Method of qualifying a machine such as an exposure apparatus

Abstract

Disclosed is a computer implemented method of determining representative illumination profiles for performing a qualification action on an exposure apparatus. The method comprises obtaining aberration sensitivity data for a plurality of illumination profiles, said aberration sensitivity data describing the sensitivity of an exposure error metric with aberration associated with each respective different illumination profile of said plurality of illumination profiles; grouping said plurality of illumination profiles into one or more groups according to a similarity in their corresponding aberration sensitivity data; and determining a respective representative illumination profile for each of said groups.

Description

METHOD OF QUALIFYING A MACHINE SUCH AS AN EXPOSURE APPARATUSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23185923.2 which was filed on 17 July 2023 and which is incorporated herein in its entirety by reference.FIELD

[0002] The present invention relates to methods and apparatus usable, for example, in the manufacture of devices by lithographic techniques, and to methods of manufacturing devices using lithographic techniques.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 is alternatively referred to as a mask or a reticle, may 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. including part of a die, one die, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. These target portions are commonly referred to as “fields”.

[0004] In the manufacture of complex devices, typically many lithographic patterning steps are performed, thereby forming functional features in successive layers on the substrate. A critical aspect of performance of the lithographic apparatus is therefore the ability to place the applied pattern correctly and accurately in relation to features laid down (by the same apparatus or a different lithographic apparatus) in previous layers. For this purpose, the substrate is provided with one or more sets of alignment marks. Each mark is a structure whose position can be measured at a later time using a position sensor, typically an optical position sensor. The lithographic apparatus includes one or more alignment sensors by which positions of marks on a substrate can be measured accurately. Different types of marks and different types of alignment sensors are known from different manufacturers and different products of the same manufacturer.

[0005] In other applications, metrology sensors are used for measuring exposed structures on a substrate (either in resist and / or after etch). A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. Examples of known scatterometers include angle -resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. In addition to measurement of feature shapes by reconstruction, diffraction basedoverlay can be measured using such apparatus, as described in published patent application US2006066855A1. Diffraction-based overlay metrology using dark-field imaging of the diffraction orders enables overlay measurements on smaller targets. Examples of dark field imaging metrology can be found in international patent applications WO 2009 / 078708 and WO 2009 / 106279 which documents are hereby incorporated by reference in their entirety. Further developments of the technique have been described in published patent publications US20110027704A, US20110043791 A, US2011102753A1, US20120044470A, US20120123581A, US20130258310A, US20130271740A andWO2013178422A1. These targets can be smaller than the illumination spot and may be surrounded by product structures on a wafer. Multiple gratings can be measured in one image, using a composite grating target. The contents of all these applications are also incorporated herein by reference.

[0006] It is necessary to routinely qualify or assess performance of a lithographic apparatus or exposure apparatus, for example prior to shipping the apparatus and / or when it is installed. Such qualification may comprise performing an acceptance test, with its performance being measured in terms of one or more performance metrics such as focus and overlay. To properly qualify the apparatus, the test should be performed for a number of different illumination profiles or “pupils”, where pupil in this context describes the shape of the illumination on the reticle (a conjugate image of the illumination profile is formed in a pupil plane of the projection lens). Such pupils may be individually configured for a particular pattern and therefore may be qualified for a pattern.

[0007] It is desirable to reduce the time presently spent on such qualification actions.SUMMARY OF THE INVENTION

[0008] The invention in a first aspect provides a computer implemented method of determining representative illumination profiles for performing a qualification action on an exposure apparatus (e.g., a lithographic apparatus); the method comprising: obtaining aberration sensitivity data for a plurality of illumination profiles, said aberration sensitivity data describing the sensitivity of an exposure error metric with aberration associated with each respective different illumination profile of said plurality of illumination profiles; grouping said plurality of illumination profiles into one or more groups according to a similarity in their corresponding aberration sensitivity data; and determining a respective representative illumination profile for each of said groups.

[0009] The above and other aspects of the invention will be understood from a consideration of the examples described below.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:Figure 1 depicts a lithographic apparatus; andFigure 2 illustrates schematically measurement and exposure processes in the apparatus of Figure 1 ;Figure 3 is a pairwise correlation chart illustrating correlation of aberration sensitivities for different pairs of illumination profiles; andFigure 4 comprises clustered illumination profiles in Zernike aberration space, where Figure 4a) shows the aberration sensitivities in a 3D space defined by the three Zernikes Z4, Z12, Z21, while Figures 4b), 4c) and 4d) are 2D plots of the three permutations, namely: 4b) Z12 vs Z21 sensitivities, 4c) Z4 vs Z12 sensitivities and 4d) Z4 vs Z21 sensitivities.DETAILED DESCRIPTION OF EMBODIMENTS[Oil] Before describing embodiments of the invention in detail, it is instructive to present an example environment in which embodiments of the present invention may be implemented.

[0012] Figure 1 schematically depicts a lithographic apparatus LA. The apparatus includes an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation), a patterning device support or support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; two substrate tables (e.g., a wafer table) WTa and WTb each constructed to hold a substrate (e.g., a resist coated wafer) W and each connected to a second positioner PW configured to accurately position the substrate 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., including one or more dies) of the substrate W. A reference frame RF connects the various components, and serves as a reference for setting and measuring positions of the patterning device and substrate and of features on them.

[0013] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation.

[0014] The patterning device support MT holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The patterning device support can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The patterning device support MT may be a frame or a table, for example, which may be fixed or movable as required. The patterning device support may ensure that the patterning device is at a desired position, for example with respect to the projection system.

[0015] The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern impartedto the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0016] As here depicted, the apparatus is of a transmissive type (e.g., employing a transmissive patterning device). Alternatively, the apparatus may be of a reflective type (e.g., employing a programmable mirror array of a type as referred to above, or employing a reflective mask). Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.” The term “patterning device” can also be interpreted as referring to a device storing in digital form pattern information for use in controlling such a programmable patterning device.

[0017] The term “projection system” used herein should be broadly interpreted as encompassing 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 or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

[0018] The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system and the substrate. An immersion liquid may 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.

[0019] In operation, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD including, for example, suitable directing mirrors and / or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0020] The illuminator IL may comprise an adjuster AD 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 may be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator IN and a condenser CO. The illuminator IL may be used to condition the radiation beam B, to have a desired uniformity and intensity distribution in its cross section.

[0021] The radiation beam B is incident on the patterning device MA, which is held on the patterning device support MT, and is patterned by the patterning device. Having traversed the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beamonto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF (e.g., an interferometric device, linear encoder, 2-D encoder or capacitive sensor), the substrate table WTa or WTb can be moved accurately, e.g., 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 (which is not explicitly depicted in Figure 1) can be used to accurately position the patterning device (e.g., mask) MA with respect to the path of the radiation beam B, e.g., after mechanical retrieval from a mask library, or during a scan.

[0022] The lithographic apparatus may comprise an aberration sensor for the verification of an aberration fingerprint of the projection system PS. In an embodiment such an aberration fingerprint, i.e. aberrations per field point of the projection system PS, may be determined using a such wavefront aberration sensor. A wavefront aberration sensor of a known type, for instance such as described in US2002 / 0001088 may be used. Such a wavefront aberration sensor may be based on the principle of shearing interferometry and comprises a source module and a sensor module. The source module may comprise a patterned layer of chromium that is placed in the object plane (i.e. where during production the pattern of the patterning means is) of the projection system PS and has additional optics provided above the chromium layer. The combination provides a wavefront of radiation to the entire pupil of the projection system PS. The sensor module may comprise a patterned layer of chromium that is placed in the image plane of the projection system (i.e. where during production the substrate W is) and a camera that is placed some distance behind said layer of chromium. The patterned layer of chromium on the sensor module diffracts radiation into several diffraction orders that interfere with each other giving rise to an interferogram. The interferogram is measured by the camera. The aberrations in the projection lens can be determined by software based upon the measured interferogram. The wavefront aberration sensor may be configured to transfer information with respect to the aberration fingerprint towards the control unit.

[0023] Patterning device (e.g., mask) MA and substrate W may 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 may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device (e.g., mask) MA, the mask alignment marks may be located between the dies. Small alignment marks may also be included within dies, in amongst the device features, in which case it is desirable that the markers be as small as possible and not require any different imaging or process conditions than adjacent features. The alignment system, which detects the alignment markers is described further below.

[0024] The depicted apparatus could be used in a variety of modes. In a scan mode, the patterning device support (e.g., mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The speed and direction of the substrate table WT relative to the patterning device support(e.g., mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion. Other types of lithographic apparatus and modes of operation are possible, as is well-known in the art. For example, a step mode is known. In so-called “maskless” lithography, a programmable patterning device is held stationary but with a changing pattern, and the substrate table WT is moved or scanned.

[0025] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0026] Lithographic apparatus LA is of a so-called dual stage type which has two substrate tables WTa, WTb and two stations - an exposure station EXP and a measurement station MEA - between which the substrate tables can be exchanged. While one substrate on one substrate table is being exposed at the exposure station, another substrate can be loaded onto the other substrate table at the measurement station and various preparatory steps carried out. This enables a substantial increase in the throughput of the apparatus. The preparatory steps may include mapping the surface height contours of the substrate using a level sensor LS and measuring the position of alignment markers on the substrate using an alignment sensor AS. If the position sensor IF is not capable of measuring the position of the substrate table while it is at the measurement station as well as at the exposure station, a second position sensor may be provided to enable the positions of the substrate table to be tracked at both stations, relative to reference frame RF. Other arrangements are known and usable instead of the dual-stage arrangement shown. For example, other lithographic apparatuses are known in which a substrate table and a measurement table are provided. These are docked together when performing preparatory measurements, and then undocked while the substrate table undergoes exposure.

[0027] Figure 2 illustrates the steps to expose target portions (e.g. dies) on a substrate W in the dual stage apparatus of Figure 1. On the left hand side within a dotted box are steps performed at a measurement station MEA, while the right hand side shows steps performed at the exposure station EXP. From time to time, one of the substrate tables WTa, WTb will be at the exposure station, while the other is at the measurement station, as described above. For the purposes of this description, it is assumed that a substrate W has already been loaded into the exposure station. At step 200, a new substrate W’ is loaded to the apparatus by a mechanism not shown. These two substrates are processed in parallel in order to increase the throughput of the lithographic apparatus.

[0028] Referring initially to the newly-loaded substrate W’, this may be a previously unprocessed substrate, prepared with a new photo resist for first time exposure in the apparatus. In general, however, the lithography process described will be merely one step in a series of exposure and processing steps, so that substrate W’ has been through this apparatus and / or other lithography apparatuses, several times already, and may have subsequent processes to undergo as well. Particularly for the problem of improving overlay performance, the task is to ensure that new patterns are applied in exactly the correctposition on a substrate that has already been subjected to one or more cycles of patterning and processing. These processing steps progressively introduce distortions in the substrate that must be measured and corrected for, to achieve satisfactory overlay performance.

[0029] The previous and / or subsequent patterning step may be performed in other lithography apparatuses, as just mentioned, and may even be performed in different types of lithography apparatus. For example, some layers in the device manufacturing process which are very demanding in parameters such as resolution and overlay may be performed in a more advanced lithography tool than other layers that are less demanding. Therefore some layers may be exposed in an immersion type lithography tool, while others are exposed in a ‘dry’ tool. Some layers may be exposed in a tool working at DUV wavelengths, while others are exposed using EUV wavelength radiation.

[0030] At 202, alignment measurements using the substrate marks Pl etc. and image sensors (not shown) are used to measure and record alignment of the substrate relative to substrate table WTa / WTb. In addition, several alignment marks across the substrate W’ will be measured using alignment sensor AS. These measurements are used in one embodiment to establish a “wafer grid”, which maps very accurately the distribution of marks across the substrate, including any distortion relative to a nominal rectangular grid.

[0031] At step 204, a map of wafer height (Z) against X-Y position is measured also using the level sensor LS. Conventionally, the height map is used only to achieve accurate focusing of the exposed pattern. It may be used for other purposes in addition.

[0032] When substrate W’ was loaded, recipe data 206 were received, defining the exposures to be performed, and also properties of the wafer and the patterns previously made and to be made upon it. To these recipe data are added the measurements of wafer position, wafer grid and height map that were made at 202, 204, so that a complete set of recipe and measurement data 208 can be passed to the exposure station EXP. The measurements of alignment data for example comprise X and Y positions of alignment targets formed in a fixed or nominally fixed relationship to the product patterns that are the product of the lithographic process. These alignment data, taken just before exposure, are used to generate an alignment model with parameters that fit the alignment model to the data. These parameters and the alignment model will be used during the exposure operation to correct positions of patterns applied in the current lithographic step. The model in use interpolates positional deviations between the measured positions. A conventional alignment model might comprise four, five or six parameters, together defining translation, rotation and scaling of the ‘ideal’ grid, in different dimensions. Advanced models are known that use more parameters.

[0033] At 210, wafers W’ and W are swapped, so that the measured substrate W’ becomes the substrate W entering the exposure station EXP. In the example apparatus of Figure 1 , this swapping is performed by exchanging the supports WTa and WTb within the apparatus, so that the substrates W, W’ remain accurately clamped and positioned on those supports, to preserve relative alignment between the substrate tables and substrates themselves. Accordingly, once the tables have been swapped,determining the relative position between projection system PS and substrate table WTb (formerly WTa) is all that is necessary to make use of the measurement information 202, 204 for the substrate W (formerly W’) in control of the exposure steps. At step 212, reticle alignment is performed using the mask alignment marks Ml, M2. In steps 214, 216, 218, scanning motions and radiation pulses are applied at successive target locations across the substrate W, in order to complete the exposure of a number of patterns.

[0034] By using the alignment data and height map obtained at the measuring station in the performance of the exposure steps, these patterns are accurately aligned with respect to the desired locations, and, in particular, with respect to features previously laid down on the same substrate. The exposed substrate, now labeled W” is unloaded from the apparatus at step 220, to undergo etching or other processes, in accordance with the exposed pattern.

[0035] The skilled person will know that the above description is a simplified overview of a number of very detailed steps involved in one example of a real manufacturing situation. For example rather than measuring alignment in a single pass, often there will be separate phases of coarse and fine measurement, using the same or different marks. The coarse and / or fine alignment measurement steps can be performed before or after the height measurement, or interleaved.

[0036] An acceptance test (e.g., a factory acceptance test performed before shipping or a site acceptance test performed on-site) may be performed on a lithographic apparatus to effectively replicate the apparatus’s operating conditions, in order to verify whether the system will meet its standard specifications and / or other performance criteria. Such acceptance tests are ideally performed individually for each illuminator profile or “pupil” setting that is likely to be used on the apparatus, as performance can vary significantly for different illumination profiles. However, the illumination profile is typically optimized per pattern being imaged to obtain an optimized exposure performance per pattern (e.g., in terms of focus performance and / or placement error or overlay performance).

[0037] Because of this, there is typically a large number of different illumination profiles corresponding to the multitude of products that may be produced on a particular apparatus. However, in a practical sense, during and after machine setup only a limited number of pupils can be qualified, because testing focus and overlay performance in resist for a specific pupil is a lengthy and costly process. This increases the setup time if a large number of pupils needs to be tested. However, if only a limited number of pupils can be qualified, the probability increases that performance will not be within specification for any unqualified pupil(s) used during production on the apparatus.

[0038] The inventor has appreciated that, while there may be many different relevant illumination profiles which can be used, in general some sets of the illumination profiles will tend to result in similar performance to each other. More specifically, these sets of illumination profiles may comprise illumination profiles which share similar sensitivities to (e.g., Zernike) lens aberrations and therefore may have substantially correlating aberration sensitivity data or Zernike sensitivity data.

[0039] To illustrate this, Figure 3 is a pairwise plot illustrating a degree of correlation for each pairpermutation of seven different illumination profiles P1-P7. More specifically, the plot relates to focus performance residual 3sigma variation for the different illumination profiles. Some performance is correlated between the different illumination profiles due to similar Zernike sensitivities, more specifically the pairs marked with an X. Even with this limited selection of seven illumination profiles, it can be appreciated that the number of pupils to be actually qualified may be reduced; e.g., from seven to three as illustrated by the three ringed regions. This is because qualifying pupils with similar sensitivities is redundant. Finding optimized pupils that cover multiple usecases can help to improve setup and cycle time.

[0040] As such, it is proposed to obtain aberration sensitivity data (e.g., Zernike sensitivity data) for a plurality of illumination profiles (illumination settings or pupils), e.g., for each of the illumination profiles which are envisaged to be used on a particular lithographic apparatus.

[0041] Aberration or Zernike sensitivity may describe the sensitivity or relationship of an exposure error metric (e.g., overlay error or other position error metric or an imaging error resultant from defocus) with aberration associated with a particular illumination profile (e.g., decomposed per Zernike function for some or all Zernike functions). While overlay and / or focus performance may often be the exposure error metric assessed in such acceptance tests, other exposure error metrics may be assessed within the context of this disclosure (e.g., defectivity, edge placement error etc.).

[0042] It is proposed that the Zernike sensitivity data may be simulated or at least partially simulated. The simulation may comprise simulating the effect of the different illumination profiles on the exposure of structures such as overly targets and / or focus targets, using the lithographic apparatus being qualified / tested. As such, the simulations may use a lens model optimized for that lithographic apparatus. From these simulations, sensitivities or relationships of one or more exposure error metrics (e.g., related to focus or overlay) with the Zernike aberrations can be determined. The Zernike aberrations in this context may describe residual Zernike aberrations (uncorrected aberration component) subsequent to the implementation of lens corrections.

[0043] The method may comprise grouping the Zernike sensitivity data for the different illumination profiles into one or more groups or clusters having a similar aberration sensitivity (hereafter Zernike sensitivity) response. Having a similar Zernike sensitivity response may comprise having correlated Zernike sensitivity data for two or more illumination profiles. The Zernike sensitivity data may be compared for each of the first 64 Zernike polynomial functions, or any subset thereof (e.g., comprising more than 25 or more than 50 Zernikes), for example. The clustering may be performed in a multidimensional space, with the number of dimensions corresponding to the number of Zernike polynomial functions being considered.

[0044] This grouping step may comprise performing a clustering method (e.g., employing a clustering algorithm) to cluster the per-illumination-profile Zernike sensitivity data e.g., as determined via simulation. The clustering may be such that there are fewer (e.g., one or more orders of magnitude fewer) clusters than illumination profiles used to determine the Zernike sensitivity data (i.e., Zernikesensitivities comprised within the Zernike sensitivity data). Any suitable clustering method may be used, e.g., k-means clustering, affinity propagation, mean shift, spectral clustering, hierarchical clustering, agglomerative clustering, DBSCAN (Density-based spatial clustering of applications with noise), OPTICS (Ordering points to identify the clustering structure), Gaussian mixtures or BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies). The latter few of these methods may be suitable in particular for large dimensional Zernike spaces (e.g., comprising a large number of Zernikes at once). These clustering algorithms / methods and others are well known to the skilled person and will not be described in detail herein. This list is of course non-exhaustive and alternative clustering method may instead be employed.

[0045] A representative illumination profile / pupil (and optionally target setting, e.g., pitch) may be determined for each cluster from the clustered Zernike sensitivity data. At a simplest level, this representative illumination profile may comprise any of the illumination profiles corresponding to a datapoint in each cluster. In another embodiment, the representative illumination profile may be determined, for example, based on the Zernike sensitivities described by a cluster center or centroid of (or any other suitable location within) each cluster. This may comprise determining the representative illumination profile as the illumination profile used to determine the nearest datapoint to this centroid, for each cluster. However, better performance may be obtained if an optimized representative illumination profile is determined, which has been optimized for the Zernike sensitivities described by the centroid. This optimization may optionally comprise a co-optimization with target settings such as pitch. The optimization may comprise using a suitable optimization algorithm, such as a genetic algorithm or gradient descent algorithm. The optimization may instead use a lookup table linking the Zernike sensitivities to illumination profiles (and optionally target settings).

[0046] Figure 4 illustrates the situation for a number of 50 different illumination profiles (i.e., one datapoint per illumination profile in each plot) by plotting corresponding Zernike sensitivities for Z4, Z12 and Z21. These specific Zernikes are purely illustrative. In practice, more than three Zernike sensitivities will typically be considered to find representative illumination profiles (for example all Zernikes Z2 - Z64, however more than three pupils cannot be easily illustrated graphically in one plot). Figure 4a) shows datapoints in a 3D space defined by the three Zernikes Z4, Z12, Z21, while Figures 4b) to 4d) are 2D plots of the three permutations, namely: 4b) Z12 vs Z21 sensitivities, 4c) Z4 vs Z12 sensitivities and 4d) Z4 vs Z21 sensitivities. Each illumination profile has slightly different Zernike sensitivities, as shown. While each lithographic apparatus is qualified e.g., during and / or after setup procedures to minimize Zernike aberrations, due to imperfections there is typically always a small residual remaining for all Zernike terms. This causes performance deviations in use.

[0047] In this specific example, the datapoints have been split into four different clusters Cl, C2, C3, C4; e.g., using a k-means clustering algorithm. Each cluster center (centroid) is shown as an “x”. Representative illumination profile (and target) settings for each cluster may be determined from the illumination profile dataset. In this specific example there are four clusters, which corresponds to fourrepresentative illumination profiles. The four representative illumination profiles may be determined from a lookup table of many different simulated illumination profiles or via a different optimization technique such as gradient descent or a genetic algorithm, based on the aberration sensitivity data for each respective centroid. As such, in this specific example, 50 illumination profiles have been reduced to four representative illumination profiles.

[0048] The representative illumination profiles (and determined target settings) can then be used in a qualification action such as an acceptance test, e.g., using conventional methods in resist. As such, the actual qualification / acceptance may be performed only for each of the representative illumination profiles (e.g., one per group or cluster), rather than all of the illumination profiles which will be used.

[0049] Each of these steps may be performed (e.g., separately) for different exposure error metrics, e.g., for overlay and / or relating to focus.

[0050] In this manner, the number of different illumination profiles qualified during an acceptance test may be reduced, thereby reducing the setup and potentially the recovery time, and increasing the net productivity of the lithographic apparatus.

[0051] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described.

[0052] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may 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.

[0053] The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g., having a wavelength in the range of 1-100 nm), as well as particle beams, such as ion beams or electron beams.

[0054] The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components. Reflective components are likely to be used in an apparatus operating in the UV and / or EUV ranges.

[0055] The breadth and scope of the present invention should not be limited by any of the abovedescribed exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

CLAIMS1. A computer implemented method of determining representative illumination profiles for performing a qualification action on an exposure apparatus; the method comprising: obtaining aberration sensitivity data for a plurality of illumination profiles, said aberration sensitivity data describing the sensitivity of an exposure error metric with aberration associated with each respective different illumination profile of said plurality of illumination profiles; grouping said plurality of illumination profiles into one or more groups according to a similarity in their corresponding aberration sensitivity data; and determining a respective representative illumination profile for each of said groups.

2. A method as claimed in claim 1 , wherein said grouping step comprises using a clustering algorithm to group said plurality of illumination profiles.

3. A method as claimed in claim 2, wherein said clustering algorithm comprises one or more of k-means clustering, affinity propagation, mean shift, spectral clustering, hierarchical clustering, agglomerative clustering, DBSCAN, OPTICS, Gaussian mixtures or BIRCH.

4. A method as claimed in any preceding claim, wherein said aberration sensitivity data is described in terms of one or more Zernike aberration functions.

5. A method as claimed in any preceding claim, wherein said aberration sensitivity data is described in terms of a plurality of Zernike aberration functions, and said grouping step is performed in a multi-dimensional space, the number of dimensions corresponding to the number of said plurality of Zernike aberration functions.

6. A method as claimed in any preceding claim, wherein the step of determining a respective representative illumination profile for each of said groups comprises determining each representative illumination profile as any one illumination profile comprised in each respective group.

7. A method as claimed in any of claims 1 to 5, comprising determining a respective centroid for each group; and determining a respective representative illumination profile from each centroid.

8. A method as claimed in claim 7, wherein the step of determining a respective representative illumination profile for each of said groups comprises determining each representative illumination profile as the closest illumination profile to the centroid in each respective group.

9. A method as claimed in claim 7, wherein the step of determining a respective representative illumination profile for each of said groups comprises determining each representative illumination profile as an illumination profile optimized for the aberration sensitivities described by each respective centroid.

10. A method as claimed in claim 9, wherein said obtaining aberration sensitivity data comprises simulating exposure of one or more structures with said plurality of illumination profiles to determine said aberration sensitivity data; and wherein said determining an illumination profile optimized for the aberration sensitivities described by each respective centroid comprises determining an illumination profile and one or more settings of said one more structures co-optimized for the aberration sensitivities described by each respective centroid.

11. A method as claimed in any of claims 1 to 9, wherein said obtaining aberration sensitivity data comprises simulating exposure of one or more structures with said plurality of illumination profiles to determine said aberration sensitivity data.

12. A method as claimed in any preceding claim, wherein said exposure error metric comprises one or more of overlay error or a focus error.

13. A method as claimed in any preceding claim, comprising performing a qualification test and / or acceptance test on an exposure apparatus using each of said representative illumination profiles.

14. A computer program comprising program instructions operable to perform the method of any preceding claim, when run on a suitable apparatus.

15. A non-transient computer program carrier comprising the computer program of claim 14.

16. A processing arrangement comprising: a non-transient computer program carrier comprising a computer program as claimed in claim 15, when run on a suitable apparatus; and a processor operable to run the computer program comprised on said non-transient computer program carrier.

17. A lithographic apparatus comprising the processing arrangement of claim 16.

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