Method and device for determining physical quantity

Abstract

A method of determining a physical quantity is disclosed. The method uses a sensor system configured to sample a plurality of locations in parallel, where sampling of each location uses radiation incident on an object plane patterning device (marker) and an image plane sensor. Each marker comprises a first portion and a second portion, the first portion being different from the second portion, and wherein the first portion and the second portion of at least one of the markers are transposed relative to the first portion and the second portion of the other marker. Each mark corresponds to a different sampling position. For each portion of each mark, the method comprises: performing a first measurement in a first direction; and performing a second measurement in a second direction different from the first direction. Four data sets are determined and then combined to determine a physical parameter.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European application 22180704.3 filed on June 23, 2022, and the entire contents of this European application are incorporated herein by reference. Technical Field

[0003] The invention relates to a method for determining one or more physical quantities and an associated device for performing said method. The one or more physical quantities may relate to the alignment between, for example, an object plane and an image plane of a projection system. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern onto a substrate. A lithographic apparatus may be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as a "design layout" or "design") of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (e.g., a wafer).

[0005] As semiconductor manufacturing processes continue to advance, the size of circuit elements has continued to decrease over the decades, while the amount of functional elements such as transistors per device has steadily increased, following a trend commonly referred to as "Moore's Law". In order to keep up with Moore's Law, the semiconductor industry is pursuing technologies that enable the creation of smaller and smaller features. In order 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 patterned on the substrate. Typical wavelengths currently used are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Compared to lithographic apparatus using radiation having a wavelength of, for example, 193 nm, lithographic apparatus using extreme ultraviolet (EUV) radiation having a wavelength in the range of 4 nm to 20 nm (e.g., 6.7 nm or 13.5 nm) can be used to form smaller features on a substrate.

[0006] In lithographic apparatus, many sensor systems are used to measure all kinds of physical quantities. Examples of quantities of interest are distance / position, time, velocity, acceleration, force, lens aberrations, etc. Some of these sensor systems use detectors that output a periodically varying signal. Such a periodically varying signal can be obtained using a periodic structure such as a grating. The periodically varying signal can have, for example, a sinusoidal shape.

[0007] The radiation that has been patterned by the patterning device is focused onto the substrate using a projection system. The projection system may introduce optical aberrations that cause the image formed on the substrate to deviate from the desired image (e.g., the diffraction limited image of the patterning device). Alignment in the lithographic apparatus is also an important aspect, for example to ensure that the desired image is positioned in the correct position. Further alignment of components including, for example, the substrate is also an important aspect.

[0008] It may be desirable to provide methods and apparatus for accurately determining such physical quantities as aberrations caused by the projection system so that these aberrations can be better controlled, or for determining the strength of a signal such as substrate alignment. Furthermore, it may be desirable to provide methods and apparatus for accurately determining projection alignment in a lithographic apparatus. Summary of the invention

[0009] According to a first aspect of the present disclosure, a method for determining a physical quantity is provided, the method using a sensor system configured to sample a plurality of positions, wherein sampling at each position uses an object plane pattern forming device and an image plane sensor, wherein each object plane pattern forming device includes a first part and a second part, the first part is different from the second part, and wherein the first part and the second part of at least one of the object plane pattern forming devices are transposed relative to the first part and the second part of the other object plane pattern forming devices; and wherein the method includes: using the first part of each object plane pattern forming device and performing a first measurement in a first direction to generate a first data set; using the second part of each object plane pattern forming device and performing a second measurement in the first direction to generate a second data set; using the first part of each object plane pattern forming device and performing 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 object plane pattern forming device and performing a fourth measurement in the second direction to generate a fourth data set; and combining the first data set, the second data set, the third data set, and the fourth data set to determine the physical quantity.

[0010] The method according to the first aspect is advantageous because it results in a determined physical quantity which is less sensitive to correlated intensity noise, as now discussed.

[0011] It will be appreciated that each of the first, second, third, and fourth data sets is generated using radiation and that the radiation may be subject to intensity noise (i.e., the intensity of the radiation will be subject to variations or fluctuations over time). Radiation having a common noise source is incident on each of the object plane patterning device and the image plane sensor to generate the first, second, third, and / or fourth data sets. Since the data generated within any of the first, second, third, and fourth data sets is formed using the same emission of radiation (e.g., continuous or pulsed), there will be a correlation of the intensity noise within any of the first, second, third, and fourth data sets.

[0012] The object plane patterning device may comprise a grating.

[0013] The orientation of the first portion of the object plane patterning device may be orthogonal to the orientation of the second portion.Such an arrangement is advantageous in that it minimizes the processing of data required for subsequent modeling.

[0014] The orientation of at least one object plane patterning device may be orthogonal to the second orientation of the other object plane patterning devices.

[0015] In some embodiments, the first measurement, the second measurement, the third measurement, and the fourth measurement form part of a shearing interferometry process.

[0016] In some embodiments, a first portion of the object plane pattern forming device has a first shear direction and a second portion has a second shear direction, the second shear direction being different from the first shear direction. The first direction of the first measurement may include a component parallel to the first shear direction and a component parallel to the second shear direction, and the second direction of the second measurement may include a component parallel to the first shear direction and a component parallel to the second shear direction. In the case where each of the first direction and the second direction includes a component parallel to the first shear direction and a component parallel to the second shear direction, scanning in either of the first direction and the second direction actually results in scanning in both the first shear direction and the second shear direction at the same time.

[0017] In an embodiment, one of the first direction and the second direction is such that the sign of the component of the one direction parallel to the first shear direction is opposite to the sign of the component of the one direction parallel to the second shear direction, and the other of the first direction and the second direction is such that the sign of the component of the other direction parallel to the first shear direction is the same as the sign of the component of the other direction parallel to the second shear direction. Advantageously, when scanning in one direction, it can be ensured that the sign of the error of the differential of the wavefront mapping in the other direction is different for each of the first group and the second group. In addition, this allows the correlated intensity errors to be removed by modeling. The first direction and the second direction can be aligned at 45° relative to each of the first shear direction and the second shear direction.

[0018] In some embodiments, the image sensor may include a plurality of image sensors. Each of the plurality of image plane sensors may include a second patterning device positionable to receive radiation from a corresponding object plane patterning device of the plurality of object plane patterning devices, and wherein the plurality of image plane sensors include a detector arranged to receive radiation from the plurality of second patterning devices.

[0019] In some embodiments, a method of combining a first data set, a second data set, a third data set, and a fourth data set to determine a physical quantity includes: combining the first data set with the second data set to determine at least one first physical parameter for each sampled location; combining the third data set with the fourth data set to determine at least one second physical parameter for each sampled location; and

[0020] The determined first physical parameter for each sampled position is combined with the determined second physical parameter for each sampled position to form an output corrected physical parameter for each sampled position so as to at least partially correct errors in the determined first physical parameter and the second physical parameter caused by intensity variations of radiation used to generate the first data set, the second data set, the third data set, and / or the fourth data set.

[0021] The physical quantity may include one or more aberrations of the projection system. In addition, the first physical parameter, the second physical parameter, the third physical parameter, and the fourth physical parameter may correspond to the first aberration coefficient, the second aberration coefficient, the third aberration coefficient, and the fourth aberration coefficient, respectively.

[0022] In some embodiments, combining the first data set with the second data set to determine one or more aberrations may also include: determining a first wavefront tilt coefficient in the first direction; and the step of combining the third data set with the fourth data set to determine one or more aberrations may also include: determining a second wavefront tilt coefficient in the first direction; and combining the determined first wavefront tilt coefficient in the first direction for each sampled position with the determined second wavefront tilt coefficient in the first direction for each sampled position to form an output wavefront tilt coefficient in the first direction for each sampled position so as to at least partially correct 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 changes in the radiation used to generate the first data set and the second data set.

[0023] In some embodiments, 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 may include: performing a least squares fit to simultaneously minimize: the root mean square of the difference between: (a) the determined first wavefront tilt coefficient in the first direction; and (b) the sum of the output wavefront tilt coefficient in the first direction and a first constant; the root mean square of the difference between: (a) the determined second wavefront tilt coefficient in the first direction; and (b) the sum of the products of the output wavefront tilt coefficient in the first direction and a second constant multiplied by +1 for a first portion of the grating structure of the object plane pattern forming device, and the sum of the products of the output wavefront tilt coefficient in the first direction and the second constant multiplied by -1 for a second portion of the grating structure of the object plane pattern forming device.

[0024] In some embodiments, the physical quantity includes intensity.

[0025] In some embodiments, the physical quantity includes one or more intensities of the measured radiation, and the first physical parameter, the second physical parameter, the third physical parameter, and the fourth physical parameter correspond to the first intensity value, the second intensity value, the third intensity value, and the fourth intensity value, respectively.

[0026] In some embodiments, combining the first data set, the second data set, the third data set, and the fourth data set to determine a physical quantity includes: combining the first data set with the second data set to determine a first wavefront tilt coefficient in the second step direction for each sampling position; combining the third data set with the fourth data set to determine a second wavefront tilt coefficient in the second direction for each sampling position; and combining the determined first wavefront tilt coefficient in the second direction for each sampling position with 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 so as to at least partially correct 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 changes in the intensity of radiation used to generate the second data set and the fourth data set.

[0027] In some embodiments, combining the determined first wavefront tilt coefficient in the second direction for each sampling position with 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 fit to simultaneously minimize: the root mean square of the differences between: (a) the determined first wavefront tilt coefficient in the second direction; and (b) the output wavefront tilt coefficient in the second direction plus a third constant; the root mean square of the differences between: (a) the determined second wavefront tilt coefficient in the second direction; and (b) for a first portion of the grating structure of the object plane pattern forming device, the sum of the products of the output wavefront tilt coefficient in the second direction and a fourth constant multiplied by +1, and for a second portion of the grating structure of the object plane pattern forming device, the sum of the products of the output wavefront tilt coefficient in the second direction and the fourth constant multiplied by -1.

[0028] In some embodiments, each measurement includes: illuminating a plurality of object plane pattern forming devices with a first radiation; forming an image of each of the plurality of object plane pattern forming devices on a pattern forming device of a different one of a plurality of image plane sensors; scanning at least one of the plurality of object plane pattern forming devices or a corresponding plurality of image plane sensors through a plurality of positions separated in a direction so as to generate an oscillating phase scan signal for each of a plurality of sampling positions; and determining the phase of a harmonic of the oscillating signal at a plurality of positions on a radiation detector.

[0029] The harmonic of the oscillating signal is equal to the difference of the aberration map at each of the plurality of positions on the radiation detector between a pair of positions in a pupil plane of the projection system, and the harmonic of the oscillating signal may be a first harmonic.

[0030] The pair of positions in a pupil plane of the projection system may be separated in the shearing direction by a shearing distance corresponding to twice a distance in the pupil plane between two adjacent first diffracted beams.

[0031] According to a second aspect of the present disclosure, there is a measurement system for determining a physical quantity, the measurement system comprising: a plurality of object plane pattern forming devices, the plurality of object plane pattern forming devices comprising: a first group of pattern forming devices having a first orientation; and a second group of pattern forming devices having a second orientation, the second orientation being different from the first orientation; an illumination system, the illumination system being arranged to illuminate the first group of object plane pattern forming devices and the second group of object plane pattern forming devices with radiation so as to form a plurality of first diffraction beams, the first diffraction beam from each pattern forming device in the first group of pattern forming devices being separated in a modulation direction corresponding to the first orientation and the first diffraction beam from each pattern forming device in the second group of pattern forming devices being separated in a modulation direction corresponding to the second orientation; an image plane sensor, the image plane sensor comprising a pattern forming device and a radiation detector; the illumination system being configured to form an image of each of the plurality of object plane pattern forming devices on the pattern forming device of the image plane sensor so as to form a plurality of second diffraction beams from each first diffraction beam in the first diffraction beams; a positioning device, the positioning device being configured to move the plurality of object plane pattern forming devices in a first direction or a second direction; and a controller, the controller being configured to execute the method according to the present invention.

[0032] According to a third aspect of the present disclosure, there is a measurement system for determining a physical quantity, the measurement system comprising: a plurality of object plane pattern forming devices, the plurality of object plane pattern forming devices comprising: a first group of pattern forming devices having a first orientation; and a second group of pattern forming devices having a second orientation, the second orientation being different from the first orientation; an illumination system, the illumination system being arranged to illuminate the plurality of object plane pattern forming devices with radiation so as to form a plurality of first diffraction beams, a first diffraction beam from each pattern forming device in the first group of pattern forming devices being separated in a modulation direction corresponding to the first orientation and a first diffraction beam from each pattern forming device in the second group of pattern forming devices being separated in a modulation direction corresponding to the first orientation The object plane patterns of the plurality of image plane sensors are separated in a modulation direction corresponding to the second orientation; a plurality of image plane sensors, each image plane sensor includes a pattern forming device and each image plane sensor communicates with a radiation detector; the illumination system is configured to form an image of each of the plurality of object plane pattern forming devices on the pattern forming device of the image plane sensor so as to form a plurality of second diffraction beams from each first diffraction beam in the first diffraction beams; a positioning device, the positioning device is configured to move at least one of the plurality of object plane pattern forming devices or the corresponding plurality of image plane sensors in a first direction or a second direction; and a controller, the controller is configured to perform the method according to the present invention.

[0033] According to a fourth aspect of the present disclosure, a computer-readable medium carrying a computer program including computer-readable instructions is provided, wherein the computer-readable instructions are configured to cause a computer to execute the method according to any one of the first aspect, the second aspect, and the third aspect of the present disclosure.

[0034] According to a fifth aspect of the present disclosure, a computer device is provided, comprising: a memory storing processor-readable instructions; and a processor arranged to read and execute instructions stored in the memory, wherein the processor-readable instructions include instructions arranged to control the computer to execute the method described in any one of the first aspect, the second aspect, and the third aspect of the present disclosure.

[0035] According to a sixth aspect of the present disclosure, a lithography device is provided, comprising the measurement system according to any one of the fourth and fifth aspects of the present disclosure.

[0036] According to a seventh aspect of the present disclosure, a measurement tool is provided, comprising the measurement system according to any one of the fourth and fifth aspects of the present disclosure.

[0037] It should be understood that one or more aspects or features described above or referenced in the following description may be combined with one or more other aspects or features. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Embodiments of the present disclosure will now be described as examples with reference to the accompanying schematic diagram, in which:

[0039] - Figure 1 Describe the lithographic equipment;

[0040] - Figure 2 is a schematic illustration of a measurement system according to an embodiment of the present invention;

[0041] - Figure 3A and Figure 3B It can be formed Figure 2 Schematic illustration of a patterning device and a sensor device as components of a measurement system;

[0042] - Figure 4 is a schematic illustration of a measurement system according to an embodiment of the present disclosure, the measurement system comprising a first patterned area and a second patterned area, the first patterned area being arranged to receive radiation and form a plurality of first diffracted beams;

[0043] - Figure 5 A hybrid marking device for a plane patterning device of an object is shown. Figure 3A Another example of a measurement patterning device MA' of the type shown in;

[0044] - Figure 6 is a schematic flow chart of a new method for determining one or more aberrations of a projection system according to an embodiment of the present invention;

[0045] - Figure 7 An exemplary set of phase sweep measurements is shown, which may be represented in Figure 6 Data recorded during any one of the four scanning processes of the method shown;

[0046] - Fig. 8A Shows the Figure 6 The first measurement step of the method shown is due to the intensity fluctuations Figure 5 The intensity correlation of each of the exemplary seven field points represented by the object level patterning device shown in FIG. 1 (solid arrows) and the components of such intensity correlation in each of the two scanning directions (dashed arrows);

[0047] - Figure 8B Shows the Figure 6 The second measurement step of the method shown is due to the intensity fluctuations Figure 5The intensity correlation of each of the exemplary seven field points represented by the object level patterning device shown in FIG. 1 (solid arrows) and the components of such intensity error in each of the two scanning directions (dashed arrows);

[0048] - Figure 8C Shows the Figure 6 The third measurement step of the method shown is due to the intensity fluctuations Figure 5 The intensity correlation of each of the exemplary seven field points represented by the object level patterning device shown in FIG. 1 (solid arrows) and the components of such intensity error in each of the two scanning directions (dashed arrows);

[0049] - Fig.8D Shows the Figure 6 The fourth measurement step of the method shown is due to the intensity fluctuations Figure 5 The intensity correlation of each of the exemplary seven field points represented by the object level pattern forming device shown in FIG. 1 (solid arrows) and the components of such intensity error in each of the two scanning directions (dashed arrows); and

[0050] - Fig. 9 Shows that it can be formed Figure 6 An exemplary set of sub-steps of the last step of the method shown in (wherein correlated intensity errors may be removed by modeling in the step of combining the first data set S1, the second data set S2, the third data set S3, and the fourth data set S4 in order to determine a physical quantity, which may be, for example, one or more aberrations of the projection system). DETAILED DESCRIPTION

[0051] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of 5 nm to 100 nm).

[0052] The terms "reticle", "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam that corresponds to the pattern to be produced in a target portion of the substrate. In such contexts, the term "light valve" may also be used. In addition to typical masks (transmissive or reflective, binary, phase-shift, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0053] Figure 1A lithographic apparatus LA is schematically depicted. The lithographic apparatus LA comprises an illumination system (also referred to as 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 stage) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g., a wafer stage) WT configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support 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., comprising one or more dies) of the substrate W. It will be appreciated that the projection system PS may be any system through which radiation from an illumination source passes, through which defects due to failures in the focusing of the illumination (which may occur due to, for example, lens and / or mirror defects) may be acquired. Thus, the patterning device may be positioned such as Figure 1 The kind of projection system PS shown in FIG. 1 is outside the projection system PS shown in FIG. 1 , so that the radiation beam used for the patterning device is, for example, a metrology radiation beam and is not used to expose a pattern on the resist of the substrate.

[0054] In operation, the illumination system IL receives a radiation beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various types of optical elements for directing, shaping, and / or controlling the radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and / or other types of optical elements, or any combination thereof. The illuminator IL may be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in a cross-section of the radiation beam B at the plane of the patterning device MA.

[0055] The term "projection system" PS as used herein should be interpreted broadly to cover various types of projection systems suitable for using radiation for both exposure and measurement and / or for other factors such as the use of immersion liquid or the use of vacuum, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic, and / or electrostatic optical systems or any combination thereof. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0056] The lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by a liquid, such as water, having a relatively high refractive index, so as to fill the space between the projection system PS and the substrate W - this is also known as immersion lithography. More information on immersion techniques is given in US6952253, incorporated herein by reference.

[0057] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also known as a "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel and / or a step of preparing the substrate W for subsequent exposure may be performed on a substrate W on one of the substrate supports WT while another substrate W on another substrate support WT is being used to expose a pattern on another substrate W.

[0058] In addition to the substrate support WT, the lithographic apparatus LA may also comprise a measurement platform. The measurement platform is arranged to hold sensors and / or cleaning means. The sensors may be arranged to measure properties of the projection system PS or properties of the radiation beam B. The measurement platform may hold a plurality of sensors. The cleaning means may be arranged to clean parts of the lithographic apparatus, for example parts of the projection system PS or parts of the system for providing immersion liquid. The measurement platform may be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0059] In operation, a radiation beam B is incident on a patterning device MA (e.g. a mask) held on a mask support MT and is patterned by a pattern (design layout) present on the patterning device MA. Having traversed 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 positioner PW and a position measurement system PMS, the substrate support WT can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly a further position sensor (the further position sensor not being in position) are arranged to move the substrate support WT to a desired position. Figure 1 The patterning device MA may be accurately positioned relative to the path of the radiation beam B using the mask alignment marks M1, M2 and the substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 occupy dedicated target portions as illustrated, the substrate alignment marks P1, P2 may be located in spaces between target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are referred to as scribe line alignment marks.

[0060] The substrate W may include a previously formed pattern. In such a case, the lithographic apparatus LA aligns an image formed by the patterned radiation beam B with a pattern previously formed on the substrate W.

[0061] To illustrate the present invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, namely the x-axis, the y-axis and the z-axis. Each of the three axes is orthogonal to the other two axes. The rotation around the x-axis is called the Rx rotation. The rotation around the y-axis is called the Ry rotation. The rotation around the z-axis is called the Rz rotation. The x-axis and the y-axis define a horizontal plane, while the z-axis is in a vertical direction. The Cartesian coordinate system does not limit the present invention and is only used for illustration. In fact, another coordinate system such as a cylindrical coordinate system can be used to illustrate the present invention. The orientation of the Cartesian coordinate system can be different, for example, so that the z-axis has a component along the horizontal plane.

[0062] Radiation used in measurement and / or exposure systems of lithography systems, or in metrology systems such as electron beam metrology tools, may be subject to intensity noise (i.e., the intensity of the radiation will be subject to variations or fluctuations over time). Such noise is detrimental to the accuracy of the measurement or exposure. The present disclosure relates to methods and associated apparatus for at least partially correcting for such noise.

[0063] The projection system PS of the lithography system has an optical transfer function that may be non-uniform, which may affect the pattern imaged on the substrate W. For unpolarized radiation, such effects can be fairly well described by two scalar maps that describe the transmission (apodization) and relative phase (aberration) of the radiation that varies depending on the position in the pupil plane of the radiation exiting the projection system PS. These scalar maps, which may be referred to as transmittance maps and relative phase maps, can be expressed as linear combinations of a complete set of basis functions. A particularly suitable set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. The determination of each scalar map may involve determining 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 maps by calculating the inner product of the measured scalar map with each Zernike polynomial in turn and dividing such inner product by the square of the norm of the Zernike polynomial. In the following, unless otherwise stated, any reference to Zernike coefficients should be understood to mean the Zernike coefficients of the relative phase map (also referred to herein as the aberration map). It will be appreciated that in alternative embodiments, other sets of basis functions may be used. For example, some embodiments may use Tatian Zernike polynomials, for example for masked aperture systems.

[0064] The wavefront aberration map represents the deformation of the wavefront of light from a spherical wavefront approaching a point on the image plane of the projection system PS (as a function of position in the pupil plane, or alternatively, as a function of the angle at which the radiation approaches the image plane of the projection system PS). As discussed, such a wavefront aberration map W(x, y) can be expressed as a linear combination of Zernike polynomials:

[0065]

[0066] where x and y are coordinates in the pupil plane, are Zernike polynomials, and are coefficients. It should be understood that in the following, Zernike polynomials and coefficients are labeled with indices commonly known as Noll indices. Thus, is a Zernike polynomial with Nohl index n, and are coefficients with Knoll indices of n. The wavefront aberration mapping can then be obtained by using the coefficients in this expansion The coefficients can be characterized by a set of , which can be called Zernike coefficients.

[0067] It will be appreciated that only a limited number of Zernike orders are considered. Different Zernike coefficients of the phase map may provide information about different forms of aberrations caused by the projection system PS. Zernike coefficients having a Noelle index of 1 may be referred to as first Zernike coefficients, Zernike coefficients having a Noelle index of 2 may be referred to as second Zernike coefficients, etc.

[0068] First Zernike coefficient The first Zernike coefficient may not be relevant to the performance of the projection system PS and thus the method described herein may not be used to determine the first Zernike coefficient. Related to the tilt of the measured wavefront in the x-direction. The tilt of the wavefront in the x-direction is equal to the placement in the x-direction. The third Zernike coefficient Related to the tilt of the measured wavefront in the y direction. The tilt of the wavefront in the y direction is equivalent to the placement in the y direction. The fourth Zernike coefficient is related to the defocus of the measured wavefront. The fourth Zernike coefficient is equivalent to the placement in the z-direction. Higher order Zernike coefficients are related to other forms of aberrations caused by the projection system (e.g., astigmatism, coma, spherical aberration, and other effects).

[0069] Throughout this specification, the term "aberration" should be intended to include all forms of deviations of a wavefront from a perfect spherical wavefront. That is, the term "aberration" may relate to the placement of an image (e.g., the second Zernike coefficient, the third Zernike coefficient, and the fourth Zernike coefficient) and / or to higher-order aberrations, such as aberrations with Zernike coefficients having a Noelle index of 5 or greater. Furthermore, any reference to an aberration map for a projection system may include all forms of deviations of a wavefront from a perfect spherical wavefront, including deviations due to image placement.

[0070] The relative phase of the projection system PS in a pupil plane thereof may be determined by projecting radiation from the object plane patterning device (i.e. the patterning device in the plane of the patterning device MA) via 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 the interference pattern in a plane conjugate to the pupil plane of the projection system PS.

[0071] The projection system PS comprises a plurality of optical elements. The lithographic apparatus LA further comprises an adjustment device PA for adjusting these optical elements so as to correct aberrations (any type of phase variation across the pupil plane throughout the field). To achieve such correction, the adjustment device PA may be operable to manipulate the optical elements within the projection system PS in one or more different ways. The projection system may have a coordinate system, wherein the optical axis of the coordinate system extends in the z direction (it will be appreciated that the direction of such a z axis may vary along the optical path through the projection system). The adjustment device PA may be operable to perform any combination of the following: 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 elements may be performed in any direction (x, y, z or a combination thereof). The tilting of the optical element is typically performed outside a plane perpendicular to the optical axis by rotating around an axis in the x or y direction, but rotation around the z axis may be used for non-rotationally symmetric optical elements. The deformation of the optical element may be performed, for example, by using an actuator to apply a force on the side of the optical element and / or by using a heating element to heat a selected area of ​​the optical element. Typically, it is not possible to adjust the projection system PS to correct for apodization (variations in transmission across the pupil plane).A transmission map of the projection system PS may be used when designing a mask MA for the lithographic apparatus LA.

[0072] In some embodiments the adjustment apparatus PA may be operable to move the support structure MT and / or the substrate table WT. The adjustment apparatus PA may be operable to shift the support structure MT and / or the substrate table WT (in any of the x, y, z directions or a combination thereof) and / or tilt (by rotating about an axis in the x or y direction).

[0073] The projection system PS forming part of the lithographic apparatus may periodically undergo a calibration process. 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 installation of the lithographic apparatus at the site where the lithographic apparatus is to be used, the projection system PS may be calibrated again. Further calibration of the projection system PS may be performed at regular time intervals. For example, under normal use, the projection system PS may be calibrated every few months (e.g. every three months).

[0074] Calibrating the projection system PS may include passing radiation through the projection system PS and measuring the resulting projected radiation. The measurement of the projected radiation may be used to determine aberrations of the projected radiation caused by the projection system PS. A measurement system may be used to determine the aberrations caused by the projection system PS. In response to the determined aberrations, optical elements forming the projection system PS may be adjusted to correct for the aberrations caused by the projection system PS.

[0075] Figure 2 is a schematic illustration of a measurement system 10 that may be used to determine aberrations caused by a projection system PS. The measurement system 10 comprises an illumination system IL, a measurement pattern forming device MA', a sensor device 21, and a controller CN. The measurement system 10 may form part of a lithographic apparatus. For example, Figure 2 The illumination system IL and projection system PS shown in FIG. Figure 1 The illumination system IL and projection system PS of the lithographic apparatus shown in FIG. Figure 2 Additional components of the lithographic apparatus are not shown.

[0076] 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, Figure 2 The measurement pattern forming device MA' and the sensor device 21 shown in FIG. 2 can be positioned differently from the position in which they are positioned. Figure 2 For example, during normal use of the lithographic apparatus, a patterning device MA configured to form a pattern to be transferred to a substrate W may be positioned to receive radiation from the illumination system IL, and the substrate W may be positioned to receive radiation from the projection system PS (as for example in FIG. Figure 1The measurement pattern forming device MA' and the sensor device 21 can be moved to the measurement pattern forming device MA' and the sensor device 21. Figure 2 The measurement pattern forming device MA' can be formed by, for example, Figure 1 The sensor device 21 may be supported by a support structure MT of the support structure shown in FIG. Figure 1 WT shown in . Alternatively, the sensor device 21 may be supported by a measurement table (not shown) which may be separate from the sensor table WT. It will be appreciated that the measurement system 10 may be applied in metrology applications to measure deviations in intensities rather than for aberration measurement of exposure-based projection systems.

[0077] Figure 3A and Figure 3B The measurement patterning device MA' and the sensor device 21 are shown in more detail in FIG. 3a is a schematic illustration of the measurement patterning device MA' in the xy plane, and Figure 3B is a schematic illustration of the sensor device 21 in the xy plane.

[0078] The measurement pattern forming device MA' comprises a plurality of patterned areas 15a to 15c. Each of the plurality of patterned areas 15a to 15c may be referred to as an object plane pattern forming device. Figure 2 and Figure 3A In the embodiment shown in , the measurement patterning device MA' is a transmission type patterning device MA'. Each of the patterned areas 15a to 15c comprises a transmission diffraction grating. Radiation incident on the patterned areas 15a to 15c of the measurement patterning device MA' is thereby at least partially scattered by the projection system PS and received by the projection system PS when used for aberration detection and alignment of the projection system. In contrast, radiation incident on the remaining part of the measurement patterning device MA' is not transmitted towards the projection system PS (e.g. it may be absorbed by the measurement patterning device MA').

[0079] The illumination system IL illuminates the measurement patterning device MA' with radiation. Figure 2 Although not shown, the illumination system IL may receive radiation from the radiation source SO and condition the radiation so as to illuminate the measurement pattern forming device MA'. For example, the illumination system IL may condition the radiation so as to provide radiation having a desired spatial and angular distribution. Figure 2, the illumination system IL is configured to form a separate measurement beam 17a to 17c, each measurement beam 17a to 17c illuminating a corresponding patterned area 15a to 15c of the measurement patterning device MA'. In other embodiments, the illumination system IL may be configured to illuminate all of the patterned areas 15a to 15c of the measurement patterning device MA' with a single radiation beam (in these embodiments, multiple measurement beams 17a to 17c may be formed by the patterned areas 15a to 15c).

[0080] In order to perform a determination of aberrations caused by the projection system PL, the mode of the illumination system IL may be changed so as to illuminate the measurement patterning device MA' with separate measurement beams 17a to 17c. For example, during normal operation of the lithographic apparatus, the illumination system IL may be configured to illuminate the patterning device MA with a slit of radiation. However, the mode of the illumination system IL may be changed so that the illumination system IL is configured to form separate measurement beams 17a to 17c in order to perform a determination of aberrations caused by the projection system PL. In some embodiments, different patterned areas 15a to 15c may be illuminated at different times. For example, a first subset of patterned areas 15a to 15c may be illuminated at a first time so as to form a first subset of measurement beams 17a to 17c, and a second subset of patterned areas 15a to 15c may be illuminated at a second time so as to form a second subset of measurement beams 17a to 17c.

[0081] In other embodiments, the mode of the illumination system IL may not be changed in order to perform the determination of 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 (e.g. a slit of radiation substantially corresponding to the illumination area used during exposure of the substrate). Separate measurement beams 17a to 17c may then be formed by the measurement patterning device MA', since radiation is transmitted (and diffracted) only through the patterned areas 15a to 15c towards the projection system PS.

[0082] In the figures, the Cartesian coordinate system is shown as being constant throughout the projection system PS. However, in some embodiments, the properties of the projection system PS may result in a transformation of the coordinate system. For example, the projection system PS may form an image of the measurement pattern forming device MA' that is magnified, rotated, and / or mirrored relative to the measurement pattern forming device MA'. In some embodiments, the projection system PS may rotate the image of the measurement pattern forming device MA' by approximately 180° about the z-axis. In such embodiments, the sensor device 21 may be replaced at the sensor device 21. Figure 2The relative positions of the first measurement beam 17a and the third measurement beam 17c are shown in FIG. In other embodiments, the image may be mirrored around an axis that may be in the xy plane. For example, the image may be mirrored around the x-axis or around the y-axis.

[0083] In embodiments where the projection system PS rotates the image of the measurement pattern forming 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 relative to the image projected by the projection system PS, and any rotation and / or mirroring of the image will cause a corresponding rotation and / or mirroring of the coordinate system. For ease of illustration, in the accompanying drawings, the coordinate system is shown as not being changed by the projection system PS. However, in some embodiments, the coordinate system may be transformed by the projection system PS.

[0084] exist Figure 3A In an embodiment, each of the plurality of patterned areas 15a to 15c includes a first portion 15a' to 15c' and a second portion 15a" to 15c". The first portion and the second portion of the patterned areas 15a to 15c may be irradiated with the measuring beam 17a to 17c at different times. For example, the first portion 15a' to 15c' of each of the patterned areas 15a to 15c may be irradiated by the measuring beam 17a to 17c at a first time. At a second time, the second portion 15a" to 15c" of each of the patterned areas 15a to 15c may be irradiated by the measuring beam 17a to 17c. As mentioned above, in some embodiments, different patterned areas 15a to 15c may be irradiated at different times. For example, a first portion of a first subset of the patterned areas 15a to 15c may be irradiated at a first time, and a first portion of a second subset of the patterned areas 15a to 15c may be irradiated at a second time. The second portion of the first subset of patterned areas and the second portion of the second subset may be irradiated at the same time or at different times.In general, any schedule for irradiating different portions of the patterned areas 15a to 15c may be used.

[0085] The multiple object plane pattern forming devices 15a to 15c shown in this embodiment include mixed patterned marks, as now explained. The term "mixed patterned marks" is a term of art. Each of the multiple object plane pattern forming devices 15a to 15c includes: a first portion 15a' to 15c' and a second portion 15a" to 15c", the first portion 15a' to 15c' being different from the second portion 15a" to 15c". The first portion and the second portion of at least one of the multiple object plane pattern forming devices are transposed relative to the first portion and the second portion of the other object plane pattern forming devices. Figure 3AIn the embodiment, it can be seen that the object plane pattern forming device 15b is transposed relative to the object plane pattern forming devices 15a and 15c. At least one object plane pattern forming device 15b, which has transposed the first part 15a' and the second part 15b" relative to the other object plane pattern forming devices, is called a "hybrid" patterned mark. In other words, the first part and the second part of at least one hybrid patterned mark are flipped relative to the first part and the second part of the other object plane pattern forming devices (the other object plane pattern forming devices can be referred to as "unmixed patterned marks"), so that the orientation of the grating in the first part 15b' of the at least one hybrid mark is different from the orientation of the grating in the first part of the unmixed marks 15a', 15c'. Similarly, the orientation of the grating in the second part 15b" of at least one hybrid mark is different from the orientation of the grating in the second part of the unmixed marks 15a", 15c".

[0086] exist Figure 3A In an embodiment of the present invention, the first portion 15a' comprises a diffraction grating aligned parallel to the u direction (and therefore having a shear direction in the v direction) and the second portion 15a" comprises a diffraction grating aligned parallel to the v direction (and therefore having a shear direction in the u direction). The first shear direction and the second shear direction are perpendicular to each other in such an embodiment. Both the u direction and the v direction are aligned at 45° relative to both the x and y directions and are aligned perpendicular to each other. It will be appreciated that the orientation of the grating structure is not limited to the shear direction. The first orientation and the second orientation are preferably orthogonal to each other, but other relative orientations may be used. Regardless of whether the scan is continuous or stepped (stepwise) relative to the grating direction, the direction of the scan is non-parallel, but is not limited to an alignment of 45° - this is just an example.

[0087] In use, a first portion of the object plane patterning devices 15a to 15c will be illuminated together, and at another time, a second portion of the object plane patterning devices 15a to 15c will be illuminated together. Figure 3A In the patterned mark arrangement of the hybrid mark shown in the embodiment shown in , gratings with different orientations (in this embodiment, shear directions) are illuminated simultaneously (when each of the first and second parts are illuminated).

[0088] The modified measurement beams 17a to 17c are received by the projection system PS. The projection system PS forms an image of the patterned area 15a to 15c on the sensor device 21. The sensor device 21 comprises a plurality of image plane sensors 25a to 25c. Each of the plurality of image plane sensors 25a to 25c comprises a second patterning device 19a to 19c which can be positioned to receive radiation from a corresponding object plane patterning device of the plurality of object plane patterning devices 15a to 15c. Each of the second patterning devices 19a to 19c comprises a diffraction grating 19a to 19c. The plurality of image plane sensors 25a to 25c further comprises 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 corresponding modified measurement beam 17a to 17c output from the projection system PS. The modified measurement beams 17a to 17c incident on the diffraction gratings 19a to 19c are further modified by the diffraction gratings 19a to 19c. The modified measurement beams transmitted at the diffraction gratings 19a to 19c (from the corresponding object plane patterning devices 15a to 15c) are incident on the radiation detector 23.

[0089] In a 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 positioned such that the projection system PS is arranged to form an image of a first portion 15a' to 15c' of each of the plurality of object plane patterning devices 15a to 15c on a patterning device 19a to 19c of a different one of the plurality of image plane sensors 25a to 25c. At another time, in a 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 positioned such that the projection system PS is arranged to form an image of a second portion 15a" to 15c" of each of the plurality of object plane patterning devices 15a to 15c on a patterning device 19a to 19c of a different one of the plurality of image plane sensors 25a to 25c.

[0090] The radiation detector 23 is configured to detect the spatial intensity profile of radiation incident on the radiation detector 23. For example, the radiation detector 23 may include an array of individual detector elements or sensing elements. For example, the radiation detector 23 may include an active pixel sensor, such as a CMOS (complementary metal oxide semiconductor) sensor array. Alternatively, the radiation detector 23 may include a CCD (charge coupled device) sensor array. The diffraction gratings 19a to 19c at which the modified measurement beams 17a to 17c are received and the portion of the radiation sensor 23 form an image plane sensor 25a to 25c. Each of the image plane sensors 25a to 25c may be referred to as a detector zone 25a to 25c. For example, the first diffraction grating 19a at which the first measurement beam 17a is received and the first portion of the radiation sensor 23 together form a first image plane sensor (or detector zone) 25a. Measurements of a given measurement beam 17a to 17c may be made at the corresponding detector zones 25a to 25c (as depicted). As described above, in some embodiments the relative positioning of the modified measurement beams 17a to 17c and the coordinate system may be transformed by the projection system PS.

[0091] The modification of the measurement beams 17a to 17c occurring at the diffraction gratings 19a to 19c of the patterned areas 15a to 15c and the detector areas 25a to 25c causes an interference pattern to be formed on the radiation detector 23. The interference pattern formed by each measurement beam is related to the derivative of the phase mapping in the orientation direction of the grating used at the object level (e.g. the shear direction) and depends on the noise contribution due to, for example, aberrations caused by the projection system PS. Therefore, the interference pattern can be used to determine the aberrations caused by the projection system PS.

[0092] Typically, the diffraction grating 19a to 19c of each of the detector regions 25a to 25c comprises a two-dimensional transmission diffraction grating. Figure 3B In the embodiment shown in , each of the detector zones 25a to 25c includes diffraction gratings 19a to 19c configured in the form of a checkerboard. In an alternative embodiment, each of the detector zones 25a to 25c may include a two-dimensional transmission diffraction grating 19a to 19c that is not configured in the form of a checkerboard, but this may result in a more complex interference pattern from which it may be more difficult to derive an aberration map. In a further alternative embodiment, each of the detector zones 25a to 25c may be a position on a single detector, and the diffraction gratings 19a to 19c may be positions on a single diffraction grating 19, which may, for example, be in the form of a checkerboard.

[0093] Illumination through a first portion of the patterned areas 15a to 15c may provide information about the derivative of the relative phase map in one direction, and illumination through a second portion of the patterned areas 15a to 15c may provide information about the derivative of the relative phase map in another direction.

[0094] As further described below, in an embodiment of the present disclosure, in each of the two measurement configurations for determining a physical quantity, the measurement pattern forming device MA' and / or the sensor device 21 are continuously or stepwise scanned in two perpendicular directions. For example, the measurement pattern forming device MA' and / or the sensor device 21 can be scanned relative to each other in each of the x and y directions in turn. It should be noted that the x direction and the y direction are only exemplary and any two perpendicular directions can be used so that each scan (measurement) that is actually a partial scan is mathematically orthogonal to the other scan and can therefore be combined to create a complete data set. Again, as further described below, in a first aberration measurement configuration, the measurement pattern forming device MA' and / or the sensor device 21 are scanned in a first direction (e.g., y direction) to produce a first phase scan data set and at another time are scanned in a second direction (e.g., x direction) to produce a second phase scan data set. In addition, in the second aberration measurement configuration, the measurement pattern forming device MA' and / or the sensor device 21 are scanned in a first direction (e.g., y direction) to produce a third phase scan data set and at another time are scanned in a second direction (e.g., x direction) to produce a fourth phase scan data set. Each of the first phase scan data set, the second phase scan data set, the third phase scan data set, and the fourth phase scan data set is a partial scan measurement value. No useful measurement data is provided individually. The first phase scan data set, the second phase scan data set, the third phase scan data set, and the fourth phase scan data set are combined to determine a physical quantity, which can be one or more aberrations of the projection system.

[0095] During each phase scan, the measurement pattern forming device MA' and / or the sensor device 21 can be scanned and data separated by a distance corresponding to a portion of the grating period of the diffraction grating can be captured. The measurements made at different scanning positions can be analyzed to derive information about the derivative of the wavefront in the scanning direction. For example, the phase of the first harmonic of the measured signal (the measured signal can be referred to as the phase scan signal) can contain information about the derivative of the wavefront in the shear direction of the object plane grating. Since each of the multiple object plane pattern forming devices 15a to 15c includes two parts with different orientations (e.g., different shear directions), by irradiating each part and performing a complete phase scanning process (i.e., a partial measurement scan in one direction combined with another partial measurement scan in a second direction), information about the wavefront can be derived in two different directions (specifically, this provides information about the derivative of the wavefront in each of the two shear directions), thereby allowing the complete wavefront to be reconstructed.

[0096] It will be appreciated that a variety of different arrangements of patterned areas 15a-15c and detector areas 25a-25c may be used in order to determine physical quantities such as aberrations caused by the projection system PS. The patterned areas 15a-15c and / or the detector areas 25a-25c may include a diffraction grating. In some embodiments, the patterned areas 15a-15c and / or the detector areas 25a-25c may include components other than a diffraction grating. For example, in some embodiments, the patterned areas 15a-15c and / or the detector areas may include a single slit or pinhole opening through which at least a portion of the measurement beam 17a-17c may propagate. In general, the patterned areas and / or the detector areas may include any arrangement for modifying the measurement beam.

[0097] We should further understand that Figure 2 The exemplary sensor system is not necessarily limited to use in an exposure projection system PS and is also not limited to shearing interferometry devices. For example, patterned areas 15a to 15c and detector areas 25a to 25c and patterned areas 15a to 15c and detector areas 25a to 25c in all embodiments herein can be used for intensity measurements using a dedicated metrology radiation source. Such a radiation source can, for example, be used to determine substrate alignment. It will be appreciated that the device will be suitable for many different applications. Determination of physical quantities such as intensity and its error contribution can also be determined depending on the application of such a sensor device.

[0098] The controller CN receives measurements made at the sensor device 21 and determines aberrations caused by the projection system PS from the measurements. 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 an adjustment device PA for adjusting components of the projection system PS. For example, the adjustment device PA may adjust optical elements of the projection system PS in order to correct aberrations caused by the projection system PS and determined by the controller CN.

[0099] In some embodiments, the controller CN may be operable to control an adjustment device PA for adjusting the support structure MT and / or the substrate table WT. For example, the adjustment device PA may adjust the support structure MT and / or the substrate table WT so as to correct aberrations caused by placement errors of the patterning device MA and / or the substrate W (and determined by the controller CN).

[0100] Determining aberrations (which may be caused by the projection system PS or by placement errors of the patterning device MA or substrate W) may include fitting measurements made by the sensor apparatus 21 to Zernike polynomials to obtain Zernike coefficients. Different Zernike coefficients may provide information about different forms of aberrations caused by the projection system PS. The Zernike coefficients may be determined independently at different locations in the x and / or y direction. For example, at Figure 2 , Figure 3A and Figure 3B In the embodiment shown in , a Zernike coefficient can be determined for each measurement beam 17 a to 17 c.

[0101] In some embodiments, the measurement patterning device MA' may include more than three patterned areas, the sensor device 21 may include more than three detector areas, and more than three measurement beams may be formed. This may allow the Zernike coefficients to be determined at more field positions. In some embodiments, the patterned areas and the detector areas may be distributed at different positions in both the x-direction and the y-direction. This may allow the Zernike coefficients to be determined at separated positions in both the x-direction and the y-direction.

[0102] Although in Figure 2 , Figure 3A and Figure 3B In the embodiment shown in the figure, the measurement pattern forming device MA' includes three patterned areas 15a to 15c and the sensor device 21 includes three detector areas 25a to 25c, but in other embodiments, the measurement pattern forming device MA' may include more or less than three patterned areas 15a to 15c and / or the sensor device 21 may include more or less than three detector areas 25a to 25c.

[0103] Reference now Figure 4 A method for determining aberrations caused by the projection system PS is described.

[0104] Typically, the measurement patterning device MA' comprises at least one first patterned area 15a to 15c and the sensor device 21 comprises at least one corresponding second patterned area 19a to 19c.

[0105] Figure 4 is a schematic illustration of a measurement system 30 that can be used to determine aberrations caused by the projection system PS. The measurement system 30 can be used with Figure 2 However, the measurement system 30 may have a different number of first patterned areas (on the measurement pattern forming device MA') and second patterned areas (in the sensor device 21). Figure 4 The measurement system 30 shown in FIG. 3 may include the above-described Figure 2 Any features of the measurement system 10 shown in FIG. 1 are not included, and those features will not be described further below.

[0106] exist Figure 4 In FIG. 2 , only a single first patterned area 31 is provided on the measurement patterning device MA′ and a single second patterned area 32 is provided in the sensor device 21 .

[0107] The measurement patterning device MA' is irradiated with radiation 33 from the illumination system IL. For ease of understanding, Figure 4 Only a single line is shown in FIG. 1 (which may, for example, represent a single ray, such as a principal ray, of an incident radiation beam). However, it will be appreciated that the radiation 33 will include a range of angles incident on the first patterned area 31 of the measurement patterning device MA'. That is, each point on the first patterned area 31 of the measurement patterning device MA' may be illuminated by a cone of light. Typically, each point is illuminated by approximately the same range of angles, which is characterized by the intensity of the radiation in a pupil plane of the illumination system IL (not shown).

[0108] The first patterned area 31 is arranged to receive radiation 33 and form a plurality of first diffraction beams 34, 35, 36. The central first diffraction beam 35 corresponds to the 0th order diffraction beam of the first patterned area 31, and the other two first diffraction beams 34, 36 correspond to the ±1st order diffraction beams of the first patterned area 31. It will be appreciated that, in general, there will also be more higher order diffraction beams. Again for ease of understanding, in Figure 4 Only the three first diffracted beams 34 , 35 , 36 are shown.

[0109] It will also be appreciated that because the incident radiation 33 comprises a cone of radiation converging on a point on the first patterned area 31 , each of the first diffracted beams 34 , 35 , 36 also comprises a cone of radiation diverging from a point on the first patterned area 31 .

[0110] In order to achieve the generation of the first diffracted beams 34, 35, 36, the first patterned area 31 may be in the form of a diffraction grating. For example, the first patterned area 31 may be approximately Figure 3A Specifically, at least a portion of the first patterned region 31 may belong to Figure 3A The second portion 15a" of the patterned region 15a shown in FIG. 1 is in the form of a diffraction grating which is aligned parallel to the u direction and thus has a shearing direction in the v direction (it should be noted that Figure 4 , which is shown in the zv plane). Therefore, the first diffracted beams 34 to 36 are separated in a shear direction which is the v direction.

[0111] The first diffracted beams 34 to 36 are at least partially captured by the projection system PS, as now described. How many of the first diffracted beams 34 to 36 are captured by the projection system PS will depend on: the pupil filling of the incident radiation 33 from the illumination system IL; the angular separation of the first diffracted beams 34 to 36 (which in turn depends on the pitch of the first patterned areas 31 and the wavelength of the radiation 33); and the numerical aperture of the projection system PS.

[0112] The measurement system 30 may be arranged such that the first diffraction beam 35 corresponding to the 0th order diffraction beam substantially fills the numerical aperture of the projection system PS, which may be represented by a circular area of ​​a pupil plane 37 of the projection system PS, and the first diffraction beams 34, 36 corresponding to the ±1st order diffraction beams substantially overlap the first diffraction beam 35 corresponding to the 0th order diffraction beam. With this arrangement, substantially all of the first diffraction beams 35 corresponding to the 0th order diffraction beam and most of the first diffraction beams 34, 36 corresponding to the ±1st order diffraction beams are captured by the projection system PS and projected onto the sensor device 21. (In addition, with this arrangement, a large number of diffraction beams generated by the first patterned area 31 are at least partially projected onto the sensor device 21).

[0113] The function of the first patterned region 31 is to introduce spatial coherence, as now discussed.

[0114] Typically, two rays of radiation 33 from the illumination system IL incident on the same point of the measurement patterning device MA' at different angles of incidence are incoherent. By receiving radiation 33 and forming a plurality of first diffracted beams 34, 35, 36, the first patterned area 31 may be considered to form a plurality of replicas of the incident radiation cone 33 (the replicas having substantially different phases and intensities). Within any of these replicas or first diffracted beams 34, 35, 36 (due to the properties of the illumination system IL), two rays of radiation originating from the same point on the measurement patterning device MA' but at different scattering angles are incoherent. However, for a given radiation ray in any of the first diffracted beams 34, 35, 36, there is a corresponding radiation ray in each of the other first diffracted beams 34, 35, 36 that is spatially coherent with the given ray. For example, the chief ray of each of the first diffracted beams 34 , 35 , 36 , which chief ray corresponds to the chief ray of the incident radiation 33 , is coherent and, when combined, can interfere at the amplitude level.

[0115] This coherence may be exploited by measurement system 30 to determine an aberration map of projection system PS.

[0116] The projection system PS projects a portion of the first diffracted beam 34 , 35 , 36 , which portion is captured by the numerical aperture of the projection system, onto the sensor device 21 .

[0117] exist Figure 4 In the embodiment, the sensor device 21 comprises a single second patterned area 32. As further described below, the second patterned area 32 is arranged to receive these first diffraction beams 34 to 36 from the projection system PS and form a plurality of second diffraction beams from each of the first diffraction beams. To achieve this, the second patterned area 32 comprises a two-dimensional transmission diffraction grating. Figure 4 In FIG. 3 , all radiation transmitted by the second patterned area 32 is represented as a single arrow 38. This radiation 38 is received by a detector area 39 of the radiation detector 23 and used to determine the aberration map.

[0118] Each of the first diffraction beams 34 to 36 incident on the patterned area 32 will diffract to form a plurality of second diffraction beams. Since the second patterned area 32 includes a two-dimensional diffraction grating, a two-dimensional array of secondary diffraction beams is generated from each incident first diffraction beam (the main rays of these secondary diffraction beams are separated in both the shear direction (e.g., v direction) and the direction perpendicular to the shear direction (e.g., u direction). Hereinafter, the diffraction order that is the nth order in the shear direction (v direction) and the mth order in the non-shear direction (u direction) will be referred to as the (n, m) diffraction order of the second patterned area 32. Hereinafter, in the case where it is not important which order the second diffraction beam is in the non-shear direction (u direction), the (n, m) diffraction order of the second patterned area 32 may be simply referred to as the nth order second diffraction beam.

[0119] Embodiments of the present disclosure relate to new methods for determining one or more physical quantities of a projection system PS (e.g., intensity for determining alignment of a substrate or wafer, for example in a lithographic apparatus or in a metrology system, or aberrations such as tilt of a wavefront), as now discussed.

[0120] As used herein, the object (e.g., reticle) plane and the image (e.g., wafer) plane and any other plane conjugated to the object plane and the image plane may be referred to as field planes, or simply fields. Using known methods, physical quantities may be determined for a plurality of positions. For example, the aberrations of the projection system may be determined for a plurality of field points (i.e., points in the field plane of the projection system). For each position that may be a field point, an object plane patterning device (marker) having two parts (each part having a different orientation that may be, for example, a different shearing direction) and an image plane sensor are provided. The image sensor may be a corresponding plurality of image sensors. A first part of the object plane patterning device (having a first orientation, for example, a first shearing direction) is illuminated, and an image of the part is formed on the image plane grating, optionally on a corresponding part of the image plane grating. During illumination of the first part, the object plane grating is scanned in a first direction, which may be, for example, a first shearing direction. In embodiments in which the image sensor is a corresponding plurality of image sensors and thus a plurality of image plane gratings, the image sensor may be scanned in the first direction instead of scanning the object plane grating. In either case, scanning in a first direction during illumination produces a first phase scan data set related to a physical quantity to be determined in the first direction, such as an intensity for determining alignment, or a gradient of an aberration map. Next, a second portion of the object plane patterning device (having a second orientation which may be a second shearing direction) is illuminated, and an image of the portion is formed on an image plane grating, which may be a corresponding image plane grating. During illumination of the second portion, at least one of the object plane grating and the image plane grating (wherein the image plane grating is a plurality of corresponding image plane gratings) is scanned in a second direction, which may be a second shearing direction. This produces a second phase scan data set related to a physical quantity in the second direction, such as a gradient of an aberration map. Each of the first phase scan data set and the second phase scan data set may be considered as a partial data set, since no useful information can be derived from the first phase scan data set or the second phase scan data set when used alone. The first phase scan data set and the second phase scan data set are combined to determine a physical quantity, such as an aberration (or relative phase) map of the projection system for the location (e.g., field point). In the case where the scan is performed as a continuous scan, the phase scan data may include data from a continuous scan across a discrete set of measurement points. The advantage of such a continuous scan is a faster measurement time. In the case where the scan is performed as a stepwise measurement, the phase scan data includes phase step data across a certain number of points corresponding to the number of phase steps.

[0121] Embodiments of the present disclosure relate to a new method in which a physical quantity (e.g., an aberration) is determined at multiple positions (e.g., field points). As in the known method, for each position or field point, an object plane patterning device (mark) having two parts (each part having a different orientation, such as a different shearing direction) and an image plane sensor that can be a corresponding image plane sensor for each object plane patterning device are provided. As will be described below, in the new method, the object plane patterning device (mark) includes a mixed mark having a mixture of a first orientation and a second orientation that is exposed simultaneously, and the first orientation and the second orientation can be a first shearing direction and a second shearing direction. For each part of each mark, the method includes: performing a first measurement, which can be a first continuous scanning measurement using a first scanning direction, a first stepwise measurement, and / or a first shearing interferometry measurement process; and performing a second measurement, which can be a second continuous scanning measurement using a second scanning direction, a second stepwise measurement, and / or a second step-by-step shearing interferometry measurement process. That is, each part of the object plane patterning device is used for two phase scanning processes. The first scanning direction and the second scanning direction are different from the directions of the first grating orientation and the second grating orientation. Since there are two parts to each position mark and two scanning measurements are performed for each part, four data sets are determined. Therefore, four (instead of two) data sets are generated for each position, each position can be a field point. These four determined data sets are combined in order to determine a physical quantity, which can be one or more aberrations of the projection system. This allows the relevant intensity noise contribution to be removed by modeling, as now referred to Figures 5 to 9 Discussed.

[0122] As stated above, the new method uses a hybrid marker for an object plane patterning device (marker). For example, the method can use Figure 3A The measurement pattern forming device MA' shown in and described above. Figure 5 Another example of a suitable measurement patterning device MA' is shown in .

[0123] The exemplary measurement patterning device MA' comprises seven object plane patterning devices 51 to 57. This allows physical quantities such as aberrations to be determined at seven different positions (field points). It will be appreciated that in other embodiments a different number of object plane patterning devices (and corresponding image plane sensors) may be provided.

[0124] Each of the plurality of object plane pattern forming devices 51 to 57 includes: a first portion 51a to 57a and a second portion 51b to 57b. Within each object plane pattern forming device 51 to 57, one of the first portion 51a to 57a and the second portion 51b to 57b has a first shear direction in the u direction and the other of the first portion 51a to 57a and the second portion 51b to 57b has a second shear direction in the v direction. The orientation of the object plane pattern forming device is not limited to the shear directions u and v, and will be described as such for illustrative purposes only. Within the first object plane pattern forming device 51, the first portion 51a has a first shear direction in the u direction and the second portion 51b has a second shear direction in the v direction. Similarly, within the second object plane pattern forming device 52, the second portion 52b has a first shear direction in the u direction and the first portion 52a has a second shear direction in the v direction.

[0125] As follows (reference Figure 6 ) will be further described, in the new method, as part of the phase scanning process, the first parts 51a to 57a of the object plane patterning devices 51 to 57 are illuminated simultaneously. Similarly, in the new method, the second parts 51b to 57b of the object plane patterning devices 51 to 57 are illuminated simultaneously (but at different times than the first parts 51a to 57a).

[0126] The second shear direction (v) is different from the first shear direction (u). That is, the first shear direction and the second shear direction are linearly independent. In this example, the first shear direction and the second shear direction are perpendicular to each other, but it will be appreciated that in other embodiments, the second shear direction may be oriented at a different angle relative to the first shear direction. In other embodiments, the grating structure orientation may not include a shear direction at all, but the first orientation direction will be different relative to the second orientation direction.

[0127] A plurality of object plane pattern forming devices 51 to 57 include: a first group of pattern forming devices 51, 53, 54, 55, 57, wherein the first parts 51a, 53a, 54a, 55a, 57a of the first group of pattern forming devices 51, 53, 54, 55, 57 have a first shear direction (u); and a second group of pattern forming devices 52, 56, wherein the first parts 52a, 56a of the second group of pattern forming devices 52, 56 have a second shear direction (v).

[0128] The method further uses seven image plane sensors, each image plane sensor corresponding to a different one of the object plane pattern forming devices 51 to 57. Each of the image plane sensors generally belongs to the above reference Figure 2 and Figure 3BThe image plane sensors 25a to 25c are of the type described. Each of the image plane sensors comprises a second pattern forming device (as described above with reference to Figure 2 and Figure 3B 19a to 19c of the type described above), said second patterning device may be positioned to receive radiation from a respective object plane patterning device of the plurality of object plane patterning devices 51 to 55. In an alternative embodiment, a single image plane sensor may be used.

[0129] The image plane sensor further comprises a plurality of second pattern forming devices (described above with reference to Figure 2 A detector of the type described for receiving radiation) of the radiation sensor 23.

[0130] The pattern forming device of each image plane sensor among the multiple image plane sensors is arranged to receive a first diffraction beam generated by a corresponding object plane pattern forming device among the multiple object plane pattern forming devices 51 to 57 from the projection system PS and is configured to form multiple second diffraction beams from each first diffraction beam.

[0131] In some embodiments a single detector may be provided which receives radiation from one or more patterning devices of one or more image plane sensors. Alternatively, in some embodiments each image plane sensor of a plurality of image plane sensors may be provided with a single detector.

[0132] Each of the multiple object plane pattern forming devices 51 to 57 and one or more pattern forming devices, which may be corresponding image plane sensors among the multiple image plane sensors, can be matched so that at least some of the second diffraction beams formed by at least one of the first diffraction beams are spatially coherent with the second diffraction beams formed by at least one other first diffraction beam.

[0133] It will be appreciated that matching of the object plane patterning devices 51 to 57 with the second patterning devices (so that at least some of the second diffraction beams formed from at least one of the first diffraction beams are spatially coherent with the second diffraction beams formed from at least one other of the first diffraction beams) can be achieved by matching the pitches of the object plane patterning devices 51 to 57 with the respective second patterning devices. It will be further appreciated that such matching of the pitches of the object plane patterning devices 51 to 57 with the second patterning devices takes into account any reduction factor applied by the projection system PS. With this in mind, typically the pitch of the second patterning devices may be an integer multiple of the pitch of the object plane patterning devices 51 to 57 or the pitch of the object plane patterning devices 51 to 57 may be an integer multiple of the pitch of the second patterning devices.

[0134] The detector may be referred to as a radiation detector. The radiation detector may include a two-dimensional array of sensing elements. Each sensing element may be referred to as a pixel of the radiation detector. It will be appreciated that each of the plurality of locations on the radiation detector at which the phase of the harmonics of the oscillating signal is determined may correspond to a different sensing element or pixel of the radiation detector.

[0135] In some embodiments, each of the first and second portions of the object plane patterning device may include a one-dimensional diffraction grating with a duty cycle of 50%. With such a first patterning device, the efficiency of the even diffraction orders (except the 0th diffraction order) is zero. Therefore, the only two pairs of first diffracted beams whose orders differ by ±1 (and therefore contribute to the first harmonic of such an oscillating phase scanning signal) are 0th order beams with ±1st order beams. Furthermore, with such a geometry of the first patterned area, the scattering efficiency is symmetrical, so that the efficiency of the ±1st order diffraction beams is the same.

[0136] Reference now Figure 6 A new method 60 for determining a physical quantity using a sensor system configured to sample multiple positions is described. Sampling at each position uses an object plane patterning device 51 to 57 and an image plane sensor. In an embodiment, the method determines the aberrations of a projection system PS. The method 60 may use a corresponding plurality of image plane sensors for multiple object plane patterning devices 51 to 57.

[0137] The method 60 includes four scanning measurements 61, 62, 63, 64 (each scanning measurement 61, 62, 63, 64 can be continuous or stepwise), and can include a shearing interferometry process. Figure 6 6, 63, 64 are shown in a particular order in the schematic illustration of , but it will be appreciated that the four measurements 61, 62, 63, 64 may be performed in any order. The four measurements 61, 62, 63, 64 are now described.

[0138] The first measurement 61 includes positioning a plurality of object plane patterning devices 51 to 57 and one or more image plane sensors so that incident radiation from the projection system PS can be arranged to form an image of a first portion 51a to 57a of each of the plurality of object plane patterning devices 51 to 57 at a corresponding position on the patterning device of the one or more image plane sensors. The first measurement 61 is then performed. The first measurement can be a first continuous scanning measurement, or can be a first step-by-step measurement. The first measurement can be a first shearing interferometry measurement process. The first measurement 61 includes: at least one of the plurality of object plane patterning devices 51 to 57 or the corresponding plurality of image plane sensors scans through a plurality of positions separated in a first direction to generate a first data set S1, which can be a first phase scan data set. The first direction at S1 can be the y direction. It should be noted that this is only an exemplary direction, and it will be appreciated that any direction can be used. The first direction may include a component of the directional orientation of the grating parallel to a first portion of the object plane pattern forming device (e.g., wherein the first portion of the object plane pattern forming device has a first shear direction (u) and the first direction is the y-direction) and a component of the directional orientation of the grating parallel to a second portion of the grating of the second portion of the object plane pattern forming device (e.g., wherein the second portion of the object plane pattern forming device has a second shear direction (v) and the first direction is the y-direction).

[0139] The second measurement 62 comprises positioning the plurality of object plane patterning devices 51 to 57 and at least one image plane sensor such that the incident radiation is arranged to form an image of a first portion 51a to 57a of each of the plurality of object plane patterning devices 51 to 57 on a patterning device of the at least one image plane sensor, which may be a different image plane sensor of the plurality of image plane sensors. The second measurement 62 is then performed. The second measurement 62 may be a second continuous scanning measurement, or may be a second stepwise measurement. The second measurement may be a second shearing interferometry process and comprises: at least one of the plurality of object plane patterning devices 51 to 57 or the corresponding plurality of image plane sensors scans 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 may include a component of the directional orientation of the grating parallel to a first portion of the object plane pattern forming device (e.g., wherein the first portion of the object plane pattern forming device has a first shear direction (u)), and a component of the directional orientation of the grating parallel to a second portion of the object plane pattern forming device (e.g., wherein the second portion of the object plane pattern forming device has a second shear direction (v)).

[0140] The third step measurement 63 includes positioning a plurality of object plane patterning devices 51 to 57 and at least one image plane sensor so that the incident radiation is arranged to form an image of a second portion 51b to 57b of each of the plurality of object plane patterning devices 51 to 57 on a patterning device of the image plane sensor, wherein the image plane sensor may be a plurality of corresponding image plane sensors. A third measurement 63 is then performed, which may be a third continuous scanning measurement, or may be 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 to 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.

[0141] The fourth measurement 64 includes positioning the plurality of object plane patterning devices 51 to 57 and at least one image plane sensor so that the incident radiation is arranged to form an image of the second portion 51 b to 57 b of each of the plurality of object plane patterning devices 51 to 57 on the patterning device of the image plane sensor. The fourth measurement 64 is then performed. The fourth measurement may be a fourth continuous scanning measurement, or may be 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 to 57 or the corresponding plurality of image plane sensors via 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.

[0142] The new method 60 further comprises a step 65 of combining the first, second, third, S3 and fourth data sets S4 to determine a physical quantity, which may be, for example, one or more aberrations of the projection system PS. The physical quantity may alternatively be an intensity related to, for example, the alignment of the substrate.

[0143] One of the first and second directions (e.g., y, x) may be such that the sign of the component of the one direction parallel to a first orientation, which may be, for example, a first shear direction (u), is opposite to the sign of the component of the one direction parallel to a second orientation, which may be, for example, a shear direction (v), and the other of the first and second directions (e.g., y, x) may be such that the sign of the component of the other direction parallel to the first orientation, which may be the first shear direction (u), is the same as the sign of the component of the other direction parallel to the second orientation, which may be the second shear direction (v). It will be appreciated, however, that different locations may have different orientations, and therefore different shear directions.

[0144] exist Figure 5 An example of a configuration of a first direction and a second direction (e.g., x, y) and a first orientation and a second orientation (e.g., shear directions u, v) is shown in FIG. The first direction (y) has a positive component parallel to the first shear direction (u) and a positive component parallel to the second shear direction (v). The second direction (x) has a positive component parallel to the first shear direction (u) and a negative component parallel to the second shear direction (v). Figure 5In the example shown in , the first shearing direction (u) and the second shearing direction (v) are mutually orthogonal; the first direction (y) and the second direction (x) are mutually orthogonal; and each of the first direction (y) and the second direction (x) is aligned at 45° relative to each of the first shearing direction (u) and the second shearing direction (v). It should be understood that the grating orientation is not limited to the shearing directions (u, v), and the first stepping direction and the second stepping direction are not limited to the x and y directions.

[0145] Figure 6 The method 60 schematically shown in is advantageous because it results in a determined physical quantity which may be one or more aberrations of the projection system PS or may be an intensity related to alignment measurements which is less sensitive to noise contributions, as now discussed.

[0146] It will be appreciated that each of the first dataset S1, the second dataset S2, the third dataset S3, and the fourth dataset S4 is generated using radiation B and that the radiation may be subject to intensity noise (i.e., the intensity of the radiation B will be subject to variations or fluctuations over time). The data generated within any one of the first dataset S1, the second dataset S2, the third dataset S3, and the fourth dataset S4 is formed using the same radiation emission (e.g., the same radiation pulse), and therefore there will be correlation of intensity noise errors within any one of the first dataset S1, the second dataset S2, the third dataset S3, and the fourth dataset S4.

[0147] In the case where each of the first and second directions (e.g., y, x) includes a component parallel to the first orientation (e.g., shear direction u) and a component parallel to the second orientation (e.g., shear direction v), scanning in either of the first and second directions actually results in simultaneous scanning in both the first and second orientations (e.g., u, v). Thus, although the plurality of object plane patterning devices 51 to 57 include a first set of patterning devices 51, 53, 54, 55, 57 and a second set of patterning devices 52, 56, scanning in the first or second direction (e.g., y, x) during the generation of any of the four data sets S1, S2, S3, S4 will result in scanning in the directional direction of all portions of the object plane patterning devices 51 to 57 exposed at any given time and will therefore result in phase scan data recorded by the detector 23.

[0148] Figure 7 An exemplary set of obtained phase scan measurements is shown (the exemplary set may represent data recorded during any one of the four phase scan processes 61 , 62 , 63 , 64 ). Figure 7What is shown in FIG. 5 is a single phase scan curve for each of the four object plane patterning devices 51 to 57. It will be appreciated that Figure 7 Each of the seven curves shown in may represent a single pixel from a portion of a detector corresponding to a different one of the image plane sensors (the single pixel may be associated with, for example, a single position in a pupil plane where the radiation is from projection system PS). The phases of the curves for corresponding multiple pixels on one or more image plane sensors may be used to generate a map representing the gradient of the aberration (relative phase) map in the shear direction of the currently illuminated object plane grating.

[0149] Figure 7 Each of the seven curves shown in comprises five data points to which a sinusoid has been fitted. It will be appreciated that the five data points corresponding to five phase steps are merely examples. The number of phase steps and the resulting data points to which a sin or cosine is fitted may be any number of three or more. Figure 7 Any intensity variation that occurs during the generation of the seven curves shown in (and other pixels corresponding to other positions in, for example, the pupil plane) will generally affect the positions of the data points in the seven curves. This in turn will affect the fitted sinusoids and therefore the extracted phases of the sinusoids (the extracted phase involves the difference in relative phases of two points separated in, for example, the shear direction, from different positions in, for example, the pupil plane). For example, as indicated by the arrow, an upward fluctuation in the intensity of the radiation during the capture of the second data point will shift all of the second data points upward. Furthermore, this will affect the sinusoids that are fitted to the data and therefore the phase extracted from the fitted sinusoids. It should be noted that such intensity variations will affect all seven curves, i.e., the intensity fluctuations from the seven curves are all correlated.

[0150] The phase scan data are typically related to the differential of the aberration (relative wavefront) map in the direction of the shear direction (u or v) of the portion of the object plane patterning device (i.e., the first portion 51a to 57a or the second portion 51b to 57b) illuminated with the radiation. Therefore, an intensity noise error in the data from the data sets S1, S2, S3, S4 will typically result in an error in the differential of the wavefront map in the direction of the shear direction of the portion of the object plane patterning device illuminated with the radiation.

[0151] Since the first part of the first group of pattern forming devices 51, 53, 54, 55, 57 has a first shear direction (u); and the first part of the second group of pattern forming devices 52, 56 has a second shear direction (v), when the first part of the first group of pattern forming devices 51, 53, 54, 55, 57 is illuminated, the first group of pattern forming devices will have an error (from intensity noise) in the differential of the wavefront mapping in the direction of the first shear direction (u) and the second group of pattern forming devices 52, 56 will have a related error in the differential of the wavefront mapping in the direction of the second shear direction (v).

[0152] An error in the differential of the wavefront map in the direction of the first shear direction or the second shear direction (u, v) results in an error in the differential of the wavefront map in both the first direction and the second direction (x, y). The sign(s) of the error in the differential of the wavefront map in the first direction and the second direction (x, y) depends on the sign of the error in the differential of the wavefront map in the direction of the first shear direction or the second shear direction (u, v) and the sign of the components of the first direction and the second direction (x, y) parallel to the first shear direction and the second shear direction (u, v), as described below with reference to FIG. 8A to FIG. 8D as described.

[0153] Since one of the first and second directions (y, x) is such that the sign of the component of the one direction parallel to the first shear direction (u) is opposite to the sign of the component of the one direction parallel to the second shear direction (v) and the other of the first and second directions (y, x) is such that the sign of the component of the other direction parallel to the first shear direction (u) is the same as the sign of the component of the other direction parallel to the second shear direction (v), when scanning in one direction (y, x), it can be ensured that the sign of the error in the differential of the wavefront mapping in the other direction (y, x) is different for each of the first and second pattern forming devices. In other words, the correlated intensity errors will have a higher order characteristic identity. This in turn allows such intensity errors to be removed by modeling. Now referring to FIG. 8A to FIG. 8D Describe this situation.

[0154] Fig. 8A The intensity error (solid arrow) for each of the seven field points attributable to intensity fluctuations and the component of this intensity error in each of the two directions (dashed arrow) are shown for the first measurement, in this case the first shearing interferometry process 61 .

[0155] Figure 8BThe intensity error (solid arrow) for each of the seven field points attributable to intensity fluctuations and the component of this intensity error in each of the two directions (dashed arrow) are shown for the second measurement, in this case the second shearing interferometry process 62.

[0156] Figure 8C The intensity error (solid arrow) for each of the seven field points attributable to intensity fluctuations and the component of this intensity error in each of the two directions (dashed arrow) are shown for the third measurement, in this case the third shearing interferometry process 63.

[0157] Fig.8D The intensity error (solid arrow) for each of the seven field points attributable to intensity fluctuations and the component of this intensity error in each of the two directions (dashed arrow) are shown for the fourth measurement, in this case the fourth shearing interferometry process 64.

[0158] Each Zernike coefficient can be obtained from data obtained in two directions of simultaneous fitting. During the first shearing interferometry process 61, the phase scanning 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 scanning in the positive u direction and the positive v direction. Therefore, as Fig. 8A As shown in , the intensity error for the first set of patterning devices 51, 53, 54, 55, 57 will be in the positive u direction (as previously described, in the shearing interferometry process 61, the first portion of the object plane patterning devices 51 to 57 is illuminated). Similarly, the intensity error for the second set of patterning devices 52, 56 will be in the positive v direction. Fig. 8A As shown in , 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. Therefore, an intensity error or fluctuation during the first shearing interferometry process 61 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the y direction (the error is the third Zernike coefficient ), which error has the same sign for all object plane patterning devices 51 to 57 (i.e., it will result in a shift in the positive y-direction). Furthermore, intensity errors or fluctuations during the first shearing interferometry process 61 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the x-direction (the error is the second Zernike coefficient ), the error has one sign for the first set of pattern forming devices 51, 53, 54, 55, 57 and has an opposite sign for the second set of pattern forming devices 52, 56.

[0159] During the second shearing interferometry process 62, the phase scanning direction is the positive x direction. Since the positive x direction has components in the positive u direction and the negative v direction, this is equivalent to scanning in the positive u direction and the negative v direction. Therefore, Figure 8B As shown in , the intensity error for the first set of patterning devices 51, 53, 54, 55, 57 will be in the positive u direction (as previously described, in the shearing interferometry process 61, the first portion of the object plane patterning devices 51 to 57 is illuminated). Similarly, the intensity error for the second set of patterning devices 52, 56 will be in the negative v direction. Figure 8B As shown in FIG. 6 , 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. Therefore, an intensity error or fluctuation during the second shearing interferometry process 62 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the x direction (the error is the second Zernike coefficient ), which error has the same sign for all object plane patterning devices 51 to 57 (i.e., it will result in a shift in the positive x-direction). Furthermore, intensity errors or fluctuations during the first shearing interferometry process 61 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the y-direction (the error being the third Zernike coefficient ), the error has one sign for the first set of pattern forming devices 51, 53, 54, 55, 57 and has an opposite sign for the second set of pattern forming devices 52, 56.

[0160] During the third shearing interferometry process 63, the phase scanning 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 scanning in the positive u direction and the positive v direction. Therefore, Figure 8C As shown in , the intensity error will be in the positive v direction for the first set of patterning devices 51, 53, 54, 55, 57 (as previously described, in the shearing interferometry process 61, the second portion of the object plane patterning devices 51 to 57 is illuminated). Similarly, the intensity error will be in the positive u direction for the second set of patterning devices 52, 56. Figure 8C As shown in , 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. Therefore, an intensity error or fluctuation during the third shearing interferometry process 63 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the y direction (the error is the third Zernike coefficient ), which error has the same sign for all object plane patterning devices 51 to 57 (i.e., it will result in a shift in the positive y direction). Furthermore, intensity errors or fluctuations during the third shearing interferometry process 63 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the x direction (the error is the second Zernike coefficient ), the error has one sign for the first set of pattern forming devices 51, 53, 54, 55, 57 and has an opposite sign for the second set of pattern forming devices 52, 56.

[0161] During the fourth shearing interferometry process 64, the phase scanning direction is the positive x direction. Since the positive x direction has components in the positive u direction and the negative v direction, this is equivalent to scanning in the positive u direction and the negative v direction. Therefore, Fig.8D As shown in FIG. 6 , the intensity error for the first set of patterning devices 51, 53, 54, 55, 57 will be in the negative v direction (as described above, in the shearing interferometry process 61, the first portion of the object plane patterning devices 51 to 57 is illuminated). Similarly, the intensity error for the second set of patterning devices 52, 56 will be in the positive u direction.

[0162] Also like Fig.8D As shown in FIG. 6 , 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. Therefore, an intensity error or fluctuation during the second shearing interferometry process 62 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the x direction (the error is the second Zernike coefficient ), which error has the same sign for all object plane patterning devices 51 to 57 (i.e., it will result in a shift in the positive x-direction). Furthermore, intensity errors or fluctuations during the first shearing interferometry process 61 will result in an error in the gradient (or tilt) of the reconstructed wavefront map in the y-direction (the error being the third Zernike coefficient ), the error has one sign for the first set of pattern forming devices 51, 53, 54, 55, 57 and has an opposite sign for the second set of pattern forming devices 52, 56.

[0163] The inventors have realized that if the intensity noise error is just an offset, it will be impossible to determine and correct this error without an independent measurement of the offset. In contrast, when the intensity error has a higher order signature (i.e., the errors for some field points have opposite signs to the errors for other field points), these (correlated) intensity errors can be removed by modeling.

[0164] Reference now Fig. 9The manner in which correlated intensity errors may be removed by modelling in step 65 of combining the first, second, third, S3 and fourth data sets S4 to determine a physical quantity that may be one or more aberrations of the projection system PS is discussed.

[0165] exist Fig. 9 In the example shown in , step 65 includes the following steps.

[0166] In a step 70, the first data set S1 is combined with the third data set S3. In particular, the first data set S1 and the third data set S3 may be combined so as to determine at least one Zernike coefficient for each of the seven pairs of the object plane patterning devices 51 to 57 and the image plane sensor (i.e., for each of the seven field points). For example, the first data set S1 and the third data set S3 may be combined so as to determine, for example, for each of the seven pairs of the object plane patterning devices 51 to 57 and the image plane sensor (i.e., for each of the seven field points): a first wavefront tilt coefficient in a first direction (y); ; and the first wavefront tilt coefficient in the second direction (x) This may for example involve reconstructing a first wavefront map from a first phase scan data set S1 and a third phase scan data set S3 for each of the seven pairs of object plane patterning devices 51 to 57 and image plane sensors (See equation (1)).

[0167] In a further step 71, the second data set S2 is combined with the fourth data set S4. In particular, the second data set S2 and the fourth data set S4 may be combined in order to determine at least one Zernike coefficient for each of, for example, seven pairs of object plane patterning devices 51 to 57 and image plane sensors (i.e., for each of the exemplary seven field points). For example, the second data set S2 and the fourth data set S4 may be combined in order to determine, for each of, for example, seven pairs of object plane patterning devices 51 to 57 and image plane sensors (i.e., for each of the seven field points): a second wavefront tilt coefficient in the first direction (y); ; and the first wavefront tilt coefficient in the second direction (x) This may for example involve reconstructing a second wavefront map from the second phase-stepped data set S2 and the fourth phase-scanned data set S4 for each of the seven pairs of object plane patterning devices 51 to 57 and image plane sensors (See equation (1)).

[0168] After steps 70 and 71, there will be two values ​​for each Zernike coefficient for each pair of object plane patterning device 51 to 57 and image plane sensor or field point. This redundancy is used to remove intensity noise errors by modeling to produce one correction value for each Zernike coefficient for each field point, as now discussed.

[0169] After steps 70 and 71, if there are n pairs of object plane patterning devices 51 to 57 and image plane sensors or field points (e.g., n may be seven), then for each Zernike coefficient, the method will have produced two digital arrays, each with n entries. For example, if two tilt Zernike coefficients have been produced, then there will be four arrays of n entries: the first wavefront tilt coefficient in the first direction (y) ; The second wavefront tilt coefficient in the first direction (y) ; The first wavefront tilt coefficient in the second direction (x) ; and the second wavefront tilt coefficient in the second direction (x) The intensity noise errors within each array are correlated.

[0170] At the next step 72, for each Zernike coefficient, the two arrays of n terms are combined to produce a single array of n (corrected) terms. For example, a first wavefront tilt coefficient in a first direction (eg, y) and the second wavefront tilt coefficient in the second direction (eg, x) Combined to produce a corrected wavefront tilt coefficient In particular, the combining is performed using the correlation of the intensity noise contribution in each array in order to at least partially correct for errors caused by intensity variations of the radiation used to generate the first and third data sets S1, S3.

[0171] Similarly, the first wavefront tilt coefficient in the second direction (eg, x) is and the second wavefront tilt coefficient in the first direction (e.g., y) Combined to produce a corrected wavefront tilt coefficient In particular, the combining is performed using the correlation of the intensity noise contribution in each array in order to at least partially correct for errors caused by intensity variations of the radiation used to generate the second data set S2 and the fourth data set S4.

[0172] Specifically, the combining performed in step 72 may be performed as follows.

[0173] For example, the first wavefront tilt coefficient in a first direction (eg, y) is combined and the second wavefront tilt coefficient in the second direction (eg, x) To produce a corrected wavefront tilt coefficient This can include performing a least squares fit to simultaneously minimize:

[0174]

[0175] and

[0176]

[0177] Among them, c1 and c2 are two constants (fitting parameters), is the unit array, so that for all i, ,and is an array with entries of +1 or -1, where, for the entries corresponding to the first set of object plane patterning devices 51, 53, 54, 55, 57, , and for the items corresponding to the second set of object plane patterning devices 52, 56, Therefore, for Figure 5 The exemplary arrangement of the object plane patterning devices 51 to 57 shown in FIG. That is, the array Intensity errors with higher order feature identity (intensity errors in this case come from using data in the x-direction) are modeled.

[0178] Similarly, the first wavefront tilt coefficient in the second direction (eg, x) is combined and the second wavefront tilt coefficient in the first direction (e.g., y) To produce a corrected wavefront tilt coefficient This can include performing a least squares fit to simultaneously minimize:

[0179]

[0180] and

[0181]

[0182] Among them, c3 and c4 are two constants (fitting parameters). Intensity errors with higher order feature identification (which in this case comes from using data in the y direction) are modeled.

[0183] Some embodiments of the present disclosure relate to carrying a computer including a computer configured to cause the computer to execute the above-referenced Figures 5 to 9 A computer readable medium of a computer program of computer readable instructions of the method 60 is described.

[0184] Some embodiments of the present disclosure relate to a computer device, the computer device comprising: a memory storing processor-readable instructions; and a processor arranged to read and execute instructions stored in the memory, wherein the processor-readable instructions include instructions arranged to control the computer to execute the above reference Figures 5 to 9 The method 60 is described as an instruction.

[0185] Some embodiments of the present disclosure relate to a measurement system for determining a physical quantity, the measurement system comprising: a system configured to perform the above-mentioned Figures 5 to 9 A controller for the described method 60. The apparatus may comprise or form part of a lithographic apparatus LA. Alternatively, the apparatus may comprise or form part of a metrology tool.

[0186] Although the above described embodiments use the first harmonic of the phase swept signal, it will be appreciated that in alternative embodiments, higher order harmonics of the phase swept signal may be used instead.

[0187] Although the above-described embodiments use a first patterned region 31 comprising a one-dimensional diffraction grating 31 having a duty cycle of 50%, it should be appreciated that in alternative embodiments, other first patterned regions 31 may use different geometries. For example, in some embodiments, the first patterned region 31 may include a two-dimensional checkerboard diffraction grating having a duty cycle of 50%.

[0188] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0189] Although specific reference may be made herein to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form a component of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or a mask (or other pattern forming device). These apparatuses may generally be referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0190] Where context permits, embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention may also be implemented as instructions stored on a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form that can be read by a machine (e.g., a computing device). For example, a machine-readable medium may include: a read-only memory (ROM); a random access memory (RAM); a magnetic storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.); etc. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that these descriptions are merely for convenience, and that these actions are actually caused by a computing device, a processor, a controller, or other devices that execute firmware, software, routines, instructions, etc. And doing so may cause an actuator or other device to interact with the physical world.

[0191] Although specific embodiments of the present invention have been described above, it will be appreciated that the present invention may be practiced in other ways than those described. The above description is intended to be illustrative, not restrictive. Therefore, it will be appreciated by those skilled in the art that modifications 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 following numbered aspects.

[0192] 1. A method of 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,

[0193] wherein each object plane patterning device comprises a first portion and a second portion, the first portion being different from the second portion, and wherein the first portion and the second portion of at least one of the object plane patterning devices are transposed relative to the first portion and the second portion of the other object plane patterning devices; and

[0194] Wherein, the method comprises:

[0195] using a first portion of each object plane patterning device and performing a first measurement in a first direction to generate a first data set;

[0196] using a second portion of each object plane patterning device and performing a second measurement in the first direction to generate a second data set;

[0197] using the first portion of each object plane patterning device and performing a third measurement in a second direction different from the first direction to produce a third data set;

[0198] using a second portion of each object plane patterning device and performing a fourth measurement in the second direction to generate a fourth data set; and

[0199] The first data set, the second data set, the third data set, and the fourth data set are combined to determine the physical quantity.

[0200] 2. A method according to aspect 1, wherein radiation having a common noise source is incident on each object plane pattern forming device and image plane sensor to generate the first data set, the second data set, the third data set, and / or the fourth data set.

[0201] 3. A method according to any preceding clause, wherein the object plane patterning device comprises a grating.

[0202] 4. A method according to any preceding clause, wherein the orientation of the first portion of the object plane patterning device is orthogonal to the orientation of the second portion.

[0203] 5. A method according to any preceding clause, wherein the first orientation of the at least one object plane patterning device is orthogonal to the second orientations of the other object plane patterning devices.

[0204] 6. The method of any preceding aspect, wherein the first measurement, the second measurement, the third measurement, and the fourth measurement form part of a shearing interferometry process.

[0205] 7. A method according to any preceding aspect, wherein the first portion has a first shear direction and the second portion has a second shear direction, the second shear direction being different from the first shear direction.

[0206] 8. The method of aspect 7, wherein the first direction includes a component parallel to the first shear direction and a component parallel to the second shear direction;

[0207] And wherein the second direction includes a component parallel to the first shear direction and a component parallel to the second shear direction.

[0208] 9. A method according to aspect 8, wherein one of the first direction and the second direction makes the sign of the component of the one direction parallel to the first shear direction opposite to the sign of the component of the one direction parallel to the second shear direction, and the other direction of the first direction and the second direction makes the sign of the component of the other direction parallel to the first shear direction the same as the sign of the component of the other direction parallel to the second shear direction.

[0209] 10. The method of any preceding clause, wherein the image sensor comprises a plurality of image sensors.

[0210] 11. The method of any preceding aspect, wherein the image plane sensor comprises: a second patterning device positionable to receive radiation from the plurality of object plane patterning devices; and

[0211] A detector is arranged to receive radiation from the second patterning device.

[0212] 12. The method of clause 10, wherein each of the plurality of image plane sensors comprises a second patterning device positionable to receive radiation from a corresponding object plane patterning device of the plurality of object plane patterning devices; and

[0213] Wherein, the plurality of image plane sensors comprises detectors arranged to receive radiation from the plurality of second patterning devices.

[0214] 13. The method of any preceding aspect, wherein combining the first data set, the second data set, the third data set, and the fourth data set to determine the physical quantity comprises:

[0215] combining the first data set with the second data set to determine at least one first physical parameter for each sampling location;

[0216] combining the third data set with the fourth data set to determine at least one second physical parameter for each sampling location; and

[0217] The determined first physical parameter for each sampling position is combined with the determined second physical parameter for each sampling position to form an output correction physical parameter for each sampling position so as to at least partially correct errors in the determined first physical parameter and the determined second physical parameter caused by intensity variations of radiation used to generate the first data set, the second data set, the third data set, and / or the fourth data set.

[0218] 14. A method according to any preceding clause, wherein the physical quantity comprises one or more aberrations of a projection system.

[0219] 15. A method according to aspect 13, wherein the physical quantity includes one or more aberrations of the projection system, and the first physical parameter, the second physical parameter, the third physical parameter, and the fourth physical parameter correspond to a first aberration coefficient, a second aberration coefficient, a third aberration coefficient, and a fourth aberration coefficient, respectively.

[0220] 16. The method according to aspect 15, wherein:

[0221] The step of combining the first data set with the second data set to determine one or more aberrations further comprises: determining a first wavefront tilt coefficient in the first direction; and

[0222] The step of combining the second data set and the fourth data set to determine one or more aberrations further comprises: determining a second wavefront tilt coefficient in the first direction; and

[0223] 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 are combined to form an output wavefront tilt coefficient in the first direction for each sampling position so as to at least partially correct 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 radiation used to generate the first data set and the second data set.

[0224] 17. A method according to clause 16, wherein 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 comprises:

[0225] Perform a least squares fit to simultaneously minimize:

[0226] the root mean square for each sampling position of the difference between: (a) the determined first wavefront tilt coefficient in the first direction; and (b) the sum of the output wavefront tilt coefficient in the first direction and a first constant; and

[0227] The root mean square of the difference between the following for each sampling position: (a) the determined second wavefront tilt coefficient in the first direction; and (b) the sum of the product of the output wavefront tilt coefficient in the first direction for the first portion of the grating of the object plane pattern forming device and a second constant multiplied by +1, and the sum of the product of the output wavefront tilt coefficient in the first direction for the second portion of the grating of the object plane pattern forming device and the second constant multiplied by -1.

[0228] 18. A method according to any one of aspects 1 to 13, wherein the physical quantity comprises intensity.

[0229] 19. A method according to any one of aspects 1 to 13, wherein the physical quantity includes one or more intensities of the measured radiation, and the first physical parameter, the second physical parameter, the third physical parameter, and the fourth physical parameter correspond to a first intensity value, a second intensity value, a third intensity value, and a fourth intensity value, respectively.

[0230] 20. The method of any preceding aspect, wherein combining the first data set, the second data set, the third data set, and the fourth data set to determine the physical quantity comprises:

[0231] combining the first data set with the second data set to determine, for each sampling position, a first wavefront tilt coefficient in the second direction;

[0232] combining the third data set with the fourth data set to determine, for each sampling position, a second wavefront tilt coefficient in the second direction; and

[0233] The determined first wavefront tilt coefficient in the second direction for each sampling position and the determined second wavefront tilt coefficient in the second direction for each sampling position are combined to form an output wavefront tilt coefficient in the second direction for each sampling position so as to at least partially correct 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 changes of radiation used to generate the second data set and the fourth data set.

[0234] 21. A method according to clause 20, wherein combining the determined first wavefront tilt coefficient in the second direction for each sampling position 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 comprises:

[0235] Perform a least squares fit to simultaneously minimize:

[0236] the root mean square of the difference for a plurality of sampling positions between: (a) the determined first wavefront tilt coefficient in the second direction; and (b) the output wavefront tilt coefficient in the second direction plus a third constant; and

[0237] The root mean square of the difference between the following items for multiple sampling positions: (a) the determined second wavefront tilt coefficient in the second direction; and (b) the sum of the product of the output wavefront tilt coefficient in the second direction for the first portion of the grating of the object plane pattern forming device and a fourth constant multiplied by +1, and the sum of the product of the output wavefront tilt coefficient in the second direction for the second portion of the grating of the object plane pattern forming device and a fourth constant multiplied by -1.

[0238] 22. The method of any preceding aspect, wherein each of the first and second directions is aligned at 45° relative to each of the first and second shear directions.

[0239] 23. The method according to any preceding aspect, wherein each measurement comprises:

[0240] irradiating the plurality of object plane patterning devices with a first radiation;

[0241] forming an image of each of the plurality of object plane patterning devices on a patterning device of a different one of the plurality of image plane sensors;

[0242] at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors scans through a plurality of locations separated in direction to produce an oscillating phase scan signal for each of the plurality of sampling locations; and

[0243] The phases of harmonics of the oscillating signal at a plurality of locations on the radiation detector are determined.

[0244] 24. A method according to aspect 23, wherein the harmonic of the oscillating signal is equal to the difference of the aberration map at each of the multiple positions on the radiation detector between a pair of positions in the pupil plane of the projection system, and the harmonic of the oscillating signal is the first harmonic.

[0245] 25. A method according to clause 24, wherein the pair of positions in a pupil plane of the projection system are separated in a shearing direction by a shearing distance corresponding to twice the distance in the pupil plane between two adjacent first diffracted beams.

[0246] 26. A computer-readable medium carrying a computer program, the computer program comprising computer-readable instructions configured to cause a computer to perform the method according to any one of aspects 1 to 25.

[0247] 27. A computer device comprising:

[0248] a memory storing processor-readable instructions; and

[0249] A processor arranged to read and execute instructions stored in the memory, wherein the processor-readable instructions include instructions arranged to control the computer to perform the method according to any one of aspects 1 to 25.

[0250] 28. A measurement system for determining a physical quantity, the measurement system comprising:

[0251] a plurality of object plane patterning devices, the plurality of object plane patterning devices 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;

[0252] an illumination system arranged to illuminate the plurality of object plane patterning devices with radiation so as to form a plurality of first diffraction beams, the first diffraction beam from each patterning device of the first set of patterning devices being separated in a modulation direction corresponding to a first orientation of the grating and the first diffraction beam from each patterning device of the second set of patterning devices being separated in a modulation direction corresponding to a second orientation of the grating;

[0253] an image plane sensor comprising a patterning device and a radiation detector;

[0254] the illumination system being configured to form an image of each of the plurality of object plane patterning devices on a patterning device of the image plane sensor so as to form a plurality of second diffracted beams from each of the first diffracted beams;

[0255] a positioning device configured to move the plurality of object plane patterning devices in a first direction or a second direction; and

[0256] A controller configured to perform the method according to any one of aspects 1 to 25.

[0257] 29. A measurement system for determining a physical quantity, the measurement system comprising:

[0258] a plurality of object plane patterning devices, the plurality of object plane patterning devices 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;

[0259] an illumination system arranged to illuminate the plurality of object plane patterning devices with radiation so as to form a plurality of first diffraction beams, the first diffraction beam from each patterning device of the first set of patterning devices being separated in a modulation direction corresponding to the first orientation and the first diffraction beam from each patterning device of the second set of patterning devices being separated in a modulation direction corresponding to the second orientation;

[0260] a plurality of image plane sensors, each image plane sensor including a patterning device and each image plane sensor in communication with a radiation detector;

[0261] the illumination system being configured to form an image of each of the plurality of object plane patterning devices on a patterning device of the image plane sensor so as to form a plurality of second diffracted beams from each of the first diffracted beams;

[0262] 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

[0263] A controller configured to execute the method according to any one of aspects 1 to 25.

[0264] 30. A lithographic apparatus comprising a measurement system according to clause 28 or 29.

[0265] 31. A metrology tool comprising a measurement system according to aspect 28 or 29.

Claims

1. A method of determining a physical quantity, the method using a sensor system configured to sample a plurality of locations, wherein: Sampling at each location uses an object plane patterning device and an image plane sensor, wherein each object plane patterning device comprises a first portion and a second portion, the first portion being different from the second portion, and wherein the first portion and the second portion of at least one of the object plane patterning devices are transposed relative to the first portion and the second portion of the other object plane patterning devices; and Wherein, the method comprises: using a first portion of each object plane patterning device and performing a first measurement in a first direction to generate a first data set; using a second portion of each object plane patterning device and performing a second measurement in the first direction to generate a second data set; using the first portion of each object plane patterning device and performing a third measurement in a second direction different from the first direction to produce a third data set; using a second portion of each object plane patterning device and performing a fourth measurement in the second direction to generate a fourth data set; and The first data set, the second data set, the third data set, and the fourth data set are combined to determine the physical quantity.

2. The method according to claim 1, wherein: Radiation having a common noise source is incident on each object plane patterning device and image plane sensor to generate the first data set, the second data set, the third data set, and / or the fourth data set.

3. A method according to any preceding claim, wherein: The object plane patterning device comprises a grating.

4. A method according to any preceding claim, wherein: The orientation of the first portion of the object plane patterning device is orthogonal to the orientation of the second portion.

5. A method according to any preceding claim, wherein: The first orientation of the at least one object plane patterning device is orthogonal to the second orientations of the other object plane patterning devices.

6. A method according to any preceding claim, wherein: The first measurement, the second measurement, the third measurement, and the fourth measurement form part of a shearing interferometry process.

7. A method according to any preceding claim, wherein: The first portion has a first shear direction and the second portion has a second shear direction, the second shear direction being different from the first shear direction.

8. The method according to claim 7, wherein: The first direction includes a component parallel to the first shear direction and a component parallel to the second shear direction; And wherein the second direction includes a component parallel to the first shear direction and a component parallel to the second shear direction.

9. The method according to claim 8, wherein: One of the first and second directions makes the sign of the component of the one direction parallel to the first shear direction opposite to the sign of the component of the one direction parallel to the second shear direction, and the other of the first and second directions makes the sign of the component of the other direction parallel to the first shear direction the same as the sign of the component of the other direction parallel to the second shear direction.

10. A method according to any preceding claim, wherein: The image sensor includes a plurality of image sensors.

11. A method according to any preceding claim, wherein: The image plane sensor comprises: a second patterning device positionable to receive radiation from the plurality of object plane patterning devices; and A detector is arranged to receive radiation from the second patterning device.

12. The method according to claim 10, wherein: Each image plane sensor of the plurality of image plane sensors comprises: a second patterning device positionable to receive radiation from a corresponding object plane patterning device of the plurality of object plane patterning devices; and Wherein, the plurality of image plane sensors comprises detectors arranged to receive radiation from the plurality of second patterning devices.

13. A method according to any preceding claim, wherein: Combining the first data set, the second data set, the third data set, and the fourth data set to determine the physical quantity includes: combining the first data set with the second data set to determine at least one first physical parameter for each sampled location; combining the third data set with the fourth data set to determine at least one second physical parameter for each sampled location; and The determined first physical parameter for each sampled position is combined with the determined second physical parameter for each sampled position to form an output correction physical parameter for each sampled position so as to at least partially correct errors in the determined first physical parameter and the determined second physical parameter caused by intensity variations of radiation used to generate the first data set, the second data set, the third data set, and / or the fourth data set.

14. A method according to any preceding claim, wherein: The physical quantity comprises one or more aberrations of the projection system.

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

16. The method according to claim 15, wherein: The step of combining the first data set with the second data set to determine one or more aberrations further comprises: determining a first wavefront tilt coefficient in the first direction; and The step of combining the second data set and the fourth data set to determine one or more aberrations further comprises: determining a second wavefront tilt coefficient in the first direction; and The determined first wavefront tilt coefficient in the first direction for each sampled position and the determined second wavefront tilt coefficient in the first direction for each sampled position are combined to form an output wavefront tilt coefficient in the first direction for each sampled position so as to at least partially correct 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 radiation used to generate the first data set and the second data set.

17. The method according to claim 16, wherein: 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 comprises: Perform a least squares fit to simultaneously minimize: the root mean square for each sampling position of the difference between: (a) the determined first wavefront tilt coefficient in the first direction; and (b) the sum of the output wavefront tilt coefficient in the first direction and a first constant; and The root mean square of the difference between the following items for each sampling position: (a) the determined second wavefront tilt coefficient in the first direction; and (b) for a first portion of the grating of the object plane pattern forming device, the sum of the product of the output wavefront tilt coefficient in the first direction and a second constant multiplied by +1, and for a second portion of the grating of the object plane pattern forming device, the sum of the product of the output wavefront tilt coefficient in the first direction and the second constant multiplied by -1.

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 physical parameter, the second physical parameter, the third physical parameter, and the fourth physical parameter correspond to a first intensity value, a second intensity value, a third intensity value, and a fourth intensity value, respectively.

20. A method according to any preceding claim, wherein: Combining the first data set, the second data set, the third data set, and the fourth data set to determine the physical quantity includes: combining the first data set with the second data set to determine, for each sampling position, a first wavefront tilt coefficient in the second direction; combining the third data set with the fourth data set to determine, for each sampling position, a second wavefront tilt coefficient in the second direction; and The determined first wavefront tilt coefficient in the second direction for each sampling position and the determined second wavefront tilt coefficient in the second direction for each sampling position are combined to form an output wavefront tilt coefficient in the second direction for each sampling position so as to at least partially correct 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 changes of radiation used to generate the second data set and the fourth data set.

21. The method according to claim 20, wherein: Combining the determined first wavefront tilt coefficient in the second direction for each sampling position 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 comprises: Perform a least squares fit to simultaneously minimize: the root mean square of the difference for a plurality of sampling positions between: (a) the determined first wavefront tilt coefficient in the second direction; and (b) the output wavefront tilt coefficient in the second direction plus a third constant; and The root mean square of the difference between the following items for multiple sampling positions: (a) the determined second wavefront tilt coefficient in the second direction; and (b) for a first portion of the grating of the object plane pattern forming device, the sum of the product of the output wavefront tilt coefficient in the second direction and a fourth constant multiplied by +1, and for a second portion of the grating of the object plane pattern forming device, the sum of the product of the output wavefront tilt coefficient in the second direction and a fourth constant multiplied by -1.

22. A method according to any preceding claim, wherein: The first direction and the second direction are aligned at 45° relative to each of the first shear direction and the second shear direction, respectively.

23. A method according to any preceding claim, wherein: 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 patterning device of a different one of the plurality of image plane sensors; at least one of the plurality of object plane patterning devices or the corresponding plurality of image plane sensors scans through a plurality of locations separated in direction to produce an oscillating phase scan signal for each of the plurality of sampling locations; and The phases of harmonics of the oscillating signal at a plurality of locations on the radiation detector are determined.

24. The method according to claim 23, wherein: The harmonic of the oscillating signal is equal to the difference of the aberration map at each of the plurality of positions on the radiation detector between a pair of positions in a pupil plane of the projection system, the harmonic of the oscillating signal being a first harmonic.

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

26. A computer-readable medium carrying a computer program comprising computer-readable instructions configured to cause a computer to perform the method according to any one of claims 1 to 25.

27. A computer device comprising: a memory storing processor-readable instructions; and A processor arranged to read and execute instructions stored in the memory, wherein the processor-readable instructions include instructions arranged to control the computer to perform the method according to any one of claims 1 to 25.

28. A measurement system for determining a physical quantity, the measurement system comprising: a plurality of object plane patterning devices, the plurality of object plane patterning devices 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; an illumination system arranged to illuminate the plurality of object plane patterning devices with radiation so as to form a plurality of first diffraction beams, the first diffraction beam from each patterning device of the first set of patterning devices being separated in a modulation direction corresponding to a first orientation of the grating and the first diffraction beam from each patterning device of the second set of patterning devices being separated in a modulation direction corresponding to a second orientation of the grating; an image plane sensor comprising a patterning device and a radiation detector; the illumination system being configured to form an image of each of the plurality of object plane patterning devices on a patterning device of the image plane sensor so as 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 perform the method according to any one of claims 1 to 25.

29. A measurement system for determining a physical quantity, the measurement system comprising: a plurality of object plane patterning devices, the plurality of object plane patterning devices 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; an illumination system arranged to illuminate the plurality of object plane patterning devices with radiation so as to form a plurality of first diffraction beams, the first diffraction beam from each patterning device of the first set of patterning devices being separated in a modulation direction corresponding to the first orientation and the first diffraction beam from each patterning device of the second set of patterning devices being separated in a modulation direction corresponding to the second orientation; a plurality of image plane sensors, each image plane sensor including a patterning device and each image plane sensor in communication with a radiation detector; the illumination system being configured to form an image of each of the plurality of object plane patterning devices on a patterning device of the image plane sensor so as 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 perform the method according to any one of claims 1 to 25.

30. A lithographic apparatus comprising a measurement system according to claim 28 or 29.

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

Images