WO 2022/100930
`
`PCT/EP2021/077390
`
`MEASUREMENT SYSTEM AND METHOD OF USE
`
`CROSS-REFERENCE TO RELATED APPLICATIONS
`
`[0001]
`
`This application claims priority of EP application 20207351.6 which was filed on
`
`November 13, 2020 and which is incorporated herein in its entirety by reference.
`
`FIELD
`
`[0002]
`
`The present
`
`invention relates to a measurement system and method of use. More
`
`particularly, the method may be for determining optical aberrations for a projection system or measuring
`
`10
`
`alignment.
`
`BACKGROUND
`
`[0003]
`
`A lithographic apparatus is a machine constructed to apply a desired pattern onto a
`
`substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits
`
`15
`
`(ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design
`
`layout” or “design’’) of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material
`
`(resist) provided on a substrate (e.g., a wafer).
`
`[0004]
`
`As semiconductor manufacturing processes continue to advance, the dimensionsofcircuit
`
`elements have continually been reduced while the amount of functional elements, such as transistors,
`
`per device has been steadily increasing over decades, following a trend commonly referred to as
`
`‘Moore’s law’. To keep up with Moore’s law the semiconductor industry is chasing technologies that
`
`enable to create increasingly smaller features. To project a pattern on a substrate a lithographic
`
`apparatus may use electromagnetic radiation. The wavelength ofthis radiation determines the minimum
`
`size of features which are patterned on the substrate. Typical wavelengths currently in use are 365 nm
`
`(i-line), 248 nm, 193 nm and 13.5 nm. A lithographic apparatus, which uses extreme ultraviolet (EUV)
`
`radiation, having a wavelength within a range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, may
`
`be used to form smaller features on a substrate than a lithographic apparatus which uses, for example,
`
`radiation with a wavelength of 193 nm.
`
`[0005]
`
`Radiation that has been patterned by the patterning device is focussed onto the substrate
`
`using a projection system. The projection system may introduce optical aberrations, which cause the
`
`image formed on the substrate to deviate from a desired image (for example a diffraction limited image
`
`of the patterning device). Alignment in a lithographic apparatus is also an important aspect, e.g. to
`
`make sure the desired imageis positioned in the correct position.
`
`[0006]
`
`It may be desirable to provide methods and apparatus for accurately determining such
`
`aberrations caused by a projection system such that
`
`these aberrations can be better controlled.
`
`Furthermore,
`
`it may be desirable to provide methods and apparatus for accurately determining
`
`alignmentin a lithographic apparatus.
`
`25
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`SUMMARY
`
`[0007]
`
`According to a first aspect of the invention, there is provided a measurement system, the
`
`measurement system comprising: a sensor apparatus; an illumination system arranged to illuminate the
`
`sensor apparatus with radiation, the sensor apparatus comprising a patterned region arranged to receive
`
`a radiation beam and to form a plurality of diffraction beams, the diffraction beams being separated in
`
`a shearing direction; the sensor apparatus comprising a radiation detector; wherein the patterned region
`
`is arranged such that at least someof the diffraction beams form interference patterns on the radiation
`
`detector; wherein the sensor apparatus comprises a plurality of patterned regions, and wherein pitches
`
`of the patterned regions are different in adjacent patterned regions.
`
`[0008]
`
`This has an advantage of increasing the amountof data collected in a single measurement.
`
`Advantagcously, signals corresponding to the adjacent patterned regions can be distinguished without
`
`requiring a particular spatial separation between the adjacent patterned regions.
`
`[0009]
`
`The measurement system may be arranged suchthat the interference patterns from adjacent
`
`patterned regionsat least partially overlap at the radiation detector.
`
`[00010]
`
`Thepitches of alternating patterned regions may be the same.
`
`[00011]
`
`The pitches of the adjacent patterned regions may not be even numberinteger multiples.
`
`[00012]
`
`The pitches of the adjacent patterned regions may not be integer multiples.
`
`[00013]
`
`Theplurality of patterned regions may comprise thirteen patterned regions.
`
`[00014]
`
`The plurality of patterned regions may be positioned at odd and even ficld point locations.
`
`[00015]
`
`The plurality of patterned regions may extend in an x direction and in a second direction
`
`orthogonalto the x direction.
`
`[00016]
`
`The measurement system may further comprise: a patterning device; wherein the
`
`illumination system is arranged to illuminate the patterning device with radiation, the patterning device
`
`10
`
`15
`
`20
`
`25
`comprising a first patterned region arrangedto receive the radiation beam and to formaplurality of first
`
`diffraction beams, the first diffraction beams being separated in the shearing direction; wherein the
`
`patterned region of the sensor apparatus comprises a second patterned region; the projection system
`
`being configured to project the first diffraction beams onto the sensor apparatus, the second patterned
`
`region being arranged to receive the first diffraction beams fromthe projection system and to form a
`
`plurality of second diffraction beams from each of the first diffraction beams such that the first and
`
`second patterned regions form a set; wherein the first and second patterned regions in the set are
`
`matched by matching the pitches ofthe first and second patterned regions in the shearing direction such
`that at least some of the second diffraction beams formed from atleast one ofthe first diffraction beams
`
`are spatially coherent with a second diffraction beam formed fromat least one other first diffraction
`
`beam to form interference patterns on the radiation detector; wherein the patterning device comprises a
`
`plurality of first patterned regions and the scnsor apparatus comprisesa plurality of second patterned
`
`regions such that there is a plurality of sets, each set comprising one of the plurality of first patterned
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`regions and one of the plurality of second patterned regions, and wherein the pitches of the first
`
`patterned regions are different in adjacent sets and/or the pitches of the second patterned regions are
`
`different in adjacentsets.
`
`[00017]
`
`The pitches ofthe first patterned regions and the second patterned regionsin at least one of
`
`the plurality of sets may be the same.
`
`[00018]
`
`The measurement system may further comprise a positioning apparatus configured to move
`
`at least one of the patterning device and the sensor apparatus in the shearing direction; and a controller
`
`configured to: control the positioning apparatus so as to moveat least one of the first patterning device
`
`and the sensor apparatus in the shearing direction such that an intensity of radiation received by each
`
`part of the radiation detector varies as a function of the movement in the shearing direction so as to form
`
`oscillating signals corresponding to the different pitches of the first patterned regions in adjacentsets
`
`and/or the different pitches of the second patterned regions in adjacent sects; determine from the radiation
`
`detector phases of harmonics of the oscillating signals at a plurality of posilions on the radiation
`
`detector; and determinea set of coefficients that characterize an aberration mapof the projection system
`
`from the phase of the harmonicsof the oscillating signals at the plurality of positions on the radiation
`detector.
`
`[00019]
`
`Theset of coefficients that characterize the aberration map of the projection system may be
`
`determined by equating the phases of the harmonics of the oscillating signals to a difference in the
`
`aberration map betweenpositions in the pupil plane that are separated in the shearing direction by twice
`
`a shearing distance which corresponds to the distance in the pupil plane between two adjacent first
`
`diffraction beams and solving to find the set of coefficients.
`
`[00020]
`
`Theset of coefficients that characterize the aberration mapof the projection system may be
`
`determined by simultaneously solving constraints for the shearing direction and for a second, orthogonal
`direction.
`
`[00021]
`
`Theplurality of first patterned regions and the plurality of second patterned regions may be
`
`gratings.
`
`[00022]
`
`A lithographic apparatus comprising the measurement system as described above.
`
`[00023]
`
`According to a second aspect of the present invention, there is provided a method for
`
`measurement,
`
`the method comprising:
`
`illuminating a sensor apparatus with radiation, wherein the
`
`sensor apparatus comprises a patterned region arranged to receive at least a portion of the radiation and
`
`to form a plurality of diffraction beams, the diffraction beams being separated in a shearing direction;
`
`wherein the sensor apparatus comprises a radiation detector arranged to receive at least a portion of the
`
`diffraction beams, wherein the patterned region is arranged such that at least some of the diffraction
`
`beams form interference patterns on the radiation detector; wherein the sensor apparatus comprises a
`
`plurality of patterned regions, and wherein pitches of the patterned regions are different in adjacent
`
`patterned regions.
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`[00024]
`
`The method may further comprise: illuminating a patterning device with radiation, wherein
`
`the patterning device comprises a first patterned region arranged to receive at least a portion of the
`
`radiation and to form a plurality of first diffraction beams, the first diffraction beams being separated
`
`in the shearing direction; projecting, with the projection system, at least part of the plurality offirst
`
`diffraction beams onto the sensor apparatus comprising: the patlerned region comprising a second
`
`patterned region arrangedto receive the first diffraction beams from the projection system and to form
`
`a plurality of second diffraction beams from each ofthe first diffraction beams; and a radiation detector
`
`arranged to receive at least a portion of the second diffraction beams, wherein the first and second
`
`patterned regionsin the set are matched by matching the pitches ofthe first and second patterned regions
`
`in the shearing direction such that at least some of the second diffraction beams formed fromat least
`
`one ofthe first diffraction beams are spatially coherent with a second diffraction beam formed from at
`
`Icast onc otherfirst diffraction beam to form interference patterns on the radiation detector; wherein the
`
`patterning device comprises a plurality of first patterned regions and the sensor apparatus comprises a
`
`plurality of second patterned regions such that there is a plurality of sets, each set comprising one of the
`
`plurality of first patterned regions and one of the plurality of second patterned regions, and wherein the
`
`pitches of the first patterned regions are different in adjacent sets and/or the pitches of the second
`
`patterned regions are different in adjacentsets.
`
`[00025]
`
`The method may further comprise moving at least one of the patterning device and the
`
`sensor apparatus in the shearing direction such that an intensity of radiation received by each part of the
`
`radiation detector varics as a function of the movementin the shearing direction so as to form a plurality
`
`of oscillating signals corresponding to the different pitches of the first patterned regions in adjacent sets
`
`and/or the different pitches of the second patterned regions in adjacent sets; determining from the
`
`radiation detector phases of harmonics of the oscillating signals at a plurality of positions on the
`
`radiation detector; and determining a set of coefficients that characterize an aberration map of the
`
`projection system from the phase of the harmonicsof the oscillating signals at the plurality of positions
`
`on the radiation detector.
`
`[00026]
`
`The method may further comprise determining the set of coefficients that characterize the
`
`aberration map of the projection system by equating the phases of the harmonics ofthe oscillating
`
`signals to a difference in the aberration map between positions in the pupil plane that are separated in
`
`the shearing direction by twice a shearing distance which correspondsto the distance in the pupil plane
`
`between two adjacentfirst diffraction beams and solving to find the set of coefficients.
`
`[00027]
`
`The method may further comprise determining the set of coefficients that characterize the
`
`aberration mapof the projection system by simultaneously solving constraints for the shearing direction
`
`and for a second, orthogonal direction.
`
`[00023]
`
`The method may further comprise moving the at least one of the patterning device and the
`
`sensor apparatus in the shearing direction in phase steps in a range of 4-9 to form the plurality of
`
`oscillating signals.
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`[00029]
`
`According to a third aspect of the present invention, there is provided a computer readable
`
`mediumcarrying a computer program comprising computer readable instructions configured to cause
`
`a computer to carry out a method as described above.
`
`[00030]
`
`According to a fourth aspect of the present invention,
`
`there is provided a computer
`
`apparatus comprising: a memory storing processor readable instructions, and a processor arranged to
`
`read and execute instructions stored in said memory, wherein said processor readable instructions
`
`comprise instructions arranged to control the computer to carry out the method as described above.
`
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`10
`
`15
`
`20
`
`[00031]
`
`Embodiments of the invention will now be described, by way of example only, with
`
`reference to the accompanying schematic drawings, in which:
`
`-
`
`-
`
`-
`
`Figure 1 depicts a schematic overvicw of a lithographic apparatus;
`
`Figure 2 is a schematic illustration of a measurement system according to an example;
`
`Figures 3A and 3B are schematic illustrations of a patterning device and a sensor apparatus
`
`which may form part of the measurement system of Figure 2;
`
`-
`
`Figure 4 is a schematic illustration of a measurement system according to an example, the
`
`measurement system comprising a first patterned region and a second patterned region,
`
`the first
`
`patterned region arranged to receive radiation and to form a plurality of first diffraction beams;
`
`-
`
`Figures 5A to 5C each showsa different set of second diffraction beams formed by the second
`
`patterned region of the measurement system shownin Figure 4, that sct of second diffraction beams
`
`having been produced by a different first diffraction beam formed bythe first patierned region;
`
`-
`
`Figure 6A shows the scattering efficiency for a one dimensionaldiffraction grating with a 50%
`
`duty cycle and which may represent the first patterned region of the measurement system shown in
`
`Figure 4;
`
`25
`
`-
`
`Figure 6B showsthe scattering efficiency for a two dimensional diffraction grating of the form
`
`of a checkerboard with a 50% duty cycle and which mayrepresent the second patterned region of the
`
`measurement system shownin Figure 4;
`
`-
`
`Figure 6C shows an interference strength map for the measurement system shown in Figure 4
`
`when employing the first patterned region shown in Figure 6A and the second patterned region shown
`
`in Figure 6B, each of the interference strengths shownrepresenting the second interference beams which
`
`contribute to the first harmonic of the oscillating phase-stepping signal and which have a different
`
`overlap, at the radiation detector, with a circle that represents the numerical aperture of the projection
`
`system PS;
`
`-
`
`Figures 7A, 7B and 7C show the portion of the numerical aperture of the projection system of
`
`the measurement system shown in Figure 4 thatis filled by the three different first diffraction beams
`
`shownin Figure 4;
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`-
`
`Figures 8A-8C show a portion of the radiation detector of the measurement system shown in
`
`Figure 4 which corresponds to the numerical aperture of the projection system of the measurement
`
`system and whichisfilled by three second diffraction beams which originate from thefirst diffraction
`
`beam represented by Figure 7B;
`
`-
`
`Figures 9A-9C show a portion of the radiation detector of the measurement system shown in
`
`Figure 4 which corresponds to the numerical aperture of the projection system of the measurement
`
`system and whichisfilled by three second diffraction beams which originate from the first diffraction
`
`beam represented by Figure 7A;
`
`10
`
`15
`
`20
`
`-
`
`Figures 10A-10C showa portion of the radiation detector of the measurement system shown in
`
`Figure 4 which corresponds to the numerical aperture of the projection system of the measurement
`
`system and whichisfilled by three second diffraction beams which originate from thefirst diffraction
`
`beam represented by Figure 7C;
`
`-
`
`Figure 11A shows a portion of the radiation detector of the measurement system shown in
`
`Figure 4 which corresponds to the numerical aperture of the projection system of the measurement
`
`system and which represents the overlap between the second diffraction beams shown in Figures 8B
`
`and 9A and the overlap between the second diffraction beams shown in Figures 8A and 10B;
`
`-
`
`Figure 11B shows a portion of the radiation detector of the measurement system shown in
`
`Figure 4 which corresponds to the numerical aperture of the projection system of the measurement
`
`system and which represents the overlap between the second diffraction beams shown in Figures 8B
`
`and 10C and the overlap between the second diffraction beams shown in Figures 8C and 9B;
`
`-
`
`Figure 12 is a schematic illustration of a measurement system according to an embodiment of
`
`the invention;
`
`-
`
`Figures 13A and 13B are schematic illustrations of a patterning device and a sensor apparatus
`
`which may form part of the measurement system of Figure 12;
`
`25
`
`-
`
`Figure 14 shows a spatial intensity plot of measurements taken by a measurement system
`
`according to an embodiment of the invention;
`
`-
`
`Figure 15 shows a graph of phase curves of measurements taken by a measurement system
`
`according to an embodimentofthe invention;
`
`-
`
`Figure 16 shows a graph of simulated measurement repeatability (hereinafter referred to as
`
`reproducibility) (repro (nm)) for a measurement system according to an embodimentof the invention;
`
`-
`
`Figure 17 showsa graph of simulated expected position dependence for a measurement system
`
`according to an embodiment of the invention.
`
`DETAILED DESCRIPTION
`
`[00032]
`
`In the present document, the terms “radiation” and “beam” are used to encompass all types
`
`of clectromagnetic radiation, including ultraviolet radiation (c.g. with a wavelength of 365, 248, 193,
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`157 or 126 nm) and EUV(extremeultra-violet radiation, e.g. having a wavelength in the range of about
`
`5-100 nm).
`
`[00033] The term “reticle’’, “mask” or “patterning device” as employed in this text may be broadly
`
`interpreted as referring to a generic patterning device that can be used to endow an incomingradiation
`
`beamwith a patierned cross-section, corresponding to a pattern thal is to be created in a target portion
`
`of the substrate. The term “light valve” can also be used in this context. Besides the classic mask
`
`(transmissive or reflective, binary, phase-shifting, hybrid, etc.), examples of other such patterning
`
`devices include a programmable mirror array and a programmable LCD array.
`
`[00034]
`
`Figure 1 schematically depicts a lithographic apparatus LA. The lithographic apparatus LA
`
`includes an illumination system (also referred to as illuminator) IL configured to condition a radiation
`
`beam B (e.g., UV radiation, DUV radiation or EUV radiation), a mask support (e.g., a mask table) MT
`
`constructed to support a patterning device (c.g., a mask) MA and connectedto a first positioner PM
`
`configured to accurately posilion the pallerning device MA in accordance with certain parameters, a
`
`substrate support(e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist coated wafer) W
`
`and connected to a second positioner PW configured to accurately position the substrate support in
`
`accordance with certain parameters, and a projection system (e.g., a refractive projection lens system)
`
`PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a
`
`target portion C (e.g., comprising one or more dies) of the substrate W.
`
`[00035]
`
`In operation, the illumination system IL receives a radiation beam from a radiation source
`
`SO, c.g. via a beam delivery system BD. The illumination system IL may include various types of
`
`optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and/or other
`
`types of optical components, or any combination thereof, for directing, shaping, and/or controlling
`
`radiation. The illuminator IL may be used to condition the radiation beam B to have a desired spatial
`
`and angular intensity distribution in its cross section at a plane of the patterning device MA.
`
`[00036]
`
`The term “projection system” PS used herein should be broadly interpreted as
`
`encompassing various types of projection system,
`
`including refractive,
`
`reflective, catadioptric,
`
`anamorphic, magnetic, electromagnetic and/or electrostatic optical systems, or any combination thereof,
`
`as appropriate for the exposure radiation being used, and/or for other factors such as the use of an
`
`immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be
`
`considered as synonymouswith the more general term “projection system” PS.
`
`[00037]
`
`Thelithographic apparatus LA may beof a type wherein at least a portion of the substrate
`
`may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space
`
`between the projection system PS and the substrate W — which is also referred to as immersion
`
`lithography. More information on immersion techniquesis given in US6952253, whichis incorporated
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`herein by reference.
`
`[00038]
`
`The lithographic apparatus LA may also be of a type having two or morc substrate supports
`
`WT(also named “dual stage”). In such “multiple stage’? machine, the substrate supports WT may be
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`used in parallel, and/or steps in preparation of a subsequent exposure of the substrate W may be carried
`
`out on the substrate W located on one of the substrate support WT while another substrate W on the
`
`other substrate support WT is being used for exposing a pattern on the other substrate W.
`
`[00039]
`
`In addition to the substrate support WT, the lithographic apparatus LA may comprise a
`
`Measurement stage. The measurement stage is arranged to hold a sensor and/or a cleaning device. The
`
`sensor may be arranged to measure a property of the projection system PS or a property of the radiation
`
`beam B. The measurement stage may hold multiple sensors. The cleaning device may be arranged to
`
`clean part of the lithographic apparatus, for example a part of the projection system PS or a part of a
`
`system that provides the immersion liquid. The measurement stage may move beneath the projection
`
`system PS when the substrate support WT is away from the projection system PS.
`
`[00040]
`
`In operation, the radiation beam B is incident on the patterning device, e.g. mask, MA
`
`which is held on the mask support MT, and is patterned by the pattern (design layout) present on
`
`patterning device MA. Having traversed the mask MA,
`
`the radiation beam B passes through the
`
`projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid
`
`of the second positioner PW and a position measurement system IF, the substrate support WT can be
`
`moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B
`
`at a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor
`
`(whichis not explicitly depicted in Figure 1) may be used to accurately position the patterning device
`
`MAwith respect to the path of the radiation beam B. Patterning device MA and substrate W may be
`
`aligned using mask alignment marks M1, M2 and substrate alignment marks Pl, P2. Although the
`
`substrate alignment marks Pl, P2 as illustrated occupy dedicated target portions, they may be located
`
`in spaces betweentarget portions. Substrate alignment marks P1, P2 are knownasscribe-lane alignment
`
`marks when these are located between the target portions C.
`
`[00041] To clarify the invention, a Cartesian coordinate system is used. The Cartesian coordinate
`
`system has three axes, i.e., an x-axis, a y-axis and a z-axis. Each ofthe three axes is orthogonal to the
`
`other two axes. A rotation around the x-axis is referred to as an Rx-rotation. A rotation aroundthe y-
`
`axis is referred to as an Ry-rotation. A rotation around about the z-axis is referred to as an Rz-rotation.
`
`The x-axis and the y-axis define a horizontal plane, whereas the z-axis is in a vertical direction. The
`
`Cartesian coordinate systemis not limiting the invention and is used for clarification only. Instead,
`
`another coordinate system, such as a cylindrical coordinate system, may be used to clarify the invention.
`
`The orientation of the Cartesian coordinate system may be different, for example, such that the z-axis
`
`has a componentalong the horizontal plane.
`
`[00042]
`
`In general, the projection system PS has an optical transfer function which may be non-
`
`uniform, which can affect the pattern which is imaged on the substrate W. For unpolarized radiation
`
`such effects can be fairly well described by two scalar maps, which describe the transmission
`
`(apodization) and relative phase (aberration) of radiation cxiting the projection system PS as a function
`
`of position in a pupil plane thereof. These scalar maps, which may bereferred to as the transmission
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`map andthe relative phase map, may be expressed as a linear combination of a complete set of basis
`
`functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal
`
`polynomials defined on a unit circle. A determination of each scalar map may involve determining the
`
`coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the
`
`Zermike coefficients may be obtained from a measured scalar map by calculating the inner product of
`
`the measured scalar map with each Zernike polynomial in turn and dividing this by the square of the
`
`norm of that Zernike polynomial.
`
`In the following, unless stated otherwise, any reference to Zernike
`
`coefficients will be understood to mean the Zernike coefficients of a relative phase map (also referred
`
`to herein as an aberration map).
`
`It will be appreciated that in alternative examples other sets of basis
`
`functions may be used. For example some examples may use Tatian Zernike polynomials, for example
`
`for obscured aperture systems.
`
`[00043]
`
`The wavefront abcrration map represents the distortions of the wavefront of light
`
`approaching a point in an image plane of the projection system PS from a spherical wavefront (as a
`
`function of position in the pupil plane or, alternatively, the angle at which radiation approaches the
`
`imageplane of the projection system PS). As discussed, this wavefront aberration map W (x,y) may
`
`be expressed as a linear combination of Zernike polynomials:
`
`Wy) = > Cn * Zn(X,Y)
`
`n
`
`(1)
`
`where x and y are coordinates in the pupil plane, Z,,(x, y) is the nth Zernike polynomial and c, is a
`
`coefficient.
`
`It will be appreciated that in the following, Zernike polynomials and coefficients are
`
`labelled with an index which is commonly referred to as a Noll index. Therefore, Z,,(x,y) is the
`
`Zernike polynomial having a Noll index of n and c, is a coefficient having a Noll index of n. The
`
`wavefront aberration map may then be characterized by the set of coefficients c, in such an expansion,
`
`which maybe referred to as Zernike coefficients.
`
`[00044]
`
`It will be appreciated that only a finite number of Zernike orders are taken into account.
`
`Different Zernike coefficients of the phase map may provide information about different forms of
`
`aberration which are caused by the projection system PS. The Zernike coefficient having a Noll index
`
`of | may be referred to as the first Zernike coefficient, the Zernike coefficient having a Noll index of 2
`
`may be referred to as the second Zernike cocfficicnt and so on.
`
`[00045]
`
`Thefirst Zernike coefficient relates to a mean value (which may be referred to as a piston)
`
`of a measured wavefront. The first Zernike coefficient may be irrelevant to the performance of the
`
`projection system PS and as such may not be determined using the methods described herein. The
`second Zernike coefficient relates to the tilt of a measured wavefront in the x-direction. The tilt of a
`
`wavelront in the x-direction is equivalent to a placement in the x-direction. The third Zernike
`
`coefficient relates to the tilt of a measured wavefront in the y-direction. The tilt of a wavefront in the
`
`10
`
`15
`
`20
`
`25
`
`30
`
`

`

`WO 2022/100930
`
`PCT/EP2021/077390
`
`10
`
`y-direction is equivalent to a placement in the y-direction. The fourth Zernike coefficient relates to a
`
`defocus of a measured wavefront. The fourth Zernike coefficient is equivalent to a placement in the z-
`
`direction. Higher order Zernike coefficients relate to other forms of aberration which are caused by the
`
`projection system (e.g. astigmatism, coma, spherical aberrations and other effects).
`
`[00046]
`
`Throughout this description the term “aberrations” should be intended to includeall forms
`
`of deviation of a wavefront from a perfect spherical wavefront. That is, the term “aberrations” may
`
`relate to the placement of an image(e.g. the second, third and fourth Zernike coefficients) and/or to
`
`higher order aberrations such as those which relate to Zernike coefficients having a Noll index of 5 or
`
`more. Furthermore, any reference to an aberration map for a projection system may includeall forms
`
`of deviation of a wavefront froma perfect spherical wavefront, including those due to image placement.
`
`[00047]
`
`The transmission map and the relative phase mapare field and system dependent. Thatis,
`
`in gencral, cach projection system PS will have a different Zermike expansion for cach ficld point (i.c.
`
`for each spatial location in its image plane).
`
`[00048]
`
`Aswill be described in further detail below, the relative phase of the projection system PS
`
`in its pupil plane may be determined by projecting radiation from an object plane of the projection
`
`system PS (i.e. the plane of the patterning device MA), through the projection system PS and using a
`
`shearing interferometer to measure a wavefront (i.e. a locus of points with the same phase). The
`
`shearing interferometer may comprise a diffraction grating, for example a two dimensionaldiffraction
`
`grating, in an image plane ofthe projection system (i.e. the substrate table WT) and a detector arranged
`
`to detect an interference pattern in a plane that is conjugate to a pupil plane of the projection system PS.
`
`[00049]
`
`The projection system PS comprises a plurality of optical elements (including lenses). The
`
`projection system PS may include a number of lenses (e.g. one,
`
`two, six or eight lenses). The
`
`lithographic apparatus LA further comprises adjusting means PA for adjusting these optical elements
`
`so as to correct for aberrations (any type of phase variation across the pupil plane throughoutthe field).
`
`To achieve this, the adjusting means PA may be operable to manipulate optical elements within the
`
`projection system PS in one or more different ways. The projection system may have a co-ordinate
`
`system wherein its optical axis extends in the z direction (it will be appreciated that the direction of this
`
`z axis changes along the optical path through the projection system, for example at each lens or optical
`
`element). The adjusting means PA may be operable to do any combination of the following: displace
`
`one or more optical elements; tilt one or more optical elements; and/or deform one or moreoptical
`
`elements. Displacement of optical elements may be in any direction (x, y, z or a combination thereof).
`
`Tilting of optical elementsis typically out of a plane perpendicular to the optical axis, by rotating about