Method for controlling a manufacturing apparatus and associated apparatuses

Abstract

Disclosed is a method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer. The method comprises obtaining process error data relating to said manufacturing process when forming said first sub-region on a substrate, determining a first on-product error from said process error data, said on-product error relating to an error in formation of said first sub-region; and determining, from said on-product error, a correction for said manufacturing process when forming said second sub-region on said substrate.

Description

METHOD FOR CONTROLLING A MANUFACTURING APPARATUS AND ASSOCIATED APPARATUSESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 24150622.9 which was filed on 8 January 2024 and EP application 24166061.2 which was filed on 25 March 2024 which is incorporated herein in its entirety by referenceBACKGROUNDField of the Invention

[0002] The present invention relates to methods and apparatus for applying patterns to a substrate in a lithographic process.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. 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 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. Known lithographic apparatus 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 substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

[0004] In order to monitor the lithographic process, parameters of the patterned substrate are measured. Parameters may include, for example, the overlay error between successive layers formed in or on the patterned substrate and critical linewidth (CD) of developed photosensitive resist. This measurement may be performed on a product substrate and / or on a dedicated metrology target. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. 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. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function ofwavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.

[0005] Examples of known scatterometers include angle -resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. The targets used by such scatterometers are relatively large, e.g., 40pm by 40pm, gratings and the measurement beam generates a spot that is smaller than the grating (i.e., the grating is underfilled). In addition to measurement of feature shapes by reconstruction, diffraction based overlay 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 US20110027704 A, US20110043791 A, US2011102753A1, US20120044470A, US20120123581A, US20130258310A, US20130271740A and WO2013178422A1. 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] In performing lithographic processes, such as application of a pattern on a substrate or measurement of such a pattern, process control methods are used to monitor and control the process. Such process control techniques are typically performed to obtain corrections for control of the lithographic process. It would be desirable to improve such process control methods.

[0007] In particular, it is sometimes necessary to “stitch” together a die from two or more sub-regions, e.g., where each sub-region corresponds to an exposure field of a particular lithographic apparatus and the die size is larger than the field size. It would be desirable to improve on process control methods to expose stitched dies.SUMMARY OF THE INVENTION

[0008] In a first aspect of the invention, there is provided a method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second subregion in a common layer; the method comprising: obtaining process error data relating to said manufacturing process when forming said first sub-region on a substrate; determining a first on-product error from said process error data, said on-product error relating to an error in formation of said first sub-region; and determining, from said on-product error, a correction for said manufacturing process when forming said second sub-region on said substrate.

[0009] In a second aspect of the invention, there is provided a method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer, wherein the first sub-region and second sub-region comprise a common stitching area defined by an area of overlap of the first sub-region and second sub-region; the method comprising: obtaining process error data relating to said manufacturing process when forming said first sub-region and second sub-region on a substrate; determining, from said process error data, a co-optimized correction for each of said at least a first sub-region and a second sub-region, wherein said determining a co-optimized correction comprising applying at least one of: a stitching area performance penalty and / or constraint which imposes a penalty and / or constraint on at least one parameter of interest within stitching area; and / or a through-stack penalty and / or constraint which imposes a penalty and / or constraint on overlay error with respect to at least one subsequent layer, exposed subsequent to said common layer.

[0010] In a third aspect of the invention, there is provided a processing device for determining a correction for control of at least one manufacturing apparatus configured to provide product structures to a substrate in a manufacturing process, the processing device being configured to perform the method of the first or second aspect.

[0011] In a fourth aspect of the invention, there is provided a computer program comprising program instructions operable to perform the method of the first aspect or second aspect when run on a suitable apparatus.

[0012] In a fifth aspect of the invention, there is provided a manufacturing apparatus configured to provide product structures to a substrate in a manufacturing process, said manufacturing apparatus comprising the processing device of the third aspect.

[0013] Further aspects, features and advantages of the invention, as well as the structure and operation of various embodiments of the invention, are described in detail below with reference to the accompanying drawings. It is noted that the invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings in which:Figure 1 depicts a lithographic apparatus together with other apparatuses forming a production facility for semiconductor devices;Figure 2 comprises a schematic diagram of a scatterometer for use in measuring targets according to embodiments of the invention;Figure 3 illustrates a stitched die arrangement with stitching targets shown in detail;Figure 4 illustrates a multi-pass multiple exposure sequence for exposing stitched dies;Figure 5 is a flowchart of a method for determining a stitching correction for a sub-region of a stitched die according to an embodiment;Figure 6 schematically illustrates a stitched exposure using two reticles, illustrating a method for increasing the depth of focus within a stitching area of the stitched exposure;Figure 7 schematically illustrates a stitched exposure using two reticles, illustrating a method for distributing corrections between the two exposures within the stitching area of the stitched exposure; andFigure 8 schematically illustrates a stitched exposure using two reticles, illustrating a method for measuring stitched overlay without the need for dedicated targets.DETAILED DESCRIPTION

[0015] 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.

[0016] Figure 1 at 200 shows a lithographic apparatus LA as part of an industrial production facility implementing a high-volume, lithographic manufacturing process. In the present example, the manufacturing process is adapted for the manufacture of for semiconductor products (integrated circuits) on substrates such as semiconductor wafers. The skilled person will appreciate that a wide variety of products can be manufactured by processing different types of substrates in variants of this process. The production of semiconductor products is used purely as an example which has great commercial significance today.

[0017] Within the lithographic apparatus (or “litho tool” 200 for short), a measurement station MEA is shown at 202 and an exposure station EXP is shown at 204. A control unit LACU is shown at 206. In this example, each substrate visits the measurement station and the exposure station to have a pattern applied. In an optical lithographic apparatus, for example, a projection system is used to transfer a product pattern from a patterning device MA onto the substrate using conditioned radiation and a projection system. This is done by forming an image of the pattern in a layer of radiation- sensitive resist material.

[0018] 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. The patterning MA device may be a mask or reticle, which imparts a pattern to a radiation beam transmitted or reflected by the patterning device. Well-known modes of operation include a stepping mode and a scanning mode. As is well known, the projection system may cooperate with support and positioning systems for the substrate and the patterning device in a variety of ways to apply a desired pattern to many targetportions across a substrate. Programmable patterning devices may be used instead of reticles having a fixed pattern. The radiation for example may include electromagnetic radiation in the deep ultraviolet (DUV) or extreme ultraviolet (EUV) wavebands. The present disclosure is also applicable to other types of lithographic process, for example imprint lithography and direct writing lithography, for example by electron beam.

[0019] The lithographic apparatus LA described herein may be used in a method for manufacturing a semiconductor device. A semiconductor device manufacturing method comprises receiving a substrate W with a photoresist layer. The method further comprises directing a radiation beam from a radiation source to transfer a pattern from a mask onto the photoresist layer. This could be achieved by a patterning device which is configured to form a patterned radiation beam, imparting the patterned radiation beam onto the photoresist layer. The method for manufacturing a semiconductor device further comprises the step of removing a portion of the photoresist layer to form the pattern over the substrate W.

[0020] The substrate W may be made of silicon or other semiconductor materials. Alternatively or additionally, the substrate W may include other semiconductor materials such as germanium (Ge) or carbon (C). In some embodiments, the semiconductor substrate is made of a compound semiconductor such as IILV compound semiconductors, II-V compound semiconductors, and / or any suitable integration of Group IV materials. In some embodiments, the substrate W may be a silicon-on-insulator (SOI) or a germanium-on-insulator (GOI) substrate.

[0021] The semiconductor device made from the substrate W may have various device elements. Examples of semiconductor device elements that are formed over the substrate W include transistors (e.g., planar or non-planar metal oxide semiconductor field effect transistors (MOSFET), bipolar junction transistors (BJT), high-voltage transistors, high-frequency transistors, etc.), diodes, CMOS image sensors, passive devices, and / or other applicable elements. Various processes may be performed to form the semiconductor device elements, such as deposition, etching, implantation, epitaxial growth, polishing, thermal treatment, and / or other suitable processes. In some embodiments, the substrate W is coated with a photoresist layer sensitive to the DUV or EUV wavebands.

[0022] The lithographic apparatus control unit LACU which controls all the movements and measurements of various actuators and sensors to receive substrates W and reticles MA and to implement the patterning operations. LACU also includes signal processing and data processing capacity to implement desired calculations relevant to the operation of the apparatus. In practice, control unit LACU will be realized as a system of many sub-units, each handling the real-time data acquisition, processing and control of a subsystem or component within the apparatus.

[0023] Before the pattern is applied to a substrate at the exposure station EXP, the substrate is processed in at the measurement station MEA so that various preparatory steps may be carried out. The preparatory steps may include mapping the surface height of the substrate using a level sensor and measuring the position of alignment marks on the substrate using an alignment sensor. The alignmentmarks are arranged nominally in a regular grid pattern. However, due to inaccuracies in creating the marks and also due to deformations of the substrate that occur throughout its processing, the marks deviate from the ideal grid. Consequently, in addition to measuring position and orientation of the substrate, the alignment sensor in practice must measure in detail the positions of many marks across the substrate area, if the apparatus is to print product features at the correct locations with very high accuracy. The apparatus may be of a so-called dual stage type which has two substrate tables, each with a positioning system controlled by the control unit LACU. While one substrate on one substrate table is being exposed at the exposure station EXP, another substrate can be loaded onto the other substrate table at the measurement station MEA so that various preparatory steps may be carried out. The measurement of alignment marks is therefore very time-consuming and the provision of two substrate tables enables a substantial increase in the throughput of the apparatus. 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. Lithographic apparatus LA may for example is of a so-called dual stage type which has two substrate tables and two stations - an exposure station and a measurement station- between which the substrate tables can be exchanged.

[0024] Within the production facility, apparatus 200 forms part of a “litho cell” or “litho cluster” that contains also a coating apparatus 208 for applying photosensitive resist and other coatings to substrates W for patterning by the apparatus 200. At an output side of apparatus 200, a baking apparatus 210 and developing apparatus 212 are provided for developing the exposed pattern into a physical resist pattern. Between all of these apparatuses, substrate handling systems take care of supporting the substrates and transferring them from one piece of apparatus to the next. These apparatuses, which are often collectively referred to as the track, are under the control of a track control unit which is itself controlled by a supervisory control system SCS, which also controls the lithographic apparatus via lithographic apparatus control unit LACU. Thus, the different apparatus can be operated to maximize throughput and processing efficiency. Supervisory control system SCS receives recipe information R which provides in great detail a definition of the steps to be performed to create each patterned substrate.

[0025] Once the pattern has been applied and developed in the litho cell, patterned substrates 220 are transferred to other processing apparatuses such as are illustrated at 222, 224, 226. A wide range of processing steps is implemented by various apparatuses in a typical manufacturing facility. For the sake of example, apparatus 222 in this embodiment is an etching station, and apparatus 224 performs a post-etch annealing step. Further physical and / or chemical processing steps are applied in further apparatuses, 226, etc.. Numerous types of operation can be required to make a real device, such as deposition of material, modification of surface material characteristics (oxidation, doping, ion implantation etc.), chemical-mechanical polishing (CMP), and so forth. The apparatus 226 may, in practice, represent a series of different processing steps performed in one or more apparatuses. As another example, apparatus and processing steps may be provided for the implementation of self-aligned multiple patterning, to produce multiple smaller features based on a precursor pattern laid down by the lithographic apparatus.

[0026] As is well known, the manufacture of semiconductor devices involves many repetitions of such processing, to build up device structures with appropriate materials and patterns, layer-by-layer on the substrate. Accordingly, substrates 230 arriving at the litho cluster may be newly prepared substrates, or they may be substrates that have been processed previously in this cluster or in another apparatus entirely. Similarly, depending on the required processing, substrates 232 on leaving apparatus 226 may be returned for a subsequent patterning operation in the same litho cluster, they may be destined for patterning operations in a different cluster, or they may be finished products to be sent for dicing and packaging.

[0027] Each layer of the product structure requires a different set of process steps, and the apparatuses 226 used at each layer may be completely different in type. Further, even where the processing steps to be applied by the apparatus 226 are nominally the same, in a large facility, there may be several supposedly identical machines working in parallel to perform the step 226 on different substrates. Small differences in set-up or faults between these machines can mean that they influence different substrates in different ways. Even steps that are relatively common to each layer, such as etching (apparatus 222) may be implemented by several etching apparatuses that are nominally identical but working in parallel to maximize throughput. In practice, moreover, different layers require different etch processes, for example chemical etches, plasma etches, according to the details of the material to be etched, and special requirements such as, for example, anisotropic etching.

[0028] The previous and / or subsequent processes 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.

[0029] In order that the substrates that are exposed by the lithographic apparatus are exposed correctly and consistently, it is desirable to inspect exposed substrates to measure properties such as overlay errors between subsequent layers, line thicknesses, critical dimensions (CD), etc. Accordingly a manufacturing facility in which litho cell LC is located also includes metrology system which receives some or all of the substrates W that have been processed in the litho cell. Metrology results are provided directly or indirectly to the supervisory control system SCS. If errors are detected, adjustments may be made to exposures of subsequent substrates, especially if the metrology can be done soon and fast enough that other substrates of the same batch are still to be exposed. Also, already exposed substrates may be stripped and reworked to improve yield, or discarded, thereby avoiding performing furtherprocessing on substrates that are known to be faulty. In a case where only some target portions of a substrate are faulty, further exposures can be performed only on those target portions which are good.

[0030] Also shown in Figure 1 is a metrology apparatus 240 which is provided for making measurements of parameters of the products at desired stages in the manufacturing process. A common example of a metrology station in a modern lithographic production facility is a scatterometer, for example a dark-field scatterometer, an angle-resolved scatterometer or a spectroscopic scatterometer, and it may be applied to measure properties of the developed substrates at 220 prior to etching in the apparatus 222. Using metrology apparatus 240, it may be determined, for example, that important performance parameters such as overlay or critical dimension (CD) do not meet specified accuracy requirements in the developed resist. Prior to the etching step, the opportunity exists to strip the developed resist and reprocess the substrates 220 through the litho cluster. The metrology results 242 from the apparatus 240 can be used to maintain accurate performance of the patterning operations in the litho cluster, by supervisory control system SCS and / or control unit LACU 206 making small adjustments over time, thereby minimizing the risk of products being made out-of-specification, and requiring re-work.

[0031] Additionally, metrology apparatus 240 and / or other metrology apparatuses (not shown) can be applied to measure properties of the processed substrates 232, 234, and incoming substrates 230. The metrology apparatus can be used on the processed substrate to determine important parameters such as overlay or CD.

[0032] A metrology apparatus suitable for use in embodiments of the invention is shown in Figure 2(a). This is purely an example metrology apparatus and any suitable metrology apparatus for measuring a process parameter such as overlay on a substrate may be used. A target T and diffracted rays of measurement radiation used to illuminate the target are illustrated in more detail in Figure 2(b). The metrology apparatus illustrated is of a type known as a dark field metrology apparatus. The metrology apparatus may be a stand-alone device or incorporated in either the lithographic apparatus LA, e.g., at the measurement station, or the lithographic cell LC. An optical axis, which has several branches throughout the apparatus, is represented by a dotted line O. In this apparatus, light emitted by source 11 (e.g., a xenon lamp) is directed onto substrate W via a beam splitter 15 by an optical system comprising lenses 12, 14 and objective lens 16. These lenses are arranged in a double sequence of a 4F arrangement. A different lens arrangement can be used, provided that it still provides a substrate image onto a detector, and simultaneously allows for access of an intermediate pupil-plane for spatial- frequency filtering. Therefore, the angular range at which the radiation is incident on the substrate can be selected by defining a spatial intensity distribution in a plane that presents the spatial spectrum of the substrate plane, here referred to as a (conjugate) pupil plane. In particular, this can be done by inserting an aperture plate 13 of suitable form between lenses 12 and 14, in a plane which is a back- projected image of the objective lens pupil plane. In the example illustrated, aperture plate 13 has different forms, labeled 13N and 13S, allowing different illumination modes to be selected. Theillumination system in the present examples forms an off-axis illumination mode. In the first illumination mode, aperture plate 13N provides off-axis from a direction designated, for the sake of description only, as ‘north’ . In a second illumination mode, aperture plate 13S is used to provide similar illumination, but from an opposite direction, labeled ‘south’. Other modes of illumination are possible by using different apertures. The rest of the pupil plane is desirably dark as any unnecessary light outside the desired illumination mode will interfere with the desired measurement signals.

[0033] As shown in Figure 2(b), target T is placed with substrate W normal to the optical axis O of objective lens 16. The substrate W may be supported by a support (not shown). A ray of measurement radiation I impinging on target T from an angle off the axis O gives rise to a zeroth order ray (solid line 0) and two first order rays (dot-chain line +1 and double dot-chain line -1). It should be remembered that with an overfilled small target, these rays are just one of many parallel rays covering the area of the substrate including metrology target T and other features. Since the aperture in plate 13 has a finite width (necessary to admit a useful quantity of light, the incident rays I will in fact occupy a range of angles, and the diffracted rays 0 and +1 / -1 will be spread out somewhat. According to the point spread function of a small target, each order +1 and -1 will be further spread over a range of angles, not a single ideal ray as shown. Note that the grating pitches of the targets and the illumination angles can be designed or adjusted so that the first order rays entering the objective lens are closely aligned with the central optical axis. The rays illustrated in Figure 2(a) and 2(b) are shown somewhat off axis, purely to enable them to be more easily distinguished in the diagram.

[0034] At least the 0 and +1 orders diffracted by the target T on substrate W are collected by objective lens 16 and directed back through beam splitter 15. Returning to Figure 2(a), both the first and second illumination modes are illustrated, by designating diametrically opposite apertures labeled as north (N) and south (S). When the incident ray I of measurement radiation is from the north side of the optical axis, that is when the first illumination mode is applied using aperture plate 13N, the +1 diffracted rays, which are labeled +1(N), enter the objective lens 16. In contrast, when the second illumination mode is applied using aperture plate 13S the -1 diffracted rays (labeled - 1 (S)) are the ones which enter the lens 16.

[0035] A second beam splitter 17 divides the diffracted beams into two measurement branches. In a first measurement branch, optical system 18 forms a diffraction spectrum (pupil plane image) of the target on first sensor 19 (e.g. a CCD or CMOS sensor) using the zeroth and first order diffractive beams. Each diffraction order hits a different point on the sensor, so that image processing can compare and contrast orders. The pupil plane image captured by sensor 19 can be used for many measurement purposes such as reconstruction used in methods described herein. The pupil plane image can also be used for focusing the metrology apparatus and / or normalizing intensity measurements of the first order beam.

[0036] In the second measurement branch, optical system 20, 22 forms an image of the target T on sensor 23 (e.g. a CCD or CMOS sensor). In the second measurement branch, an aperture stop 21 isprovided in a plane that is conjugate to the pupil-plane. Aperture stop 21 functions to block the zeroth order diffracted beam so that the image of the target formed on sensor 23 is formed only from the -1 or + 1 first order beam. The images captured by sensors 19 and 23 are output to processor PU which processes the image, the function of which will depend on the particular type of measurements being performed. Note that the term ‘image’ is used here in a broad sense. An image of the grating lines as such will not be formed, if only one of the -1 and +1 orders is present.

[0037] The particular forms of aperture plate 13 and field stop 21 shown in Figure 2 are purely examples. In another embodiment of the invention, on-axis illumination of the targets is used and an aperture stop with an off-axis aperture is used to pass substantially only one first order of diffracted light to the sensor. In yet other embodiments, 2nd, 3rdand higher order beams (not shown in Figure 2) can be used in measurements, instead of or in addition to the first order beams.

[0038] The target T may comprise a number of gratings, which may have differently biased overlay offsets in order to facilitate measurement of overlay between the layers in which the different parts of the composite gratings are formed. The gratings may also differ in their orientation, so as to diffract incoming radiation in X and Y directions. In one example, a target may comprise two X-direction gratings with biased overlay offsets +d and -d, and Y-direction gratings with biased overlay offsets +d and -d. Separate images of these gratings can be identified in the image captured by sensor 23. Once the separate images of the gratings have been identified, the intensities of those individual images can be measured, e.g., by averaging or summing selected pixel intensity values within the identified areas. Intensities and / or other properties of the images can be compared with one another. These results can be combined to measure different parameters of the lithographic process

[0039] The largest area which can be exposed in a single exposure of a lithographic apparatus is defined by its maximum scanning field area. This is defined by the width of the exposure slit in a first direction (often designated the x-direction) and the maximum scan length in the orthogonal direction of the same (substrate) plane (often designated the y-direction). In some cases, the die area (the substrate area of the device being manufactured, referred to herein as the substrate field area or substrate region area) is larger than the maximum scanning field area. In this situation, some or all layers of the device need to be exposed on the substrate region (or substrate field) in multiple (e.g., two) separate adjacent exposures. For example: a substrate region twice as large as the maximum scanning field area may be exposed in two exposures: a first exposure using a first reticle comprising a first pattern is used to print a first substrate sub-region (e.g., first half in terms of area on the substrate) of the layer, and a second reticle comprising a second pattern is used to print a second sub-region of the layer (e.g., the second half, although there may be a small overlap) on the substrate, adjacent the first half therefore forming the complete layer of a die. The two halves can be referred to as having been “stitched” together, with the process sometimes referred to as intra-die stitching.

[0040] Reasons for die stitching may be two-fold. Die sizes are increasing such that dies may be larger than the field size of conventional lithographic apparatuses. In addition to this, newer or proposedEUV lithographic apparatuses, which have a large numerical aperture (NA), have a reduced field size; more specifically a half-field size, i.e., the field size is half that of a conventional field size in one of the substrate plane dimensions.

[0041] As already discussed, one or more performance parameters, such as overlay, are measured using a metrology device on processed substrates and process corrections are determined which aim to minimize the overlay error for subsequent substrates and / or subsequent layers of the same substrate. The process corrections are typically implemented by the lithographic apparatus in a feedback loop.

[0042] For a stitched die, the positioning of each sub-region of the stitched die (i.e., where a stitched die comprises two or more sub-regions, typically exposure fields, stitched together) with respect to the other sub-regions of the stitched die is an important positioning metric which is additional to conventional overlay (position with respect to one or more earlier exposed layers). Measurement of the position of one sub-region with respect to one or more other sub-regions of the stitched die may be referred to herein as “stitched overlay”, which is a positional metric which differs from conventional true overlay (another positioning metric) as it relates to relative positioning within a single layer.

[0043] Stitched overlay may be monitored and therefore controlled in a similar manner to conventional overlay, e.g., by measuring targets, herein referred to as stitching targets, comprising a first structure exposed with a first sub-region being stitched and a second structure exposed with a second sub-region being stitched. For example, the first and second structures may comprise respective boxes, e.g., in a box-in-box type arrangement or adjacent box arrangement. Such a stitching target may comprise a first image of a box in (e.g., at a periphery of) the first sub-region being formed inside or adjacent to a second image of a box in (e.g., at a periphery of) the second sub-region, the two subregions overlapping in the boundary area where the stitching target is formed. Alternatively, the two images may each comprise grating structures which are designed to be interlaced when imaged at the boundary area. Misalignment of such an interlaced target would manifest as asymmetry which could then be measured similarly to overlay targets, or else the position of the second structure may be determined with respect to first structure in terms of a vector. Such a stitching target may be formed over another grating in another layer (or another grating formed over it) to provide for a stitched overlay target, for which overlay to the other layer can also be measured.

[0044] Figure 3 illustrates an exemplary stitched die 300 comprising four sub-regions 310a, 310b, 310c, 310d. The two sub-regions may be overlapping (at least partially) to define stitching boundary areas 320 where sub-regions are stitched. In the stitching boundary areas 320 are stitching targets 330a, 330b, 330c, 330d. Stitching targets 330a, 330b are shown in larger detail. Each of these stitching targets 330a, 330b, 330c, 330d, comprises a two box structure, each exposed with a different sub-region. Referring to stitching target 330a, the gray box is formed with sub-region 3 lOd and the black box formed with sub-region 310a. Similarly, for stitching target 330b, the gray box is formed with sub-region 310b and the black box formed with sub-region 310a. The dotted boxes represent nominal positions for the respective boxes. The arrows represent vectors describing the positional difference from a first box(structure) to a second box (structure), from which can be measure and a positional correction can be determined (e.g. in a feedback method). Note that this is only an example arrangement, and the stitching targets or stitched die may differ from that shown (e.g., a common arrangement may comprise two halffield sub-regions stitched together).

[0045] Figure 4 illustrates an exposure sequence for exposing substrates in multiple passes to obtain a stitched die. Shown are a first wafer handling stage 400, which is at atmospheric pressure, a second wafer handling stage 405 in a vacuum and a wafer stage arrangement 410 also in a vacuum (a vacuum assumes an EUV apparatus is being used, however the concepts disclosed herein are not limited to EUV and therefore there all operations may be performed at atmospheric pressure). The wafer stage arrangement 410 may comprise a measure side or measurement station 415 and an exposure side or exposure station 420 (although the concepts herein are not limited to dual-stage apparatuses). A first chuck 417 and second chuck 422 transports each substrate within wafer stage arrangement 410.

[0046] The gray arrow describes a conventional single-pass sequence, wherein each substrate is prealigned 425, loaded 430, admitted into the second wafer handling stage 405 via load lock 435, undergoes further pre-alignment 445 and is loaded onto a stage 450. Following measurement (fine alignment) and exposure at the measure side 415 and exposure side 420 respectively, the substrate is stage-unloaded 460 to exit the vacuum chamber 405, then unloaded 470 and discharged 475.

[0047] The black arrow describes a multi-pass exposure sequence for exposing stitched dies, where every substrate would be loaded, measured, and exposed twice or more times. To maximize the throughput of multi-reticle exposure, a new hardware component, referred to as a Stocker 465, may be used to store substrates between exposures. Therefore, at the end of the first pass (or any pass except the final pass), the substrate is unloaded 470, held in the Stocker 465 (e.g., for a few minutes during which the reticle may be changed), then aligned 425 and loaded 430 to begin another pass.

[0048] When a series of fields are exposed at different points in time, a residual error made in a first exposure series will impact stitching quality if it is not anticipated.

[0049] Additionally, when multiple passes are used, a single and pre-determined alignment strategy (a fixed set of mark types, sampling, color recipe, and models) for all passes may no longer accurately measure and predict the substrate deformation, because the alignment marks and wafers can be deformed differently every time passing through the measure / exposure sides.

[0050] A manufacturing apparatus such as an exposure apparatus or lithographic apparatus (and / or associated devices) typically generates process error information or process error data relating to the manufacturing process or exposure process, e.g., relating to various modules and / or actions. Such process error data may comprise inter alia lens model error data (e.g., lens model residual data), lens fingerprint data (lens error distributions), actuation error or residual data (e.g. servo error data), lens overpressure error data, alignment data, alignment residual data (residuals after fitting an alignment model).

[0051] It is proposed herein to use such process error data, e.g., process error data generated during the manufacturing process or lithographic exposure process and / or generated within the manufacturing / lithographic apparatus when performing at least a first exposure sequence to expose at least one first sub-region of a stitched die, to determine, e.g., predict, the resultant on-product or position metric error of the first sub-region, determining a correction which compensates and / or mitigates the determined on-product or position metric error when exposing at least one second sub-region of the stitched die. The method may then apply the correction when performing at least a second exposure sequence to expose the at least one second sub-region of the stitched die area. For example, the correction may be determined to match any overlay and / or positional errors from the at least one first sub-region.

[0052] As such, a method is disclosed for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer; the method comprising: obtaining process error data relating to said manufacturing process when forming said first sub-region; determining a first on-product error from said process error data, said on- product error relating to an error in formation of said first sub-region; and determining a correction for said manufacturing process when forming said second sub-region from said on-product error.

[0053] The on-product error may comprise an error in terms of at least one positioning metric such as positioning or placement of structures within said first sub-region, such that a determined correction minimizes stitched overlay error (error in relative positioning of one sub-region with respect to at least one other sub-region of a stitched die). Alternatively or in addition, the positioning metric may be (e.g., conventional) overlay to another layer. As such, the method may comprise matching overlay (error) for the two sub-regions. The method may also comprise a co-optimized correction for stitched overlay and conventional overlay (which may be optionally weighted in favor of one or the other overlay types).

[0054] Figure 5 is a flowchart describing a method according to an embodiment. Process error data 500 relating to a first exposure sequence is obtained, e.g., to expose (e.g., multiple repetitions of) a first sub-region over a substrate, each first sub-region comprising a first portion of a stitched die. Process error data 500 may comprise for example actuation error data 505 (e.g., actuation residual data or servo error / residual data) and / or lens error data 510. The actuation error data 505 may comprise for example one or more of: servo MA (moving average actuation residual data), servo dx (x-displacement actuation residual data), servo dy (y -displacement actuation residual data) or servo dRz (rotation around z axis actuation residual data). The lens error data 510 may comprise e.g., aberration error (aberration residuals) of lens corrections actuated during the first sub-region exposure, for example expressed in terms of Zernike functions. Other types of error data may also be used, for example alignment residual data may be used in this method.

[0055] At step 520, an on-product error (e.g., stitching and / or conventional overlay error) relating to the first sub-region exposure may be determined or predicted from error data 500. This on-product errormay be determined from the actuation error data 505 as obtained from the respective servo driver. The lens error data 510 may be converted to an on-product error using the relevant overlay Zernike sensitivities 515. A correction 535 may be determined 530 based on the determined on-product error so as to improve stitching of the to-be-exposed second sub-region to the first sub-region (e.g., to match on-product error of the first and second sub-regions).

[0056] The correction determination step 530 may also be subject to rules and / or constraints 525 such as possible and / or allowable actuations, allowed error for field deformation and / or other overlays (e.g., if conventional overlay is being matched for the sub-regions by the correction, a constraint may be imposed here for the stitched overlay and vice versa). For example, particular actuation capabilities may be specified and / or prohibited; e.g., to specify that field translations are to be used to correct lens errors in horizontal stitching. In another example, a maximum amount of stitching correction may be specified, e.g., in absolute terms (e.g., nm) or relative terms (percentage). This can be used to balance conventional overlay (if relevant) or image deformation and stitched overlay. Such balancing can be done per actuation parameter, e.g., separately for x-translation Tx and y-translation Ty per sub-region. Additionally it may be appreciated that some lens related errors such as x magnification (Mag x) contributes twice to the stitching error and therefore correction of such errors may be favored over correction of other errors.

[0057] The determined correction 535 may be a feed- forward correction, which is actuated in the during a second exposure sequence 540 to expose (e.g., multiple repetitions of) a second sub-region, each second sub-region comprising a second portion of a stitched die. Any actuation error for the stitching may subsequently be reported.

[0058] In an embodiment, the (e.g., second) exposure sequence may be determined or optimized to ensure sufficient computation time is available for determining the on-product error and consequent correction. Such an exposure sequence may provide sufficient computation time while maintaining queue depth stable (e.g., currently it is 5 sub-regions / fields). It is important to note that there is typically a reticle change involved in exposing the first and second series of sub-regions substantially adding to the budget for computational effort.

[0059] In an embodiment, alignment data (e.g., as-measured / pre-modeled and / or modeled alignment data) may be fed forward from the first exposure sequence to the second exposure sequence. This may enable alignment measurement and / or model data from different exposure sequences to be mixed. This may mean that the metrology effort (number of alignment marks) may be reduced for the second exposure sequence, leading to a throughput improvement when the exposure is measure-side limiting, e.g. exposing smaller fields (e.g., half-fields where exposure time is halved) or using a low dose. In an extreme case, should it be assumed / determined that in-plane deformation is constant between exposure sequences, the full model results from the first exposure sequence may be used for the second exposure sequence, with equivalent steps of the measure sequence skipped (e.g. pre-align and / or fine alignment) of the second exposure sequence. Alternatively, such alignment feed-forward may be used to improvethe alignment e.g., capture the dynamic deformation. When the process-induced wafer deformation stays constant / stable between the sequences, the wafer model results from the first sequence can be reused and the second sequence metrology can focus on capturing the dynamic deformation (e.g. wafer reload, lens / reticle heating) by measuring more marks optimized for this or enabling in-situ adjustment (e.g. measuring additional marks on stitched areas to improve stitched overlay).

[0060] In a further embodiment of the method of the present invention comprises defining and / or using more than one pre-determined alignment strategy (e.g., mark types, color recipes, sampling scheme and alignment model) per exposure sequence. The method may further comprise using and or defining an alignment strategy and / or configuration of the lithography apparatus for each pass or exposure sequence including when there are multiple pass or exposure sequence exposing the single layer of a substrate. Advantageously, this embodiment allows capturing the dynamic change between the exposure sequence and provide a better accuracy of wafer alignment. The dynamic changes may be produced by substrate reload, different machine components dynamics, lens / reticle heating, mark asymmetry, etc. A non-limitative example of this embodiment may be when a high NA EUV exposed layer is aligned to a previous high NA EUV exposed layer, AL marks on the first layer exposed may suffer different mark asymmetries due to different mark types, exposure settings, mark-to-device offsets, and imaging-induced asymmetries. Therefore, when both layers are aligned, different color recipe or intra-field model per pass can well capture the differences on mark asymmetry and intra-field fingerprint, between both exposure sequences.

[0061] In a further embodiment, the method of the invention further comprises using or mixing measurement / model data from different exposure sequences. Advantageously, this embodiment reduces the amount of AL marks to measure in the second exposure sequence leading to a throughput improvement of a lithography apparatus when the exposure sequence throughout is measure side limited. In a further embodiment when the in-plane deformation stays constant between passes, the method further comprises reusing the model results for the first exposure sequence and skips certain steps of the measure sequence in the second exposure sequence. In this embodiment, it is proposed to use the extra time to measure in certain areas of interest to obtain a better modeling of the fingerprint in one area.

[0062] In a further embodiment, the method of the invention further comprises performing a simulation of different alignment strategies within the exposure sequence to obtain overlay, EPE, CD, CDU impact of the processed substrate. Advantageously, this embodiment provides an indication on the magnitude of the dynamic deformation between the passes, and whether there is a need to apply different alignment strategies per exposure sequence and co-optimize them. It also provides the advantage to assess whether the measurement from first exposure sequence can be re-used for the second exposure sequence to improve the throughput.

[0063] In a particular embodiment, the same concept of the previous paragraphs may be further extended to other functions in the measure sequence or other data measure within the lithographyapparatus, for instance data measured by the level sensor: substrate levelling and / or substrate height map and / or substrate z-map.

[0064] In the embodiments disclosed herein, conventional overlay and / or stitched overlay corrections may be determined as coefficients (sometimes referred to as k-parameters) for a polynomial in a best fit method such that a correction based on the polynomial minimizes the respective measured conventional overlay and / or stitched overlay (e.g., on average over the fitted area) when applied. Such an optimization may be performed separately for conventional overlay or stitched overlay (e.g., completely separately or to optimize one with one or more constraints on the other), or else a cooptimization of these different overlays may be performed. The determined coefficients may be fed back to the lithographic apparatus in the form of a sub-recipe characterized by the coefficients.

[0065] A specific example of the proposed methods disclosed may comprise a co-optimization of the stitching error in the merit function of the trajectory calculation. The stitching error may result from at least two sources. A first source may be result from a discontinuous correction request whereby, should requested corrections be different per sub-region and the actuation error be nonzero, the residuals at the boundary between the sub-regions will not exactly match resulting in a stitching error. A second source may result from scanner actuation, whereby the correction potential is greater at the top and bottom edges of the field due to a scan-in / scan-out effect.

[0066] In this embodiment, it is proposed that the stitching error is reduced by including it in the merit function of the trajectory calculation. The stitching error may be represented as a difference between second actuation error data or actuation residuals of the second sub-region exposure and first actuation error data or actuation residuals of the first sub-region exposure. As such, the first sub-region exposure is performed conventionally without taking stitching into account and the second sub-region exposure uses the actuation residuals of the first exposure to improve the stitching error (stitched overlay error) Ar = rB— rAwhere rAand rBare the actuation residuals of the first sub-region exposure and second sub-region exposure respectively.

[0067] In a specific example, the actuation error merit function may take the form:where M is the model matrix, p is the vector of coefficients of the actuation profiles, d is the vector of distortion values (per grid point) and w0is the stitching weight.

[0068] This method is not limited to improving the stitching error in the overlay domain.It can also be used to stitch the focus, MSD or higher order Zernikes.

[0069] As such, methods disclosed herein determine corrections of the to be exposed (half) fields which anticipate errors made in one or more already exposed (half) fields such that at least stitching errors at the boundaries can be reduced.

[0070] Overlay corrections are determined for actuation (as far as it is possible) within the lithographic apparatus, However, when different lithographic apparatuses are used in different layers (e.g., a first lithographic apparatus having an exposure field at half of a conventional field size and a second lithographic apparatus having an exposure field at the full conventional field size, each having respective different correction and / or actuation capabilities), corrections determined per sub-region in the first layer may introduce patterns that are not correctable in the second layer (e.g., any subsequent layer). Alternatively or in addition, the stitched overlay or relative positions of the sub-fields in the first layer is also an important parameter which can result in irregularities in the stitching area (overlap area of the two sub-regions) if not properly controlled.

[0071] An additional embodiment will be described, for which a correction for each of the two subregions which are to be stitched together is co-optimized or co-determined, rather than determined as a feed-forward correction from one sub-region to the other. Such a method may determine a correction based on overlay data measured from one or more substrates of a previous lot (e.g., for a per-lot correction), e.g., a feedback correction. Alternatively, such a method may be performed per-substrate (e.g., to make a rework decision). Advantageously, this embodiment reduces the possibility of manifesting discontinuities in the stitching area between two sub-regions and / or poor overlay performance with respect to a subsequent layer, reducing the number of non-yielding dies.

[0072] Such a method may optimize overlay corrections simultaneously for each sub-region while also taking into account stitching area performance and / or corrections for one or more subsequent layer(s). This may be achieved by applying a stitching area performance constraint and / or penalty to the relevant optimization. As such, a method may comprise determining a co-optimized correction for two or more sub-regions which is constrained by stitching area (or boundary) performance, where the stitching area may describe an area of overlap of two sub-regions. More generally, the proposed method may optimize any process corrections (including inter alia overlay, dose, focus, other parameter of interest or any combination thereof).

[0073] Alternatively or in addition, the co-optimized correction can take into account actuation capability of one or more subsequent layers (e.g., the actuation capability of a lithographic apparatus used to expose the one or more subsequent layers. This can be realized by one or both of constraining the objective function and / or adding penalty terms to the objective function. For example, the constraint and / or penalty may be imposed in terms of through-stack performance, e.g., overlay or other parameter of interest performance with respect to one or more subsequent layers, and in particular one or more subsequent layers subject to different correction capability and / or field size. In particular, two or more sub-regions may be exposed in a first layer by a first lithographic apparatus having a first correction capability and / or first field size (e.g., a field size which defines the size of the sub-regions) and the oneor more subsequent layers may be exposed in a second layer by a second lithographic apparatus having a second correction capability and / or second field size (e.g., a field size larger than said sub-regions, such as twice the size of the first layer sub-regions, 2.5x the size of the first layer sub-regions or 3.5x the size of the first layer sub-regions). For example, a proposed high-NA EUV apparatus has a field size which is half of that of many present DUV or EUV apparatuses. Differences in correction capability may arise, for example, from one or more of different actuation parameterization, different actuation capability and / or different modelling capability / models used.

[0074] The stitching area performance penalty and / or constraint may be a soft constraint which constrains and / or penalizes the difference in (overlay) residual values in the stitching area(s). The specific example described below does not explicitly restrict the stitching error, but rather penalizes stitching overlay error through a stitching variable a which is used as a penalty in the objective function.

[0075] This stitching variable a may be included (e.g., as a normed value) in the objective function as a stitching regularization term (e.g., in addition to the usual minimization of residuals). Optionally, the size or weight of the effect of this stitched overlay penalty may be tuned via a stitching hyperparameter z. The stitching hyperparameter value may be automatically determined based on the use case. Optionally, a stitching deadband threshold d may also be included in the stitched overlay penalty (or constraint), which defines a minimum relevant difference in the stitching area residuals, below which the stitching area residuals can be considered insignificant.

[0076] Regarding the through-stack setting, a through-stack penalty and / or constraint may be imposed, e.g., via a through-stack regularization term in the objective function comprising a through- stack variable ft. The through stack penalty and / or constraint may, for example, penalize the objective value via the (e.g., normed) through-stack variable [1 in a similar manner to how the stitching variable a penalizes the objective value for the stitched overlay. This through-stack penalty may comprise a further soft constraint which constrains the corrections to be applied in the first layer (e.g., comprising two or more sub-regions, each sub-region being exposed in a separate exposure), such that the first layer exposures can be followed (at least to degree or within an acceptable margin) in subsequent layer(s) which are to be exposed by a different lithographic apparatus with different correction capability. As such, the through-stack penalty and / or constraint may penalize differences between first layer corrections described in terms of the correction capability of the first layer and subsequent layer corrections described in terms of the correction capability of the one or more subsequent layers. The through-stack penalty and / or constraint may also comprise a through-stack hyperparameter v to set the constraint weight.

[0077] A (e.g., user specified) through-stack deadband threshold, d may be defined which defines a minimum relevant difference in through stack residuals. In this context, the subsequent layer design matrix C may be constructed for example using a union (or a subset thereof) of the optimization gridsfor the first layer sub-region fields. More generally, the subsequent layer design matrix C may comprise any suitable "through-stack grid", which need not relate to the optimization grid(s).

[0078] In a specific illustrative embodiment, the merit function may take a form where the stitching area performance penalty and / or constraint and through-stack penalty and / or constraint each penalize the choice of corrections via their corresponding normed error term rather than constraining the error; e-g-,: argminwhere the constraints / regularization comprise:4iPi < b, and A2p2< b2[First layer actuation] Ap < b [Subsequent layer actuation]| C*1p1+ z[ — C2p2— z21 < a + d [stitched overlay penalty]C11 [P1l — Cp < p + d [through — stack penalty] cd tp2J and where (in addition to the terms already defined) C17C2are the design matrices of a first sub-region and a second sub-region of the first layer, pt, p2are the correction parameters (vector of coefficients of the actuation profiles) of the first sub-region and second sub-region, zt,z2is the process error data (overlay data) for the first sub-region and second sub-region, C[, C2, z[,z2describe the first layer design matrices and process error data (with the subscript designating the sub-region as before) for the stitching area (boundary area) only, C and p are the design matrix and correction parameters for a subsequent layer,b A2, b2,A, b describe the actuation constraints for actuating the first subregion, second sub-region and subsequent layer respectively and y, y sets the norm applied to the stitched overlay penalty and through-stack penalty respectively.

[0079] It can be appreciated that while the specific merit function example given is stated for only two sub-regions per field and only two layers, this formulation can be generalized to more sub-regions per field and / or more layers. Additionally, while the parameter of interest is overlay, it can also be applied to other parameters of interest.

[0080] Note that such a stitched overlay penalty and / or constraint can also be applied to Equation 1 above. In addition, a through-stack penalty and / or constraint may also be applied to Equation 1, although this may be applied separately to each sub-region optimization.

[0081] A number of refinements relating to the stitching area of a stitched die will now be described, which can be applied to any of the above embodiments. At the stitching area the patterns might have a discontinuity which will reduce the electrical performance of the device.

[0082] Figure 6 is a schematic drawing which illustrates a first stitching area exposure control method. The Figure shows a first sub-region 600 and second sub-region 605, with a stitching area 610 defined by the region of overlap of first sub-region 600 and second sub-region 605. Note that first subregion 600 and second sub-region 605 are exposed in a common layer. In an embodiment, each subregion is exposed using a respective different reticle, e.g., first sub-region 600 is exposed with reticle A RET A and second sub-region 605 is exposed with reticle B RET B (although the same reticle may be used for the two sub-regions). Below this, a set focus profile is shown which describes the focus settings during exposure of first sub-region 600, second sub-region 605 and stitching area 610. In this simplistic example, the applied focus profile comprises a single set value 615a, 615b respectively for exposure of the first sub-region 600 (gray line) and second sub-region 605 (black continuous line) outside of the stitching area 610. However it is proposed to enlarge the focus offset (or defocus) within the stitching area only 610, such that each exposure is performed at two different focus levels. As a consequence of this, a larger depth of focus tolerance is obtained.

[0083] In a particular embodiment, it is proposed that a respective opposite focus offset 620a, 620b is applied during exposure of the first sub-region 600 and second sub-region 605 within the stitching area. An opposite focus offset may comprise a defocus or focus offset of the same magnitude but different direction for each of the first sub-region 600 and second sub-region 605, with respect to a nominal focus setting outside of the stitching area. The focus offsets 620a, 620b applied may therefore be such that the average 625 of the two focus offsets 620a, 620b is the same as the single set value 615a, 615b or nominal focus used outside of the stitching area 610.

[0084] As such, the proposed method may comprise exposing the stitching area (i.e., the resist there) twice, each at a different focus level. This is similar to focus drilling techniques in which multiple exposures may be performed at a common area of a substrate at respective different focus levels.

[0085] Note that optionally the pattern within the stitching area of each reticle may be optimized for the focus offset such that CD is acceptable when exposed at the offset focus. This may be achieved using standard optical proximity correction (OPC) methods.

[0086] Also shown in the Figure is the depth of focus or focus window 630a, 630b corresponding to exposure of the first sub-region 600, second sub-region 605 outside the stitching area, and the depth of focus or focus window 630c corresponding to exposure of stitching area 610. The depth of focus or focus window 630a, 630b, 630c defines a focus range for which exposure performance (e.g., in terms of one or more performance parameters such as critical dimension CD) is acceptable.

[0087] It can be seen that the imposed opposite focus offset 620a, 620b results in an increased depth of focus 630c for the stitching area compared to the depth of focus 630a, 630b. A larger depth of focus enables larger tolerance for levelling and other focus errors. The throughput impact of the overlapping exposures can be partially compensated due to larger tolerance for settling at the start of the exposures. This allows for a different optimum to be set for optical proximity correction OPC and illumination settings (e.g., using a MEMS illuminator) in the stitching area.

[0088] Alternatively or in addition to an imposed opposite focus offset 620a, 620b, the full dose may also be shared over the two exposures within the stitching area, e.g., such that each exposure receives a portion (e.g., a half) of the nominal target dose used for exposure outside the stitching area. Since the stitching area is exposed at lower dose per image, Reticle / Mirror / W afer heating effects will be lower in the overlapping area and therefore better patterning performance may be achieved.

[0089] More generally, it is proposed to distribute corrections between the two exposures within the stitching area, e.g., co-optimize applied complementary corrections within the stitching area. The combination of complementary corrections comprising a first correction profile for exposure of the first sub-region 700 and a second correction profile for the second sub-region 705 can be determined such that the combined effect of the complementary corrections improves and / or optimizes patterning within the stitching area. Such correction profiles may be determined for any exposure setting such as dose, focus or in-plane position (e.g., stitched overlay and / or conventional overlay).

[0090] Figure 7 illustrates a such method within the context of dose correction profiles. Shown is a first dose correction profile 720a and an opposite second dose correction profile 720b, which are imposed during exposure of the first sub-region 700 and second sub-region 705 within the stitching area 710. In an embodiment, each sub-region may be exposed using a different reticle, first sub-region 700 is exposed with reticle A RET A and second sub-region 705 is exposed with reticle B RET B (although the same reticle may be used for the two sub-regions).

[0091] The dose profiles 720a, 720b applied may be such that the sum of the dose profiles 725 is the same as the single set value 715a, 715b or nominal dose used to expose the sub-region 700, 705 outside of the stitching area 710. Advantageously, both dose profiles from reticle A and B are considered in the stitching zone reducing the discontinuity between for sub-regions 700 and 705.

[0092] In an embodiment, the combination of first dose correction profile 720a and second dose correction profile 720b in the stitching area 710 may be configured such that their combined effect optimizes patterning. Differences in disturbances between the exposures may be averaged out. This may be similar in principle to using a “vote taking” strategy such as used to mitigate mask defect. Votetaking sums up N different mask images with identical content, each at 1 / N dose, to mitigate the defects on each individual mask. The assumption is that the mask defects do not correlate in position from mask to mask, and so each individual defect will be blended with good images from the other N-l masks.

[0093] The optimization may take the form for example of minimization of an exposure performance metric such as critical dimension uniformity (CDU) and the combined effect of the first dose profile 720a and second dose profile 720b. As such, an inter-field dose correction profile may be distributed between exposure of the first sub-region 700 and exposure of the second sub-region 705 such that the sum of the doses results in the lowest CD variation from the target CD (CDU):where Dj and D2are the dose values during exposure (within the stitching area 710) of the first subregion 700 and second sub-region 705 respectively, y is the scanning direction, and S1and S2are tunable CD sensitivities for dose for the first sub-region 700 and second sub-region 705, assuming CD is a linear function with dose (i.e., CD = S1D1(y~) + S2D2(y)). More generally, the optimization or minimization may simply be expressed as co-optimizing doses D1(y'),D2(y) to minimize CDU (or other performance metric which is a function of dose); i.e.,: min| CDUf -L (y), D2(y)) |

[0094] A plot of the resultant CD along scanning direction y is shown, comprising a first CD trace 730a corresponding to exposure of the first sub-region 700 outside of the stitching area 710, a second CD trace 730b corresponding to exposure of the second sub-region 705 outside of the stitching area 710 and a third CD trace 730c corresponding to exposure of sub-region 700, 705 within the stitching area 710. It can be observed that the CDU 735c is smaller within the stitching area, than the CDU 735a, 735b outside of the stitching area.

[0095] Different overlay corrections for exposure of the first sub-region 700 and second sub-region 705 will widen the CD. This can partly be compensated by dose, or by synchronizing the overlay correction differences between the two exposures in the stitching area. Similarly, different focus corrections for exposure of the first sub-region 700 and second sub-region 705 will widen the CD. This can partly be compensated by dose or by synchronizing the focus correction differences of the two exposures in the stitching area.

[0096] In an embodiment, some or all of dose corrections D1D2, in-plane positional corrections CLX- , dX2, dY1, dY2(e.g., for stitched overlay, which describes relative alignment of first sub-region 700 and second sub-region 705 and / or conventional overlay corrections) and focus corrections dFltdF2applied respectively during exposure of the first sub-region 700 and second sub-region 705 may be jointly optimized within the stitching area, so as to minimize or optimize an exposure performance metric such as edge placement error EPE: min|E'PE'(£)1 / D2, dXltdX2, dYltdY2, dFltdF2) |

[0097] Since both exposures can be used for corrections, and disturbances are averaged over the two exposures it is expected that the EPE between the exposures will be reduced.

[0098] Figure 8 illustrates a further embodiment which enables stitched overlay to be measured directly on the device pattern (product structure) without the need for dedicated stitched overlay targets (structures in each of the first sub-region 800 and second sub-region 805, within the stitching area 810). Such stitched overlay targets are relatively large and occupy real estate which therefore cannot be usedfor the device structure (functional structure). In an embodiment, each sub-region uses a different reticle, e.g., first sub-region 800 is exposed with reticle A RET A and second sub-region 805 is exposed with reticle B RET B (although the same reticle may be used for the two sub-regions). When this occurs, it is very difficult to determine which is the displacement contributor for each reticle in the stitching area.

[0099] Shown is a first stitched overlay dX, dY plot 815a corresponding to exposure of first subregion 800 and a second stitched overlay dX, dY plot 815b corresponding to exposure of second subregion 805 (each showing stitched overlay along the scanning direction y). It can be seen that there is a mismatch between plot 815a and plot 815b being indicative of a stitched overlay error. A corresponding CD plot is also shown, comprising a first CD plot 820a corresponding to exposure of the first sub-region 800 outside of the stitching area 810, a second CD trace 820b corresponding to exposure of the second sub-region 805 outside of the stitching area 810 and a third CD trace 820c corresponding to exposure of sub-region 800, 805 within the stitching area 810.

[0100] It can be seen that CD is significantly greater for the third CD trace 820c than the first and second CD traces 820a, 820b. This results from the stitched overlay error or relative positional difference between the first sub-region 800 and the second sub-region 805. The reason for this is that the image formed in the stitching area 810 comprises a compound image formed from an overlapping first image and second image in the respective sub-regions 800, 805. If the first image is displaced (a small amount) from the second image, there will be an effective increase in CD (and therefore local CDU, LCDU) of the compound image. A plot 825 of CD or LCDU against stitched overlay dx,dy is shown. It can be seen that there is a CD or LCDU minimum at zero stitched overlay, with CD / LCDU increasing with increasing stitched overlay dx,dy magnitude.

[0101] It is proposed to use this displacement to calculate the stitched overlay introduced in the stitching area. Advantageously, the relative displacement between exposure of reticle A and the exposure of reticle B in the stitching area 810 can be determined. Alternatively or in addition to enabling better control of placement of each of sub-regions 800, 805 with respect to each other, this relative displacement may be used to improve overlay control with respect to one or more other layers.

[0102] Examples of compound images are shown. A first compound image 830 is shown which is formed within the stitching area 810 from a first image 830a and a second image 830b, while a second compound image 830’ is formed within the stitching area 810 from a first image 830a’ and a second image 830b’. In each case, the first image 830a, 830a’ is exposed during exposure of first sub-region 800 and the second image 830b, 830b’ is exposed during exposure of second sub-region 805. The first compound image 830 is what may be seen when there is stitched overlay error in the y-direction only, while the second compound image 830’ is what may be seen when there is stitched overlay error in the x-direction only. Of course, in a real example, there may be a stitched overlay error in both in-plane directions.

[0103] It is therefore proposed that CD and / or LCDU (i.e., a critical dimension parameter) is measured from structures and used to determine the stitched overlay. The structures measured may comprise functional product structure rather than dedicated stitching targets, although small simple CD stitching targets could be used instead. The method may comprise calibrating the relationship between stitched overlay and CD and / or LCDU and using the calibrated relationship to infer stitched overlay. Such a calibration may comprise exposing a plurality of stitched fields with different known stitching target offsets and measuring the resultant CD and / or LCDU of compound structures. For example, a calibration model can be fitted to a plot of the measured CD and / or LCDU against stitched overlay or a machine learning model may be trained to map CD and / or LCDU to stitched overlay.

[0104] The following numbered clauses describe various aspects and / or embodiments of the invention:1. A method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer; the method comprising: obtaining process error data relating to said manufacturing process when forming said first subregion on a substrate; determining a first on-product error from said process error data, said on-product error relating to an error in formation of said first sub-region; and determining, from said on-product error, a correction for said manufacturing process when forming said second sub-region on said substrate.2. A method according to clause 1, wherein said correction is determined to reduce or minimize any difference in said on-product error of said first sub-region and an on-product error of said second sub-region.3. A method according to clause 1 or 2, wherein said on-product error relates, at least in part, to a position of structures to said first sub-region; and said correction reduces or minimizes a stitched overlay error describing a relative positioning error between said first sub-region and said second sub-region.4. A method according to any preceding clause, wherein said on-product error relates, at least in part, to an overlay error of said first sub-region with respect to a preceding layer; and said correction reduces or minimizes an overlay error of said second sub-region with respect to the preceding layer.5. A method according to any preceding clause, wherein said on-product error relates to a position of structures to said first sub-region and to an overlay error of said first sub-region with respect to a preceding layer; and said correction co-optimizes a stitched overlay error describing a relative positioning error between said first sub-region and said second sub-region and an overlay error of said second sub-region with respect to the preceding layer.6. A method according to any preceding clause, wherein said correction comprises a feedforward correction for exposure of said second sub-region on the same substrate as said first sub-region was exposed to obtain said process error data.7. A method according to any preceding clause, wherein said process error data comprises error data generated during the manufacturing process and / or generated within the manufacturing apparatus when forming said first sub-region.8. A method according to any preceding clause, wherein said process error data comprises one or more of: lens model error data, lens fingerprint data, actuation error data, lens overpressure error data, alignment data and / or alignment residual data.9. A method according to any preceding clause, wherein said manufacturing process is a lithographic and / or exposure process and said manufacturing apparatus is a lithographic and / or exposure apparatus.10. A method according to any preceding clause, wherein said step of determination a correction comprises determining said correction subject to one or more rules and / or constraints.11. A method according to clause 10, wherein said one or more rules and / or constraints comprises possible and / or allowable actuations, preferred actuations, prohibited actuations, allowed error for sub-region deformation, allowed overlay error and / or stitched overlay error.12. A method according to any preceding clause, wherein said correction is determined as an additional term of a merit function for determining an actuation trajectory for forming said second sub-region, said additional term comprising a difference of actuation residuals relating to formation of the second sub-region and actuation residuals relating to formation of the first sub-region.13. A method according to any preceding clause, wherein said first sub-region is formed multiple times on the substrate in a first exposure sequence, and the second sub-region is to be formed multiple times on the substrate in a second exposure sequence.14. A method according to clause 13, wherein the method comprises determining the second exposure sequence to ensure sufficient computation time is available for determining the on-product error and the correction.15. A method according to clause 14, wherein said sufficient computation time comprises ensuring sufficient computation time to maintain a substantially stable queue depth for queuing of the second sub-region formations.16. A method according to clause 13, 14 or 15, further comprising forwarding measured alignment data and / or modeled alignment data relating to said first exposure sequence for using when performing said second exposure sequence.17. A method according to clause 16, further comprising configuring the lithography apparatus in a first configuration for the first exposure sequence and in a second configuration for the second exposure sequence.18. A method according to clause 17, wherein the first and second configurations are based on alignment mark types, color recipes, alignment mark sampling strategy and alignment model.19. A method according to clause 13, 14 or 15, further comprising forwarding measured levelling data and / or modeled level data relating to said first exposure sequence for using when performing said second exposure sequence.20. A method according to any preceding clause, wherein said manufacturing process provides said structures on said substrate in a plurality of exposures, each exposure defining a respective one of said sub-regions, said sub-regions being exposed substantially adjacently to define said region.21. A method according to clause 20, wherein being exposed substantially adjacently comprises a small overlap region.22. A method according to clause 20 or 21, wherein the region has an area larger than a maximum scanning field area of the manufacturing apparatus.23. A method according to clause 22, wherein each sub-region has an area defined by the maximum field area of the manufacturing apparatus.24. A method according to any preceding clause, wherein the first sub-region and second sub-region comprise a common stitching area defined by an area of overlap of the first subregion and second sub-region; and the method comprises: exposing said first sub-region and second sub-region with a respective complementary focus and / or dose setting within said stitching area.25. A method according to clause 24, wherein said respective complementary focus comprises applying, with respect to a nominal focus, an equal magnitude focus offset in opposite directions when respectively exposing said first sub-region and second sub-region.26. A method according to clause 24 or 25, wherein said respective complementary dose comprises dividing a nominal dose between exposing said first sub-region and second subregion, such that the combined dose in exposing said first sub-region and second sub-region comprises said nominal dose.27. A method according to any preceding clause, wherein the first sub-region and second sub-region comprise a common stitching area defined by an area of overlap of the first subregion and second sub-region; and the method comprises: exposing, within said stitching area, said first sub-region and second sub-region with a respective complementary correction for one or more exposure settings.28. A method according to clause 27, wherein said one or more exposure settings comprise one or more of dose, focus and / or in-plane position.29. A method according to clause 27 or 28, comprising co-optimizing said respective complementary corrections in terms of improving and / or optimizing an exposure performance metric within said stitching area.30. A method according to clause 29, wherein the exposure performance metric comprises critical dimension uniformity or edge placement error.31. A method according to any preceding clause, wherein the first sub-region and second sub-region comprise a common stitching area defined by an area of overlap of the first subregion and second sub-region; and the method comprises: measuring a critical dimension parameter of a compound image formed by a first image exposed in the stitching area of said the first sub-region and an overlapping second image exposed in the stitching area of said the second sub-region; and determining stitching overlay between said first sub-region and second sub-region from said critical dimension parameter.32. A method according to clause 31 , wherein said determining stitching overlay comprises determining the stitching overlay using a pre-calibrated relationship and / or model for mapping said critical dimension parameter to said stitching overlay.33. A method according to clause 31 or 32, wherein the compound image measured comprises functional product structure.34. A method according to any preceding clause, wherein said step of determining a correction comprises applying a stitching area performance penalty and / or constraint whichimposes a constraint on stitched overlay error between the first sub-region and second subregion.35. A method according to clause 34, wherein said stitching area performance penalty constrains and / or penalizes a difference, within a stitching area defined by an area of overlap of the first sub-region and second sub-region, in residual values of one or more of, alone or any combination: focus, dose, overlay or stitched overlay.36. A method according to clause 35, wherein said stitching area performance penalty comprises a stitching deadband threshold which defines a minimum relevant difference in said residual values, below which the said residual values are considered insignificant.37. A method according to clause 34, 35 or 36, comprising tuning the effect of said stitching area performance penalty via a stitching hyperparameter.38. A method according to any preceding clause, wherein said step of determining a correction comprises applying a through-stack penalty and / or constraint which imposes a constraint and / or penalty on overlay error with respect to at least one subsequent layer, exposed subsequent to said common layer.39. A method according to clause 38, wherein said through-stack penalty constrains corrections to be applied in the common layer such that the first layer exposures can be performed acceptably in the subsequent layer, wherein said common layer and first layer are exposed using different lithographic apparatuses having different correction capabilities and / or different field sizes.40. A method according to clause 39, wherein said through-stack penalty comprises a through-stack deadband threshold which defines a minimum relevant difference in through stack residual values.41. A method according to clause 38, 39 or 40, comprising tuning the effect of said through- stack penalty via a through-stack hyperparameter.42. A method according to any preceding clause, comprising performing said manufacturing process to form said first sub-region and said second sub-region, such that said second sub-region is formed in accordance with said correction.43. A method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer, wherein the first sub-region and second sub-region comprise a common stitching area defined by an area of overlap of the first sub-region and second sub-region; the method comprising:obtaining process error data relating to said manufacturing process when forming said first subregion and second sub-region on a substrate; determining, from said process error data, a co-optimized correction for each of said at least a first sub-region and a second sub-region, wherein said determining a co-optimized correction comprises applying at least one of: a stitching area performance penalty and / or constraint which imposes a penalty and / or constraint on at least one parameter of interest within stitching area; and / or a through- stack penalty and / or constraint which imposes a penalty and / or constraint on overlay error with respect to at least one subsequent layer, exposed subsequent to said common layer.44. A method according to clause 43, wherein said at least one parameter of interest comprises one or more of, alone or any combination: focus, dose, overlay or stitched overlay.45. A method according to clause 43 or 44, wherein said stitching area performance penalty and / or constraint constrains and / or penalizes a difference in residual values of the parameter of interest within the stitching area.46. A method according to clause 45, wherein said stitching area performance penalty and / or constraint comprises a stitching deadband threshold which defines a minimum relevant difference in said residual values, below which the said residual values are considered insignificant.47. A method according to any of clauses 41 to 46, wherein said through-stack penalty and / or constraint penalizes and / or constrains corrections to be applied in the common layer such that the first layer exposures can be performed acceptably in the subsequent layer, wherein said common layer and first layer are exposed using different lithographic apparatuses having different correction capabilities and / or different field sizes.48. A method according to clause 47, wherein said through-stack penalty comprises a through-stack deadband threshold which defines a minimum relevant difference in through stack residual values.49. A method according to any of clauses 41 to 48, comprising tuning the effect of each of one or both of said stitching area performance penalty and / or constraint and / or said through- stack penalty and / or constraint via a respective hyperparameter.50. A processing device for determining a correction for control of at least one manufacturing apparatus configured to provide product structures to a substrate in a manufacturing process, the processing device being configured to perform the method of any of clauses 1 to 49.51. A manufacturing apparatus configured to provide product structures to a substrate in a manufacturing process, said manufacturing apparatus comprising the processing device according to clause 50.52. A manufacturing apparatus according to clause 51, wherein the manufacturing apparatus comprises a lithographic apparatus having: a substrate stage for holding a substrate; a reticle stage for holding a patterning device; a processor operable to control a manufacturing process using said correction.53. A computer program comprising program instructions operable to perform the method of any of clauses 1 to 49 when run on a suitable apparatus.54. A non-transient computer program carrier comprising the computer program of clause 53.55. A method for manufacturing a semiconductor device using a manufacturing process comprising, receiving a substrate with a photoresist layer, determining a correction of the manufacturing process according to any of the clauses 1 to 49, controlling a radiation beam in accordance with the determined correction, wherein the radiation beam is directed from a radiation source to transfer a pattern from a mask onto the photoresist layer, removing a portion of the photoresist layer to form the pattern over the substrate.

[0105] While the above description describes corrections for a lithographic apparatus / scanner, the determined corrections may also be used for any process and by any integrated circuit (IC) manufacturing apparatus in an IC manufacturing process, e.g., an etch apparatus, which has an effect on the position and / or a dimension of the structures formed within a layer.

[0106] The terms “radiation” and “beam” used in relation to the lithographic apparatus 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 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0107] 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.

[0108] The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art, readily modify and / or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations andmodifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description by example, and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance.

[0109] 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 method for determining a correction for control of at least one manufacturing apparatus used in a manufacturing process for providing structures to at least one region on a substrate, said region comprising at least a first sub-region and a second sub-region in a common layer; the method comprising: obtaining process error data relating to said manufacturing process when forming said first subregion on a substrate; determining a first on-product error from said process error data, said on-product error relating to an error in formation of said first sub-region; and determining, from said on-product error, a correction for said manufacturing process when forming said second sub-region on said substrate.

2. A method as claimed in claim 1, wherein said correction is determined to reduce or minimize any difference in said on-product error of said first sub-region and an on-product error of said second sub-region.

3. A method as claimed in claim 1 or 2, wherein said on-product error relates, at least in part, to a position of structures to said first sub-region; and said correction reduces or minimizes a stitched overlay error describing a relative positioning error between said first sub-region and said second sub-region.

4. A method as claimed in any preceding claim, wherein said on-product error relates, at least in part, to an overlay error of said first sub-region with respect to a preceding layer; and said correction reduces or minimizes an overlay error of said second sub-region with respect to the preceding layer and / or wherein said on-product error relates to a position of structures to said first subregion and to an overlay error of said first sub-region with respect to a preceding layer; and said correction co-optimizes a stitched overlay error describing a relative positioning error between said first sub-region and said second sub-region and an overlay error of said second sub-region with respect to the preceding layer.

5. A method as claimed in any preceding claim, wherein said correction comprises a feed-forward correction for exposure of said second sub-region on the same substrate as said first sub-region was exposed to obtain said process error data.

6. A method as claimed in any preceding claim, wherein said correction is determined as an additional term of a merit function for determining an actuation trajectory for forming said second subregion, said additional term comprising a difference of actuation residuals relating to formation of the second sub-region and actuation residuals relating to formation of the first sub-region.

7. A method as claimed in any preceding claim, wherein said first sub-region is formed multiple times on the substrate in a first exposure sequence, and the second sub-region is to be formed multiple times on the substrate in a second exposure sequence, wherein the method further comprising forwarding measured alignment data and / or modeled alignment data relating to said first exposure sequence for using when performing said second exposure sequence.

8. A method as claimed in any preceding claim, wherein the first sub-region and second subregion comprise a common stitching area defined by an area of overlap of the first sub-region and second sub-region; and the method comprises: exposing said first sub-region and second sub-region with a respective complementary focus and / or dose setting within said stitching area.

9. A method as claimed in any preceding claim, wherein the first sub-region and second subregion comprise a common stitching area defined by an area of overlap of the first sub-region and second sub-region; and the method comprises: exposing, within said stitching area, said first sub-region and second sub-region with a respective complementary correction for one or more exposure settings.

10. A method as claimed in claim 9, comprising co-optimizing said respective complementary corrections in terms of improving and / or optimizing an exposure performance metric within said stitching area.

11. A method as claimed in any preceding claim, wherein the first sub-region and second subregion comprise a common stitching area defined by an area of overlap of the first sub-region and second sub-region; and the method comprises: measuring a critical dimension parameter of a compound image formed by a first image exposed in the stitching area of said the first sub-region and an overlapping second image exposed in the stitching area of said the second sub-region; and determining stitching overlay between said first sub-region and second sub-region from said critical dimension parameter.

12. A method as claimed in any preceding claim, wherein said step of determining a correction comprises applying a stitching area performance penalty and / or constraint which imposes a constraint on stitched overlay error between the first sub-region and second sub-region.

13. A method as claimed in claim 12, wherein said stitching area performance penalty constrains and / or penalizes a difference, within a stitching area defined by an area of overlap of the first sub-region and second sub-region, in residual values of one or more of, alone or any combination: focus, dose, overlay or stitched overlay.

14. A method as claimed in any preceding claim, wherein said step of determining a correction comprises applying a through-stack penalty and / or constraint which imposes a constraint and / or penalty on overlay error with respect to at least one subsequent layer, exposed subsequent to said common layer.

15. A computer program comprising program instructions operable to perform the method of any of claims 1 to 14 when run on a suitable apparatus.

16. A method for manufacturing a semiconductor device using a manufacturing process comprising, receiving a substrate with a photoresist layer, determining a correction of the manufacturing process according to any of the claims 1 to 14, controlling a radiation beam in accordance with the determined correction, wherein the radiation beam is directed from a radiation source to transfer a pattern from a mask onto the photoresist layer, removing a portion of the photoresist layer to form the pattern over the substrate.

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