Method and apparatus for determining a physical quantity

Abstract

A method for determining a physical quantity is disclosed. This method uses a sensor system configured to sample a plurality of positions in parallel, and for sampling each position, radiation incident on an object plane patterning device (mark) and an image plane sensor is used. Each mark is composed of a first part and a second part, the first part being different from the second part, and the first part and the second part of at least one mark are transposed with respect to the first part and the second part of other marks. Each mark corresponds to a different sampling position. This method includes performing a first measurement in a first direction and a second measurement in a second direction different from the first direction for each part of each mark. Four data sets are determined and then combined to determine physical parameters.

Description

Technical Field

[0001] [Cross-reference to Related Applications] This application claims the priority of European Application No. 22180704.3 filed on June 23, 2022, which is incorporated herein by reference in its entirety.

[0002] [Technical Field] The present invention relates to a method for determining one or more physical quantities and a related apparatus for performing this method. The one or more physical quantities may be related, for example, to the alignment between the object plane and the image plane of a projection system.

Background Art

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus can project a pattern (also referred to as a "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).

[0004] As semiconductor manufacturing processes progress, the dimensions of circuit elements are continuously reduced, while the amount of functional elements such as transistors per device has steadily increased over several decades according to a trend generally known as "Moore's Law". The semiconductor industry is pursuing technologies that can achieve ever finer features so as not to lag behind Moore's Law. To project a pattern onto a substrate, a lithographic apparatus can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features to be patterned on the substrate. Representative wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Using a lithographic apparatus that uses extreme ultraviolet (EUV) radiation having a wavelength in the range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, smaller features can be formed on the substrate than with a lithographic apparatus that uses radiation having a wavelength of 193 nm.

[0005] In lithographic apparatuses, many sensor systems are used to measure all kinds of physical quantities. Examples of interesting physical quantities include distance / position, time, velocity, acceleration, force, lens aberration, etc. Some of these sensor systems use detectors that output signals that vary periodically. Such periodically varying signals can be obtained using a periodic structure such as a grating. The periodically varying signal can have, for example, the shape of a sine wave.

[0006] The radiation patterned by the patterning device is focused onto the substrate using a projection system. Optical aberrations are generated by the projection system, and the image formed on the substrate may deviate from the desired image (e.g., the diffraction-limited image of the patterning device). Alignment in a lithographic apparatus is also an important aspect, for example, to confirm that the desired image is placed in the correct position. Furthermore, alignment of components including, for example, the substrate is also an important aspect. SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION

[0007] It may be desirable to provide a method and apparatus for accurately measuring such physical quantities, such as aberrations caused by a projection system, so that these aberrations can be appropriately controlled, or for accurately determining the intensity of a signal for, for example, determining the alignment of a substrate. Further, it is desirable to provide a method and apparatus for accurately determining the projection alignment in a lithographic apparatus.

Means for Solving the Problem

[0008] According to a first aspect of the present disclosure, a method for determining a physical quantity is provided. The method uses a sensor system configured to sample a plurality of positions, and the sampling at each position uses an object plane patterning device and an image plane sensor. Each object plane patterning device includes a first portion and a second portion, the first portion being different from the second portion, and the first portions and the second portions of at least one object plane patterning device are transposed with respect to the first portions and the second portions of other object plane patterning devices. The method includes using the first portion of each object plane patterning device to perform a first measurement in a first direction to generate a first data set, using the second portion of each object plane patterning device to perform a second measurement in the first direction to generate a second data set, using the first portion of each object plane patterning device to perform a third measurement in a second direction, different from the first direction, to generate a third data set, using the second portion of each object plane patterning device to perform a fourth measurement in the second direction to generate a fourth data set, and combining the first, second, third, and fourth data sets to determine the physical quantity.

[0009] The method according to the first aspect has the advantage that, as will be explained herein, the determined physical quantity becomes less sensitive to correlation intensity noise.

[0010] Each of the first, second, third, and fourth data sets is generated using radiation, which is understood to be subject to the effects of intensity noise (i.e., the intensity of the radiation changes or varies over time). Radiation having a common noise source impinges on each object plane patterning device and the image plane sensor to generate the first, second, third, and / or fourth data sets. Since the data generated in any of the first, second, third, and fourth data sets is formed by the same radiation emission (such as continuous or pulsed), there will be a correlation in the noise intensity among any of the first, second, third, and fourth data sets.

[0011] The object plane patterning device may comprise a grating.

[0012] The orientation of the first portion of the object plane patterning device may be orthogonal to the orientation of the second portion. This arrangement is advantageous in that it minimizes the data processing required for subsequent modeling.

[0013] The orientation of at least one object plane patterning device may be orthogonal to the second orientation of another object plane patterning device.

[0014] In some embodiments, the first, second, third, and fourth measurements form part of a shearing interferometry process.

[0015] In some embodiments, the first portion of the object plane patterning device has a first shearing direction, the second portion has a second shearing direction, and the second shearing direction is different from the first shearing direction. The first direction of the first measurement includes a component parallel to the first shearing direction and a component parallel to the second shearing direction, and the second direction of the second measurement may include a component parallel to the first shearing direction and a component parallel to the second shearing direction. When each of the first direction and the second direction includes a component parallel to the first shearing direction and a component parallel to the second shearing direction, scanning in either the first direction or the second direction will substantially result in scanning in both the first shearing direction and the second shearing direction simultaneously.

[0016] In one embodiment, for one of the first direction and the second direction, the sign of the component parallel to the first shearing direction is opposite to the sign of the component parallel to the second shearing direction, and for the other of the first direction and the second direction, the sign of the component parallel to the first shearing direction is the same as the sign of the component parallel to the second shearing direction. Advantageously, when scanning in one direction, it is ensured that the sign of the error in the differentiation of the wavefront map in the other direction is different for each of the first set and the second set. This enables the correlated intensity errors to be modeled and eliminated. The first direction and the second direction may be aligned at 45 degrees with respect to each of the first shearing direction and the second shearing direction.

[0017] In some embodiments, the image sensor may include a plurality of image sensors. Each of the plurality of image plane sensors includes a second patterning device that can be arranged to receive radiation from a corresponding one of the plurality of object plane patterning devices, and the plurality of image plane sensors includes a detector arranged to receive radiation from the plurality of second patterning devices.

[0018] In some embodiments, a method of determining a physical quantity by combining first, second, third, and fourth data sets includes combining the first data set and the second data set to determine at least one first physical parameter for each sampling position. Combining the third data set and the fourth data set to determine at least one second physical parameter for each sampling position. And combining the determined first physical parameter for each sampling position with the determined second physical parameter for each sampling position to form an output corrected physical parameter for each sampling position, and at least partially correcting errors in the determined first and second physical parameters caused by intensity variations of the radiation used to generate the first, second, third, and / or fourth data sets.

[0019] The physical quantity can include one or more aberrations of the projection system. Further, the first, second, third, and fourth physical parameters can respectively correspond to first, second, third, and fourth aberration coefficients.

[0020] In some embodiments, combining the first data set and the second data set to determine one or more aberrations can further include determining a first wavefront tilt coefficient in a first direction. The step of combining the third data set and the fourth data set to determine one or more aberrations can further include the step of determining a second wavefront tilt coefficient in the first direction. And combining the determined first wavefront tilt coefficient in the first direction for each sampling position with the determined second wavefront tilt coefficient in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position, and at least partially correcting errors in the determined first wavefront tilt coefficient in the first direction and the determined second wavefront tilt coefficient in the first direction caused by intensity variations of the radiation used to generate the first data set and the second data set.

[0021] In some embodiments, combining a first wavefront tilt coefficient determined in a first direction for each sampling position and a second wavefront tilt coefficient determined in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position may include performing a least squares approximation to, for each sampling position, determine a root mean square of the squares of the differences between (a) the first wavefront tilt coefficient in the determined first direction and (b) a value obtained by adding a first constant to the output wavefront tilt coefficient in the first direction, and, for each sampling position, determine a root mean square of the squares of the differences between (a) the second wavefront tilt coefficient in the determined first direction and (b) a value obtained by adding a second constant, which is multiplied by +1 for a first portion of the lattice of the object plane patterning device and multiplied by -1 for a second portion of the lattice of the object plane patterning device, to the output wavefront tilt coefficient in the first direction.

[0022] In some embodiments, the physical quantity includes intensity.

[0023] In some embodiments, the physical quantity includes one or more intensities of the measured radiation, and the first, second, third, and fourth physical parameters respectively correspond to the first, second, third, and fourth intensity values.

[0024] In some embodiments, determining the physical quantity by combining the first, second, third, and fourth data sets includes combining the first data set and the second data set to determine, for each sampling position, a first wavefront tilt coefficient in a second step direction. Combining the third data set and the fourth data set to determine a second wavefront tilt coefficient in a second direction for each sampling position. Then, combining the first wavefront tilt coefficient in the second direction determined for each sampling position and the second wavefront tilt coefficient in the second direction determined for each sampling position to form an output wavefront tilt coefficient in the second direction for each sampling position, and at least partially correcting errors in the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction caused by intensity fluctuations of the radiation used to generate the second data set and the fourth data set.

[0025] In some embodiments, combining the first wavefront tilt coefficient determined in the second direction for each sampling position and the second wavefront tilt coefficient determined in the second direction for each sampling position to form the output wavefront tilt coefficient in the second direction for each sampling position includes performing a least squares approximation to, for a plurality of sampling positions, the root mean square of the difference between (a) the determined first wavefront tilt coefficient in the second direction and (b) a value obtained by adding a third constant to the output wavefront tilt coefficient in the second direction, and, for a plurality of sampling positions, the root mean square of the difference between (a) the determined second wavefront tilt coefficient in the second direction and (b) a value obtained by adding a fourth constant, which is multiplied by +1 for the first part of the grating of the object plane patterning device and multiplied by -1 for the second part of the grating of the object plane patterning device, to the output wavefront tilt coefficient in the second direction, and simultaneously minimizing them.

[0026] In some embodiments, each measurement includes irradiating a plurality of object plane patterning devices with a first radiation. Forming an image of each of the plurality of object plane patterning devices on a different one of the plurality of image plane sensors, and scanning at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors through a plurality of positions spaced apart in a direction to generate a vibration phase scan signal for each of the plurality of sampling positions. Determining the phase of the harmonics of the vibration signal at a plurality of positions on the radiation detector.

[0027] The harmonic of the vibration signal equal to the difference in the aberration map between a pair of positions in the pupil plane of the projection system at each of the plurality of positions on the radiation detector may be the first harmonic.

[0028] The pair of positions in the pupil plane of the projection system may be separated in the shearing direction by a shearing distance corresponding to twice the distance in the pupil plane between two adjacent first diffracted beams.

[0029] A second aspect of the present disclosure is a measurement system for determining a physical quantity, comprising a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation, wherein the second orientation is different from the first orientation; a plurality of object plane patterning devices; an illumination system arranged to irradiate the plurality of object plane patterning devices with radiation to form a plurality of first diffracted beams, wherein the first diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of a grating, and the first diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating; an image plane sensor including a patterning device and a radiation detector; an illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second diffracted beams from each of the first diffracted beams; a positioning device configured to move the plurality of object plane patterning devices in a first direction or a second direction; and a controller configured to execute the method according to the present invention.

[0030] A third aspect of the present disclosure is a measurement system for determining a physical quantity, comprising a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation, wherein the second orientation is different from the first orientation; a plurality of object plane patterning devices; an illumination system arranged to irradiate the plurality of object plane patterning devices with radiation to form a plurality of first diffracted beams, wherein the first diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of a grating, and the first diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating; a plurality of image plane sensors, each comprising a patterning device and communicating with a radiation detector; an illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second diffracted beams from each of the first diffracted beams; a positioning device configured to move at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors in a first direction or a second direction; and a controller configured to execute a method according to the present invention.

[0031] According to a fourth aspect of the present disclosure, there is provided a computer-readable medium having recorded thereon a computer program comprising computer-readable instructions configured to cause a computer to execute a method according to any one of the first, second, and third aspects of the present disclosure.

[0032] According to a fifth aspect of the present disclosure, there is provided a computer device comprising a memory storing processor-readable instructions and a processor configured to read and execute the instructions stored in the memory, the processor-readable instructions including instructions configured to control a computer to execute a method according to any one of the first, second, and third aspects of the present disclosure.

[0033] According to a sixth aspect of the present disclosure, a lithography apparatus is provided that includes a measurement system according to any one of the fourth and fifth aspects of the present disclosure.

[0034] According to a seventh aspect of the present disclosure, a metrology tool is provided that includes a measurement system according to any one of the fourth and fifth aspects of the present disclosure.

[0035] It will be understood that one or more of the aspects or features described above, or referred to in the following description, can be combined with one or more other aspects or features.

Brief Description of the Drawings

[0036] Embodiments of the present invention are described by way of example only with reference to the accompanying schematic drawings.

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DETAILED DESCRIPTION OF THE INVENTION

[0037] In this specification, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation including ultraviolet light (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of about 5 - 100 nm).

[0038] As used herein, the terms “reticle,” “mask,” or “patterning device” can be broadly interpreted to refer to a general patterning device that can be used to impart a patterned cross-section corresponding to a pattern to be created in a target portion of a substrate to an incident radiation beam. The term “light valve” can also be used in this context. In addition to standard masks (transmission or reflection, binary, phase-shift, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0039] FIG. 1 schematically shows a lithographic apparatus LA. The lithographic apparatus LA includes an illumination system (also called an illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation), a mask support (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioning device PM configured to accurately position the patterning device MA according to 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 positioning device PW configured to accurately position the substrate support according to certain parameters; and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W. The projection system PS is any system through which radiation from an illumination source passes and where defects can occur due to a failure of the illumination to converge, which can occur, for example, due to defects in lenses and / or mirrors. Thus, the patterning device is arranged outside the projection system PS as shown in FIG. 1, and the radiation beam used for the patterning device is, for example, a measurement radiation beam and not for exposing a pattern on the resist of the substrate.

[0040] During operation, the illumination system IL receives a beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various optical elements, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and / or other types of optical elements, or any combination thereof, for directing, shaping, and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B such that it has a desired spatial and angular intensity distribution in its cross-section in the plane of the patterning device MA.

[0041] As used herein, the term "projection system" PS is to be construed broadly to encompass any type of projection system, including, for example, refractive optical systems, reflective optical systems, catadioptric optical systems, anamorphic optical systems, magneto-optical systems, electro-optic optical systems, and / or electrostatic optical systems, or any combination thereof, as appropriate for the radiation used for both exposure and measurement, and / or other factors such as the use of immersion liquid or the use of a vacuum. When the term "projection lens" is used herein, this can be regarded as synonymous with the more general term "projection system" PS.

[0042] The lithographic apparatus LA may be of a type in which at least a portion of the substrate is covered by a liquid (e.g., water) having a relatively high refractive index so as to fill the gap between the projection system PS and the substrate W. This is also referred to as immersion lithography. Details of immersion techniques are described in U.S. Patent No. 6,952,253, which is incorporated herein by reference.

[0043] The lithographic apparatus LA can also be of the type having two or more substrate supports WT (also referred to as a "dual stage"). In such a "multi-stage" machine, the substrate supports WT can be used in parallel and / or steps in the preparation of subsequent exposure of the substrate W can be carried out on the substrate W located on one of the substrate supports WT. The substrate W on the other substrate support WT is being used to expose a pattern on the other substrate W.

[0044] In addition to the substrate support WT, the lithographic apparatus LA may include a measurement stage. The measurement stage is arranged to hold a sensor and / or a cleaning device. The sensor can be arranged to measure the characteristics of the projection system PS or the characteristics of the radiation beam B. The measurement stage can hold a plurality of sensors. The cleaning device can be configured to clean a part of the lithographic apparatus, for example, a part of the projection system PS or a part of the system providing the immersion liquid. When the substrate support WT is away from the projection system PS, the measurement stage can move under the projection system PS.

[0045] During operation, the radiation beam B is incident on a patterning device, for example a mask MA, held on a mask support MT, and is patterned by the pattern (design layout) present on the patterning device MA. After passing through the mask MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioning device PW and a position measurement system PMS, the substrate support WT can be accurately moved so that different target portions C within the path of the radiation beam B are located at focused and aligned positions. Similarly, a first positioning device PM and optionally another position sensor (not explicitly shown in FIG. 1) can be used to accurately position the patterning device MA relative to the path of the radiation beam B. The patterning device MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. The illustrated substrate alignment marks P1, P2 occupy dedicated target portions, but they may also be arranged in the spaces between the target portions. The substrate alignment marks P1, P2 are known as scribe lane alignment marks when they are arranged between the target portions C.

[0046] The substrate W may include a pre-formed pattern. In this case, the lithographic apparatus LA aligns the image formed by the patterned radiation beam B with the pattern previously formed on the substrate W.

[0047] For the sake of clarity, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes: an x-axis, a y-axis and a z-axis. Each of the three axes is orthogonal to the other two axes. A rotation about the x-axis is called an Rx rotation. A rotation about the y-axis is called an Ry rotation. A rotation about the z-axis is called an Rz rotation. The x-axis and the y-axis define a horizontal plane, while the z-axis is in the vertical direction. The Cartesian coordinate system is not intended to limit the present invention and is used only for the purpose of explanation. Instead, another coordinate system, such as a cylindrical coordinate system, can be used to clarify the present invention. For example, the directions of the Cartesian coordinate system may be different, such that the z-axis has a component along the horizontal plane.

[0048] The radiation used in a lithography system's measurement and / or exposure system, or in a measurement system such as an electron beam measurement tool, can be affected by intensity noise (i.e., the radiation intensity changes or fluctuates over time). Such noise has an adverse effect on the accuracy of measurement and exposure. The present disclosure relates to methods and related apparatuses for at least partially correcting such noise.

[0049] The projection system PS of a lithography system may have a non-uniform optical transfer function and can affect the pattern imaged on the substrate W. In the case of non-polarized radiation, such an effect can be fairly appropriately represented by two scalar maps that represent the transmittance (apodization) and relative phase (aberration) of the radiation emerging from the projection system PS as functions of the position within its pupil plane. These scalar maps, also called transmittance maps and relative phase maps, can be expressed as a linear combination of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. Determining each scalar map can involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients can be obtained from the measured scalar map by successively calculating the inner product of the measured scalar map and each Zernike polynomial and dividing it by the square of the norm of that Zernike polynomial. Unless otherwise specified, hereinafter, references to Zernike coefficients are understood to mean the Zernike coefficients of the relative phase map (also called the aberration map in this specification). It will be understood that in alternative embodiments, other sets of basis functions may be used. For example, in some embodiments, for example, for an obscured aperture system, Tchebychev-Zernike polynomials may be used.

[0050] The wavefront aberration map represents the distortion of the wavefront of light approaching a point in the image plane of the projection system PS from a spherical wavefront (as a function of the position within the pupil plane or, alternatively, as the angle at which the radiation approaches the image plane of the projection system PS). As described above, this wavefront aberration map W(x,y) can be expressed as a linear combination of Zernike polynomials. [Number] Here, x and y are the coordinates of the pupil plane, and z n (x,y) is a Zernike polynomial of order n, and Z n is the coefficient. In the following, it will be understood that the Zernike polynomials and coefficients are generally labeled with an index called the Noll index. Thus, z n (x,y) is a Zernike polynomial with a Noll index of n, and Z n is the coefficient with a Noll index of n. The wavefront aberration map is characterized by the set of coefficients Z n in such an expansion and is sometimes called the Zernike coefficients.

[0051] It will be understood that only a finite number of Zernike orders are considered. The different Zernike coefficients of the phase map provide information about the various forms of aberration caused by the projection system PS. The Zernike coefficient with a Noll index of 1 is called the first-order Zernike coefficient, and the Zernike coefficient with a Noll index of 2 is called the second-order Zernike coefficient.

[0052] The first-order Zernike coefficient Z1 is related to the average value of the measured wavefront (sometimes called piston). The first-order Zernike coefficient may be independent of the performance of the projection system PS and, thus, may not be determined using the method described herein. The second-order Zernike coefficient Z2 is related to the tilt of the measured wavefront in the x direction. The tilt of the wavefront in the x direction corresponds to the placement in the x direction. The third-order Zernike coefficient Z3 is related to the tilt of the measured wavefront in the y direction. The tilt of the wavefront in the y direction corresponds to the placement in the y direction. The fourth-order Zernike coefficient Z4 is related to the defocus of the measured wavefront. The fourth-order Zernike coefficient corresponds to the placement in the z direction. Higher-order Zernike coefficients are related to other forms of aberration (astigmatism, coma, spherical aberration, other effects, etc.) caused by the projection system.

[0053] Throughout this description, the term "aberration" is intended to include any form of deviation of the wavefront from a perfect spherical wavefront. That is, the term "aberration" may relate to the placement of the image (e.g., second-, third-, and fourth-order Zernike coefficients) and / or higher-order aberrations related to Zernike coefficients with Noll indices of 5 or greater. Further, reference to the aberration map of the projection system may include any form of deviation of the wavefront from a perfect spherical wavefront, including those due to the placement of the image.

[0054] The relative phase at the pupil plane of the projection system PS can be determined by projecting radiation from an object plane patterning device (i.e., a patterning device in the plane of the patterning device MA) onto the projection system PS and measuring the wavefront (i.e., the locus of points having the same phase) using a shearing interferometer. Such a shearing interferometer may comprise a diffraction grating, e.g., a two-dimensional diffraction grating, in the image plane of the projection system (i.e., the substrate table WT), and a detector arranged to detect an interference pattern in a plane conjugate to the pupil plane of the projection system PS.

[0055] The projection system PS comprises a plurality of optical elements. The lithographic apparatus LA further comprises adjustment means PA for adjusting these optical elements to correct for aberrations (any type of phase change over the pupil plane across the entire field of view). To achieve this, the adjustment means PA is operable to operate the optical elements within the projection system PS in one or more different ways. The projection system can have a coordinate system with its optical axis extending in the z-direction (it will be understood that the direction of this z-axis may vary along the optical path through the projection system). The adjustment means PA is operable to perform any combination of displacing one or more optical elements, tilting one or more optical elements, and / or deforming one or more optical elements. The displacement of the optical element can be in any direction (x, y, z or combinations thereof). The tilting of the optical element is typically performed by rotating about an axis in the x- or y-direction from a plane perpendicular to the optical axis, although for non-rotationally symmetric optical elements, rotation about the z-axis can also be possible. The deformation of the optical element can be carried out, for example, by applying a force to the side surface of the optical element using an actuator and / or by heating a selected area of the optical element using a heating element. In general, it may not be possible to adjust the projection system PS to correct for apodization (variation of the transmittance across the entire pupil plane). The transmittance map of the projection system PS can be used when designing the mask MA for the lithographic apparatus LA.

[0056] In some embodiments, the adjustment means PA may be operable to move the support structure MT and / or the substrate table WT. The adjustment means PA is operable to move the support structure MT and / or the substrate table WT (in any of the x, y, z directions, or combinations thereof) and / or to tilt them (by rotating about an axis in the x- or y-direction).

[0057] A projection system PS forming part of a lithographic apparatus may be subject to a calibration process periodically. For example, when the lithographic apparatus is manufactured in a factory, the optical elements forming the projection system PS may be set up by performing an initial calibration process. After the lithographic apparatus has been installed at the location where it is to be used, the projection system PS can be calibrated again. Further calibrations of the projection system PS can be performed periodically. For example, in normal use, the projection system PS can be calibrated every few months (e.g., every three months).

[0058] Calibration of the projection system PS may include passing radiation through the projection system PS and measuring the resulting projection radiation. The measured values of the projection radiation can be used to determine the aberration of the projection radiation produced by the projection system PS. The aberration produced by the projection system PS can be determined using a measurement system. Depending on the determined aberration, the optical elements forming the projection system PS can be adjusted to correct the aberration produced by the projection system PS.

[0059] FIG. 2 is a schematic view of a measurement system 10 that can be used to determine the aberration produced by the projection system PS. The measurement system 10 includes an illumination system IL, a measurement patterning device MA’, a sensor device 21, and a controller CN. The measurement system 10 may form part of a lithographic apparatus. For example, the illumination system IL and the projection system PS shown in FIG. 2 may be the illumination system IL and the projection system PS of the lithographic apparatus shown in FIG. 1. For ease of illustration, additional components of the lithographic apparatus are not shown in FIG. 2.

[0060] The measurement patterning device MA’ is arranged to receive radiation from the illumination system IL. The sensor device 21 is arranged to receive radiation from the projection system PS. During normal use of the lithographic apparatus, the measurement patterning device MA’ and the sensor device 21 shown in FIG. 2 can be arranged at positions different from those shown in FIG. 2. For example, during normal use of the lithographic apparatus, a patterning device MA configured to form a pattern to be transferred onto a substrate W can be arranged to receive radiation from the illumination system IL, and the substrate W can be arranged to receive radiation from the projection system PS (e.g., as shown in FIG. 1). The measurement patterning device MA’ and the sensor device 21 may be moved to the positions shown in FIG. 2 in order to determine aberrations caused by the projection system PS. The measurement patterning device MA’ may be supported by a support structure MT such as the support structure shown in FIG. 1. The sensor device 21 may be supported by a substrate table such as the substrate table WT shown in FIG. 1. Alternatively, the sensor device 21 may be supported by a measurement table (not shown) separate from the sensor table WT. It should be understood that the measurement system 10 may be applied for measuring intensity deviations in metrology applications rather than for measuring aberrations of an exposure-based projection system.

[0061] The measurement patterning device MA’ and the sensor device 21 are shown in more detail in FIGS. 3A and 3B. FIG. 3A is a schematic view in the x-y plane of the measurement patterning device MA’, and FIG. 3B is a schematic view in the x-y plane of the sensor device 21.

[0062] The measurement patterning device MA’ includes a plurality of pattern formation regions 15a to 15c. Each of the plurality of pattern formation regions 15a to 15c may be called an object plane patterning device. In the embodiments shown in FIGS. 2 and 3A, the measurement patterning device MA’ is a transmissive patterning device MA’. The pattern formation regions 15a to 15c each include a transmissive diffraction grating. The radiation incident on the pattern formation regions 15a to 15c of the measurement patterning device MA’ is thereby at least partially scattered and received by the projection system PS when used for aberration detection and alignment of the projection system. In contrast, the radiation incident on the remaining part of the measurement patterning device MA’ is not transmitted towards the projection system PS (for example, it may be absorbed by the measurement patterning device MA’).

[0063] The illumination system IL illuminates the measurement patterning device MA’ with radiation. Although not shown in FIG. 2, the illumination system IL can receive radiation from the radiation source SO and adjust the radiation to irradiate the measurement patterning device MA’. For example, the illumination system IL can adjust the radiation to provide radiation having a desired spatial distribution and angular distribution. In the embodiment shown in FIG. 2, the illumination system IL is configured to form individual measurement beams 17a to 17c, and each measurement beam 17a to 17c irradiates a respective pattern formation region 15a to 15c of the measurement patterning device MA’. In other embodiments, the illumination system IL can be configured to irradiate all of the pattern formation regions 15a to 15c of the measurement patterning device MA’ with a single radiation beam (in such an embodiment, the plurality of measurement beams 17a to 17c are formed by the pattern formation regions 15a to 15c).

[0064] To perform the determination of the aberrations caused by the projection system PL, the mode of the illumination system IL can be changed to irradiate the measurement patterning device MA' with separate measurement beams 17a - 17c. For example, during the normal operation of a lithographic apparatus, the illumination system IL can be configured to irradiate the patterning device MA with a radiation slit. However, the mode of the illumination system IL can be changed to configure the illumination system IL to form separate measurement beams 17a - 17c to perform the determination of the aberrations caused by the projection system PL. In some embodiments, different pattern formation regions 15a - 15c may be irradiated at different times. For example, a first subset of the pattern regions 15a - 15c is illuminated at a first time to form a first subset of the measurement beams 17a - 17c, and a second subset of the pattern regions 15a - 15c is illuminated at a second time to form a second subset of the measurement beams 17a - 17c.

[0065] In other embodiments, the mode of the illumination system IL may not be changed to perform the determination of the aberrations caused by the projection system PL. For example, the illumination system IL may be configured to illuminate the measurement patterning device MA' with a slit of radiation (substantially corresponding to the illumination area used during the exposure of the substrate). Since only the pattern regions 15a - 15c transmit (and diffract) the radiation towards the projection system PS, individual measurement beams 17a - 17c may be formed by the measurement patterning device MA'.

[0066] In the figure, the orthogonal coordinate system is shown as not changing through the projection system PS. However, in some embodiments, the characteristics of the projection system PS may lead to a transformation of the coordinate system. For example, the projection system PS may form an image of the measurement patterning device MA’ that is enlarged, rotated, and / or mirrored with respect to the measurement patterning device MA’. In some embodiments, the projection system PS may rotate the image of the measurement patterning device MA’ by approximately 180° about the Z axis. In such embodiments, the relative positions of the first measurement beam 17a and the third measurement beam 17c shown in FIG. 2 may be exchanged at the sensor device 21. In other embodiments, the image may be mirrored about an axis in the x-y plane. For example, the image may be mirrored about the x axis or the y axis.

[0067] In embodiments where the projection system PS rotates the image of the measurement patterning device MA’ and / or the image is mirrored by the projection system PS, the projection system is considered to transform the coordinate system. That is, the coordinate system referred to herein is defined with respect to the image projected by the projection system PS, and the rotation and / or mirroring of the image causes a corresponding rotation and / or mirroring of the coordinate system. For ease of explanation, the coordinate system is shown in the figures as not being changed by the projection system PS. However, in some embodiments, the coordinate system may be transformed by the projection system PS.

[0068] In the embodiment of FIG. 3A, each of the plurality of pattern formation regions 15a to 15c includes a first portion 15a' to 15c' and a second portion 15a'' to 15c''. The first and second portions of the pattern regions 15a to 15c are irradiated with the measurement beams 17a to 17c at different times. For example, the first portions 15a' to 15c' of each of the pattern regions 15a to 15c are irradiated with the measurement beams 17a to 17c at a first time. At a second time, the second portions 15a'' to 15c'' of each of the pattern regions 15a to 15c are irradiated with the measurement beams 17a to 17c. As described above, in some embodiments, different pattern regions 15a to 15c are irradiated at different times. For example, the first portions of a first subset of the pattern regions 15a to 15c are irradiated at a first time, and the first portions of a second subset of the pattern regions 15a to 15c are irradiated at a second time. The second portions of the first and second subsets of the pattern formation regions may be irradiated simultaneously or at different times. In general, any schedule for irradiating different portions of the pattern formation regions 15a to 15c may be used.

[0069] The plurality of object plane patterning devices 15a to 15c shown in this embodiment include a hybrid patterning mark, as will be described below. The term "hybrid patterning mark" is a technical term. Each of the plurality of object plane patterning devices 15a to 15c includes a first portion 15a' to 15c' and a second portion 15a'' to 15c'', and the first portion 15a' to 15c' is different from the second portion 15a'' to 15c''. At least one first portion and second portion of the plurality of object plane patterning devices are transposed with respect to the first portion and second portion of other object plane patterning devices. In the embodiment of FIG. 3A, it can be seen that the object plane patterning device 15b is transposed with respect to the object plane patterning devices 15a and 15c. At least one object plane patterning device 15b having a first portion 15a' and a second portion 15b'' transposed with respect to other object plane patterning devices is known as a "hybrid" patterning mark. In other words, the first portion and the second portion of at least one hybrid patterning mark are inverted with respect to the first portion and the second portion of other object plane patterning devices (which may also be called "non-hybrid patterning marks"), and the lattice orientation of the first portion 15b' of at least one hybrid mark is different from the lattice orientation of the first portion of the non-hybrid marks 15a', 15c'. Similarly, the lattice orientation in the second portion 15b'' of at least one hybrid mark is different from the lattice orientation in the second portion 15a'', 15c'' of the non-hybrid marks.

[0070] In the embodiment of FIG. 3A, the first portion 15a' includes a diffraction grating aligned parallel to the u direction (thus having a shearing direction in the v direction), and the second portion 15a'' includes a diffraction grating aligned parallel to the v direction (thus having a shearing direction in the u direction). In this embodiment, the first and second shearing directions are perpendicular to each other. The u direction and the v direction are both aligned at 45° with respect to both the x direction and the y direction and are perpendicular to each other. It will be understood that the orientation of the grating structure is not limited to the shearing direction. Although it is desirable that the first direction and the second direction be orthogonal to each other, other relative directions can also be used. The scan direction is not parallel, but is not limited to a 45° arrangement, regardless of whether it is a continuous scan or a stepped scan with respect to the grating direction. This is merely an example.

[0071] In use, the first portions of the object plane patterning devices 15a - 15c are irradiated simultaneously, and at other times, the second portions of the object plane patterning devices 15a - 15c are irradiated simultaneously. Thus, as shown in the embodiment of FIG. 3A, in a patterning mark arrangement including hybrid marks, gratings having different directions (in this embodiment, the shearing directions) are irradiated simultaneously (when the first and second portions are irradiated respectively).

[0072] The corrected measurement beams 17a to 17c are received by the projection system PS. The projection system PS forms an image of the pattern formation regions 15a to 15c on the sensor device 21. The sensor device 21 includes a plurality of image plane sensors 25a to 25c. Each of the plurality of image plane sensors 25a to 25c includes second patterning devices 19a to 19c that can be arranged to receive radiation from a corresponding one of the plurality of object plane patterning devices 15a to 15c. Each of the second patterning devices 19a to 19c includes diffraction gratings 19a to 19c. The plurality of image plane sensors 25a to 25c further includes a radiation detector 23 arranged to receive radiation from the plurality of second patterning devices 19a to 19c. The diffraction gratings 19a to 19c are arranged such that each diffraction grating 19a to 19c receives a respective corrected measurement beam 17a to 17c output from the projection system PS. The corrected measurement beams 17a to 17c incident on the diffraction gratings 19a to 19c are further corrected by the diffraction gratings 19a to 19c. The corrected measurement beams transmitted through the diffraction gratings 19a to 19c (from the corresponding object plane patterning devices 15a to 15c) are incident on the radiation detector 23.

[0073] In the first aberration measurement configuration, the plurality of object plane patterning devices 15a to 15c and the plurality of image plane sensors 25a to 25c are arranged such that the projection system PS is configured to form an image of each first portion 15a' to 15c' of the plurality of object plane patterning devices 15a to 15c on a different one of the plurality of image plane sensors 25a to 25c on one of the patterning devices 19a to 19c. At another time point, in the second aberration measurement configuration, the plurality of object plane patterning devices 15a to 15c and the plurality of image plane sensors 25a to 25c are arranged such that the projection system PS is configured to form an image of each second portion 15a'' to 15c'' of the plurality of object plane patterning devices 15a to 15c on a different one of the plurality of image plane sensors 25a to 25c on one of the patterning devices 19a to 19c.

[0074] The radiation detector 23 is configured to detect the spatial intensity profile of the radiation incident on the radiation detector 23. The radiation detector 23 may comprise, for example, an array of individual detector elements or sensor elements. For example, the radiation detector 23 may comprise an active pixel sensor such as a CMOS (complementary metal oxide semiconductor) sensor array. Alternatively, the radiation detector 23 may comprise a CCD (charge coupled device) sensor array. The diffraction gratings 19a - 19c and the portions of the radiation sensor 23 where the modified measurement beams 17a - 17c are received form the image plane sensors 25a - 25c. Each of the image plane sensors 25a - 25c may sometimes be referred to as a detector region 25a - 25c. For example, the first diffraction grating 19a and the first portion of the radiation sensor 23 where the first measurement beam 17a is received together form the first image plane sensor (or detector region) 25a. The measurement of the specific measurement beams 17a - 17c can be performed in their respective detector regions 25a - 25c (as shown in the figure). As described above, in some embodiments, the relative positions of the modified measurement beams 17a - 17c and the coordinate system can be converted by the projection system PS.

[0075] By modifying the measurement beams 17a - 17c generated by the diffraction gratings 19a - 19c in the pattern regions 15a - 15c and the detector regions 25a - 25c, an interference pattern is formed on the radiation detector 23. The interference pattern formed from each measurement beam is related to the derivative of the phase map in the orientation direction of the grating used at the object level, for example, the shearing direction, and depends on the noise contribution due to aberrations caused by, for example, the projection system PS. Therefore, the interference pattern can be used to determine the aberrations caused by the projection system PS.

[0076] Generally, each of the diffraction gratings 19a to 19c in the detector regions 25a to 25c includes a two-dimensional transmission diffraction grating. In the embodiment shown in FIG. 3B, the detector regions 25a to 25c each include diffraction gratings 19a to 19c configured in the shape of a checkerboard. In an alternative embodiment, the detector regions 25a to 25c can each include two-dimensional transmission diffraction gratings 19a to 19c that are not configured in the shape of a checkerboard, but this may result in a more complex interference pattern and may make it more difficult to derive the aberration map. In a further alternative embodiment, the detector regions 25a to 25c are each positions on a single detector, and the diffraction gratings 19a to 19c may be positions on a single diffraction grating 19 that may be, for example, in the shape of a checkerboard.

[0077] When illuminating the first portions of the pattern regions 15a to 15c, information regarding the derivative of the relative phase map in one direction is obtained, and when illuminating the second portions of the pattern regions 15a to 15c, information regarding the derivative of the relative phase map in the other direction is obtained.

[0078] As will be further described below, in embodiments of the present disclosure, in each of two measurement configurations for determining a physical quantity, the measurement patterning device MA' and / or the sensor device 21 is scanned continuously or stepwise in two orthogonal directions. For example, the measurement patterning device MA' and / or the sensor device 21 may be scanned sequentially relative to each other in each of the x-direction and the y-direction. The x-direction and the y-direction are merely exemplary, and it should be noted that any two orthogonal directions may be used as long as each scan (measurement), which is substantially a partial scan, is mathematically orthogonal to the other and can thus be combined to create a complete data set. Also, as will be further described below, in the first aberration measurement configuration, the measurement patterning device MA' and / or the sensor device 21 is scanned in a first direction (e.g., the y-direction) to generate a first phase scan data set and at another time point is scanned in a second direction (e.g., the x-direction) to generate a second phase scan data set. Further, in the second aberration measurement configuration, the measurement patterning device MA' and / or the sensor device 21 is scanned in a first direction (e.g., the y-direction) to generate a third phase scan data set and at another time point is scanned in a second direction (e.g., the x-direction) to generate a fourth phase scan data set. Each of the first, second, third, and fourth phase scan data sets is a partial scan measurement. Alone, no useful measurement data is provided. The first, second, third, and fourth phase scan data sets are combined to determine a physical quantity that may be one or more aberrations of the projection system.

[0079] In the respective scan processes, the measurement patterning device MA' and / or the sensor device 21 can scan and acquire data separated by a distance corresponding to a part of the grating period of the diffraction grating. The measurements performed at different scan positions can be analyzed to derive information regarding the derivative of the wavefront in the scan direction. For example, the phase of the first harmonic of the measurement signal (which may be referred to as the phase scan signal) may include information regarding the derivative of the wavefront in the shearing direction of the object plane grating. Since each of the plurality of object plane patterning devices 15a to 15c includes, for example, two parts in different orientations, by irradiating each of the different shearing directions and performing a complete phase scan process (i.e., a combination of a partial measurement scan in one direction and another partial measurement scan in a second direction), information regarding the wavefront can be derived in two different directions (in particular, providing information regarding the derivative of the wavefront in each of the two shearing directions), thereby enabling the reconstruction of the complete wavefront.

[0080] It will be understood that various different arrangements of the pattern regions 15a to 15c and the detector regions 25a to 25c may be used to determine physical quantities such as aberrations caused by the projection system PS. The pattern regions 15a to 15c and / or the detector regions 25a to 25c can include a diffraction grating. In some embodiments, the pattern regions 15a to 15c and / or the detector regions 25a to 25c can include components other than the diffraction grating. For example, in some embodiments, the pattern regions 15a to 15c and / or the detector regions can include a single slit or pinhole aperture through which at least a part of the measurement beams 17a to 17c can propagate. In general, the pattern region and / or the detector region can include any arrangement useful for modifying the measurement beam.

[0081] The exemplary sensor system of FIG. 2 need not be limited to use in an exposure projection system PS, and it will further be understood that it is not limited to a shearing interferometer arrangement either. For example, the pattern regions 15a-15c and the detector regions 25a-25c, and all embodiments thereof in the present disclosure, may be used for intensity measurements using a dedicated measurement radiation source. Such a radiation source may be used, for example, to determine the alignment of a substrate. It will be understood that this arrangement is suitable for many different applications. Depending on the application of such a sensor arrangement, physical quantities such as intensity and its error contributions may also be determined.

[0082] The controller CN receives the measurement values taken by the sensor device 21 and determines the aberrations caused by the projection system PS from the measurement values. The controller may be configured to control one or more components of the measurement system 10. For example, the controller CN may control a positioning device PW operable to move the sensor device 21 and / or the measurement patterning device MA' relative to each other. The controller may control adjustment means PA for adjusting the components of the projection system PS. For example, the adjustment means PA may adjust the optical elements of the projection system PS so as to correct the aberrations caused by the projection system PS and determined by the controller CN.

[0083] In some embodiments, the controller CN may operate to control adjustment means PA for adjusting the support structure MT and / or the substrate table WT. For example, the adjustment means PA may adjust the support structure MT and / or the substrate table WT so as to correct the aberrations (determined by the controller CN) caused by the arrangement errors of the patterning device MA and / or the substrate W.

[0084] The determination of aberrations (which may be caused by the projection system PS or by misalignment of the patterning device MA or the substrate W) can include applying the measurements made by the sensor device 21 to a Zernike polynomial to obtain Zernike coefficients. Different Zernike coefficients can provide information regarding different forms of aberrations caused by the projection system PS. The Zernike coefficients can be determined independently at different positions in the x direction and / or the y direction. For example, in the embodiments shown in FIGS. 2, 3A, and 3B, the Zernike coefficients can be determined for each measurement beam 17a - 17c.

[0085] In some embodiments, the measurement patterning device MA' comprises three or more pattern formation regions, the sensor device 21 comprises three or more detector regions, and three or more measurement beams may be formed. Thereby, the Zernike coefficients can be determined at more field positions. In some embodiments, the pattern regions and the detector regions may be dispersed at different positions in both the x direction and the y direction. Thereby, the Zernike coefficients can be determined at positions separated in both the x direction and the y direction.

[0086] In the embodiments shown in FIGS. 2, 3A, and 3B, the measurement patterning device MA' includes three pattern formation regions 15a - 15c, and the sensor device 21 includes three detector regions 25a - 25c, but in other embodiments, the measurement patterning device MA' can include more or fewer than three pattern formation regions 15a - 15c and / or the sensor device 21 can include more or fewer than three detector regions 25a - 25c.

[0087] Next, a method for determining the aberrations caused by the projection system PS will be described with reference to FIG. 4.

[0088] Generally, the measurement patterning device MA' comprises at least one first pattern formation region 15a - 15c, and the sensor device 21 comprises at least one corresponding second pattern formation region 19a - 19c.

[0089] Figure 4 is a schematic diagram of a measurement system 30 that can be used to determine aberrations caused by the projection system PS. The measurement system 30 may be the same as the measurement system 10 shown in FIG. 2, but the number of the first pattern formation regions (on the measurement patterning device MA') and the second pattern formation regions (within the sensor device 21) may be different. Thus, the measurement system 30 shown in FIG. 4 can include any features of the measurement system 10 shown in FIG. 2 described above, and these features will not be further described below.

[0090] In FIG. 4, only a single first pattern formation region 31 is provided on the measurement patterning device MA', and a single second pattern formation region 32 is provided within the sensor device 21.

[0091] The measurement patterning device MA' is irradiated with radiation 33 from the illumination system IL. For ease of understanding, only one line (for example, representing one ray such as the chief ray of the incident radiation beam) is shown in FIG. 4. However, it is understood that the radiation 33 includes the range of angles at which it is incident on the first pattern formation region 31 of the measurement patterning device MA'. That is, each point on the first pattern formation region 31 of the measurement patterning device MA' can be illuminated by a cone of light. Generally, each point is illuminated in a substantially the same range of angles, which is characterized by the intensity of the radiation at the pupil plane of the illumination system IL (not shown).

[0092] The first pattern formation region 31 is arranged to receive the radiation 33 and form a plurality of first diffracted beams 34, 35, 36. The central first diffracted beam 35 corresponds to the zero-order diffracted beam of the first pattern formation region 31, and the other two first diffracted beams 34, 36 correspond to the ±1-order diffracted beams of the first pattern formation region 31. Generally, it will be seen that there are also more higher-order diffracted beams. Again, for ease of understanding, only three first diffracted beams 34, 35, 36 are shown in FIG. 4.

[0093] Also, since the incident radiation 33 constitutes a cone of radiation converging to a point on the first pattern formation region 31, it is understood that each of the first diffracted beams 34, 35, 36 also constitutes a cone of radiation diverging from that point on the first pattern formation region 31.

[0094] To generate the first diffracted beams 34, 35, 36, the first pattern formation region 31 may be in the form of a diffraction grating. For example, the first pattern formation region 31 may be in the form of the pattern region 15a shown in FIG. 3A. In particular, at least a part of the first pattern formation region 31 may be in the form of the second part 15a’’ of the pattern formation region 15a shown in FIG. 3A, that is, a diffraction grating aligned parallel to the u direction and thus having a shearing direction in the v direction (note that FIG. 4 is shown in the z-v plane). Thus, the first diffracted beams 34 to 36 are separated in the shearing direction, that is, the v direction.

[0095] The first diffracted beams 34 to 36 are at least partially captured by the projection system PS as described herein. The amount of the first diffracted beams 34 to 36 captured by the projection system PS depends on the pupil fill of the incident radiation 33 from the illumination system IL, the angular separation of the first diffracted beams 36 to 36 (which depends on the pitch of the first pattern formation region 31 and the wavelength of the radiation 33), and the numerical aperture of the projection system PS.

[0096] The measurement system 30 substantially satisfies the numerical aperture of the projection system PS, where the first diffracted beam 35 corresponding to the zero-order diffracted beam can be represented by a circular region of the pupil plane 37 of the projection system PS, and the first diffracted beams 34, 36 corresponding to the ± first-order diffracted beams can be arranged so as to significantly overlap with the first diffracted beam 35 corresponding to the zero-order diffracted beam. With such an arrangement, almost all of the first diffracted beam 35 corresponding to the zero-order diffracted beam and most of the first diffracted beams 34, 36 corresponding to the ± first-order diffracted beams are captured by the projection system PS and projected onto the sensor device 21. (Furthermore, with such an arrangement, a large number of diffracted beams generated by the first pattern region 31 are at least partially projected onto the sensor device 21).

[0097] The role of the first pattern region 31 is to introduce spatial coherence, as will be described here.

[0098] Generally, two emissions 33 from the illumination system IL incident at different incident angles on the same point of the measurement patterning device MA' are not coherent. By receiving the emissions 33 and forming a plurality of first diffracted beams 34, 35, 36, the first pattern formation region 31 is considered to form a plurality of copies of the incident emission cone 33 (generally, copies with different phases and intensities). Within any one of these copies, that is, within any one of the first diffracted beams 34, 35, 36, two emissions that originate from the same point on the measurement patterning device MA' but occur at different scattering angles are not coherent (due to the characteristics of the illumination system IL). However, for a specific emission included in any one of the first diffracted beams 34, 35, 36, there is a corresponding emission that is spatially coherent with that specific emission in each of the other first diffracted beams 34, 35, 36. For example, the chief rays of each of the first diffracted beams 34, 35, 36 (corresponding to the chief rays of the incident emissions 33) are coherent and may interfere at the amplitude level when combined.

[0099] This coherence can be utilized by the measurement system 30 to determine the aberration map of the projection system PS.

[0100] The projection system PS projects a part of the first diffracted beams 34, 35, 36 (captured by the numerical aperture of the projection system) onto the sensor device 21.

[0101] In FIG. 4, the sensor device 21 comprises a single second pattern area 32. As will be further explained below (see FIGS. 5A - 5C), the second pattern area 32 is arranged to receive these first diffracted beams 34 - 36 from the projection system PS and to form a plurality of second diffracted beams from each first diffracted beam. To achieve this, the second pattern area 32 comprises a two - dimensional transmissive diffraction grating. In FIG. 4, all the radiation transmitted by the second pattern area 32 is represented as a single arrow 38. This radiation 38 is received by the detector area 39 of the radiation detector 23 and is used to determine the aberration map.

[0102] Each of the first diffracted beams 34 - 36 incident on the pattern formation area 32 diffracts to form a plurality of second diffracted beams. Since the second pattern formation area 32 includes a two - dimensional diffraction grating, an array of two - dimensional second - order diffracted beams is generated from each incident first diffracted beam (the chief rays of these second - order diffracted beams are separated in both the shearing direction (e.g., the v - direction) and the direction perpendicular thereto (e.g., the u - direction)). Hereinafter, the diffraction order of n in the shearing direction (v - direction) and m in the non - shearing direction (u - direction) will be referred to as the (n, m) - order diffraction order of the second pattern formation area 32. Hereinafter, when it is not important what order the second diffracted beam is in the non - shearing direction (u - direction), the (n, m) - order diffraction order of the second pattern area 32 may be simply referred to as the n - th second diffracted beam.

[0103] Embodiments of the present disclosure relate to a new method for determining one or more physical quantities, such as the intensity for determining the alignment of a substrate or wafer in a lithographic apparatus or metrology system, or the aberration (such as the slope of the wavefront) of the projection system PS described herein.

[0104] As used herein, the object (e.g., reticle) plane and the image (e.g., wafer) plane, and other planes conjugate thereto may be referred to as the field plane, or simply the field. By known methods, physical quantities can be determined at a plurality of positions. For example, the aberrations of a projection system can be determined at a plurality of field points (i.e., points within the field plane of the projection system). For each position, which may be a field point, an object plane patterning device (mark) and an image sensor having two portions (each having a different orientation, e.g., may have different shearing directions) are provided. The image sensor may be a plurality of corresponding image sensors. The first portion of the object plane patterning device (having a first orientation, e.g., a first shearing direction) is illuminated, and an image of that portion is formed on the image plane grating, optionally on the corresponding portion of the image plane grating. During illumination of the first portion, the object plane grating is scanned in a first direction. The first direction is, for example, the first shearing direction. In an embodiment where the image sensor is a plurality of corresponding image sensors, and thus a plurality of image plane gratings, the image sensor may be scanned in the first direction instead of the object plane grating. In either case, the scan in the first direction during illumination generates a first set of phase scan data related to the physical quantity determined in the first direction, e.g., intensity for alignment determination, or the gradient of the aberration map. Next, the second portion of the object plane patterning device (having a second orientation which is the second shearing direction) is illuminated, and an image of that portion is formed on the image plane grating which is the corresponding image plane grating. During illumination of the second portion, at least one of the object plane grating and the image plane grating (the image plane grating being a plurality of corresponding image plane gratings) is scanned in a second direction, which may be the second shearing direction. Thereby, a second set of phase scan data related to the physical quantity in the second direction, e.g., the gradient of the aberration map, is generated. Since each of the first and second sets of phase scan data cannot yield useful information alone, they can be regarded as partial data sets. The first and second sets of phase scan data are combined to determine the physical quantity, e.g., the aberration (or relative phase) map of the projection system for that position, e.g., the field point.When the scan is performed as a continuous scan, the phase scan data can include data from a continuous scan over a set of discrete measurement points. The advantage of such a continuous scan is that the measurement time is faster. When the scan is performed as a stepwise measurement, the phase scan data is composed of phase step data over a number of points corresponding to the number of phase steps.

[0105] Embodiments of the present disclosure relate to a new method in which a physical quantity such as aberration is determined at a plurality of positions, for example, field points. Similar to known methods, for each position or field point, an object plane patterning device (mark) having two parts (each having a different orientation, for example, a different shearing direction) and an image plane sensor corresponding to each object plane patterning device may be provided. As will be described below, in this new method, the object plane patterning device (mark) includes a mixed mark in which first and second orientations (which may be first and second shearing directions) that are simultaneously exposed are mixed. This method includes performing a first measurement for each part of each mark, which may be a first continuous scan measurement, a first stepwise measurement, and / or a first shearing interferometry process using a first scan direction. Then, a second measurement is performed. The second measurement may be a second continuous scan measurement, a second stepwise measurement, and / or a second stepwise shearing interferometry process using a second scan direction. That is, each part of the object plane patterning device is used in two phase scan processes. The first and second scan directions are different from the directions of the first and second grating directions. Since each position mark has two parts and two scan measurements are performed for each, four data sets are determined. Therefore, four (rather than two) data sets are generated for each position, and each position may be a field point. These four determined data sets are combined to determine a physical quantity that may be one or more aberrations of the projection system. Thereby, the correlation intensity noise contribution can be modeled, which will be described here with reference to FIGS. 5 to 9.

[0106] As described above, in the new method, a mixed mark is used for the object plane patterning device (mark). For example, in this method, as shown in FIG. 3A and described above, the measurement patterning device MA' can be used. Another example of a suitable measurement patterning device MA' is shown in FIG. 5 and will be described herein.

[0107] The exemplary measurement patterning device MA' includes seven object plane patterning devices 51 to 57. Thereby, physical quantities such as aberrations can be determined at seven different positions (field points). In other embodiments, it will be understood that a different number of object plane patterning devices (and corresponding image plane sensors) may be provided.

[0108] Each of the plurality of object plane patterning devices 51 to 57 includes a first portion 51a to 57a and a second portion 51b to 57b. Within each object plane patterning device 51 to 57, one of the first portion 51a to 57a and the second portion 51b to 57b has a first shearing direction in the u direction, and the other has a second shearing direction in the v direction. The orientation of the object plane patterning device is not limited to the shearing directions u and v and is described as such merely for illustrative purposes. In the first object plane patterning device 51, the first portion 51a has a first shearing direction in the u direction, and the second portion 51b has a second shearing direction in the v direction. Similarly, in the second object plane patterning device 52, the second portion 52b has a first shearing direction in the u direction, and the first portion 52a has a second shearing direction in the v direction.

[0109] As will be further described below (see FIG. 6), in the new method, the first portions 51a to 57a of the object plane patterning devices 51 to 57 are irradiated simultaneously as part of a phase scan process. Similarly, in the new method, the second portions 51b to 57b of the object plane patterning devices 51 to 57 are irradiated simultaneously (but at a different time from the first portions 51a to 57a).

[0110] The second shearing direction (v) is different from the first shearing direction (u). That is, the first and second shearing directions are linearly independent. In this example, the first and second shearing directions are perpendicular to each other, but it will be understood that in other embodiments, the second shearing direction may be oriented at a different angle with respect to the first shearing direction. In other embodiments, the orientation of the lattice structure may not include any shearing direction at all, but the first orientation direction is different from the second orientation direction.

[0111] The plurality of object plane patterning devices 51-57 includes a first set of patterning devices 51, 53, 54, 55, 57 having first portions 51a, 53a, 54a, 55a, 57a with the first shearing direction (u), and a second set of patterning devices 52, 56 having first portions 52a, 56a with the second shearing direction (v).

[0112] This method further uses seven image plane sensors, each sensor corresponding to a different one of the object plane patterning devices 51-57. Each image plane sensor is generally of the type of image plane sensors 25a-25c described above with reference to FIGS. 2 and 3B. Each image plane sensor includes a second patterning device (of the type of second patterning devices 19a-19c described above with reference to FIGS. 2 and 3B) that can be arranged to receive radiation from a corresponding one of the plurality of object plane patterning devices 51-55. In an alternative embodiment, a single image plane sensor may be used.

[0113] The image plane sensor further includes a detector arranged to receive radiation from a plurality of second patterning devices (radiation sensors 23 of the type described above with reference to FIG. 2).

[0114] The patterning device of each of the plurality of image plane sensors is arranged to receive a first diffracted beam generated by a corresponding one of the plurality of object plane patterning devices 51-57 from the projection system PS and to form a plurality of second diffracted beams from each first diffracted beam.

[0115] In some embodiments, a single detector may be provided to receive radiation from one or more patterning devices of one or more image plane sensors. Alternatively, in some embodiments, a single detector may be provided for each of a plurality of image plane sensors.

[0116] Each of the plurality of object plane patterning devices 51-57 and one or more patterning devices, which may be a corresponding one of the plurality of image plane sensors, may be aligned such that at least a portion of a second diffracted beam formed from at least one first diffracted beam is spatially coherent with a second diffracted beam formed from at least one other first diffracted beam.

[0117] It is understood that the matching of the object plane patterning devices 51-57 and the second patterning device (such that at least a portion of a second diffracted beam formed from at least one first diffracted beam is spatially coherent with a second diffracted beam formed from at least one other first diffracted beam) can be achieved by matching the pitch of the object plane patterning devices 51-57 and the corresponding second patterning device. It is further understood that this matching of the pitch of the object plane patterning devices 51-57 and the second patterning device takes into account the reduction factor applied by the projection system PS. Taking this into account, generally, the pitch of the second patterning device is an integer multiple of the pitch of the object plane patterning devices 51-57, or the pitch of the object plane patterning devices 51-57 is an integer multiple of the pitch of the second patterning device.

[0118] The detector may be referred to as a radiation detector. The radiation detector may comprise a two-dimensional array of sensor elements. Each sensor element may be referred to as a pixel of the radiation detector. It will be understood that the plurality of positions on the radiation detector at which the phase of the harmonic of the vibration signal is determined may each correspond to a different sensor element or pixel of the radiation detector.

[0119] In some embodiments, the first and second portions of the object plane patterning device may each comprise a one-dimensional diffraction grating having a 50% duty cycle. In such a first patterning device, the efficiency of even diffraction orders (excluding the zero order diffraction order) is zero. Thus, only two sets of first diffracted beams that differ only in order by ±1 (and thus contribute to the first harmonic of such a vibration phase scan signal) are either the zero order beam and one of the ±1 order beams. Further, for this shape of the first pattern formation region, the scattering efficiency is symmetric and the efficiencies of the ±1 order diffracted beams are both the same.

[0120] A new method 60 for determining a physical quantity using a sensor system configured to sample a plurality of positions will be described with reference to FIG. 6. Sampling at each position uses object plane patterning devices 51-57 and an image plane sensor. In one embodiment, this method determines the aberration of the projection system PS. Method 60 can use a plurality of image plane sensors corresponding to the plurality of object plane patterning devices 51-57.

[0121] Method 60 includes four scan measurements 61, 62, 63, 64, each scan measurement being continuous or stepwise (stepped) and can include a shearing interferometry process. Although shown in a particular order in the schematic diagram of FIG. 6, it will be understood that the four measurements 61, 62, 63, 64 can be performed in any order. The four measurements 61, 62, 63, 64 will be described next.

[0122] The first measurement 61 includes arranging a plurality of object plane patterning devices 51-57 and one or more image plane sensors such that the incident radiation from the projection system PS forms images of respective first portions 51a-57a of the plurality of object plane patterning devices 51-57 at corresponding positions on the patterning devices of the one or more image plane sensors. Next, the first measurement 61 is performed. The first measurement may be a first continuous scan measurement or a first stepwise measurement. The first measurement may be a first shearing interferometry process. The first measurement 61 includes scanning at least one of the plurality of object plane patterning devices 51-57 or the corresponding plurality of image plane sensors through a plurality of positions separated in a first direction to generate a first data set S1 which may be a first phase scan data set. The first direction in S1 may be the y direction. This is merely an exemplary direction and it will be understood that any direction can be used. The first direction can include a component parallel to the orientation of the lattice of the first portion of the object plane patterning device (e.g., when the first portion of the object plane patterning device has a first shearing direction (u) and the first direction is the y direction) and a component parallel to the orientation of the lattice of the second portion of the lattice of the second portion of the object plane patterning device (e.g., when the second portion of the object plane patterning device has a second shearing direction (v) and the first direction is the y direction).

[0123] The second measurement 62 includes arranging a plurality of object plane patterning devices 51-57 and at least one image plane sensor such that the incident radiation forms an image of each of the first portions 51a-57a of the plurality of object plane patterning devices 51-57 on the patterning device of the at least one image plane sensor. This patterning device may be a different one of the plurality of image plane sensors. Next, the second measurement 62 is performed. The second measurement 62 may be a second continuous scan measurement or a second stepwise measurement. The second measurement may be a second shearing interference method process or scan at least one of the plurality of object plane patterning devices 51-57 or the corresponding plurality of image plane sensors through a plurality of positions separated in a second direction (e.g., x) to generate a second data set S2 which may be a second phase scan data set. The second direction (e.g., x) is different from the first direction (e.g., y). The second direction can include a component parallel to the orientation of the lattice of the first portion of the object plane patterning device (e.g., when the first portion of the object plane patterning device has a first shearing direction (u)) and a component parallel to the orientation of the lattice of the second portion of the object plane patterning device (e.g., when the second portion of the object plane patterning device has a second shearing direction (v)).

[0124] The third step measurement 63 includes arranging a plurality of object plane patterning devices 51-57 and at least one image plane sensor such that incident radiation forms images of respective second portions 51b-57b of the plurality of object plane patterning devices 51-57 on the patterning device of the image plane sensor. Here, the image plane sensor may be a plurality of corresponding image plane sensors. Next, the third measurement 63 may be a third continuous scan measurement or a third stepwise measurement. The third measurement may be a shearing interferometry process. The third measurement 63 includes scanning at least one of the plurality of object plane patterning devices 51-57 or the corresponding plurality of image plane sensors through a plurality of positions separated in a first direction (e.g., y) to generate a third data set S3 which may be a third phase scan data set.

[0125] The fourth measurement 64 includes arranging a plurality of object plane patterning devices 51-57 and at least one image plane sensor such that incident radiation is arranged to form images of respective second portions 51b-57b of the plurality of object plane patterning devices 51-57 on the patterning device of the image plane sensor. Next, the fourth measurement 64 is performed. The fourth measurement may be a fourth continuous scan measurement or a fourth stepwise measurement. The fourth measurement may be a shearing interferometry process. The fourth measurement 64 includes scanning at least one of the plurality of object plane patterning devices 51-57 or the corresponding plurality of image plane sensors through a plurality of positions separated in a second direction (e.g., x) to generate a fourth data set S4 which may be a fourth phase scan data set.

[0126] The new method 60 further comprises a step 65 of combining the first, second, third, and fourth data sets S1, S2, S3, S4 to determine a physical quantity, which may be, for example, one or more aberrations of the projection system PS. Alternatively, the physical quantity may be, for example, an intensity related to the arrangement of the substrate.

[0127] One of the first direction and the second direction (e.g., y, x) can be such that the sign of the component parallel to the first direction (e.g., the first shearing direction (u)) is opposite to the sign of the component parallel to the second direction (e.g., the second shearing direction (v)). The first direction (e.g., x, y) may be a direction such that the sign of the component parallel to the first shearing direction (u) in the first orientation is the same as the sign of the component parallel to the second shearing direction (v) in the second orientation. However, it will be understood that if the positions are different, the orientations will be different, and thus the shearing directions will also be different.

[0128] An example of the configuration of the first and second directions (e.g., x, y) and the first and second orientations (e.g., the shearing directions u, v) is shown in FIG. 5. The first direction (y) has a positive component parallel to the first shearing direction (u) and a positive component parallel to the second shearing direction (v). The second direction (x) has a positive component parallel to the first shearing direction (u) and a negative component parallel to the second shearing direction (v). In the example shown in FIG. 5, the first shearing direction (u) and the second shearing direction (v) are orthogonal to each other, the first direction (y) and the second direction (x) are orthogonal to each other, and the first direction (y) and the second direction (x) are each aligned at 45° with respect to the first shearing direction (u) and the second shearing direction (v), respectively. It will be understood that the orientation of the lattice is not limited to the shearing directions (u, v), and the first and second step directions are not limited to the x and y directions.

[0129] The method 60 schematically shown in FIG. 6 is advantageous because the determined physical quantity (such as one or more aberrations of the projection system PS or the intensity related to the alignment measurement) is less affected by the noise contribution as described herein.

[0130] Each of the first, second, third, and fourth data sets S1, S2, S3, and S4 is generated using radiation B, and it is understood that the radiation may be affected by intensity noise (i.e., the intensity of radiation B changes or varies over time). Since the data generated within any one of the first, second, third, and fourth data sets S1, S2, S3, and S4 is formed by the same radiation, for example, the same pulse of radiation, there is a correlation in intensity noise errors within any one of the first, second, third, and fourth data sets S1, S2, S3, and S4.

[0131] If each of the first and second directions (e.g., y, x) includes a component parallel to the first direction (e.g., the shearing direction u) and a component parallel to the second direction (e.g., the shearing direction v), then a scan in either the first or second direction results in a scan substantially in both the first and second directions (e.g., u, v) simultaneously. Thus, the plurality of object plane patterning devices 51-57 consists of a first set of patterning devices 51, 53, 54, 55, 57 and a second set of patterning devices 52, 56. However, during the generation of any one of the four data sets S1, S2, S3, and S4, if a scan is made in either the first or second direction (e.g., y, x), it is scanned in the orientation direction of all parts of the object plane patterning devices 51-57 that are being exposed at any given time, and thus, phase scan data will be recorded by the detector 23.

[0132] FIG. 7 is a set showing an example of phase scan measurement (which can represent data recorded in any of four phase scan processes 61, 62, 63, 64). Shown in FIG. 7 are single phase scan curves for each of four object plane patterning devices 51-57. Each of the seven curves shown in FIG. 7 can represent a single pixel from a part of a detector corresponding to a different one of the image plane sensors (which may be related to a single position in the pupil plane where there is radiation from, for example, projection system PS). Using the phases of the curves of corresponding multiple pixels on one or more image plane sensors, a map can be generated that represents the gradient of an aberration (relative phase) map in the shearing direction of the currently illuminated object plane grating.

[0133] Each of the seven curves shown in FIG. 7 is composed of five data points to which a sine curve is fitted. It will be understood that the five data points corresponding to the five phase steps are merely examples. The number of phase steps to which sine or cosine is fitted and the resulting number of data points can be any number of three or more. The intensity changes that occur during the generation of the seven curves shown in FIG. 7 (and other pixels corresponding to other positions in the pupil plane, for example) generally affect the positions of the data points within the seven curves. This then affects the fitted sine curve, and thus the phase extracted from the fitted sine curve (which is related to the difference in relative phase of, for example, two points from different positions in the pupil plane separated in the shearing direction). For example, as indicated by the arrow, if the intensity of the radiation varies upward during the capture of the second data point, all the second data points move upward. This then affects the sine curve fitted to the data, and thus also affects the phase extracted from the fitted sine curve. Note that such intensity changes affect all seven curves, that is, the intensity fluctuations from all seven curves are all correlated.

[0134] Phase scan data is typically related to the differentiation of the aberration (relative wavefront) map in the direction of the shearing direction (u or v) of a portion of the object plane patterning device (i.e., the first portion 51a - 57a or the second portion 51b - 57b) illuminated by radiation. Thus, the intensity noise errors in the data from data sets S1, S2, S3, S4 typically introduce errors in the differentiation of the wavefront map in the direction of the shearing direction of the portion of the object plane patterning device illuminated by radiation.

[0135] Since the first portions of the first set of patterning devices 51, 53, 54, 55, 57 have a first shearing direction (u) and the first portions of the second set of patterning devices 52, 56 have a second shearing direction (v), when the first portions of the first set of patterning devices 51, 53, 54, 55, 57 are being irradiated, the first set of patterning devices has an error (due to intensity noise) in the differentiation of the wavefront map in the direction of the first shearing direction (u), and the second set of patterning devices 52, 56 has a correlation error in the differentiation of the wavefront map in the direction of the second shearing direction (v).

[0136] Differentiation errors in the wavefront map in the direction of the first or second shearing direction (u, v) lead to differentiation errors in the wavefront map in both of the first and second directions (x, y). The signs of the differentiation errors in the wavefront map in the first and second directions (x, y) depend on both the sign of the differentiation error in the wavefront map in the direction of the first or second shearing direction (u, v) and the signs of the components of the first and second directions (x, y) parallel to the first and second shearing directions (u, v). This will be described later with reference to FIGS. 8A - 8D.

[0137] One of the first and second directions (y, x) is such that the sign of the component parallel to the first shearing direction (u) is opposite to the sign of the component parallel to the second shearing direction (v), and the other of the first and second directions (y, x) is such that the sign of the component parallel to the first shearing direction (u) is the same as the sign of the component parallel to the second shearing direction (v). Therefore, when scanning one direction (y, x), it is guaranteed that the sign of the error in the differentiation of the wavefront map in the other direction (y, x) is different in each of the first and second sets. In other words, the correlated intensity error will have a higher-order fingerprint. As a result, such intensity errors can be modeled. This will be described with reference to FIGS. 8A to 8DS.

[0138] FIG. 8A shows the intensity error of each of seven field points due to intensity fluctuations (solid line arrows) in the first measurement (in this case, the first shearing interferometry process 61), and the components (dotted line arrows) of this intensity error in each of two directions.

[0139] FIG. 8B shows the intensity error of each of seven field points due to intensity fluctuations (solid line arrows) in the second measurement (in this case, the second shearing interferometry process 62), and the components (dotted line arrows) of this intensity error in each of two directions.

[0140] FIG. 8C shows the intensity error of each of seven field points due to intensity fluctuations (solid line arrows) in the third measurement (in this case, the third shearing interferometry process 63), and the components (dotted line arrows) of this intensity error in each of two directions.

[0141] FIG. 8D shows the intensity error of each of seven field points due to intensity fluctuations (solid line arrows) in the fourth measurement (in this case, the fourth shearing interferometry process 64), and the components (dotted line arrows) of this intensity error in each of two directions.

[0142] Each Zernike coefficient can be obtained from data acquired in two directions that are simultaneously fitted. During the first shearing interference process 61, the phase scan direction is the positive y direction. Since the positive y direction has components in the positive u direction and the positive v direction, this corresponds to scans in the positive u direction and the positive v direction. Thus, as shown in FIG. 8A, the intensity errors of the first set of patterning devices 51, 53, 54, 55, 57 are in the positive u direction (recall that in the shearing interference process 61, the first part of the object plane patterning devices 51 - 57 is illuminated). Similarly, the intensity errors are in the positive v direction of the second set of patterning devices 52, 56. As also shown in FIG. 8A, the positive u direction has components in the positive y direction and the positive x direction, and the positive v direction has components in the positive y direction and the negative x direction. Thus, due to the intensity errors or variations during the first shearing interference process 61, an error occurs in the y - direction gradient (or slope) of the reconstructed wavefront map (which is the third - order Zernike coefficient Z3). This error has the same sign for all object plane patterning devices 51 - 57 (i.e., a positive y - direction offset occurs). Further, due to the intensity errors or variations during the first shearing interference process 61, an error occurs in the x - direction gradient (or slope) of the reconstructed wavefront map (which is the second - order Zernike coefficient Z2). This error has one sign for the first set of patterning devices 51, 53, 54, 55, 57 and the opposite sign for the second set of patterning devices 52, 56.

[0143] In the second shearing interferometry process 62, the phase scan direction is the positive x direction. Since the positive x direction has components in the positive u direction and the negative v direction, this corresponds to scans in the positive u direction and the negative v direction. Thus, as shown in FIG. 8B, the intensity errors of the first set of patterning devices 51, 53, 54, 55, 57 are in the positive u direction (recall that in the shearing interferometry process 61, the first portion of the object plane patterning devices 51 - 57 is illuminated). Similarly, the intensity errors are in the negative v direction for the second set of patterning devices 52, 56. As also shown in FIG. 8B, the positive u direction has components in the positive y direction and the positive x direction, and the negative v direction has components in the negative y direction and the positive x direction. Thus, the intensity errors or fluctuations during the second shearing interferometry process 62 result in an error in the x - direction gradient (or slope) of the reconstructed wavefront map (which is the second - order Zernike coefficient Z2), and this has the same sign for all the object plane patterning devices 51 - 57 (i.e., it is an offset in the positive x direction). Further, the intensity errors or fluctuations during the first shearing interference process 61 result in an error in the y - direction gradient (or slope) of the reconstructed wavefront map (which is the third - order Zernike coefficient Z3). This error has one sign for the first set of patterning devices 51, 53, 54, 55, 57 and the opposite sign for the second set of patterning devices 52, 56.

[0144] During the third shearing interference process 63, the phase scan direction is the positive y direction. Since the positive y direction has components in the positive u direction and the positive v direction, this is equivalent to scans in the positive u direction and the positive v direction. Thus, as shown in FIG. 8C, the intensity error is in the positive v direction of the first set of patterning devices 51, 53, 54, 55, 57 (recall that in the shearing interference process 61, the second part of the object plane patterning devices 51 - 57 is illuminated). Similarly, the intensity error is in the positive u direction of the second set of patterning devices 52, 56. As shown in FIG. 8C, the positive u direction has components in the positive y direction and the positive x direction, and the positive v direction has components in the positive y direction and the negative x direction. Thus, the intensity error or variation during the third shearing interference process 63 results in an error in the y - direction gradient (or slope) of the reconstructed wavefront map (which is the third - order Zernike coefficient Z3). This error has the same sign for all object plane patterning devices 51 - 57 (i.e., this is an offset in the positive y direction). Further, the intensity error or variation during the third shearing interference process 63 results in an error in the x - direction gradient (or slope) of the reconstructed wavefront map (which is the second - order Zernike coefficient Z2), which has one sign for the first set of patterning devices 51, 53, 54, 55, 57 and the opposite sign for the second set of patterning devices 52, 56.

[0145] During the fourth shearing interference process 64, the phase scan direction is the positive x direction. Since the positive x direction has components in the positive u direction and the negative v direction, this corresponds to scans in the positive u direction and the negative v direction. Thus, as shown in FIG. 8D, the intensity error is in the negative v direction for the first set of patterning devices 51, 53, 54, 55, 57 (recall that in the shearing interference process 61, the first part of the object plane patterning devices 51 - 57 is illuminated). Similarly, the intensity error is in the positive u direction for the second set of patterning devices 52, 56.

[0146] As also shown in FIG. 8D, in the positive u direction, there are components in the positive y direction and the positive x direction, and in the negative v direction, there are components in the negative y direction and the positive x direction. Therefore, due to the intensity error or variation during the second shearing interference method process 62, an error occurs in the x-direction gradient (or inclination) of the reconstructed wavefront map (which is the second-order Zernike coefficient Z2). This error has the same sign for all object plane patterning devices 51-57 (i.e., a positive x-direction offset occurs). Furthermore, due to the intensity error or variation during the first shearing interference method process 61, an error occurs in the y-direction gradient (or inclination) of the reconstructed wavefront map (which is the third-order Zernike coefficient Z3). This error has one sign for the first set of patterning devices 51, 53, 54, 55, 57 and the opposite sign for the second set of patterning devices 52, 56.

[0147] The inventor recognized that when the intensity noise error is just an offset, it is impossible to determine and correct this error without independently measuring the offset. In contrast, when the intensity error has a higher-order fingerprint (i.e., when the errors of some field points have the opposite sign to the errors of other field points), these (correlated) intensity errors can be removed by modeling.

[0148] Here, referring to FIG. 9, a method for removing the correlated intensity error by modeling in step 65 of determining a physical quantity (which may be one or more aberrations of the projection system PS) by combining the first, second, third, and fourth data sets S1, S2, S3, S4 will be described.

[0149] In the example shown in FIG. 9, step 65 includes the following steps.

[0150] In one step 70, the first dataset S1 and the third dataset S3 are combined. In particular, the first dataset S1 and the third dataset S3 are combined to determine at least one Zernike coefficient for each of the seven sets of object plane patterning devices 51-57 and the image plane sensor (i.e., for each of the seven field points). For example, by combining the first dataset S1 and the third dataset S3, for each of the seven sets of object plane patterning devices 51-57 and the image plane sensor (i.e., for each of the seven field points), the first wavefront tilt coefficient Z3 in the first direction (y) (1) , and the first wavefront tilt coefficient Z2 in the second direction (x) (1) can be determined. This involves, for example, reconstructing the first wavefront map W (1) (x, y) for each of the object plane patterning devices 51-57 and the image plane sensor from the first phase scan dataset S1 and the third phase scan dataset S3 (see Equation (1)).

[0151] In another step 71, the second dataset S2 and the fourth dataset S4 are combined. In particular, the second dataset S2 and the fourth dataset S4 are combined to determine at least one Zernike coefficient for each of the seven sets of object plane patterning devices 51-57 and the image plane sensor (i.e., for each of the exemplary seven field points). For example, the second dataset S2 and the fourth dataset S4 are combined to determine, for each of the seven sets of object plane patterning devices 51-57 and the image plane sensor (i.e., for each of the seven field points), the second wavefront tilt coefficient Z3 in the first direction (y) (2) , and the first wavefront tilt coefficient Z2 in the second direction (x) (2) are combined to be determined. This involves, for example, reconstructing the second wavefront map W (2) (x, y) from the second phase step dataset S2 and the fourth phase scan dataset S4 for each of the seven sets of object plane patterning devices 51-57 and the image plane sensor (see Equation (1)).

[0152] Following steps 70 and 71, for each set of object plane patterning devices 51-57 and the image plane sensor, or field points, there are two values for each Zernike coefficient. This redundancy is used to model and remove intensity noise errors and to generate one corrected value for each Zernike coefficient of each field point, as will be described next.

[0153] Following steps 70 and 71, if there are n sets of object plane patterning devices 51-57 and the image plane sensor, or field points (for example, n = 7), for each Zernike coefficient, this method generates an array of two numbers, each array having n entries. For example, if both tilt Zernike coefficients are generated, there are four arrays of n entries: the first wavefront tilt coefficient Z3 in the first direction (y) (1) (n), the second wavefront tilt coefficient Z3 in the first direction (y) (2) (n), the first wavefront tilt coefficient Z2 in the second direction (x) (1) (n), and the second wavefront tilt coefficient Z2 in the second direction (x) (2) (n). The intensity noise errors within each array are correlated.

[0154] In the next step 72, for each Zernike coefficient, the two arrays of n entries are combined to generate a single array of n (corrected) entries. For example, the first wavefront tilt coefficient Z3 in the first direction (for example y) (1) (n) is combined with the second wavefront tilt coefficient Z3 in the second direction (for example x) (2) (n) to generate a corrected wavefront tilt coefficient Z3 (c) (n). In particular, this combination is done using the correlation of the intensity noise contributions of each array and corrects at least in part the errors caused by the intensity variations of the radiation used to generate the first data set S1 and the third data set S3.

[0155] Similarly, the first wavefront tilt coefficient Z2 in the second direction (for example x) (1) (n) and the second wavefront tilt coefficient Z2 in the first direction (for example y) (2)(n) are combined to obtain a corrected wavefront tilt coefficient Z2 (c) (n) is generated. In particular, this combination is performed using the correlation of the intensity noise contributions in each array, and at least partially corrects the error caused by the intensity fluctuations of the radiation used to generate the second data set S2 and the fourth data set S4

[0156] In particular, the combination performed in step 72 can be carried out as follows

[0157] For example, combining the first wavefront tilt coefficient Z3 (1) (n) in the first direction (e.g., y) and the second wavefront tilt coefficient Z3 (2) (n) in the second direction (e.g., x) to obtain a corrected wavefront tilt coefficient Z3 (c) (n) may include performing a least squares approximation to simultaneously minimize the following [Number] and [Number] Here, c1 and c2 are two constants (fitting parameters), I(i) is an identity array where I(i) = 1 for all i, V(i) is an array with entries of +1 or -1, and V(i) = 1 for entries corresponding to the first set of object plane patterning devices 51, 53, 54, 55, 57, and V(i) = -1 for entries corresponding to the second set of object plane patterning devices 52, 56. Thus, in the example of the arrangement of the object plane patterning devices 51 - 57 shown in FIG. 5, V=(1, -1, 1, 1, 1, -1, 1). That is, the array V(i) models the intensity error with a higher - order fingerprint (obtained from data using the x - direction in this case).

[0158] Similarly, the first wavefront tilt coefficient Z2 (1) (n) in the second direction (e.g., x) and the second wavefront tilt coefficient Z2 in the first direction (e.g., y)(2) Combine (n) to obtain the modified wavefront tilt coefficient Z2 (c) Generating (n) may include performing a least squares approximation to simultaneously minimize the following. [Number] And [Number] Here, c3 and c4 are two constants (fitting parameters). The array V(i) models the intensity error with a higher-order fingerprint (obtained from data using the y-direction in this case).

[0159] Some embodiments of the present disclosure relate to a computer-readable medium recording a computer program including computer-readable instructions configured to cause a computer to execute the method 60 described above with reference to FIGS. 5 to 9.

[0160] Some embodiments of the present disclosure relate to a computer device including a memory storing processor-readable instructions and a processor configured to read and execute the instructions stored in the memory, wherein the processor-readable instructions include instructions configured to control a computer to execute the method 60 described above with reference to FIGS. 5 to 9.

[0161] Some embodiments of the present disclosure relate to a measurement system for determining a physical quantity, the measurement system comprising a controller configured to execute the method 60 described above with reference to FIGS. 5 to 9. The apparatus may comprise or form part of a lithographic apparatus LA. Alternatively, the apparatus may comprise or form part of a metrology tool.

[0162] Although the first harmonic of the phase scan signal is used in the above embodiments, it will be understood that in alternative embodiments, harmonics of the phase scan signal may be used instead.

[0163] In the above-described embodiment, the first pattern region 31 including the one-dimensional diffraction grating 31 with a 50% duty cycle is used. However, it will be understood that in alternative embodiments, the first pattern region 31 may use a different shape. For example, in some embodiments, the first pattern region 31 may include a two-dimensional checkerboard diffraction grating with a 50% duty cycle.

[0164] Although specific reference may be made in this specification to the use of a lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described in this specification may have other applications. Other possible applications include the manufacture of guidance and detection patterns for integrated optical systems, magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, and the like.

[0165] Although embodiments of the present invention may be specifically referred to in this specification in the context of a lithographic apparatus, embodiments of the present invention can be used in other apparatuses. Embodiments of the present invention can form part of an apparatus for measuring or processing an object such as a mask inspection apparatus, a metrology apparatus, or a wafer (or other substrate) or a mask (or other patterning device). These apparatuses are sometimes generally referred to as lithographic tools. Such lithographic tools can use vacuum conditions or ambient (non-vacuum) conditions.

[0166] Whenever circumstances permit, embodiments of the present invention can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention can also be implemented as instructions stored on a machine-readable medium, which instructions are read and executed by one or more processors. A machine-readable medium includes any mechanism for storing or transmitting information in a form readable by a machine (such as a computing device). For example, a machine-readable medium includes read-only memory (ROM), random access memory (RAM), magnetic storage media, optical storage media, flash memory devices, electrical, optical, acoustic, or other forms of propagated signals (such as carrier waves, infrared signals, digital signals, etc.). Further, firmware, software, routines, instructions can be described herein as performing certain actions. However, such descriptions are for convenience only, and such actions are actually performed by a computing device, processor, controller, or other device that executes firmware, software, routines, instructions, etc. By doing so, actuators and other devices can interact with the physical world. While particular embodiments of the present invention have been described above, it will be understood that the present invention may be practiced otherwise than as described. The above description is intended by way of illustration and not limitation. Thus, it will be apparent to those skilled in the art that changes may be made to the described invention without departing from the scope of the claims set forth below. Other aspects of the present invention are set forth in the numbered paragraphs below. 1. A method for determining a physical quantity, the method using a sensor system configured to sample a plurality of positions, wherein the sampling at each position uses an object plane patterning device and an image plane sensor, Each of the object plane patterning devices includes a first part and a second part, the first part being different from the second part, and the first part and the second part of at least one of the object plane patterning devices being transposed with respect to the first part and the second part of the other object plane patterning devices. The method is using the first part of each of the object plane patterning devices to perform a first measurement in a first direction to generate a first data set; using the second part of each of the object plane patterning devices to perform a second measurement in the first direction to generate a second data set; using the first part of each of the object plane patterning devices to perform a third measurement in a second direction to generate a third data set, the second direction being different from the first direction; using the second part of each of the object plane patterning devices to perform a fourth measurement in the second direction to generate a fourth data set; combining the first, second, third, and fourth data sets to determine a physical quantity. A method comprising 2. The method according to item 1, wherein radiation having a common noise source is incident on each of the object plane patterning devices and the image plane sensor to generate the first, second, third, and / or fourth data sets. 3. The method according to any of the preceding items, wherein the object plane patterning device includes a grating. 4. The method according to any of the preceding items, wherein the orientation of the first part of the object plane patterning device is orthogonal to the orientation of the second part. 5. The method according to any of the preceding items, wherein the first orientation of at least one of the object plane patterning devices is orthogonal to the second orientation of the other object plane patterning devices. 6. The method according to any of the preceding items, wherein the first, second, third, and fourth measurements form part of a shearing interferometry process. 7. The method according to any one of the preceding paragraphs, wherein the first part has a first shearing direction, the second part has a second shearing direction, and the second shearing direction is different from the first shearing direction. 8. The method according to paragraph 7, wherein the first direction includes a component parallel to the first shearing direction and a component parallel to the second shearing direction, and the second direction includes a component parallel to the first shearing direction and a component parallel to the second shearing direction. 9. The method according to paragraph 8, wherein for one of the first direction and the second direction, the sign of the component parallel to the first shearing direction is opposite to the sign of the component parallel to the second shearing direction, and for the other of the first direction and the second direction, the sign of the component parallel to the first shearing direction is the same as the sign of the component parallel to the second shearing direction. 10. The method according to any one of the preceding paragraphs, wherein the image sensor includes a plurality of image sensors. 11. The method according to any one of the preceding paragraphs, wherein the image plane sensor includes a second patterning device that can be arranged to receive radiation from a plurality of the object plane patterning devices, and a detector arranged to receive radiation from the second patterning device. 12. The method according to paragraph 10, wherein each of the plurality of image plane sensors includes a second patterning device that can be arranged to receive radiation from a corresponding one of the plurality of object plane patterning devices, and the plurality of image plane sensors includes a detector arranged to receive radiation from the plurality of second patterning devices. 13. Combining the first, second, third, and fourth data sets to determine a physical quantity includes combining the first data set and the second data set to determine at least one first physical parameter for each sampling position, combining the third data set and the fourth data set to determine at least one second physical parameter for each sampling position, Combining the determined first physical parameter for each sampling position and the determined second physical parameter for each sampling position to form an output corrected physical parameter for each sampling position, and at least partially correcting errors in the determined first and second physical parameters caused by the intensity change of the radiation used to generate the first, second, third, and / or fourth data sets. The method according to any one of the preceding items. 14. The method according to any one of the preceding items, wherein the physical quantity includes one or more aberrations of the projection system. 15. The physical quantity includes one or more aberrations of the projection system, The method according to item 13, wherein the first, second, third, and fourth physical parameters respectively correspond to first, second, third, and fourth aberration coefficients. 16. Determining one or more aberrations by combining the first data set and the second data set further includes determining a first wavefront tilt coefficient in the first direction, Determining one or more aberrations by combining the second data set and the fourth data set further includes determining a second wavefront tilt coefficient in the first direction, Combining the determined first wavefront tilt coefficient in the first direction for each sampling position and the determined second wavefront tilt coefficient in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position, and at least partially correcting errors in the determined first wavefront tilt coefficient in the first direction and the determined second wavefront tilt coefficient in the first direction caused by the intensity variation of the radiation used to generate the first data set and the second data set. The method according to item 15. 17. Combining the determined first wavefront tilt coefficient in the first direction for each sampling position and the determined second wavefront tilt coefficient in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position is Performing a least squares approximation to For each sampling position, the root mean square of the difference between (a) the determined first wavefront tilt coefficient in the first direction and (b) the value obtained by adding a first constant to the output wavefront tilt coefficient in the first direction, and For each sampling position, the root mean square of the difference between (a) the determined second wavefront tilt coefficient in the first direction and (b) the value obtained by adding a second constant, which is multiplied by +1 for the first part of the grating of the object plane patterning device and multiplied by -1 for the second part of the grating of the object plane patterning device, to the output wavefront tilt coefficient in the first direction, The method according to claim 16, comprising simultaneously minimizing the above. 18. The method according to any one of claims 1 to 13, wherein the physical quantity includes intensity. 19. The method according to any one of claims 1 to 13, wherein the physical quantity includes one or more intensities of the measured radiation, and the first, second, third, and fourth physical parameters respectively correspond to the first, second, third, and fourth intensity values. 20. Determining the physical quantity by combining the first, second, third, and fourth data sets comprises combining the first data set and the second data set to determine the first wavefront tilt coefficient in the second direction for each sampling position; combining the third data set and the fourth data set to determine the second wavefront tilt coefficient in the second direction for each sampling position; combining the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction for each sampling position to form the output wavefront tilt coefficient in the second direction for each sampling position, and at least partially correcting the errors of the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction caused by the intensity fluctuations of the radiation used to generate the second data set and the fourth data set; The method according to any one of the preceding claims, comprising the above. 21. Combining the first wavefront tilt coefficient in the second direction determined for each sampling position and the second wavefront tilt coefficient in the second direction determined for each sampling position to form an output wavefront tilt coefficient in the second direction for each sampling position is to perform a least squares approximation, for a plurality of sampling positions, the root mean square of the square of the difference between (a) the determined first wavefront tilt coefficient in the second direction and (b) a value obtained by adding a third constant to the output wavefront tilt coefficient in the second direction, and for a plurality of sampling positions, the root mean square of the square of the difference between (a) the determined second wavefront tilt coefficient in the second direction and (b) a value obtained by adding a fourth constant, which is multiplied by +1 for the first part of the grating of the object plane patterning device and -1 for the second part of the grating of the object plane patterning device, to the output wavefront tilt coefficient in the second direction, The method according to claim 20, comprising simultaneously minimizing. 22. The method according to any one of the preceding items, wherein the first direction and the second direction are each aligned at 45° with respect to the first shearing direction and the second shearing direction, respectively. 23. Each measurement is irradiating the plurality of object plane patterning devices with a first radiation, forming an image of each of the plurality of object plane patterning devices on a different one of the plurality of image plane sensors, scanning at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors through a plurality of positions spaced apart in a direction to generate a vibration phase scan signal for each of the plurality of sampling positions, determining the phase of the harmonics of the vibration signal at a plurality of positions on the radiation detector, The method according to any one of the preceding items, comprising. 24. The harmonic of the vibration signal equal to the difference between the aberration maps between a pair of positions in the pupil plane of the projection system at each of the plurality of positions on the radiation detector is the first harmonic. The method according to claim 23. 25. The method according to claim 24, wherein a pair of positions in the pupil plane of the projection system are separated in the shearing direction by a shearing distance corresponding to twice the distance in the pupil plane between two adjacent first-order diffracted beams. 26. A computer-readable medium having recorded thereon a computer program including computer-readable instructions configured to cause a computer to execute the method according to any one of claims 1 to 25. 27. A memory storing processor-readable instructions, a processor configured to read and execute the instructions stored in the memory, the processor-readable instructions including instructions configured to control a computer to execute the method according to any one of claims 1 to 25, a computer device. 28. A measurement system for determining a physical quantity, a plurality of object plane patterning devices including a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation different from the first orientation, an illumination system arranged to irradiate the plurality of object plane patterning devices with radiation to form a plurality of first-order diffracted beams, wherein the first-order diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of the grating, and the first-order diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating, an illumination system, an image plane sensor including a patterning device and a radiation detector, an illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second-order diffracted beams from each of the first-order diffracted beams, a positioning device configured to move the plurality of object plane patterning devices in a first direction or a second direction, a controller configured to execute the method according to any one of claims 1 to 25, a measurement system comprising. A measurement system for determining a physical quantity, comprising a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation, the second orientation being different from the first orientation, a plurality of object plane patterning devices, An illumination system arranged to irradiate a plurality of object plane patterning devices with radiation to form a plurality of first diffracted beams, wherein the first diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of a grating, and the first diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating, an illumination system, A plurality of image plane sensors, each comprising a patterning device and each communicating with a radiation detector, An illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second diffracted beams from each of the first diffracted beams, A positioning device configured to move at least one of the plurality of object plane patterning devices or corresponding plurality of image plane sensors in a first direction or a second direction, A controller configured to execute the method according to any one of claims 1 to 25, A measurement system comprising the same. 30. A lithography apparatus comprising the measurement system according to claim 28 or 29. 31. A metrology tool comprising the measurement system according to claim 28 or 29.

Claims

1. A method for determining a physical quantity, the method using a sensor system configured to sample a plurality of positions, wherein the sampling at each position uses an object plane patterning device and an image plane sensor, each of said object plane patterning devices includes a first part and a second part, said first part being different from said second part, and said first part and said second part of at least one of said object plane patterning devices being transposed with respect to said first part and said second part of other said object plane patterning devices, the method comprising: using said first part of each of said object plane patterning devices to perform a first measurement in a first direction to generate a first data set; using said second part of each of said object plane patterning devices to perform a second measurement in said first direction to generate a second data set; using said first part of each of said object plane patterning devices to perform a third measurement in a second direction to generate a third data set, said second direction being different from said first direction; using said second part of each of said object plane patterning devices to perform a fourth measurement in said second direction to generate a fourth data set; combining said first, second, third and fourth data sets to determine a physical quantity.

2. The method according to claim 1, wherein radiation having a common noise source is incident on each of said object plane patterning devices and said image plane sensor to generate said first, second, third and / or fourth data sets.

3. The method according to claim 1 or 2, wherein said object plane patterning device includes a grating.

4. The method according to any one of claims 1 to 3, wherein the orientation of said first part of said object plane patterning device is orthogonal to the orientation of said second part.

5. The method according to any one of claims 1 to 4, wherein the first orientation of at least one of said object plane patterning devices is orthogonal to the second orientation of other said object plane patterning devices.

6. The method according to any one of claims 1 to 5, wherein the first, second, third and fourth measurements form part of a shearing interferometry process.

7. The method according to any one of claims 1 to 6, wherein the first part has a first shearing direction, the second part has a second shearing direction, and the second shearing direction is different from the first shearing direction.

8. The first direction includes a component parallel to the first shearing direction and a component parallel to the second shearing direction, The method according to claim 7, wherein the second direction includes a component parallel to the first shearing direction and a component parallel to the second shearing direction.

9. For one of the first direction and the second direction, the sign of the component parallel to the first shearing direction is opposite to the sign of the component parallel to the second shearing direction, and for the other of the first direction and the second direction, the sign of the component parallel to the first shearing direction is the same as the sign of the component parallel to the second shearing direction. The method according to claim 8.

10. The method according to any one of claims 1 to 9, wherein the image sensor includes a plurality of image sensors.

11. The image plane sensor includes a second patterning device that can be arranged to receive radiation from a plurality of the object plane patterning devices, A detector arranged to receive radiation from the second patterning device. The method according to any one of claims 1 to 10.

12. Each of the plurality of image plane sensors includes a second patterning device that can be arranged to receive radiation from a corresponding one of the plurality of object plane patterning devices, The plurality of image plane sensors includes a detector arranged to receive radiation from the plurality of second patterning devices. The method according to claim 10.

13. Combining the first, second, third, and fourth data sets to determine a physical quantity includes Combining the first data set and the second data set to determine at least one first physical parameter for each sampling position, Combining the third data set and the fourth data set to determine at least one second physical parameter for each sampling position, Combining the determined first physical parameter for each sampling position and the determined second physical parameter for each sampling position to form an output corrected physical parameter for each sampling position, and at least partially correcting errors in the determined first and second physical parameters caused by the intensity change of the radiation used to generate the first, second, third, and / or fourth data sets, the method according to any one of claims 1 to 12.

14. The method according to any one of claims 1 to 13, wherein the physical quantity includes one or more aberrations of the projection system.

15. The physical quantity includes one or more aberrations of the projection system, The method according to claim 13, wherein the first, second, third, and fourth physical parameters respectively correspond to first, second, third, and fourth aberration coefficients.

16. Determining one or more aberrations by combining the first data set and the second data set further includes determining a first wavefront tilt coefficient in the first direction, Determining one or more aberrations by combining the second data set and the fourth data set further includes determining a second wavefront tilt coefficient in the first direction, Combining the determined first wavefront tilt coefficient in the first direction for each sampling position and the determined second wavefront tilt coefficient in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position, and at least partially correcting errors in the determined first wavefront tilt coefficient in the first direction and the determined second wavefront tilt coefficient in the first direction caused by the intensity variation of the radiation used to generate the first data set and the second data set, the method according to claim 15.

17. Combining the determined first wavefront tilt coefficient in the first direction for each sampling position and the determined second wavefront tilt coefficient in the first direction for each sampling position to form an output wavefront tilt coefficient in the first direction for each sampling position includes Performing a least squares approximation, For each sampling position, the root mean square of the square of the difference between (a) the determined first wavefront tilt coefficient in the first direction and (b) the value obtained by adding a first constant to the output wavefront tilt coefficient in the first direction, and For each sampling position, the root mean square of the difference between (a) the determined second wavefront tilt coefficient in the first direction and (b) a value obtained by adding a second constant, which is obtained by multiplying +1 for the first portion of the grating of the object plane patterning device and -1 for the second portion of the grating of the object plane patterning device, to the output wavefront tilt coefficient in the first direction. The method according to claim 16, comprising simultaneously minimizing the above. **Claim 18** The method according to any one of claims 1 to 13, wherein the physical quantity includes intensity. **Claim 19** The method according to any one of claims 1 to 13, wherein the physical quantity includes one or more intensities of the measured radiation, and the first, second, third, and fourth physical parameters respectively correspond to the first, second, third, and fourth intensity values. **Claim 20** Determining the physical quantity by combining the first, second, third, and fourth data sets includes: Combining the first data set and the second data set to determine, for each sampling position, a first wavefront tilt coefficient in the second direction; Combining the third data set and the fourth data set to determine, for each sampling position, a second wavefront tilt coefficient in the second direction; Combining the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction for each sampling position to form an output wavefront tilt coefficient in the second direction for each sampling position, and at least partially correcting errors of the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction caused by intensity fluctuations of the radiation used to generate the second data set and the fourth data set; The method according to any one of claims 1 to 19, including the above. **Claim 21** Combining the determined first wavefront tilt coefficient in the second direction and the determined second wavefront tilt coefficient in the second direction for each sampling position to form an output wavefront tilt coefficient in the second direction for each sampling position includes: Performing a least squares approximation to For a plurality of sampling positions, the root mean square of the difference between (a) the determined first wavefront tilt coefficient in the second direction and (b) a value obtained by adding a third constant to the output wavefront tilt coefficient in the second direction, and For a plurality of sampling positions, the root mean square of the difference between (a) the determined second wavefront tilt coefficient in the second direction and (b) a value obtained by adding a fourth constant obtained by multiplying +1 for the first portion of the grating of the object plane patterning device and -1 for the second portion of the grating of the object plane patterning device to the output wavefront tilt coefficient in the second direction. The method according to claim 20, comprising simultaneously minimizing.

22. The method according to any one of claims 1 to 21, wherein the first direction and the second direction are each aligned at 45° with respect to the first shearing direction and the second shearing direction, respectively.

23. Each measurement includes irradiating the plurality of object plane patterning devices with a first radiation; forming an image of each of the plurality of object plane patterning devices on a different one of the plurality of pattern devices of the plurality of image plane sensors; scanning at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors through a plurality of positions spaced apart in a certain direction to generate a vibration phase scan signal for each of the plurality of sampling positions; determining the phase of the harmonics of the vibration signal at a plurality of positions on the radiation detector; The method according to any one of claims 1 to 22, comprising.

24. The harmonic of the vibration signal equal to the difference between the aberration maps between a pair of positions within the pupil plane of the projection system at each of the plurality of positions on the radiation detector is the first harmonic, according to the method of claim 23.

25. The method according to claim 24, wherein a pair of positions within the pupil plane of the projection system are separated in the shearing direction by a shearing distance corresponding to twice the distance within the pupil plane between two adjacent first-order diffracted beams.

26. A computer-readable medium storing a computer program including computer-readable instructions configured to cause a computer to execute the method according to any one of claims 1 to 25.

27. A memory storing processor-readable instructions; A processor configured to read and execute the instructions stored in the memory, the processor-readable instructions including instructions configured to control a computer to execute the method according to any one of claims 1 to 25, a computer device.

28. A measurement system for determining a physical quantity, comprising: a plurality of object plane patterning devices including a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation, the second orientation being different from the first orientation; an illumination system arranged to irradiate the plurality of object plane patterning devices with radiation to form a plurality of first diffracted beams, wherein the first diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of a grating, and the first diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating; an image plane sensor including a patterning device and a radiation detector; an illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second diffracted beams from each of the first diffracted beams; a positioning device configured to move the plurality of object plane patterning devices in a first direction or a second direction; a controller configured to execute the method according to any one of claims 1 to 25; A measurement system comprising the above. **Claim 29** A measurement system for determining a physical quantity, comprising: a plurality of object plane patterning devices including a first set of patterning devices having a first orientation and a second set of patterning devices having a second orientation, the second orientation being different from the first orientation; an illumination system arranged to irradiate the plurality of object plane patterning devices with radiation to form a plurality of first diffracted beams, wherein the first diffracted beams from each of the first set of patterning devices are separated in a modulation direction corresponding to a first direction of a grating, and the first diffracted beams from each of the second set of patterning devices are separated in a modulation direction corresponding to a second direction of the grating; a plurality of image plane sensors each including a patterning device and each communicating with a radiation detector; an illumination system configured to form an image of each of the plurality of object plane patterning devices on the patterning device of the image plane sensor and to form a plurality of second diffracted beams from each of the first diffracted beams; A positioning device configured to move at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors in a first direction or a second direction; A controller configured to execute the method according to any one of claims 1 to 25; A measurement system comprising the same.

30. A lithography apparatus comprising the measurement system according to claim 28 or 29.

31. A metrology tool comprising the measurement system according to claim 28 or 29.

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