WO2025219040A1

WO2025219040A1 - Positioning measurement correction

Info

Publication number: WO2025219040A1
Application number: PCT/EP2025/058376
Authority: WO
Inventors: Cornelis Melchior BROUWER; Tom Antonius Cornelius Johannes Maria ALBERS; Frederik Eduard De Jong; Bram Paul Theodoor VAN GOCH; Coen BAKKER
Original assignee: ASML Netherlands BV
Current assignee: ASML Netherlands BV
Priority date: 2024-04-15
Filing date: 2025-03-27
Publication date: 2025-10-23
Anticipated expiration: 2026-10-15

Abstract

The invention provides a method to correct a positioning measurement signal, the method comprising the steps of: a) obtaining a first positioning measurement signal; b) determining a first vibrational mode of the second element with respect to the first element; c) determining first modal displacement; d) determining a first sensitivity coefficient; e) multiplying the first modal displacement with the first sensitivity coefficient; f) correcting the first positioning measurement signal The invention furthermore provides a position control system for positioning an operative point at a position in space, wherein the position control system is configured to: A. determine a first vibrational mode B. determine first modal displacement C. determine a first sensitivity coefficient D. multiply the first modal displacement with the first sensitivity coefficient to obtain a first correction value; E. control an actuator to position the operative point at a desired position.

Description

POSITIONING MEASUREMENT CORRECTION

CROSS-REFERENCE TO RELATED APPLICATION

[001] The application claims priority of European application number 24170211.7 which was filed on 15 April 2024 and which is incorporated herein in its entirety by reference.

FIELD

[002] The present invention relates to a method to correct a positioning measurement signal, a positioning system for positioning an operative point, an exposure apparatus comprising a positioning system, a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method, and a computer-readable medium comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method.

BACKGROUND

[003] An exposure apparatus is a machine constructed to apply a desired pattern onto a substrate. An exposure apparatus or system may for example be a lithographic apparatus, and can be used, for example, in the manufacture of integrated circuits (ICs). An exposure apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer).

[004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as ‘Moore’s law’. To keep up with Moore’s law the semiconductor industry is chasing technologies that enable to create increasingly smaller features. To project a pattern on a substrate an exposure apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. A lithographic apparatus which uses extreme ultraviolet (EUV) radiation, having a wavelength within a range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[005] To create small features of circuit elements, a high accuracy of the pattern being projected on the substrate is required. This requires high positioning accuracy of the substrate with respect to the patterning device and/or a source of electromagnetic radiation used to irradiate the patterning device. Furthermore, to achieve a high output of ICs, the substrate and patterning device and/or source of electromagnetic radiation are moved with respect to each other at high speeds, using high accelerations. Such high accelerations may cause vibrations within the exposure apparatus due to excitation of vibrational modes, yielding inaccuracies in the relative position of parts of the exposure apparatus as said parts vibrate and thus move and/or deform. Other influences such as outside perturbations can also excite vibrational modes of the exposure apparatus. This leads to errors in positioning signals of sensors that determine the relative position of parts of the exposure apparatus, which may for example be a lithographic apparatus, which are movable with respect to each other.

SUMMARY

[006] It is thus an object of the invention to provide a method to correct a positioning measurement signal. It is an object of the invention to provide a positioning system for positioning an operative point at a position in space at a higher accuracy than known positioning systems. It is an object of the invention to provide an exposure apparatus with a higher manufacturing accuracy than known exposure apparatuses. It is an object of the invention to provide a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out a method to correct a positioning measurement signal. It is an object of the invention to provide a computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out a method to correct a positioning measurement signal.

[007] According to a first aspect of the invention, there is provided a method to correct a positioning measurement signal from a position measurement system configured to determine a position of an operative point based on at least one positioning measurement signal, the position measurement system comprising a first positioning sensor arranged in a first positioning location, the method comprising the steps of: a) obtaining a first positioning measurement signal from the first positioning sensor, wherein the first positioning measurement signal is representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system; b) determining a first vibrational mode of the second element with respect to the first element; c) determining first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point with respect to the first primary positioning point in the first vibrational mode; d) determining a first sensitivity coefficient representing a sensitivity of a position and/or orientation of the operative point to a position deviation of the first secondary positioning point with respect to the first primary positioning point; e) multiplying the first modal displacement with the first sensitivity coefficient to obtain a first correction value; f) correcting the first positioning measurement signal based on the first correction value to determine a corrected position of the operative point.

[008] According to a second aspect of the invention, there is provided a position control system for positioning an operative point at a position in space, the system comprising: a position measurement system comprising a first positioning sensor, wherein the first positioning sensor is configured to provide a first positioning measurement signal representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system and the operative point is arranged on the first element of the position measurement system; an actuator configured to move the first element of the position measurement system with respect to the second element of the position measurement system; a correction controller configured to:

A. determine a first vibrational mode of the second element with respect to the first element;

B. determine first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point with respect to the first primary positioning point in the first vibrational mode;

C. determine a first sensitivity coefficient representing a sensitivity of a position and/or orientation of the operative point to a position deviation of the first secondary positioning point with respect to the first primary positioning point;

D. multiply the first modal displacement with the first sensitivity coefficient to obtain a first correction value;

E. based on the first positioning measurement signal and the first correction value, control the actuator to move the first element of the position measurement system with respect to the second element of the position measurement system such that the operative point is positioned at a desired position.

[009] According to a third aspect of the invention, there is provided an exposure apparatus comprising a position control system according to the second aspect of the invention, wherein the first element comprises a wafer table of the exposure apparatus, wherein the second element comprises a metrology frame of the exposure apparatus, wherein the position control system is configured to control a position of the wafer table.

[010] According to a fourth aspect of the invention, there is provided an inspection system comprising a position control system according to the second aspect of the invention, wherein the first element comprises a substrate support of the inspection system, wherein the second element comprises a frame of the inspection system, wherein the position control system is configured to control a position of the substrate support.

[Oil] According to a fifth aspect of the invention, there is provided a metrology tool comprising a position control system according to the second aspect of the invention, wherein the first element comprises a substrate support of the metrology tool, wherein the second element comprises a frame of the metrology tool, wherein the position control system is configured to control a position of the substrate support.

[012] According to a sixth aspect of the invention, there is provided a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of the first aspect of the invention.

[013] According to a seventh aspect of the invention, there is provided a computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method according to the first aspect of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

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

Figure 1 depicts a schematic overview of a lithographic apparatus;

Figure 2 depicts a detailed view of a part of the lithographic apparatus of Figure 1;

Figure 3 schematically depicts a position control system;

Figure 4 schematically depicts a method to correct a positioning measurement signal from a position measurement system according to the invention;

Figures 5A, 5B, 5C, 5D schematically depict the position control system of figure 3, with the addition that the correction value is used in a respective implementation position.

DETAILED DESCRIPTION

[015] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[016] The term “reticle”, “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective, binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array. [017] Figure 1 schematically depicts a lithographic apparatus LA, which is an example exposure apparatus. The lithographic apparatus LA includes an illumination system (also referred to as illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation or EUV radiation), a mask support (e.g ., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA in accordance with certain parameters, a substrate support (e g., a wafer table) WT constructed to hold a substrate (e g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support in accordance with certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e g., comprising one or more dies) of the substrate W.

[018] In operation, the illumination system IL receives a radiation beam from a radiation source SO, e.g. via abeam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and/or other types of optical components, or any combination thereof, for directing, shaping, and/or controlling radiation. The illuminator IL may be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in its cross section at a plane of the patterning device MA.

[019] The term “projection system” PS used herein should be broadly interpreted as encompassing various types of projection system, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and/or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, and/or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system” PS.

[020] The lithographic apparatus LA may be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system PS and the substrate W - which is also referred to as immersion lithography. More information on immersion techniques is given in US6952253, which is incorporated herein by reference.

[021] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also named “dual stage”). In such “multiple stage” machine, the substrate supports WT may be used in parallel, and/or steps in preparation of a subsequent exposure of the substrate W may be carried out on the substrate W located on one of the substrate support WT while another substrate W on the other substrate support WT is being used for exposing a pattern on the other substrate W. [022] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measurement stage. The measurement stage is arranged to hold a sensor and/or a cleaning device The sensor may be arranged to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning device may be arranged to clean part of the lithographic apparatus, for example a part of the projection system PS or a part of a system that provides the immersion liquid. The measurement stage may move beneath the projection system PS when the substrate support WT is away from the projection system PS.

[023] In operation, the radiation beam B is incident on the patterning device, e.g. mask, MA which is held on the mask support MT, and is patterned by the pattern (design layout) present on paterning device MA. Having traversed the paterning device MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position measurement system PMS, the substrate support WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor (which is not explicitly depicted in Figure 1) may be used to accurately position the paterning device MA with respect to the path of the radiation beam B. Paterning device MA and substrate W may be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks Pl, P2 as illustrated occupy dedicated target portions, they may be located in spaces between target portions. Substrate alignment marks Pl, P2 are known as scribe-lane alignment marks when these are located between the target portions C.

[024] To clarify the invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, i.e., an x-axis, a y-axis and a z-axis. Each of the three axes is orthogonal to the other two axes. A rotation around the x-axis is referred to as an Rx-rotation. A rotation around the y- axis is referred to as an Ry-rotation. A rotation around about the z-axis is referred to as an Rz-rotation. The x-axis and the y-axis define a horizontal plane, whereas the z-axis is in a vertical direction. The Cartesian coordinate system is not limiting the invention and is used for clarification only. Instead, another coordinate system, such as a cylindrical coordinate system, may be used to clanfy the invention. The orientation of the Cartesian coordinate system may be different, for example, such that the z-axis has a component along the horizontal plane.

[025] Figure 2 shows a more detailed view of a part of the lithographic apparatus LA of Figure 1. The lithographic apparatus LA may be provided with a base frame BF, a balance mass BM, a metrology frame MF and a vibration isolation system IS. The metrology frame MF supports the projection system PS. Additionally, the metrology frame MF may support a part of the position measurement system PMS. The metrology frame MF is supported by the base frame BF via the vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce vibrations from propagating from the base frame BF to the metrology frame MF.

[026] The second positioner PW is arranged to accelerate the substrate support WT by providing a driving force between the substrate support WT and the balance mass BM. The driving force accelerates the substrate support WT in a desired direction. Due to the conservation of momentum, the driving force is also applied to the balance mass BM with equal magnitude, but at a direction opposite to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the masses of the moving part of the second positioner PW and the substrate support WT. [027] In an embodiment, the second positioner PW is supported by the balance mass BM. For example, wherein the second positioner PW comprises a planar motor to levitate the substrate support WT above the balance mass BM. In another embodiment, the second positioner PW is supported by the base frame BF. For example, wherein the second positioner PW comprises a linear motor and wherein the second positioner PW comprises a bearing, like a gas bearing, to levitate the substrate support WT above the base frame BF.

[028] The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the substrate support WT. The position measurement system PMS may comprise any type of sensor that is suitable to determine a position of the mask support MT. The sensor may be an optical sensor such as an interferometer or an encoder. The position measurement system PMS may comprise a combined system of an interferometer and an encoder. The sensor may be another type of sensor, such as a magnetic sensor, a capacitive sensor or an inductive sensor. The position measurement system PMS may determine the position relative to a reference, for example the metrology frame MF or the projection system PS. The position measurement system PMS may determine the position of the substrate table WT and/or the mask support MT by measuring the position or by measuring a time derivative of the position, such as velocity or acceleration.

[029] The position measurement system PMS may comprise an encoder system. An encoder system is known from for example, United States patent application US2007/0058173A1, filed on September 7, 2006, hereby incorporated by reference. The encoder system comprises an encoder head 59, a grating 60 and a sensor 61. The encoder system may receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam as well as the secondary radiation beam originate from the same radiation beam, i.e., the original radiation beam. At least one of the primary radiation beam and the secondary radiation beam is created by diffracting the original radiation beam with the grating. If both the primary radiation beam and the secondary radiation beam are created by diffracting the original radiation beam with the grating, the primary radiation beam needs to have a different diffraction order than the secondary radiation beam. Different diffraction orders are, for example, + 1^st order, -1^st order, +2^nd order and -2^nd order. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. A sensor in the encoder head determines a phase or phase difference of the combined radiation beam. The sensor generates a signal based on the phase or phase difference. The signal is representative of a position of the encoder head relative to the grating. One of the encoder head and the grating may be arranged on the substrate structure WT. The other of the encoder head and the grating may be arranged on the metrology frame MF or the base frame BF. For example, a plurality of encoder heads are arranged on the metrology frame MF, whereas a grating is arranged on a top surface of the substrate support WT. In another example, a grating is arranged on a bottom surface of the substrate support WT, and an encoder head is arranged below the substrate support WT.

[030] The position measurement system PMS may comprise an interferometer system. An interferometer system is known from, for example, United States patent US6,020,964, filed on July 13, 1998, hereby incorporated by reference. The interferometer system may comprise a beam splitter, a mirror, a reference mirror and a sensor. A beam of radiation is split by the beam splitter into a reference beam and a measurement beam. The measurement beam propagates to the mirror and is reflected by the mirror back to the beam splitter. The reference beam propagates to the reference mirror and is reflected by the reference mirror back to the beam splitter. At the beam splitter, the measurement beam and the reference beam are combined into a combined radiation beam. The combined radiation beam is incident on the sensor. The sensor determines a phase or a frequency of the combined radiation beam. The sensor generates a signal based on the phase or the frequency. The signal is representative of a displacement of the mirror. In an embodiment, the mirror is connected to the substrate support WT. The reference mirror may be connected to the metrology frame MF. In an embodiment, the measurement beam and the reference beam are combined into a combined radiation beam by an additional optical component instead of the beam splitter.

[031] The first positioner PM may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT relative to the long-stroke module with a high accuracy over a small range of movement. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. With the combination of the long-stroke module and the short-stroke module, the first positioner PM is able to move the mask support MT relative to the projection system PS with a high accuracy over a large range of movement. Similarly, the second positioner PW may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT relative to the long-stroke module with a high accuracy over a small range of movement. The long-stroke module is arranged to move the short-stroke module relative to the projection system PS with a relatively low accuracy over a large range of movement. With the combination of the long-stroke module and the short-stroke module, the second positioner PW is able to move the substrate support WT relative to the projection system PS with a high accuracy over a large range of movement.

[032] The first positioner PM and the second positioner PW each are provided with an actuator to move respectively the mask support MT and the substrate support WT. The actuator may be a linear actuator to provide a driving force along a single axis, for example the y-axis. Multiple linear actuators may be applied to provide driving forces along multiple axis. The actuator may be a planar actuator to provide a driving force along multiple axis. For example, the planar actuator may be arranged to move the substrate support WT in six degrees of freedom, i.e. three orthogonal linear directions and rotation around said three orthogonal directions The actuator may be an electro- magnetic actuator comprising at least one coil and at least one magnet. The actuator is arranged to move the at least one coil relative to the at least one magnet by applying an electrical current to the at least one coil. The actuator may be a moving -magnet type actuator, which has the at least one magnet coupled to the substrate support WT respectively to the mask support MT. The actuator may be a moving-coil type actuator which has the at least one coil coupled to the substrate support WT respectively to the mask support MT. The actuator may be a voice-coil actuator, a reluctance actuator, a Lorentz-actuator or a piezo-actuator, or any other suitable actuator.

[033] The lithographic apparatus LA comprises a position control system PCS as schematically depicted in Figure 3. The position control system PCS comprises a setpoint generator SP, a feedforward controller FF and a feedback controller FB. The position control system PCS provides a drive signal to the actuator ACT. The actuator ACT may be the actuator of the first positioner PM or the second positioner PW. The actuator ACT drives the plant P, which may comprise the substrate support WT or the mask support MT. An output of the plant P is a position quantity such as position or velocity or acceleration. The position quantity is measured with the position measurement system PMS. The position measurement system PMS generates a signal, which is a position signal representative of the position quantity of the plant P. The setpoint generator SP generates a signal, which is a reference signal representative of a desired position quantity of the plant P. For example, the reference signal represents a desired trajectory of the substrate support WT. A difference between the reference signal and the position signal forms an input for the feedback controller FB. Based on the input, the feedback controller FB provides at least part of the drive signal for the actuator ACT. The reference signal may form an input for the feedforward controller FF. Based on the input, the feedforward controller FF provides at least part of the drive signal for the actuator ACT. The feedforward FF may make use of information about dynamical characteristics of the plant P, such as mass, stiffness, resonance modes and eigenfrequencies.

[034] In an exposure apparatus, such as a lithographic apparatus LA, it is important to accurately position the wafer W on the wafer table WT with respect to the projection system PS in order to obtain the desired accuracy and resolution. To this end, the relative position of the wafer table WT with respect to the metrology frame MF is measured. Deformations of the wafer table WT and/or the metrology frame MF, e.g. due to vibrations, induce inaccuracies because the measured relative positions on certain points of the wafer table WT and the metrology frame MF are then no longer representative for the relative position of the wafer W with respect to the projection system PS. [035] Furthermore, in an exposure apparatus, such as a lithographic apparatus LA, it is also important to accurately position other components, for example (parts of) the projection system PS. Positioning accuracy of such other components also suffers from inaccuracies induced from deformations of the wafer table WT and/or the metrology frame MF. Furthermore, such other components may also vibrate themselves. [036] The positioning measurement system PMS is configured to determine a position of an operative point 2 based on at least one positioning measurement signal generated by at least one positioning sensor such as a first positioning sensor 3. The first positioning sensor 3 is arranged in a first positioning location 4 and provides a first positioning measurement signal representative of a position in a measurement plane 5 of a first primary positioning point 6 of the first positioning sensor 3 with respect to a first secondary positioning point 7 of the first positioning sensor 3. The first primary positioning point 6 is arranged on a first element 8 of the position measurement system (e g. the wafer table WT of a lithographic apparatus LA) and the first secondary positioning point is arranged on a second element of the position measurement system (e g. the metrology frame MF of a lithographic apparatus). The operative point may in that case be a point on the wafer W, which operative point is to be positioned accurately with respect to the projection system PS such that a projection operation may be performed on said operative point 2 of the wafer W by the projection system PS. The first positioning sensor 3 may comprise an encoder system or interferometer system as discussed above.

[037] The invention provides a method to correct a positioning measurement signal from the position measurement system PMS. Alternatively, this position measurement signal may be generated by a different system, e g. a subsystem configured to determine a position of another components, for example (parts of) the projection system PS.

[038] The method comprises determining a first vibrational mode of the second element 9 with respect to the first element 8. Subsequently, the method comprises determining for that first vibrational mode a first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point 7 with respect to the first primary positioning point 6. It is noted here that the term ‘first vibrational mode’ does not imply that it concerns the lowest harmonic vibration. Instead, it merely refers to a certain vibrational mode that is being corrected for using this method. This may or may not be the first harmonic oscillation. The first vibrational mode and/or the first modal displacement may be determined based on e g. finite element modelling or empirical measurements.

[039] The first modal displacement may be determined by:

- acquiring a time series of position data of the second element 9 of the position measurement system PMS with respect to the first element 8 of the position measurement system PMS;

- applying a bandpass filter to said position data allowing only signal with a frequency substantially equal to the first modal frequency value to pass through the filter;

- determining the amplitude and phase of the thus filtered position data.

[040] Said time series may be determined by e.g. physical measurements or other empirical data, or by a finite element modelling simulation. Empirical data may be beneficial for calibrating individual exposure apparatuses [041] Empirical determination of said time series for the purposes of determining the first vibrational mode and/or the first modal displacement may be performed by a third sensor system acquiring positional data in one or more location of the exposure apparatus. Alternatively or additionally, positional data for this purpose may be acquired by the first positioning sensor 3 and/or other positioning sensors. The empirical determination of said time series may be performed during standstill of the exposure apparatus, for example in a special test mode of the exposure apparatus The empirical data may comprise measurements obtained at various relative positions of the first element of the position measurement system with respect to the second element of the position measurement system, such that a sensitivity and/or phase shift may be determined dependent on said relative position.

[042] Besides determining the first vibrational mode, the method also comprises determining a first sensitivity coefficient 55 representing a sensitivity of a position and/or orientation of the operative point 2 to a position deviation of the first secondary positioning 7 point with respect to the first primary positioning point 6. This sensitivity coefficient 55 determines how much deviation is generated in the position of the operative point 2 by a certain error of the first positioning measurement signal. The first sensitivity coefficient 55 may be dependent on a relative position of the first element 8 of the position measurement system PMS with respect to the second element 9 of the position measurement system PMS, e.g. when the wafer table WT with the wafer W is moved with respect to the metrology frame MF and the projection system PS, the sensitivity coefficient 55 may change. The first sensitivity coefficient 55 may be determined based on e g. finite element modelling or empirical measurements.

[043] Then, the first modal displacement is multiplied with the first sensitivity coefficient 55 to obtain a first correction value. This first correction value is used to correct the first positioning measurement signal, e g. by subtracting the first correction value from the first positioning measurement signal. This provides a corrected first positioning measurement signal which can be used to determine a corrected position of the operative point 2. This corrected position may then be used for positioning the operative point 2, preferably by controlling the position control system PCS. [044] The first vibrational mode may have a phase offset, i.e. the displacement of first primary positioning point with respect to a first secondary positioning point may have a temporal offset with respect to a displacement of the operative point due to the first vibrational mode. Therefore, the method optionally comprises determining, of the first vibrational mode, a modal frequency value, a modal amplitude value, and a modal phase value, the modal frequency value optionally comprising a peak frequency and/or a bandwidth. Then, the first modal displacement may be determined based on the first modal displacement based on the first modal frequency value, the first modal amplitude value, and the first modal phase value. Additionally or alternatively, the sensitivity coefficient 55 may comprise a complex value comprising an amplitude representing the first modal amplitude value and a phase representing the first modal phase value. Alternatively to being integrated in the complex sensitivity coefficient 55, the phase offset may be translated into a time offset. In that case, a time delay or advance corresponding with the modal phase value may be applied to the first modal displacement or to the first correction value to account for phase differences between the first modal displacement and the vibration of the operative point as a result of the first vibrational mode.

[045] The first modal displacement generated by the vibrational mode may comprise a temporally periodically varying value, such as a sine wave. The first modal displacement may comprise a narrow or relatively broad frequency bandwidth. To account for this, the modal amplitude value and/or the modal phase value used in the method may be frequency dependent.

[046] The first sensitivity coefficient 55 may comprise a matrix of positional sensitivities, each positional sensitivity comprising multiple directional sensitivities representing sensitivities of position in different directions and/or orientational sensitivities of orientation around different axes 33 of the operative point 2 in response to position deviations in different directions of the first primary positioning point 6 with respect to the first secondary positioning point 7. For example, the position of the first primary positioning point 6 with respect to the first secondary positioning point 7 may deviate along three orthogonal spatial axes 33 (x, y, z), and the first primary positioning point 6 may also be rotated with respect to the first secondary positioning point 7 around those three axes. Similarly, the operative point 2 may be displaced along those three axes 33 or rotated around those three axes. This may yield a sensitivity matrix of 6x6 entries, including all combinations of sensitivity of displacement along and rotation around the three axes 33 of the operative point 2 in response to displacement along and rotation around the three axes 33 of the first primary positioning point 6 with respect to the first secondary positioning point 7.

[047] Above, the method is described using a single first positioning sensor 3. However, this may be extended to two, three, four or more positioning sensors. A total number of four positioning sensors, including the first positioning sensor 3, is preferred. In the case of two positioning sensors, a second positioning sensor 40 arranged at a second positioning location 41 is used, the second positioning location 41 being at a distance 42from the first positioning location 4. The positioning sensors can have multiple outputs or measurement axes. Preferably, the combination of all positioning sensors covers all six degrees of freedom, i.e. movement along the three axes 33 (x, y, z) and rotation around said axes 33. This way, the position and orientation may be fully determined.

[048] The method steps related to the first positioning sensor are also performed for the second positioning sensor. These steps comprise:

- obtaining a second positioning measurement signal representative of a position in the measurement plane 5 of the second primary positioning point 6A of the second positioning sensor 40 with respect to a second secondary positioning point 7A of the second positioning sensor 40;

- determining the second modal displacement comprising a time dependent displacement of the second secondary positioning point 7A with respect to the second primary positioning point 6A in the first vibrational mode; - determining a second sensitivity coefficient 55 representing a sensitivity of a position and/or orientation of the operative point 2 to a position deviation of the second secondary positioning point 7A with respect to the second primary positioning point 6A;

- multiplying the second modal displacement with the second sensitivity coefficient 55 to obtain a second correction value;

- correcting the second positioning measurement signal based on the second correction value to determine a corrected position of the operative point.

[049] The second modal displacement may be determined in the same way as the first modal displacement, for example by empirical measurements or finite element modelling. Determining the second modal displacement may thus comprise:

- determining the amplitude and phase of the thus filtered position data.

[050] Figure 4 schematically depicts an embodiment of the method. An input signal 52 is passed through a band filter 53. The band filter 53 only allows a certain range of frequencies to pass through, for example the frequency of a vibrational mode to be corrected for. The input signal may be the positioning measurement signal or any other signal representative of a position of the operative point 2. A phase correction 54 may be applied to correct for phase differences between the input signal 52 and the position of the operative point 2, after which a multiplication 56 is performed of the filtered, phase corrected input signal 52 with the sensitivity coefficient 55. Alternatively, the phase correction may be achieved by using a complex sensitivity coefficient 55. This results in the correction value 57. [051] The correction value 57 can be used in different correction implementation positions 58 within the control logic of the position control system PCS. Figures 5A, 5B, 5C, and 5D show the position control system of figure 3, with the addition that the correction value 57 is used in a respective implementation position 58 in each of figures 5A, 5B, 5C, 5D by implementing the correction controller 47 at said respective implementation positions 58. The correction value 57 is in those positions subtracted from the respective signal or value. In figure 5A, the correction value 57 is used to modify the signal sent to the actuator ACT directly. In figure 5B, the correction value is used to modify the signal sent to the feedback controller FB by position measurement system PMS. Figures 5C and 5D have a subtle difference. In figure 5C, the correction value 57 is used to correct the signal used as input for the position measurement system PMS and directly modifies the output of the plant P. In figure 5D, the correction value 57 is also used to correct the signal used as input for the position measurement system PMS, with the difference that only the output of the plant P is not directly modified by the correction value 57. Additionally or alternatively, the correction value 57 may be used to correct other signals and/or values. In each case, the correction value will be tailored to the specific correction implementation position 58, for example by using an appropriate sensitivity coefficient 55 representing the sensitivity of the signal or value at the correction implementation position 58 to deviations or errors in the input signal 52 that result from vibrational modes.

[052] From the above, it is clear that one, two, or multiple sensors can be used and that the positioning measurement signal of each positioning sensor can be corrected separately using the above method. If more than two positioning sensors are used, the steps above are repeated for each of the further positioning sensors 43.

[053] The invention also provides a computer program comprising instructions which, when the program is executed by a computer 50, cause the computer to carry out the steps of the method as described above. Furthermore, the invention also provides a computer-readable medium 51 comprising instructions which, when the program is executed by a computer 50, cause the computer to carry out the steps of the method.

[054] The invention also provides a position control system PCS and a lithographic apparatus LA comprising a position control system PCS. The position control system PCS may be configured for performing any of the methods described above.

[055] The position control system PCS is configured for positioning an operative point 2 at a position in space. The position control system PCS comprises a position measurement system (PMS) comprising a first positioning sensor 3. The first positioning sensor 3 is configured to provide a first positioning measurement signal representative of a position in a measurement plane 5 of a first primary positioning point 6 of the first positioning sensor 3 with respect to a first secondary positioning point 7 of the first positioning sensor 3. The first primary positioning point 6 is arranged on a first element 8 of the position measurement system PMS and the first secondary positioning point 7 is arranged on a second element 9 of the position measurement system PMS. The operative point 2 is arranged on the first element 8 of the position measurement system PMS. As discussed above, the first element 8 may comprise a wafer table WT of the lithographic apparatus LA, wherein the second element 9 comprises a metrology frame MF of the lithographic apparatus LA. The position control system PCS is then configured to control a position of the wafer table WT, for example the position of the wafer table WT with respect to the metrology frame MF and/or the projection system PS of the lithographic apparatus LA.

[056] The position control system PCS comprises an actuator ACT configured to move the first element 8 of the position measurement system PMS with respect to the second element 9 of the position measurement system PMS. This way, the position control system PCS can influence the position of the operative point 2.

[057] The position control system PCS comprises a correction controller 47. The correction controller 47 is configured to:

A. determine a first vibrational mode of the second element 9 with respect to the first element 8; B. determine first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point 7 with respect to the first primary positioning point 6 in the first vibrational mode;

C. determine a first sensitivity coefficient 55 representing a sensitivity of a position and/or orientation of the operative point 2 to a position deviation of the first secondary positioning point 7 with respect to the first primary positioning point 6;

D. multiply the first modal displacement with the first sensitivity coefficient 55 to obtain a first correction value;

E. based on the first positioning measurement signal and the first correction value, control the actuator ACT to move the first element 8 of the position measurement system PMS with respect to the second element 9 of the position measurement system PMS such that the operative point 2 is positioned at a desired position 48.

[058] The position control system PCS may comprise a second positioning sensor 40, arranged at a second positioning location 41. The position control system PCS is then configured to perform the method comprising the method steps related to the second positioning sensor 40 as discussed above.

These steps comprise:

- determining the second modal displacement comprising a time dependent displacement of the second secondary positioning point 7A with respect to the second primary positioning point 6A in the first vibrational mode;

- determining a second sensitivity coefficient 55 representing a sensitivity of a position and/or orientation of the operative point 2 to a position deviation of the second secondary positioning point 7A with respect to the second primary positioning point 6A;

[059] The second modal displacement may be determined in the same way as the first modal displacement, for example by empirical measurements or finite element modelling. Determining the second modal displacement may thus comprise:

- determining the amplitude and phase of the thus filtered position data. [060] The position control system PCS may comprise at least two further positioning sensors 43, preferably three further positioning sensors 43, such that the position control system PCS comprises a total of four positioning sensors. The position control system PCS is then configured to perform the method steps described above for the second positioning sensor 40 for each of the further positioning sensors 43. The positioning sensors may for example be arranged on the four comers of a wafer table WT

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

[062] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatuses, including other exposure apparatuses. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, an inspection tool or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools, metrology tools, or inspection tools. Such a lithographic, metrology or inspection tool may use vacuum conditions or ambient (non-vacuum) conditions.

[063] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention, where the context allows, is not limited to optical lithography and may be used in other applications, for example imprint lithography.

[064] Where the context allows, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine -readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g. carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world. [065] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below. Other aspects of the invention are set-out as in the following numbered clauses.

1. A method to correct a positioning measurement signal from a position measurement system configured to determine a position of an operative point based on at least one positioning measurement signal, the position measurement system comprising a first positioning sensor arranged in a first positioning location, the method comprising the steps of: a) obtaining a first positioning measurement signal from the first positioning sensor, wherein the first positioning measurement signal is representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system; b) determining a first vibrational mode of the second element with respect to the first element; c) determining a first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point with respect to the first primary positioning point in the first vibrational mode; d) determining a first sensitivity coefficient representing a sensitivity of a position and/or orientation of the operative point to a position deviation of the first secondary positioning point with respect to the first primary positioning point; e) multiplying the first modal displacement with the first sensitivity coefficient to obtain a first correction value; f) correcting the first positioning measurement signal based on the first correction value to determine a corrected position of the operative point.

2. Method according to clause 1, the method further comprising the steps of: g) determining, of the first vibrational mode, a modal frequency value, a modal amplitude value, and a modal phase value, the modal frequency value optionally comprising a peak frequency and/or a bandwidth; h) determining the first modal displacement based on the first modal frequency value, the first modal amplitude value, and the first modal phase value.

3. Method according to clause 2, the method further comprising in step e) applying a time delay or advance corresponding with the modal phase value to the first modal displacement or to the first correction value. 4. Method according to any of the preceding clauses, wherein the first sensitivity coefficient comprises a complex value comprising an amplitude representing a first modal amplitude value and a phase representing a first modal phase value.

5. Method according to any of clauses 2 - 4, wherein the modal amplitude value is frequency dependent and/or the modal phase value is frequency dependent.

6. Method according to any of the preceding clauses, wherein the first sensitivity coefficient is dependent on at least a relative position of the first element of the position measurement system with respect to the second element of the position measurement system.

7. Method according to any of the preceding clauses, wherein the first sensitivity coefficient is determined based on finite element modelling or based on empirical measurements.

8. Method according to any of the preceding clauses, wherein the first sensitivity coefficient comprises a matrix of positional sensitivities comprising multiple directional sensitivities representing sensitivities of position in different directions and/or orientational sensitivities of orientation around different axes of the operative point in response to position deviations in different directions of the first primary positioning point with respect to the first secondary positioning point.

9. Method according to any of the preceding clauses, wherein the first vibrational mode and/or the first modal displacement is determined based on finite element modelling or based on empirical measurements.

10. Method according to any of the preceding clauses, wherein the first modal displacement comprises a temporally periodically varying value, such as a sine wave.

11. Method according to the preceding clauses, wherein the first element comprises a wafer table of an exposure apparatus, wherein the second element comprises a metrology frame of the exposure apparatus.

12. Method according to any of the preceding clauses, wherein the first modal displacement is determined by: i) acquiring a time series of position data of the second element of the position measurement system with respect to the first element of the position measurement system; j) applying a bandpass filter to said position data allowing only signal with a frequency substantially equal to the first modal frequency value to pass through the filter; k) determining the amplitude and phase of the thus filtered position data.

13. Method according to any of the preceding clauses, the position measurement system comprising a second positioning sensor arranged in a second positioning location at a distance from the first positioning location, the method further comprising performing steps a), c), d), e) and f) for the second positioning sensor in addition to performing said steps for the first positioning sensor, wherein the method optionally comprises the features of clause 11 and the method optionally comprises performing steps i), j), and k) for the second positioning sensor in addition to performing said steps for the first positioning sensor. 14. Method according to any of the preceding clauses, the position measurement system comprising at least two further positioning sensors, preferably three further positioning sensors, wherein each positioning sensor is arranged in a respective positioning location at a distance from the other positioning locations, the method further comprising performing steps a), c), d), e) and f) for each further positioning sensor in addition to performing said steps for the first positioning sensor, wherein the method optionally comprises the features of clause 11 and the method optionally comprises performing steps i), j), and k) for each further positioning sensor in addition to performing said steps for the first positioning sensor.

15. Method for positioning an operative point, the method comprising correcting a positioning measurement signal according to any of the preceding clauses, the method further comprising positioning the operative point based on the corrected position of the operative point, preferably by controlling a position control system.

16. Position control system for positioning an operative point at a position in space, the system comprising: a position measurement system comprising a first positioning sensor, wherein the first positioning sensor is configured to provide a first positioning measurement signal representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system and the operative point is arranged on the first element of the position measurement system; an actuator configured to move the first element of the position measurement system with respect to the second element of the position measurement system; a correction controller configured to:

E. based on the first positioning measurement signal and the first correction value, control the actuator to move the first element of the position measurement system with respect to the second element of the position measurement system such that the operative point is positioned at a desired position. 17. Position control system according to clause 16, configured to perform the method of any of clauses 1 - 15.

18. Position control system according to clause 16 or 11, further comprising a second positioning sensor, wherein the position control system is configured to perform the method of clause 12.

19. Position control system according to any of clauses 16 - 18, comprising at least two further positioning sensors, preferably three further positioning sensors, wherein the position control system is configured to perform the method of clause 14.

20. An exposure apparatus comprising a position control system according to any of clauses 15 - 18, wherein the first element comprises a wafer table of the exposure apparatus, wherein the second element comprises a metrology frame of the exposure apparatus, wherein the position control system is configured to control a position of the wafer table.

21. An inspection system comprising a position control system according to any of clauses 15 - 18, wherein the first element comprises a substrate support of the inspection system, wherein the second element comprises a frame of the inspection system, wherein the position control system is configured to control a position of the substrate support.

22. A metrology tool comprising a position control system according to any of clauses 15 - 18, wherein the first element comprises a substrate support of the metrology tool, wherein the second element comprises a frame of the metrology tool, wherein the position control system is configured to control a position of the substrate support.

23. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of any of clauses 1 - 15.

24. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method of any of clauses 1 - 15.

Claims

1. A method to correct a positioning measurement signal from a position measurement system configured to determine a position of an operative point based on at least one positioning measurement signal, the position measurement system comprising a first positioning sensor arranged in a first positioning location, the method comprising the steps of a) obtaining a first positioning measurement signal from the first positioning sensor, wherein the first positioning measurement signal is representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system; b) determining a first vibrational mode of the second element with respect to the first element; c) determining a first modal displacement, the first modal displacement comprising a time dependent displacement of the first secondary positioning point with respect to the first primary positioning point in the first vibrational mode; d) determining a first sensitivity coefficient representing a sensitivity of a position and/or orientation of the operative point to a position deviation of the first secondary positioning point with respect to the first primary positioning point; e) multiplying the first modal displacement with the first sensitivity coefficient to obtain a first correction value; f) correcting the first positioning measurement signal based on the first correction value to determine a corrected position of the operative point.

2. Method according to claim 1, the method further comprising the steps of: g) determining, of the first vibrational mode, a modal frequency value, a modal amplitude value, and a modal phase value, the modal frequency value optionally comprising a peak frequency and/or a bandwidth; h) determining the first modal displacement based on the first modal frequency value, the first modal amplitude value, and the first modal phase value.

3. Method according to claim 2, the method further comprising in step e) applying a time delay or advance corresponding with the modal phase value to the first modal displacement or to the first correction value.

4. Method according to any of the preceding claims, wherein the first sensitivity coefficient comprises a complex value comprising an amplitude representing a first modal amplitude value and a phase representing a first modal phase value.

5. Method according to any of claims 2 - 4, wherein the modal amplitude value is frequency dependent and/or the modal phase value is frequency dependent.

6. Method according to any of the preceding claims, wherein the first sensitivity coefficient is dependent on at least a relative position of the first element of the position measurement system with respect to the second element of the position measurement system.

7. Method according to any of the preceding claims, wherein the first sensitivity coefficient comprises a matrix of positional sensitivities comprising multiple directional sensitivities representing sensitivities of position in different directions and/or orientational sensitivities of orientation around different axes of the operative point in response to position deviations in different directions of the first primary positioning point with respect to the first secondary positioning point.

8. Method according to the preceding claims, wherein the first element comprises a wafer table of an exposure apparatus, wherein the second element comprises a metrology frame of the exposure apparatus.

9. Method according to any of the preceding claims, wherein the first modal displacement is determined by: i) acquiring a time series of position data of the second element of the position measurement system with respect to the first element of the position measurement system; j) applying a bandpass filter to said position data allowing only signal with a frequency substantially equal to the first modal frequency value to pass through the filter; k) determining the amplitude and phase of the thus filtered position data.

10. Method according to any of the preceding claims, the position measurement system comprising a second positioning sensor arranged in a second positioning location at a distance from the first positioning location, the method further comprising performing steps a), c), d), e) and f) for the second positioning sensor in addition to performing said steps for the first positioning sensor, wherein the method optionally comprises the features of claim 8 and the method optionally comprises performing steps i), j), and k) for the second positioning sensor in addition to performing said steps for the first positioning sensor. i

11. Method for positioning an operative point, the method comprising correcting a positioning measurement signal according to any of the preceding claims, the method further comprising positioning the operative point based on the corrected position of the operative point, preferably by controlling aposition control system.

12. Position control system for positioning an operative point at aposition in space, the system comprising: a position measurement system comprising a first positioning sensor, wherein the first positioning sensor is configured to provide a first positioning measurement signal representative of a position in a measurement plane of a first primary positioning point of the first positioning sensor with respect to a first secondary positioning point of the first positioning sensor, wherein the first primary positioning point is arranged on a first element of the position measurement system and the first secondary positioning point is arranged on a second element of the position measurement system and the operative point is arranged on the first element of the position measurement system; an actuator configured to move the first element of the position measurement system with respect to the second element of the position measurement system; a correction controller configured to:

13. Position control system according to claim 12, configured to perform the method of any of claims 1 - 11.

14. Position control system according to claim 12 or 13, further comprising a second positioning sensor, wherein the position control system is configured to perform the method of claim 9.

15. An exposure apparatus comprising a position control system according to any of claims 12-14, wherein the first element comprises a wafer table of the exposure apparatus, wherein the second element comprises a metrology frame of the exposure apparatus, wherein the position control system is configured to control a position of the wafer table.