Metrology method, system and lithographic apparatus

Abstract

Disclosed is a method of determining a position reference for an alignment measurement of an alignment mark. The method comprises obtaining component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement; obtaining weights for the component position data, the weights being determined to minimize variance of an estimator comprising said weights and the component position data; and determining said position reference from a combination of said weights and the component position data.

Description

METROLOGY METHOD, SYSTEM AND LITHOGRAPHIC APPARATUSCROS REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U. S. Application No. 63 / 769,392, filed March 10, 2025, and which is incorporated herein in its entirety by reference.FIELD

[0002] The present disclosure relates to metrology systems, for example, an alignment system for measuring alignment mark positions in lithographic apparatuses and systems.BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which can be a mask or a reticle, can be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiationsensitive material (photoresist or simply “resist”) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatuses include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the target portions parallel or anti-parallel to this scanning direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

[0004] During lithographic operation, different processing steps can entail different layers to be sequentially formed on the substrate. Accordingly, it may be necessary to position the substrate relative to prior patterns formed thereon with a high degree of accuracy. Generally, alignment marks are placed on the substrate to be aligned and are located with reference to a second object. A lithographic apparatus can use an alignment apparatus for detecting positions of the alignment marks and for aligning the substrate using the alignment marks to ensure accurate exposure from a mask. Misalignment between the alignment marks at two different layers is measured as overlay error.

[0005] In some metrology applications, such as in position metrology using alignment sensors, a complementary stage position monitoring (SPM) sub-system which operates complementarily with the alignment sensor. Such a SPM subsystem monitors the position difference between the stage (a wafer stage / substrate stage and / or reticle stage) and the sensor and determines a correction for positioningand / or movement of the stage. Such a SPM subsystem could monitor the position of the stage, the position of the sensor (or any particular component of the sensor) and any combination thereof.

[0006] It is desirable to improve metrology, e.g., in terms of accuracy, using such a stage position monitoring sub- system.SUMMARY

[0007] In a first aspect of the invention there is provided a method of determining a position reference for an alignment measurement of an alignment mark, the method comprising: obtaining component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement; obtaining weights for the component position data, the weights being determined to minimize variance of an estimator comprising said weights and the component position data; and determining said position reference from a combination of said weights and the component position data.

[0008] In a second aspect of the invention there is provided a method of determining weights for applying to component position data to obtain a position reference for an alignment measurement of an alignment mark, said component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement, the method comprising: obtaining training data relating to vibrations of the at least one component; and determining the weights from covariances of said training data.

[0009] Further features of various aspects of the present disclosure are described in detail below with reference to the accompanying drawings. It is noted that the present disclosure is not limited to the specific aspects described herein. Such aspects are presented herein for illustrative purposes only. Additional aspects will be apparent to those skilled in the relevant art(s) based on the teachings contained herein.BRIEF DESCRIPTION OF THE DRAWINGS / FIGURES

[0010] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the present disclosure and, together with the description, further serve to explain the principles of the present disclosure and to enable those skilled in the relevant art(s) to make and use aspects described herein.

[0011] Figure 1A shows a reflective lithographic apparatus, according to some aspects;

[0012] Figure 1B shows a transmissive lithographic apparatus, according to some aspects;

[0013] Figure 2 shows more details of a reflective lithographic apparatus, according to some aspects;

[0014] Figure 3 shows a lithographic cell, according to some aspects;

[0015] Figures 4A and 4B are schematic illustrations of metrology apparatuses;

[0016] Figure 5 is a simplified schematic illustration of an alignment metrology system comprising an substrate stage position metrology subsystem and an alignment sensor position metrology subsystem;

[0017] Figure 6 is a flow diagram of a known method for determining an aligned position value using the alignment metrology system of Figure 5;

[0018] Figure 7 is a flow diagram of an example method for determining an aligned position value using the alignment metrology system of Figure 5 according to concepts disclosed herein; and

[0019] Figure 8 is a flow diagram of an example method for determining weights for the method described by Figure 7 according to concepts disclosed herein.

[0020] The features of the present disclosure will become more apparent from the detailed description set forth below when taken in conjunction with the drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and / or structurally similar elements. Additionally, generally, the leftmost digit(s) of a reference number identifies the drawing in which the reference number first appears. Unless otherwise indicated, the drawings provided throughout the disclosure should not be interpreted as to-scale drawings.DETAILED DESCRIPTION

[0021] The aspects described herein, and references in the specification to “one aspect,” “an aspect,” “an exemplary aspect,” “an example aspect,” etc., indicate that the aspects described can include a particular feature, structure, or characteristic, but every aspect may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same aspect. Further, when a particular feature, structure, or characteristic is described in connection with an aspect, it is understood that it is within the knowledge of those skilled in the art to effect such feature, structure, or characteristic in connection with other aspects whether or not explicitly described.

[0022] Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “on,” “upper” and the like, can be used herein for ease of description to describe one element or feature’s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus can be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein can likewise be interpreted accordingly.

[0023] The terms “about,” “approximately,” or the like can be used herein to indicate the value of a given quantity that can vary based on a particular technology. Based on the particular technology, the terms “about,” “approximately,” or the like can indicate a value of a given quantity that varies within, for example, 10-30% of the value (e.g., ±10%, ±20%, or ±30% of the value).

[0024] Aspects of the present disclosure can be implemented in hardware, firmware, software, or any combination thereof. Aspects of the disclosure can also be implemented as instructions stored on a computer-readable medium, which can be read and executed by one or more processors. A machine-readable medium can include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine -readable medium can include readonly memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Furthermore, firmware, software, routines, and / or instructions can be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. The term “machine -readable medium” can be interchangeable with similar terms, for example, “computer program product,” “computer-readable medium,” “non-transitory computer-readable medium,” or the like. The term “non-transitory” can be used herein to characterize one or more forms of computer readable media except for a transitory, propagating signal.

[0025] Before describing such aspects in more detail, however, it is instructive to present an example environment in which aspects of the present disclosure can be implemented.

[0026] Example lithographic systems

[0027] FIGS. 1A and 1B show a lithographic apparatus 100 and a lithographic apparatus 100’, respectively, in which aspects of the present disclosure can be implemented. Lithographic apparatus 100 and lithographic apparatus 100’ each include the following: an illumination system (illuminator) IL configured to condition a radiation beam B (for example, deep ultra violet or extreme ultra violet radiation); a support structure (for example, a mask table) MT configured to support a patterning device (for example, a mask, a reticle, or a dynamic patterning device) MA and connected to a first positioner PM configured to accurately position the patterning device MA; and, a substrate table (for example, a wafer table) WT configured to hold a substrate (for example, a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate W. Lithographic apparatus 100 and 100’ also have a projection system PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion (for example, comprising one or more dies) C of the substrate W. In lithographic apparatus 100, the patterning device MA and the projection system PS are reflective. In lithographic apparatus 100’, the patterning device MA and the projection system PS are transmissive.

[0028] The illumination system IL can include various types of optical components, such as refractive, reflective, catadioptric, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof, for directing, shaping, or controlling the radiation beam B.

[0029] The support structure MT holds the patterning device MA in a manner that depends on the orientation of the patterning device MA with respect to a reference frame, the design of at least one of the lithographic apparatus 100 and 100’, and other conditions, such as whether or not the patterning device MA is held in a vacuum environment. The support structure MT can use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterning device MA. The support structure MT can be a frame or a table, for example, which can be fixed or movable. By using sensors, the supportstructure MT can ensure that the patterning device MA is at a desired position, for example, with respect to the projection system PS.

[0030] The term “patterning device” MA should be broadly interpreted as referring to any device that can be used to impart a radiation beam B with a pattern in its cross-section, such as to create a pattern in the target portion C of the substrate W. The pattern imparted to the radiation beam B can correspond to a particular functional layer in a device being created in the target portion C to form an integrated circuit.

[0031] The patterning device MA can be transmissive (as in lithographic apparatus 100’ of Figure IB) or reflective (as in lithographic apparatus 100 of Figure 1A). Examples of patterning devices MA include reticles, masks, programmable mirror arrays, or programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase shift, or attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam B, which is reflected by a matrix of small mirrors.

[0032] The term “projection system” PS can encompass any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors, such as the use of an immersion liquid on the substrate W or the use of a vacuum. A vacuum environment can be used for EUV or electron beam radiation since other gases can absorb too much radiation or electrons. A vacuum environment can therefore be provided to the whole beam path with the aid of a vacuum wall and vacuum pumps.

[0033] Lithographic apparatus 100 and / or lithographic apparatus 100’ can be of a type having two (dual stage) or more substrate tables WT (and / or two or more mask tables). In such “multiple stage” machines, the additional substrate tables WT can be used in parallel, or preparatory steps can be carried out on one or more tables while one or more other substrate tables WT are being used for exposure. In some situations, the additional table may not be a substrate table WT.

[0034] The lithographic apparatus can also be of a type wherein at least a portion of the substrate can be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system and the substrate. An immersion liquid can also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid. For example, a liquid can be located between the projection system and the substrate during exposure.

[0035] Referring to FIGS. 1A and 1B, the illuminator IL receives a radiation beam from a radiation source SO. The source SO and the lithographic apparatus 100, 100’ can be separate physical entities,for example, when the source SO is an excimer laser. In such cases, the source SO is not considered to form part of the lithographic apparatus 100 or 100’, and the radiation beam B passes from the source SO to the illuminator IL with the aid of a beam delivery system BD (in Figure 1B) including, for example, suitable directing mirrors and / or a beam expander. In other cases, the source SO can be an integral part of the lithographic apparatus 100, 100’, for example, when the source SO is a mercury lamp. A radiation system can comprise the source SO, the illuminator IL, and / or the beam delivery system BD.

[0036] The illuminator IL can include an adjuster AD (in Figure 1B) for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and / or inner radial extent (commonly referred to as “o-outer” and “o-inner,” respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL can comprise various other components (in Figure 1B), such as an integrator IN and a condenser CO. The illuminator IL can be used to condition the radiation beam B to have a desired uniformity and intensity distribution in its cross section.

[0037] Referring to Figure 1A, the radiation beam B is incident on the patterning device (for example, mask) MA, which is held on the support structure (for example, mask table) MT, and is patterned by the patterning device MA. In lithographic apparatus 100, the radiation beam B is reflected from the patterning device (for example, mask) MA. After being reflected from the patterning device (for example, mask) MA, the radiation beam B passes through the projection system PS, which focuses the radiation beam B onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF2 (for example, an interferometric device, linear encoder, or capacitive sensor), the substrate table WT can be moved accurately (for example, so as to position different target portions C in the path of the radiation beam B). Similarly, the first positioner PM and another position sensor IF1 can be used to accurately position the patterning device (for example, mask) MA with respect to the path of the radiation beam B. Patterning device (for example, mask) MA and substrate W can be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[0038] Referring to Figure 1B, the radiation beam B is incident on the patterning device (for example, mask MA), which is held on the support structure (for example, mask table MT), and is patterned by the patterning device. 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. The projection system has a pupil conjugate PPU to an illumination system pupil IPU. Portions of radiation emanate from the intensity distribution at the illumination system pupil IPU and traverse a mask pattern without being affected by diffraction at the mask pattern and create an image of the intensity distribution at the illumination system pupil IPU.

[0039] The projection system PS projects an image of the mask pattern MP, where the image is formed by diffracted beams produced from the mark pattern MP by radiation from the intensity distribution, onto a photoresist layer coated on the substrate W. For example, the mask pattern MP can include an array of lines and spaces. A diffraction of radiation at the array and different from zeroth orderdiffraction generates diverted diffracted beams with a change of direction in a direction perpendicular to the lines. Undiffracted beams (i.e., so-called zeroth order diffracted beams) traverse the pattern without any change in propagation direction. The zeroth order diffracted beams traverse an upper lens or upper lens group of the projection system PS, upstream of the pupil conjugate PPU of the projection system PS, to reach the pupil conjugate PPU. The portion of the intensity distribution in the plane of the pupil conjugate PPU and associated with the zeroth order diffracted beams is an image of the intensity distribution in the illumination system pupil IPU of the illumination system IL. The aperture device PD, for example, is disposed at or substantially at a plane that includes the pupil conjugate PPU of the projection system PS.

[0040] The projection system PS is arranged to capture (e.g., using a lens or lens group L) the zeroth order diffracted beams, first order diffracted beams, and / or higher order diffracted beams (not shown). In some aspects, dipole illumination for imaging line patterns extending in a direction perpendicular to a line can be used to utilize the resolution enhancement effect of dipole illumination. For example, first-order diffracted beams interfere with corresponding zeroth-order diffracted beams at the level of the wafer W to create an image of the line pattern MP at highest possible resolution and process window (i.e., usable depth of focus in combination with tolerable exposure dose deviations). In some aspects, astigmatism aberration can be reduced by providing radiation poles (not shown) in opposite quadrants of the illumination system pupil IPU. Further, in some aspects, astigmatism aberration can be reduced by blocking the zeroth order beams in the pupil conjugate PPU of the projection system associated with radiation poles in opposite quadrants. This is described in more detail in US 7,511,799 B2, issued Mar.31, 2009, which is incorporated by reference herein in its entirety.

[0041] With the aid of the second positioner PW and position sensor IFD (for example, an interferometric device, linear encoder, or capacitive sensor), the substrate table WT can be moved accurately (for example, so as to position different target portions C in the path of the radiation beam B). Similarly, the first positioner PM and another position sensor (not shown in Figure 1B) can be used to accurately position the mask MA with respect to the path of the radiation beam B (for example, after mechanical retrieval from a mask library or during a scan).

[0042] In general, movement of the mask table MT can be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT can be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the mask table MT can be connected to a short-stroke actuator or can be fixed. Mask MA and substrate W can be aligned using mask alignment marks Ml, M2, and substrate alignment marks Pl, P2. Although the substrate alignment marks (as illustrated) occupy dedicated target portions, they can be located in spaces between target portions (known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks can be located between the dies.

[0043] Mask table MT and patterning device MA can be in a vacuum chamber V, where an in-vacuum robot IVR can be used to move patterning devices such as a mask in and out of vacuum chamber. Alternatively, when mask table MT and patterning device MA are outside of the vacuum chamber, an out-of-vacuum robot can be used for various transportation operations, similar to the in-vacuum robot IVR. Both the in-vacuum and out-of-vacuum robots can be calibrated for a smooth transfer of any payload (e.g., mask) to a fixed kinematic mount of a transfer station.

[0044] The lithographic apparatus 100 and 100’ can be used in at least one of the following modes: 1. In step mode, the support structure (for example, mask table) MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam B is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.2. In scan mode, the support structure (for example, mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam B is projected onto a target portion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (for example, mask table) MT can be determined by the (de-)magnification and image reversal characteristics of the projection system PS.3. In another mode, the support structure (for example, mask table) MT is kept substantially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam B is projected onto a target portion C. A pulsed radiation source SO can be employed and the programmable patterning device is updated as needed after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes a programmable patterning device, such as a programmable mirror array.

[0045] Combinations and / or variations on the described modes of use or entirely different modes of use can also be employed.

[0046] In some aspects, lithographic apparatus 100 includes an extreme ultraviolet (EUV) source, which is configured to generate a beam of EUV radiation for EUV lithography. In general, the EUV source is configured in a radiation system, and a corresponding illumination system is configured to condition the EUV radiation beam of the EUV source.

[0047] In some aspects, lithographic apparatus 100’ includes a deep ultraviolet (DUV) source, which is configured to generate a beam of DUV radiation for DUV lithography. In general, the DUV source is configured in a radiation system, and a corresponding illumination system is configured to condition the DUV radiation beam of the DUV source.

[0048] Figure 2 shows the lithographic apparatus 100 in more detail, including the source collector apparatus SO, the illumination system IL, and the projection system PS. The source collector apparatus SO is constructed and arranged such that a vacuum environment can be maintained in an enclosing structure 220 of the source collector apparatus SO. An EUV radiation emitting plasma 210 can beformed by a discharge produced plasma source. EUV radiation can be produced by a gas or vapor, for example Xe gas, Li vapor, or Sn vapor in which EUV radiation emitting plasma 210 is created to emit radiation in the EUV range of the electromagnetic spectrum. The EUV radiation emitting plasma 210 is created by, for example, an electrical discharge causing at least a partially ionized plasma. Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor can be used for efficient generation of the radiation. In some aspects, a plasma of excited tin (Sn) (e.g., excited via a laser) is provided to produce EUV radiation.

[0049] The radiation emitted by the EUV radiation emitting plasma 210 is passed from a source chamber 211 into a collector chamber 212 via an optional gas barrier or contaminant trap 230 (in some cases also referred to as contaminant barrier or foil trap), which is positioned in or behind an opening in source chamber 211. The contaminant trap 230 can include a channel structure. Contamination trap 230 can also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further indicated herein at least includes a channel structure.

[0050] The collector chamber 212 can include a radiation collector CO, which can be a so-called grazing incidence collector. Radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation that traverses collector CO can be reflected off a grating spectral filter 240 to be focused in a virtual source point INTF. The virtual source point INTF is commonly referred to as the intermediate focus, and the source collector apparatus is arranged such that the intermediate focus INTF is located at or near an opening 219 in the enclosing structure 220. The virtual source point INTF is an image of the EUV radiation emitting plasma 210. Grating spectral filter 240 is used in particular for suppressing infra-red (IR) radiation.

[0051] Subsequently the radiation traverses the illumination system IL, which can include a faceted field mirror device 222 and a faceted pupil mirror device 224 arranged to provide a desired angular distribution of the radiation beam 221, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the beam of radiation 221 at the patterning device MA, held by the support structure MT, a patterned beam 226 is formed and the patterned beam 226 is imaged by the projection system PS via reflective elements 228, 229 onto a substrate W held by the wafer stage or substrate table WT.

[0052] More elements than shown can generally be present in illumination optics unit IL and projection system PS. The grating spectral filter 240 can optionally be present, depending upon the type of lithographic apparatus. Further, there can be more mirrors present than those shown in the Figure 2, for example there can be one to six additional reflective elements present in the projection system PS than shown in Figure 2.

[0053] Collector optic CO, as illustrated in Figure 2, is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, just as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are disposed axially symmetric around an optical axis Oand a collector optic CO of this type is preferably used in combination with a discharge produced plasma source, often called a DPP source.

[0054] Example Lithographic Cell

[0055] Figure 3 shows a lithographic cell 300, also sometimes referred to a lithocell or cluster, according to some aspects. Lithographic apparatus 100 or 100’ can form part of lithographic cell 300. Lithographic cell 300 can also include one or more apparatuses to perform pre- and post-exposure processes on a substrate. Conventionally these include spin coaters SC to deposit resist layers, developers DE to develop exposed resist, chill plates CH, and bake plates BK. A substrate handler, or robot, RO picks up substrates from input / output ports I / O I, I / O2, moves them between the different process apparatuses and delivers them to the loading bay LB of the lithographic apparatus 100 or 100’. These devices, which are often collectively referred to as the track, are under the control of a track control unit TCU, which is itself controlled by a supervisory control system SCS, which also controls the lithographic apparatus via lithography control unit LACU. Thus, the different apparatuses can be operated to maximize throughput and processing efficiency.

[0056] Example Inspection Apparatus

[0057] In order to control the lithographic process to place device features accurately on the substrate, alignment marks are generally provided on the substrate, and the lithographic apparatus includes one or more alignment apparatuses and / or inspection apparatuses for accurate positioning of marks on a substrate. These alignment apparatuses are effectively position measuring apparatuses. Different types of marks and different types of alignment apparatuses and / or systems are known from different times and different manufacturers. A type of system widely used in current lithographic apparatus is based on a self -referencing interferometer as described in U. S. Patent No. 6,961,116 (den Boef etal.). Generally marks are measured separately to obtain X- and Y-positions. A combined X- and Y-measurement can be performed using the techniques described in U. S. Publication No. 2009 / 195768 A (Bijnen et al.), however. The full contents of both of these disclosures are incorporated herein by reference.

[0058] Figure 4A shows a cross-sectional view of an inspection apparatus 400 that can be implemented as a part of lithographic apparatus 100 or 100’, according to some aspects. In some aspects, inspection apparatus 400 can be configured to align a substrate (e.g., substrate W) with respect to a patterning device (e.g., patterning device MA). Inspection apparatus 400 can be further configured to detect positions of alignment marks on the substrate and to align the substrate with respect to the patterning device or other components of lithographic apparatus 100 or 100’ using the detected positions of the alignment marks. Such alignment of the substrate can ensure accurate exposure of one or more patterns on the substrate.

[0059] The terms “inspection apparatus,” “metrology system,” or the like can be used herein to refer to, e.g., a device used for measuring a property of a structure (e.g., overlay sensor, critical dimension sensor, or the like), a device or system used in a lithographic apparatus to inspect an alignment of a wafer (e.g., alignment sensor), or the like.

[0060] In some aspects, inspection apparatus 400 can include an illumination system 412, a beam splitter 414, an interferometer 426, a detector 428, a beam analyzer 430, and a processor 432. Illumination system 412 can be configured to provide an electromagnetic narrow band radiation beam 413 having one or more passbands. In an example, the one or more passbands can be within a spectrum of wavelengths between about 500 nm to about 900 nm. In another example, the one or more passbands can be discrete narrow passbands within a spectrum of wavelengths between about 500 nm to about 900 nm. Illumination system 412 can be further configured to provide one or more passbands having substantially constant center wavelength (CWL) values over a long period of time (e.g., over a lifetime of illumination system 412). Such configuration of illumination system 412 can help to prevent the shift of the actual CWL values from the desired CWL values, as discussed above, in current alignment systems. And, as a result, the use of constant CWL values can improve long-term stability and accuracy of alignment systems (e.g., inspection apparatus 400) compared to the current alignment apparatuses.

[0061] In some aspects, beam splitter 414 can be configured to receive radiation beam 413 and split radiation beam 413 into at least two radiation sub-beams. For example, radiation beam 413 can be split into radiation sub-beams 415 and 417, as shown in Figure 4A. Beam splitter 414 can be further configured to direct radiation sub-beam 415 onto a substrate 420 placed on a stage 422. In one example, the stage 422 is movable along direction 424. Radiation sub-beam 415 can be configured to illuminate an alignment mark or a target 418 located on substrate 420. Alignment mark or target 418 can be coated with a radiation sensitive film. In some aspects, alignment mark or target 418 can have one hundred and eighty degrees (i.e., 180°) symmetry. That is, when alignment mark or target 418 is rotated 180° about an axis of symmetry perpendicular to a plane of alignment mark or target 418, rotated alignment mark or target 418 can be substantially identical to an unrotated alignment mark or target 418. The target 418 on substrate 420 can be (a) a resist layer grating comprising bars that are formed of solid resist lines, or (b) a product layer grating, or (c) a composite grating stack in an overlay target structure comprising a resist grating overlaid or interleaved on a product layer grating. The bars can alternatively be etched into the substrate. This pattern is sensitive to chromatic aberrations in the lithographic projection apparatus, particularly the projection system PL, and illumination symmetry and the presence of such aberrations will manifest themselves in a variation in the printed grating. One in-line method used in device manufacturing for measurements of line width, pitch, and critical dimension makes use of a technique known as “scatterometry”. Methods of scatterometry are described in Raymond et al., “Multiparameter Grating Metrology Using Optical Scatterometry”, J. Vac. Sci. Tech. B, Vol. 15, no. 2, pp. 361-368 (1997) and Niu et al., “Specular Spectroscopic Scatterometry in DUV Lithography”, SPIE, Vol. 3677 (1999), which are both incorporated by reference herein in their entireties. In scatterometry, light is reflected by periodic structures in the target, and the resulting reflection spectrum at a given angle is detected. The structure giving rise to the reflection spectrum is reconstructed, e.g. using Rigorous Coupled- Wave Analysis (RCWA) or by comparison to a library of patterns derived by simulation. Accordingly, the scatterometry data of the printed gratings is used to reconstruct thegratings. The parameters of the grating, such as line widths and shapes, can be input to the reconstruction process, performed by processing unit PU, from knowledge of the printing step and / or other scatterometry processes.

[0062] In some aspects, beam splitter 414 can be further configured to receive diffraction radiation beam 419 and split diffraction radiation beam 419 into at least two radiation sub-beams, according to an aspect. Diffraction radiation beam 419 can be split into diffraction radiation sub-beams 429 and 439, as shown in Figure 4A.

[0063] It should be noted that even though beam splitter 414 is shown to direct radiation sub-beam 415 towards alignment mark or target 418 and to direct diffracted radiation sub-beam 429 towards interferometer 426, the disclosure is not so limiting. Other optical arrangements can be used to obtain the similar result of illuminating alignment mark or target 418 on substrate 420 and detecting an image of alignment mark or target 418.

[0064] As illustrated in Figure 4A, interferometer 426 can be configured to receive radiation sub-beam 417 and diffracted radiation sub-beam 429 through beam splitter 414. In an example aspect, diffracted radiation sub-beam 429 can be at least a portion of radiation sub-beam 415 that can be reflected from alignment mark or target 418. In an example of this aspect, interferometer 426 comprises any appropriate set of optical-elements, for example, a combination of prisms that can be configured to form two images of alignment mark or target 418 based on the received diffracted radiation sub-beam 429. It should be appreciated that a good quality image need not be formed. It can be enough to have the features of alignment mark 418 resolved. Interferometer 426 can be further configured to rotate one of the two images with respect to the other of the two images 180° and recombine the rotated and unrotated images interferometrically.

[0065] In some aspects, detector 428 can be configured to receive the recombined image via interferometer signal 427 and detect interference as a result of the recombined image when alignment axis 421 of inspection apparatus 400 passes through a center of symmetry (not shown) of alignment mark or target 418. Such interference can be due to alignment mark or target 418 being 180° symmetrical, and the recombined image interfering constructively or destructively, according to an example aspect. Based on the detected interference, detector 428 can be further configured to determine a position of the center of symmetry of alignment mark or target 418 and consequently, detect a position of substrate 420. According to an example, alignment axis 421 can be aligned with an optical beam perpendicular to substrate 420 and passing through a center of image rotation interferometer 426. Detector 428 can be further configured to estimate the positions of alignment mark or target 418 by implementing sensor characteristics and interacting with wafer mark process variations.

[0066] In a further aspect, detector 428 determines the position of the center of symmetry of alignment mark or target 418 by performing one or more of the following measurements:1. measuring position variations for various wavelengths (position shift between colors);2. measuring position variations for various orders (position shift between diffraction orders);3. measuring position variations for various polarizations (position shift between polarizations); and 4. measuring intensity difference between opposite orders of a diffraction order pair (e.g., to characterize and correct for asymmetry).

[0067] This data can be obtained using any type of alignment sensor, for example, a SMASH (SMart Alignment Sensor Hybrid) sensor, as described in U. S. Patent No. 6,961,116 that employs a selfreferencing interferometer with a single detector and four different wavelengths, and extracts the alignment signal in software, or Athena (Advanced Technology using High order ENhancement of Alignment), as described in U. S. Patent No. 6,297,876, which directs each of seven diffraction orders to a dedicated detector, which are both incorporated by reference herein in their entireties.

[0068] In some aspects, beam analyzer 430 can be configured to receive and determine an optical state of diffracted radiation sub-beam 439. The optical state can be a measure of beam wavelength, polarization, or beam profile. Beam analyzer 430 can be further configured to determine a position of stage 422 and correlate the position of stage 422 with the position of the center of symmetry of alignment mark or target 418. As such, the position of alignment mark or target 418 and, consequently, the position of substrate 420 can be accurately known with reference to stage 422. Alternatively, beam analyzer 430 can be configured to determine a position of inspection apparatus 400 or any other reference element such that the center of symmetry of alignment mark or target 418 can be known with reference to inspection apparatus 400 or any other reference element. Beam analyzer 430 can be a point or an imaging polarimeter with some form of wavelength-band selectivity. In some aspects, beam analyzer 430 can be directly integrated into inspection apparatus 400, or connected via fiber optics of several types: polarization preserving single mode, multimode, or imaging, according to other aspects.

[0069] In some aspects, beam analyzer 430 can be further configured to determine the overlay data between two patterns on substrate 420. One of these patterns can be a reference pattern on a reference layer. The other pattern can be an exposed pattern on an exposed layer. The reference layer can be an etched layer already present on substrate 420. The reference layer can be generated by a reference pattern exposed on the substrate by lithographic apparatus 100 and / or 100’. The exposed layer can be a resist layer exposed adjacent to the reference layer. The exposed layer can be generated by an exposure pattern exposed on substrate 420 by lithographic apparatus 100 or 100’. The exposed pattern on substrate 420 can correspond to a movement of substrate 420 by stage 422. In some aspects, the measured overlay data can also indicate an offset between the reference pattern and the exposure pattern. The measured overlay data can be used as calibration data to calibrate the exposure pattern exposed by lithographic apparatus 100 or 100’, such that after the calibration, the offset between the exposed layer and the reference layer can be minimized.

[0070] In some aspects, beam analyzer 430 can be further configured to determine a model of the product stack profile of substrate 420, and can be configured to measure overlay, critical dimension, and focus of target 418 in a single measurement. The product stack profile contains information on the stacked product such as alignment mark, target 418, or substrate 420, and can include mark processvariation-induced optical signature metrology that is a function of illumination variation. The product stack profile can also include product grating profile, mark stack profile, and mark asymmetry information. An example of beam analyzer 430 is Yieldstar™, manufactured by ASML, Veldhoven, The Netherlands, as described in U. S. Patent No. 8,706,442, which is incorporated by reference herein in its entirety. Beam analyzer 430 can be further configured to process information related to a particular property of an exposed pattern in that layer. For example, beam analyzer 430 can process an overlay parameter (an indication of the positioning accuracy of the layer with respect to a previous layer on the substrate or the positioning accuracy of the first layer with respective to marks on the substrate), a focus parameter, and / or a critical dimension parameter (e.g., line width and its variations) of the depicted image in the layer. Other parameters are image parameters relating to the quality of the depicted image of the exposed pattern.

[0071] In some aspects, an array of detectors (not shown) can be connected to beam analyzer 430, and allows the possibility of accurate stack profile detection as discussed below. For example, detector 428 can be an array of detectors. For the detector array, a number of options are possible: a bundle of multimode fibers, discrete pin detectors per channel, or CCD or CMOS (linear) arrays. The use of a bundle of multimode fibers enables any dissipating elements to be remotely located for stability reasons. Discrete PIN detectors offer a large dynamic range but each need separate pre-amps. The number of elements is therefore limited. CCD linear arrays offer many elements that can be read-out at high speed and are especially of interest if phase-stepping detection is used.

[0072] In some aspects, a second beam analyzer 430’ can be configured to receive and determine an optical state of diffracted radiation sub-beam 429, as shown in Figure 4B. The optical state can be a measure of beam wavelength, polarization, or beam profile. Second beam analyzer 430’ can be identical to beam analyzer 430. Alternatively, second beam analyzer 430’ can be configured to perform one or more of the functions of beam analyzer 430, such as determining a position of stage 422 and correlating the position of stage 422 with the position of the center of symmetry of alignment mark or target 418. As such, the position of alignment mark or target 418 and, consequently, the position of substrate 420, can be accurately known with reference to stage 422. Second beam analyzer 430’ can also be configured to determine a position of inspection apparatus 400, or any other reference element, such that the center of symmetry of alignment mark or target 418 can be known with reference to inspection apparatus 400, or any other reference element.

[0073] In some aspects, second beam analyzer 430’ can be directly integrated into inspection apparatus 400, or it can be connected via fiber optics of several types: polarization preserving single mode, multimode, or imaging, according to other aspects. Alternatively, second beam analyzer 430’ and beam analyzer 430 can be combined to form a single analyzer (not shown) configured to receive and determine the optical states of both diffracted radiation sub-beams 429 and 439.

[0074] In some aspects, processor 432 receives information from detector 428 and beam analyzer 430. Processor 432 can create a basic correction algorithm based on the information received from detector428 and beam analyzer 430, including but not limited to the optical state of the illumination beam, the alignment signals, associated position estimates, and the optical state in the pupil, image, and additional planes. The pupil plane is the plane in which the radial position of radiation defines the angle of incidence and the angular position defines the azimuth angle of the radiation. Processor 432 can utilize the basic correction algorithm to characterize the inspection apparatus 400 with reference to wafer marks and / or alignment marks 418.

[0075] Alignment metrology typically requires additional complementary component metrology subsystems which complement the alignment sensor itself. These component metrology subsystems may comprise one or both of an alignment sensor measurement subsystem (an alignment reference axis sensor or ARA) and a stage position measurement (SPM) subsystem.

[0076] The SPM subsystem monitors the position of a substrate stage and determines a correction for positioning and / or movement of the stage compared to where it should be (sensor feedback during movement). This correction takes into account the fact that the stage, when set to standstill at a particular position or move at a certain speed, will not necessarily follow the requested positions / movement (e.g., as determined using the alignment sensor measuring alignment marks on the wafer) exactly; instead there will be some variation around the set value. As such, the stage position (or each stage position in a twin-stage or multi-stage apparatus) may be measured by (e.g., respective) SPM encoders or other sensors on, for example, the relevant stage and / or a reference frame (metrology frame) of the system. For example, one of the stage and reference frame may comprise an encoder and the other of the stage and reference frame may comprise a reference structure (e.g., grating or grid) such that the encoder measures the stage position with respect to the reference structure and therefore the reference frame.

[0077] The stage position may be measured during measurement of an alignment mark (i.e., during an alignment scan). The resultant substrate stage position data is used as a position reference for the corresponding alignment measurement (aligned position of the corresponding mark). As such, the stage measurement or SPM subsystem measures the position of the substrate stage with respect to a reference structure such as a metrology frame (or metro-frame) of the lithographic apparatus.

[0078] In addition, the alignment sensor itself is not completely stationary, which can also affect the measured alignment position. An alignment sensor measurement subsystem, sometimes referred to as an alignment reference axis (ARA) sensor, may be provided to measure the alignment sensor position (e.g., also with respect to the reference structure / metrology frame and / or the substrate stage). The ARA sensor information can then be combined into the stage position measurement data for determining the position reference.

[0079] As such, component position data within the context of this disclosure may comprise stage position data (e.g., as measured by SPM subsystem), and / or sensor position data (e.g., as measured by an ARA); this may include any combination of stage position data or alignment sensor position data. The component position data may describe a relative position difference between the sensor and the stage.

[0080] In alignment signal processing, the raw alignment data typically undergoes a fitting step, e.g., using a suitable fitting algorithm (e.g., a Fast Fourier Transform FFT), to determine the phase of the alignment signal and therefore the position of the mark being measured. These alignment fit algorithms use the substrate stage position data and alignment sensor position data to determine the position reference for the aligned position (alignment mark position on the wafer or one of the wafer stage fiducials) from an alignment scan over the mark. The substrate stage position data and alignment sensor position data are collected periodically over an alignment scan during which an alignment mark is measured (i.e., scanned), to obtain a respective series of position values for each of the substrate stage position and alignment sensor position over the scan period.

[0081] Figure 5 is a simplified schematic illustration of an alignment metrology system according to examples described herein. An alignment sensor 500 is shown, being mounted on a reference frame or metrology frame 510. Also mounted to the metrology frame 510 are reference structures 520 (e.g., grid plates or grating plates). A substrate stage 540 may comprise a substrate stage position sensor (e.g., an encoder) 550 which measures the reference structures 520 (the solid arrows represent measurements performed by each respective sensor). During a time when the alignment sensor 500 is measuring a structure or alignment mark 540 (e.g., on the substrate stage or substrate carried by the substrate stage), the substrate stage position sensor 550 performs multiple measurements or samples of reference structures 520 thereby generating substrate stage position data SPM (the dotted arrows each represent a respective sensor signal and / or sensor data) with respect to the reference structures 520 and therefore metrology frame 510. While the sensor 550 is shown on the stage 540 and the reference structures 520 on the metrology frame 510, these can be swapped, or each may comprise both.

[0082] At the same time as the alignment sensor 500 measures alignment mark 540, an ARA sensor 530 measures both the alignment sensor 550 and reference structures 520 to generate alignment sensor position data ARA (e.g., the position of alignment sensor 500 with respect to the reference structures 520 and therefore metrology frame 510). The substrate stage position data SPM and alignment sensor position data ARA is combined to provide substrate stage position data SPM’ measured with respect to the alignment sensor 500 position. This latter substrate stage position data SPM’ is then combined with alignment sensor signal data AS to finally calculate the aligned position AP value for the alignment mark 540.

[0083] Figure 6 is a flow diagram illustrating a present method for determining the aligned position AP value. In a typical present method, for each of the substrate stage position data and alignment sensor position data, the fitting algorithm uses an average (i.e., mean) of the values of values measured during the alignment scan period. The Figure 6 flow relates to the substrate stage position data SPM only. The alignment sensor signal data AS 600 undergoes a fitting step 610 (e.g., a FFT fit) and the phase of the alignment sensor signal data AS is extracted 620. This phase may effectively comprise an averaged phase computed from the alignment sensor signal.

[0084] Substrate stage position data 630 is obtained simultaneously to the capture of the alignment sensor signal data AS 600 (i.e., an alignment scan on an alignment mark). A processing step 640 processes this substrate stage position data 630, e.g., to temporally match (align) the alignment signal data 600 and substrate stage position data 630 (which may have respective different signal frequencies). This processing step may comprise an interpolation and / or extrapolation of one or both signals, for example. The processed substrate stage position data 630 is then averaged 650 to determine a mean stage position over the scan period.

[0085] The aligned position 660 of the alignment mark is determined from (e.g., as the sum of) the mean substrate stage position determined in the averaging step 650 and the phase of the alignment signal determined at step 620.

[0086] When alignment sensor position data is also used, an averaging step may also be performed on the alignment sensor position data to determine a mean alignment sensor position value, before combining this mean alignment sensor position value with the mean stage position value. Alternatively, the data sets may be combined prior to averaging, with the averaging performed on the combined data (i.e., substrate stage position data SPM’ in Figure 5).

[0087] This current approach of using the arithmetic mean of the stage position would be optimal if the samples of the wafer stage position signal and alignment sensor position signal were statistically independent. However, this is not the case due to the presence of known system dynamics (machine vibrations), which cause the signal samples to be correlated with each other. Therefore, in order to more optimally estimate the mark position reference during the scan, these correlations should be accounted for.

[0088] It is therefore proposed to account for system dynamics by training an estimator on the vibrations to train weights. The trained weights from the estimator can then be used to calculate the mark position reference from the stage position and / or alignment sensor position sampled values, instead of using the mean of these values. Such an approach may be based upon the Wiener Theorem, where the Power Spectrum Density (PSD), here the PSD of the mechanical vibrations, is the Fourier Transform of the Auto-Correlation Function (ACF) of the measured data.

[0089] In a specific example, the estimator may comprise a minimum variance estimator (MVE). In such an example, the trained weights (weight vector) are trained to minimize the long-term, steady-state variance of the estimator (corresponding to maximum likelihood, and minimum reproducibility contribution) under the weight sum constraint that the weights sum to unity. As such, the optimized weights are those which have a minimal effect on mean of the sampled data, but which minimizes variance of the estimator.

[0090] Given discrete examples xLof component position data xws(tj), e.g., substrate stage position data and / or alignment sensor position data at respective time instances t(- over a long time period (e.g., over a period which may be approximated as infinite), then:xi —XWS ( / i) —XWS (i ’ ^s)1TS =, i = 1,2 NJswhere fsis the sampling frequency. For the sake of a closed-form analytical expression, the estimator is a linear expression of the given samples (array of weights). The estimator p may be defined as a product (e.g., dot product) of the weight vector w being trained and the component position data vector x:p = wTx EQ. [1]where:x = (x1,x2,x3,...,xJV)Tw = (w1,w2,w3,..., WN~)TTo ensure that the estimator is unbiased, its expected value E(p) should be the long-term mean xmeanof the sampled data:1-^meanxmeanand therefore the weights should sum to unity:wTl = 1In an initial optimization or training stage, therefore, the trained / optimized weights woptshould be optimized to minimize the long-term, steady-state variance of the estimator D2(p), subject to the aforementioned constraints:wopt= argmin D2(p) EQ. [2]

[0091] The variance of the estimator may be expanded analytically down to the level of the underlying covariances between the sampled data:D2(p) = E[(p mean) ]expressing (p — xmean)2 as atranspose product and expanding each factor, taking advantage of the fact that the vector w is to sum to unity:D (p) E[(p Xmean)(P ^mean) ] i'fw (x 'Lxmcan)(x Xm(:(lnl )w]= wT[E(xxT) - lx^eanlT]w= wTcov(x, x) w EQ. [3]

[0092] The key idea of the MVE is to minimize the estimator variance over the space of the weight vectors, under the weight sum constraint.

[0093] As is well known, converting a constrained optimization problem to an unconstrained one requires introducing a Lagrangian L with a multiplier A for the deviation from the weight sum constraint involved:L = D2(p) + A(WT1 - 1)= wTcov(x, x) W + A(WT1 — 1)

[0094] The Lagrangian L may be minimized by setting the partial derivatives over the weight vector w and the multiplier A to zero.dL- — = 2 cov(x, x) w + 1A = 0dwdL— =WT1 — 1 = 0 => wTl = ldA

[0095] This leads to a system of linear equations in the weight vector and the multiplier A, which can be solved analytically. Rewriting the equations in the matrix form, where 1 denotes a unity column: / cov(x,x) 1\ / w\ _ / 0\\ 1TOA ' W

[0096] Note that the factor 2 for the covariance matrix has been removed. This can be done without any loss of generality, since the particular value of the multiplier A is of no interest. The resulting linear system of equations may be solved by inverting the system matrix. The solution represents the sought optimal weight vector which constitutes the estimator for the component measurement data.(")=(covnx)

[0097] Solving equation EQ. [4] represents one way of determining the estimator weights. However, inverting a single large matrix is computationally demanding. Therefore it is proposed in an example to represent the system matrix as a block matrix where:A = cov(x,x), B = 1, C = 1T, D = 0

[0098] Taking advantage of the well-known formula for inverting block matrices yields: / A B\1> / A1+ A1B(I) - CA1B)1CA1A1B(D - CA 'B) A VC DJ \ — (D - CA1B)1CA1(D - CA ' B)1Jw = A1B(D - CA-1B)-11 = A-1B(CA-1B)-11This allows the formula for the optimal weight arrays to be simplified to:w = cov(x,x)-11 • (1Tcov(x,x)-11)1EQ. [5]note that the last factor under an inverse is simply a normalizing scalar. Also note that the estimator w will be symmetric about the window center, due to the symmetry of the covariance matrix. It will cancel out any linear trend.

[0099] Once trained, the weight vector may be applied to the sampled component position data, e.g., using Equation EQ. [1], to determine the reference for the aligned position, i.e., instead of simply using the mean of the sampled data.

[0100] In a specific example, it is proposed that a training step uses this Equation EQ. [5] (although Equation EQ. [4] may be used) to determine the optimized weight vector from training data x. The training data may comprise component position data such as substrate stage SPM data and / or ARA data. Alternatively or in addition, the training data may comprise vibration data, the vibration data being representative of the mechanical vibrations to which the component being measured is subject (e.g., substrate stage vibration and / or alignment sensor vibration). This data is already collected as part of a static scan test. In a static scan test, vibration measurements of the component are obtained without an alignment scan being performed (and therefore with the substrate table(s) static other than the induced vibrations). The training of the weights may be performed during this test and / or on the vibration data resulting from this test.

[0101] When computing the covariance matrix cov(x, x) from such vibration data, it can be appreciated that the sub-diagonals contain identical entries due to the time shift which does not affect sample statistics:(COv(xl, Xl) COv(x1, X2) ••• COvQp.qj)COv(x2, X1) cov(x2,x2) ••• cov(x2,xN)COv(Xy^, X^) cov(xw,x2) ••• cov(xw,xw) cov x1,x1) = cov(x2,x2) = ••• = cov(xN,xN)cov(x1,x2) = cov(x2,x3) = ••• = cov(xN-,xN')

[0102] That the rows and columns are shifted versions of each other does not imply that the covariance matrices are circulant. The sample does not repeat indefinitely, as implied by the discrete Fourier Transform. The covariance cov(x,xN) is not equal to cov(x2,x1), which would be the case for a circulant matrix.

[0103] Each covariance between the SPM data at two known samples can be interpreted as the value of the Auto- Correlation Function (ACF) or Cross-Correlation Function (CCF) taken at the appropriate time interval:cov(xi,x7) = J (Xi(t) - xmean)(xj(t) - Xmean)dt ~ J x(t - tl)x(t - tj)dt = ACFxx(tj- tl)

[0104] The approximation is possible due to the long-term mean being close to zero. Applying the Wiener Theorem (i.e., Power Spectrum Density (PSD) is the Fourier Transform of the ACF):PSD(ai) = F[ACF(t)] = ACF t) exp(— jait) dtd1 fACF(t) = F~1[PSD a>)] = — PSD(a>) expQ'mt) da) EQ. [6]2TT J

[0105] Therefore covariance matrices may be computed by Fourier transforming vibration data, e.g., as obtained from a static scan test or otherwise and as represented in terms of PSD. There are advantages in storing and using vibration data represented in terms of PSD. This is because PSD representation should be constant per machine, per chuck, per location, per dimension, lends itself to reproducibility estimation in the frequency domain, and is also easier to interpret visually. Alternatively, or in addition the covariance matrix can be computed (e.g., via Equation EQ. [4] or [5] with no need for a Fourier transform) directly from raw vibration data, e.g., represented as a time signal or time series. Such raw vibration data may be acquired per machine, per location, per chuck, per dimension.

[0106] For the sake of completeness, the multiplier is solved below and the solution analytically verified:A= (D — CA-1B)-11 = — (CA-1B)-11 = -(1Tcov^x)-11)”1 / cov(x,x) 1\ rw\ > ( cov(x,x) cov(x,x)-11(1Tcov(x,x)-11)1- 1(1Tcov(x,x)-11) \ 1T0 / y 1Tcov(x,x)-11(1Tcov(x,x)-11)1 / =(?)

[0107] By substituting the optimal estimator to the previously derived expression for the estimator variance, many factors cancel out, and what remains is related to the optimal value of the Lagrange multiplier02(p) = (lrcov(x, x)-11)-1= —2The unity vectors represent the addition of all the elements of the inverse covariance matrix. The result corresponds to 1 / 3 of the best repro squared, which is achievable theoretically with this approach. The upper bound on the variance corresponds to the case of SPM samples being totally uncorrelated. In such case, the covariance matrix and its inverse are diagonal, and the estimator is equivalent to the mean and the minimum estimator variance is 1 / N*sample variance (as is to be expected):repro « 3 / D2(p)12(p) < (lrdiag(cov(x, x))11)1= ( / Vcov(x, x) ’)x= — cov(x, x)1. Figure 7 is a flowchart of a method of determining an aligned position value when performing alignment metrology according to an embodiment. The method is based on the known method embodied in Figure 6, but using the estimator approach disclosed herein. Alignment sensor signal data AS 600 undergoes a fitting step 610 (e.g., a FFT fit) and the phase of the alignment sensor signal data AS is extracted 620. Component position data 630 (e.g., substrate stage position data and / or alignment sensor position data) is obtained simultaneously to the capture of the alignment sensor signal data AS 600 (i.e., an alignment scan on an alignment mark). A processing step 640 processes this component position data 630, e.g., to temporally match (align) the alignment signal data 600 and SPM signal data 630. This processing step may comprise an interpolation and / or extrapolation of one or both signals, for example. These steps are essentially the same as those of Figure 6.2. The trained weights 770 (e.g., as determined via Equations EQ. [4] or [5]) are then applied 750 to the processed component position data, e.g., as a dot product in accordance with Equation EQ. [1].This provides the reference for the alignment measurement (e.g., an estimate for the center of the mark). The aligned position 760 of the alignment mark is determined from (e.g., as the sum of) the position reference determined in step 750 and the phase of the alignment signal determined at step 620.3. The component position data 630 may comprise substrate stage position data, alignment sensor position data or a combination of both (e.g., substrate stage position data corrected using the alignment sensor position data). In each case, the trained weights 770 may have been trained on the appropriate data (e.g., vibrations of the corresponding component).4. Figure 8 is a flowchart of a calibration or training method according to concepts disclosed herein, for training the weights 770. Scan settings 800 (e.g., the number of signal samples during a scan) and training data 810 is used in a training step 820 to train the weights 770. The training data may comprise stage position data and / or alignment position data, for example, as measured during a static scan test and therefore comprising only or mostly vibration data. The training may comprise an optimization determined in accordance with Equations EQ. [4] or [5], based on determining covariance of the training data. As such, the weights may be determined to minimize the variance of an estimator such as a dot product of the weights (weight vector) and training data (data vector), e.g., as recited in Equation [1]. The required covariance matrices may be determined by Fourier transforming PSD data (i.e., the training data or derived from the training data) and / or computing a covariance matrix directly from raw vibration data.

[0108] In the above description, an analytic expression for a linear minimum variance estimator is derived which operates on component position data such as stage position and / or alignment sensor position data. The estimator is unbiased (preserves the long-term, steady-state mean) and minimizes the repro contribution from vibrations (long-term, steady-state variance).

[0109] The proposed method provides a more accurate position reference than simply using the mean of the measured data. The improvement is greater as scanning speeds increase (i.e., the speed of scanning of the alignment mark during alignment metrology).

[0110] It can be demonstrated that the proposed estimator has a dual representation in the frequency domain. The new estimator proposed herein counteracts substrate stage vibrations by inverting the vibration spectrum and thus suppressing the undesirable frequencies and cancelling or reducing their impact. In this respect, the method effectively creates an automatic filter inside the stage position measurement part of the alignment fit algorithm, which can be trained on available vibration data.

[0111] The terms “radiation,” “beam,” “light,” “illumination,” or the like can be used herein to refer to one or more types of electromagnetic radiation, for example, ultraviolet (UV) radiation (for example, having a wavelength / . of 365, 248, 193, 157 or 126 nm), extreme ultraviolet (EUV or soft X-ray) radiation (for example, having a wavelength in the range of 5-100 nm such as, for example, 13.5 nm), or hard X-ray working at less than 5 nm, as well as particle beams, such as ion beams or electron beams. Generally, radiation having wavelengths between about 400 to about 700 nm is considered visible radiation; radiation having wavelengths between about 780-3000 nm (or larger) is considered IRradiation. UV refers to radiation with wavelengths of approximately 100-400 nm. Within lithography, the term “UV” also applies to the wavelengths that can be produced by a mercury discharge lamp: G-line 436 nm; H-line 405 nm; and / or, I-line 365 nm. Vacuum UV, or VUV (i.e., UV absorbed by gas), refers to radiation having a wavelength of approximately 100-200 nm. Deep UV (DUV) generally refers to radiation having wavelengths ranging from 126 nm to 428 nm, and in some aspects, an excimer laser can generate DUV radiation used within a lithographic apparatus. It should be appreciated that radiation having a wavelength in the range of, for example, 5-20 nm relates to radiation with a certain wavelength band, of which at least part is in the range of 5-20 nm.

[0112] In the following, further features, characteristics, and exemplary technical solutions of the present disclosure will be described in terms of clauses that may be optionally claimed in any combination:1. A method of determining a position reference for an alignment measurement of an alignment mark, the method comprising:obtaining component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement; obtaining weights for the component position data, the weights being determined to minimize variance of an estimator comprising said weights and the component position data; and determining said position reference from a combination of said weights and the component position data.2. A method as described in clause 1, wherein the estimator comprises a dot product of the weights and the component position data.3. A method as described in clause 1 or 2, wherein the component position data comprises substrate stage position data describing a position of a substrate stage.4. A method as described in any preceding clause, wherein the component position data comprises alignment sensor position data describing a position of an alignment sensor.5. A method as described in any preceding clause, wherein said weights sum to unity.6. A method as described in any preceding clause, wherein said position reference describes a position of a center of said alignment mark in at least one direction.7. A method as described in any preceding clause, wherein the weights have been trained on training data relating to vibrations of the at least one component.8. A method as described in clause 7, comprising training said estimator to obtain said weights, the method comprising:obtaining training data relating to vibrations of the at least one component; and determining the weights from covariances of said training data.9. A method as described in clause 8, comprising determining said covariances from a Fourier transform of said training data.10. A method as described in any of clauses 7 to 9, comprising representing said training data as a data vector;constructing a covariance matrix from said data vector; anddetermining the weights from the covariance matrix.11. A method as described in any of clauses 7 to 10, comprising inducing vibrations in said at least one component; andmeasuring the vibrations to obtain said vibration data.12. A method as described in clause 11, wherein said step of inducing vibrations in said at least one component is performed with said component being otherwise stationary.13. A method as described in any preceding clause, comprising combining said alignment measurement and said position reference to obtain an aligned position for the alignment mark.14. A method as described in any preceding clause, comprising performing alignment metrology to obtain said alignment measurement.15. A method as described in any preceding clause, wherein said step of obtaining component position data comprises measuring the position of said component with respect to a reference frame.16. A method of determining weights for applying to component position data to obtain a position reference for an alignment measurement of an alignment mark, said component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement, the method comprising:obtaining training data relating to vibrations of the at least one component; and determining the weights from covariances of said training data.17. A method as described in clause 16, comprising determining said covariances from a Fourier transform of said training data.18. A method as described in clause 16 or 17, comprising representing said training data as a data vector;constructing a covariance matrix from said data vector; anddetermining the weights from the covariance matrix.19. A method as described in any of clauses 16 to 18, wherein said weights are constrained to sum to unity.20. A method as described in any of clauses 16 to 19, comprising inducing vibrations in said at least one component; andmeasuring the vibrations to obtain said vibration data.21. A method as described in clause 20, wherein said step of inducing vibrations in said at least one component is performed with said component being otherwise stationary.22. A method as described in any of clauses 16 to 21, wherein said position reference describes a position of a center of said alignment mark in at least one direction.23. A method as described in any of clauses 16 to 22, wherein the component position data comprises substrate stage position data describing a position of a substrate stage.24. A method as described in any of clauses 16 to 23, wherein the component position data comprises alignment sensor position data describing a position of an alignment sensor.25. A computer program comprising program instructions operable to perform the method of any preceding clause, when run on a suitable apparatus.26. A non-transient computer program carrier the computer program of clause 25.27. A processing apparatus comprising:at least one processor; andthe non-transient computer program carrier of clause 26.28. A component position metrology subsystem, comprising:at least one sensor and / or encoder;a reference structure; andthe processing apparatus of clause 27.29. A component position metrology subsystem as described in clause 28, wherein said component comprises a substrate stage.30. A component position metrology subsystem as described in clause 28 or 29, wherein said at least one sensor and / or encoder is comprised on said component; andsaid reference structure is comprised on a reference frame.31. A component position metrology subsystem as described in clause 28 or 29, wherein said at least one sensor and / or encoder is comprised on a reference frame; andsaid reference structure is comprised on said component.32. A component position metrology subsystem as described in clause 28, wherein said component comprises an alignment sensor.33. A component position metrology subsystem as described in clause 32, wherein said at least one sensor and / or encoder is configured to measure said alignment sensor and said reference structure.34. An alignment system, comprising:an alignment sensor; andthe component position metrology subsystem of any of clauses 28 to 33.35. A lithographic apparatus comprising:a substrate stage for supporting a substrate; andthe alignment system of clause 34.

[0113] Although some aspects of the present disclosure are described in the context of lithographic apparatuses in the manufacture of ICs, it should be understood that lithographic apparatuses described herein can be used in other applications, for example, in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, LCDs, thin-filmmagnetic heads, etc. Those skilled in the art will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein can be considered as specific examples of the more general terms “substrate” or “target portion”, respectively. A substrate can be processed before or after exposure in, for example, a track unit (a tool that typically applies a layer of resist to a substrate and develops the exposed resist) and / or a metrology unit. Where applicable, aspects disclosed herein can be applied to such and other substrate processing tools. Furthermore, a substrate can be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein can also refer to a substrate that already contains multiple processed layers.

[0114] Furthermore, although some aspects of the present disclosure are described in the context of optical lithography, it should be understood that aspects of the present disclosure are not limited to optical lithography. For example, in imprint lithography, a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device can be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

[0115] It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by those skilled in relevant art(s) in light of the teachings herein.

[0116] The present disclosure has been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. The foregoing description of specific aspects will so fully reveal the general nature of the present disclosure that others can, by applying knowledge within the skill of the art, readily modify and / or adapt for various applications such specific aspects, without undue experimentation and without departing from the general concept of the present disclosure. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed aspects, based on the teaching and guidance presented herein.

[0117] It is to be understood that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections can set forth one or more, but not necessarily all, aspects of the present disclosure as contemplated by the inventor(s), and thus, are not intended to limit the present disclosure and the appended claims in any way. The breadth and scope of the protected subject matter should not be limited by any of the above-described aspects, but should be defined in accordance with the following claims and their equivalents.

Claims

CLAIMS1. A method of determining a position reference for an alignment measurement of an alignment mark, the method comprising:obtaining component position data describing a position of at least one component of a lithographic apparatus, sampled at a plurality of time instances during the alignment measurement;obtaining weights for the component position data, the weights being determined to minimize variance of an estimator comprising said weights and the component position data; and determining said position reference from a combination of said weights and the component position data.

2. A method as claimed in claim 1, wherein the estimator comprises a dot product of the weights and the component position data.

3. A method as claimed in claim 1 or 2, wherein the component position data comprises substrate stage position data describing a position of a substrate stage.

4. A method as claimed in any preceding claim, wherein the component position data comprises alignment sensor position data describing a position of an alignment sensor.

5. A method as claimed in any preceding claim, wherein said weights sum to unity.

6. A method as claimed in any preceding claim, wherein said position reference describes a position of a center of said alignment mark in at least one direction.

7. A method as claimed in any preceding claim, wherein the weights have been trained on training data relating to vibrations of the at least one component.

8. A method as claimed in claim 7, comprising training said estimator to obtain said weights, the method comprising:obtaining training data relating to vibrations of the at least one component; and determining the weights from covariances of said training data.

9. A method as claimed in claim 8, comprising determining said covariances from a Fourier transform of said training data.

10. A method as claimed in any of claims 7 to 9, comprising representing said training data as a data vector;constructing a covariance matrix from said data vector; anddetermining the weights from the covariance matrix.

11. A method as claimed in any of claims 7 to 10, comprising inducing vibrations in said at least one component; andmeasuring the vibrations to obtain said vibration data.

12. A method as claimed in claim 11, wherein said step of inducing vibrations in said at least one component is performed with said component being otherwise stationary.

13. A method as claimed in any preceding claim, comprising combining said alignment measurement and said position reference to obtain an aligned position for the alignment mark.

14. A method as claimed in any preceding claim, comprising performing alignment metrology to obtain said alignment measurement.

15. A method as claimed in any preceding claim, wherein said step of obtaining component position data comprises measuring the position of said component with respect to a reference frame.

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