WO2025036637A1

WO2025036637A1 - Method and system for generating an overlay-tolerant mask pattern design

Info

Publication number: WO2025036637A1
Application number: PCT/EP2024/070060
Authority: WO
Inventors: Abraham SLACHTER; Marie-Claire VAN LARE; Koenraad VAN INGEN SCHENAU; Peter David ENGBLOM; Parul Dhagat; Luis Alberto COLINA SANTAMARIA; Shih-Hsiang Liu
Original assignee: Asml Netherlands B.V.
Priority date: 2023-08-14
Filing date: 2024-07-15
Publication date: 2025-02-20

Abstract

Described a method and system for determining a placement and geometry of a sub-resolution assist feature (SRAF) in an area proximate to a mask pattern to reduce sensitivity to an overlay between portions of the mask pattern on a substrate. The mask pattern corresponds to a target pattern to be printed on the substrate in two adjacent exposure fields. The geometry of the mask pattern is adjusted to reduce the sensitivity to the overlay by generating a first portion of the pattern with varying CD and a second portion of the pattern with varying CD for use in printing the target pattern on the substrate in the two adjacent exposure fields respectively.

Description

METHOD AND SYSTEM FOR GENERATING AN OVERLAY-TOLERANT MASK PATTERN DESIGN

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63/532,598, which was filed on August 14, 2023, and U.S. Application No. 63/546,309, which was filed on October 30, 2023, both of which are incorporated herein in their entireties by reference.

TECHNICAL FIELD

[0002] The description herein relates to masks for use in lithography, and more particularly to designing a mask pattern.

BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer). This manufacturing process may be referred to as a patterning process or a lithographic process. For example, an IC chip in a smart phone, can be as small as a person’s thumbnail, and may include over 2 billion transistors. Making an IC is a complex and timeconsuming process, with circuit components in different layers and including hundreds of individual steps. Errors in even one step have the potential to result in problems with the final IC and can cause device failure. High process yield and high wafer throughput can be impacted by the presence of defects, especially if operator intervention is required for reviewing the defects.

[0004] The patterning device may refer to device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. An example of such a patterning device is a mask. The concept of a mask is well known in lithography, and it includes mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. Placement of such a mask in the radiation beam causes selective transmission (in the case of a transmissive mask) or reflection (in the case of a reflective mask) of the radiation impinging on the mask, according to the pattern on the mask. In the case of a mask, the support structure will generally be a mask table, which ensures that the mask can be held at a desired position in the incoming radiation beam, and that it can be moved relative to the beam if so desired.

[0005] An emerging candidate for finer resolution lithography uses Extreme Ultraviolet (EUV) light to image patterns on an area of a wafer. EUV light has a wavelength in a range of about 10 nm to 20 nm, in particular about 13.4 nm to 13.5 nm. EUV lithography (EUVL) employs reflective masks rather than transmissive masks since the EUV light at such a small wavelength is prone to be absorbed by materials used in a transmissive mask.

[0006] EUVL masks include a reflective film (e.g., a Bragg reflector) arranged on an ultra-low expansion (ULE) substrate and a pattern of absorber material on the reflective film. The exposure light is incident on the mask at a shallow angle, e.g., about 5 or 6 degrees, relative to the perpendicular direction to the mask. Some of the incident light is reflected by the reflective film and some of the incident light is absorbed by the absorber material, thus producing a predefined pattern of light that is ultimately applied onto an area of a wafer, e.g., to expose a pattern in a photoresist on the wafer.

[0007] The pattern of absorber material and exposed portions of the reflective film are contained in an active area (also referred to as a primary pattern, pattern region, image field, etc.) of the EUVL mask. The EUVL mask also includes a border region (also referred to as a black border area) composed of an about 2-3 mm wide strip of absorber material that surrounds the active area. The same EUVL mask may be used many times in succession to provide the same predefined pattern of light on different areas (e.g., different dies) of a single wafer, and the border region is used to isolate the individual patterns as they are exposed on the wafer surface.

SUMMARY

[0008] In some embodiments, the techniques described herein relate to a method for generating a mask pattern design for use in imaging of a pattern on a substrate using a lithographic apparatus, the method including: determining a placement and a geometry of a sub-resolution assist feature (SRAF) in an area proximate to a pattern to reduce sensitivity to an overlay between portions on the pattern on a substrate, wherein the pattern corresponds to a target pattern to be printed on the substrate in two adjacent exposure fields; and adjusting a geometry of the pattern to reduce the sensitivity to the overlay, wherein the adjusting includes generating a first portion of the pattern and a second portion of the pattern for use in printing the pattern on a substrate in the two adjacent exposure fields respectively.

[0009] In some embodiments, the techniques described herein relate to a method for generating a mask pattern design for use in imaging of a pattern on a substrate using a lithographic apparatus, the method comprising: identifying a first area in a first mask pattern design having a mask pattern, wherein the mask pattern corresponds to a target pattern to be printed on a specified location on a substrate; and determining a placement and a geometry of an SRAF to be placed in an absorber layer of a second mask pattern design based on the first area, wherein the SRAF is configured to enhance an image contrast at the specified location for printing the target pattern using overlapping exposures of the first mask pattern design and the second mask pattern design. [0010] In some embodiments, the techniques described herein relate to an apparatus, the apparatus including: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above embodiments.

[0011] In some embodiments, the techniques described herein relate to a non-transitory computer- readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus 10A, according to an embodiment.

[0013] Figure 2 is a schematic diagram of a lithographic projection apparatus, according to an embodiment.

[0014] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment.

[0015] Figure 4 shows overlay-tolerant mask pattern designs for printing a target pattern on a substrate across two adjacent exposure fields on a substrate, consistent with various embodiments. [0016] Figure 5 is a flow diagram of a process for generating an overlay-tolerant mask pattern design, consistent with various embodiments.

[0017] Figure 6 is a block diagram of the overlay-tolerant mask pattern design, consistent with various embodiments.

[0018] Figure 7 is a flow diagram of a process for generating an overlay-tolerant mask pattern design, consistent with various embodiments.

[0019] Figure 8A illustrates adjusting of aerial image intensities of mask patterns to generate an overlay-tolerant mask pattern design, consistent with various embodiments.

[0020] Figure 8B illustrates aerial image intensity of the mask pattern and aerial image intensity of the stitched pattern, consistent with various embodiments.

[0021] Figure 9A shows a graph illustrating critical dimension (CD) variation due to overlay for various CD values, consistent with various embodiments.

[0022] Figure 9B shows sidelobes for various line distance values of a sub-resolution assist feature, consistent with various embodiments.

[0023] Figure 10 shows a graph illustrating CD of a stitched pattern at transition regions before and after adjustment of mask CD, consistent with various embodiments.

[0024] Figure 11 illustrates mask pattern designs for printing a target pattern using a brightfield mask, consistent with various embodiments.

[0025] Figure 12 is a block diagram for enhancing image contrast at a location on a substrate by overlapping exposures of different mask patterns, consistent with various embodiments. [0026] Figure 13 shows stitching of a pattern by overlapping exposures of multiple mask patterns, consistent with various embodiments.

[0027] Figure 14 illustrates designing of mask patterns to reduce contrast loss in stitching of the mask patterns, consistent with various embodiments.

[0028] Figure 15 is a graph illustrating improved image contrast in a critical stitching area of a stitched pattern, consistent with various embodiments.

[0029] Figure 16 illustrates assist features designed for various types of mask patterns, consistent with various embodiments.

[0030] Figure 17 is a flow diagram of a method for designing a mask pattern to reduce contrast loss in stitching of the mask patterns, consistent with various embodiments.

[0031] Figure 18 is a block diagram that illustrates a computer system which can assist in implementing the systems and methods disclosed herein.

DETAILED DESCRIPTION

[0032] In lithography, to print a target pattern (also often referred to as “design layout” or “design”) on a substrate, a pattern corresponding to the target pattern printed on a patterning device (e.g., a mask) is projected onto a layer of resist provided on the substrate (e.g., on a wafer). The mask pattern may be projected onto one or more dies of the substrate. If a die is larger than a lithographic exposure field, multiple exposures may be required to print a layer of the pattern. The adjacent exposures may be stitched (“pattern stitching”) together to form a layer. In some embodiments, a pattern is stitched by exposing a first portion of the pattern in a first exposure and a second portion of the pattern in a second exposure on the substrate in a location adjacent to the first exposure (as an example, as such stitching is certainly not limited to two exposures, as even more exposures can all be stitched together in the x and/or y directions). In some embodiments, when a pattern is printed across two adjacent exposure fields, there can be an overlay error (e.g., shift from the actual intended position) between the patterns in the two adjacent exposures in any direction on the substrate (e.g., y-direction or an x- direction). In some embodiments, a critical dimension (CD) of the pattern stitched may vary due to an overlay between patterns of the two adjacent exposures. Some embodiments design a bulge (e.g., by adding a sub-resolution assist feature (SRAF), such as a sub-resolution grating (SRG) in the mask pattern near the stitching area), that improves a contrast of the image of the pattern and tolerance to overlay errors (e.g., in the y-direction). However, the CD may still be strongly impacted which may have an impact on performance of the circuit. For example, the drop in CD can cause reliability issues in the circuit, or affect the timing of the circuits. In another example, via patterns may have process transfer sensitivity that prohibits increasing CD without creating defects during pattern into underlying substrate, thereby limiting the overlay window. In various stitching embodiments, a radiation dose profile is applied over the slit to make the stitching of the pattern more tolerant to overlay in the y-direction. The EUV curved slit (e.g., curved shape and size of slit) limits this use of the dose profile. The CD of the mask pattern may be adjusted to make the CD variation more tolerant to the overlay. However, this may not be helpful for an EUV low-n mask because of the large background intensity of the EUV mask absorber which can cause sidelobe issues.

[0033] According to the present disclosure, CD variation of a pattern stitched across two adjacent exposure fields on a substrate may be reduced by determining a placement and geometry of an SRAF and adjusting a geometry of the pattern such that the CD variation due to an overlay between the two adjacent exposure fields in both directions (e.g., perpendicular directions such as x and y direction on the substrate) is reduced. For example, for stitching a target pattern such as an isolated vertical space/line/bar across a field boundary, a mask pattern design is generated by placing SRAFs in an area proximate (e.g., adjacent to) a mask pattern corresponding to the target pattern. The SRAFs are of a determined CD and are placed at a determined distance from the mask pattern. For example, the SRAFs includes a first set of SRGs that are placed proximate a first edge of the mask pattern (e.g., near a bottom short edge of the isolated vertical bar) and a second set of SRGs are placed proximate the opposite edges perpendicular to the first edge (e.g., near opposite longer edges of such a vertical bar). The SRAFs have a determined CD, pitch, and line distance (e.g., distance from the SRAF to the mask pattern). Next, the geometry of the mask pattern is also adjusted by varying the CD of the mask pattern. For example, the mask pattern can be adjusted to have multiple segments with different CDs (e.g., segments with increasing or decreasing CDs). In some embodiments, adjusting a geometry of the mask pattern can include generating two portions of the mask pattern, which are then projected onto the substrate in two adjacent exposure fields, respectively. For example, adjusting the geometry of the pattern may include generating a first portion of the mask pattern by varying the CD of the mask pattern, and generating a second portion of the mask pattern by varying the CD of the mask pattern in which each segment of the second portion has a complementary CD relative to a CD of the corresponding segment of the first portion of the mask pattern. In some embodiments, a pair of CD values are said to be complementary if the CD of a resulting pattern printed on the substrate matches a target CD (e.g., CD of the target pattern). The target pattern may be printed on the substrate by exposing (a) a first mask pattern design having the SRAFs and the first portion of the mask pattern, and (b) a second mask pattern design having the SRAFs and the second portion of the mask pattern in two adjacent exposure fields on the substrate, which in effect stitches the first portion of the mask pattern with the second portion of the mask pattern to generate a “stitched” pattern on the substrate. The specifically created design of the SRAFs (e.g., geometry and placement) not only reduces the CD variation of the stitched pattern to an overlay in a first direction (e.g., x-direction on the substrate), but also reduces the sidelobe effects and enhances a peak intensity of a composite image of the mask patterns, which reduces development defects. Further, such a design of the pattern (e.g., with varying CDs) along with the SRAFs also ensure that the CD variation of the stitched pattern to an overlay in a second direction (e.g., y-direction on the substrate) is also reduced. [0034] In some embodiments, in conventional pattern stitching, when portions of the pattern are stitched together by exposing the respective mask patterns on the substrate, absorber reflection- induced background intensity at the stitching region on the substrate may cause the contrast of the image (e.g., near the stitching boundary) to degrade, which may result in the stitched pattern being defective.

[0035] According to the present disclosure, the degradation of the imaging contrast near the stitching boundary may be reduced by adding overlapping assist features in each of the two half-field masks. Wafer features lying in a critical stitching region (e.g., region with double exposure) are built by the superposition of two overlapping images. Each pattern in the critical stitching region is imaged twice by using the two half-field masks, which can have the same geometry shapes of the pattern, but different or the same mask feature sizes. For example, corresponding to a contact hole array on a certain wafer location in the critical stitching region, the contact hole array on a first mask has the same pitch as a second mask but smaller hole size. Each half-field mask may have mask features corresponding to the wafer features that are printed on either side of the stitching boundary on the substrate. For example, a first mask pattern (e.g., of a first-half field mask) has (a) a first set of features (e.g., contact holes) corresponding to target features in a design layout to be printed on the substrate near the stitching boundary, and (b) overlapping assist features - referred to as third set of features, and a second mask pattern (e.g., of a second-half field mask) has (a) a second set of features (e.g., contact holes) corresponding to the target features to be printed on the substrate near the stitching boundary, and (b) overlapping assist features - referred to as a fourth set of features. The features are placed in the first mask pattern such that when the first mask pattern is exposed on the substrate the first set of features and the third set of features are exposed on either side of the stitching boundary. The features are placed similarly in the second mask pattern as well.

[0036] The wafer features in the critical stitching region are built by the superposition of features from two mask patterns such that wafer features on a first side of the stitching boundary are printed by the superposition of the first set of features of the first mask pattern with the fourth set of features of the second mask pattern, and on a second side of the stitching boundary by the superposition of the second set of features of the second mask pattern with the third set of features of the first mask pattern. The third set of features (e.g., the overlapping assist features) in the first mask pattern have the same geometrical shape and pitch as the second set of features in the second mask pattern, and the fourth set of features (e.g., overlapping assist features) in the second mask pattern have the same geometrical shape and pitch as the first set of features in the first mask pattern. However, the size of the fourth set of features may be different from that of the first set of features, and the size of the third set of features may be different from that of the second set of features. In some embodiments, an optimal size of the features (e.g., a size that aids in improving the contrast of the aerial image of the pattern) may be determined by simulating a lithographic process using the mask patterns. By designing each mask to have a continuous pattern across the stitching boundary, the reversed phase at the stitching boundary in the image is effectively removed, and not only the image could be printed uniformly across the stitching boundary, but also the contrast of the imaging is enhanced.

[0037] In the present disclosure, although specific reference may be made to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle”, “wafer” or “die” in this text should be considered as interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0038] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range of about 5-100 nm). In the present document, the term “radiation source” or “source” is used to encompass all types of sources of radiation, including laser sources, incandescent sources, etc. which may include treatment of the radiation between the radiation source and the target or other parts of the optics, including filtering, collimating, focusing, etc.

[0039] A patterning device can comprise, or can form, one or more design layouts. The design layout can be generated utilizing CAD (computer-aided design) programs. This process is often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts/patterning devices. These rules are set based processing and design limitations. For example, design rules define the space tolerance between devices (such as gates, capacitors, etc.) or interconnect lines, to ensure that the devices or lines do not interact with one another in an undesirable way. One or more of the design rule limitations may be referred to as a “critical dimension” (CD). A critical dimension of a device can be defined as the smallest width of a line or hole, or the smallest space between two lines or two holes. Thus, the CD regulates the overall size and density of the designed device. One of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0040] The term “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation. Using an appropriate filter, the said undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. Examples of other such patterning devices also include a programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0041] The term “projection optics” as used herein should be broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping, or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting and/or projecting radiation from the source before the radiation passes the patterning device, and/or optical components for shaping, adjusting and/or projecting the radiation after the radiation passes the patterning device. The projection optics generally exclude the source and the patterning device.

[0042] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus 10A, according to an embodiment. Major components are a radiation source 12A, which may be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (the lithographic projection apparatus itself need not have the radiation source), illumination optics which, e.g., define the partial coherence (denoted as sigma) and which may include optics 14A, 16Aa and 16Ab that shape radiation from the source 12A; a patterning device (or mask) 18 A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A.

[0043] A pupil 20A can be included with transmission optics 16Ac. In some embodiments, there can be one or more pupils before and/or after mask 18 A. As described in further detail herein, pupil 20A can provide patterning of the light that ultimately reaches substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics may restrict the range of beam angles that impinge on the substrate plane 22A, where the largest possible angle defines the numerical aperture of the projection optics NA= n sin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics, and ©max is the largest angle of the beam exiting from the projection optics that can still impinge on the substrate plane 22A.

[0044] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device and projection optics direct and shape the illumination, via the patterning device, onto a substrate. This is not to disclaim that the source does not itself provide patterning, directing, or shaping to the radiation or that patterning, directing, or shaping does not occur between the source and the projection optics. The projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB) and development). Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image and can be defined in an optical model. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics. Details of techniques and models used to transform a design layout into various lithographic images (e.g., an aerial image, a resist image, etc.), apply OPC using those techniques and models and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosure of each which is hereby incorporated by reference in its entirety.

[0045] One aspect of understanding a lithographic process is understanding the interaction of the radiation and the patterning device. The electromagnetic field of the radiation after the radiation passes the patterning device may be determined from the electromagnetic field of the radiation before the radiation reaches the patterning device and a function that characterizes the interaction. This function may be referred to as the mask transmission function (which can be used to describe the interaction by a transmissive patterning device and/or a reflective patterning device).

[0046] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in the binary form may be referred to as a binary mask. Another form is continuous. Namely, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the location on the patterning device. A mask transmission function in the continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, the CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of binary value of either 0 or 1. In an embodiment, CTM may be a pixelated gray scale image, where each pixel having values (e.g., within a range [-255, 255], normalized values within a range [0, 1] or [-1, 1] or other appropriate ranges).

[0047] The thin-mask approximation, also called the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction of the radiation and the patterning device. The thin-mask approximation assumes that the thickness of the structures on the patterning device is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin-mask approximation assumes the electromagnetic field after the patterning device is the multiplication of the incident electromagnetic field with the mask transmission function. However, as lithographic processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device become smaller and smaller, the assumption of the thin-mask approximation can break down. For example, interaction of the radiation with the structures (e.g., edges between the top surface and a sidewall) because of their finite thicknesses (“mask 3D effect” or “M3D”) may become significant. Encompassing this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of the radiation with the patterning device. A mask transmission function under the thin-mask approximation may be referred to as a thin-mask transmission function. A mask transmission function encompassing M3D may be referred to as a M3D mask transmission function.

[0048] Figure 2 schematically depicts an exemplary lithographic projection apparatus whose illumination source could be optimized utilizing the methods described herein. The apparatus comprises:

- an illumination system IL, to condition a beam B of radiation. In this particular case, the illumination system also comprises a radiation source SO;

- a first object table (e.g., mask table, patterning device table or reticle stage) MT provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS;

- a second object table (substrate table or wafer stage) WT provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS;

- a projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) to image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0049] As depicted herein, the apparatus is of a transmissive type (i.e., has a transmissive mask). However, in general, it may also be of a reflective type, for example (with a reflective mask). Alternatively, the apparatus may employ another kind of patterning device as an alternative to the use of a classic mask; examples include a programmable mirror array or LCD matrix.

[0050] The source SO (e.g., a mercury lamp or excimer laser) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AD for setting the outer or inner radial extent (commonly referred to as o-outer and o-inncr, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0051] It should be noted with regard to Figure 2 that the source SO may be within the housing of the lithographic projection apparatus (as is often the case when the source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam that it produces being led into the apparatus (e.g., with the aid of suitable directing mirrors); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[0052] The beam B subsequently intercepts the patterning device MA, which is held on a patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PS, which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of beam B. Similarly, the first positioning means can be used to accurately position the patterning device MA with respect to the path of the beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in Figure 11. However, in the case of a wafer stepper (as opposed to a step-and-scan tool) the patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[0053] The depicted tool can be used in two different modes:

- In step mode, the patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x or y directions so that a different target portion C can be irradiated by the beam B;

- In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single “flash”. Instead, the patterning device table MT is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that the projection beam B is caused to scan over a patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, in which M is the magnification of the lens PS (typically, M = 1/4 or 1/5). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0054] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment. As will be appreciated, the models may represent a different patterning process and need not comprise all the models described below. A source model 300 represents optical characteristics (including radiation intensity distribution, bandwidth and/or phase distribution) of the illumination of a patterning device. The source model 300 can represent the optical characteristics of the illumination that include, but not limited to, numerical aperture settings, illumination sigma (o) settings as well as any particular illumination shape (e.g., off-axis radiation shape such as annular, quadrupole, dipole, etc.), where o (or sigma) is outer radial extent of the illuminator.

[0055] A projection optics model 310 represents optical characteristics (including changes to the radiation intensity distribution and/or the phase distribution caused by the projection optics) of the projection optics. The projection optics model 310 can represent the optical characteristics of the projection optics, including aberration, distortion, one or more refractive indexes, one or more physical sizes, one or more physical dimensions, etc.

[0056] The patterning device / design layout model module 320 captures how the design features are laid out in the pattern of the patterning device and may include a representation of detailed physical properties of the patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In an embodiment, the patterning device / design layout model module 320 represents optical characteristics (including changes to the radiation intensity distribution and/or the phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to a feature of an integrated circuit, a memory, an electronic device, etc.), which is the representation of an arrangement of features on or formed by the patterning device. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the illumination and the projection optics. The objective of the simulation is often to accurately predict, for example, edge placements and CDs, which can then be compared against the device design. The device design is generally defined as the pre-OPC patterning device layout, and will be provided in a standardized digital file format such as GDSII or OASIS.

[0057] An aerial image 330 can be simulated from the source model 300, the projection optics model 310 and the patterning device / design layout model module 320. An aerial image (Al) is the radiation intensity distribution at substrate level. Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image.

[0058] A resist layer on a substrate is exposed by the aerial image and the aerial image is transferred to the resist layer as a latent “resist image” (RI) therein. The resist image (RI) can be defined as a spatial distribution of solubility of the resist in the resist layer. A resist image 350 can be simulated from the aerial image 330 using a resist model 340. The resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model 340 typically describes the effects of chemical processes which occur during resist exposure, post exposure bake (PEB) and development, in order to predict, for example, contours of resist features formed on the substrate and so it typically related only to such properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake and development). In an embodiment, the optical properties of the resist layer, e.g., refractive index, film thickness, propagation, and polarization effects — may be captured as part of the projection optics model 310. [0059] So, in general, the connection between the optical and the resist model is a simulated aerial image intensity within the resist layer, which arises from the projection of radiation onto the substrate, refraction at the resist interface and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) is turned into a latent “resist image” by absorption of incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the realistic 3- dimensional intensity distribution in the resist stack by a 3-dimensional aerial (and resist) image. [0060] In an embodiment, the resist image 350 can be used an input to a post-pattern transfer process model module 360. The post-pattern transfer process model module 360 defines performance of one or more post-resist development processes (e.g., etch, development, etc.).

[0061] Simulation of the patterning process can, for example, predict contours, CDs, edge placement (e.g., edge placement error), etc. in the resist and/or etched image. Thus, the objective of the simulation is to accurately predict, for example, edge placement, and/or aerial image intensity slope, and/or CD, etc. of the printed pattern. These values can be compared against an intended design to, e.g., correct the patterning process, identify where a defect is predicted to occur, etc. The intended design is generally defined as a pre-OPC design layout which can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0062] Thus, the model formulation describes most, if not all, of the known physics and chemistry of the overall process, and each of the model parameters desirably corresponds to a distinct physical or chemical effect. The model formulation thus sets an upper bound on how well the model can be used to simulate the overall manufacturing process.

[0063] The following paragraphs describe designing a mask pattern design for stitching a pattern across adjacent exposure fields on the substrate such that a variation of the CD of the pattern printed on the substrate (“stitched pattern”) due to an overlay between the two adjacent exposure fields on the substrate is reduced. Note that a pattern in the mask pattern design is referred to as a “mask pattern.” As noted above, such mask pattern is specifically designed (e.g., mask pattern design) on the mask to print a specific “design layout” or “target pattern” onto a substrate. Also note that a CD of a mask pattern may be referred to as “mask CD.”

[0064] Figure 4 shows overlay-tolerant mask pattern designs for printing a target pattern on a substrate across two adjacent exposure fields on the substrate, consistent with various embodiments. A target pattern 402 (e.g., an isolated vertical space/line/bar) may be printed on a substrate by projecting a first mask pattern design 412 and a second mask pattern design 422 in adjacent exposure fields 451 and 452, in effect “stitching” a first portion 430a of a mask pattern with a second portion 430b of the mask pattern across a field boundary 450 of the adjacent exposure fields 451 and 452 to print a stitched pattern corresponding to the target pattern 402 on the substrate. Note that the mask pattern 430a and 430b may be referred to as two portions of a mask pattern (e.g., a first portion 430a of a mask pattern and a second portion 430b of the mask pattern), or as two mask patterns (e.g., a first mask pattern 430a and a second mask pattern 430b). Regardless of how the two mask patterns are referred to, it should be understood that the target pattern 402 may be printed on the substrate as a composite of these two mask patterns 430a and 430b. The two mask patterns 430a and 430b may also be collectively referred to as mask pattern 430.

[0065] In the illustrated embodiment, the mask patterns 430a and 430b have similar or the same shapes, although inverted with respect to one another (in some embodiments, they may have some differences (e.g., resulting from OPC corrections)). For example, mask pattern 430a has an elongated configuration, with a thicker end and a thinner end. The mask pattern has stepped side surfaces, such that the configuration of the mask pattern 430a narrows from an end with a longer side edge 442 to an end with a shorter side edge 440, as shown.

[0066] In some embodiments, when a pattern is printed across two adjacent exposure fields, there can be an overlay error (e.g., shift from the actual intended position) between the patterns in the two adjacent exposures in any direction on the substrate (e.g., y-direction 461 or an x-direction 462), which can cause the CD of the stitched pattern (e.g., pattern printed on the substrate) to vary. In some embodiments, to reduce the CD variation of the stitched pattern due to the overlay, the mask pattern and SRAFs may be designed as illustrated in the mask pattern designs 412 and 422. For example, the first mask pattern design 412 includes a first SRAF 414 located proximate to (or alongside) a first edge 440 of the first mask pattern 430a (e.g., near a short edge or near the smallest segment of the first mask pattern 430a). The first mask pattern design also includes a second SRAF 416 (in this embodiment, a pair of SRAFs 416a and 416b), which are on opposite sides of the mask pattern 430a and located proximate (alongside) the opposite edges of the mask pattern. In this embodiment, the opposite edges of the mask pattern run perpendicular to the first edge 440 (e.g., on either sides of the stepped longer edges).

[0067] The geometry of the first SRAF 414 and the second SRAF 416 is also designed in a specific way, which is described in greater detail at least with reference to Figures 4 and 7-10. For example, the pitch, CD, and line distance of the SRAFs are designed to be of specific values. By designing the SRAF as described herein, the sensitivity of the CD of the stitched pattern to the overlay (e.g., CD variation due to the overlay), at least in the x-direction 462, is reduced. Additionally, the present design of the SRAFs may also reduce the sidelobe effects.

[0068] The geometry of the mask pattern 430 is also adjusted in a specific way to reduce the sensitivity of the CD of the stitched pattern to overlay, which is described in greater detail at least with reference to Figures 4 and 7-10. For example, the first mask pattern 430a is configured to have multiple segments 418 (e.g., three segments 418a, 418b, and 418c) of varying CD. That is, in one embodiment, each of the segments 418a, 418b, and 418c have different CDs. Similarly, the second mask pattern 430b is adjusted to have multiple segments 428 (e.g., three segments 428a, 428b, and 428c) of varying CD. In other embodiments, two segments may have the same CD as long as other segments have different CDs. In some embodiments, the segments in the second mask pattern 430b have a complementary CD to the CD of the corresponding segment in the first mask pattern 430a. Specifically, a pair of mask CD values may be considered to be complementary if the CD of the stitched pattern matches the target CD. For example, consider that the first segment 418a of the first mask pattern 430a has a first mask CD and the third segment 428c of the second mask pattern 430b has a second mask CD, and that the target pattern 402 has a target CD. The first mask CD and the second mask CD are said to be complementary if the stitched pattern on the substrate resulting from the exposure of the first segment 418a of the first mask pattern 430a and the third segment 428c of the second mask pattern 430b (e.g., at the region 471) has a CD matching the target CD. In some embodiments, the first mask pattern 430a and the second mask pattern 430b are symmetric across an axis 475 passing through the segments of the first and second mask patterns 430a and 430b, respectively, that have the same CD. Accordingly, the first mask pattern design 412 (which includes SRAFs 414 and 416 and the first mask pattern 430a) and the second mask pattern design 422 (which includes SRAFs 424, 426a and 426b and the second mask pattern 430b) are symmetric across the axis 475 as shown. As also shown, in one embodiment the SRAF’s have stepped configuration that complements the stepped configuration of the mask pattern. For example, using the first mask pattern 430a, it can be seen that the SRAFs along the opposite long edges of the first mask pattern are stepped such that they remain closely spaced (e.g., have the same line distance). In one embodiment the spacings are the same for both mask patterns 430a and 430b. By designing the mask patterns 430a and 430b with varying CD, the sensitivity of the CD of the stitched pattern to the overlay is reduced (e.g., at least in the y-direction 461).

[0069] The following paragraphs describe a method of generating an overlay-tolerant mask pattern design that facilitates reducing the sensitivity of the CD of the stitched pattern to an overlay. While Figures 5 and 6 describe the method in a brief manner, Figures 7-10 describe the method in greater detail.

[0070] Figure 5 is a flow diagram of a process for generating an overlay-tolerant mask pattern design, consistent with various embodiments. Figure 6 is a block diagram of the overlay-tolerant mask pattern design, consistent with various embodiments. At process P510, a design (e.g., placement and geometry) of SRAFs to be placed proximate a mask pattern to reduce the sensitivity of the CD of the stitched pattern to an overlay is determined. In some embodiments, determining the placement of the SRAF includes identifying a first location proximate the first mask pattern 430a for the placement of the first SRAF 414 to reduce the sensitivity of the CD of the stitched pattern to the overlay in a first direction (e.g., y-direction 461 on the substrate). For example, the first location includes an area near the first edge 440 of the first mask pattern 430a (e.g., near a short edge of the first mask pattern 430a). [0071] In some embodiments, the SRAF can include a sub-resolution grating (SRG), and the SRGs may be horizontal SRGs (e.g., perpendicular to the target pattern) or vertical SRGs (e.g., parallel to the target pattern). The SRGs depicted in Figure 6 are horizontal SRGs. As illustrated in Figure 6, the first SRAF 414 includes a set of SRGs 414 and a second SRAF 416 includes a first set of SRGs 416a and a second set of SRGs 416b. The number of SRGs in the first SRAF 414 or the second SRAF 416 may be more or less than the number depicted in Figure 6.

[0072] In some embodiments, determining the placement of the second SRAF 416 includes identifying a second location proximate the first mask pattern 430a to reduce the sensitivity of the CD of the stitched pattern to the overlay in a second direction perpendicular to the first direction (e.g., x- direction 462 on the substrate). For example, the second location includes an area near the opposite edges of the pattern 430a perpendicular to the first edge 440 (e.g., on either sides of the longer edges). The first set of SRGs 416a are placed on one side of the first mask pattern 430a and the second set of SRGs 416b are placed on the other side of the first mask pattern 430a.

[0073] The geometry of the SRAFs 414 and 416 is also designed in a specific way. Some of the geometrical parameters that are determined include a pitch 605, CD_SRG 610, line end distance 615, and a line distance 620 of the SRAFs. The pitch 605 is a distance between two consecutive SRGs, the CD_SRG 610 is the CD of the SRG, line end distance 615 is the distance between the SRG of the first SRAF 414 and a shorter edge of the pattern 430a, and the line distance 620 is the distance between the SRG and the pattern 430a. In some embodiments, the values of the geometrical parameters may be determined based on a simulation of the lithographic process (e.g., described at least with reference to Figure 3). For example, the pitch 605 (e.g., minimum pitch) is determined based on an illumination source of the lithographic apparatus (e.g., illumination source IL of the lithographic apparatus described at least with reference to Figures 1 and 2), and then the CD_SRG 610 is determined based on the pitch 605. In some embodiments, specular reflection from an absorber layer of the mask may be minimized by placing an SRG in a mask pattern design. Such reduction of the specular reflection may be achieved when a design or geometry and placement of the SRG in the mask pattern design is appropriate. For example, by configuring the pitch 605 and the CD_SRG 610 to a specified value, scattering of a first order intensity of light outside the pupil of the illumination source is maximized while a zeroth order intensity of light is suppressed or canceled and the variation in CD of the stitched pattern may be minimized. Such geometrical parameters may be determined by simulating the lithographic process (e.g., process described at least with reference to Figure 3). Additional details regarding the determination of the pitch 605 and the CD_SRG 610 are described in U.S. Provisional Application No. 63/398,929 filed on August 18, 2022, the disclosure of which is hereby incorporated by reference in its entirety. The line distance 620 of the second SRAF 416 is determined by simulating the lithography process for various line distance values, determining the CD variation of the pattern due to the overlay for each line distance value, and then selecting a line distance value for which the CD variation of the pattern due to the overlay is less than a threshold value (e.g., CD variation is the least) or the sidelobe effect is less than a threshold value (e.g., sidelobe effect is the least). Additional details of determining the line distance 620 is described at least with reference to Figures 7-10. By designing the SRAF as described above, the sensitivity of the CD of the stitched pattern to the overlay is reduced (at least in the x-direction 462).

[0074] At process P520, a design (e.g., geometry) of the mask pattern 430 is adjusted. For example, the target pattern 402 is designed as two separate mask patterns - first mask pattern 430a and second mask pattern 430b - as illustrated in the first mask pattern design 412 and the second mask pattern design 422, respectively. The first mask pattern 430a is adjusted to have multiple segments of different CDs. For example, as illustrated in Figure 6, the first mask pattern 430a includes three segments - 418a, 418b, and 418c of varying CD (e.g., gradually increasing/decreasing CD). For example, the first segment 418a has a first mask CD 618a, the second segment 418b has a second mask CD 618b greater than the first mask CD 618a, and the third segment 418c has a third mask CD 618c greater than the second mask CD 618b. While Figure 6 depicts three segments, the first mask pattern 430a may be designed to have any number of segments. Similarly, the second mask pattern 430b is adjusted to have multiple segments 428 (e.g., three segments 428a, 428b, and 428c) of varying CD. In some embodiments, the segments in the second mask pattern 430b have complementary CD to the CD of the corresponding segment in the first mask pattern 430a. In some embodiments, a pair of mask CD values are said to be complementary if the CD of the stitched pattern matches the target CD. For example, consider that a first segment 418a of the first mask pattern 430a has a first mask CD 618a and a third segment 428c of the second mask pattern 430b has a second mask CD 628c. The first mask CD 618a and the second mask CD 628a are said to be complementary, when the stitched pattern resulting from the exposure of the first segment 418a of the first mask pattern 430a and the third segment 428c of the second mask pattern 430b (e.g., at the region 471) has a CD value matching the target CD. Additional details regarding determining the CD of the segments of the mask pattern 430 are described at least with reference to Figures 7-10. By designing the mask patterns 430a and 430b with varying CD, the sensitivity of the CD of the stitched pattern to the overlay is reduced (e.g., at least in the y-direction 461).

[0075] At process P530, a mask is manufactured based on the first mask pattern design 412 and the second mask pattern design 422 for use in a lithographic process to print a target pattern on the substrate.

[0076] At process P540, a lithographic process may be executed using the mask to project the first mask pattern design 412 and the second mask pattern design 422 in two adjacent exposure fields on the substrate to print a pattern corresponding to the target pattern 402.

[0077] Figure 7 is a flow diagram of a process for generating an overlay-tolerant mask pattern design, consistent with various embodiments. In some embodiments, the process of Figure 7 may be executed as part of the process of Figure 5 to generate the mask pattern design for printing or stitching the target pattern 402 across two adjacent exposure fields on the substrate. [0078] In some embodiments, a CD of the stitched pattern may be made tolerant to the overlay in x- direction 462 by generating aerial images of the first and second mask patterns 430 such that the aerial image intensities are linear proximate a reference point, as illustrated in Figure 8A. The graph 830 shows a portion of the aerial image intensities 831 and 832 of the first and second mask patterns 430, respectively. The first aerial image intensity 831 of the first mask pattern 430a and the second aerial image intensity 832 of the second mask pattern 430b are adjusted to be linear near a reference point that is located on the aerial image intensities and proximate an aerial image intensity threshold 815 (e.g., a reference point 825 on the aerial image intensity threshold 815). Further, the aerial image intensities 831 and 832 are also adjusted to be symmetrical (e.g., mirror symmetry) across the axes (815 and 816) passing through the reference point 825 in perpendicular directions. For example, a first portion of the aerial image intensity that is greater than the aerial image intensity at the reference point 825 and the second portion of the aerial image intensity that is lesser than the aerial image intensity at the reference point 825 are adjusted to be mirror symmetric across the reference point 825. When the aerial image intensities of the first and second mask patterns 430 are adjusted to be linear, the aerial image intensity 835 of the stitched pattern may increase at first location 846 (e.g., a first intersection of the aerial image intensity 835 and the aerial image intensity threshold 815) and drop at second location 847 (e.g., a second intersection of the aerial image intensity 835 and the aerial image intensity threshold 815), as illustrated in graph 845, compared to the aerial image intensities at the corresponding locations, as illustrated in the graph 840, where the aerial image intensities of the first and second mask pattern 430 are not adjusted to be linear and symmetric. By adjusting the aerial image intensities to be linear and mirror symmetric, the increase and decrease in the aerial image intensity 835 of the stitched pattern at locations 846 and 847, respectively, may be made to be equal, thereby preventing, or minimizing, any variation in the CD value of the stitched pattern (e.g., even at significant overlay values), although causing the position of the stitched pattern on the substrate to shift in x-direction. In some embodiments, the greater the mirror symmetry and the more linear the aerial image intensities at the reference point 825, the more tolerant is, or the lesser is the variation of, the CD of the stitched pattern to the overlay in x-direction 462. The graph 850 illustrates a variation of the CD of the stitched pattern (e.g., for various CD values of the stitched pattern) with respect to the overlay in x-direction. The y-axis of graph 850 is indicative of the CD of the stitched pattern and the x-axis is indicative of overlay values with the overlay being “0” at position 852 on the x-axis. As indicated in the graph 850, the CD variation 851 (e.g., corresponding to the first CD value of the stitched pattern) is the least among the CD variation corresponding to other CD values. In some embodiments, the above adjustments to the aerial images may be achieved through the use of SRAFs and by designing the SRAFs as described below.

[0079] At process P710, a design of the first SRAF 414 (e.g., placement and geometry) is determined. In some embodiments, determining the placement of the first SRAF 414 includes identifying a first location proximate the pattern 430a to reduce the sensitivity of the CD of the stitched pattern to the overlay in a first direction (e.g., y-direction 461 on the substrate). For example, the first location includes an area near the first edge 440 of the first mask pattern 430a (e.g., near a short edge of the first mask pattern 430a). In some embodiments, determining the geometry of the first SRAF 414 includes determining geometrical parameters such as the pitch 605 and the CD_SRG 610 of the first SRAF. In some embodiments, the pitch 605 is a distance between two consecutive SRGs, the CD_SRG 610 is the CD of the SRG, and the line end distance 615 is the distance between the SRG of the first SRAF 414 and the first edge 440 of the first mask pattern 430a (e.g., a line end of the pattern 430a) parallel to the first SRAF 414. In some embodiments, the values of the geometrical parameters may be determined based on a simulation of the lithographic process (e.g., described at least with reference to Figure 3). For example, the pitch 605 (e.g., minimum pitch) is determined based on an illumination source of the lithographic apparatus (e.g., illumination source IL of the lithographic apparatus described at least with reference to Figures 1 and 2), and then the CD_SRG 610 is determined based on the pitch 605. In some embodiments, by determining an appropriate placement and geometrical parameters of the first SRAF 414 not only the sensitivity of CD of the stitched pattern to overlay in y- direction is reduced, the specular reflection from an absorber layer of the mask may also be minimized. For example, by configuring the pitch 605 and the CD_SRG 610 of the first SRAF 414 to a specified value, scattering of a first order intensity of light outside the pupil of the illumination source is maximized while a zeroth order intensity of light is suppressed or canceled and the variation in CD of the stitched pattern may be minimized. In some embodiments, the line end distance 615 contributes to a variation in CD of the stitched pattern printed on the substrate. By simulation, the line end distance value for which the CD variation of the stitched pattern is the least may be selected. Additional details regarding the determination of the pitch 605, the CD_SRG 610 and the line end distance 615 are described in the U.S. Provisional Application No. 63/398,929.

[0080] At process P720, a design of the second SRAF 416 (e.g., placement and geometry) is determined. In some embodiments, determining the placement of the second SRAF 416 includes identifying a second location proximate the pattern 430a to reduce the sensitivity of the CD of the stitched pattern to the overlay in a second direction perpendicular to the first direction (e.g., x- direction 462 on the substrate). For example, the second location includes an area near the opposite edges of the pattern 430a perpendicular to the first edge 440 (e.g., on either sides of the longer edges). The second SRAF 416 includes a first set of SRGs 416a that are placed on one side of the pattern 430a and a second set of SRGs 416b that are placed on the opposite side of the pattern 430a. In some embodiments, the pitch 605 and the CD_SRG 610 of the second SRAF 416 are the same as the pitch 605 and the CD_SRG 610 of the first SRAF 414 determined in process P710.

[0081] The line distance 620, which is the distance between the SRGs of the second SRAF 416 and the pattern 430a, is determined by simulating the lithography process for various line distance values and then selecting a line distance value for which the CD variation of the pattern due to the overlay is less than a threshold value. A range of line distance values may be considered (e.g., minimum distance allowed to pitch 605). The CDs of segments of the mask pattern 430 are also determined by simulating the lithography process for various mask CD values. A range of mask CD values may be considered (e.g., minimum CD allowed to n times target CD such as 1.5 to 2 times target CD). The line distance 620 and CD values of the segments of the pattern are determined as follows.

[0082] At process P730, the line distance 620 of the second SRAF 416 is set to an initial line distance value (e.g., minimum distance allowed as per mask rule check (MRC)) from the range of line distance values.

[0083] At process P740, an initial CD value of the range of mask CD values is obtained (e.g., CD 618a). The initial CD value may be assigned as the mask CD of a first segment of the first mask pattern 430a (e.g., first segment 418a).

[0084] At process P750, a CD value that is complementary to the initial CD value is determined. For example, the mask CD 628c may be determined to be complementary to the initial CD value. Accordingly, the CD of the third segment of the second mask pattern 430b (e.g., third segment 428c) may be set to the mask CD 628c. In some embodiments, a pair of mask CD values (e.g., mask CD 618a, mask CD 628c) are said to be complementary if the CD of the stitched pattern matches the target CD.

[0085] After the complementary CD is determined for the initial CD value, the method iterates through processes P740 and P750 to obtain a next CD value (e.g., mask CD 618b) from the range of mask CD values to be assigned for a next segment of the first mask pattern 430a (e.g., second segment 418b) and determine a complementary CD value (e.g., mask CD 628b) for the next CD value. In some embodiments, the processes P740 and P750 may be repeated until the CD value to be assigned to a segment of the first mask pattern 430a and the complementary CD value to be assigned to the corresponding segment of the second mask pattern 430b are the same. For example, referring to Figure 6, the process of P740 and P750 may execute twice - (a) once for determining the complementary CD value (e.g., mask CD 628c - which is the CD of third segment 428c of second mask pattern 430b) for the CD of first segment 418a of first mask pattern 430a (e.g., mask CD 618a), and (b) a second time for determining the complementary CD (e.g., CD 628b, which is the CD of second segment 428b of second mask pattern 430b) for the CD of second segment 418b of first mask pattern 430a (e.g., CD 618b). Since both the CDs in the pair of mask CDs (e.g., CD 618b, CD 628b) after the second execution has the same value, the execution of the processes P740 and P750 may stop, and the method may proceed to process P760. Since both mask patterns 430a and 430b are symmetric across the axis 475, the CD of the remaining segments of one mask pattern may be determined based on the CD of the segments of the other mask pattern. For example, while the CD of the first segment 418a and the second segment 418b of the first mask pattern 430a, and the CD of the third segment 428c and the second segment 428b of the second mask pattern 430b, are determined based on the above processes of P740-P750, (a) the CD of the third segment 418c of the first mask pattern 430a (e.g., CD 618c) will be the same as the CD of the third segment 428c of the second mask pattern 430b (e.g., CD 628c), and (b) the CD of the first segment 428a (e.g., CD 628a) will be the same as the CD of the first segment 418a of the first mask pattern 430a (e.g., CD 618a). While the number of segments in the mask pattern 430 is depicted as three segments, in some embodiments, the pattern 430 may be adjusted to include more or lesser number of segments (e.g., which may depend on the incremental value of mask CD for each iteration of process P740-P750). Thus, the mask CD of various segments of both mask patterns are determined as described.

[0086] In some embodiments, the complementary CDs of the segments of the mask pattern 430 described above may be determined by simulating an aerial image intensity of mask patterns 430a and 430b and the stitched pattern, as illustrated in Figure 8B. Figure 8B illustrates aerial image intensity of the mask pattern and aerial image intensity of the stitched pattern, consistent with various embodiments. The first graph 875 shows the aerial image generated for various mask CD values (e.g., a range of mask CD values). For example, the aerial image 805a indicates the aerial image intensity for a mask pattern with a first CD (e.g., CD value less than MRC) and the aerial image 805b indicates the aerial image intensity for a mask pattern with a second CD (e.g., CD value 810). In some embodiments, the CD value of a mask pattern may be determined from the aerial image intensity graph as a distance between two points on the x-axis that correspond to the points on the threshold intensity 815 where the aerial image intensity curve intersects with threshold intensity 815. The second graph 880 illustrates an aerial image intensity of a simulated stitched pattern, which is a composite of two mask patterns. For example, the aerial image 805c is the aerial image intensity of the stitched pattern that is a composite of a first mask pattern with a first CD (e.g., corresponding to the aerial image 805a) and a second mask pattern with a second CD 810 (e.g., corresponding to the aerial image 805b). The CD 820 indicates a CD of the stitched pattern. In some embodiments, the first CD (e.g., CD of the pattern corresponding to the aerial image 805a) and the second CD 810 are considered to be complementary if the CD 820 of the stitched pattern matches a target CD of the pattern. Note that the second graph 880 shows the aerial images of stitched patterns composed using different CD pairs, and like the aerial image 805c, the aerial images of stitched patterns composed using different CD pairs yield a CD that matches the target CD. In some embodiments, a complementary CD for a given CD value may be determined using the aerial images by obtaining (e.g., via simulation) a first aerial image for a given mask CD value (e.g., aerial image 805a and its corresponding CD value) and a second aerial image for a candidate CD value (e.g., second aerial image 805b and its CD value 810). The aerial image intensity of the second aerial image may be adjusted until a CD of the stitched pattern (e.g., CD 820 of aerial image 805c) matches the target CD, and the candidate CD value associated with the adjusted second aerial image for which the CD of the stitched pattern matches the target CD is selected as the complementary CD for the given CD value. [0087] At process P760, for a given line distance (e.g., line distance value set in process P730), the sensitivity of the CD of the stitched pattern to a range of overlay values is determined. In some embodiments, the sensitivity of the CD of the stitched pattern, that is a variation of the CD of the stitched pattern due to overlay, may be determined for a range of overlay values (e.g., overlay in x-direction 462) by simulation of the lithographic process for various CD values of the first mask pattern 430a. Figure 9A shows a graph illustrating CD variation of the stitched pattern due to overlay for various mask CD values, consistent with various embodiments. In some embodiments, the y-axis of the graphs indicate a CD of the stitched pattern (e.g., nominal CD of the stitched pattern) and the x-axis indicates overlay values in x-direction with the overlay being “0” at position 916 on the x-axis. For example, the first graph 910 shows the variation of CD of the stitched pattern over a range of overlay-x values for the given line distance value. In some embodiments, a first CD variation curve 911 indicates a variation of the CD of the stitched pattern for a first CD of the first mask pattern 430a, a second CD variation curve 912 indicates a variation of the CD of the stitched pattern for a second CD of the first mask pattern 430a and so on. In some embodiments, the flatter the CD variation curve the lesser the sensitivity of the CD of the stitched pattern to the overlay.

[0088] After determining the sensitivity of the CD to the overlay for the given line distance, a next line distance value is chosen from the range of line distance values and the processes P730-P760 is repeated for various such line distance values, and the sensitivity of the CD of the stitched pattern to the overlay is determined for each of the line distance values.

[0089] At process P770, a line distance value for which the sensitivity of the CD of the stitched pattern to the overlay (e.g., determined in process P760) is below a specified threshold (e.g., CD variation is the least) is selected as the value for the line distance 620. For example, as illustrated in Figure 9 A, the three different graphs - the first graph 910, a second graph 920 and a third graph 930 show the sensitivity of the CD of the stitched pattern to the overlay for three different line distance values, respectively. In some embodiments, the sensitivity of the CD of the stitched pattern to the overlay in the first graph 910 is the least, and accordingly the line distance value associated with the first graph 910 is selected as the value for the line distance 620.

[0090] In some embodiments, the line distance value may also have an impact on the sidelobes. Figure 9B shows sidelobes for various line distance values of an SRAF, consistent with various embodiments. For example, the graph 950 shows a plot of aerial image intensity for various line distance values and the sidelobes 951a and 951b associated with the respective line distance values. The graph 950 may be generated by simulation of a lithographic process for various line distance values. As illustrated by aerial image intensity plots 961 and 962, the sidelobe effects are lesser for line distance value associated with aerial image intensity plot 962 than the line distance value associated with aerial image intensity plot 961. Accordingly, by adjusting the line distance value, the sidelobes may be suppressed or minimized. In some embodiments, the line distance value selected in process P770, which is the line distance value for which the sensitivity of the CD of the stitched pattern to the overlay is below a specified threshold (e.g., CD variation is the least), may also be the line value distance that may suppress or minimize the sidelobes. However, in embodiments where the sidelobes are still remaining, the line distance value may be further adjusted until the sidelobes are suppressed or minimized and the adjusted line distance value may be selected as the value for the line distance 620.

[0091] At process P780, an image representation of the first mask pattern design 412 and second mask pattern design 422 are generated based on the parameters determined in the above steps. For example, a first mask image 782 of the first mask pattern design 412 is generated based on a pitch 605, CD_SRG 610, line end distance 615, and a line distance 620 of the SRAFs and the CDs of the segments of the first mask pattern 430a (e.g., CDs 618a-618c). Similarly, a second mask image 784 of the second mask pattern design 422 may be generated based on a pitch 605, CD_SRG 610, line end distance 615, and a line distance 620 of the SRAFs and the complementary CDs (e.g., CDs 628a- 628c) corresponding to the CDs of the segments of the first mask pattern 430a.

[0092] At process P790, a mask CD in a first transition region 471 of the first mask pattern 430a and a second transition region 472 of the second mask pattern 430b are adjusted. As described above at least with reference to Figure 4, the target pattern 402 may be printed on the substrate by exposing the first mask pattern design 412 and the second mask pattern design 472 in the adjacent exposure fields 451 and 452. The mask pattern 430a and 430b are exposed across the field boundary 450 such that a tip of the second mask pattern 430b transitions into the first transition region 471 on the first mask pattern 430a and a tip of the first mask pattern 430a transitions into the second transition region 472 on the second mask pattern 430b. That is, the first transition region 471 corresponds to a region on the first mask pattern 430a where a tip of the second mask pattern 430b transitions into when the first and second mask patterns 430a and 430b are printed on the substrate in the two adjacent exposure fields 451 and 452. Similarly, the second transition region 472 corresponds to a region on the second mask pattern 430b where a tip of the first mask pattern 430a transitions into when the first and second mask patterns 430a and 430b are printed on the substrate in the two adjacent exposure fields 451 and 452. [0093] In some embodiments, there may be a dip (e.g., decrease) in the CD of the stitched pattern at locations corresponding to the first transition region 471 and the second transition region 472, (e.g., due to mask 3D effect) as illustrated in Figure 10. Figure 10 shows a graph illustrating CD of a stitched pattern at transition regions before and after adjustment of mask CD, consistent with various embodiments. The x-axis of the graphs corresponds to the y-direction and the y-axis corresponds to the CD of the stitched pattern. The graph 1005 shows a dip in the CD of the stitched pattern at locations 1006, which correspond to the first and second transition regions 471 and 472. In some embodiments, the dip in the CD may be adjusted (e.g., dip can be reduced by increasing the CD) by performing an optimal proximity correction (OPC) process to increase the CD of the mask patterns 430a and 430b in the first transition region 471 and the second transition region 472, respectively, such that CD of the stitched pattern matches the target CD. After performing the OPC process, the CD of the stitched pattern at the locations 1006 corresponding to the first and second transition regions 471 and 472 is increased (e.g., the dip is reduced), as illustrated in the graph 1010. In some embodiments, the graphs 1005 and 1010 may be generated by simulating the lithographic process. [0094] After performing the OPC, the mask images 782 and 784 of the mask pattern designs 412 and 422, respectively, may be used in manufacturing the mask for use in a lithographic process to print the target pattern 402 on the substrate.

[0095] While the above paragraphs describe stitching of a pattern using darkfield masks, the above embodiments may also be implemented for brightfield masks as described below. Figure 11 illustrates mask pattern designs for printing a target pattern using a brightfield mask, consistent with various embodiments. In some embodiments, generating the brightfield mask pattern design for printing the target pattern 402 across the adjacent field exposures on a substrate is similar to generating the darkfield mask pattern design (e.g., the first mask pattern design 412 and the second mask pattern design 422) described above. For example, for a first brightfield mask pattern design 1112, a design of the first SRAF 1114 such as the placement, pitch 1105 and CD_SRG 1110 of the first SRAF 1114 may be determined in a way similar to the placement, pitch 605 and CD_SRG 610 of the first SRAF 414 of the first mask pattern design 412. However, in some embodiments, the first SRAF 1114 of the brightfield mask pattern design 1112 may be placed proximate the largest segment (e.g., segment 1128) of the mask pattern 1130a, unlike the first SRAF 414 in the darkfield mask pattern design 412 where the first SRAF 414 is placed proximate the smallest segment of the first mask pattern 430a.

[0096] In some embodiments, designing the second SRAF 1116 includes determining a placement of the second SRAF 1116 within the mask pattern 1130a, unlike the second SRAF 416 in the darkfield mask pattern design 412 where the second SRAFs 416a and 416b are placed on either sides of the first mask pattern 430a. The second SRAF 1116 can be a two-dimensional (2D) entity (e.g., a square, rectangle, or other 2D entity). The line distance 1120, which is a distance between the second SRAF 1116 and an edge of each segment of the mask pattern 1130a, is determined in a way similar to the line distance 620 of the darkfield mask pattern design 412. Additionally, in the brightfield mask pattern design 1112, a check has to be performed whether adding the second SRAFs helps or does not help in minimizing the dip in the CD in the transition regions. For example, having the second SRAF 1116 in the smallest segment 1118a may not be helpful as the CD of the segment 1118a is significantly lesser compared to that of the segment 1118d and therefore, may not be included. Further, the size of second SRAF 1116 may also be a determining factor in determining whether the second SRAF 1116 of a particular size may be included in the design. For example, the size of the second SRAF 1116 in the segments keep decreasing as the CD of the segments 1118a-d keep decreasing and the SRAF 1116 may not be included in a segment if the size of the SRAF 1116 is lesser than the minimum size specified in the MRC. Accordingly, in some embodiments, the brightfield mask pattern design 1112 may have one or more segments without an SRAF.

[0097] In some embodiments, the segments 1118a, 1118b, 1118c and 1118d of the mask pattern 1130a are also designed similarly to that of the segments 418a-418c of the darkfield mask pattern design 412. For example, the segments 1118a-l 118d have a varying CD.

[0098] The second mask pattern design 1122 is designed similarly to that of the second darkfield mask pattern design 422. For example, each segment of the mask pattern 1130b has a complementary CD to the CD of the corresponding segment of the mask pattern 1130a in the first mask pattern design 1112. Further, the first mask pattern design 1112 and the second mask pattern design 1122 are symmetric across an axis passing through the segment of the mask pattern 1130a and the segment of the mask pattern 1130b that have the same CD. Thus, the mask pattern design for brightfield masks may be designed as described above.

[0099] While the foregoing techniques facilitate stitching a pattern across adjacent exposure fields such that a variation of the CD of the stitched pattern due to the overlay is reduced, the foregoing techniques also facilitate in enhancing the peak intensity of a composite image of the mask patterns, which reduces development defects. For example, as illustrated in graph 845, the peak intensity of the aerial image intensity 835 corresponding to the stitched pattern is greater than the peak intensities of either of the aerial image intensities 831 and 832 corresponding to the mask patterns 430a and 430b, respectively. That is, by printing a target pattern as a composite of two mask patterns rather than a single mask pattern, the peak intensity of the composite image (e.g., aerial image corresponding to the stitched pattern) is enhanced relative to the peak intensity of the single image (e.g., aerial image of either of the mask patterns 430).

[00100] In some embodiments, the above technique of printing a target pattern as a composite of two mask patterns rather than a single mask pattern, also enhances image contrast in at least a portion of the overlapping exposure fields, as described below.

[00101] Figure 12 is a block diagram for enhancing image contrast at a location on a substrate by overlapping exposures of different mask patterns, consistent with various embodiments. In some embodiments, an image contrast at a location on the substrate where a target pattern 1201 is to be printed may be enhanced by exposing two separate mask pattern designs. In a first example, a first mask pattern design 1205 having a mask pattern 1206 corresponding to the target pattern 1201, and a second mask pattern design 1210 having an opening 1206 in a black border or absorber layer 1204 (e.g., created by removing the absorber layer) of the mask is generated. An SRAF (an SRG 1208 or other SRAFs) may be designed in the opening 1206. The opening 1206 may be created in an area of the black border 1204 corresponding to the area of the mask pattern 1206 in the first mask pattern design 1205. The first mask pattern design 1205 may be exposed on the substrate in a first exposure and the second mask pattern design 1205 may be exposed in a second exposure such that the opening 1206 overlaps with the location where the mask pattern 1206 is exposed on the substrate to enhance the image contrast in the location on the substrate where a pattern corresponding to the mask pattern 1206 is printed. [00102] In a second example, a third mask pattern design 1215 having an SRAF (an SRG 1212 or other SRAFs) may be generated. The SRG 1212 may be created in an area corresponding to the area of the mask pattern 1206 in the first mask pattern design 1205. The first mask pattern design 1205 may be exposed on the substrate in a first exposure and the third mask pattern design 1215 may be exposed in a second exposure such that the SRG 1212 overlaps with the location where the mask pattern 1206 is exposed on the substrate to enhance the image contrast in the location on the substrate where a pattern corresponding to the mask pattern 1206 is printed.

[00103] The following paragraphs describe reducing imaging contrast loss in pattern stitching by adding overlapping assist features (e.g., printable assist features or non-printable assist features such as sub-resolution assist features (SRAF)) near the stitching boundary in each of the mask patterns to be stitched. Wafer features lying in a critical stitching region (e.g., region with double exposure) are built by the superposition of two overlapping images. Each pattern in the critical stitching region is imaged twice by using two half-field masks, which can have the same geometry shapes of the pattern, but different or the same mask feature sizes. For example, corresponding to a contact hole array on a certain wafer location in the critical stitching region, the contact hole array on a first mask has the same pitch as a second mask but smaller hole size. Each half-field mask may have mask features corresponding to the wafer features that are printed on either side of the stitching boundary on the substrate. By designing each mask to have a continuous pattern across the stitching boundary, the reversed phase at the stitching boundary in the image is effectively removed, and not only the image may be printed uniformly across the stitching boundary, but also the contrast of the imaging is enhanced.

[00104] Figure 13 shows stitching of a pattern by overlapping exposures of multiple mask patterns, consistent with various embodiments. A first half-field mask 1301 (referred to as “first mask 1301”) has two areas - a first area 1304 where a first mask pattern having a first set of features to be printed on a substrate is designed, and a second area 1310 corresponding to a black border (e.g., absorber layer). Similarly, a second half-field mask 1302 (referred to as “second mask 1302”) has two areas - a first area 1308 where a second mask pattern having a second set of features to be printed on a substrate is designed, and a second area 1306 having an absorber material. In some embodiments, the first mask pattern and the second mask pattern may be the same and may be stitched together (e.g., to obtain a stitched pattern corresponding to a target pattern), e.g., by exposing them in different orientations (e.g., opposite orientations).

[00105] In some embodiments, the first mask pattern and the second mask pattern may be stitched by overlapping the exposures of the mask patterns across a stitching boundary 1325 (or field boundary) on the substrate (e.g., as described at least with reference to a first mask pattern design 412 and a second mask pattern design 422 of Figure 4). The overlapping exposures constitute various areas on the substrate. For example, a first stitching area 1320, which is referred to as “critical stitching area” or “region of interest” is an area where there is an overlap between features from both mask patterns, that is, features of each mask pattern superposes with features of the other mask pattern when the exposures of the half field masks are overlapped. A second stitching area 1318, which is referred to as “full stitching area,” is an area where there is (a) an overlap between features from one of the mask patterns with features of the other mask pattern, or (b) an overlap between features from one of the mask patterns with an absorber area of the other mask pattern. In other words, the full stitching area 1318 corresponds to an area where wafer features are formed by (a) an overlapping of features from both half-field masks, or (b) an overlapping features from one of the masks with an absorber area of the other mask. In some embodiments, the critical stitching area 1320 is a subset of the full stitching area 1318. In some embodiments, the techniques described in the following paragraphs reduces the imaging contrast loss in the region of interest 1320.

[00106] Figure 14 illustrates designing of mask patterns to reduce contrast loss in stitching of the mask patterns, consistent with various embodiments. As illustrated, the first mask 1301 includes a first mask pattern 1401 having in a first set of features 1441 (e.g., contact holes) and a first black border area 1310 (e.g., absorber material). Similarly, the second mask 1302 includes a second mask pattern 1402 having a second set of features 1442 (e.g., contact holes) and a second black border area 1306 (e.g., absorber material).

[00107] In some embodiments, to reduce the image contrast loss experienced in stitching the first mask pattern 1401 with the second mask pattern 1402, additional features (referred to as "overlapping assist features”) may be added to each of the mask patterns. The overlapping assist features may be features that are printable on the substrate, or may non-printable features such as SRAFs. In some embodiments, whether the overlapping assist feature is printable or not may depend on the size of the overlapping assist feature. For example, if the size of the overlapping assist feature is below a specified threshold, the overlapping assist feature may act as an SRAF and not print on the substrate. Figure 14 shows the overlapping assist features 1443 and 1444 added to the masks 1401 and 1402. For example, a third set of features 1443 (e.g., overlapping assist features) may be added to the first mask pattern 1401 (e.g., in the first black border area 1310) and a fourth set of features 1444 (e.g., overlapping assist features) may be added to the second mask pattern 1402 (e.g., in the second black border area 1306) to generate an adjusted first mask pattern 1411 and an adjusted second mask pattern 1412, respectively. During lithography exposure, the adjusted mask patterns 1411 and 1412 may be imaged and stitched to generate a stitched pattern (not illustrated) on the wafer with an improved contrast. In some embodiments, the patterns on adjusted mask patterns 1411 and 1412 may be stitched by overlapping the exposures across the stitching boundary 1325 such that wafer features on a first side 1321 of the stitching boundary 1325 are formed by an overlapping of the first set of features 1441 of the adjusted first mask pattern 1411 with the fourth set of features 1444 of the adjusted second mask pattern 1412, and the wafer features on a second side 1322 of the stitching boundary 1325 is formed by an overlapping the second set of features 1442 of the adjusted second mask pattern 1412 with the third set of features 1443 of the adjusted first mask pattern 1411. By designing each mask to have a continuous pattern across the stitching boundary 1325, the reversed phase at the stitching boundary 1325 in the image is effectively removed, and not only is the image printed uniformly across the stitching boundary 1325, but also the contrast of the imaging is enhanced. As described earlier, in some embodiments, the image contrast is enhanced in the critical stitching area (e.g., as evident in Figure 15). In some embodiments, the entire area illustrated in Figure 14 where the features from the adjusted mask patterns 1411 and 1412 overlap on the substrate is the critical stitching area 1320.

[00108] Figure 15 is a graph illustrating improved image contrast in the critical stitching area of a stitched pattern, consistent with various embodiments. A first graph 1525 illustrates an image contrast of the stitched pattern that is stitched using (a) a conventional method - using mask patterns without the overlapping assist features (e.g., first and second mask patterns 1401 and 1402), and (b) the disclosed method - using mask patterns with overlapping assist features (e.g., adjusted mask patterns 1411 and 1412 with the overlapping assist features 1443 and 1444, respectively). Note that the y-axis is the image contrast (e.g., NILS) and the x-axis is y-direction on the substrate (e.g., y- direction 461 of Figure 4). For example, a first line 1506 indicates the image contrast of the stitched pattern that is stitched using the conventional method, and the second line 1508 indicates the image contrast of the stitched pattern that is stitched using the adjusted mask patterns. It is evident from the second line 1508 that the contrast of the stitched pattern that is stitched using the adjusted mask patterns is greater and more uniform (e.g., across the y-direction as illustrated by circled portion 1504) than the contrast of the stitched pattern stitched using the conventional method.

[00109] The graphs 1551-1553 also illustrate that the contrast of the stitched pattern stitched using the conventional method and the adjusted mask patterns. The y-axis in the graphs 1551-1553 is the aerial image intensity and the x-axis is y-direction on the substrate (e.g., y-direction 461 of Figure 4). The graph 1551 corresponds to a first exposure of a first mask pattern 1401 and the adjusted first mask pattern 1411 in which the line 1562 indicates the aerial image intensity associated with the exposure of first mask pattern 1401 and the line 1561 indicates the aerial image intensity associated with the exposure of the adjusted first mask pattern 1411.

[00110] Similarly, the graph 1552 corresponds to a second exposure of the second mask pattern 1402 and the adjusted second mask pattern 1412 in which the line 1562 indicates the aerial image intensity associated with the exposure of the second mask pattern 1402 and the line 1561 indicates the aerial image intensity associated with the exposure of the adjusted second mask pattern 1412.

[00111] The graph 1553 corresponds to the aerial image intensities of the stitched pattern. In the graph 1553, the line 1562 indicates a graph of the aerial image intensity of the stitched pattern stitched using the conventional method, and the line 1561 indicates a graph of the aerial image intensity of the stitched pattern stitched using the adjusted mask patterns. It is evident from the line 1562 in the graph 1553 that the contrast of the stitched pattern stitched using the adjusted mask patterns is greater and more uniform (e.g., as illustrated by circled portion 1560) than the contrast of the stitched pattern stitched using the conventional method.

[00112] Referring to Figure 14, the overlapping assist features may be configured with certain geometrical parameters to aid in the reduction of the image contrast loss. In some embodiments, the overlapping assist features on a mask may have the same geometrical shape as that of the set of mask features with which it overlaps during the exposure. For example, the third set of features 1443 added in the adjusted first mask pattern 1411 may have the same geometrical shape as that of the second set of features 1442 in the adjusted second mask pattern 1412. Similarly, the fourth set of features 1444 added in the adjusted second mask pattern 1412 may have the same geometrical shape as that of the first set of features 1441 in the adjusted first mask pattern 1411.

[00113] In some embodiments, the overlapping assist features may have the same pitch (e.g., distance between two features of the overlapping assist features) as that of the set of mask features with which it overlaps during the exposure. For example, the third set of features 1443 added in the adjusted first mask pattern 1411 may have the same pitch as that of the second set of features 1442 in the adjusted second mask pattern 1412. Similarly, the fourth set of features 1444 added in the adjusted second mask pattern 1412 may have the same pitch as that of the first set of features 1441 in the adjusted first mask pattern 1411.

[00114] While the geometrical shape and pitch of the overlapping assist features may be same as that of the features it is configured to overlap with during the exposure, the size of the assist features may be the same as, or different from, that of the features they are configured to overlap with. In some embodiments, the size of the overlapping assist features is lesser than that of the features they are configures to overlap with. For example, the third set of features 1443 added in the adjusted first mask pattern 1411 may be of a smaller size than the second set of features 1442 in the adjusted second mask pattern 1412 (e.g., as illustrated in Figure 14). Similarly, the fourth set of features 1444 added in the adjusted second mask pattern 1412 may be of a smaller size than the first set of features 1441 in the adjusted first mask pattern 1411 (e.g., as illustrated in Figure 14). In the example, in each half field mask, the features on one side of the stitching boundary 1325 have a different size than the features on the other side of the boundary 1325. In some embodiments, the first exposure using the first half field mask may produce the features of the different sizes (two sizes in the illustrated example) in the stitch region on the wafer. Through the second exposure using the second half field mask, in the same stitch region, the larger size features from the first half field mask overlaps with the smaller size features from the second half field, and vice versa. As a result, the features in the stitch region on the wafer may all have the same size due to the stitching.

[00115] In some embodiments, when the overlapping assist features are configured to be of the same size as that of the mask features they are configured to overlap with, the reduction in image contrast loss may not be significant, or may be lesser than the reduction achieved when the overlapping assist features are of smaller size than the mask features they are configured to overlap with. In some embodiments, an optimal size of the overlapping assist features (e.g., a size that aids in improving the contrast of the aerial image of the pattern) may be determined by simulating a lithographic process using the adjusted mask patterns (e.g., using the process of Figure 3).

[00116] Further, in some embodiments, the size of the mask features in the mask pattern (e.g., main features that correspond to a target pattern, such as first set of features 1441) may also be adjusted using an optical proximity correction (OPC) process to further enhance the image contrast. The size of the mask features or the overlapping assist features may be adjusted (e.g., iteratively) until the simulation of the lithographic process achieves a desired improvement in the image contrast of the stitched pattern.

[00117] Figure 16 illustrates overlapping assist features designed for various types of mask patterns, consistent with various embodiments. The overlapping assist features may be designed for various types of mask patterns. For example, as illustrated by a first layout 1610, the overlapping assist features 1604 may be designed for a mask pattern having uniformly placed features such as contact holes 1602. That is, as illustrated in Figure 14, for a first mask pattern 1401 having a set of uniformly placed contact holes 1441, overlapping assist features 1444 may be designed by placing them uniformly on the adjusted second mask pattern 1412. The illustration in Figure 16 may only show a portion of the stitching region.

[00118] In another example, as illustrated in the second layout 1620, the overlapping assist features 1614 may be designed for a mask pattern having randomly placed features, such as contact holes 1612. That is, for a first mask pattern having a set of randomly placed contact holes 1612, overlapping assist features 1614 may be designed by placing them on a second mask pattern at locations corresponding to the locations of the contact holes 1612 on the first mask pattern such that they overlap with each other when exposed on the substrate.

[00119] In another example, as illustrated in the third layout 1625, the overlapping assist features 1624 may be designed for a mask pattern having mask features, such as vertical line spaces 1622. That is, for a first mask pattern having a set of vertical line spaces 1622, overlapping assist features 1624 may be designed by placing them on a second mask pattern at locations corresponding to the locations of the vertical line spaces 1622 on the first mask pattern such that they overlap with each other when exposed on the substrate.

[00120] In another example, as illustrated in the fourth layout 1630, the overlapping assist features 1634 may be designed for a mask pattern having mask features, such as horizontal line spaces 1632. That is, for a first mask pattern having a set of horizontal line spaces 1632, overlapping assist features 1634 may be designed by placing them on a second mask pattern at locations corresponding to the locations of the horizontal line spaces 1632 on the first mask pattern such that they overlap with each other when exposed on the substrate. The overlapping assist features may be designed for mask patterns having various such features and configurations. In the examples described with reference to Figure 16, on each half field mask, each assist feature may be designed to have a different size than the corresponding overlapping feature located on the other half field mask, similar as in 1411 and 1412.

[00121] Figure 17 is a flow diagram of a method for designing a mask pattern to reduce contrast loss in stitching of the mask patterns, consistent with various embodiments. At process P1710, a target pattern 1710 to be printed on a substrate is obtained. The target pattern 1710 could be input in any of various formats. For example, the target pattern 1710 may be provided as GDS file. Continuing with example, the target pattern 1710 may include features such as contact holes.

[00122] At process P1720, a first mask pattern having a first set of mask features and a second mask pattern having a second set of mask features are obtained. In some embodiments, each mask pattern is associated with a respective half field mask for the target pattern 1710. For example, a first mask 1301 includes a first mask pattern 1401 having a first set of features 1441 (e.g., contact holes) and a second mask 1302 includes a second mask pattern 1402 having a second set of features 1442 (e.g., contact holes). Both the first mask pattern 1401 and the second mask pattern 1402 together correspond to the target pattern 1710.

[00123] At process P1730, a third set of features (e.g., overlapping assist features) to be added to the first mask pattern is determined. For example, the third set of features 1443 is added to the first mask pattern 1401 to generate an adjusted first mask pattern 1411. The third set of features 1443 may be configured such that they have the same geometric shape and pitch as, but different sizes (e.g., smaller sizes) than, that of the corresponding second set of features 1442 of the second mask pattern 1402. The third set of features 1443 is positioned on the first mask 1301 such that the first set of features

1441 and the third set of features 1443 are located on different sides of a stitching boundary 1325 across which exposures of the half field masks are to be overlapped.

[00124] Similarly, a fourth set of features (e.g., overlapping assist features) to be added to the second mask pattern is determined. For example, the fourth set of features 1444 is added to the second mask pattern 1402 to generate an adjusted second mask pattern 1412. The fourth set of features 1444 is configured such that they have the same geometric shape and pitch as, but different sizes (e.g., smaller sizes) than, that of the corresponding first set of features 1441 of the first mask pattern 1401. The fourth set of features 1444 is positioned on the second mask 1302 such that the second set of features

1442 and the fourth set of features 1444 are located on different sides of the stitching boundary 1325 across which exposures of the half field masks are to be overlapped. In some embodiments, the assist features are positioned on the masks such that the third set of features 1443 and the second set of features 1442 correspond to the same location on the substrate when the exposures of the adjusted mask patterns 1411 and 1412 are overlapped.

[00125] At process P1740, a lithography process is simulated (e.g., by implementing the process of Figure 3) to predict an image 1740 of a stitched pattern printed on the substrate using the adjusted mask patterns 1411 and 1412. In some embodiments, the predicted image 1740 corresponds to an overlapping of the features from the adjusted first mask pattern with the features from the adjusted second mask pattern such that the features in one mask pattern superposes with the features of the other mask pattern within a region of interest, and the overlapping images correspond to different mask feature sizes on the two mask patterns. For example, as illustrated in Figure 14, the predicted image 1740 corresponds to an overlapping of features from the adjusted first mask pattern 1411 with the features from the adjusted second mask pattern 1412 such that the third set of features 1443 (smaller than the second set of feature 1442) is superposed with the second set of features 1442 and the fourth set of features 1444 (smaller than the first set of feature 1441) is superposed with the first set of features 1441 within the region of interest 1320. As described above, the region of interest 1320 is an area proximate the stitching boundary 1325 where features of the two mask patterns are configured to superpose on the substrate when the exposures of the half field masks are overlapped. In some embodiments, the generation of the predicted image 1740 includes generating a first mask image corresponding to the adjusted first mask pattern 1411, and a second mask image corresponding to the adjusted second mask pattern 1412, and then generating the predicted image 1740 by superposing the first mask image and the second mask image such that the superposing causes an overlap between (a) the third set of features 1443 and the second set of features 1442, and (b) the first set of features 1441 and the fourth set of features 1444 within the region of interest 1320.

[00126] At process P1750, a contrast of the predicted image 1740 is determined. For example, the contrast of the predicted image 1740 is determined near the stitching boundary 1325 (e.g., as illustrated in Figure 15). In some embodiments, if the contrast of the predicted image 1740 does not satisfy a specified criterion, the size of any of the mask features (e.g., the first set of features 1441 or the second set of features 1442) or the overlapping assist features (e.g., the third set of features 1443 or the fourth set of features 1444) may be adjusted. For example, the size of the third set of features 1443 or the first set of features 1441 may be adjusted (e.g., increased or decreased) and a first mask image corresponding to the adjusted first mask pattern 1411 may be generated, or the size of the fourth set of features 1444 or the second set of features 1442 may be adjusted (e.g., increased or decreased) and a second mask image corresponding to the adjusted second mask pattern 1412 may be generated. The two mask images may be superposed to generate the predicted image 1740. The contrast of the predicted image 1740 may be determined. In some embodiments, the above process (e.g., process P1730-P1750) of adjusting the size of the mask features or the overlapping assist features and determining the contrast may be performed (e.g., iteratively) until the contrast of the predicted image 1740 satisfies the specified criterion. In some embodiments, the specified criterion includes the contrast of the predicted image, an increase in the contrast of the predicted image, or a reduction in contrast loss of the predicted image exceeding a specified threshold.

[00127] After the method of Figure 17 successfully completes, the adjusted first mask pattern 1411 and the adjusted second mask pattern 1412 may be used to manufacture the corresponding masks which may be employed in a lithography process to print a stitched pattern on a substrate using a lithographic apparatus (e.g., lithographic apparatus of Figures 1 or 2). [00128] Figure 18 is a block diagram that illustrates a computer system 100 which can assist in implementing the systems and methods disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled with bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random-access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 104. Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[00129] Computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is cursor control 116, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[00130] According to one embodiment, portions of the optimization process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In an alternative embodiment, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[00131] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[00132] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 either before or after execution by processor 104.

[00133] Computer system 100 also preferably includes a communication interface 118 coupled to bus 102. Communication interface 118 provides a two-way data communication coupling to a network link 120 that is connected to a local network 122. For example, communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[00134] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. ISP 126 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet” 128. Local network 122 and Internet 128 both use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[00135] Computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, a server 130 might transmit a requested code for an application program through Internet 128, ISP 126, local network 122 and communication interface 118. One such downloaded application may provide for the illumination optimization of the embodiment, for example. The received code may be executed by processor 104 as it is received, and/or stored in storage device 110, or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[00136] Embodiments of the present disclosure may be further described by the following embodiments.

1. A method for generating a mask pattern design for use in imaging of a pattern on a substrate using a lithographic apparatus, the method comprising: determining a placement and a geometry of a sub-resolution assist feature (SRAF) in an area proximate to a pattern to reduce sensitivity to an overlay between portions on the pattern on a substrate, wherein the pattern corresponds to a target pattern to be printed on the substrate in two adjacent exposure fields; and adjusting a geometry of the pattern to reduce the sensitivity to the overlay, wherein the adjusting includes generating a first portion of the pattern and a second portion of the pattern for use in printing the pattern on a substrate in the two adjacent exposure fields respectively.

2. The method of clause 1, wherein determining the placement of the SRAF includes: identifying a first location proximate the pattern to place a first SRAF to reduce the sensitivity to the overlay in a first direction; and identifying a second location proximate the pattern to place a second SRAF to reduce the sensitivity to the overlay in a second direction.

3. The method of clause 2, wherein the first location is proximate a first edge of the pattern and the second location is proximate opposite edges of the pattern that are perpendicular to the first edge.

4. The method of clause 3, wherein the second SRAF includes a first set of gratings to be placed proximate one of the opposite edges and a second set of gratings to be placed proximate another one of the opposite edges.

5. The method of clause 2, wherein the first direction and the second direction are perpendicular directions.

6. The method of clause 2, wherein determining the geometry of the SRAF includes: determining, by simulating, a pitch of the first SRAF based on an illumination source of the lithographic apparatus; and determining, based on the pitch, a critical dimension (CD) of the first SRAF.

7. The method of clause 2, wherein determining the geometry of the SRAF includes: iteratively varying a line distance between the second SRAF and the pattern to simulate a variation of a nominal CD of the pattern on the substrate over a range of overlay values for each line distance; and selecting a specified line distance for which the variation of the nominal CD is less than a threshold distance.

8. The method of clause 2, wherein determining the geometry of the SRAF includes: iteratively varying a line distance between the second SRAF and the pattern to simulate a sidelobe effect for each line distance; and selecting a specified line distance for which the sidelobe effect is less than a specified threshold.

9. The method of clause 8, wherein determining the geometry of the SRAF includes: generating an aerial image for the pattern for each line distance to generate a set of aerial images by simulating a lithography process; and selecting the specified line distance based on a specified aerial image in which the sidelobe effect is below a specified threshold.

10. The method of clause 1, wherein adjusting the geometry of the pattern includes: adjusting a geometry of the pattern by varying a CD of the pattern.

11. The method of clause 1, wherein adjusting the geometry of the pattern includes: generating the first portion of the pattern with varying CD, wherein the first portion of the pattern includes multiple segments having different CDs; and generating the second portion of the pattern with varying CD, wherein the second portion of the pattern includes multiple segments in which each segment has a complementary CD relative to a CD of the corresponding segment of the first portion of the pattern.

12. The method of clause 11, wherein adjusting the geometry of the pattern includes: for each CD of the first portion of the pattern, determining the complementary CD of the second portion of the pattern that yields a target CD of the target pattern when the first portion of the pattern and the second portion of the pattern are imaged in the two adjacent exposure fields.

13. The method of clause 12, wherein determining the complementary CD of the second portion of the pattern includes: obtaining, by simulation, a first aerial image for the first portion of the pattern having a first CD; obtaining, by simulation, a second aerial image for the pattern with a candidate CD; varying an aerial image intensity of the second aerial image until the second aerial image provides the candidate CD for which a CD of a stitched pattern to be printed on the substate matches the target CD; and selecting the candidate CD associated with an adjusted second aerial image as the complementary CD for the first CD.

14. The method of clause 11, wherein the first portion of the pattern and the second portion of the pattern are symmetric along an axis passing through the segments of the first portion and the second portion, respectively, that have the same CD.

15. The method of clause 11 further comprising: adjusting a CD of the pattern in a first transition region of the first portion of the pattern and a second transition region of the second portion of the pattern. 16. The method of clause 15, wherein adjusting the CD of the pattern includes: performing an optimal proximity correction (OPC) process to increase the CD of the pattern in the first transition region and the CD of the pattern in the second transition region to match a target CD of the target pattern.

17. The method of clause 15, wherein the first transition region corresponds to a region on the first portion of the pattern where a tip of the second portion of the pattern transitions into when the first portion and the second portion are printed on the substrate in the two adjacent exposure fields.

18. The method of clause 15, wherein the second transition region corresponds to a region on the second portion of the pattern where a tip of the first portion of the pattern transitions into when the first portion and the second portion are printed on the substrate in the two adjacent exposure fields.

19. The method of clause 1, wherein the SRAF is a horizontal or vertical grating.

20. The method of clause 1 , wherein the pattern is a brightfield pattern or an isolated space in a mask pattern design.

21. The method of clause 20, wherein determining the placement of the SRAF includes: identifying the area on the mask pattern design within the pattern for placement of the SRAF to reduce background intensity.

22. The method of clause 20, wherein determining the geometry of the SRAF includes: determining the SRAF as a block of a particular shape.

23. The method of clause 20, wherein determining the placement of the SRAF includes: determining a line distance from the SRAF to an edge of the pattern identifying the area on a mask pattern design within the pattern.

24. The method of clause 1, wherein determining the placement and geometry of the SRAF includes: adjusting aerial image intensities of the first portion of the pattern and the second portion of the pattern proximate a reference point located on the aerial image intensities and that is proximate an aerial image intensity threshold; and adjusting the aerial image intensities to be mirror symmetric across the reference point.

25. The method of clause 1 further comprising: generating a first mask image based on the SRAF and the first portion of the pattern; and generating a second mask image based on the second portion of the pattern and the SRAF.

26. The method of clause 25 further comprising: generating a mask pattern based on the first mask image and the second mask image, the mask pattern further including patterns corresponding to a target design layout to be printed on the substrate.

27. The method of clause 26 further comprising: performing a patterning step using the mask pattern to print the patterns on the substrate via a lithographic process. 28. The method of clause 1, wherein the lithographic apparatus is an extreme ultraviolet (EUV) lithographic apparatus.

29. A method for generating a mask pattern design for use in imaging of a pattern on a substrate using a lithographic apparatus, the method comprising: identifying a first area in a first mask pattern design having a mask pattern, wherein the mask pattern corresponds to a target pattern to be printed on a specified location on a substrate; and determining a placement and a geometry of a sub-resolution feature (SRAF) to be placed in an absorber layer of a second mask pattern design based on the first area, wherein the SRAF is configured to enhance an image contrast at the specified location for printing the target pattern using overlapping exposures of the first mask pattern design and the second mask pattern design.

30. The method of clause 29, wherein determining the placement and geometry of the SRAF includes: creating a second area in the absorber layer by removing the absorber layer, wherein the second area is in an area corresponding to the first area of the mask pattern in the first mask pattern design; and adding an SRAF in the second area.

31. The method of clause 29, wherein determining the placement and geometry of the SRAF includes: adding a sub-resolution grating in a second area corresponding to the first area of the mask pattern in the first mask pattern design.

32. A method for generating a mask pattern design for use in imaging of a pattern on a substrate using a lithographic apparatus, the method comprising: obtaining a target pattern to be printed on a substrate; obtaining a first mask pattern having a first set of features and a second mask pattern having a second set of features, wherein each mask pattern is associated with a respective half field mask for the target pattern; and determining a third set of features on the first mask pattern to be added to the first mask pattern, wherein the third set of features has the same geometric shape as the second set of features, and wherein the third set of features and the second set of features correspond to the same location on the substrate, and wherein the third set of features and the first set of features are located on different sides of a stitching boundary across which exposures of the half field masks are to be overlapped, and wherein a respective feature in the third set of features has a different size than a corresponding feature in the second set of features.

33. The method of clause 32 further comprising: generating a predicted image on the wafer level that corresponds to an overlapping of the first mask pattern with the second mask pattern, wherein the overlapping causes the third set of features to superpose with the second set of features within a region of interest. 34. The method of clause 33, wherein the region of interest is an area proximate the stitching boundary where features of the first mask pattern are configured to superpose with features of the second mask pattern when the exposures of the half field masks are overlapped.

35. The method of clause 33, wherein the region of interest is a subset of a stitching area, wherein the stitching area corresponds to an area where there is (a) an overlap between features from both mask patterns, or (b) an overlap between features from one of the mask patterns with an absorber area of the other mask pattern.

36. The method of clause 35, wherein the region of interest corresponds to an area where both portions of the mask patterns that overlap with each other include features.

37. The method of clause 32 further comprising: determining a fourth set of features on the second mask pattern to be added to the second mask pattern, wherein the fourth set of features has the same geometric shape as the first set of features, and wherein the fourth set of features and the first set of features are to be exposed on a second location on the substrate, and wherein the second location on the substrate is within a region of interest, and wherein a respective feature in the fourth set of features has a smaller size than a corresponding feature in the first set of features..

38. The method of clause 37 further comprising: generating a predicted image that corresponds to an overlapping of the first mask pattern with the second mask pattern, wherein the overlapping causes the third set of features to superpose with the second set of features and the first set of features to superpose with the fourth set of features within a region of interest.

39. The method of clause 32, wherein the first mask pattern and the second mask pattern are the same.

40. The method of clause 39, wherein the first mask pattern and the second mask pattern are exposed on the substrate in different orientations.

41. The method of clause 39, wherein the first set of features and the second set of features are located on different sides of a stitching boundary.

42. The method of clause 32, wherein the first set of features and third set of features have the same pitch.

43. The method of clause 32, wherein the first set of features and third set of features have the same size.

44. The method of clause 43, wherein both the first set of features and third set of features are configured to print on the substrate when they are superposed within a region of interest.

45. The method of clause 32, wherein the third set of features are smaller than the first set of features.

46. The method of clause 45, wherein the third set of features are configured as sub-resolution assist features that do not print on the substrate.

47. The method of clause 32, wherein determining the third set of features includes: simulating a lithography process to determine a size of the first set of features and the third set of features on the wafer level based on a contrast of image resulting from superposing the first mask pattern and the second mask pattern.

48. The method of clause 47, wherein simulating the lithography process includes: adjusting the size of the first set of features or the third set of features until the contrast of the image satisfies a specified criterion.

49. The method of clause 48, wherein the specified criterion includes the contrast of the image, or an increase in the contrast of the image, exceeding a specified threshold.

50. The method of clause 47, wherein simulating the lithography process includes: adjusting the size of the first set of features or the third set of features to generate a first mask image corresponding to the first mask pattern; adjusting the size of the second set of features or a fourth set of features of the second mask pattern to generate a second mask image corresponding to the second mask pattern; and generating a predicted image by superposing the first mask image and the second mask image, wherein the superposing causes an overlap between the third set of features and the second set of features and an overlap between the first set of features and the fourth set of features within a region of interest.

51. The method of clause 50 further comprising: determining a contrast of the predicted image, wherein the predicted image is an aerial image, resist image, or etch image.

52. An apparatus, the apparatus comprising: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above clauses.

53. A non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above clauses.

[00137] While the concepts disclosed herein may be used for imaging on a substrate such as a silicon wafer, it shall be understood that the disclosed concepts may be used with any type of lithographic imaging systems, e.g., those used for imaging on substrates other than silicon wafers.

[00138] The terms “optimizing” and “optimization” as used herein refers to or means adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc. such that results and/or processes have more desirable characteristics, such as higher accuracy of projection of a design pattern on a substrate, a larger process window, etc. Thus, the term “optimizing” and “optimization” as used herein refers to or means a process that identifies one or more values for one or more parameters that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for those one or more parameters. "Optimum" and other related terms should be construed accordingly. In an embodiment, optimization steps can be applied iteratively to provide further improvements in one or more metrics.

[00139] Aspects of the invention can be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs which may be carried on an appropriate carrier medium which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communications signal). Embodiments of the invention may be implemented using suitable apparatus which may specifically take the form of a programmable computer running a computer program arranged to implement a method as described herein. Thus, embodiments of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the disclosure may also be implemented as instructions stored on a machine -readable medium, which may be read and executed by one or more processors. A machine -readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[00140] In block diagrams, illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software or hardware modules that are differently organized than is presently depicted, for example such software or hardware may be intermingled, conjoined, replicated, broken up, distributed (e.g., within a data center or geographically), or otherwise differently organized. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine readable medium. In some cases, third party content delivery networks may host some or all of the information conveyed over networks, in which case, to the extent information (e.g., content) is said to be supplied or otherwise provided, the information may be provided by sending instructions to retrieve that information from a content delivery network.

[00141] Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device. [00142] The reader should appreciate that the present application describes several inventions. Rather than separating those inventions into multiple isolated patent applications, these inventions have been grouped into a single document because their related subject matter lends itself to economies in the application process. But the distinct advantages and aspects of such inventions should not be conflated. In some cases, embodiments address all of the deficiencies noted herein, but it should be understood that the inventions are independently useful, and some embodiments address only a subset of such problems or offer other, unmentioned benefits that will be apparent to those of skill in the art reviewing the present disclosure. Due to costs constraints, some inventions disclosed herein may not be presently claimed and may be claimed in later filings, such as continuation applications or by amending the present claims. Similarly, due to space constraints, neither the Abstract nor the Summary sections of the present document should be taken as containing a comprehensive listing of all such inventions or all aspects of such inventions.

[00143] It should be understood that the description and the drawings are not intended to limit the present disclosure to the particular form disclosed, but to the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the inventions as defined by the appended claims.

[00144] Modifications and alternative embodiments of various aspects of the inventions will be apparent to those skilled in the art in view of this description. Accordingly, this description and the drawings are to be construed as illustrative only and are for the purpose of teaching those skilled in the art the general manner of carrying out the inventions. It is to be understood that the forms of the inventions shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and embodiments or features of embodiments may be combined, all as would be apparent to one skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description. [00145] As used throughout this application, the word “may” is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). The words “include”, “including”, and “includes” and the like mean including, but not limited to. As used throughout this application, the singular forms “a,” “an,” and “the” include plural referents unless the content explicitly indicates otherwise. Thus, for example, reference to “an” element or "a” element includes a combination of two or more elements, notwithstanding use of other terms and phrases for one or more elements, such as “one or more.” As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component may include A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component may include A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. [00146] Terms describing conditional relationships, e.g., "in response to X, Y," "upon X, Y,", “if X, Y,” "when X, Y," and the like, encompass causal relationships in which the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributory causal condition of the consequent, e.g., "state X occurs upon condition Y obtaining" is generic to "X occurs solely upon Y" and "X occurs upon Y and Z." Such conditional relationships are not limited to consequences that instantly follow the antecedent obtaining, as some consequences may be delayed, and in conditional statements, antecedents are connected to their consequents, e.g., the antecedent is relevant to the likelihood of the consequent occurring. Statements in which a plurality of attributes or functions are mapped to a plurality of objects (e.g., one or more processors performing steps A, B, C, and D) encompasses both all such attributes or functions being mapped to all such objects and subsets of the attributes or functions being mapped to subsets of the attributes or functions (e.g., both all processors each performing steps A-D, and a case in which processor 1 performs step A, processor 2 performs step B and part of step C, and processor 3 performs part of step C and step D), unless otherwise indicated. Further, unless otherwise indicated, statements that one value or action is “based on” another condition or value encompass both instances in which the condition or value is the sole factor and instances in which the condition or value is one factor among a plurality of factors. Unless otherwise indicated, statements that “each” instance of some collection have some property should not be read to exclude cases where some otherwise identical or similar members of a larger collection do not have the property, i.e., each does not necessarily mean each and every. References to selection from a range includes the end points of the range.

[00147] In the above description, any processes, descriptions or blocks in flowcharts should be understood as representing modules, segments or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternate implementations are included within the scope of the exemplary embodiments of the present advancements in which functions can be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending upon the functionality involved, as would be understood by those skilled in the art.

[00148] To the extent certain U.S. patents, U.S. patent applications, or other materials (e.g., articles) have been incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is only incorporated by reference to the extent that no conflict exists between such material and the statements and drawings set forth herein. In the event of such conflict, any such conflicting text in such incorporated by reference U.S. patents, U.S. patent applications, and other materials is specifically not incorporated by reference herein.

[00149] While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the present disclosures. Indeed, the novel methods, apparatuses and systems described herein can be embodied in a variety of other forms; furthermore, various omissions, substitutions, and changes in the form of the methods, apparatuses and systems described herein can be made without departing from the spirit of the present disclosures. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the present disclosures.

Claims

2. The method of claim 1, wherein determining the placement of the SRAF includes: identifying a first location proximate the pattern to place a first SRAF to reduce the sensitivity to the overlay in a first direction; and identifying a second location proximate the pattern to place a second SRAF to reduce the sensitivity to the overlay in a second direction, wherein the first location is proximate a first edge of the pattern and the second location is proximate opposite edges of the pattern that are perpendicular to the first edge, wherein the first direction and the second direction are perpendicular directions.

3. The method of claim 2, wherein the second SRAF includes a first set of gratings to be placed proximate one of the opposite edges and a second set of gratings to be placed proximate another one of the opposite edges.

4. The method of claim 1, wherein determining the geometry of the SRAF includes: determining, by simulating, a pitch of the first SRAF based on an illumination source of the lithographic apparatus; and determining, based on the pitch, a critical dimension (CD) of the first SRAF.

5. The method of claim 2, wherein determining the geometry of the SRAF includes: iteratively varying a line distance between the second SRAF and the pattern to simulate a variation of a nominal CD of the pattern on the substrate over a range of overlay values for each line distance; and selecting a specified line distance for which the variation of the nominal CD is less than a threshold distance.

6. The method of claim 2, wherein determining the geometry of the SRAF includes: iteratively varying a line distance between the second SRAF and the pattern to simulate a sidelobe effect for each line distance; and selecting a specified line distance for which the sidelobe effect is less than a specified threshold, wherein determining the geometry of the SRAF includes: generating an aerial image for the pattern for each line distance to generate a set of aerial images by simulating a lithography process; and selecting the specified line distance based on a specified aerial image in which the sidelobe effect is below a specified threshold, wherein the SRAF is a horizontal or vertical grating.

7. The method of claim 1, wherein adjusting the geometry of the pattern includes: generating the first portion of the pattern with varying CD, wherein the first portion of the pattern includes multiple segments having different CDs; and generating the second portion of the pattern with varying CD, wherein the second portion of the pattern includes multiple segments in which each segment has a complementary CD relative to a CD of the corresponding segment of the first portion of the pattern.

8. The method of claim 7, wherein adjusting the geometry of the pattern includes: for each CD of the first portion of the pattern, determining the complementary CD of the second portion of the pattern that yields a target CD of the target pattern when the first portion of the pattern and the second portion of the pattern are imaged in the two adjacent exposure fields, wherein determining the complementary CD of the second portion of the pattern includes: obtaining, by simulation, a first aerial image for the first portion of the pattern having a first CD; obtaining, by simulation, a second aerial image for the pattern with a candidate CD; varying an aerial image intensity of the second aerial image until the second aerial image provides the candidate CD for which a CD of a stitched pattern to be printed on the substate matches the target CD; and selecting the candidate CD associated with an adjusted second aerial image as the complementary CD for the first CD.

9. The method of claim 7, wherein the first portion of the pattern and the second portion of the pattern are symmetric along an axis passing through the segments of the first portion and the second portion, respectively, that have the same CD.

10. The method of claim 7 further comprising: adjusting a CD of the pattern in a first transition region of the first portion of the pattern and a second transition region of the second portion of the pattern, wherein adjusting the CD of the pattern includes: performing an optimal proximity correction (OPC) process to increase the CD of the pattern in the first transition region and the CD of the pattern in the second transition region to match a target CD of the target pattern.

11. The method of claim 10, wherein the first transition region corresponds to a region on the first portion of the pattern where a tip of the second portion of the pattern transitions into when the first portion and the second portion are printed on the substrate in the two adjacent exposure fields, wherein the second transition region corresponds to a region on the second portion of the pattern where a tip of the first portion of the pattern transitions into when the first portion and the second portion are printed on the substrate in the two adjacent exposure fields.

12. The method of claim 1, wherein the pattern is a brightfield pattern or an isolated space in a mask pattern design, wherein determining the placement of the SRAF includes: identifying the area on the mask pattern design within the pattern for placement of the SRAF to reduce background intensity.

13. The method of claim 12 wherein determining the geometry of the SRAF includes one or more of: determining the SRAF as a block of a particular shape; determining a line distance from the SRAF to an edge of the pattern identifying the area on a mask pattern design within the pattern.

14. The method of claim 1, wherein determining the placement and geometry of the SRAF includes: adjusting aerial image intensities of the first portion of the pattern and the second portion of the pattern proximate a reference point located on the aerial image intensities and that is proximate an aerial image intensity threshold; and adjusting the aerial image intensities to be mirror symmetric across the reference point.

15. The method of claim 1 further comprising: generating a first mask image based on the SRAF and the first portion of the pattern; generating a second mask image based on the second portion of the pattern and the SRAF; and generating a mask pattern based on the first mask image and the second mask image, the mask pattern further including patterns corresponding to a target design layout to be printed on the substrate.