, and is the bandpass filter transfer function H bandpass (s) is substantially the same as given in Equation 6 above.

number

[0121] In certain embodiments, the filter control element output C i (jω k ) is calculated as C k (jω k ) can be approximately equal to the transfer function C i ω in (s) k This is because the use of notch filters in allows for the separation of control of different vibration modes at frequencies of interest, eg, 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 (e.g., determined independently of the other filter control elements). For example, C(jω k ) is given by Equation 14 above, C k (jω k ), so the target frequency ω rThe sum of the phase angles of Equation 7 for the k-th filter control element in can be expressed as Equation 15 below.

number

[0123] Phase delay θ of the kth filter control element k Therefore, it can be expressed as the following equation 16.

number

[0124] When phase correction is applied according to the second equation in the system of equations 10 above, the phase-corrected transfer function of the attenuation filter of the kth filter control element can be expressed as follows:

number

[0125] The control systems and methods described above can significantly reduce the amplitude of vibration in one or more vibration modes of a structure when a disturbance force is applied to the structure. The control systems and methods described above can also significantly reduce the settling time of the system compared to an undamped response. For example, the control systems and methods described herein were applied to control / damping vibrations excited by an impulse applied to an experimental system 600 shown in FIG. 14. FIG. 14 is a top plan 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 top surface of the plate member 602 at the unsupported corner. The actuator system 604 included an actuator configured as a voice coil motor (VCM) 606 and a sensor configured as an accelerometer 608 attached to the top of the VCM 606 (e.g., co-located with the VCM).

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

[0127] The top graphs in Figures 16A-16C show the acceleration measured by accelerometer 608 when system 600 is excited by an impulse caused by striking plate member 602. The bottom graphs in Figures 16A-16C show the acceleration versus frequency of system 600. The undamped / uncontrolled response of the system (Figure 16A) is shown along with the response of the system when control system 610 is operated to damp the first vibration mode (e.g., using filter control element 612A) (Figure 16B) and the response when the control system is operated to damp both the first and second vibration modes (e.g., using both filter control elements 612A and 612B) (Figure 16C). Figure 17 shows Bode plots illustrating the magnitude and phase of the frequency response of the system without feedback control, with damping control of the first vibration mode, and with damping control of both the first and second modes. As can be seen from FIGS. 16A-16C and 17, the control system 610 reduces the acceleration of the plate member vibration to approximately 0 m / s within about 0.1 seconds. 2 The maximum amplitude was significantly reduced 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 remote from the actuator. In other words, the system's accelerometer or sensors need not be co-located with 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 adjusted accordingly to account for, for example, phase angle differences resulting from the distance between the accelerometer and the actuator and / or phase differences associated with modal deformations of the structure in different vibration modes.

[0129] For example, FIG. 18 is a side elevation view of another experimental system 700, which included a rectangular cross-section metal beam member 702 clamped to two support members 704 and 706 spaced apart along the length of the beam member 702. System 700 further included an actuator system, generally designated 708, attached to the top 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 attached to the top of VCM 710, while the other accelerometer sensor 714 was attached directly to the beam member 702 at a location spaced apart from VCM 710. Actuator system 708 was controlled by a control system similar to control system 610 shown in FIG. 15 .

[0130] Figure 19 schematically illustrates the first and second vibration modes of the beam member 702 and 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 degrees out of phase. Thus, the damping filter of each filter control element was configured to apply a phase correction based on the associated accelerometer signal such that the VCM acts in the correct direction to damp vibration of the beam member in both the first and second vibration modes.

[0131] 20 is a Bode plot showing the magnitude and phase of the open-loop frequency response of system 700 as measured by accelerometers 712 and 714. A peak corresponding to the first beam vibration mode is seen at approximately 80 Hz, and a peak corresponding to the second beam mode is seen 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° out of phase at the second mode frequency.

[0132] Figure 21 is a Bode plot illustrating the open-loop frequency response of the system 700 and the frequency response implementing control using position data derived from a first accelerometer 712 co-located with the VCM 710. Figures 22A and 22B include acceleration versus time and fast Fourier transform (FFT) plots illustrating the open-loop impulse response of the system (Figure 22A) and the impulse response of the system implementing control using position data derived from the first accelerometer 712 (Figure 22B). Both plots show that the vibrations decay relatively quickly and the peak amplitudes of the first and second mode frequencies are relatively low when damped using an actuator system.

[0133] FIG. 23 is a Bode plot illustrating the open-loop frequency response of the system 700 and the frequency response for implementing control using position data derived from a second accelerometer 714 remote from the VCM 710. FIGS. 24A and 24B include plots of acceleration versus time and fast Fourier transforms showing the system's open-loop impulse response (FIG. 24A) and the impulse response (FIG. 24B) for implementing control using position data derived from the second accelerometer 714. FIGS. 23 and 24A-24B also show that vibrations decay relatively quickly and the peak amplitudes of the first and second mode frequencies are relatively low when damped using the actuator system. Based on the phase lag information from the Bode plot, the phase correction term of the damping filter of each filter control element can be adjusted to control the actuator system using either the first accelerometer 712, the second accelerometer 714, or both. Thus, control can be implemented using data from sensors co-located with the actuators or sensors located elsewhere in the system remote from the actuators, and the filters of the various filter control elements can be adjusted.

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

[0135] In certain embodiments, using the filters and phase correction methods described herein, the disclosed control system can also be configured to damp structural vibration modes having frequencies lower than the vibration mode frequency of the actuator system (e.g., the frequency at which the actuator vibrates relative to the structural element to which it is attached when the actuator is active). For example, FIG. 25 shows an experimental structural system 800 controlled using a control system configured similarly to control system 610 of FIG. 15. Structural system 800 included a T-shaped metal member 802 supported at both ends by flexure members 804 and 806. T-shaped metal member 802 included a first main portion 808 and a second portion 810 located at or near the center of main portion 808 and extending downward from and perpendicular to main portion 808. Flexure members 804 and 806 were coupled to a base member 812 coupled to a bench member 814 (e.g., an optical bench). Flexure members 804 and 806 suspended T-shaped metal member 802 above base member 812 .

[0136] An actuator system 816, including a VCM 818 and an accelerometer 820, was coupled to the second portion 810 of the T-shaped metal member 802 and configured to act in the x-direction. The accelerometer 820 was coupled to the housing of the VCM 818 (in other words, the accelerometer was co-located with the VCM). A vibration exciter in the form of a VCM 822 was positioned between the second portion 810 of the T-shaped metal member 802 and a bracing member 824 fixed to the base member 812. The vibration exciter VCM 822 was configured to apply an impulse disturbance force to the system 800. The vibration mode frequencies of the system were changed by adding a weight 826 to the T-shaped metal member 802.

[0137] In one configuration, system 800 was configured to vibrate at 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 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 frequency 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 26-28, respectively. The damping gain k d The results of control by changing the value of k are shown in Figs. 27 and 28. As can be seen from Figs. 26 to 28, the attenuation gain k of the attenuation filter d By adjusting (Equation 17), the control system can be tuned to effectively damp modal frequencies of the structural system that are lower than the vibration modal frequencies of the actuator system 816. In particular, k d A value of 75 reduced the maximum amplitude of the 15.7 Hz mode by approximately 20 dB and the amplitude of the 21.7 Hz mode by 10–15 dB compared to the open-loop response. d Setting the value of 412 reduced the maximum amplitude of the 22.8 Hz mode by approximately 15 dB. The settling time of each vibration mode was also reduced to less than 0.2 seconds, compared to a maximum of 5 seconds for the 15.7 Hz mode in the undamped system.

[0138] Example 5: Control system and method for damping vibrational mode frequencies from external sources using peak filter control

[0139] In certain embodiments, the control systems described herein can also be configured to damp / 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 can include a peak filter (e.g., a bandpass filter) instead of or in addition to the damping filters described above. For example, in certain embodiments, one or more filter control elements of the control system can implement damping filter control as described above, and one or more filter control elements can be configured to implement peak filter control as described below.

[0140] In certain embodiments, the peak filter can be tuned to pass one or more target vibration frequencies to be damped. In certain embodiments, the peak filter can be configured to perform phase correction as described above to compensate for phase lags associated with, for example, remote positioning of the accelerometer sensor, actuator amplifier time delays, signal conditioning, and / or digital control time delays. In certain embodiments, the phase correction can enable the peak filter to damp vibrations of the structural system below the modal frequencies of the actuator system, as described above. In certain embodiments, the peak filters described herein have less impact on high-frequency dynamics than damping filter control and therefore can be implemented in combination with damping filters to control low-frequency modes with limited coupling between damped vibration modes.

[0141] 29 shows an embodiment of a control system 900 configured to implement a peak filter control channel in parallel with a damping filter control channel. The control system 900 includes a system block 902 configured to represent the dynamic response of a controlled structural system, an integrating element 904 configured similarly to that described above, and two filter control elements 906 and 908 implemented in parallel. The filter control element 906 can implement a phase-compensated damping filter control C1(s) based on the transfer function of Equation 17 above, for example. The filter control element 908 can implement a combination of phase-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 certain embodiments, the transfer function H of the peak filter peak (s) can be given by the following equation 19, where k a is the attenuation gain, and d p is the damping ratio, and ω p is the target frequency of the peak filter.

number

[0143] In a particular embodiment, the bandpass filter control transfer function H bandpass (s) is the same as Equation 6 above, and the transfer function H of the notch filter notch (s) can be similar to 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 can take into account both the resonant frequencies of the structure and / or the vibration modes of the structure excited by the actuator when damping other modes. In certain embodiments, the peak filter can include derivative, proportional, and / or integral control similar to the damping filters described above.

[0144] In an exemplary embodiment, control system 900 of FIG. 29 was used to control / dampen vibrations of structural system 800 of FIG. 25 when an impulse force was applied to bench member 814 by vibration exciter VCM 828, shown in dashed lines. In this embodiment, VCM 822 was removed from the system. VCM 828 was offset from structural system 800 along the z-axis (e.g., into the plane of the paper in FIG. 25 ). The impulse disturbance force applied to bench member 814 by VCM 828 resulted in a 19.5 Hz vibration mode of bench member 814 and a 45 Hz vibration mode of structural system 800. The 45 Hz vibration mode of structural system 800 was damped using filter control element 906, which implements phase-compensated damping filter control, and the 19.5 Hz vibration mode of the optical bench was damped using filter control element 908, which implements phase-compensated 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 a vibration exciter VCM 828 coupled 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 response when both damping filter control channel 906 and peak filter control element 908 are applied. In Figures 30-32, the lines labeled "Feedback 1" indicate the response when the peak filter is k a =160, and the "Feedback 2" line shows the response of the system tuned to a = 300. As can be seen from Figures 30 and 31, filter control elements 906 and 908 are avalues, significantly reducing the maximum amplitudes of the bench member modes and the structural system modes compared to the undamped system. Referring to Figure 32, both control strategies also reduced the measured accelerations associated with both modes and reduced the settling time of the structural system 800 to less than 0.3 seconds.

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

[0147] In certain embodiments, an actuator system can include multiple sensors located at different locations on the structural system being controlled, and data from multiple such sensors can be used in multiple control loops to damp multiple vibration modes of the structure. A control system for such a structure can include multiple control loops that include filter control elements with feedback from different sensors in the structural system. In certain embodiments, the outputs of the various control loops can be summed to generate force commands for the actuator system.

[0148] For example, FIG. 33 shows a top plan view of a structural system 1000 including a rectangular plate member 1002 and an actuator system generally designated 1004. The actuator system 1004 included a VCM 1006 and multiple accelerometer sensors 1008, 1010, 1012, 1014, and 1016. In the illustrated configuration, accelerometer sensor 1008 was co-located with VCM 1006, and the remaining sensors were arranged around the edge of the plate member 1002. In FIG. 33, accelerometer 1010 was located near the center of the top edge of the plate member, and accelerometer 1016 was located near the center of the bottom edge 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 connected to and suspended above an optical bench or another support by three support members 1018A-C in the triangular arrangement shown. A vibration exciter configured as a VCM 1020 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 sensor, the accelerometer sensor may sense certain vibration modes of the structural system and may not sense other vibration modes, depending on whether the sensor's location coincides with a node of the vibration mode. For example, the plate member 1002 configured as shown in FIG. 33 exhibited four relatively low-frequency vibration modes when excited by impulse disturbance forces from the actuator VCM 1006 and / or the vibrator VCM 1020. The first mode was at 61 Hz, the second mode was at 96 Hz, the third mode was at 165 Hz, and the fourth mode was at 282 Hz. The accelerometer 1008 positioned on the VCM 1006 successfully detected the second, third, and fourth modes, but did not provide a strong signal from the first mode. The accelerometer 1014 provided a clear signal of the first vibration mode.

[0150] Various vibration modes in such structural systems can be controlled using a control system implementing the damping filter and / or peak filter control architecture described herein in multiple parallel control loops, each configured to damp vibrations in one or more modes based on feedback from sensors positioned to sense vibrations of the structure in one or more target modes of the control loop. For example, FIG. 34 shows a representative control system 1030 including two control loops (also referred to as control channels) that can be used to control vibrations in four modes of the structure 1000 of FIG. 33. The first control loop is generally designated 1032, and the second control loop is generally designated 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 integrating element 1038 and three filter control elements 1040, 1042, and 1044 implemented in parallel. The position signal output from integrator element 1038 is subtracted from position command signal x(s) to obtain a position error signal, which is input to filter control elements 1040-1044. Filter control elements 1040-1044 can be configured to implement filter control based on transfer functions C1(s), C2(s), and C3(s). The filter control elements can be configured to implement phase-compensated damping 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. Filter control elements 1040-1044 can be tuned for particular target modal frequencies of structural system 1000. In certain embodiments, filter control elements 1040-1044 are configured to control the second, third, and fourth modes of structural system 1000, respectively.

[0151] The second control loop 1034 also includes an integral element 1048 and a summing junction 1050 that outputs a position error signal to a filter control element 1052 after subtracting the integral element's position signal from the position command signal x(s). The filter control element 1052 can implement filter control based on a transfer function C4(s), which can include a phase-compensated damping filter control similar to Equations 13-17 above, or a phase-compensated peaking filter control as described with reference to Equations 18 and 19, tuned for a particular target modal frequency of the structural system 1000. In certain embodiments, the filter control element 1048 of the second control loop is tuned to damp a first vibration mode of the structural system 1000.

[0152] The outputs of the filter control elements 1040-1044 of the first control loop 1032 may be summed with the output of the filter control element 1052 of the second control loop 1034 at summing junction 1054 to provide the command signal u that is provided to the actuator system. u is represented as being combined with the force command signal at summing junction 1056 before the command signal is provided to structural system block 1036.

[0153] When used to damp vibrations of the structural system 1000 of FIG. 33 , the first control loop 1032 can operate using acceleration data obtained from an accelerometer 1008 co-located with 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 be configured to control the first vibration mode of the plate member 1002 utilizing acceleration data obtained from the accelerometer 1014. Thus, in the illustrated embodiment, the first accelerometer signal acc1 from the accelerometer 1008 is sent to an integrating element 1038 of the first control loop 1032. The integrating element 1038 outputs a position signal pos1 to a summing junction 1046, which is subtracted from the position command signal x(s) to obtain a position error signal that is provided to the filter control elements 1040-1044. The equation for the first accelerometer signal acc1 is given by Equation 20 below, where:

number

number

number

[0154] With respect to the second control loop 1034, the second accelerometer signal acc2 from the accelerometer 1014 is sent to the second control loop integrator element 1048. The integrator element 1048 outputs a position signal pos2 to a summing junction 1050 where it is subtracted from the position command signal x(s) to obtain a position error signal. The position error signal is provided to a filter control element 1052. The equation for the second accelerometer signal acc2 is given below in Equation 21, where:

number

number

number

[0155] Equations 20 and 21 relate to how the feedback filter controller and sensors 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 prior to actually implementing the control system.

[0156] FIG. 35 shows a Bode plot of the open-loop frequency response of the system 1000 of FIG. 33 when excited by an impulse from the vibration exciter VCM 1020. Peaks are observed at the 61 Hz, 96 Hz, 165 Hz, and 282 Hz modes. As shown in FIG. 35, the accelerometer 1014 provided a clear signal for the 61 Hz mode, while the accelerometer 1008 provided clear signals for the second, third, and fourth modes. FIG. 36 shows a Bode plot of the frequency response of a system that uses an actuator system to control all four modes based on force commands from the control system 1030 of FIG. 34. Noticeable reductions in the maximum amplitudes for each vibration mode are evident in FIG. 36.

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

[0158] The control loop of the control system 1030 can be configured in a variety of ways depending on factors such as the shape and size of the structural system, the positioning of the accelerometer sensors 1010-1016, the location of the actuator 1006, and the location of the vibration exciter VCM. FIG. 38 shows an alternative arrangement of the four accelerometers 1010-1016, the actuator VCM 1006, and the vibration exciter VCM 1020 on the plate member 1002. The accelerometer 1008 has been removed from the actuator VCM 1006. The configuration of FIG. 38 illustrates four vibration modes of the plate member 1002 similar to those described above with reference to FIG. 33. In a particular embodiment, the accelerometer 1014 provides distinct signals for the first and third vibration modes, and the accelerometer 1010 provides distinct signals for the second and fourth modes. 39, such that signal acc1 from accelerometer 1010 is fed back to filter control elements 1040 and 1044 arranged in parallel in a first control loop 1032 and configured to generate control signals for damping vibrations in the first and third modes. Signal acc2 from accelerometer 1014 is fed back to filter control elements 1042 and 1052 arranged in parallel in a second control loop 1034 and configured to generate control signals for damping the second and fourth modes. Thus, the control systems described herein can 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 target modes in the system, etc.

[0159] Example 7: Structural System Dynamics Model and Sensor and Actuator Placement

[0160] In certain embodiments, the amplitude of a force command to suppress / control vibration of a structural system at a particular vibration mode frequency can be estimated based on the amplitude of vibration at that modal frequency. In certain embodiments, the amplitude of vibration of a particular mode can be determined experimentally and / or using any of various models of the system and its frequency response, such as a finite element analysis (FEA) model, a state-space model, etc. In certain embodiments, the displacement of a structural system at a first location in response to a force applied to the structural system at a second location can be determined from such a system model. Information from such a model and / or measurements of the system can be used to select actuator locations and / or one or more accelerometer sensor locations to effectively damp one or more selected vibration modes of the structure.

[0161] For example, in a representative example, the dynamics of a structural system, such as plate member 1002 in Figure 38, can be transformed into decoupled 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 Equation 23 below. Here, ω 2 are the eigenvalues, φ are the eigenvectors, and ω k 2 is the square of the natural frequency of the kth mode (a scalar quantity), and φ k is a vector representing the mode shape of the kth mode, where k = 1, . . . N, and N is three times the number of nodes in the 3D FEA model.

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

number

number

[0164] Modal stiffness matrix K of the FEA model modal can be given by the following equation 24, where the modal stiffness of the kth mode is k k =m k ω k 2 is.

number

[0165] The mode shape matrix Φ is given by the identity

number

number

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

[0167] The modal stiffness matrix can be normalized to yield the following Equation 26, where ω k 2 is the modal mass of the kth mode.

number

[0168] This is expressed as the displacement v of the structural system at the first position j according to Equation 27 below: j and the force u applied at the second position ii yields the mass-normalized mode shape equation, which is the ratio of

number

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

number

[0170] In certain embodiments, the plant model for the flexible modal dynamics of the structural system can be expressed as a second order transfer function as shown in Equation 29 below.

number

[0171] The transfer function of Equation 29 can be transformed into modal coordinates using the relationship v=Φq to obtain Equation 30.

number

[0172] Modal mass matrix term Φ T MΦ can be given by Equation 23 above, and the modal 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 the following equation 31.

number

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

number

[0174] The reduced - order model of the 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 in FIG. 38 according to the above - mentioned 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 certain embodiments, 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 a large displacement of the plate surface for a 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, especially 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, swapping the location of the actuator VCM with various accelerometers, effectively changing the input and output locations of the system, can result in a similar vibration response by the structural system. For example, placing actuator VCM 1006 in the location of accelerometer 1010 in Figure 38, and vice versa, can result in a similar vibration profile in response to disturbance forces from the actuator VCM.

[0178] Example 8: Estimation of the amplitude of the control force

[0179] In certain embodiments, a model of structural system dynamics as described herein, optionally in combination with measured vibration amplitudes at selected frequencies to be damped, can be used to estimate force command amplitudes sufficient to damp vibrations at selected modal frequencies. In certain embodiments, rigid body modes (and / or flexible modes) of a structural element can be modeled using modal decomposition techniques. For example, in certain instances, the displacement at location j on a plate member similar to plate member 1002 of FIG. 38 is given by Equation 35 below:

number

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

number

[0181] In certain embodiments, the magnitude of the displacement of the plate member at position j due to vibration in target mode k is not subject to control (e.g., u i =0), v j Absolute value of, for example, |v j(jω k )|. Therefore, the magnitude of the force command to damp vibration at position j due to vibration of mode k can be given by Equation 37 below:

number

[0182] In certain embodiments, a model of the structural system dynamics in modal space can consider rigid body vibration modes of the structural system. Figure 41 shows a structural model with a length L and a force u i is the x-coordinate x applied (for example, by an actuator in an actuator system) i A, force u i Displacement v of member 1100 in response to j x coordinate of j 11 shows a schematic diagram of an unconstrained structural element 1100 shown with ω = 0. In a particular embodiment, for the first mode φ, when ω = 0, φ 1,i and φ 1,j is given in Equation 38 below:

number

number

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

number

number

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

number

number

[0185] When two rigid body modes φ1 and φ2 are considered, Equation 41 expresses the input force u i The dynamics from these two rigid body modes are expressed as the output positions v j A similar formulation can be extended to flexible modes of structural elements.

[0186] An example of a rotational mode about the z-axis is shown in FIG. 44 and can be expressed according to Equation 42 below.

number

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

number

[0188] In certain embodiments, controllability can be improved by placing actuators at locations on a structural system that result in relatively large mode shape displacements in response to force application / input. 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, placing accelerometer sensors at locations that have relatively large mode shape displacements for selected vibration modes can improve the accelerometer sensors' ability to sense displacements of the structural element associated with the selected modes. Therefore, in certain embodiments, it is beneficial to place actuators and / or sensors at locations that have relatively large mode shape displacements associated with the specified vibration modes to be damped.

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

number

number

[0190] The following Equation 45 is

number

number

[0191] In certain embodiments, the SISO system may include a term representing the residual elasticity associated with the omitted higher order modes, which may be similar to Equation 34 above.

[0192] Equation 46 provides an example 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, SISO and / or MIMO state-space models of the structural system can be used to represent the system dynamics decoupled according to modal coordinates, which is more convenient in simulation than transfer function models. In certain embodiments, the parameter φ in Equation 44 and Equation 46 k,j and φ k,i can be used to determine actuator and sensor placement as described above, since they are related to the mode shapes.

[0195] One or more of the actuator systems, control systems, and / or control methods described herein can provide 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 damp vibrations of various structures within a lithography system. For example, the systems described herein can damp 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 approximately 10 kHz (or the sampling and bandwidth limits of the system), 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 a structural element associated with one or more vibration modes of the structural element. This can reduce relative motion of different structures within a precision system, such as the optical table, substrate stage, and / or mask stage of a lithography exposure apparatus. When one structural element serves as a positional 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 structural systems after excitation by disturbance forces. Such systems can be implemented, for example, to reduce vibrations in exposure apparatus caused by movement of the substrate stage and / or mask stage. As noted above, certain configurations of the systems described herein can reduce the settling time of structural systems similar to optical tables from over 1 second to 0.2 seconds or less. This can significantly increase the throughput of the exposure apparatus by reducing the time required between exposures for vibrations to settle 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 table, a substrate stage, a mask stage, or any other structure in an exposure apparatus where damping of structural vibrations may be indicated. The control system can be configured to damp vibrations excited by one, two, three, four, five, or more vibration modes of the structural system, as well as control of other modes. The control system can also be configured to utilize feedback from sensors located at the actuator and / or from sensors located remotely from the actuator by implementing the phase correction methods described herein. The phase correction methods described herein can also be used to damp vibration modes of the structure having frequencies lower than the actuator-structure interaction mode frequency, 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 a variety of precision systems, such as various types of lithography systems, including the lithography exposure systems described above, and other wafer processing systems and methods. The control systems and methods can also be used in combination with any of the precision system embodiments and methods and / or their associated structural elements or subsystems described below with reference to Figures 45-49. Referring to Figure 45, certain features of an immersion lithography system (an exemplary precision system) are shown: light source 1340, illumination optics 1342, reticle stage 1344, projection optics 1346, and wafer (substrate) stage 1348, all arranged along optical axis A. Light source 1340 is configured to generate a pulsed beam of illumination light, such as 248 nm DUV light generated by a KrF excimer laser, 193 nm DUV light generated by an ArF excimer laser, or 157 nm DUV light generated by an F2 excimer laser. The illumination optics 1342 includes an optical integrator and at least one lens that conditions and shapes the illumination beam to illuminate a specific area of ​​a patterned reticle 1350 mounted on a reticle stage 1344. The pattern defined on the reticle 1350 corresponds to the pattern to be lithographically transferred to a wafer 1352 held on a wafer stage 1348. Lithographic transfer in this system is achieved by projecting an aerial image of the pattern from the reticle 1350 onto the wafer 1352 using the projection optics 1346. The projection optics 1346 typically includes 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 a suitable exposure-sensitive material called a "resist."

[0200] The reticle stage 1344 is configured to move the reticle 1350 in the X-axis, the Y-axis, and rotationally about the Z-axis. To this end, the reticle stage includes one or more linear motors with 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 main controller positions the reticle 1350 based on this detection.

[0201] The wafer 1352 is held by a wafer holder ("chuck," not shown) on the wafer stage 1348. The wafer stage 1348 includes mechanisms (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 image plane of the projection optical system 1346. These actuators preferably include linear motors, one or more planar motors, or both.

[0202] The wafer stage 1348 also has a mechanism for adjusting the tilt angle of the wafer 1352 using autofocus and autoleveling methods. 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 sent from the main controller to a drive circuit that drives the wafer stage. During exposure, the light passing through the projection optical system is moved sequentially from one position on the wafer to another using a step-and-repeat or step-and-scan method, following the pattern on the reticle.

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

[0204] Immersion liquid 1354 is supplied from a liquid supply 1356, which may include a tank, pump, and temperature regulator (not separately shown). The liquid 1354 is gently dispensed into the gap between the objective lens 1353 and the wafer surface by a nozzle mechanism 1355. A liquid recovery system 1358 includes recovery nozzles 1357 that remove liquid from the gap as the supply 1356 supplies new liquid 1354. As a result, a substantially constant volume of continuously replaced immersion liquid 1354 is provided between the objective lens 1353 and the wafer surface. The temperature of the liquid is regulated to be approximately the same as the temperature within the chamber in which the lithography system itself is located.

[0205] Also shown is a sensor window 1360 that extends across a recess 1362 defined in the wafer stage 1348 in which a sensor 1364 is located. The window 1360 therefore isolates the sensor 1364 within the recess 1362. By moving the wafer stage 1348 so that the window 1360 is located under the objective lens 1353 while continuously replacing the immersion liquid 1354, the light beam that has passed through the projection optics 1346 passes through the immersion liquid and the window 1360 to reach the sensor 1364.

[0206] An interrogation beam source 1380 is positioned to direct an interrogation light beam 1381 toward the reticle 1350, and a detection system 1382 is configured to detect a portion of the interrogation beam modulated by the reticle 1350. The detected beam can be used to assess 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] 46, an alternative embodiment of a precision system that can include one or more electromagnetic actuators with actively cooled coils as described herein is shown in EUVL system 1400, an exemplary precision system incorporating an electromagnetic actuator as described herein. The illustrated system 1400 includes a vacuum chamber 1402 including vacuum pumps 1406a, 1406b arranged to allow a desired vacuum level to be established and maintained within respective chambers 1408a, 1408b of the vacuum chamber 1402. For example, vacuum pump 1406a maintains a vacuum level of approximately 50 mTorr within upper chamber (reticle chamber) 1408a, and vacuum pump 1406b maintains a vacuum level of less than approximately 1 mTorr within lower chamber (optics chamber) 1408b. The two chambers 1408a, 1408b are separated from each other by a partition wall 1420. Various components of EUVL system 1400 are not shown for ease of illustration, but it will be understood that EUVL system 1400 can 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 coupled to a reticle stage 1410. The reticle stage 1410 holds the reticle 1416 and can move it laterally to scan it during use, for example, for lithography exposure. A blind device is located between the reticle 1416 and a partition wall 1420. An illumination source 1424 generates an EUV illumination beam 1426 that enters the optical chamber 1408b, reflects off one or more mirrors 1428, and illuminates a desired location on the reticle 1416 via illumination optics 1422. When the illumination beam 1426 reflects off the reticle 1416, the beam is "patterned" by the portion of the pattern actually illuminated on the reticle. The partition wall 1420 acts as a differential pressure barrier and can function as a reticle shield to protect the reticle 1416 from particle contamination during use. The partition 1420 defines an opening 1434 through which an 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 pattern-defining elements on the reticle, and the resulting patterned beam 1430 propagates generally downward, through projection optics 1438, and onto the surface of a wafer 1432 held by a wafer chuck 1436 on a wafer stage 1440 that effects scanning motion of the wafer during exposure. This projects an image of the reticle pattern onto the wafer 1432.

[0209] The wafer stage 1440 may include a positioning stage, which may be driven by, for example, a planar motor or one or more linear motors, and a wafer table magnetically coupled to the positioning stage using, for example, an EI core actuator (details omitted). The wafer chuck 1436 is coupled 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 electromagnetic forces generated by two-dimensionally arranged magnets and corresponding armature coils. The positioning stage is configured to be movable with, for example, three to six degrees of freedom so that the wafer 1432 can be positioned at a desired position and orientation relative to the projection optical system 1438 and the reticle 1416.

[0210] An EUVL system, including the EUV source and illumination optical 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. To establish these standards before, during, and after assembly, the various subsystems (particularly the illumination optics 1422 and projection optics 1438) are evaluated and adjusted as needed to achieve the specified precision standards. Similar evaluations and adjustments are also made to mechanical and electrical subsystems and assemblies as needed. Assembly of the various subsystems and assemblies includes creating the necessary optical and mechanical interfaces, electrical interconnections, and piping interconnections between assemblies and subsystems. After the EUVL system is assembled, further evaluations, calibrations, and adjustments are made as needed to ensure the specified system accuracy and precision of operation are achieved. To maintain certain standards of cleanliness and contamination avoidance, the EUVL system (and certain subsystems and assemblies of the system) are assembled in cleanrooms or other facilities where particle contamination, temperature, and humidity are controlled.

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

[0212] Semiconductor devices can be manufactured by a process including microlithography steps performed using a microlithography system as described above. Referring to FIG. 47, in step 1501, the function 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 steps. Meanwhile, in step 1503, a substrate (wafer) is fabricated and coated with an appropriate 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, distortion of the reticle during exposure can be estimated. In step 1505, the semiconductor devices are assembled (including "dicing," in which individual devices or "chips" are cut from the wafer; "bonding," in which wires are bonded to specific locations on the chips; and "packaging," in which the devices are enclosed in appropriate packages for use). In step 1506, the assembled devices are tested and inspected.

[0213] Exemplary details of a wafer processing process including microlithography steps are shown in Figure 48. 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 evaporation. In step 1614 ("Ion Implantation"), ions are implanted into the wafer surface. These steps 1611-1614 constitute exemplary "pre-processing" steps for the wafer, with each step selected according to processing requirements.

[0214] At each stage of wafer processing, once the pre-processing steps are complete, the following "post-processing" steps are performed. The first post-processing step is step 1615 ("Photoresist Formation"), in which a suitable resist is applied to the surface of the wafer. Next, in step 1616 ("Exposure"), a pattern is lithographically transferred from a reticle to a resist layer on the wafer using the microlithography system described above. Reticle distortions 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 in the resist on the wafer that corresponds to the resist pattern. In step 1618 ("Etch"), 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 remaining developed resist is removed ("Stripped") from the wafer.

[0215] By repeating the pre-processing and post-processing steps as necessary, multiple interconnect layers of circuit patterns can be formed on the wafer, with a set of pre-processing and post-processing steps typically being performed to form each layer.

[0216] The present disclosure includes any of a variety of precision systems, including stages for holding workpieces or other articles useful in manufacturing. An example of a precision system is a microlithography system or exposure “tool” used to fabricate semiconductor devices. A schematic diagram of an exemplary microlithography system 1710 incorporating features of the technology described herein is shown in FIG. 49. System 1710 includes a system frame 1712, an illumination system 1714, an imaging optical system 1716, reticle stage assemblies 1718A-1718B, substrate stage assemblies 1720A-1720B, positioning systems 1722A-1722D, and a system controller 1724. The configuration of components in system 1710 is particularly useful for transferring an integrated circuit pattern (not shown) from a reticle 1726 onto a semiconductor wafer 1728. System 1710 is mounted to a mounting base 1730, such as a ground, base, floor, or other support structure. The system also includes a metrology system that measures the position of a lithographic 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 the substrate stage assembly 1720 include a multi-blade holding apparatus as described in the exemplary embodiments above.

[0217] In certain examples, the designated vibrational mode frequency can be 5 Hz to 10 kHz, 5 Hz to 5 kHz, 5 Hz to 1 kHz, 5 Hz to 500 Hz, 5 Hz to 300 Hz, 5 Hz to 200 Hz, 5 Hz to 100 Hz, 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, 2 Hz to 100 Hz, 1 Hz to 10 kHz, 1 Hz to 5 kHz, 1 Hz to 1 kHz, 1 Hz to 500 Hz, 1 Hz to 300 Hz, 1 Hz to 200 Hz, 1 Hz to 100 Hz, or any range between any of the frequencies described herein. The designated vibrational mode frequency can also be less than 1 Hz.

[0218] Example 10: Representative Computing Environment

[0219] 50 shows a generalized example of a computing environment 1800 in which software and control algorithms for the described embodiments 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 computing environment 1800, may be a local computing system integrated as part of an exposure apparatus assembly, or may be a remote computing system as described herein.

[0220] The computing environment 1800 is not intended to suggest any limitation as to the scope of use or functionality of the technology, which may be implemented in a variety of general-purpose or special-purpose computing environments. For example, the disclosed technology may be implemented with other computer system configurations, including programmable automation controllers, programmable logic controllers, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), handheld devices, multiprocessor systems, programmable consumer electronics, network PCs, minicomputers, etc. The disclosed control methods may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0221] Referring to FIG. 50, a computing environment 1800 includes at least one processing unit 1810 and memory 1820. In FIG. 50, this most basic configuration 1830 is included within the dashed line. The processing unit 1810 executes computer-executable instructions and may be a real or virtual processor. In a multiprocessing system, multiple processing units execute computer-executable instructions to increase processing power; thus, multiple processors may 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 includes storage 1840, one or more input devices 1850, one or more output devices 1860, and one or more communication connections 1870. An interconnection mechanism (not shown), such as a bus, controller, or network, interconnects the components of computing environment 1800. Typically, operating system software (not shown) provides an operating environment for other software executing within computing environment 1800 and coordinates the activities of the components of computing environment 1800.

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

[0223] The input device(s) 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, a voice input device, a scanning device, or another device that provides input to the computing environment 1800. The output device(s) 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(s) 1870 enable communication to devices or computing entities over a communication medium (e.g., a connection network). The communication medium conveys information such as control signals, computer-executable instructions, sensor inputs or outputs, or other data in modulated data signals. The communication connection(s) 1870 are not limited to wired connections (e.g., Megabit or Gigabit Ethernet, InfiniBand, Fibre Channel over electrical or optical fibre connections) but also include wireless technologies (e.g., Bluetooth, WiFi (IEEE 802.11a / b / n), WiMax, cellular, satellite, laser, RF connections over infrared), and other suitable communication connections for providing network connectivity to the disclosed controlled devices.

[0225] Some embodiments of the disclosed methods may be performed using computer-executable instructions that implement all or a portion of the disclosed techniques in a computing cloud 1890 or other remote computing system. For example, the disclosed methods may be performed on a processing unit 1810 located in the computing environment 1830, or the disclosed methods may be performed on a server located in the computing cloud 1890.

[0226] Computer-readable media are any available media that can be accessed within computing environment 1800. By way of example, and not limitation, in computing environment 1800, computer-readable media include memory 1820 and / or storage 1840. As will be readily understood, the term computer-readable storage media includes media for data storage, such as memory 1820 and storage 1840, and does not include transmission media, such as modulated data signals.

[0227] Terminology

[0228] For purposes of this description, certain aspects, advantages, and novel features of the disclosed embodiments are described herein. The disclosed methods, devices, and systems are not limited in any way. Rather, the present disclosure is directed to all novel features and aspects of the various disclosed embodiments, alone and in various combinations and subcombinations with one another. The methods, devices, 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 be present or problems be solved. The scope of the present disclosure includes any feature disclosed herein in combination with any other feature disclosed herein, unless physically impossible.

[0229] Although some operations of the disclosed embodiments are described in a particular sequential order for convenience of presentation, it should be understood that this method of description encompasses reordering unless a particular order is required by specific language set forth herein. For example, operations described sequentially may, in some cases, be reordered or performed simultaneously. Moreover, for purposes of simplicity, the accompanying figures may not show the various ways in which the disclosed components can be used with other components.

[0230] As used in this disclosure and claims, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. Furthermore, the term "comprises" means "comprising." Furthermore, the terms "coupled" and "associated" generally mean electrically, electromagnetically, and / or physically (e.g., mechanically or chemically) coupled or connected, and do not exclude the presence of intermediate elements between coupled or associated elements, unless specific language to the contrary is present.

[0231] In some instances, a value, procedure, or device may be referred to as a "lowest," "best," "smallest," etc. Such statements are intended to indicate that a choice can be made among many alternatives, and that such a choice is not necessarily better, lesser, or more preferable than other choices.

[0232] Certain terms may be used throughout the specification, such as "top," "bottom," "upper," "lower," "horizontal," "vertical," "left," and "right." These terms are used, where applicable, to provide some clarity when dealing with relative relationships. However, these terms are not intended to imply absolute relationships, positions, and / or orientations. For example, with respect to an object, the "top" surface can become the "bottom" surface simply by flipping the object over, yet they are still the same thing.

[0233] Unless otherwise indicated, all numbers used in this specification or claims expressing frequencies, material quantities, angles, pressures, molecular weights, percentages, temperatures, times, and the like should be understood to be modified by the term "about." Thus, unless otherwise indicated, implicitly or explicitly, the numerical parameters described are approximations that may depend on the desired properties and / or detection limits sought under testing conditions / methods familiar to those skilled in the art. When directly and explicitly distinguishing an embodiment from the discussed prior art, the numbers of the embodiments are not approximations unless the word "about" is recited. Furthermore, not all alternatives described herein are necessarily equivalent.

[0234] The existence of alternatives for the various components, parameters, operating conditions, etc. described herein does not imply that the alternatives are necessarily equivalent and / or perform equally well, nor does it imply that the alternatives are listed in order of preference unless otherwise stated.

[0235] In view of 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 the disclosure. Rather, the scope of the disclosure is at least as broad as the following claims and their equivalents. We therefore claim all that comes within the scope and spirit of those claims.

Claims

1. receiving data on the position of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and the designated position of the structural element; determining force commands for damping the specified vibration mode frequencies of the structural element based at least in part on the position error signal and the specified vibration mode frequencies; transmitting 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; A method comprising:

2. The method of claim 1 , wherein determining the force command further comprises applying a phase correction to the position error signal.

3. The method of claim 2 , wherein determining the force command further comprises filtering the position error signal with a low pass filter.

4. The method of claim 3 , wherein the low pass filter includes a derivative control.

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

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

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

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

9. 10. The method of any preceding claim, wherein the designated vibrational mode frequency is between 2 Hz and 10 kHz, between 2 Hz and 5 kHz, between 2 Hz and 1 kHz, between 2 Hz and 500 Hz, between 2 Hz and 300 Hz, between 2 Hz and 200 Hz, or between 2 Hz and 100 Hz.

10. 10. The method of any preceding claim, wherein the specified vibration frequency is lower than a vibration mode frequency of the actuator.

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

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

13. an exposure apparatus including a structural element; an actuator system coupled to the structural element, the actuator system comprising an actuator and a sensor; receiving data on the position of the structural element from the sensor; determining a position error signal based at least in part on the position data and the designated position of the structural element; determining force commands for damping the designated vibrational mode frequencies based at least in part on the position error signal and the designated vibrational mode frequencies of the structural element; sending the force command to the 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; a control system; A system comprising:

14. The system of claim 13 , wherein the control system applies a phase correction to the position error signal.

15. The system of claim 14 , wherein the control system filters the position error signal with a low pass filter.

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

17. 17. The system of claim 15 or 16, wherein the phase correction is applied by the low pass filter.

18. 18. The system of any one of claims 13 to 17, wherein the control system filters the position error signal with a bandpass filter.

19. the control system filtering the position error signal using a notch filter; 19. A system according to any one of claims 13 to 18.

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

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

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

23. receiving data on the position of a structural element of an exposure apparatus; determining a position error signal based at least in part on the position data and the designated position of the structural element; filtering the position error signal with a low pass filter including a differential control; applying a phase correction to the position error signal using the low pass filter; determining force commands for damping specified vibration mode frequencies of the structural element based at least in part on the filtered, phase-corrected position error signal; sending the force command to an actuator coupled to the structural element 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; A method comprising:

Images