Systems and methods for optical proximity correction (OPC) model calibration in a stitching region

Abstract

Systems and methods for optical proximity correction (OPC) model calibration in a stitching region, including obtaining an aerial image profile of a black-border region and an absorber region of a mask; and calibrating a model characterizing a transition region between the black-border region and the absorber region of a mask using the aerial image profile. Systems and methods may include obtaining stochastic variation data across a transition region between a black-border region and an absorber region of a mask from a measured aerial image; and modeling variability in a critical dimension across the black-border region of the mask.

Description

SYSTEMS AND METHODS FOR OPTICAL PROXIMITY CORRECTION (OPC) MODELCALIBRATION IN A STITCHING REGIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 677,947 which was filed on July 31, 2024 and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to the field of lithographic apparatuses, methods, and systems, and more particularly to methods for optical proximity correction (OPC) model calibration in a stitching region.BACKGROUND

[0003] A lithographic apparatus can be used, for example, in the manufacturing of integrated circuits (ICs). In such a case, a mask or a reticle may contain or provide a circuit pattern corresponding to an individual layer of the IC (“design layout”), and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer). In some applications, in-die stitching may be used to facilitate production of large die sizes with high resolution. An optical proximity correction (OPC) can take into account effects from the stitching of the two exposures in mask pattern design. There lacks an effective mechanism of modeling the mask black-border’s impact on imaging performance in the stitching region.SUMMARY

[0004] Embodiments of the present disclosure provide systems and methods for calibrating an optical proximity correction (OPC) model. Systems and methods may include obtaining an aerial image profile of a black-border region and an absorber region of a mask; and calibrating a model characterizing a transition region between the black-border region and the absorber region of a mask using the aerial image profile.

[0005] Systems and methods may include applying a function to an aerial image of a transition region between a black-border region and an absorber region of a mask; and calibrating parameters of the function.

[0006] Systems and methods may include calibrating parameters of a function applied to an aerial image of a transition region between a black-border region and an absorber region of a mask.

[0007] Systems and methods may include obtaining stochastic variation data across a transition region between a black-border region and an absorber region of a mask from a measured aerial image; and modeling variability in a critical dimension across the black-border region of the mask.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Fig. 1 is a block diagram of various subsystems of a lithography system, consistent with embodiments of the present disclosure.

[0009] Fig. 2 is a block diagram of simulation models corresponding to the subsystems in Fig. 1, consistent with embodiments of the present disclosure.

[0010] Fig. 3 is a flow chart of an example method of source or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0011] Figs. 4 and 5 shows example diagrams of aerial image stitching, consistent with embodiments of the present disclosure.

[0012] Fig. 6 shows an example process flow of an OPC model calibration, consistent with embodiments of the present disclosure.

[0013] Fig. 7 shows an example process of an OPC model calibration, consistent with embodiments of the present disclosure.

[0014] Fig. 8 shows an example process of an OPC model calibration, consistent with embodiments of the present disclosure.

[0015] Fig. 9 shows an example process of an OPC model calibration, consistent with embodiments of the present disclosure.

[0016] Fig. 10 shows an example graph of an OPC model calibration, consistent with embodiments of the present disclosure.

[0017] Fig. 11 shows an example process of an OPC model calibration, consistent with embodiments of the present disclosure.

[0018] Fig. 12 shows an example process flow of an OPC model, consistent with embodiments of the present disclosure.

[0019] Fig. 13 shows an example diagram of an impact of the black-border transition profde on the critical dimension error in the stitching region.

[0020] Fig. 14 illustrates a block diagram of an example apparatus for processing data, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0021] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations consistent with the disclosure. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the subject matter recited in the appended claims.

[0022] Electronic devices are constructed of circuits formed on a piece of silicon called a substrate. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. The size of these circuits has decreased dramatically so that many more of them can fit on the substrate. For example, an IC chip in a smart phone can be as small as a thumbnail and yet may include over 2 billion transistors, the size of each transistor being less than 1 / 1000th the size of a human hair.

[0023] Making these extremely small ICs is a complex, time-consuming, and expensive process, often involving hundreds of individual steps. Errors in even one step have the potential to result in defects in the finished IC rendering it useless. Thus, one goal of the manufacturing process is to avoid such defects to maximize the number of functional ICs made in the process, that is, to improve the overall yield of the process.

[0024] A lithographic apparatus can be used, for example, in the manufacturing of ICs. In such a case, a mask or a reticle may contain or provide a circuit pattern corresponding to an individual layer of the IC (“design layout”), and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer) that has been coated with a layer of radiation-sensitive material (“resist”), by methods such as irradiating the target portion through the circuit pattern on the mask. Lithography scanner systems currently used in semiconductor manufacturing typically print dies with a rectangular field size of 26mm x 33mm. High numerical aperture (NA) lithography systems employ anamorphic projection and typically expose a field size of 26mm x 16.5mm. It is half the size in the scanning-direction. As a result, to print the field size of 26mm x 33mm, two exposures are performed using the masks. The printed wafer patterns from the two exposures are thus stitched together.

[0025] In addition, some applications require dies that are even larger than a field size. In-die stitching may be used to facilitate production of large die sizes with high resolution. In-die stitching involves the creation of an image of a single die by means of two separate exposures with two reticles. In-die stitching may be used to create an electrical connection between the upper and lower fields in a high-NA layer (e.g., by stitching vertical lines or spaces) (see, e.g., Figs. 4 and 5). In order to achieve this connection, images from two exposures on the wafer must be accurately aligned (which can include overlapped) in the stitching region. The exposures are from a scanner that create images in a photoresist that can be developed.

[0026] In-die stitching may include generating stitched aerial images (e.g., aerial images 406 and 408 of Fig. 4) from two exposures on the wafer. The stitched aerial images may include contributors to the images in the stitching area, including an aerial image stitching region (e.g., overlap between a first aerial image of a first exposure and a second aerial image of a second exposure), an absorber reflection region, an absorber to black border transition region (e.g., a transition region between the absorber and black-border of a first aerial image may “land” on the pattern or lines of a second aerial image during stitching), a black-border accuracy / vicinity region, a black-border reflection region,.The aerial image overlap region, absorber reflection region, absorber to black-border transition region, black border accuracy / vicinity region, and black-border reflection region may need to be determined to accurately stitch the aerial images together. The stitched aerial image may have various regions that may impact the final pattern accuracy (see, e.g., Fig. 5).

[0027] Optical proximity correction (OPC) steps can be used to correct for any errors arising during the stitching of the two exposures. One of the steps in the OPC involves the simulation of aerial images using an aerial image model. Another step involves a calibration of the said aerial image model to match measurements of the exposed region. Increasing the simulation accuracy of the aerial image model directly increases the quality of the stitching region in terms of stitching critical dimension (CD) uniformity and alignment of the two regions.

[0028] Therefore, in order to increase the quality of the stitching region for high-NA extreme ultraviolet lithography (EUV), accurate characterization and modeling of the aerial image profile at the black-border to absorber transition edge is needed.

[0029] In existing systems, the aerial image of the black-border transition region may be modeled by assuming that the reflectivity change at the black-border edge is a step like function. The reflectivity in the black-border is 0 and the reflectivity at the absorber is calculated by using the absorber material’s and multilayer material’s n and k values and Fresnel’s equations for reflection and transmission.

[0030] In typical systems, computational models are used to simulate the effect of the black-border. The models require key parameters regarding the mask reflectivity, such as the exact mask-multilayer n and k values and thickness values; absorber thickness and reflectivity values at different parts of the mask; black-border reflectivity; and surface roughness and multilayer variability information, e.g., to simulate the impact of stochastic process effects.

[0031] Typical systems, however, suffer from constraints, such as lack of accurate knowledge of key parameters, which influence the accuracy of the aerial image model. For example, the n and k values and multilayer layer thicknesses on the photomask are not accurately known, thereby resulting in incorrect inputs to the aerial image model (e.g., particularly the values regarding the Mo / Si intermixing layer). The black-border reflectivity which is assumed to be zero is not exactly zero. Typically, the black-border reflectivity is about 0.02%. There is also surface roughness in both the black-border region and the absorber region, which is not taken into account currently by the aerial image model (e.g., while modelling the local critical dimension uniformity and stochastic edge placement error modeling in the stitching region).

[0032] Thus, typical computational models cannot accurately predict the imaging performance in the stitching region. This inaccuracy introduces error into the OPC corrections made in the stitching region and negatively impacts device performance and yield.

[0033] Therefore, accurate mask information is needed to increase pattern fidelity in the stitching region and also to increase accuracy in model predictions and calibrations.

[0034] The disclosed embodiments provide systems and methods that address some or all of these disadvantages by providing inventive OPC models. The OPC models of the disclosed embodiments may be used to correct for any effects from the stitching of the two exposures by measuring the transition area between the absorber region and the black-border region directly (e.g., using any aerial image measurement system, one example being an aerial image sensor), modeling the measurement using the OPC model, and correcting for the effects of the stitching aerial images using the OPC model (e.g., to correct at regions where two aerial images overlap) in predicting an aerial image or a mask image (e.g., in a forward direction prediction process). That is, direct aerial image metrology of the black-border to absorber transition region may be obtained and fed into a OPC model calibration flow, e.g., for high-NA EUV applications.

[0035] The disclosed embodiments provide systems and methods that include methods for calibrating an OPC model, including applying a novel function to an aerial image of a transition region between the black-border region and the absorber region of a mask and calibrating the parameters of the function.

[0036] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings, the same or like reference numbers refer to the same or like components or entities, and only the differences with respect to the individual embodiments are described.

[0037] 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.

[0038] Without limiting the scope of the present disclosure, some embodiments may be described in the context of providing detectors and detection methods in systems utilizing electron beams. However, the disclosure is not so limited. Other types of charged particle beams may be similarly applied. Furthermore, systems and methods for detection may be used in other imaging systems, such as optical imaging, photon detection, x-ray detection, ion detection, etc.

[0039] Although specific reference may be made in this text 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 applications, use of the terms “reticle,” “wafer,” or “die” in this text may be interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0040] In the present document, the terms “radiation” and “beam” may be 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 5-20 nm).

[0041] The term “optimizing” and “optimization” as used herein may indicate adjusting a lithographic projection apparatus such that results or processes of lithography have more desirable characteristics, such as higher accuracy of projection of design layouts on a substrate, larger process windows, etc.

[0042] Further, the lithographic projection apparatus may be of a type having two or more substrate tables (or two or more patterning device tables). In such “multiple stage” devices the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposures. Twin stage lithographic projection apparatuses are described, for example, in U.S. Patent No. 5,969,441, incorporated herein by reference in its entirety.

[0043] The patterning device referred to above comprises or can form design layouts. The design layouts can be generated utilizing CAD (computer-aided design) programs, this process often being referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts / patteming devices. These rules are set by processing and design limitations. For example, design rules define the space tolerance between circuit devices (such as gates, capacitors, etc.) or interconnect lines, so as to ensure that the circuit devices or lines do not interact with one another in an undesirable way. The design rule limitations are typically referred to as “critical dimensions” (CD). A critical dimension of a circuit 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 determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit fabrication is to faithfully reproduce the original circuit design on the substrate (via the patterning device).

[0044] 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 fdter, the 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 beperformed using suitable electronic means. More information on such mirror arrays can be gleaned, for example, from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference in their entirety.

[0045] Another example of such patterning devices includes 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 in its entirety.

[0046] As a brief introduction, Fig. 1 illustrates an example lithographic projection apparatus 10A, consistent with embodiments of the present disclosure. 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 (as discussed above, the lithographic projection apparatus itself need not have the radiation source), illumination optics which define the partial coherence (denoted as sigma) and which may include optic components 14 A, 16Aa and 16 Ab that shape radiation from the source 12A; a patterning device 14A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A 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) where n is the index of reflection of the media between the last lens element to the substrate.

[0047] In an optimization process of a system, a figure of merit of the system can be represented as a cost function. The optimization process boils down to a process of finding a set of parameters (design variables) of the system that minimizes the cost function. The cost function can have any suitable form depending on the goal of the optimization. For example, the cost function can be weighted root mean square (RMS) of deviations of certain characteristics (evaluation points) of the system with respect to the intended values (e.g., ideal values) of these characteristics; the cost function can also be the maximum of these deviations (e.g., worst deviation). The term “evaluation points” herein should be interpreted broadly to include any characteristics of the system. The design variables of the system can be confined to finite ranges or be interdependent due to practicalities of implementations of the system. In case of a lithographic projection apparatus, the constraints are often associated with physical properties and characteristics of the hardware such as tunable ranges, or patterning device manufacturability design rules, and the evaluation points can include physical points on a resist image on a substrate, as well as non-physical characteristics such as dose and focus.

[0048] In a lithographic projection apparatus, a source provides illumination (e.g., light); projection optics direct and shape the illumination via a patterning device and onto a substrate. The term “projection optics” is broadly defined here to include any optical component that may alter the wavefront of the radiation beam. For example, 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 layer on the substrate is exposed 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 spatialdistribution of solubility of the resist in the resist layer. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in commonly assigned U.S. Patent No. 8,200,468, disclosure of which is hereby incorporated by reference in its entirety. The resist model is related only 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 source, the patterning device, and the projection optics) dictate the aerial image. 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.

[0049] An example flow chart for simulating lithography in a lithographic projection apparatus is illustrated in Fig. 2, consistent with embodiments of the present disclosure. A source model 31 represents optical characteristics (including radiation intensity distribution or phase distribution) of the source. A projection optics model 32 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by the projection optics) of the projection optics. A design layout model 35 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by a given design layout) of a design layout, which is the representation of an arrangement of features on or formed by a patterning device. An aerial image 36 can be simulated from the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using a resist model 37. Simulation of lithography can, for example, predict contours and CDs in the resist image.

[0050] More specifically, it is noted that the source model 31 can represent the optical characteristics of the source that include, but are not limited to, NA-sigma (o) settings as well as any particular illumination source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical characteristics of the projection optics that include aberration, distortion, refractive indexes, physical sizes, physical dimensions, etc. The design layout model 35 can also represent physical properties of a physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. The objective of the simulation is to accurately predict, for example, edge placements, aerial image intensity slopes and CDs, which can then be compared against an intended design. The intended design is generally defined as a pre-optical proximity correction (OPC, sometimes also referred to as “optical and process correction”) design layout which can be provided in a standardized digital file format. The layout file can be in a Graphic Database System (GDS) format, Graphic Database System II (GDS II) format, an Open Artwork System Interchange Standard (OASIS) format, a Caltech Intermediate Format (CIF), etc. The wafer design may include patterns or structures for inclusion on the wafer. The patterns or structures can be mask patterns used to transfer features fromthe photolithography masks or reticles to a wafer. In some embodiments, a layout in GDS or OASIS format, among others, may comprise feature information stored in a binary fde format representing planar geometric shapes, text, and other information related to the wafer design.

[0051] From this design layout, one or more portions may be identified, which are referred to as “clips”. In some embodiments, a set of clips is extracted, which represents the complicated patterns in the design layout (typically about 50 to 1000 clips, although any number of clips may be used). As will be appreciated by those skilled in the art, these patterns or clips represent small portions (e.g., circuits, cells or patterns) of the design and especially the clips represent small portions for which particular attention or verification is needed. In other words, clips may be the portions of the design layout or may be similar or have a similar behavior of portions of the design layout where critical features are identified either by experience (including clips provided by a customer), by trial and error, or by running a full-chip simulation. Clips usually contain one or more test patterns or gauge patterns.

[0052] An initial larger set of clips may be provided a priori by a customer based on known critical feature areas in a design layout which require particular image optimization. Alternatively, in some embodiments, the initial larger set of clips may be extracted from the entire design layout by using some kind of automated (such as, machine vision) or manual algorithm that identifies the critical feature areas.

[0053] In some embodiments, an optimization process (e.g., source mask optimization (SMO)) relates to one or more of a patterning process that employs process models (e.g., an optics model, a mask model, a resist model etc. of Fig. 2). The optimization process may involve execution of the one or more process models and computation of a cost function which may be reduced by modifying one or more characteristics (e.g., source, mask pattern, etc.) of the patterning process. In some embodiments, the one or more characteristics may be described by design variables. Hence, an optimized characteristic may also be referred to as an optimized design variable, where a design variable is optimized based on a cost function (e.g., CF).

[0054] In some embodiments, the modifying of the characteristic is based on a gradient of the cost function that guides how the characteristic should be modified to reduce the cost function. In some embodiments, such a cost function is a function of certain continuous metric such as an edge placement error (e.g., a difference between contours of printed pattern and a target pattern). Using continuous metric or cost function of continuous nature allows use of gradient-based optimizing algorithms that have acceptable runtime performance of an optimization process.

[0055] In some embodiments, non-smooth or discontinuous cost functions (e.g., based on defect counts) are not employed, as such non-smooth cost function necessitates use of non-continuous optimizers which have relatively high runtime compared to the continuous cost function based optimization. In addition, such optimizers may not provide best solutions. In some embodiments, use of non-smooth cost function such as related to defects may be desired so that optimization may beperformed to reduce a particular defect or several defects that may potentially be appear on a printed substrate.

[0056] The present disclosure provides methods that employ non-smooth cost function, for example, to reduce the number of defects and thereby improve yield of the patterning process. It can be understood by a person skilled in the art that concepts of a guide function (e.g., a pseudo-gradient) and discrete cost function (e.g., a first cost function discussed herein) may be applied to any aspect of the patterning process comprising an optimization process and not limited to a particular aspect of the patterning process. In some embodiments, the concepts are explained with respect to a source mask optimization process for better understandability.

[0057] Details of techniques and models used to transform a patterning device pattern into various lithographic images (e.g., an aerial image, a resist image, etc.), apply OPC (e.g., using 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, 2010-0180251 and 2011-0099526, the disclosure of each which is hereby incorporated by reference in its entirety.

[0058] For example, Fig. 3 is a flow chart 300 of a method of source or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0059] In a typical high-end design almost every feature edge requires some modification in order to achieve printed patterns that come sufficiently close to the target design. These modifications may include shifting or biasing of edge positions or line widths as well as application of ‘assist’ features that are not intended to print themselves, but will affect the properties of an associated primary feature. Furthermore, optimization techniques applied to the source of illumination may have different effects on different edges and features. Optimization of illumination sources can include the use of pupils to restrict source illumination to a selected pattern of light. Embodiments of the present disclosure provides optimization methods that can be applied to both source and mask configurations.

[0060] In general, a method of performing source and mask optimization (SMO) according to embodiments of the invention enables full chip pattern coverage while lowering the computation cost by intelligently selecting a small set of critical design patterns from the full set of clips to be used in SMO. SMO is performed only on these selected patterns to obtain an optimized source. The optimized source is then used to optimize the mask (e.g. using OPC and LMC) for the full chip, and the results are compared. If the results are comparable to conventional full-chip SMO, the process ends (e.g., at step 328), otherwise various methods are provided for iteratively converging on the successful result.

[0061] One example SMO method according to embodiments of the invention will be explained in connection with the flow chart 300.

[0062] A target design 300 (typically comprising a layout in a standard digital format such as OASIS, GDSII, etc.) for which a lithographic process is to be optimized includes memory, test patterns and logic. From this design, a full set of clips 302 is extracted, which represents all thecomplicated patterns in the design 300 (typically about 50 to 1000 clips). As will be appreciated by those skilled in the art, these clips represent small portions (i.e., circuits, cells or patterns) of the design for which particular attention and / or verification is needed.

[0063] As generally shown in 304, a small subset of clips 306 (e.g., 15 to 50 clips) is selected from the full set 302. As will be explained in more detail below, the selection of clips is preferably performed such that the process window of the selected patterns as closely as possible matches the process window for the full set of critical patterns. The effectiveness of the selection is also measured by the total turn run time (pattern selection and SMO) reduction.

[0064] In 308, SMO is performed with the selected patterns (15 to 50 patterns) 306. More particularly, an illumination source is optimized for the selected patterns 306. This optimization can be performed using any of a wide variety of known methods, for example those described in U.S. Patent Pub. No. 2004 / 0265707, the contents of which are incorporated herein by reference.

[0065] In 310, manufacturability verification of the selected patterns 306 is performed with the source obtained in 308. More particularly, verification includes performing an aerial image simulation of the selected patterns 306 and the optimized source and verifying that the patterns will print across a sufficiently wide process window. This verification can be performed using any of a wide variety of known methods, for example those described in U.S. Pat. No. 7,342,646, the contents of which are incorporated herein by reference.

[0066] If the verification in 310 is satisfactory, as determined in 312, then processing advances to full chip optimization in 314. Otherwise, processing returns to 308, where SMO is performed again but with a different source or set of patterns. For example, the process performance as estimated by the verification tool can be compared against thresholds for certain process window parameters such as exposure latitude and depth of focus. These thresholds can be predetermined or set by a user.

[0067] In 316, after the selected patterns meet lithography performance spec as determined in 312, the optimized source 314 will be used for optimization of the full set of clips.

[0068] In 318, model-based sub-resolution assist feature placement (MB-SRAF) and optical proximity correction (OPC) for all the patterns in the full set of clips 316 is performed. This process can be performed using any of a wide variety of known methods, for example those described in U.S. Pat. Nos. 5,663,893, 5,821,014, 6,541,167 and 6,670,081.

[0069] In 320, using processes similar to step 310, full pattern simulation based manufacturability verification is performed with the optimized source 314 and the full set of clips 316 as corrected in 318.

[0070] In 322, the performance (e.g., process window parameters such as exposure latitude and depth of focus) of the full set of clips 316 is compared against the subset of clips 306. In one example embodiment, the pattern selection is considered complete and / or the source is fully qualified for the full chip when the similar (<10%) lithography performances are obtained for both selected patterns (15 to 20) 306 and all critical patterns (50 to 1000) 316.

[0071] Otherwise, in 324, hotspots are extracted, and in 326 these hotspots are added to the subset 306, and the process starts over. For example, hotspots (i.e., features among the full set of clips 316 that limit process window performance) identified during verification 320 are used for further source tuning or to re-run SMO. The source is considered fully converged when the process window of the full set of clips 316 are the same between the last run and the run before the last run of 322.

[0072] OPC calibration may be performed by modelling or simulation. For example, for the desired yield, the total number of features and their respective probabilities of failure, simulation may be performed to optimize OPC for lowest yielding feature.

[0073] OPC addresses the fact that, in addition to any demagnification by the lithographic projection apparatus, the final size and placement of an image of the patterning device pattern projected on the substrate will not be identical to, or simply depend only on the size and placement of, the corresponding patterning device pattern features on the patterning device.

[0074] In some embodiments, the measurement data (e.g., stochastic variations) related to the printed pattern may be employed in optimization of patterning process or adjusting parameters of the patterning process. It is noted that the terms “mask”, “reticle”, “patterning device” are utilized interchangeably herein. Also, person skilled in the art will recognize that, especially in the context of lithography simulation / optimization, the term “mask” / “patterning device” and “design layout” can be used interchangeably, as in lithography simulation / optimization, a physical patterning device is not necessarily used but a design layout can be used to represent a physical patterning device. For the small feature sizes and high feature densities present on some design layout, the position of a particular edge of a given feature will be influenced to a certain extent by the presence or absence of other adjacent features. These proximity effects arise from minute amounts of radiation coupled from one feature to another or non-geometrical optical effects such as diffraction and interference.Similarly, proximity effects may arise from diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching that generally follow lithography.

[0075] In order to ensure that the projected image of the patterning device pattern is in accordance with requirements of a given target design, proximity effects should be predicted and compensated for, using sophisticated numerical models, corrections or pre-distortions of the patterning device pattern. The article “Full-Chip Lithography Simulation and Design Analysis — How OPC Is Changing IC Design”, C. Spence, Proc. SPIE, Vol. 5751, pp 1-14 (2005) provides an overview of current “model-based” optical proximity correction processes. In a typical high-end design almost every feature of the patterning device pattern has some modification in order to achieve high fidelity of the projected image to the target design. These OPC modifications may include shifting or biasing of edge positions or line widths and / or application of “assist” features that are intended to assist projection of other features.

[0076] Application of model-based OPC to a target design involves good process models and considerable computational resources, given the many millions of features typically present in adevice design. However, applying OPC is generally not an exact science, but an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the effect of OPC, e.g., patterning device patterns after application of OPC and any other resolution enhancement technique (RET), should be verified by design inspection, e.g., intensive full-chip simulation using calibrated numerical process models, in order to reduce or minimize the possibility of design flaws being built into the patterning device pattern. This is driven by the enormous cost of making high-end patterning devices, which run in the multi-million dollar range, as well as by the impact on turnaround time by reworking or repairing actual patterning devices once they have been manufactured. Both OPC and full-chip RET verification may be based on numerical modelling systems and methods as described, for example in, U.S. Pat. No. 7,003,758 and an article titled “Optimized Hardware and Software For Fast, Full Chip Simulation”, by Y. Cao et al., Proc. SPIE, Vol. 5754, 405 (2005), which are incorporated herein in their entireties by reference.

[0077] In a typical high-end design almost every feature of the design layout has some modification in order to achieve high fidelity of the projected image to the target design. These modifications may include shifting or biasing of edge positions or line widths (e.g., SEPE NC contour band widths) as well as application of “assist” features that are intended to assist projection of other features.

[0078] The illumination source can also be optimized, either jointly with patterning device optimization or separately, in an effort to improve the overall lithography fidelity. The terms “illumination source” and “source” are used interchangeably in this document. Since the 1990s, many off-axis illumination sources, such as annular, quadrupole, and dipole, have been introduced. As is known, off-axis illumination is a proven way to resolve fine structures (e.g., target features) contained in the patterning device.

[0079] However, when compared to a traditional illumination source, an off-axis illumination source usually provides less radiation intensity for the aerial image (Al). Thus, it becomes desirable to attempt to optimize the illumination source to achieve the optimal balance between finer resolution and reduced radiation intensity.

[0080] Numerous illumination source optimization approaches can be found, for example, in an article by Rosenbluth et al., titled “Optimum Mask and Source Patterns to Print A Given Shape”, Journal of Microlithography, Microfabrication, Microsystems 1(1), pp.13-20, (2002). The source is partitioned into several regions, each of which corresponds to a certain region of the pupil spectrum. Then, the source distribution is assumed to be uniform in each source region and the brightness of each region is optimized for process window. However, such an assumption that the source distribution is uniform in each source region is not always valid, and as a result the effectiveness of this approach suffers. In another example set forth in an article by Granik, titled “Source Optimization for Image Fidelity and Throughput”, Journal of Microlithography, Microfabrication, Microsystems 3(4), pp.509-522, (2004), several existing source optimization approaches are overviewed and a method based on illuminator pixels is proposed that converts the source optimization problem into aseries of non-negative least square optimizations. Though these methods have demonstrated some successes, they typically require multiple complicated iterations to converge. In addition, it may be difficult to determine the appropriate / optimal values for some extra parameters, such as y in Granik’ s method, which dictates the trade-off between optimizing the source for substrate image fidelity and the smoothness requirement of the source.

[0081] For low ki photolithography, optimization of both the source and patterning device is useful to ensure a viable process window for projection of critical circuit patterns. Some algorithms (e.g., Socha et. Al. Proc. SPIE vol.5853, 2005, p.180) discretize illumination into independent source points and mask into diffraction orders in the spatial frequency domain, and separately formulate a cost function (which is defined as a function of selected design variables) based on process window metrics such as exposure latitude which could be predicted by optical imaging models from source point intensities and patterning device diffraction orders. The term “design variables” as used herein comprises a set of parameters of a lithographic projection apparatus or a lithographic process, for example, parameters a user of the lithographic projection apparatus can adjust, or image characteristics a user can adjust by adjusting those parameters (e.g., source or mask design variables). It should be appreciated that any characteristics of a lithographic projection process, including those of the source, the patterning device, the projection optics, or resist characteristics can be among the design variables in the optimization. The cost function is often a non-linear function of the design variables. Then standard optimization techniques are used to minimize the cost function.

[0082] To help ensure that circuit design can be produced on to the substrate with workable process window, source-patterning device optimization (referred to herein as source-mask optimization or SMO) is becoming a significant RET for 2x nm node.

[0083] A source and patterning device (design layout) optimization method and system that allows for simultaneous optimization of the source and patterning device using a cost function without constraints and within a practicable amount of time is described in a commonly assigned International Patent Application No. PCT / US2009 / 065359, filed on November 20, 2009, and published as W02010 / 059954, titled “Fast Freeform Source and Mask Co-Optimization Method”, which is hereby incorporated by reference in its entirety.

[0084] Another source and mask optimization method and system that involves optimizing the source by adjusting pixels of the source is described in a commonly assigned U.S. Patent Application No.12 / 813456, fded on June 10, 2010, and published as U.S. Patent Application Publication No. 2010 / 0315614, titled “Source-Mask Optimization in Lithographic Apparatus”, which is hereby incorporated by reference in its entirety.

[0085] Figs. 4 and 5 show example diagrams 400 and 500, respectively, representing aerial image stitching, consistent with embodiments of the present disclosure. Some applications require dies that are larger than a field size. In-die stitching may be used to facilitate fabrication of large die sizes with high resolution. In-die stitching involves the creation of an image of a single larger die by means oftwo separate exposures with two reticles. In order to achieve this connection, images from two exposures on the wafer need to be overlapping with a high alignment accuracy.

[0086] Fig. 4 shows a desired aerial image 402 on a wafer with lines 404 (e.g., aerial image 402 may be projected onto the wafer). Image 406 is an aerial image from one exposure with lines 404a in an absorber region and image 408 is an aerial image from another exposure with lines 404b in an absorber region. In some embodiments, the black-border region may be beyond the edges shown in the image (e.g., 404c shows a distance between lines 804a and the black-border region).

[0087] In Fig. 5, diagram 500 illustrates the stitching of a larger pattern with two exposures. Image 501 represents the aerial image of a pattern located at the top of the stitching region. Aerial image 501 includes regions 503, 504, and 505. Region 503 is the aerial image of the black-border region. Region 503 has a roughness induced optical scattering in it (as shown in aerial images 1210 and 1212 of Fig 12). Region 504 is the aerial image of the absorber region. Region 504 typically has a reflectivity of 1.3% and has a roughness induced optical scattering in it. Region 505 is the aerial image of the patterned area where the absorber is cleared out and the multilayers reflect light, which exposes the resist.

[0088] Image 502 represents the aerial image of the pattern located at the bottom of the stitching region. Aerial image 502 includes regions 506, 507, and 508. Region 506 is the aerial image of the black-border region, region 507 is the aerial image of the absorber region, and region 508 is the aerial image of the patterned area. In the stitching process, aerial images 501 and 502 are overlay ed on each other (exposed on the wafer one after the other). The resulting stitched image 513 has four regions, which may impact the final pattern accuracy. That is, regions 509, 510, 511, and 512 show contributors to the stitched image 513. Region 509 is the result of the overlap of the black-border region 506 (from aerial image 502) with the pattern area region 504 (from aerial image 501). Region 510 is the overlap of the absorber area region 507 (from aerial image 502) with the pattern area region 505 (from aerial image 501). Region 511 is the overlap of the absorber area region 504 (from aerial image 501) with the pattern area region 508 (from aerial image 502). Region 512 is the overlap of the black-border region 503 (from aerial image 501) and patterned area region 508 (from aerial image 502).

[0089] As illustrated in Fig. 5, the stitching region comprises various overlaps of the patterned region (regions 505 and 508), absorber region (regions 504 and 507), and the black-border region (regions 503 and 506). During a stitching step, the spatial distribution of exposure light (the dose) forming the patterned lines is different in regions 509, 510, 511, and 512. In lithography, the dimensions of the patterned lines depend on the dose of the exposure light. Therefore, without any corrective step, the patterned dimensions (e.g., width of the lines) may be non-uniform, which is undesirable.

[0090] In order for the patterned lines to be formed with uniform width, an OPC model should be aware of the spatial dose distribution in each of the regions 509, 510, 511, and 512.

[0091] Fig. 6 shows an example process flow 600 of an OPC model calibration, consistent with embodiments of the present disclosure.

[0092] According to embodiments of the present disclosure, an OPC model is used to correct for any imaging errors arising from the contributors discussed in Fig. 5 (e.g., the variations in spatial distribution of exposure light forming the patterned lines, as shown in Fig. 5) from the stitching of the two exposures. As discussed above, an OPC model should be aware of the spatial dose distribution in the stitching region (e.g., each of the regions 509, 510, 511, and 512 of Fig. 5) for the patterned lines to be formed with uniform width.

[0093] The inputs of the OPC model may include an aerial image of a stitching region of a mask or an aerial image of a black-border to absorber transition region of a mask, including the mask layout of different parts of the mask with various patterns. The OPC model generates a predicted aerial image of a stitching region of the mask or a black-border to absorber transition region of the mask, where the predicted aerial image corrects for variations on the mask (e.g., variations in the critical dimensions) caused by dose variations from the exposure. The OPC model may take the form of any of the OPC models described in Figs. 8-11, discussed below.

[0094] The OPC model may accurately calculate the spatial dose distribution (e.g., aerial image) and may modify the dimensions of the patterns (e.g., regions 505 and 508 of Fig. 5) so as to compensate for the change in dimensions during the stitching step. According to embodiments of the present disclosure, the accuracy of the OPC model is improved by using the aerial image measurements of the black-border to absorber transition area to model the aerial image in the stitching region, thereby correcting the design and dimensions of the features on the mask.

[0095] That is, the OPC model may be used to correct for the effects of the stitching aerial images (e.g., to correct for spatial dose variations arising from the overlap of the absorber and black-border regions, such as regions 509, 510, 511, and 512 of Fig. 5 ) in predicting an aerial image or a mask image (e.g., in a forward direction prediction process).

[0096] Direct aerial image metrology of the black-border to absorber transition region may be obtained and fed into a OPC model calibration flow. Calibration of the OPC model may be performed by measuring the transition area between the absorber region and the black-border region (e.g., such as patterned area 604 and black border areas 606 as shown in Fig. 6A) directly (e.g., using the aerial image measurement system) and using the measured profile directly or modeling the measured profile using a mathematical parametric function.

[0097] An aerial image sensor may measure an aerial image and corresponding aerial image profile of a black-border region and an absorber region of a mask. The aerial image may be directly measured at selected locations at the edge of the black-border to absorber transition region to measure the edge transition profile (e.g., an aerial image profile). The aerial images may be measured with the same illumination settings that will be used for wafer exposures on the scanner. This measurement providesthe aerial image profiles of the black-border to absorber transition region, the absorber and blackborder reflectivity, and statistics of surface roughness induced speckle.

[0098] For example, diagram 602 of Fig. 6 shows a mask with a patterned area 604 (e.g., absorber area) and a black-border area 606 with a measurement area (e.g., 608 and 610) to be obtained from an aerial image of a wafer. For example, measurement area 608 may be in black-border area 606 and measurement area 610 may be in a transition region between patterned area 604 and black-border area 606.

[0099] As shown in Fig. 6, aerial image 612 (e.g., aerial image inputs in calibrations below) shows intensity transition profde values of the aerial image at the absorber to black-border edge (e.g., intensity transition profde value 614 is in the absorber region and intensity transition profile value 616 is in the black-border region) in measurement area 610 with respect to a position along the mask. For example, intensity transition profde value 614 may correspond to a first position within measurement box 610 and intensity transition profde value 616 may correspond to a second position within measurement box 610. Aerial image 618 shows intensity values of the aerial image at the blackborder region (e.g., intensity value 620) in measurement area 608 with respect to a position along the mask.

[0100] A model characterizing the transition region between the black-border region and the absorber region may be calibrated using the measured aerial image or corresponding measured aerial image profde. The measurements of the aerial image profde may be made at multiple locations on the mask, as illustrated by the measurement areas 608 and 610 of Fig. 6. The measurements may be averaged to yield an averaged profde. The averaged profde may be fed as an input to the OPC model calibration to calibrate the OPC model using the aerial image in the stitching region (e.g., a region where two aerial images are stitched or a region including the transition region). For example, a model may be calibrated using aerial images 612 and 618, further described below with respect to Figs. 8-11.

[0101] For example, in Fig. 6, graph 622 shows measured profdes 626 of the absorber to blackborder transition region (e.g., intensity values 624 in the aerial image) with respect to a distance along a mask (e.g., along diagram 602), where each curve may correspond to a measurement area (e.g., measurement areas 608, 610) of diagram 602. For example, measured profde 628 may correspond to a first measurement area of diagram 602 and measured profile 630 may correspond to a second measurement area of diagram 602. Point 632 may correspond to a position on the mask at which the intensity of an aerial image of a measurement box transitions from patterned area 634 (region 604) to black-border area 636 (region 606).

[0102] Graph 638 in Fig. 6 shows an averaged measured profile 640 (e.g., an average of profiles 626) of the absorber to black-border transition region with respect to a distance x along the mask. The directly measured profiles are used to create an average profile and a variability map across the blackborder edge. Advantageously, the accuracy of the OPC model may be increased since it accounts fordata in the transition region from the absorber to the black-border (e.g., typical systems do not account for the transition region from the absorber to the black-border).

[0103] The model (which may be incorporated into the OPC model) may predict or generate a simulated aerial image across the transition image. For example, the OPC model may generate an aerial image that includes effects from the absorber to black-border region of the mask. For example, the OPC model may build geometric correspondences with at least one 3D object representing a physical structure.

[0104] The OPC model may be applied to compensate for absorber reflection and absorber to blackborder transition and optimize the shape of the pattern at the stitch (e.g., so that the patterns of the two exposures have the same width when stitched together).

[0105] Metrology data from the masks (e.g., data from a microscope that may measure an aerial image on the wafer directly without exposing the wafer) may be fed to the OPC model to improve the accuracy of the OPC model. For example, the OPC model may be calibrated by measuring an aerial image of an absorber to black-border transition region. In some embodiments, the OPC model may be calibrated by feeding the OPC model simulation results or measurements of the wafer at regions corresponding to the stitching of aerial images. For example, the model may be calibrated until the predicted aerial image matches or corresponds to the measured wafer data. In some embodiments, the OPC model may be calibrated by feeding the OPC model GDS data.

[0106] In some embodiments, the data from the OPC model may be used to adjust the focus and dose of light during lithography. In some embodiments, an SEM image of a wafer may be generated to verily the accuracy of the stitched aerial image.

[0107] The OPC model may be calibrated to capture the aerial image trend at the transition region. The model may be calibrated based on the absorber to black-border transition region in an aerial image profile measured by an aerial image sensor (). Different functions can be fit to the profile for model calibration (e.g., different functions may be used to determine the profile). That is, any one of the following different model forms may be used to calibrate the OPC model to account for the transition region between the absorber and the black-border.

[0108] For example, the methods described below may take an existing model (which predicts a first aerial image) and add information to the model so that the predicted aerial image includes physical effects of the transition region.

[0109] That is, the shape of the transition region may be measured, parameters may be fitted in a model (e.g., one of the four models below), one of the four fitted models may be added into the OPC model such that the OPC model is aware of transition region effects. Advantageously, when the OPC model predicts an aerial image, the effects of the transition region are included in the predicted aerial image. The OPC model may correct for effects of the transition region in addition to performing other corrections.

[0110] Fig. 7 shows an example process 700 of an OPC model calibration, consistent with embodiments of the present disclosure.[oni] At step 702, a system (e.g., computer system 1300 of Fig. 13) may apply a function to an aerial image of a black-border region and an absorber region of a mask.

[0112] At step 704, the system may calibrate parameters of the function.

[0113] Embodiments of process 700 are further described below with respect to Figs. 8-11.

[0114] Fig. 8 shows an example process 800 of an OPC model calibration, consistent with embodiments of the present disclosure.

[0115] For example, a OPC model may predict a first aerial image 802 with a first intensity trendline 804 (showing intensity with respect to position on the mask) that does not account for the absorber to black-border transition region. The first aerial image 802 may be a binary image (e.g., a black and white image) that corresponds to a design shape that is added to the reticle.

[0116] A second modeling step incorporated into the OPC model calibration flow may apply a blur to the first aerial image by applying a Gaussian (or Lorenztian, etc.) filter 806 to the first aerial image 802 (or mask image) at the absorber to black-border transition region with a tuned intensity and radius. Intensity and radius of the filter 806 can be calibrated by measuring aerial image error relative to an aerial image measurement or by using an aerial image to generate a wafer resist profile and measuring error relative to wafer critical dimensions from a SEM. Advantageously, only two variables (intensity and radius) may be tuned with this calibration method.

[0117] The calibrated OPC model may generate or predict a second aerial image 808 with a second intensity trendline 810 (showing intensity with respect to position on the mask) (e.g., graph 638 of Fig. 6B) that includes physical effects of the absorber to black-border transition region. In some embodiments, the input to the second model may be GDS data or a measured aerial image or measured wafer images (e.g., the model may be calibrated until the predicted aerial image matches the profile from the measured wafer images).

[0118] Fig. 9 shows an example process 900 of an OPC model calibration, consistent with embodiments of the present disclosure.

[0119] In some embodiments, the aerial image 902 (or mask image) may be generated as a weighted sum of sub-images 910. For example, the weighted (wi, W2, W3 ... , wn) sum of sub-images 910 may include the original image 902 (e.g., images 612 and 618 of Fig. 6A) from an applied thin mask model, plus images 912, 914, 916, etc. where a gradient or derivative or other term has been applied to the original image 902 to affect the aerial image slope at the transition. Original image 902 may have an intensity trendline 904 (showing intensity with respect to position on the mask) and may be predicted or generated by an OPC model. Original image 902 may be a binary image (e.g., a black and white image) that corresponds to a design shape that is added to the reticle. Original image 902 does not account for the absorber to black-border transition region. In some embodiments, original image may be a predicted aerial image.

[0120] A second model, incorporated into the OPC model may apply the weighted sum of subimages 910 to the original image 902. For example, fi, I?. F, ... , fnmay be functions such as blur, gradient, truncation of two-dimensional image operations, etc. The calibrated OPC model may generate or predict an aerial image 906 with an intensity trendline 908 (showing intensity with respect to position on the mask) (e.g., graph 638 of Fig. 6B) that includes physical effects of the absorber to black-border transition region. In some embodiments, the input to the second model may be GDS data or measured wafer data (e.g., the model may be calibrated until the predicted aerial image matches the measured wafer data).

[0121] Fig. 10 shows an example graph 1000 of an OPC model calibration, consistent with embodiments of the present disclosure.

[0122] A OPC model may predict a first aerial image that does not account for the absorber to blackborder transition region. The first aerial image may be a binary image (e.g., a black and white image) that corresponds to a design shape that is added to the reticle. The first aerial image may be a simulated or empirical image.

[0123] A second modeling step incorporated into the OPC model calibration model may generate an empirical aerial image profile 1002 (e.g., graph 638 of Fig. 6A). For example, empirical aerial image profile 1002 is generated using terms or parameters of aerial image intensity in the black-border region (a) (e.g., image 618 of Fig. 6A), aerial image intensity in the absorber region (b) (e.g., image 612 of Fig. 6B), slope of the transition (c), magnitude of over (d) and undershoot (e), wavelength of oscillation in the overshoot decay region (1), and exponential decay envelope characteristic length in the overshoot decay region (g). These parameters may be calibrated by measuring aerial image error relative to Aerial image measurement or by using an aerial image to generate a wafer resist profile and measuring error relative to the wafer critical dimension data from a charged particle beam inspection system (e.g., SEM).

[0124] The calibrated OPC model may generate or predict a second aerial image that includes physical effects of the absorber to black-border transition region. In some embodiments, the input to the second model may be GDS data or measured aerial images or measured wafer data (e.g., the model may be calibrated until the predicted aerial image matches the measured wafer data).

[0125] Fig. 11 shows an example process 1100 of an OPC model calibration, consistent with embodiments of the present disclosure.

[0126] A OPC model may predict a first aerial image with a mask layout 1102 that does not account for the absorber to black-border transition region. The first aerial image may be a binary image (e.g., a black and white image) that corresponds to a design shape that is added to the reticle. In some embodiments, the first aerial image may be a measured aerial image (e.g., measured by an aerial image sensor, measured by an Aerial image sensor tool, etc.) (e.g., images 612 and 618 of Fig. 6A) with a corresponding intensity trendline, rather than a predicted aerial image.

[0127] A second model, incorporated into the OPC model, may apply image + filters 1404, such as a fdter F for a polygon area of the mask layout, a filter FHfor the horizontal edges of the mask layout, a fdter Fvfor the vertical edges of the mask layout, a fdter Fcfor the comers of the mask layout, a fdter FBB for the black-border of the mask layout, etc. to the transition edge of the first aerial image using library -based fdter generation (e.g., as is done for absorber / multilayer transition edges). This method effectively creates specific image filters specific to black-border transition horizontal and vertical edges.

[0128] Additionally, the measured transition aerial image variation (e.g., variation observed in the profiles 622 of Fig. 6A) can be used to derive information about the variation and reproducibility of the lithography process. The measured transition aerial images can be used as input to current software which predicts the stochastic process variation and its impact on the CD uniformity across the stitching region. The calibrated OPC model may generate or predict a second aerial image (or mask image) 1406 that includes physical effects of the absorber to black-border transition region. In some embodiments, the input to the second model may use GDS data or measured aerial images or measured wafer data (e.g., the model may be calibrated until the predicted aerial image matches the measured wafer data).

[0129] In some embodiments, stochastic variation data across the transition region (e.g., between a black-border region and an absorber region of a mask) may be obtained from a measured aerial image. The variability in a critical dimension across the black-border region of the mask may be modeled using the obtained stochastic variation data.

[0130] Fig. 12 shows an example process flow 1200 of an OPC model, consistent with embodiments of the present disclosure.

[0131] At step 1202, an apparatus (e.g., apparatus 1400 of Fig. 14) may generate an OPC model that captures an aerial image in a transition region between a black-border region (e.g., region 606 of Fig. 6) and an absorber region (e.g., region 604 of Fig. 6) of a mask.

[0132] According to embodiments of the present disclosure, an OPC model may be used to correct for any imaging errors arising from the contributors discussed in Fig. 5 (e.g., the variations in spatial distribution of exposure light forming the patterned lines, as shown in Fig. 5) from the stitching of the two exposures. As discussed above, an OPC model should be aware of the spatial dose distribution in the stitching region (e.g., each of the regions 509, 510, 511, and 512 of Fig. 5) for the patterned lines to be formed with uniform width.

[0133] The inputs of the OPC model may include an aerial image of a stitching region of a mask or an aerial image of a black-border to absorber transition region of a mask, including the mask layout of different parts of the mask with various patterns. The OPC model generates a predicted aerial image of a stitching region of the mask or a black-border to absorber transition region of the mask, where the predicted aerial image corrects for variations on the mask (e.g., variations in the critical dimensions)caused by dose variations from the exposure. The OPC model may take the form of any of the OPC models described in Figs. 8-11, discussed below.

[0134] The OPC model may accurately calculate the spatial dose distribution (e.g., aerial image) and may modify the dimensions of the patterns (e.g., regions 505 and 508 of Fig. 5) so as to compensate for the change in dimensions during the stitching step. According to embodiments of the present disclosure, the accuracy of the OPC model is improved by using the aerial image measurements of the black-border to absorber transition area to model the aerial image in the stitching region, thereby correcting the design and dimensions of the features on the mask.

[0135] That is, the OPC model may be used to correct for the effects of the stitching aerial images (e.g., to correct for spatial dose variations arising from the overlap of the absorber and black-border regions, such as regions 509, 510, 511, and 512 of Fig. 5 ) in predicting an aerial image or a mask image (e.g., in a forward direction prediction process).

[0136] At step 1204, the apparatus may generate, using the OPC model, a predicted aerial image of a plurality of patterns across the transition region. For example, the model (which may be incorporated into the OPC model) may predict or generate a simulated aerial image across the transition image. For example, the OPC model may generate an aerial image that includes effects from the absorber to black-border region of the mask. For example, the OPC model may build geometric correspondences with at least one 3D object representing a physical structure.

[0137] The OPC model may be applied to compensate for absorber reflection and absorber to blackborder transition and optimize the shape of the pattern at the stitch (e.g., so that the patterns of the two exposures have the same width when stitched together).

[0138] In some embodiments, the data from the OPC model may be used to adjust the focus and dose of light during lithography. In some embodiments, an SEM image of a wafer may be generated to verily the accuracy of the stitched aerial image.

[0139] The OPC model may be calibrated, as discussed above with respect to Figs. 6-11.

[0140] Fig. 13 shows an example diagram 1300 of the impact of the black-border transition profde on the critical dimension error in the stitching region.

[0141] Embodiments of the present disclosure provide improvements to typical OPC models, such as improved OPC model calibration accuracy in the stitch region to enable high-NA stitching by eliminating sources of uncertainty, improved OPC model calibration accuracy outside the stitch region by direct measurement of absorber and multilayer reflectivity, reduced mask-manufacturing turn-around time by removing the need to expose wafers and measure them, and providing a method independent of wafer effects (e.g., existing methods are resist dependent and need to be repeated if the wafer stack is adjusted).

[0142] The impact of the black-border on critical dimension of features in the stitching region has been extensively characterized. The impact on critical dimension variation can be as high as 1 nm and depends strongly on the illumination used, pattern pitch, and resist. Typically, the impact of the black-border is quantified by wafer metrology in the stitching region. The wafer metrology is performed through focus and dose adjustments. Wafer metrology costs time and resources and the results are impacted by resist processing effects. Aerial image measurements are not affected by the resist and can thus reduce both the metrology time and also the error introduced in the critical dimension measurement by the resist.

[0143] Image 1202 of Fig. 13 shows a black-border region 1304 and an absorber region 1306. Lines 1308 represent lines that are positioned across the black-border region 1304 and the absorber region 1306. Aerial image 1310 shows intensity values at a transition region between the black-border region 1304 and the absorber region 1306 and aerial image 1312 shows intensity values at the black-border region 1304.

[0144] Graph 1314 shows critical dimension of the lines 1308 with respect to a position of the lines 1308 along the Y-axis, measured from aerial images 1310 and 1312 with and without, respectively, effects from the black-border to absorber transition region (e.g., without calibrating the OPC model to account for the transition region). Curve 1322, which corresponds to the critical dimension of the lines 1308 measured from aerial image 1312, shows a relatively constant critical dimension, which corresponds to the measured critical dimension of the lines 1308.

[0145] In contrast, curve 1320, which corresponds to the critical dimension of the lines 1308 taking into account the measurement of the black-border transition aerial image 1310, shows that the critical dimension varies greatly. That is, when the OPC model is not calibrated to account for the transition region, the predicted aerial image does not accurately represent the critical dimension of lines 1308 on the wafer, especially in the transition region.

[0146] Fig. 14 illustrates a block diagram of an example apparatus 1400 for processing data, consistent with embodiments of the present disclosure. In some embodiments, the machine -learning model may be trained using at least one apparatus 1400, and the trained model may be implemented on a lithography apparatus (e.g., lithographic projection apparatus 10A of Fig. 1) or a charged particle beam inspection system. For example, apparatus 1400 may be a preprocessor, an image processor, an encoder, or a decoder. As shown in Fig. 14, apparatus 1400 may include processor 1402. When processor 1402 executes instructions described herein, apparatus 1400 can become a specialized machine for processing data, preprocessing, encoding, or decoding image data. Processor 1402 can be any type of circuitry capable of manipulating or processing information. For example, processor 1402 can include any combination of any number of a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), a neural processing unit (“NPU”), a microcontroller unit (“MCU”), an optical processor, a programmable logic controller, a microcontroller, a microprocessor, a digital signal processor, an intellectual property (IP) core, a Programmable Logic Array (PLA), a Programmable Array Logic (PAL), a Generic Array Logic (GAL), a Complex Programmable Logic Device (CPLD), a Field-Programmable Gate Array (FPGA), a System On Chip (SoC), an Application-Specific Integrated Circuit (ASIC), or the like. In some embodiments, processor 1402 canalso be a set of processors grouped as a single logical component. For example, as shown in Fig. 14, processor 1402 may include multiple processors, including processor 1402a, processor 1402b, and processor 1402n.

[0147] Apparatus 1400 may further include memory 1404 configured to store data (e.g., a set of instructions, computer codes, intermediate data, or the like). For example, as shown in Fig. 14, the stored data may include program instructions (e.g., program instructions for implementing one or more steps in methods or flows of Figs. 2 and 3, 6A, 6B, and 7-11) and data for processing (e.g., metrology data, model data, statistical analysis data, or the like). Processor 1402 may access the program instructions and data for processing via bus 1410), and execute the program instructions to perform an operation or manipulation on the data for processing. Memory 1404 can include a highspeed random-access storage device or a non-volatile storage device. In some embodiments, memory 1404 may include any combination of any number of a random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or the like. Memory 1404 can also be a group of memories (not shown) grouped as a single logical component.

[0148] Bus 1410 may be a communication device that transfers data between components inside apparatus 1400, such as an internal bus (e.g., a CPU-memory bus), an external bus (e.g., a universal serial bus port, a peripheral component interconnect express port), or the like.

[0149] For ease of explanation without causing ambiguity, processor 1402 and other data processing circuits are collectively referred to as a “data processing circuit” in this disclosure. The data processing circuit can be implemented entirely as hardware, or as a combination of software, hardware, or firmware. In addition, the data processing circuit can be a single independent module or can be combined entirely or partially into any other component of apparatus 1400.

[0150] Apparatus 1400 may further include network interface 1406 to provide wired or wireless communication with a network (e.g., the Internet, an intranet, a local area network, a mobile communications network, or the like). In some embodiments, network interface 1406 can include any combination of any number of a network interface controller (NIC), a radio frequency (RF) module, a transponder, a transceiver, a modem, a router, a gateway, a wired network adapter, a wireless network adapter, a Bluetooth adapter, an infrared adapter, a near-field communication (“NFC”) adapter, a cellular network chip, or the like.

[0151] In some embodiments, optionally, apparatus 1400 may further include peripheral interface 1408 to provide a connection to one or more peripheral devices. As shown in Fig. 14, the peripheral device can include, but is not limited to, a cursor control device (e.g., a mouse, a touchpad, or a touchscreen), a keyboard, a display (e.g., a cathode-ray tube display, a liquid crystal display, or a light-emitting diode display), a video input device (e.g., a camera or an input interface coupled to a video archive), or the like.

[0152] A non-transitory computer readable medium may be provided that stores instructions for a processor of a controller (e.g., apparatus 1400 of Fig. 14, etc.) for controlling the electron beam tool, the lithographic system or apparatus, or other systems of other systems and servers, or components thereof, consistent with embodiments in the present disclosure. These instructions may allow the one or more processors to carry out image processing, data processing, beamlet scanning, graphical display, operations of a charged particle beam apparatus, or another imaging device, or the like for providing operations consistent with those described above for Figs. 2 and 3, 6A, 6B, and 7-11. In some embodiments, the non-transitory computer readable medium may be provided that stores instructions for a processor to perform the steps of the methods of the disclosed embodiments.Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read Only Memory (PROM), and Erasable Programmable Read Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0153] The embodiments may further be described using the following clauses:1. A method for optical proximity correction (OPC), comprising: obtaining an aerial image profde of a black-border region and an absorber region of a mask; and calibrating a model characterizing a transition region between the black-border region and the absorber region of a mask using the aerial image profde.2. The method of clause 1, wherein the model comprises an OPC model that corrects for effects of stitching aerial images.3. The method of any one of clauses 1-2, wherein the aerial image profde is a measured aerial image profde obtained by an aerial image sensor.4. The method of clause 3, wherein obtaining the measured aerial image profde comprises measuring the mask on a wafer at a plurality of locations at an edge of the black-border region and the absorber region.5. The method of clause 4, wherein the plurality of locations comprises a location within the blackborder region.6. The method of any one of clauses 4-5, wherein the plurality of locations comprises a location within both the black-border region and the absorber region.7. The method of any one of clauses 3-6, wherein obtaining the measured aerial image profile comprises measuring an aerial image at illumination settings to be used for wafer exposures.8. The method of clause 7, wherein the measured aerial image comprises a plurality of intensity values.9. The method of any one of clauses 7-8, wherein calibrating the model comprises applying a function to the measured aerial image and calibrating parameters of the function.10. The method of clause 9, wherein the function comprises a Gaussian or Lorentzian fdter.11. The method of clause 9, wherein the parameters comprise intensity and radius values of the function.12. The method of clause 11, wherein calibrating the intensity and radius values of the function comprises measuring an aerial image error of the measured aerial image.13. The method of clause 12, wherein the aerial image error is measured relative to a measurement of the aerial image sensor.14. The method of clause 12, wherein the aerial image error is measured relative to wafer measurements from a charged particle tool.15. The method of clause 9, wherein the function comprises any one of blur, gradient, or truncation of two-dimensional image operations.16. The method of clause 15, further comprising determining a weighted sum of sub-images, the subimages comprising an original of the measured aerial image and the measured aerial image with the applied function.17. The method of clause 9, wherein the function comprises a filter corresponding to a mask layout on a wafer.18. The method of clause 17, wherein the filter comprises any one of a polygon area of the mask layout, horizontal edges of the mask layout, vertical edges of the mask layout, comers of the mask layout, black-border of the mask layout.19. The method of any one of clauses 17-18, wherein applying the function to the measured aerial image comprises applying the fdter to a transition edge of the measured aerial image.20. The method of clause 19, wherein the transition edge is between the black-border region and the absorber region.21. The method of clause 9, wherein applying the function comprises generating an empirical aerial image profde.22. The method of clause 21, wherein the parameters comprise any one of aerial image intensity in the black-border region, aerial image intensity in the absorber region, magnitude of overshoot of aerial image intensity, magnitude of undershoot of aerial image intensity, wavelength of oscillation in overshoot decay region of aerial image intensity, or exponential decay envelope characteristic length in the overshoot decay region.23. The method of any one of clauses 21-22, wherein calibrating the parameters comprises measuring an aerial image error relative to a measurement from the aerial image sensor.24. The method of any one of clauses 21-22, wherein calibrating the parameters comprises generating a wafer resist profile and measuring an error relative to a wafer measurement from a charged particle tool.25. A method for calibrating an optical proximity correction (OPC) model, comprising: applying a function to an aerial image of a transition region between a black-border region and an absorber region of a mask; and calibrating parameters of the function.26. The method of clause 25, wherein the aerial image is a measured aerial image.27. The method of clause 25, wherein the aerial image is a predicted image.28. The method of any one of clauses 25-27, wherein the function comprises a Gaussian or Lorentzian filter.29. The method of clause 28, wherein the parameters comprise intensity and radius values of the function.30. The method of clause 29, wherein calibrating the intensity and radius values of the function comprises measuring an aerial image error of the aerial image.31. The method of clause 30, wherein the aerial image error is measured relative to a measurement of an aerial image sensor.32. The method of clause 30, wherein the aerial image error is measured relative to wafer measurements from a charged particle tool.33. The method of any one of clauses 25-27, wherein the function comprises any one of blur, gradient, or truncation of two-dimensional image operations.34. The method of clause 33, further comprising determining a weighted sum of sub-images, the subimages comprising an original of the aerial image and the aerial image with the applied function.35. The method of any one of clauses 25-27, wherein the function comprises a fdter corresponding to a mask layout on a wafer.36. The method of clause 35, wherein the filter comprises any one of a polygon area of the mask layout, horizontal edges of the mask layout, vertical edges of the mask layout, comers of the mask layout, black-border of the mask layout.37. The method of any one of clauses 35-36, wherein applying the function to the aerial image comprises applying the fdter to a transition edge of the aerial image.38. The method of clause 37, wherein the transition edge is between the black-border region and the absorber region.39. The method of any one of clauses 25-27, wherein applying the function comprises generating an empirical aerial image profile.40. The method of clause 39, wherein the parameters comprise any one of aerial image intensity in the black-border region, aerial image intensity in the absorber region, magnitude of overshoot of aerial image intensity, magnitude of undershoot of aerial image intensity, wavelength of oscillation inovershoot decay region of aerial image intensity, or exponential decay envelope characteristic length in the overshoot decay region.41. The method of any one of clauses 39-40, wherein calibrating the parameters comprises measuring an aerial image error relative to a measurement from an aerial image sensor.42. The method of any one of clauses 39-40, wherein calibrating the parameters comprises generating a wafer resist profde and measuring an error relative to a wafer measurement from a charged particle tool.43. A method for calibrating an optical proximity correction (OPC) model, comprising: calibrating parameters of a function applied to an aerial image of a transition region between a black-border region and an absorber region of a mask.44. The method of clause 43, wherein the aerial image is a measured aerial image.45. The method of clause 43, wherein the aerial image is a predicted image.46. The method of any one of clauses 43-45, wherein the function comprises a Gaussian or Lorentzian filter.47. The method of clause 46, wherein the parameters comprise intensity and radius values of the function.48. The method of clause 47, wherein calibrating the intensity and radius values of the function comprises measuring an aerial image error of the aerial image.49. The method of clause 48, wherein the aerial image error is measured relative to a measurement of an aerial image sensor.50. The method of clause 48, wherein the aerial image error is measured relative to wafer measurements from a charged particle tool.51. The method of any one of clauses 43-45, wherein the function comprises any one of blur, gradient, or truncation of two-dimensional image operations.52. The method of clause 51, further comprising determining a weighted sum of sub-images, the subimages comprising an original of the aerial image and the aerial image with the applied function.53. The method of any one of clauses 43-45, wherein the function comprises a fdter corresponding to a mask layout on a wafer.54. The method of clause 53, wherein the filter comprises any one of a polygon area of the mask layout, horizontal edges of the mask layout, vertical edges of the mask layout, comers of the mask layout, black-border of the mask layout.55. The method of any one of clauses 53-54, wherein applying the function to the aerial image comprises applying the fdter to a transition edge of the aerial image.56. The method of clause 55, wherein the transition edge is between the black-border region and the absorber region.57. The method of any one of clauses 43-45, wherein applying the function comprises generating an empirical aerial image profile.58. The method of clause 57, wherein the parameters comprise any one of aerial image intensity in the black-border region, aerial image intensity in the absorber region, magnitude of overshoot of aerial image intensity, magnitude of undershoot of aerial image intensity, wavelength of oscillation in overshoot decay region of aerial image intensity, or exponential decay envelope characteristic length in the overshoot decay region.59. The method of any one of clauses 57-58, wherein calibrating the parameters comprises measuring an aerial image error relative to a measurement from an aerial image sensor.60. The method of any one of clauses 57-58, wherein calibrating the parameters comprises generating a wafer resist profde and measuring an error relative to a wafer measurement from a charged particle tool.61. A method for calibrating an optical proximity correction (OPC) model, comprising: obtaining stochastic variation data across a transition region between a black-border region and an absorber region of a mask from a measured aerial image; and modeling variability in a critical dimension across the black-border region of the mask.62. A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to cause the computing device to perform operations for optical proximity correction (OPC) according to any one of clauses 1-24.63. A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to cause the computing device to perform operations for calibrating an optical proximity correction (OPC) model according to any one of clauses 25-61.64. A system for optical proximity correction (OPC), the system comprising: a memory storing a set of instructions; and one or more processors configured to execute the set of instructions to cause the system to perform operations according to any one of clauses 1-24.65. A system for calibrating an optical proximity correction (OPC) model, the system comprising: a memory storing a set of instructions; and one or more processors configured to execute the set of instructions to cause the system to perform operations according to any one of clauses 25-61.

[0154] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims

CLAIMS1. A computer implemented method for optical proximity correction (OPC), comprising: obtaining an aerial image profde of a black-border region and an absorber region of a mask; and calibrating a model characterizing a transition region between the black-border region and the absorber region of a mask using the aerial image profde.

2. The method of claim 1, wherein the model comprises an OPC model that corrects for effects of stitching aerial images.

3. The method of claim 1, wherein the aerial image profile is a measured aerial image profde obtained by an aerial image sensor.

4. The method of claim 3, wherein obtaining the measured aerial image profde comprises measuring the mask on a wafer at a plurality of locations at an edge of the black-border region and the absorber region, and wherein the plurality of locations comprises a location within the black-border region.

5. The method of claim 4, wherein the plurality of locations comprises a location within both the black-border region and the absorber region.

6. The method of claim 3, wherein obtaining the measured aerial image profde comprises measuring an aerial image at illumination settings to be used for wafer exposures.

7. The method of claim 6, wherein calibrating the model comprises applying a function to the measured aerial image and calibrating parameters of the function.

8. The method of claim 7, wherein the function comprises a Gaussian or Lorentzian fdter.

9. The method of claim 7, wherein the parameters comprise intensity and radius values of the function, wherein calibrating the intensity and radius values of the function comprises measuring an aerial image error of the measured aerial image.

10. The method of claim 9, wherein the aerial image error is measured relative to a measurement of the aerial image sensor, or to wafer measurements from a charged particle tool.

11. The method of claim 7, wherein the function comprises any one of blur, gradient, or truncation of two-dimensional image operations.

12. The method of claim 11, further comprising determining a weighted sum of sub-images, the sub- images comprising an original of the measured aerial image and the measured aerial image with the applied function.

13. The method of claim 11, wherein the function comprises a filter corresponding to a mask layout on a wafer, wherein applying the function to the measured aerial image comprises applying the fdter to a transition edge between the black-border region and the absorber region of the measured aerial image.

14. The method of claim 13, wherein the fdter comprises any one of a polygon area of the mask layout, horizontal edges of the mask layout, vertical edges of the mask layout, comers of the mask layout, black-border of the mask layout.

15. The method of claim 7, wherein applying the function comprises generating an empirical aerial image profde.

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