Computational lithography simulation using linear-fading-aware source-mask optimization

Abstract

A non-transitory computer-readable medium stores a set of instructions that is executable by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing an illumination source and mask used in a lithography process. The operations include obtaining a pupil profile. The operations also include simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process. The operations also include calculating a cost function based on the predictions. The cost function includes a linear fading effect term that is indicative of a linear fading effect on the predictions. The operations also include adjusting the pupil profile based on the linear fading effect term.

Description

COMPUTATIONAL LITHOGRAPHY SIMULATION USING LINEAR-FADING- AW ARE SOURCE-MASK OPTIMIZATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 738,380 which was filed on 23 December 2024 and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to lithographic apparatuses and processes. More particularly, the description herein relates computational lithography and simulations for three-dimensional mask modeling.BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate by illuminating a mask that includes the pattern. Lithographic apparatuses are used in the manufacture of integrated circuits (ICs) having very small nanoscale features. An IC chip (e.g., a processor) can be as small as a person’s thumbnail and yet include billions of transistors. Nanofabrication is possible using pattern transfer techniques of photolithography. Making an IC is a complex and time-consuming process, with circuit components in different layers and including hundreds of individual steps. Errors in even one lithography step has the potential to result in problems with the final IC and can cause device failure. High process yield and high wafer throughput can be impacted by the presence of defects.

[0004] As feature sizes become significantly smaller than the wavelength of the illumination used to transfer the pattern, it is increasingly more difficult to maintain adequate process margins in the lithography process. For example, an aerial image created by a mask and exposure tool lose contrast and sharpness as the ratio of feature size to wavelength decreases. Loss of sharpness and contrast decreases accuracy of pattern transfer. Computational lithography techniques can be used to improve lithographic accuracy by simulating a lithography process while adjusting process parameters. Some process parameters can relate to patterns on the mask. For example, illumination can have process parameters for dose and focus. Illumination can also have specific spatial distribution shape (cross-sectional intensity profile). Interaction of the illumination and a mask pattern can be simulated, which is followed by simulation of an aerial image (patterned illumination that interacts with resist on a substrate), a resist image (chemical alteration of the resist), and etch image (etch of the altered resist).

[0005] Faster and more accurate simulations of lithography processes are desired, particularly methods that can assess and reduce fading effects that accompany certain lithographic scanning techniques. Such fading effects are not taken into account in conventional optimization methods.SUMMARY

[0006] Embodiments of the present disclosure provide a method for optimizing an illumination source and mask used in a lithography process.

[0007] In some embodiments, a non-transitory computer-readable medium that stores a set of instructions is provided. The set of instructions can be executed by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing an illumination source and mask used in a lithography process. The operations can comprise obtaining a pupil profile. The operations can also comprise simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process. The operations can also comprise calculating a cost function based on the predictions. The cost function can comprise a linear fading effect term that is indicative of a linear fading effect on the predictions. The operations can also comprise adjusting the pupil profile based on the linear fading effect term.

[0008] In some embodiments, a method for optimizing an illumination source and mask used in a lithography process is provided. The method can comprise obtaining a pupil profile. The method can also comprise simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process. The method can also comprise calculating a cost function based on the predictions. The cost function can comprise a linear fading effect term that is indicative of a linear fading effect on the predictions. The method can also comprise adjusting the pupil profile based on the linear fading effect term.

[0009] In some embodiments, a system for optimizing an illumination source and mask used in a lithography process is provided. The system can comprise one or more processors and one or more memory devices configured to store a set of instructions. The set of instructions can be executed by the one or more processors to cause the system to perform operations for optimizing an illumination source and mask used in a lithography process. The operations can comprise obtaining a pupil profile. The operations can also comprise simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process. The operations can also comprise calculating a cost function based on the predictions. The cost function can comprise a linear fading effect term that is indicative of a linear fading effect on the predictions. The operations can also comprise adjusting the pupil profile based on the linear fading effect term.BRIEF DESCRIPTION OF FIGURES

[0010] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0011] FIG. 1A shows example subsystems of a lithographic apparatus, consistent with embodiments of the present disclosure.

[0012] FIG. IB shows example subsystems of a lithographic apparatus, consistent with embodiments of the present disclosure.

[0013] FIG. 2 shows a flowchart of an example method for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure.

[0014] FIG. 3 shows a flowchart of an example method for source or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0015] FIG. 4 shows subsystems of an example lithographic apparatus, consistent with embodiments of the present disclosure.

[0016] FIG. 5 shows a graph for describing linear fading effects in terms of contrast loss, consistent with embodiments of the present disclosure.

[0017] FIG. 6 shows a flowchart of an exemplary method for performing computational lithography simulations using linear-fading-aware source-mask optimization, consistent with embodiments of the present disclosure.

[0018] FIG. 7 shows a flowchart of an exemplary method for performing linear-fading-aware source-mask optimization, consistent with embodiments of the present disclosure.

[0019] FIG. 8 shows a flowchart of an exemplary method for performing computational lithography simulations using linear-fading-aware source-mask optimization, consistent with embodiments of the present disclosure

[0020] FIG. 9 shows a flowchart of an exemplary method for optimizing an illumination source and mask used in a lithography process, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0021] Reference will now be made in detail to example embodiments, examples of which are illustrated in the 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 example embodiments do not represent all implementations consistent with the invention. Instead, they are merely examples of apparatuses, systems, and methods consistent with aspects related to subject matter that may be recited in the appended claims.

[0022] A lithography process can include creating a mask, then projecting an image from the mask onto a resist-coated substrate in order to create a pattern that matches the design intent of defining on the device wafer (e.g., functional elements such as transistor gates, contacts, or the like). The projection of the patterned illumination can be achieved via precise and complex projection optical systems. Yield increases the more times a master pattern is successfully replicated within the design specifications. Yield is a metric that characterizes failure rate in device fabrication, which relates to cost and efficiency. Wafers or chips with lithography errors are a sunk cost and lost time for a fab.

[0023] The technology trend towards “subwavelength lithography” makes it increasingly difficult to maintaining adequate process margins in the lithography process. There is limited practical flexibility in choosing the exposure wavelength. And the numerical aperture (NA) of exposure tools are nearphysical limits. Consequently, the continuous reduction in device feature sizes requires more and more aggressive reduction of the kl factor in lithography processes, conducting imaging at or below the classical resolution limits (the kl factor quantifies the ratio of feature size to wavelength, which is defined as the NA of the exposure tool times the minimum feature size divided by the wavelength). Methods to enable low-kl lithography can include adjusting the mask pattern to include non-printing “assist features” that are shapes that are not meant to be printed, but rather instigate proximity effects to provide a correction, thereby generating main print features that are more faithful to the intended design pattern. These correction methods can be referred to as optical proximity correction (OPC) methods.

[0024] Computationally optimizing an illumination source (“source”) via lithography simulation can be referred to as source optimization (SO), which can entail iterative adjustment of a “shape” of illumination of the source (e.g., how illumination is distributed at a pupil plane of the source).Computationally optimizing a mask via lithography simulation can be referred to as mask optimization (MO), which can entail iterative adjustment of assist features (e.g., biasing the mask) that bias the simulations toward more accurate pattern transfers and larger process windows (e.g., larger tolerances for process parameters). Computationally co-optimizing a source and a mask via lithography simulation can be referred to as source-mask optimization (SMO). Other optimizations directed to other parameters of lithography processes can also be implemented using embodiments of the present disclosure.

[0025] A problem of scanning lithography is image displacement, which can also be referred to as linear fading. A distortion of an aerial image can be quantified using low frequency components associated with the scanning movement of the wafer stage (e.g., to account for stage vibration). The distribution of the low frequency components can be referred to as a moving standard deviation. Linear fading can be proportional to a rate of change of the image displacement as a function of a scanning y-direction. Conventional SO / MO / SMO methods lack a way to assess linear fading impact on imaging performance.

[0026] It is desirable to provide source, mask, or source-mask optimizations that account for linear fading impact on imaging performance, thereby allowing for more accurate simulations and improved yield of lithographic systems.

[0027] Embodiments of the present disclosure provide a system and method for performing linear-fading-aware SMO / MO to generate pupil profiles, masks, and models that use linear-fading term in the simulation cost function to penalize fading impact on imaging performance. The linear-fading quantity can be implemented as a perturbation in a process window.

[0028] Objects and advantages of the disclosure can be realized by the elements and combinations as set forth in embodiments described herein. However, embodiments of the present disclosure are not necessarily required to achieve such exemplary objects or advantages. Some embodiments canachieve a different feature or enhancement without necessarily achieving any expressly stated object or advantage.

[0029] 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 can comprise A or B, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or A and B. As a second example, if it is stated that a component can comprise A, B, or C, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0030] 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.

[0031] The term “patterning device” may be considered synonymous with similar terms of art, such as “reticle” or “mask.” The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a pattern on a cross section of a radiation beam. The radiation beam then can recreate the pattern in a target portion of a substrate.

[0032] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system.”

[0033] Illumination can be understood to be a form of radiation. The terms “radiation” and “illumination” can be used herein interchangeably. Embodiments described in the context of illumination are also applicable in the context of radiation in general. Furthermore, the terms “radiation” and “beam” can 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, such as 13.5 nm).

[0034] It is to be appreciated that image information can be represented in several forms. For example, a graphical representation of an image (e.g., displayed at a display device) can also be represented as digital data (e.g., saved as a file in memory). An analog representation can be in the form of electrical signals that convey the image information. The present disclosure can refer to generating, analyzing, or processing of images. It is to be appreciated that such operations directed to images can be performed with respect to any representation of an image (e.g., graphical, electrical signal, binary data, or the like). For example, generating an image can refer to generating an actual graphical representation of the image or generating a binary-data representation of the image that can be read and processed by a computing device.

[0035] FIG. 1A shows example subsystems of a lithographic apparatus 100, consistent with embodiments of the present disclosure. In some embodiments, lithographic apparatus 100 comprises a source 102, which can be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (the lithographic apparatus itself need not have the source), illumination optics which define the partial coherence (denoted as sigma) and which can include optic components 104, 106a, and 106b that shape illumination from source 102; a patterning device 108; and transmission optics 106c that project an image of the patterning device pattern onto a substrate plane 109. An adjustable filter or aperture 107 at disposed in among the optics can restrict the range of beam angles that impinge on the substrate plane 109. A largest possible angle 0max can define the numerical aperture NA of the projection optics as NA = n sin(0max), where n is the index of reflection of the medium in which the final lens element is working (e.g., a lens closest to the substrate). And while the example of FIG. 1A illustrates a transmissive lithographic apparatus (e.g., patterning device 108 is transmissive), embodiments described herein are not so limited. For example, embodiments described herein are also applicable to reflective lithographic apparatuses that use a reflective patterning device. An example of a lithographic apparatus with reflection optics is described in reference to FIG. IB.

[0036] In an optimization process of a lithographic projection system, a figure of merit of the system can be represented as a cost function. The optimization process can determine 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 a 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 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 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 of the illumination used.

[0037] In a lithographic apparatus, a source can provide illumination. Projection optics can direct and shape the illumination via a patterning device and onto a substrate. The term “projection optics” is broadly defined to include any optical component that can alter the wavefront of the radiation beam. For example, projection optics can include at least some of components 104, 106a, 106b, and 106c. An aerial image is the radiation intensity distribution at substrate level (e.g., at substrate plane 109). A resist layer on the substrate is exposed and the aerial image is transferred to the resist layer as a latent “resist image” therein. The resist image can be defined as a spatial distribution of solubility of theresist in the resist layer. A resist model can be used to calculate the resist image from the aerial image. An example of a resist model can be found in U.S. Patent No. 8,200,468, the contents of which are incorporated herein by reference in their entirety. The resist model is related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB), and development). Optical properties of the lithographic 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 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 apparatus including at least the source and the projection optics.

[0038] FIG. IB shows example subsystems of a lithographic apparatus 100’, consistent with embodiments of the present disclosure. In some embodiments, lithographic apparatus 100’ is a reflective-type lithographic scanner. Lithographic apparatus 100’ can comprise a mask 110 (e.g., reflective mask) and a projection system 112 (e.g., a projection optics box (POB)). An illumination source 114 can generate a beam of illumination 116. Illumination source 114 can be an integral part of lithographic apparatus 100’ or can be a separate system (e.g., modular). Projection system 112 can comprise optical elements to direct illumination. Any suitable number and types of optical elements can be used. For example purposes, mirrors Ml, M2, M3, M4, M5 and M6 are shown (more or fewer optical elements can be used, e.g., one or more). A cross-sectional intensity distribution of beam of illumination 116 can be different at different stages of propagation (e.g., in accordance with Fourier optics). For example, at a pupil plane PP of illumination source 114, the intensity distribution profile can be as shown in pupil profile 118 (e.g., when beam of illumination 116 is yet to be focused). The intensity distribution profile at mask 110 can be as shown in slit profile 120 (e.g., when beam of illumination 116 is focused).

[0039] In some embodiments, the bright spots of pupil profile 118 indicate how the photon energy of beam of illumination 116 is distributed across pupil plane PP. Dark portions of pupil profile 118 can indicate lack of photon energy. The shape of pupil profile 118 can be controlled via a system of independently controllable field facet mirrors 122. Each bright dot in pupil profile 118 can be indicative of a field facet mirror that is in the “on” state (e.g., photons directed toward mask 110 come from field facet mirrors 118 that are turned on). The quality of illumination (e.g., the quality of slit profile 120) can greatly affect the quality of lithographic pattern transfer from mask 110 to wafer 124. Since slit profile 120 can be the conjugate of pupil profile 118, optimizing the quality of illumination can entail optimizing the mirror configuration of field facet mirrors 122. Optimization of source parameters can be performed via computational lithography simulation (an optimization process often referred to as source optimization (SO)).

[0040] In some embodiments, inset 126 illustrates a scanning arrangement for transferring a pattern of mask 110 to substrate 124 via projection system 112. Beam of illumination 116 can be incident upon pattern 128 of mask 110. The interaction between beam of illumination 116 and mask 110 canproduce a patterned beam of illumination 130. Patterned beam of illumination 130 can have an intensity distribution profile (a patterned slit profile 132) based on slit profile 120 and pattern 128. Patterned slit profile 132 is illustrated in another inset at the bottom of FIG. IB, which is incident upon a region 134 of substrate 124 (the region can be a field or die). To perform a pattern transfer via scanning, mask 110 and substrate 124 can be scanned along a plane perpendicular to a propagation direction of patterned beam of illumination 130 (e.g., an example scan motion is indicated via translation double arrows next to mask 110 and substrate 124). Double arrows next to mask 110 and substrate 124 illustrate an example translation along a y-direction (example coordinate axes are provided in FIG. IB). Movement of mask 110 and substrate 124 can be achieved via respective translation stages (not shown).

[0041] At nanoscales, the pattern image formed on substrate 124 can deviate significantly from the likeness of pattern 128 due to various uncertainties and physics-based limitations of the chosen lithography process. The scanning technique described above can introduce fading of the pattern image, which blurs and degrades the sharpness of pattern edges. An example of the image fading effect is provided in Schmidt et al., “Characterization ofEUV image fading induced by overlay corrections using pattern shift response metrology,” International Conference on Extreme Ultraviolet Lithography 2019 (Vol. 11147, pp. 103-111), SPIE (2019, October).

[0042] It is desirable to increase fidelity between computational lithography simulations and actual lithographic fabrication by programming the computational simulations to account for causes of exposure errors, such as image fading. Furthermore, a lithography process can be flexible enough to allow for some adjustments of optical characteristics (e.g., focus) for optimizing exposures. This flexibility can also be taken into account by computational lithography simulations.

[0043] In some embodiments, inset 136 shows a shorthand representation of optical characteristics of lithographic apparatus 100’. Reticle 110 can be disposed at an ideal object plane 138 with respect to projection system 112. The NA of projection system 112 is represented as NA plane 140. The collimation characteristic of projection system 112 is presented by objective lens plane 142. Substrate 124 can be disposed at an ideal image plane 144 with respect to mask 110 and projection system 112. Overlay effects can be introduced when a position of mask 110 is subject to a focus offset Az.Computational lithography simulations can be more accurate if such overlay effects are taken into account.

[0044] FIG. 2 shows a flowchart of an exemplary method 200 for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure. In some embodiments, a source model 202 represents optical characteristics of the source (e.g., including radiation intensity distribution, phase distribution, or the like). A projection optics model 204 can represent optical characteristics of the projection optics (e.g., including changes to radiation intensity / phase distribution caused by the projection optics). A design layout model 206 can represent optical characteristics of a design layout (e.g., including changes to radiation intensity / phase distribution caused by a givendesign layout), which is the representation of an arrangement of features on, or formed by, a patterning device. An aerial image 208 can be simulated from source model 202, projection optics model 204, and design layout model 206. A resist image 212 can be simulated from aerial image 208 using a resist model 210. Simulation of lithography can, for example, predict lithographic pattern transfer results, which can include feature contours, edge placement errors (EPE), critical dimensions (CDs), or the like, in the resist image.

[0045] It is noted that the source model 202 can represent 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.). Projection optics model 204 can represent the optical characteristics of the projection optics that include, but are not limited to, aberration, distortion, refractive indexes, physical sizes, physical dimensions, or the like. Design layout model 206 can represent physical properties of a physical patterning device. An example of a design layout model can be found in U.S. Patent No. 7,587,704, the contents of which are incorporated herein by reference in their entirety. A goal of the simulation is to accurately predict feature contours, edge placement errors (EPE), critical dimensions (CDs), or the like, which can then be compared against an intended design for a device (e.g., a simulation to determine whether a mass fabrication of a new CPU architecture is feasible). The intended design is generally defined as a pre-optical proximity correction (OPC) design layout (OPC is sometimes also referred to as “optical and process correction”), 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), or the like. The intended design layout can include patterns or structures for transferring onto a wafer. The patterns or structures can be mask patterns used to transfer features from photolithography masks or reticles to a wafer. In some embodiments, a layout in GDS or OASIS format, among others, can include feature information stored in a binary file format representing planar geometric shapes, text, and other information related to the wafer design.

[0046] From the design layout, one or more portions can 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 can be used). It is to be appreciated that 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 desirable. In other words, clips can be the portions of the design layout or can 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 fullchip simulation. Clips can contain one or more test patterns or gauge patterns.

[0047] An initial larger set of clips can be provided a priori by a customer based on known critical feature areas in a design layout that could benefit from image optimization. Alternatively, in someembodiments, the initial larger set of clips is extracted from the entire design layout by using some kind of automated algorithm (e.g., machine vision) or manual algorithm that identifies the critical feature areas.

[0048] 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 can involve execution of the one or more process models and computing a cost function that can 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 is described by design variables. Hence, an optimized characteristic can also be referred to as an optimized design variable, where a design variable is optimized based on a cost function.

[0049] In some embodiments, modifying the one or more characteristics is based on a gradient of the cost function that guides how the characteristic should be modified to reduce the cost function. A cost function can be a function of a certain continuous metric such as an edge placement error (e.g., a difference between contours of printed pattern and a target pattern). Using a continuous metric or a cost function of a continuous nature allows use of gradient-based optimizing algorithms that have acceptable runtime performance of an optimization process.

[0050] Details of example techniques and models used to transform a patterning device pattern into various lithographic images (e.g., an aerial image, a resist image, an etch image, etc.), apply OPC (e.g., using models) and evaluate performance (e.g., in terms of process window) can be found in U.S. Patent Nos. 7,695,876; 7,707,538; 7,747,978; 7,882,480; 8,413,081; 8,438,508; and 9,360,766, the contents of which are incorporated herein by reference in their entirety.

[0051] FIG. 3 illustrates a flowchart of an exemplary method 300 for implementing SMO and OPC, consistent with embodiments of the present disclosure. In a typical high-end design, almost every feature edge can benefit from some modification to achieve printed patterns that come sufficiently close to the target design. These modifications can 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 can affect the properties of an associated primary feature. Furthermore, optimization techniques applied to the source of illumination can 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 provide optimization methods that can be applied to both source and mask configurations.

[0052] A method of performing source and mask optimization (SMO) can allow 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 can be performed on these selected patterns to obtain an optimized source. The optimized source can then be used to optimize the mask(e.g., using OPC and local mechanical-stress control) for the full chip, and the results can be compared. Various methods are provided for iteratively converging on an optimal result.

[0053] A target design 301 (e.g., comprising a layout in a standard digital format such as OAIS, GDSII, etc.) for which a lithography process is to be optimized can include memory, test patterns, and logic. From this design, a full set of clips 302 can be extracted, which represents complex patterns in design 301 (e.g., about 50 to 1000 clips). It is to be appreciated that these clips represent small portions (i.e., circuits, cells, or patterns) of the design for which particular attention and / or verification is of interest. At operation 304, a small subset of clips 306 (e.g., 15 to 50 clips) can be selected from full set of clips 302. As will be explained in more detail below, the selection of clips can be performed such that the process window of the selected patterns matches the process window for the full set of critical patterns as close as possible. The effectiveness of the selection can be measured by the total run time (pattern selection and SMO) reduction.

[0054] At operation 308, SMO can be performed with the selected patterns (15 to 50 patterns) of subset of clips 306. In particularly, an illumination source can be optimized for the selected patterns of subset of clips 306. Source optimization can be performed as described below with respect to FIGS. 5-9. Examples of other source optimization methods can be found in, for example, U.S. Patent Application Publication No. 2004 / 0265707, the contents of which are incorporated herein by reference in their entirety.

[0055] At operation 310, manufacturability verification of the selected patterns of subset of clips 306 can be performed with the source obtained in operation 308. In particular, verification can include performing an aerial image simulation of the selected patterns of subset of clips 306 and the optimized source and verifying that the patterns will print across a sufficiently wide process window. An example verification process can be found in U.S. Patent No. 7,342,646, the contents of which are incorporated herein by reference in their entirety. If the verification at operation 310 is satisfactory, as determined in operation 312, then processing can advance to full chip optimization (e.g., advanced to operations using optimized source 314). Otherwise, processing can return to operation 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.

[0056] After the selected patterns meet lithography performance specification as determined in step 312, the optimized source 314 can be used for optimization of the full set of clips 316 (e.g., originating from full set of clips 302).

[0057] At operation 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 can be performed. Examples of MB-SRAF and OPC can be found in U.S. Patent Nos. 5,663,893; 5,821,014; 6,541,167; and 6,670,081, the contents of which are incorporated herein by reference in their entirety.

[0058] At operation 320, using processes similar to step 310, manufacturability verification based on full pattern simulation can be performed with the optimized source 314 and the full set of clips 316 as corrected in step 318.

[0059] At operation 322, the performance (e.g., process window parameters such as exposure latitude and depth of focus) of the full set of clips 316 can be compared against subset of clips 306. For example, the pattern selection can be considered complete and / or the source is fully qualified for the full chip when the similar lithography performances are obtained for both selected patterns of subset of clips 306 and critical patterns of full set of clips 316.

[0060] Otherwise, at operation 324, hotspots can be extracted. At operation 326, the hotspots can be added to subset of clips 306 and the process starts over. For example, hotspots (e.g., features among the full set of clips 316 that limit process window performance) identified during verification step 320 can be used for further source tuning or to run SMO of operation 308 again. The source can be 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 operation 322.

[0061] OPC calibration can be performed by modeling or simulation. For example, for the desired yield, the total number of features, and their respective probabilities of failure, simulation can be performed to optimize OPC for a lowest yielding feature. 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.

[0062] In some embodiments, the measurement data (e.g., stochastic variations) related to the printed pattern can be employed in optimizing the patterning process or adjusting parameters of the patterning process. For small feature sizes and high feature densities present on some design layouts, the position of a particular edge of a given feature can 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 can arise from diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching that generally follow lithography.

[0063] To ensure that the projected image of the patterning device pattern is in accordance with tolerances 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 “model-based” optical proximity correction processes, the contents of which are incorporated herein by reference in their entirety. In a typical high-end design, almost every feature of the patterning device pattern has some modification to achieve high fidelity of the projected image to the target design. These OPCmodifications can 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.

[0064] Application of model-based OPC to a target design can involve good process models and considerable computational resources, given the many millions of features typically present in a device design. However, applying OPC is generally 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, 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, as well as by the impact on turn-around time by reworking or repairing existing patterning devices once they have been manufactured. OPC and full-chip RET verification can be based on numerical modelling systems and methods. Examples of such methods can be found 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), the contents of which are incorporated herein by reference in their entirety.

[0065] The above-described computational lithography operations of FIGS.2 and 3 can be applied to transmissive lithographic apparatus (e.g., as in the example of FIG. 1A), as well as reflective lithographic apparatuses (e.g., as in the example of FIG. IB). The quality of computational lithography results from operations of FIGS. 2 and 3 can be enhanced by introducing linear fading effects in the simulation process.

[0066] FIG. 4 shows subsystems of an example lithographic apparatus 400, consistent with embodiments of the present disclosure. In some embodiments, lithographic apparatus 400 can be substantially the same as lithographic apparatus 100’ (FIG. IB). Different operational configurations are described in reference to lithographic apparatus 400 (e.g., mask and substrate are tilted, focus offset). Some redundant descriptions and element illustrations are omitted for brevity and are to be inferred from FIG. IB. For some corresponding elements, the leading (left-most) digit(s) can denote the figure in which the elements first appear while the trailing (right-most) digit(s) can identify the element. Examples of corresponding elements can include a mask 410, a projection system 412 (and constituent mirror(s)), a illumination source 414, a beam of illumination 416, a pupil profile 418, a pupil plane PP, a slit profile 420, a field facet mirrors 422, a substrate 424, and patterned beam of illumination 430.

[0067] In some embodiments, a plane of mask 410 is represented by mask plane 446. A plane of resist on substrate 424 can be represented by substrate plane 448. Distortions of projected patterns can depend on the positions of mask plane 448 and substrate plane 448. To increase fidelity between computational lithography simulations and actual lithographic fabrication, aerial image deformation can be accounted for implementing a cost function term that is sensitive to linear fading.

[0068] An aerial image 450 is shown in insets at the bottom of FIG.4. Aerial image 450 can correspond to aerial image 208 generated by the operations described in reference to FIGS. 2 and 3. Aerial image 450 can be resolved at substrate plane 448. Aerial image 450 can be adjusted (e.g., magnified, translated, tilted, or the like), which is denoted as adjusted aerial image 450’. Different examples of adjusted aerial image 450’ are shown, for example, a focus offset dz, a y-axis rotation Ry= -dz / dx, and an x-axis rotation Rx= -dz / dy. Such adjustments to an aerial image can generate a corresponding distortion of projected patterns on substrate 424. For computational lithography, a suitable representation of the distortion can be used, for example using a polynomial expansion with so-called k-factors. Example polynomial expansions for distortions along the x-direction (dx) and along the y-direction (dy) are provided in equations 1 and 2 (e.g., y-direction can be a scanning direction as shown in inset 126 (FIG. 1)).Dx = k1+ k3x + k5y + k7x2+ k9xy + k41y2+ k13x3+ k15x2y + k17xy2+ ••• (Eq. 1)Dy = k2+ k4y + k6x + ksy2+ kwxy + k12x2+ k14y3+ k16y2+ k18x2y + ••• (Eq. 2)

[0069] In the example nomenclature used here, the k-factors k; (i = 1, 2, 3, ...) can be used. Other distortions can include magnification of the image (e.g., Mxor Mymagnifications) or translations of the image (e.g., Txor Tytranslations).

[0070] Unintended (parasitic) distortions can also be accounted for. For example, a focus offset dz can be used to intentionally introduce a magnification Mx. A parasitic distortion of a translation Tycan accompany the requested (intended) magnification. In another example, a requested ki2 distortion for a rotation Rxcan introduce a higher order parasitic at kn. In another example, a requested k? distortion for a rotation Rycan introduce a parasitic of the same order at k& as well as a higher order parasitic at kzo- Another way to describe a distortion is that the intended image is displaced, or deviates from, the intended shape, size, orientation, etc. Intrafield overlay corrections can comprise corrections that address parasitic distortions. Another type of correction is associated with overlay effects from wafer bonding. The associated active correction that addresses wafer bonding can be aggressive, resulting in enhancement of the fading effect. Linear fading due to stage movement and wafer bonding fading are types of fading effects that warrant the use of appropriate correction terms.

[0071] Intrafield overlay corrections for scanner operations can be achieved by dynamic scan routing modulations and therefore contribute to image degradation due to fading. The magnitude for the correction can depend on the specific overlay correction term’ s routing characteristics.. A distortion of an aerial image can be quantified using low frequency components associated with the scanning movement of the wafer stage (e.g., to account for stage vibration). The distribution of the low frequency components can be characterized in a quantity referred to as a moving standard deviation (MSD). Linear fading can be proportional to a rate of change of the image displacement as a functionof the scanning direction (e.g., y-direction). Linear fading can be normalized based on MSD. For example, once the dominant distortion k-factors are identified, liner fading can be derived by calculating the rate of change of the distortion with respect to scanning direction (e.g., taking the derivative of Dx and Dy in equations 1 and 2 with respect to y).

[0072] An important effect to accurately model the linear fading impact is the thru-Y pupil variation effect (e.g., a so-called sunrise / sunset effect). An example of simulating linear fading using MSD can be found in WO 2024 / 217856 Al, the contents of which are incorporated herein by reference in their entirety. Imaging degradation has an impact on one or more patterning parameters such as CD, uniformity (CDU), image log slope (ILS), normalized image log slope (NILS), edge placement error (EPE) distribution, process window, line edge roughness (LER), local CDU (LCDU), or pattern placement error (PPE).

[0073] FIG. 5 shows a graph 500 for describing linear fading effects in terms of contrast loss, consistent with embodiments of the present disclosure. In some embodiments, graph 500 is associated with a circle pattern in an aerial image. The circle pattern can be used for CD characterization. In particular, intensity data of graph 500 is associated with the cross-sectional line AA’ (e.g., along a y-direction). Baseline plot 502 is associated with inset 504. The baseline excludes fading effects. Plot 506 of graph 500 is associated with inset 508, which is part of an aerial image where fading effects are taken into account (e.g., via suitable usage of k-factors).

[0074] A visual comparison of insets 504 (no fading) and 508 (with fading) shows that the boundaries of the CD circle structure is not as clearly defined in inset 504. In graph 500, the fading is manifested in loss of contrast. Maximum contrast can be achieved by ensuring that dark areas are optimally dark (e.g., lack of photons or zero intensity) and bright areas are optimally bright (e.g., maximum photon count or maximum intensity). Baseline plot 502 (no fading) is associated with an intensity contrast AL Plot 506 (with fading) is associated with a subdued intensity contrast Al'.

[0075] Furthermore, the linear fading effect can be directional, or vary with directions based on the scanning direction (see inset 126 (FIG. 1)). Inset 504 (no fading) can represent a substantially circular pattern, whereas the same pattern can be distorted with a directional bias in image printed contour when fading is introduced. Inset 508 can represent the same pattern as inset 504, but the printed contour is stretched vertically, indicating directional biases (e.g., vertical up and down) as compared to horizontal fading biases. The directionality of the fading can vary depending on position (e.g., can be tensorial in nature).

[0076] Conventional lithography simulation techniques are lacking in that some optimization processes (e.g., SMO) do not have a convergence mechanism that accounts for the linear fading due to a scanning motion and direction of the wafer stage. In other words, conventional techniques do not consider image quality degradation under linear fading conditions in the cost function for optimization. Some embodiments of the present disclosure are directed to performing linear-fading-aware SO / MO / SMO by implementing a linear-fading term in the cost function to penalize fadingimpact on imaging performance. The linear-fading quantity can be implemented as a perturbation in a process window.

[0077] FIG. 6 shows a flowchart of an exemplary method 600 for performing computational lithography simulations using linear-fading-based SMO that uses a linear-fading term in cost function, consistent with embodiments of the present disclosure. In some embodiment, method 600 is a high level overview of a process that includes linear-fading-aware SMO. Further details are described with respect to subsequent figures.

[0078] In some embodiments, at operation 602, a baseline SMO is performed. The baseline SMO can be performed as described in reference to operation 308 (FIG.3). The baseline SMO may not include a process or steps to account for linear fading effects.

[0079] At operation 604, critical linear fading patterns are identified, which can also be referred to as linear fading hotspots. Operation 604 can be performed as described in reference to operation 324 (FIG. 3). Certain parameters of a lithography process can be adjusted within a certain range of values (e.g., a range for focus dZ, a range for illumination dose, or the like). A design pattern can constrain the feasible range of the process parameter values. For example, it is feasible to use a large range of focus and dose to fabricate a simple pattern with large CD. Conversely, a complex pattern with small CD can demand a very narrow range of values for focus and dose. The wide range of values can be referred to as a large process window while a narrow range of values can be referred to as a small process window.

[0080] A large process window is better in general. The linear fading hotspots can be identified by their tendency to shrink the process window below a given threshold. The linear fading hotspots can be assessed based on their tendency to cause contrast reduction as described in reference to FIG. 5. In identifying linear fading hotspots, the direction of linear fading can be identified. Linear fading can be directional. A pattern can be afflicted by one or more fading directions (e.g., tensorial) along the xy-plane of substrates 124 or 424 (FIGS. IB and 4). During simulations, a variety of patterns can be generated with a sufficiently large process window (e.g., overlapping process window). By using the linear-fading perturbation described herein, the linear-fading hotspots that are limiting the overlapping process window can be mitigated.

[0081] At operation 606, a linear-fading-aware SMO can be performed. In some embodiments, the linear-fading-aware SMO process can be similar to the baseline SMO of operations 604 and 324 (FIG. 3) with one or more modifications. For example, the linear-fading-aware SMO can use a custom cost function term that comprises a fading effect term. The custom cost function term can cause the SMO iterations to converge on enhanced contrast. More details about linear-fading-aware SMO are provided below with respect to subsequent figures.

[0082] At operation 608, the results of the baseline SMO and the linear-fading-aware SMO can be evaluated. For example, the baseline SMO generates a baseline pupil profile (e.g., similar to pupil profiles 118 or 418 (FIGS. IB and 4) while the linear-fading-aware SMO generates a different pupilprofile. The differences in the different pupil profiles can be ascertained via comparison (pupil profile can also be referred to as pupil topology, in reference to the spatial information (shape) of illumination intensity).

[0083] At operation 610, OPC model calibration can be performed. Operation 610 can be performed as described in reference to operation 318 (FIG.3). Computational lithography simulation can rely on a plurality of physical models, which simulate light projection, image forming process, and lightmatter interactions (e.g., optical model, mask model, resist model, etch model, stochastic edge placement error (SEPE) model, or the like). For example, models can be based on rigorous simulation, empirical, machine learning, or a combination thereof. Physical properties of a mask and its interaction with incident illumination can be approximated in a mask model to various degrees of complexity.

[0084] At operation 612, large-clip OPC or large-clip MO can be performed. Large-clips or full-chip OPC can be performed as described in reference to operation 320 (FIG. 3). Large-clips mask optimization can be performed using a custom cost function term. The custom cost function term can be substantially similar to the custom cost function term described above in reference to operation 606.

[0085] At operation 614, OPC verification can be performed. OPC verification can be performed as described in reference to operation 322 (FIG.3). Operation 614 can be used to ascertain that impact of hotspots are eliminated or mitigated.

[0086] At operation 616, fading sensitivity of the linear-fading-aware model can be verified via OPC verification similar to operation 614. OPC verification with linear fading model can potentially detect hotspots that escape detection at operation 614.

[0087] FIG. 7 shows a flowchart of an exemplary method 700 for performing linear-fading-aware SMO, consistent with embodiments of the present disclosure. In some embodiment, method 700 provides more details for one or more operations described above in reference to FIG.6.

[0088] To identify critical linear fading, a design target mask 702 can be analyzed, design target mask 702 can be a pattern layout in a layout file (e.g., GDS coordinate information). The analysis can comprise testing different regions (e.g., clips) for linear fading sensitivity 704 to determine one or more hotspots and the most sensitive linear fading vector direction. As explained above, linear fading can be directional and can vary from region to region of design target mask 702. Linear fading sensitivity can be ascertained via linear fading simulation (e.g., intrafield overlay corrections) as described in reference to FIG. 4. A threshold condition can be implemented for which a critical linear fading region of the layout can be determined based on whether a magnitude of the linear fading effect meets the threshold condition (e.g., equal to or greater than the threshold magnitude).

[0089] Based on test results of linear fading sensitivity 704, critical linear fading 706 can be identified. Critical linear fading can be assessed via one or more metrics 706. Any suitable metric can be used. An example metric is shown in FIG. 7 — NILS, which provides an indication of contrast.NILS is a useful metric to judge the lithographic usefulness of an aerial image. Since the NILS is a measure of image quality, it can be used to investigate how optical parameters affect image quality. Simulation predictions include, for example, NILS different linear fading directions (e.g., full angle) and ANILS (NILS change).

[0090] With the regions of critical linear fading identified, iterative simulations can be performed while perturbing the values of different parameters of a process window 712 (e.g., dose, mask bias, focus, or the like). In the simulations, fading data can be converted to wavefront expressions (e.g., Tatian, Zernike, etc.) such that the imaging impact from the converted wavefront is similar to that from the fading data. The converted wavefront can be used for simulating the imaging impact. A linear portion of the fading data can be converted to the wavefront expressions (e.g., linear wavefront expressions such as Zernike Z2 and Z3 parameters). The simulation of the imaging impact can comprise extracting a linear portion of the fading data, converting the linear portion to wavefront expressions (e.g., Z2 and Z3 parameters), and simulating the imaging impact based on the wavefront expressions. During simulations, the perturbation can include linear fading perturbation 710.

[0091] The iterations also try different configurations of field facet mirrors (e.g., many different pupil profiles are simulated).

[0092] Aside from linear-fading perturbation, a custom cost-function can be evaluated at each iteration. The algorithm can converge on a minimum cost function value. For example, a custom cost function (CCF) term 714 can be programmed into the cost function. In custom cost function term 714, EPEncan represent cumulative edge placement error and PW can represent the process window conditions. The complete cost function used for the simulations can comprise an accumulation of various effects that negatively impact a lithography process. An example cost function (CF) is provided in equation 3, which includes a CCF term. An example CCF term is provided in equation 4."

[0093] In equations 3 and 4, PWeval can represent the process window conditions under evaluation and EPE is an edge placement error metric. Imax and Imincan respectively represent the maximum and minimum intensity of plot 506 (FIG.5), which carry linear fading information (e.g., reduced contrast), Threshold can represent an intensity threshold associated with printing to a target CD (e.g., an intensity below the threshold may fail to provide enough dose to properly expose resist). IOffset can represent an optional term in scenarios where the threshold is to be adjusted (e.g., mask bias of thedose anchor feature can prompt changing of the threshold). The summation in equation 4 can be performed over a custom gauge on the linear fading limiting critical hotspots that falls within the process window.

[0094] From among the different perturbations, the values that correspond to the lowest cost function value can be considered optimal values. This iterative perturbation process can be referred to as source and mask optimization (SMO) as both the source parameters (e.g., dose and pupil profile) and mask parameters including assist features (focus and mask bias) are co-optimized.

[0095] Some example budgets (ranges) for focus, dose, and mask bias perturbations are shown. Other suitable budgets can be used. Parameter perturbations can include perturbations of the linear fading effect. In the example shown in FIG. 7, the linear fading perturbation is an add-on perturbed linear fading condition for each perturbed dose condition (e.g., for one dose perturbation, different linear fading perturbations are simulated). Other permutations of perturbation conditions can be used (e.g., linear fading perturbations as an add-on to a perturbed focus condition).

[0096] A result of the SMO process of method 700 is an optimization of design target mask 702 (e.g., adjusted to include assist features), as well as a linear-fading- aware optimized pupil profile 716. For comparison, an example baseline pupil profile 718 is also shown (generated using a baseline SMO process that did not account for linear fading). Linear-fading-aware optimized pupil profile 716 can be a further optimization of a baseline pupil profile 718. An optimized pupil profile can also be referred to as an optimized source. Based on the operations of method 700, both the optimized mask and optimized source are less sensitive to process variations such as focus, dose, mask error effects, and linear fading.

[0097] FIG. 8 shows a flowchart of an exemplary method 800 for performing computational lithography simulations using linear-fading-aware SMO, consistent with embodiments of the present disclosure. In some embodiment, method 800 provides more details for one or more operations described above in reference to FIGS.6 and 7. The shorthand versions of linear fading (LF) and process window (PW) are used in FIG.8.

[0098] The flow of method 800 can use separate branches. The branches fork out from a baseline SMO job, which can be executed at operation 802 (can correspond to operation 602 (FIG. 6)). The output of the baseline SMO can be a baseline final mask 802-1, a baseline pupil profile 802-2, and a baseline model 802-3 that are consistent with the parameters of the baseline SMO (without linear fading perturbation). At operation 804, a baseline simulation can be performed. Operation 804 can comprise simulating linear fading based on the output of the baseline SMO job (baseline simulation) to ascertain the impact of degraded contrast of an aerial image.

[0099] In some embodiments, the other branch of method 800 pertains to linear fading SMO. At operation 806, the output from the baseline job is analyzed for linear fading sensitivity (e.g., as described in reference to operation 704 (FIG.7)). Operation 806 can correspond to operation 604 (FIG. 6).

[0100] At operation 808, critical linear fading pattern(s) (hotspot(s)) and vectors (direction and magnitude) can be selected. Determination of critical linear fading is described in reference to operation 706 (FIG.7).

[0101] At operation 810, linear-fading-aware SMO can be performed using perturbed linear fading conditions (e.g., as described in reference to operation 710 (FIG. 7)). Operation 810 can correspond to operation 606 (FIG. 6). The linear-fading-aware SMO process is performed using the baseline model from the baseline SMO job, which initially would not include linear fading optimization. The output of linear-fading-aware SMO can be a linear-fading-optimized final mask 810-1, a linear-fading-optimized final pupil profile 810-2, and a linear-fading optimized model 810-3.

[0102] At operation 812, linear fading can be simulated on the linear-fading-optimized final mask (similar to operation 804, but with different input).

[0103] At operation 814, the results from operations 804 and 812 and Y are compared. The comparison can be performed using any suitable metric. Example metrics include overlapping process window size, NILS, CD difference, CD error, or the like.

[0104] FIG. 9 shows a flowchart of an exemplary method 900 for optimizing an illumination source 114 / 414 and mask 110 / 410 used in a lithography process, consistent with embodiments of the present disclosure. In some embodiments, method 900 includes operations that correspond to devices and functions described above with reference to FIGS. 1-8.

[0105] At operation 902, a computing system can obtain a pupil profile from a baseline SMO (e.g., pupil 718 or 802-2 from operations 602 or 802). Other baseline SMO outputs can be obtained, for example, a baseline final mask or a baseline physical model (e.g., baseline pupil profile 802-1 or baseline model 802-3).

[0106] At operation 904, a lithography process can be simulated using the pupil profile to generate predictions resulting from the lithography process. The predictions can include an aerial image.

[0107] At operation 906, an additional cost function term can be calculated based on the predictions (e.g., equation 3). The cost function can comprise a fading effect term (e.g., equation 4) that is indicative of a fading effect on the predictions.

[0108] At operation 908, the pupil profile can be adjusted based on the fading effect term. Iterative adjustments of the pupil profile can result in the output of an adjusted pupil profile (e.g., linear-fading-optimized pupil profile 810-2). Adjustments to a mask and model can also be performed (e.g., to generate linear-fading-optimized final mask 810-1 and linear-fading-optimized model 810-3).

[0109] Some embodiments of the present disclosure can include additional or alternative method operations based on the description of FIGS. 1A-9. For example, the simulating can comprise simulating under perturbed process conditions such as perturbed dose condition and an add-on perturbed linear fading condition for each perturbed dose condition.

[0110] A non-transitory computer-readable medium can store instructions for a processor of a controller for simulating a lithography process according to the exemplary flowcharts of FIGS. 2, 3,and 6-9, consistent with embodiments in the present disclosure. For example, the instructions stored in the non-transitory computer-readable medium can be executed by the circuitry of the controller of, or corresponding to, a lithography system for performing methods 200, 300, 600, 700, 800, or 900 in part or entirely. A non-exhaustive list of common forms of non-transitory media includes, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, 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 Read-Only Memory, (ROM), a Programmable Read-Only Memory (PROM), a Field-Programmable Gate Array (FPGA), 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.

[0111] Embodiments of the present disclosure can be further described by the following clauses. 1. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing an illumination source and mask used in a lithography process, the operations comprising:obtaining a pupil profile;simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process;calculating a cost function based on the predictions, wherein the cost function comprises a linear fading effect term that is indicative of a linear fading effect on the predictions;adjusting the pupil profile based on the linear fading effect term.2. The non-transitory computer-readable medium of clause 1, wherein the linear fading effect term is a function of:an intensity threshold associated with an aerial image; andimaging contrast.3. The non-transitory computer-readable medium of clause 1, wherein the simulating comprises simulating under perturbed process conditions comprising:perturbed dose conditions; andan add-on perturbed linear fading condition for each perturbed dose condition.4. The non-transitory computer-readable medium of clause 1, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; analyzing regions of the design pattern to identify one or more regions affected by linear fading whose linear fading magnitude exceed a linear fading threshold value and given process window condition.5. The non-transitory computer-readable medium of clause 1, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; adjusting the design pattern via optical proximity correction;verifying an outcome of the optical proximity correction to determine a linear fading sensitivity of the adjusted design pattern.6. The non-transitory computer-readable medium of clause 1, wherein:the pupil profile is output by a baseline source-mask optimization (SMO) process;the adjusting is part of a linear-fading-based SMO process; andthe operations further comprise:comparing an output of the baseline SMO process and the linear-fading-based SMO process.7. The non-transitory computer-readable medium of clause 6, wherein the comparing is based on a metric comprising:a process window;an image log slope; ora critical dimension error.8. The non-transitory computer-readable medium of clause 1, wherein the linear fading effect is quantified using a rate of change of a distortion of the prediction with respect to a scanning direction used in the lithography process.9. The non-transitory computer-readable medium of clause 1, wherein the linear fading effect is associated with a wafer-bonding linear fading effect.10. The non-transitory computer-readable medium of clause 1, wherein the linear fading effect is quantified using a distribution of moving standard deviation associated with vibrations of a scanning operation used in the lithography process.11. A method for optimizing an illumination source and mask used in a lithography process, the method comprising:obtaining a pupil profile;simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process;calculating a cost function based on the predictions, wherein the cost function comprises a linear fading effect term that is indicative of a linear fading effect on the predictions;adjusting the pupil profile based on the linear fading effect term.12. The method of clause 11, wherein the linear fading effect term is a function of:an intensity threshold associated with an aerial image; andimaging contrast.13. The method of clause 11, wherein the simulating comprises simulating under perturbed process conditions comprising:perturbed dose conditions; andan add-on perturbed linear fading condition for each perturbed dose condition.14. The method of clause 11, further comprising:obtaining design pattern information comprising a layout to be projected onto a substrate; analyzing regions of the design pattern to identify one or more regions affected by linear fading whose linear fading magnitude exceed a linear fading threshold value and given process window condition.15. The method of clause 11, further comprising:obtaining design pattern information comprising a layout to be projected onto a substrate; adjusting the design pattern via optical proximity correction;verifying an outcome of the optical proximity correction to determine a linear fading sensitivity of the adjusted design pattern.16. The method of clause 11, wherein:the pupil profile is output by a baseline source-mask optimization (SMO) process;the adjusting is part of a linear-fading-based SMO process; andthe method further comprises:comparing an output of the baseline SMO process and the linear-fading-based SMO process.17. The method of clause 16, wherein the comparing is based on a metric comprising:a process window;an image log slope; ora critical dimension error.18. The method of clause 11, wherein the linear fading effect is quantified using a rate of change of a distortion of the prediction with respect to a scanning direction used in the lithography process. 19. The method of clause 11, wherein the linear fading effect is associated with a wafer-bonding linear fading effect.20. The method of clause 11, wherein the linear fading effect is quantified using a distribution of moving standard deviation associated with vibrations of a scanning operation used in the lithography process.21. A system comprising:one or more processorsone or more memory devices configured to store a set of instructions that is executable by the one or more processors to cause the system to perform operations for optimizing an illumination source and mask used in a lithography process, the operations comprising:obtaining a pupil profile;simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process;calculating a cost function based on the predictions, wherein the cost function comprises a linear fading effect term that is indicative of a linear fading effect on the predictions;adjusting the pupil profile based on the linear fading effect term.22. The system of clause 21, wherein the linear fading effect term is a function of:an intensity threshold associated with an aerial image; andimaging contrast.23. The system of clause 21, wherein the simulating comprises simulating under perturbed process conditions comprising:perturbed dose conditions; andan add-on perturbed linear fading condition for each perturbed dose condition.24. The system of clause 21, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; analyzing regions of the design pattern to identify one or more regions affected by linear fading whose linear fading magnitude exceed a linear fading threshold value and given process window condition.25. The system of clause 21, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; adjusting the design pattern via optical proximity correction;verifying an outcome of the optical proximity correction to determine a linear fading sensitivity of the adjusted design pattern.26. The system of clause 21, wherein:the pupil profile is output by a baseline source-mask optimization (SMO) process;the adjusting is part of a linear-fading-based SMO process; andthe operations further comprise:comparing an output of the baseline SMO process and the linear-fading-based SMO process.27. The system of clause 26, wherein the comparing is based on a metric comprising:a process window;an image log slope; ora critical dimension error.28. The system of clause 21, wherein the linear fading effect is quantified using a rate of change of a distortion of the prediction with respect to a scanning direction used in the lithography process. 29. The system of clause 21, wherein the linear fading effect is associated with a wafer-bonding linear fading effect.30. The system of clause 21, wherein the linear fading effect is quantified using a distribution of moving standard deviation associated with vibrations of a scanning operation used in the lithography process.

[0112] 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 can be made without departing from the scope thereof.

Claims

CLAIMS1. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing an illumination source and mask used in a lithography process, the operations comprising:obtaining a pupil profile;simulating the lithography process using the pupil profile to generate predictions resulting from the lithography process;calculating a cost function based on the predictions, wherein the cost function comprises a linear fading effect term that is indicative of a linear fading effect on the predictions;adjusting the pupil profile based on the linear fading effect term.

2. The non-transitory computer-readable medium of claim 1, wherein the linear fading effect term is a function of:an intensity threshold associated with an aerial image; andimaging contrast.

3. The non-transitory computer-readable medium of claim 1, wherein the simulating comprises simulating under perturbed process conditions comprising:perturbed dose conditions; andan add-on perturbed linear fading condition for each perturbed dose condition.

4. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; analyzing regions of the design pattern to identify one or more regions affected by linear fading whose linear fading magnitude exceed a linear fading threshold value and given process window condition.

5. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise:obtaining design pattern information comprising a layout to be projected onto a substrate; adjusting the design pattern via optical proximity correction;verifying an outcome of the optical proximity correction to determine a linear fading sensitivity of the adjusted design pattern.

6. The non-transitory computer-readable medium of claim 1, wherein:the pupil profile is output by a baseline source-mask optimization (SMO) process;the adjusting is part of a linear-fading-based SMO process; andthe operations further comprise:comparing an output of the baseline SMO process and the linear-fading-based SMO process.

7. The non-transitory computer-readable medium of claim 6, wherein the comparing is based on a metric comprising:a process window;an image log slope; ora critical dimension error.

8. The non-transitory computer-readable medium of claim 1, wherein the linear fading effect is quantified using a rate of change of a distortion of the prediction with respect to a scanning direction used in the lithography process.

9. The non-transitory computer-readable medium of claim 1, wherein the linear fading effect is associated with a wafer-bonding linear fading effect.

10. The non-transitory computer-readable medium of claim 1, wherein the linear fading effect is quantified using a distribution of moving standard deviation associated with vibrations of a scanning operation used in the lithography process.

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