Patterning device and system, product, and method for generating the pattern therefor.

Abstract

To provide systems, products, and methods for generating patterning devices and patterns therefor.SOLUTION: Described herein is a method for improving a design of a patterning device. The method includes (i) obtaining mask points of a design of a mask feature, wherein the mask feature corresponds to a target feature in a target pattern to be printed on a substrate; and (ii) adjusting locations of the mask points to generate a modified design of the mask feature based on the adjusted mask points.SELECTED DRAWING: Figure 6B

Description

Technical Field

[0001] Cross - Reference to Related Applications

[0001] This application claims the priority of U.S. Patent Application No. 63 / 034,343, filed on June 3, 2020, U.S. Patent Application No. 63 / 037,513, filed on June 10, 2020, and U.S. Patent Application No. 63 / 122,760, filed on December 8, 2020, the entire contents of which are incorporated herein by reference.

[0002]

[0002] The description herein generally relates to patterning devices and systems, products, and methods for generating patterns thereof.

Background Art

[0003]

[0003] Lithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device (e.g., a mask) can contain or provide patterns ("design layouts") corresponding to individual layers of the IC, and these patterns can be transferred onto target portions (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) coated with a layer of radiation-sensitive material ("resist") by methods such as irradiating target portions through the pattern on the patterning device. Generally, a single substrate contains multiple adjacent target portions (one target portion at a time) onto which patterns are successively transferred by the lithography projection equipment. In some types of lithography projection equipment, the pattern on the entire patterning device is transferred onto one target portion at a time, and such equipment is generally called a stepper. In alternative equipment, generally called a step-and-scan device, the projection beam moves the substrate parallel or antiparallel to a given reference direction ("scan" direction) in synchronization with scanning the patterning device in this reference direction. Different parts of a pattern on a patterning device are progressively transferred to a single target area. Generally, since the lithography projection apparatus has a reduction ratio M (e.g., 4), the speed F at which the substrate is moved is the speed at which the projection beam scans the patterning device × 1 / M. Further information regarding lithography devices such as those described herein can be found, for example, in U.S. Patent No. 6,046,792, incorporated herein by reference.

[0004]

[0004] Before transferring the pattern from the patterning device to the substrate, the substrate may undergo various procedures such as priming, resist coating, and soft baking. After exposure, the substrate may undergo other procedures such as post-bake (PEB), development, hard baking, and measurement / inspection of the transferred pattern ("post-exposure procedures"). These numerous procedures are used as a basis for creating the individual layers of a device, such as an IC. The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, and chemical mechanical polishing (all intended to finish the individual layers of the device). If several layers are required for the device, the entire procedure or variations thereof are repeated for each layer. Finally, the device is present in each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, so that the individual devices can be mounted on a carrier, connected to pins, etc.

[0005]

[0005] Accordingly, manufactured devices such as semiconductor devices generally involve processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the device. Such layers and features are generally manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices may be fabricated on multiple dies on a substrate and then separated into individual devices. This device manufacturing process can be considered a patterning process. The patterning process includes a patterning step such as optical and / or nanoimprint lithography using a patterning device in a lithography apparatus to transfer a pattern on the patterning device to a substrate, and generally (but optionally) includes one or more related pattern processing steps such as resist development with a developing apparatus, baking of the substrate with a baking tool, and etching using the pattern with an etching apparatus.

[0006]

[0006] As described above, lithography is a central step in the manufacturing of devices such as ICs, where patterns formed on a substrate define the functional elements of devices such as microprocessors and memory chips. Similar lithography techniques are also used in the formation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007]

[0007] As semiconductor manufacturing processes continue to advance, the dimensions of functional elements are continuously decreasing, while the number of functional elements, such as transistors, per device has steadily increased over decades, following a trend generally known as "Moore's Law." In the current technological state, layers of devices are manufactured using lithography projection equipment that projects a design layout onto a substrate using illumination from a deep ultraviolet light source, producing individual functional elements with dimensions far below 100 nm (i.e., less than half the wavelength of radiation from the light source (e.g., a 193 nm light source)).

[0008]

[0008] This process, in which features with dimensions below the classical limiting resolution of a lithography projector are printed, is generally known as low-k1 lithography, given by the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently, in most cases, 248 nm or 193 nm), NA is the numerical aperture of the projection optical system in the lithography projector, CD is the "critical dimension" (generally the smallest feature size to be printed), and k1 is the empirical resolution coefficient. Generally, the smaller k1, the more difficult it becomes to reproduce on the substrate a pattern that closely resembles the shape and dimensions planned by the designer to achieve a particular electrical functionality and performance. To overcome these difficulties, state-of-the-art fine-tuning steps are applied to the lithography projector, design layout, or patterning device. These include, for example, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shift patterning devices, optical proximity effect correction (OPC, sometimes also called "optical and process correction") in design layouts, or other methods generally defined as “resolution enhancement techniques” (RET). As used herein, the term “projection optics” is to be broadly interpreted to encompass a variety of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractory optics. The term “projection optics” may also include components that operate according to any of these design types to guide, shape, or control the projected beam of radiation, either collectively or individually. The term “projection optics” may include any optical component within a lithography projection apparatus, regardless of where the optical component is located in the optical path of the lithography projection apparatus. A projection optical system may include optical components for shaping, adjusting, and / or projecting radiation before it passes through a patterning device, and / or optical components for shaping, adjusting, and / or projecting radiation after it has passed through a patterning device. Generally, the projection optical system excludes the source and the patterning device. [Overview of the Initiative]

[0009]

[0009] According to one embodiment, a non-temporary computer-readable medium is provided which, when executed by a computer, causes the computer to perform a method for improving the design of a patterning device, the method comprising (i) obtaining mask points of a design of a mask feature, the mask feature corresponding to a target feature in a target pattern to be printed on a substrate, and (ii) adjusting the position of the mask points to generate a modified design of the mask feature based on the adjusted mask points.

[0010]

[0010] According to one embodiment, a non-temporary computer-readable medium is provided which, when executed by a computer, causes the computer to perform a method for improving the design of a patterning device, the method comprising: (i) obtaining mask points of a design of mask features, the mask features corresponding to target features in a target pattern to be printed on a substrate; and (ii) adjusting the position of the mask points to increase the process window, the process window being associated with a patterning process for printing the target pattern on a substrate, and the adjustment including generating a modified design based on the adjusted position.

[0011]

[0011] According to one embodiment, a method is provided for improving the design of a patterning device, the method comprising (i) obtaining mask points of a design of a mask feature, the mask feature corresponding to a target feature in a target pattern to be printed on a substrate, and (ii) adjusting the position of the mask points to generate a modified design of the mask feature based on the adjusted mask points. [Brief explanation of the drawing]

[0012] [Figure 1]

[0012] Block diagrams of various subsystems of the lithography system are shown. [Figure 2]

[0013] This shows exemplary categories of process variables. [Figure 3]

[0014] A schematic flow of a patterning simulation method according to one embodiment is shown. [Figure 4]

[0015] A schematic diagram of the measurement simulation method according to one embodiment is shown below. [Figure 5A]

[0016] This is a flowchart of a method for generating or improving the design of a mask feature corresponding to a target pattern, which is consistent with various embodiments. [Figure 5B]

[0017] This is a flowchart of a method for generating an initial design of a mask feature that is consistent with various embodiments. [Figure 5C]

[0018] This is a flow diagram of the process for optimizing the initial design of a mask feature, consistent with various embodiments. [Figure 6A]

[0019] This shows target features and initial mask points with control points, consistent with various embodiments. [Figure 6B]

[0020] This shows a mask feature design obtained from a different process, consistent with various embodiments. [Figure 7]

[0021] This describes a process for applying a smoothing treatment to mask points, consistent with various embodiments. [Figure 8]

[0022] This shows a perturbed version of the initial design of the mask feature, consistent with various embodiments. [Figure 9]

[0023] This shows an optimized design for mask features that is consistent with various embodiments. [Figure 10A]

[0024] An application example of a point-based optimization process is shown that generates an optimized design of mask features for a target feature of a first shape that is consistent with various embodiments. [Figure 10B]

[0025] An application example of a point-based optimization process is shown that generates an optimized design of mask features for a target feature of a second shape that is consistent with various embodiments. [Figure 10C]

[0026] An application example of a point-based optimization process is shown that generates an optimized design of mask features for a target feature and a sub-resolution assist feature (SRAF) that is consistent with various embodiments. [Figure 10D]

[0027] An application example of a point-based optimization process is shown that generates an optimized design of mask features for a target feature rather than an SRAF that is consistent with various embodiments. [Figure 11]

[0028] A block diagram of an exemplary computer system according to one embodiment. [Figure 12]

[0029] A schematic diagram of a lithographic projection apparatus according to one embodiment. [Figure 13]

[0030] A schematic diagram of another lithographic projection apparatus according to one embodiment. [Figure 14]

[0031] A more detailed view of the apparatus of FIG. 12 according to one embodiment. [Figure 15]

[0032] A more detailed view of the source collector module SO of the apparatuses of FIGS. 13 and 14 according to one embodiment. [Figure 16A]

[0033] A curved design of mask features is shown that is consistent with various embodiments. [Figure 16B]

[0034] A polygonal design of mask features is shown that is consistent with various embodiments. [Figure 16C]

[0035] Curved and polygonal designs for mask features, consistent with various embodiments, are shown. [Figure 16D]

[0036] Curved and polygonal designs for mask features, consistent with various embodiments, are shown. [Figure 17]

[0037] This demonstrates a hybrid design of mask features that is consistent with various embodiments. [Figure 18]

[0038] This shows that a flow diagram for implementing the "full-angle OPC" method described in Figure 5A may be implemented, which is consistent with various embodiments. [Modes for carrying out the invention]

[0013]

[0039] In lithography, a patterning device (e.g., a mask) may provide a mask pattern (e.g., a mask design layout) corresponding to a target pattern (e.g., a target design layout), which may be transferred onto a substrate by transmitting light through the mask pattern. However, due to various constraints, the transferred pattern may appear with many irregularities and therefore may not resemble the target pattern. Optical proximity correction (OPC) is a commonly used extension technique when designing mask patterns to compensate for image errors caused by diffraction or other process effects in lithography. Current OPC techniques enhance the design of mask features by iteratively adjusting segments of the design (e.g., to minimize signals such as resist image or etching image signals), and then stitch the corrected segments together to form a corrected design. Some techniques enhance the design to optimize cost functions, such as edge placement error, mask rule check, symmetry, etc. Some techniques optimize the cost function by correcting all segments together. Some techniques use image-based extension methods such as freeform techniques. In this technique, a freeform mask design is generated from an initial image (e.g., a CTM (Continuum Transmission Mask) image), and this freeform mask design is iteratively refined to optimize image variable pixels. However, at least some of the current techniques are inefficient. This is because they may suffer from convergence problems, have limited process window sizes, require the user to adjust numerous parameters to achieve the desired result, or consume significant amounts of computer resources, such as execution time and memory. These factors prevent the use of these techniques in manufacturing lines.

[0014]

[0040] This disclosure provides a method and system for improving a mask pattern using point-based OPC, or as referred herein, “full-angle OPC.” In point-based OPC, depending on the embodiment, initial mask points may be generated for target features from a target pattern and associated with control points on the target features, for example, one control point may be associated with one or more mask points. The mask points are adjusted to generate a curve pattern (e.g., their position is changed). The mask points may be moved by a specific amount along a specific direction (e.g., the local normal of the curve pattern, or another predetermined direction) to optimize the cost function at the control points, for example. The above process of adjusting the mask points can be repeated to update the curve pattern and achieve convergence.

[0015]

[0041] In some embodiments, point-based OPC provides a final or intermediate design for a mask with a curved pattern, which is more natural than an extended design generated from known techniques. In some embodiments, multiple mask points can be consistently moved to optimize the cost function at one or more control points, which may allow for finer and more precise local control of the mask design and improve overall lithography performance. In some embodiments, the association between control points and mask points may be dissociated and re-established, for example, when the mask design deviates significantly from the target feature, which allows for more efficient optimization at control points by intelligently selecting the mask points to be corrected (in contrast, in the prior art, the association between a segment and a control point remains fixed even when the segment is already considerably far from the control point (e.g., near a corner of the target feature)). Using full-angle OPC technology, it is possible to generate curved patterns, non-curved patterns (e.g., polygonal patterns where the angle between the pattern segment or line and the horizontal axis is 45*n degrees or 90*n degrees (where n is an integer)), or hybrid designs (e.g., designs that are partially curved and partially polygonal) for mask features.

[0016]

[0042] Briefly, Figure 1 shows an exemplary lithography projection apparatus 10A. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including an extreme ultraviolet (EUV) source (as described above, the lithography projection apparatus itself does not need to have a radiation source); an illumination optical system which may include optical systems 14A, 16Aa, and 16Ab that define partial coherence (represented by sigma) and shape the radiation from the source 12A; a patterning device 18A; and a transmission optical system 16Ac that projects an image of the pattern of the patterning device onto the substrate surface 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optical system can limit the range of beam angles that collide with the substrate surface 22A, where the maximum possible angle defines the numerical aperture NA = n sin(Θmax) of the projection optical system, where n is the refractive index of the medium between the substrate and the last element of the projection optical system, and Θmax is the maximum angle of the beam leaving the projection optical system that can still collide with the substrate surface 22A.

[0017]

[0043] In a lithography projection apparatus, a source provides illumination (i.e., radiation) to a patterning device, and a projection optical system guides and shapes the illumination onto the substrate via the patterning device. The projection optical system may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The spatial image (AI) is the radiation intensity distribution at the substrate level. A resist image can be calculated from the spatial image using a resist model, an example of which can be found in U.S. Patent Application Publication 2009-0157360, the disclosure of which is incorporated herein by reference in whole. The resist model is concerned only with the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of the lithography projection apparatus (e.g., properties of the illumination, patterning device, and projection optical system) determine the spatial image, which can be defined by the optical model. Since the patterning device used in a lithography projection apparatus can be modified, it is desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithography projection apparatus, including at least the source and projection optics. Details of the above techniques and models used to convert design layouts into various lithographic images (e.g., spatial images, resist images, etc.), to apply OPC using techniques and models, and to evaluate performance (e.g., in terms of process window) are described in U.S. Patent Publications 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the contents of which are incorporated herein by reference in whole.

[0018]

[0044] A patterning device may contain or form one or more design layouts. Design layouts can be generated using a CAD (computer-aided design) program, a process often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules to create functional design layouts / patterning devices. These rules are set by processing and design constraints. For example, design rules define space tolerances between devices (gates, capacitors, etc.) or interconnection lines to ensure that devices or lines do not interact with each other in undesirable ways. One or more of these design rule constraints are sometimes called "critical dimensions" (CDs). The critical dimension of a device may be defined as the minimum width of a line or hole, or the minimum space between two lines or two holes. Thus, the CD determines the overall size and density of the designed device. Naturally, one of the goals of device manufacturing is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0019]

[0045] As used herein, the terms “mask” or “patterning device” can be broadly interpreted to refer to any general patterning device that can be used to impart a patterned cross-section to an incoming radiation beam, corresponding to a pattern to be generated on a target portion of a substrate. The term “light bulb” may also be used in this context. In addition to conventional masks (transmissive or reflective, binary, phase-shifted, hybrid, etc.), other examples of such patterning devices include: - Programmable mirror arrays. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and reflective surfaces. The basic principle behind such a device is that (for example) the address area of ​​the reflective surface reflects incident radiation as diffracted radiation, while the non-addressed area reflects incident radiation as non-diffracted radiation. Using appropriate filters, the aforementioned non-diffracted radiation can be removed from the reflected beam, leaving only the diffracted radiation behind, so that the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be carried out using appropriate electronic means. - Programmable LCD array. An example of such a structure is given by U.S. Patent No. 5,229,872, which is incorporated herein.

[0020]

[0046] One aspect of understanding the lithography process is to understand the interaction between radiation and the patterning device. The electromagnetic field of the radiation after it has passed through the patterning device can be determined from the electromagnetic field of the radiation before it reaches the patterning device and a function that characterizes the interaction. This function is sometimes called the mask transmission function (this function can be used to describe the interaction between transmission and / or reflection patterning devices).

[0021]

[0047] The variables of the patterning process are called “process variables.” The patterning process may include upstream and downstream processes of the actual transfer of the pattern in the lithography apparatus. Figure 2 shows exemplary categories of process variables 370. The first category may be variables 310 of the lithography apparatus or any other apparatus used in the lithography process. Examples of this category include variables such as the illumination, projection system, and substrate stage of the lithography apparatus. The second category may be variables 320 of one or more procedures performed in the patterning process. Examples of this category include focus control or focus measurement, dose control or dose measurement, bandwidth, exposure duration, development temperature, and chemical composition used in development. The third category may be variables 330 of the design layout and the implementation of the design layout in or using the patterning device. Examples of this category include the shape and / or position of assist features, the amount of adjustment applied by resolution enhancement techniques (RET), and the CD of mask features. The fourth category may be variables 340 of the substrate. Examples include the structural features beneath the resist layer, the chemical composition and / or physical dimensions of the resist layer. The fifth category may be features of the time variation of one or more variables in the patterning process.350 Examples of this category include features of high-frequency stage movement (e.g., frequency, amplitude, etc.), high-frequency changes in laser bandwidth (e.g., frequency, amplitude, etc.), and / or high-frequency changes in laser wavelength. These high-frequency changes or movement exceed the response time of the mechanisms for adjusting the underlying variables (e.g., stage position, laser intensity). The sixth category may be features of upstream or downstream processes of pattern transfer in a lithography apparatus, such as spin coating, post-exposure baking (PEB), development, etching, deposition, doping, and / or packaging.360

[0022]

[0048] As will be understood, many, if not all, of these variables influence the parameters of the patterning process, often the parameters of interest. Non-limiting examples of patterning process parameters include critical dimension (CD), critical dimension uniformity (CDU), focus, overlay, edge position or placement, sidewall angle, and pattern shift. Often, these parameters represent errors from nominal values ​​(e.g., design values, mean values, etc.). Parameter values ​​can be values ​​for individual pattern features or statistical values ​​of group features (e.g., mean, variance, etc.).

[0023]

[0049] Some or all of the process variables, or their associated parameters, may be determined by appropriate methods. For example, their values ​​may be determined from data obtained using various measuring tools (e.g., substrate measuring tools). Their values ​​may be obtained from various sensors or systems of the equipment in the patterning process (e.g., sensors such as leveling or alignment sensors in a lithography apparatus, control systems of a lithography apparatus (e.g., substrate or patterning device table control systems), sensors in track tools, etc.). Their values ​​may also come from the patterning process operator.

[0024]

[0050] Figure 3 shows an exemplary flowchart for modeling and / or simulating a portion of the patterning process. It will be understood that the model may represent different patterning processes and does not necessarily include all the models described below. The radiator model 1200 represents the optical characteristics of the illumination of the patterning device (including radiant intensity distribution, bandwidth, and / or phase distribution). The radiator model 1200 may represent optical characteristics of illumination including, but not limited to, numerical aperture settings, illumination sigma (σ) settings, and any specific illumination shape (e.g., annular, quadrupole, dipole, or other off-axis radiating shapes), (where σ (i.e., sigma) is the outer radius range of the illuminator).

[0025]

[0051] Projection optical system model 1210 represents the optical characteristics of the projection optical system (including changes in the radiant intensity distribution and / or phase distribution caused by the projection optical system). Projection optical system model 1210 can represent the optical characteristics of the projection optical system, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0026]

[0052] The patterning device / design layout model module 1220 captures how design features are arranged within the pattern of the patterning device and may include a representation of the detailed physical properties of the patterning device, as described in, for example, U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In one embodiment, the patterning device / design layout model module 1220 represents the optical properties of the design layout (e.g., a device design layout corresponding to features such as integrated circuits, memory, or electronic devices) (which is a representation of the arrangement of features on or formed by the patterning device), including changes in radiant intensity distribution and / or phase distribution caused by a given design layout. Since the patterning device used in a lithography projection apparatus can be modified, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithography projection apparatus, including at least the illumination and projection optics. The purpose of the simulation is often to accurately predict, for example, edge placement and CD, which may then be compared to the device design. Device designs are generally defined as pre-OPC patterned device layouts and are provided in standard digital file formats such as GDSII or OASIS.

[0027]

[0053] The spatial image 1230 can be simulated from the radiation source model 1200, the projection optics model 1210, and the patterning device / design layout model 1220. The spatial image (AI) is the radiation intensity distribution at the substrate level. The optical properties of the lithography projection apparatus (e.g., illumination, patterning device, and projection optics properties) define the spatial image.

[0028]

[0054] A resist layer on a substrate is exposed by a spatial image, and the spatial image is transferred to the resist layer as a potential “resist image” (RI). The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. The resist image 1250 can be simulated from the spatial image 1230 using a resist model 1240. An example of calculating a resist image from a spatial image using a resist model is described in U.S. Patent Application Publication 2009-0157360, which is incorporated herein by reference in its entirety. The resist model typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development, for example, to predict the contour of resist features formed on a substrate, and thus the resist model typically relates only to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and development). In one embodiment, optical properties of the resist layer, such as refractive index, film thickness, propagation, and polarization effects, may be captured as part of a projection optics model 1210.

[0029]

[0055] Therefore, generally, the link between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which arises from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections within the resist film stack. This radiation intensity distribution (spatial image intensity) is transformed into a potential "resist image" by the absorption of incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the actual three-dimensional intensity distribution within the resist stack using a two-dimensional spatial (and resist) image.

[0030]

[0056] In one embodiment, the resist image may be used as input to the post-pattern transfer process model module 1260. The post-pattern transfer process model module 1260 defines the performance of one or more post-resist development processes (e.g., etching, development, etc.).

[0031]

[0057] By simulating the patterning process, it is possible to predict, for example, contours, CD, and edge placement (e.g., edge placement error) in the resist and / or etched image. Therefore, the purpose of the simulation is to accurately predict, for example, the edge placement of the printed pattern, and / or the spatial image intensity gradient, and / or CD. These values ​​may be compared to the intended design, for example, to correct the patterning process or to identify locations where defects are expected to occur. The intended design is generally defined as a pre-OPC design layout, which can be provided in a standard digital file format such as GDSII, OASIS, or other file formats.

[0032]

[0058] Therefore, it is desirable that the model representation describes most, if not all, of the known physical and chemical phenomena of the entire process, and that each model parameter corresponds to a different physical or chemical effect. Thus, the model representation sets an upper limit on how well the entire manufacturing process can be simulated using that model.

[0033]

[0059] Figure 4 shows an exemplary flowchart for modeling and / or simulating the measurement process. As will be understood, the following models may represent different measurement processes and do not necessarily include all the models described below (for example, several models may be combined). Radiation source model 1300 represents the optical characteristics of the illumination of the measurement target (including radiant intensity distribution, radiant wavelength, polarization, etc.). Radiation source model 1300 can represent optical characteristics of illumination including, but not limited to, wavelength, polarization, illumination sigma (σ) setting (where σ (i.e., sigma) is the radial range of illumination of the illuminator), and any specific illumination shape (e.g., off-axis radiation shapes such as ring, quadrupole, or dipole).

[0034]

[0060] The measurement optics model 1310 represents the optical characteristics of the measurement optics (including changes in the radiant intensity distribution and / or phase distribution produced by the measurement optics). The measurement optics model 1310 can represent the optical characteristics of the illumination of the measurement target by the measurement optics, and the optical characteristics of the transmission of radiation redirected from the measurement target to the measurement device detector. The measurement optics model can represent various characteristics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc., including the illumination of the target and the transmission of radiation redirected from the measurement target to the detector.

[0035]

[0061] The measurement target model 1320 can represent the optical characteristics of illumination redirected by the measurement target (including changes in the illumination radiation intensity distribution and / or phase distribution caused by the measurement target). Therefore, the measurement target model 1320 can model the conversion from illumination radiation to radiation redirected by the measurement target. Thus, the measurement target model can simulate the resulting illumination distribution from the redirected radiation from the measurement target. The measurement target model can represent various features, including one or more refractive indices, one or more physical sizes of the measurement, the physical layout of the measurement target, etc., including the illumination of the target and the generation of redirected radiation from the measurement. Since the measurement target used can be changed, it is desirable to separate the optical characteristics of the measurement target from the optical characteristics of the rest of the measurement device, including at least the illumination and projection optics and detector. Often, the purpose of the simulation is to accurately predict, for example, intensity, phase, etc., which can then be used to derive parameters of interest in the patterning process, such as overlay, CD, and focus.

[0036]

[0062] The pupil or spatial image 1330 can be simulated from the radiation source model 1300, the measurement optics model 1310, and the measurement target model 1320. The pupil or spatial image is the radiation intensity distribution at the detector level. The optical properties of the measurement optics and measurement target (e.g., illumination, measurement target, and measurement optics properties) define the pupil or spatial image.

[0037]

[0063] The detector of the measuring device is exposed to a pupil or spatial image and detects one or more optical properties of the pupil or spatial image (e.g., intensity, phase, etc.). The detection model module 1320 represents how radiation from the measuring optical system is detected by the detector of the measuring device. The detection model can describe how the detector detects the pupil or spatial image and may include signal-to-noise, sensitivity to incident radiation to the detector, etc. Thus, generally, what connects the measuring optical system model and the detector model is a simulated pupil or spatial image, which arises from the illumination of the measurement target by the optical system, the redirection of radiation by the target, and the transmission of the redirected radiation to the detector. The radiation distribution (pupil or spatial image) is converted into a detection signal by the absorption of incident energy on the detector.

[0038]

[0064] By simulating the measurement process, it is possible to predict other calculated values ​​from the detection system, such as spatial intensity signals and spatial phase signals in the detector, or overlay and CD values ​​based on detection of the pupil or spatial image by the detector. Therefore, the purpose of the simulation is to accurately predict, for example, the detector signal corresponding to the measurement target, or the derived values ​​of overlay, CD, etc. By comparing these values ​​with the intended design values, it is possible to, for example, correct the patterning process or identify locations where defects are expected to occur.

[0039]

[0065] Therefore, it is desirable that the model representation explains most, if not all, of the known physical and chemical phenomena of the entire measurement process, and that each model parameter corresponds to a different physical and / or chemical effect in the measurement process.

[0040]

[0066] The various patterns on or provided by a patterning device may have different process windows, i.e., the space of process variables that generate the pattern within the specified range. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlap, resist top loss, resist undercut, and / or bridging. Typically, the process window is defined for two process variables, namely dose and focus, so that the CD obtained after patterning can be within ±10% of the desired CD of the pattern features. The process window for all patterns on the patterning device or its area may be obtained by combining (e.g., overlapping) the process windows of each individual pattern.

[0041]

[0067] Figure 5A is a flowchart of an exemplary method 500 for generating or improving the design of mask features corresponding to a target pattern printed on a substrate via a patterning process including a lithography process, consistent with various embodiments. In one embodiment, the target pattern may be a binary design layout, a continuous tone design layout, or another suitable design layout. The target pattern may include one or more target features to be printed on the substrate, and the mask pattern may include mask features corresponding to one or more target features. In some embodiments, the design of the target features may be polygonal, and the design of the corresponding mask features may be a curved pattern. The mask features may be primary features corresponding to target features or subresolution assist features (SRAFs).

[0042]

[0068] In process P501, mask points are obtained for the design of the mask feature. Depending on the embodiment, mask points are a set of points located on the mask feature. The design of the mask feature can be modified by adjusting the mask points (for example, by moving them to different locations). The mask points are derived from an existing design of the mask feature or from a target feature, in which case the mask points are connected by lines (smoothly) to form the initial design. Depending on the embodiment, the initial design is a curved pattern. Further details of obtaining mask points or generating the initial design are described with reference to process 550 in Figure 5B at least.

[0043]

[0069] In process P503, the initial design is optimized by adjusting the position of mask points. Adjusting the position of mask points generates a modified design of the mask features (hence the term "point-based optimization process"). Depending on the embodiment, the position of mask points is adjusted so that a cost function is optimized. The cost function may include one or more of the following: edge placement error (EPE), simulated signals such as the resist image signal (or etching image signal), mask rule check (MRC) penalty, process window, etc. Process P503 may use one or more cost functions, and different cost functions may be optimized in different ways.

[0044]

[0070] For example, process P503 may optimize a cost function such as EPE by reducing the EPE of one or more target features (e.g., until it is minimized). In some embodiments, EPE is the distance between a point on a contour in the resist image (e.g., a contour corresponding to a mask feature) and the intended location of that point (e.g., a control point on a target feature).

[0045]

[0071] In another example, process P503 may optimize a cost function such as the simulated signal by reducing the simulated signal of one or more target features (e.g., until it is minimized). In some embodiments, the simulated signal may be obtained from a resist image (or etching image), which may be obtained from a modified design of the mask feature, for example, by simulating it using a resist model (or etching model).

[0046]

[0072] In another example, process P503 may optimize a cost function, such as an MRC violation penalty, by reducing the MRC violation penalty (e.g., until it is minimized). Depending on the embodiment, MRC is an image regularization method for reducing the complexity of the mask patterns that can be generated. MRC refers to a constraint on the mask manufacturing process or apparatus. The penalty may be a term in the cost function, which depends on the amount of violation, e.g., the difference between a mask measurement and a given MRC or mask parameter (e.g., the width of the mask pattern and the allowable (e.g., minimum or maximum) mask pattern width).

[0047]

[0073] In another example, process P503 may optimize a cost function such as the process window by increasing the process window (e.g., until it is maximized). In some embodiments, increasing the process window includes increasing the range of dose or focus values. In some embodiments, the process window of a patterning process includes the range of values ​​for radiation source parameters such as dose and focus of a lithography apparatus used to print a target pattern onto a substrate using a mask pattern.

[0048]

[0074] In some embodiments, the position adjustment process P503 is an iterative process, and the adjustment iterations are performed until a specified condition is met. This condition may be that a predetermined number of iterations are performed, or that the cost function is optimized. Furthermore, the modified design is updated with each iteration (e.g., by adjusting the position of one or more mask points), and the output of the final iteration, e.g., the final modified design, may be used to manufacture a mask pattern. The mask pattern may have additional structural features, such as an SRAF corresponding to the modified design. The mask pattern may then be used to transfer the modified design onto a substrate using a lithography apparatus.

[0049]

[0075] Further details regarding the optimization of the initial design of the mask feature are explained by referring at least to process 575 in Figure 5C.

[0050]

[0076] Figure 5B is a flowchart of method 550 for generating an initial design of a mask feature, consistent with various embodiments. In some embodiments, process 550 is performed as part of process P501 of process 500. In process P505, a target pattern 501 is obtained. The target pattern 501 may include one or more target features, such as the target feature 602 in Figure 6A. Figure 6A shows a target feature and initial mask point with control points, consistent with various embodiments. The target feature can be any shape, e.g., a circle, an ellipse, a polygon, etc. For example, target feature 602 is rectangular in shape. Continuing with process P505, target feature 602 is associated with several control points, such as control point 656 and control point 662. In some embodiments, the control points are associated with target feature 602 by dividing target feature 602 into several segments and placing one or more control points on the edges of target feature 602 in each segment. In the example in Figure 6A, control point 656 and another similar control point are located at the midpoint of the short side of the target feature 602, while several control points, including control point 662, are located on the long side of the target feature 602. Depending on the embodiment, control points on the target feature may be located at user-defined locations on one or more sides of the target feature.

[0051]

[0077] Multiple mask points 503, such as mask points 604 and 606, are derived from the target feature 602. The mask points 503 are a set of points that form the design of the mask feature corresponding to the target feature 602. The mask points 503 may be connected using lines (e.g., curves or straight lines) to form the design of the mask feature. In some embodiments, the mask points 503 are connected using curves to form a curved design. In some embodiments, the process of deriving the mask points 503 from the target feature 602 includes, for example, generating the mask points 503 at user-defined locations on or near the target feature 602. As shown in Figure 6A, some mask points, such as mask point 604, are located on the edges of the target feature 602, and some mask points, such as mask point 606, are located near the edges or corners of the target feature 602. The mask points 503 may be adjusted, for example, by changing the position of the mask points, to update the design (at least as described below with reference to Figure 5C).

[0052]

[0078] A point-based OPC process may begin with an initial design of a mask feature generated in various ways. For example, the initial design of the mask feature may be generated from the target feature 602 by using mask points 503 derived from the target feature 602 (as further described below). In another example, the input design 502 of the mask feature may be provided to process P505. The input design 502 may be obtained from or generated using another OPC process. Examples of such OPC processes include machine learning freeform OPC, CTM freeform OPC, CTM+ freeform OPC, segment-based OPC, inverse lithography techniques (ILT), and machine learning (ML) based OPC. Figure 6B shows a mask feature design obtained from another process, consistent with various embodiments. The mask feature design 654 (e.g., input design 502) may be generated from the target feature 602 using one of the OPC processes described above. Furthermore, the design 654 may have a curved shape. If the process receives design 654 as input design 502, the mask points 503 are derived from design 654. For example, the mask points 503 could be a set of points at user-defined locations on design 654.

[0053]

[0079] In process P507, mask points 503 are associated with control points to generate a number of control point-mask point associations 507. For example, a first association is generated between a pair of mask points 658 and a control point 656. This association may be generated based on user-defined input. For example, the user may select a pair of mask points 658 to be associated with a control point 656. In some embodiments, the associations are generated so that each control point is associated with the same number of mask points. For example, as shown in Figure 6B, each control point is associated with three mask points (the association between mask points and control points is shown using edges connecting the mask points and the corresponding control points). However, this is merely an example. Any other suitable mode of associating one or more mask points with each control point can be used without departing from the scope of this disclosure. In some embodiments, the cost function is optimized at the control points by adjusting the position of one or more mask points associated with the control points, as described below with reference to Figure 5C. Furthermore, the association between the mask points and the control points can be changed during the position adjustment process, as will be explained below with reference to Figure 5C.

[0054]

[0080] Process P509 applies a smoothing process to the mask points 503 to generate a mask feature design 509. In some embodiments, the smoothing process may include curve fitting, which is the process of constructing a curve that best fits a set of data points (e.g., constrained). Curve fitting may involve either interpolation, which requires an exact fit to the data, or smoothing, which constructs a “smoothing” function that roughly fits the data. Figure 7 shows a process for applying a smoothing process to mask points that is consistent with various embodiments. In Figure 7, the smoothing process is applied to mask points 503 (e.g., mask points 604 and 606) to generate a curve pattern 702 (e.g., design 509).

[0055]

[0081] In process P511, a perturbation process is applied to design 509 to generate an enlarged (or reduced) design 511, which is an enlarged (or reduced) version of design 509. In some embodiments, the perturbation process enlarges (or reduces) design 509 by moving each of the mask points in a specified direction (e.g., local normal) (e.g., by a specified distance). Figure 8 shows a perturbed version of the initial design of a mask feature, consistent with various embodiments. For example, by applying a perturbation process to a curve pattern 702 (e.g., design 509 generated by a smoothing process), an enlarged version 802 of the curve pattern 702 is generated. The enlarged version 802 may be input into the design optimization process in Figure 5C as the initial design 511 of the mask feature.

[0056]

[0082] Figure 5C is a flow diagram of process 575 for optimizing the design of a mask feature, consistent with various embodiments. In some embodiments, process 575 is performed as part of process P503 of process 500. In process P521, the initial design 511 is received as input. Process models, such as a resist model and an etching model, are applied to the initial design to obtain a simulated image (e.g., a resist image or an etching image), and this simulated image is used to calculate a cost function 521. In some embodiments, the cost function 521 is determined for each control point associated with the target feature 602. As described above, the cost function 521 may be one or more of EPE, simulated signal, process window, etc. For example, a cost function such as EPE may be determined using the simulated image by extracting contours of the mask feature from the simulated image and comparing these contours with the target feature 602 to obtain the EPE at the control points.

[0057]

[0083] In process P523, the position adjustment data 523 for each control point is determined, at least partially based on the cost function 521. Depending on the embodiment, the position adjustment data 523 may include distance and gradient values ​​to which one or more mask points associated with the control point must be moved in order to optimize the cost function 521 (e.g., reduce or minimize EPE). For example, the position adjustment data 523 for a control point 656 may indicate the distance and direction (e.g., a direction such as the local normal of the design or another direction) to which one or more mask points from a set of mask points 658 must be moved to minimize EPE at the control point 656. In determining the position adjustment data 523, the current position of the mask point associated with the control point and geometric information (e.g., shape) of the target feature may also be considered. For example, in determining the position adjustment data 523 for a control point 656, the current position of the mask point 658 and geometric information (e.g., shape) of the target feature 602 may be considered.

[0058]

[0084] In process P525, the positions of one or more mask points associated with each control point are adjusted based on position adjustment data 523 to optimize the cost function 521. Adjusting the positions of one or more mask points generates a modified design 525, for example, as shown in Figure 9.

[0059]

[0085] Figure 9 shows an optimized design of the mask feature consistent with various embodiments. Adjusting the position of one or more mask points in the initial design 511 generates a modified design 902a (e.g., modified design 525). Figure 9 shows that by moving one or more mask points 658 associated with the control point 656, the cost function 521, such as EPE at the control point 656, is reduced from its initial value to "3.5 nm". In some embodiments, the EPE is determined by obtaining a simulated image (e.g., a resist image or an etching image) from the modified design 902a, extracting a contour 912a from the simulated image, and measuring the distance between a point on the contour 912a and the control point 656. In some embodiments, when adjusting the mask points, the process may divide the design into multiple fragments (e.g., arc-shaped fragments) and then adjust those fragments of the design. For example, multiple mask points may be adjusted collectively (e.g., consistently) or individually (e.g., individually).

[0060]

[0086] Process P527 applies a smoothing process to the modified design 902a. As described above, the smoothing process may be a curve fitting process, which constructs a curve that best fits a set of data points (e.g., adjusted mask points).

[0061]

[0087] Process P529 further updates the modified design 902a by applying MRC treatment to ensure that the modified design 902a conforms to the constraints of the mask manufacturing process or equipment (e.g., the mask design width is within the range of an acceptable (e.g., minimum or maximum) mask design width).

[0062]

[0088] In the determination process P531, it is determined whether the optimization conditions have been met. If the optimization conditions are met (for example, the cost function 521 has been optimized, or a predetermined number of iterations have been performed), process 575 terminates. If the optimization conditions are not met, the modified design 902a is input to process P521, and process 575 is repeated to further optimize the cost function 521 by adjusting the mask points and generating another modified design. In some embodiments, process 575, which optimizes the design of the mask features (for example, the initial design 511 or the modified design 902a), is an iterative process, and the iterations (for example, processes P521 to P529 described above) are repeated until the cost function 521 is optimized, or until a predetermined number of iterations have been performed, generating a modified design in each iteration by adjusting one or more mask points. After several iterations, the final modified mask design 525 is generated. In some embodiments, the cost function 521 associated with the final modified design 525 is optimized. For example, in Figure 9, after several iterations, the final modified design 902b (e.g., the final modified design 525) is generated. Note that the cost function 521, such as EPE, in the final modified design 902b at control point 656 is "1.1 nm", which is smaller than the EPE of "3.5 nm" in the first iteration. That is, the EPE decreases as the number of iterations increases (e.g., the cost function 521 is optimized). In some embodiments, the EPE of "1.1 nm" may not be further optimized, and therefore the modified design 902b may be considered the final optimized design of the mask feature corresponding to the target feature 602. In some embodiments, the EPE is determined by obtaining a contour 912b (e.g., from a simulated image as described above) and measuring the distance between a point on the contour 912b and the control point 656.

[0063]

[0089] Depending on the embodiment, the association between mask points and control points may be either "fixed" or "dynamic" while optimizing the modified design 525 over several iterations. For example, in fixed mode, if a first set of mask points is associated with a first control point in the first iteration, the first set of mask points remains associated with the first control point in all iterations. In dynamic mode, if a first set of mask points is associated with a first control point in the first iteration, one or more mask points from the first set of mask points may be associated with a second control point in the second iteration to optimize the cost function 521. That is, existing associations between mask points and control points may be broken and new associations may be established. Such dynamic adjustments are useful in various scenarios, for example, when the modified design has become significantly different from the shape of the target feature (which may be determined by comparing the modified design to the target feature). In this way, the cost function 521 at the control points can be more effectively optimized by intelligently selecting the mask points to be corrected.

[0064]

[0090] In yet another association mode called “soft” mode, there may be no defined association between the mask point and the control point. The mask point may be adjusted based on a cost function 521 associated with each of the control points within a specific distance range of the mask point. Depending on the embodiment, the “soft” mode of the selected association may depend on the geometry of the target feature 602. For example, the amount of adjustment of the mask point may depend on the distance between the mask point and the control point, and the angle between the line connecting the mask point and the control point and the local normal at the mask point.

[0065]

[0091] The above explanation of optimizing cost function 521 has been described in relation to EPE, but other cost functions such as simulated signals or process windows can also be used. If cost function 521 is a simulated signal, process 575 may optimize the simulated signal by adjusting the position of the mask points to reduce the simulated signal (e.g., until it is minimized). In another example, if cost function 521 is a process window, process 575 may optimize the process window by adjusting the position of the mask points to increase the process window (e.g., until it is maximized). In yet another example, if cost function 521 is a combination of one or more metrics such as EPE and process window, process 575 may optimize EPE and process window by adjusting the position of the mask points to reduce EPE (e.g., until it is minimized) and increase the process window (e.g., until it is maximized). Depending on the embodiment, cost functions such as simulated signals or EPE are local cost functions, e.g., cost functions local to control points, while cost functions such as process windows are global cost functions, which relate to one or more target features in general. In some embodiments, conflicts may arise when optimizing both local and global cost functions, in which case the optimization is achieved through compromise (for example, one or more local cost functions may not be optimized while other local cost functions or global costs are optimized, or vice versa). For example, if a simulated signal or EPE at one control point is affected by a simulated signal or EPE at another control point, such as an adjacent control point, both local cost functions may not be optimized simultaneously, and a compromise optimization may be adopted, for example, one of them may be optimized, or both may be optimized to the extent that one does not affect the other (for example, the EPE may be reduced but not minimized).

[0066]

[0092] While the above description concerns the optimization of the design of a single mask feature, a mask pattern may have multiple such mask features corresponding to multiple target features in a target pattern. A point-based optimization process (e.g., process 500) may be performed on all mask features in the mask pattern to generate optimized designs for the corresponding mask features. A mask pattern with optimized designs for the mask features, such as the optimized design 902b, can then be used in the manufacture of a mask that may be used when transferring the mask pattern to a substrate.

[0067]

[0093] The point-based optimization process for design generation or optimization of mask features can be used for a variety of applications. Figures 10A to 10D show various application examples of the design optimization process, consistent with various embodiments. Figure 10A shows an example of the point-based optimization process being applied to generate an optimized design (e.g., optimized design 1002) of a mask feature for a target feature such as a square (e.g., target feature 1001). Figure 10B shows an example of the point-based optimization process being applied to generate an optimized design (e.g., optimized design 1008) of a mask feature for a target feature such as a circle or ellipse (e.g., target feature 1007). Figure 10C shows an example of the point-based optimization process being applied to generate an optimized design of a mask feature for a target feature such as a diagonal pattern. In Figure 10C, the point-based optimization process does not separate the main feature (e.g., target feature) and different types of mask features such as SRAF; that is, the optimized design is generated for both the main feature and the SRAF. For example, mask pattern 1003 includes mask features corresponding to the main feature (e.g., target feature) and SRAF. The point-based optimization process generates an optimized design 1010 for the mask feature corresponding to the target feature 1005. In Figure 10D, the point-based optimization process separates different types of mask features and generates an optimized design for the mask feature for the main feature rather than the SRAF. For example, mask pattern 1017 includes mask features corresponding to both the main feature (e.g., target feature) and SRAF. The point-based optimization process generates an optimized design 1025 for the mask feature corresponding to the target feature 1020.

[0068]

[0094] Point-based optimization processes can generate initial designs for mask features from target features and optimize these initial designs. They can also be used to refine mask feature designs generated by other OPC processes, such as freeform processes. In the examples in Figures 10C and 10D, initial designs for mask features are generated using a freeform process, and these initial designs are then fed into a point-based optimization process to optimize them into optimized designs 1010 and 1025.

[0069]

[0095] In some embodiments, point-based optimization processes are more efficient than other OPC processes. For example, a point-based optimization process can optimize the cost function in fewer iterations than other processes, thereby minimizing the computing resources consumed when generating the optimized design, such as processor execution time and memory. In another example, a point-based optimization process achieves better cost function optimization compared to other OPC processes while consuming fewer computing resources, such as processor execution time and memory.

[0070]

[0096] Depending on the embodiment, using a point-based optimization process in combination with other OPC processes is more efficient than using other OPC processes without a point-based optimization process. Specifically, further efficiency can be achieved by generating an initial design using other OPC processes and then optimizing it using a point-based optimization process. For example, a point-based optimization process can generate an optimized design from an initial design using fewer computing resources, such as processor execution time and memory, than other processes would consume to generate an optimized design without using a point-based optimization process. Furthermore, a point-based optimization process may achieve a better cost function optimization compared to the optimization achieved by other OPC processes without using a point-based optimization process.

[0071]

[0097] In some embodiments, a point-based optimization process can be incorporated into a source mask optimization (SMO) flow by optimizing the process window by optimizing the position of mask points together with the radiation source of the lithography apparatus. For example, in each iteration of the SMO, the direction and amount of movement of each mask point moved may depend on the shape of the radiation source, which is also optimized in the same iteration of the SMO. The mask output from the SMO then consists of smoothly connected optimized mask points (e.g., using a smoothing process).

[0072]

[0098] Figure 11 is a block diagram of a computer system 100 that can assist in the implementation of a method, flow, or apparatus disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information and a processor 104 (or a plurality of processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes main memory 106 coupled to the bus 102 for storing information and instructions executed by the processor 104, such as random access memory (RAM) or other dynamic storage device. The main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions executed by the processor 104. The computer system 100 further includes read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0073]

[0099] The computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT), flat panel, or touch panel display, for displaying information to the computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 to communicate information and command selections to the processor 104. Another type of user input device is a cursor control unit 116, such as a mouse, trackball, or cursor directional keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. This input device generally has two degrees of freedom (a first axis (e.g., x) and a second axis (e.g., y)) that allow the device to be positioned in a plane. A touch panel (screen) display may be used as an input device.

[0074]

[0100] According to one embodiment, a portion of one or more methods described herein may be performed by a computer system 100 in response to a processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as a storage device 110. The execution of the sequence of instructions contained in main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multiprocessing configuration may be used to execute the sequence of instructions contained in main memory 106. In one alternative embodiment, hardwired circuitry may be used instead of, or together with, software instructions. Thus, the description herein is not limited to any particular combination of hardware circuitry and software.

[0075]

[0101] As used herein, the term “computer-readable medium” refers to any medium involved in providing instructions to the processor 104 for execution. Such mediums can take many forms, but are not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks such as storage device 110. Volatile media include dynamic memory such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers (including wires including bus 102). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, and other magnetic media, CD-ROMs, DVDs, and other optical media, punch cards, paper tapes, and other physical media having perforation patterns, RAM, PROMs, and EPROMs, FLASH-EPROMs, and other memory chips or cartridges, carrier waves as described below, or other media that can be read by a computer.

[0076]

[0102] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially reside on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send them over a telephone line using a modem. A modem local to computer system 100 can receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 can receive the data carried by the infrared signal and load that data onto bus 102. Bus 102 transports the data to main memory 106, from which the processor 104 reads and executes the instructions. Instructions received by main memory 106 may optionally be stored in a storage device 110 before or after execution by the processor 104.

[0077]

[0103] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 also provides bidirectional data communication coupled to a network link 120 connected to a local network 122. For example, the communication interface 118 may be an ISDN (Integrated Services Digital Network) card or modem that provides data communication connectivity to a corresponding type of telephone line. Alternatively, the communication interface 118 may be a local area network (LAN) card that provides data communication connectivity to a compatible LAN. A wireless link may also be implemented. In such an implementation, the communication interface 118 transmits and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0078]

[0104] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide connection to data equipment operated by a host computer 124 or an Internet service provider (ISP) 126 through a local network 122. The ISP 126 then provides data communication services via the World Wide Packet Data Network (now commonly referred to as the "Internet" 128). Both the local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals to carry digital data streams. Signals across various networks, and signals on the network link 120 and through the communication interface 118, carrying digital data to and from the computer system 100, are examples of carrier wave forms that carry information.

[0079]

[0105] Computer system 100 can send messages and receive data, including program code, through one or more networks, network links 120, and communication interfaces 118. In the Internet example, server 130 may send request code for an application program through the Internet 128, ISP 126, local network 122, and communication interfaces 118. Such a downloaded application may provide all or part of the methods described herein. The received code may be executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 may obtain application code in carrier form.

[0080]

[0106] Figure 12 schematically illustrates an exemplary lithography projection apparatus that can be used in combination with the techniques described herein. This apparatus includes: - Illumination system IL for adjusting radiation beam B. In this particular case, the illumination system also includes radiation source SO; - A first object table (e.g., a patterning device table) MT, which includes a patterning device holder for holding a patterning device MA (e.g., a reticle) and is connected to a first positioner for precisely positioning the patterning device relative to an item PS; - A second object table (substrate table) WT, comprising a substrate holder for holding a substrate W (e.g., a resist-coated silicon wafer) and connected to a second positioner for precisely positioning the substrate relative to an item PS; - A projection system ("lens") PS (e.g., a refractive, reflective, or reflective-refracting optical system) that images the irradiated portion of the patterning device MA onto the target portion C of the substrate W (e.g., including one or more dies).

[0081]

[0107] As described herein, the apparatus is transmissive (i.e., has a transmissive patterning device). However, it may generally be reflective (having a reflective patterning device), for example. The apparatus may use a different type of patterning device than conventional masks, examples of which include a programmable mirror array or an LCD matrix.

[0082]

[0108] The source SO (e.g., a mercury lamp or excimer laser, LPP (laser-generated plasma), or EUV source) generates a radiant beam. This beam is supplied to the illumination system (illuminator) IL either directly or after passing through a regulating means such as a beam expander Ex. The illuminator IL may include regulating means AD for setting the outer and / or inner radial ranges of the beam's intensity distribution (generally referred to as σ-outer and σ-inner, respectively). Furthermore, it generally includes various other components such as an integrator IN and a capacitor CO. In this way, the beam B that strikes the patterning device MA has the desired uniformity and intensity distribution in cross-section.

[0083]

[0109] Regarding Figure 12, it should be noted that the source SO may be located within the housing of the lithography projection apparatus (in most cases, when the source SO is, for example, a mercury lamp), or it may be located away from the lithography projection apparatus, with the emitted beam it generates being guided into the apparatus (for example, using appropriate guide mirrors). This latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF, or F2 lathing).

[0084]

[0110] Next, beam B intersects with the patterning device MA held on the patterning device table MT. After traversing the patterning device MA, beam B passes through lens PL, which focuses beam B onto a target portion C on the substrate W. Using a second positioning means (and interferometric measurement means IF), the substrate table WT can be precisely moved to position, for example, a different target portion C within the path of beam B. Similarly, for example, after or during a machine search of the patterning device MA from the patterning device library, the patterning device MA can be precisely positioned relative to the path of beam B using the first positioning means. In general, the movement of the object tables MT and WT is achieved using long-stroke modules (coarse positioning) and short-stroke modules (fine positioning), which are not explicitly shown in Figure 12. However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to or fixed only to short-stroke actuators.

[0085]

[0111] The drawn tool can be used in two different modes: - In step mode, the patterning device table MT remains essentially stationary, and the entire patterning device image is projected onto the target portion C in a single pass (i.e., a single "flash"). The substrate table WT is then shifted in the x and / or y directions so that different target portions C can be illuminated by the beam B; -In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single "flash." Instead, the patterning device table MT is movable at velocity v in a given direction (the so-called "scan direction," e.g., the y-direction) so that the projection beam B can scan over the patterning device image. In parallel, the substrate table WT is simultaneously moved at velocity V=Mv (where M is the magnification of the lens PL (generally M=1 / 4 or 1 / 5)) in the same or opposite direction. In this way, a relatively large target portion C can be exposed without compromising resolution.

[0086]

[0112] Figure 13 schematically shows another exemplary lithography projection apparatus 1000 that can be used in conjunction with the technology described herein.

[0087]

[0113] The lithography projection device 1000 includes the following: - Source collector module SO - Illumination system (illuminator) IL configured to adjust radiation beam B (e.g., EUV radiation) - A support structure (e.g., a patterning device table) MT connected to a first positioner PM, which is constructed to support a patterning device (e.g., a mask or reticle) MA and configured to precisely position the patterning device. - A substrate table (e.g., wafer table) WT connected to a second positioner PW, which is constructed to hold a substrate (e.g., a resist-coated wafer) W and configured to precisely position the substrate, and - A projection system (e.g., a reflective projection system) PS configured to project a pattern applied to a radiating beam B by a patterning device MA onto a target portion C of a substrate W (e.g., including one or more dies).

[0088]

[0114] As depicted here, apparatus 1000 is reflective (for example, using a reflective patterning device). Note that since most materials are absorbent in the EUV wavelength range, the patterning device may have a multilayer reflector, for example, a multi-stack of molybdenum and silicon. In one example, the multi-stack reflector has 40 layers of molybdenum and silicon, with each layer having a thickness of one-quarter of a wavelength. Even smaller wavelengths can be produced using X-ray lithography. Since most materials are absorbent at EUV and X-ray wavelengths, a thin piece of patterned absorbent material on the patterning device topography (e.g., a TaN absorber on a multilayer reflector) defines where features are printed (positive resist) or not printed (negative resist).

[0089]

[0115] Referring to Figure 13, the illuminator IL receives an extreme ultraviolet (EUV) radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) with one or more emission lines in the EUV range. In one such method, often called laser-generated plasma ("LPP"), the plasma can be generated by irradiating a fuel, such as droplets, streams, or clusters of material having a line-emitting element, with a laser beam. The source collector module SO may also be part of an EUV radiation system including a laser (not shown in Figure 13) that provides the laser beam for exciting the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector located in the source collector module. The laser and source collector module may be separate entities, for example, if a CO2 laser is used to provide the laser beam for fuel excitation.

[0090]

[0116] In such cases, the laser is not considered to form part of the lithography apparatus, and the emitted beam is delivered from the laser to the source collector module using a beam delivery system, for example, including appropriate guide mirrors and / or beam expanders. In other cases, for example, if the source is a discharge-generated plasma EUV generator, often called a DPP source, the source may be an integrated part of the source collector module.

[0091]

[0117] An illuminator (IL) may include adjusters for adjusting the angular intensity distribution of the radiated beam. Generally, at least the outer and / or inner radial ranges of the intensity distribution at the pupil surface of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) can be adjusted. Furthermore, an illuminator (IL) may include various other components such as facet fields and pupil mirror devices. Using an illuminator, the radiated beam can be tuned to have desired uniformity and intensity distribution in cross-section.

[0092]

[0118] A radiating beam B is incident on a patterning device (e.g., a mask) MA held on a support structure (e.g., a patterning device table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., a mask) MA, the radiating beam B passes through a projection system PS that focuses the beam onto a target portion C of the substrate W. A second positioner PW and a position sensor PS2 (e.g., an interference device, a linear encoder, or a capacitance sensor) can be used to precisely move the substrate table WT to position, for example, different target portions C within the path of the radiating beam B. Similarly, a first positioner PM and another position sensor PS1 can be used to precisely position the patterning device (e.g., a mask) MA relative to the path of the radiating beam B. The patterning device (e.g., a mask) MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0093]

[0119] The depicted device 1000 can be used in at least one of the following modes: 1. In step mode, the support structure (e.g., patterning device table) MT and substrate table WT remain essentially stationary (i.e., single static exposure) while the entire pattern applied to the radiation beam is projected onto the target portion C in a single pass. The substrate table WT is then shifted in the X and / or Y directions so that different target portions C can be exposed. 2. In scan mode, the support structure (e.g., patterning device table) MT and the substrate table WT are scanned synchronously (i.e., single dynamic exposure) while the pattern applied to the radiation beam is projected onto the target portion C. The speed and direction of the substrate table WT relative to the support structure (e.g., patterning device table) MT can be determined by the reduction and image inversion characteristics of the projection system PS. 3. In another mode, while the pattern applied to the radiation beam is projected onto the target portion C, the support structure (e.g., patterning device table) MT remains essentially stationary, holding the programmable patterning device, and the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is generally used, and the programmable patterning device is updated as needed after each movement of the substrate table WT or between consecutive radiation pulses during scanning. This operating mode can be readily applied to maskless lithography utilizing programmable patterning devices such as the type of programmable mirror array mentioned above.

[0094]

[0120] Figure 14 shows the apparatus 1000 in more detail, including a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and positioned so that a vacuum environment can be maintained within the enclosed structure 220 of the source collector module SO. The EUV radiation emission plasma 210 can be formed by a discharge-generating plasma source. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor, from which the ultra-high temperature plasma 210 is made to emit radiation in the EUV range of the electromagnetic spectrum). The ultra-high temperature plasma 210 is made, for example, by a discharge that produces at least a partially ionized plasma. A partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required for efficient generation of radiation. In one embodiment, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0095]

[0121] Radiation emitted by the high-temperature plasma 210 is passed from the source chamber 211 into the collector chamber 212 via an optional gas barrier or contaminant trap 230 (sometimes also called a contaminant barrier or foil trap) located within or behind the opening of the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further described herein includes at least a channel structure, as is known in the art.

[0096]

[0122] The collector chamber 211 may include a radiation collector CO, which may be a so-called oblique incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation crossing collector CO is reflected by the grating spectral filter 240 and can be focused to a virtual source point IF along the optical axis indicated by the dashed line "O". The virtual source point IF is generally called the intermediate focus, and the source collector module is positioned such that the intermediate focus IF is located at or near the aperture 221 of the closed structure 220. The virtual source point IF is an image of the radiation-emitting plasma 210.

[0097]

[0123] Next, the radiation traverses an illumination system IL which may include faceted field mirror devices 22 and faceted pupil mirror devices 24 arranged in the patterning device MA to provide a desired angular distribution of the radiation beam 21 and a desired uniformity of radiation intensity in the patterning device MA. Upon reflection of the radiation beam 21 in the patterning device MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS onto a substrate W held by the substrate table WT via reflective elements 28, 30.

[0098]

[0124] In general, more elements than those shown in the illustrations may be present in the illumination optical system unit IL and the projection system PS. A grating spectral filter 240 may be optionally present depending on the type of lithography apparatus. Furthermore, more mirrors than those shown in the illustrations may be present; for example, 1 to 6 additional reflective elements may be present in the projection system PS than those shown in Figure 12.

[0099]

[0125] The CO collector system shown in Figure 12 is depicted as a nested collector with obliquely incident reflectors 253, 254, and 255, as just one example of a collector (or collector mirror). The obliquely incident reflectors 253, 254, and 255 are arranged axially with respect to the optical axis O, and this type of CO collector system can be used in combination with a discharge-generating plasma source, often referred to as a DPP source.

[0100]

[0126] Alternatively, the source collector module SO may be part of the LPP emission system, as shown in Figure 15. The laser LA is positioned to deposit laser energy onto a fuel such as xenon (Xe), tin (Sn), or lithium (Li) to generate a highly ionized plasma 210 with an electron temperature of several tens of eV. The energy radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by the near-normal incident collector system CO, and focused onto the aperture 221 of the closed structure 220.

[0101]

[0127] As described above with reference to at least Figures 5A to 10D, the “Full Angle OPC” technique generates a curved pattern of mask features corresponding to target features in a target pattern. The curved pattern is generated by adjusting mask points that can be derived from the input mask features or corresponding target features until the cost function is optimized. In some embodiments, the “Full Angle OPC” technique may generate a non-curved design (e.g., a polygonal pattern where the angle between the pattern segment or line and the horizontal axis is 45*n degrees or 90*n degrees (where n is an integer)) or a hybrid design (e.g., a design that is partially curved and partially polygonal) for the mask features. Furthermore, such designs may be generated for mask features that are either (a) primary features corresponding to target features, or (b) SRAFs. The terms “polygonal design” or “polygonal pattern” as used in this disclosure refer to a pattern where the angle between the pattern segment or line and the horizontal axis is 45*n degrees or 90*n degrees (where n is an integer). In some embodiments, polygonal patterns may be generated using the methods described with reference to at least Figures 5A-5C by adjusting the mask points so that the angle between two straight lines in the final design (e.g., the final modified design 525 or 902b) is 45*n degrees or 90*n degrees. For example, a smoothing process described with reference to at least Figure 5B or a cost function 521 (used to determine the position adjustment data of the mask points) described with reference to at least Figure 5C may be fitted to generate a polygonal or hybrid design instead of a curved design for the mask feature.

[0102]

[0128] The type of design generated (e.g., curved, polygonal, or hybrid) may be determined based on one or more parameters. In some embodiments, mask features may be generated as a polygonal or hybrid design based on user preference. For example, a user can choose to generate mask features as a polygonal or hybrid design instead of a curved design to minimize the complexity when manufacturing patterning devices with curved designs. In some embodiments, generating mask features as a polygonal or hybrid design may optimize cost functions (e.g., EPE, MRC violation penalty) better than can be achieved with a curved design. For example, if mask features are generated using a curved design, cost functions such as EPE may be reduced to a first value, but if mask features are generated using a polygonal or hybrid design, they may be further reduced to a second value (second value < first value). In some embodiments, if the target pattern has densely arranged target features, the mask features may be generated as a polygonal or hybrid design, while generating a curved design may violate one or more MRC constraints, such as mask feature size, width, distance between two mask features, or other MRC constraints. For example, the distance between two mask features may be less than the minimum distance threshold if the mask features are generated as a curved design, but greater than or equal to the minimum distance threshold if the mask features are generated as a polygonal or hybrid design. In some embodiments, the mask features may be generated as a curved design for certain parts of the target feature and as a polygonal design for other parts of the target feature. For example, the mask features may be generated as a curved design for parts of the target feature near one or more vertices or line ends of the target feature (as shown in Figure 17), and as a polygonal design for the rest of the target feature.Depending on the embodiment, the mask feature may be generated as a polygonal design or a hybrid design instead of a curved design in order to minimize the computer resources consumed when generating the curved design.

[0103]

[0129] Figure 16A shows a curved design of a mask feature consistent with various embodiments. Mask feature 1604, corresponding to target feature 1602, is generated as a curved design. In some embodiments, mask feature 1604 resembles the modified design 902b in Figure 9, and target feature 1602 resembles target feature 602.

[0104]

[0130] Figure 16B shows a polygonal design of the mask feature consistent with various embodiments. The mask feature 1606 corresponding to the target feature 1602 is generated as a polygonal design (for example, a design constructed using straight lines). In some embodiments, the mask feature 1606 is generated in a manner similar to the methods described with reference to at least Figures 5A to 10D, except that the mask feature 1606 is generated as a polygon rather than a curved pattern.

[0105]

[0131] Figure 16C shows curved and polygonal designs of mask features consistent with various embodiments. Mask feature 1604, corresponding to target feature 1602, is generated as a curved design. Mask feature 1614, corresponding to SRAF, is generated as a polygonal design.

[0106]

[0132] Figure 16D shows curved and polygonal designs of mask features consistent with various embodiments. Mask feature 1606 corresponding to target feature 1602 is generated as a polygonal design, while mask feature 1616 corresponding to SRAF is generated as a curved design.

[0107]

[0133] Figure 17 shows a hybrid design of a mask feature consistent with various embodiments. Mask feature 1704, corresponding to target feature 1702, is generated as a hybrid design, in which the first part 1706 is generated as a polygonal design and the second part 1708 (for example, near the vertices of target feature 1702) is generated as a curved design. In some embodiments, mask feature 1704 resembles modified design 902b in Figure 9 (distinguishing in that mask feature 1704 is generated as a polygonal and curved pattern), and target feature 1702 resembles target feature 602.

[0108]

[0134] Figures 16C and 16D show specific combinations of mask feature designs, such as the curved design of the primary mask feature 1604 and the polygonal design of the SRAF mask feature 1614 in Figure 16C, and the polygonal design of the primary mask feature 1606 and the curved design of the SRAF mask feature 1616 in Figure 16D, but various other combinations are possible. For example, both the primary mask feature and the SRAF mask feature may have the same design. In another example, the design of the primary mask feature may differ from the design of the SRAF mask feature. In yet another example, the SRAF mask feature may not be generated at all.

[0109]

[0135] Figure 18 shows a flow diagram for implementing the "full-angle OPC" described in Figure 5A, which is consistent with various embodiments.

[0110]

[0136] In process P1801, multiple clips 1801, which are target images corresponding to the target pattern, are input to the CTM engine, and OPC is performed on the clips 1801 to generate a CTM or CTM+ mask image 1802. Depending on the embodiment, the CTM engine may perform multiple stages of CTM and CTM+ on the clips 1801 to obtain a mask image 1802 as an optimized OPC result. The mask image 1802 may include both major features and SRAF. The mask image 1802 may be used as ground truth for training a machine learning (ML) model 1805 to generate a mask pattern (e.g., post-OPC) for any given target pattern.

[0111]

[0137] In process P1802, clip 1801 and mask image 1802 are provided to the ML model 1805 as a training dataset for training the ML model 1805. Depending on the embodiment, training the ML model 1805 may be an iterative process, each iteration of which may include determining a cost function that represents the difference between the predicted mask pattern (e.g., the mask pattern generated by the ML model 1805) and the mask image input to the ML model 1805, and adjusting the parameters of the ML model 1805 to minimize the cost function. The ML model 1805 is considered trained when the cost function is minimized (e.g., the difference between the predicted mask pattern and the input mask image falls below a threshold). After the ML model 1805 has been sufficiently trained, it can be used to generate a mask pattern for any given target pattern.

[0112]

[0138] The target image 1803 of the target pattern is input to the trained ML model 1805 to obtain the mask pattern 1804 of that target pattern. Depending on the embodiment, the mask pattern 1804 generated by the ML model 1805 may not be optimized (for example, the EPE may not be optimized).

[0113]

[0139] In process P1803, the mask pattern 1804 is input to a full-angle OPC module that performs a full-angle OPC method (for example, as described with reference to at least Figures 5A-5C) to refine the mask pattern 1804 and generate an improved mask pattern 1807. In some embodiments, the improved mask pattern 1807 resembles the final modified mask design 525 in Figure 5C. In some embodiments, the improved mask pattern 1807 may be optimized (for example, the EPE may be optimized). Furthermore, the mask pattern 1807 may have a curved, polygonal, or hybrid design.

[0114]

[0140] In some embodiments, full-angle OPC differs from freeform OPC in that full-angle OPC generates a mask pattern by adjusting mask points associated with the mask pattern, while freeform OPC generates a mask pattern by adjusting pixel values ​​in the image corresponding to the design layout. Furthermore, in conventional segment-based OPC methods, the angles of segments are preserved (e.g., segments are limited to having 45*n degrees (where n is an integer)), but the number of mask points used to adjust the mask pattern may not be preserved. In contrast, in full-angle OPC techniques, neither the number of mask points nor the angles between segments of the mask pattern may be preserved during the adjustment process, because mask points may be added or deleted during the adjustment process, and the angles between segments can be any angle (e.g., any angle such as "0" to "360" degrees for curved designs, or 45*n or 90*n degrees for polygonal designs). Moreover, in full-angle OPC techniques, the mask points can be moved in any direction, in contrast to segment-based OPC methods where the edge segments of the mask pattern are adjusted along the normal direction of the segment.

[0115]

[0141] Depending on the embodiment, the full-angle OPC technique may be combined with other OPC techniques when generating a mask pattern. Each technique can be used to generate different mask features or different parts of a mask feature in the mask pattern, and each technique can be used to generate a polygonal design or a curved design. For example, in the case of the target feature 1602 shown in Figure 16D, the mask feature 1606 can be generated using segment-based OPC or image-based OPC techniques, and the mask feature 1616 can be generated using the full-angle OPC technique.

[0116]

[0142] While this specification may specifically refer to the manufacture of ICs, it should be clearly understood that the descriptions herein have numerous other possible applications. For example, the descriptions herein can be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memory, liquid crystal display panels, thin-film magnetic heads, and the like. Those skilled in the art will understand that, in the context of such alternative applications, the terms “reticle,” “wafer,” or “die” used herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0117]

[0143] In this specification, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of approximately 5 to 100 nm).

[0118]

[0144] The concepts disclosed herein can be used to simulate or mathematically model general imaging systems for imaging subwavelength features and may be particularly useful for new imaging techniques capable of generating shorter wavelengths. New techniques already in use include EUV (extreme ultraviolet) lithography, which can generate wavelengths as short as 193 nm using ArF lasers and even 157 nm using fluorine lasers. EUV lithography can also generate wavelengths in the 20-5 nm range by using a synchrotron to generate photons, or by bombarding a material (solid or plasma) with high-energy electrons.

[0119]

[0145] The concepts disclosed herein may be used for imaging on substrates such as silicon wafers, but it should be understood that the disclosed concepts may be used in any type of lithography imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0120]

[0146] As used herein, the terms “optimize” and “optimize” refer to or mean adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc., so that the deliverable and / or process has more desirable characteristics, such as higher precision projection of the design pattern onto the substrate, a larger process window, etc. Accordingly, as used herein, the terms “optimize” and “optimize” refer to or mean the process of identifying one or more values ​​of one or more parameters that result in an improvement (e.g., a local optimal) compared to an initial set of one or more values ​​of one or more parameters in at least one relevant metric. “Optimal” and other related terms should be interpreted accordingly. In one embodiment, the optimization step can be applied iteratively to result in further improvements in one or more metrics.

[0121]

[0147] Embodiments of the present invention can be implemented in any convenient form. For example, embodiments may be implemented by one or more suitable computer programs that can be carried on a suitable carrier medium, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention may be implemented using a suitable apparatus, which may take the form of a programmable computer that runs a computer program configured to carry out a method as described herein. Accordingly, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form that can be read by a machine (e.g., a computer device). For example, a machine-readable medium may include read-only memory (ROM), random access memory (RAM), magnetic disk storage medium, optical storage medium, flash memory device, and propagated signals in electrical, optical, acoustic, or other forms (e.g., carrier waves, infrared signals, digital signals, etc.). Furthermore, firmware, software, routines, and instructions may be described herein as performing specific actions. However, such descriptions are for convenience only, and it should be understood that such actions actually result from the computer device, processor, controller, or other device that executes those firmware, software, routines, instructions, etc.

[0122]

[0148] Embodiments of this disclosure can be further described by the following clauses. 1. A non-temporary computer-readable medium having instructions that, when executed by a computer, cause the computer to execute a method for improving the design of a patterning device, wherein the method is: This involves obtaining the mask points of the mask feature design, where the mask feature is associated with a target feature in the target pattern printed on the substrate. A non-temporary computer-readable medium that includes adjusting the position of mask points and generating a modified design of mask features based on the adjusted mask points. 2. Adjusting the position of the mask point is an iterative process, and each iteration is: To determine the cost function associated with the optical proximity effect correction process or the radiation source mask optimization process, For each control point on the target feature, determine the location data of the mask point based on the cost function, To optimize the cost function, adjust the position of one or more of the mask points based on location data, the adjustment includes updating the modified design, as described in the computer-readable media of Clause 1. 3. The cost function includes edge placement error or simulated signal, and optimizing the cost function includes reducing the cost function, as described in the computer-readable media of Clause 2. 4. Determining the cost function is This involves performing a simulation using the modified design to obtain a simulated image, the simulated image including a resist image or an etched image, Extracting contours from a simulated image, A computer-readable medium as described in Clause 3, which includes determining the edge placement error based on contours and target features for each control point as a cost function. 5. Adjusting the position of the mask points includes performing multiple iterations until the edge placement error is minimized, as described in Clause 4 for computer-readable media. 6. Determining the cost function is The simulation is performed using the modified design, and the resist image signal or etching image signal is obtained as the simulated signal. A computer-readable medium as described in Clause 3, including determining a simulated signal for each control point. 7. Adjusting the position of the mask point includes performing multiple iterations until the simulated signal is minimized, as described in the computer-readable media of Clause 6. 8. The cost function includes a process window for the patterning process to print the modified design onto the substrate, and optimizing the cost function includes increasing the process window, as described in the computer-readable media of Clause 2. 9. Determining the cost function is This involves performing a simulation using the modified design to obtain a simulated image, the simulated image including a resist image or an etched image, A computer-readable medium as described in Clause 8, which includes obtaining a process window using a simulated image, wherein the process window includes a range of focus and dose values ​​such that a target pattern printed on a substrate using the modified design satisfies a given specification. 10. Adjusting the position of the mask point includes performing multiple iterations until the process window is maximized, as described in the computer-readable media of Clause 9. 11. The cost function is a computer-readable medium as described in Clause 2, including at least one of the following: edge placement error, simulated signal, process window, or mask rule check violation penalty. 12. Obtaining mask points is A computer-readable medium as described in Clause 1, including the derivation of mask points from target features. 13. Adjusting the position of the mask point is A computer-readable medium as described in Clause 2, comprising associating mask points with control points on a target feature to generate a first association between a first set of mask points and a first control point, and a second association between a second set of mask points and a second control point. 14. Adjusting the position of the mask point is A computer-readable medium as described in Clause 13, which includes modifying the association between mask points and control points based on a comparison between the modified design and the target features. 15. Each control point on the target feature is associated with the same set of mask points during each iteration, as described in the computer-readable media of Clause 13. 16. One or more control points on the target feature are associated with different sets of mask points during at least two iterations in the computer-readable medium described in Clause 13. 17. Obtaining mask points is The computer-readable medium described in Clause 1, wherein the mask points are smoothed, the smoothing process comprising fitting curves to connect the mask points with curves to generate a design as a first curved pattern. 18. Computer-readable media as described in Clause 17, further including performing image perturbations on a design to generate an enlarged version of that design. 19. Adjusting the position of one or more of the mask points, including adjusting a set of mask points together, in the computer-readable media described in Clause 2. 20. Adjusting the position of one or more mask points includes adjusting the mask points individually, as described in the computer-readable media of Clause 2. 21. A computer-readable medium as described in Clause 2, which includes gradient and distance values, wherein the positional adjustment of the corresponding mask point is performed only by the gradient and distance values ​​in relation to the control point to which the corresponding mask point is associated. 22. Computer-readable media as described in Clause 2, further including smoothing the modified design. 23. A computer-readable medium as described in Clause 22, further comprising applying a mask rule check process to the modified design to satisfy the mask rule check constraints. 24. The process of adjusting the position of mask points to generate a modified design, including performing a predetermined number of iterations, is described in the computer-readable media of Clause 2. 25. To acquire a design, The computer-readable media described in Clause 1 includes obtaining a design from a process that generates a design from target features, the process including one or more of the following: machine learning (ML) based optical proximity correction (OPC), continuous transmission mask (CTM) freeform OPC, CTM + freeform OPC, segment-based OPC, or inverse lithography techniques. 26. The mask feature is a subresolution assist feature in a computer-readable medium as described in Clause 1. 27. A computer-readable medium as described in any one of Clauses 1 to 26, further including performing a patterning step using the modified design and printing a pattern onto a substrate via the patterning process. 28. A computer-readable medium as described in any one of Clauses 1 to 27, further including manufacturing a patterning device that includes structural features corresponding to the modified design. 29. A computer-readable medium as described in Clause 28, further comprising transferring a modified design of a patterning device onto a substrate via a lithography apparatus. 30. A non-temporary computer-readable medium having instructions that, when executed by a computer, cause the computer to execute a method for improving the design of a patterning device, wherein the method is This involves obtaining the mask points of the mask feature design, where the mask feature corresponds to the target feature in the target pattern printed on the substrate. Adjusting the position of a mask point to increase the process window, the process window being associated with a patterning process for printing a target pattern onto a substrate, and the adjustment including generating a modified design based on the adjusted position, in a non-temporary computer-readable medium. 31. Adjusting the position is an iterative process, and each iteration is Obtaining a process window based on the modified design, wherein the process window includes a range of values ​​for at least one parameter of the patterning process for printing the target pattern onto the substrate using the modified design. Computer-readable media as described in Clause 30, which includes adjusting the position of one or more mask points to increase the range of values ​​for one or more parameters, and the adjustment includes updating the modified design. 32. A computer-readable medium as described in Clause 31, wherein at least one parameter includes at least one of dose or focus associated with a lithography apparatus used to print a target pattern onto a substrate. 33. A non-temporary computer-readable medium having instructions that, when executed by a computer, cause the computer to execute a method for improving the design of a patterning device, wherein the method is To obtain the design of the target pattern to be printed on the circuit board, and the mask features corresponding to the target features in the target pattern, To derive the mask points of the design, Iteratively updating a design by adjusting the position of one or more mask points based on a cost function, the updating including generating a modified design of the mask features, in a non-temporary computer-readable medium. 34. Acquiring a design is Computer-readable media as described in Clause 33, which includes obtaining a design from a process that generates a design from a target pattern, the process including one or more of the following: machine learning (ML) based optical proximity correction (OPC), continuous transmission mask (CTM) freeform OPC, CTM + freeform OPC, segment-based OPC, or inverse lithography techniques. 35. Deriving the mask point is The computer-readable media described in Clause 33, which includes associating mask points with control points on a target feature, wherein the association includes associating a first set of mask points with a first control point and a second set of mask points with a second control point. 36. Iteratively updating the design means that in each iteration, This involves determining the cost function, which includes edge placement errors. For each control point, the position data of the mask point is determined based on the cost function, To reduce the cost function, the computer-readable media described in Clause 35 adjusts the position of one or more of the mask points based on location data. 37. Iterative updating of the design includes performing multiple iterations until the cost function is minimized, as described in Clause 36 for computer-readable media. 38. Iteratively updating the design means that in each iteration, This involves determining a cost function, the cost function including a process window for the patterning process to print the modified design onto the substrate, For each control point, the position data of the mask point is determined based on the cost function, Computer-readable media as described in Clause 35, which includes adjusting the position of one or more of the mask points based on position data in order to increase the cost function. 39. Iterative updating of the design includes performing multiple iterations until the cost function is maximized, as described in Clause 38 for computer-readable media. 40. A method for improving the design of a patterning device, This involves obtaining the mask points of the mask feature design, where the mask feature corresponds to the target feature in the target pattern printed on the substrate. A method that includes adjusting the position of mask points and generating a modified design based on the adjusted mask points. 41. A method for improving the design of a patterning device, This involves obtaining the mask points of the mask feature design, where the mask feature corresponds to the target feature in the target pattern printed on the substrate. A method comprising adjusting the position of a mask point to increase the process window, wherein the process window is associated with a patterning process for printing a target pattern onto a substrate, and the adjustment includes generating a modified design based on the adjusted position. 42. A method for improving the design of a patterning device, To obtain the design of the target pattern to be printed on the circuit board, and the mask features corresponding to the target features in the target pattern, To derive the mask points of the design, A method for iteratively updating a design by adjusting the position of one or more mask points based on a cost function, wherein updating includes generating a modified design of the mask features. 43. A computer program product comprising a non-temporary computer-readable medium on which instructions are recorded, wherein, when executed by a computer, the instructions perform the method described in any one of the preceding clauses. 44. A non-temporary, tangible, computer-readable medium (CRM) that stores instructions, when executed by a processor, causing the processor to perform an optical proximity effect correction (OPC) method, This OPC method is a non-transient, tangible, computer-readable medium (CRM) that modifies the design of a mask feature by obtaining the mask points of the mask feature design and adjusting the position of the mask points by performing OPC. 45. The method further comprises obtaining control points located on the target polygon of the mask feature, each control point being associated with one or more mask points, as described in Clause 44. 46. ​​Modifying a medium as described in Clause 45, which includes fitting a curve to the mask points to obtain a modified design of the mask feature, where the edges of the mask feature in the modified design include the curve fitted between the mask points. 47. Performing OPC is the medium described in Clause 44, which includes adjusting the position of the mask point to optimize the simulated signal or EPE on the control point. 48. The simulated signal is a resist image signal, as specified in Clause 47. 49. The media described in Clause 47, which involves adjusting multiple mask points in a consistent manner to optimize the simulated signal at one or more control points. 50. The medium described in Clause 47, which includes adjusting mask points individually to optimize the simulated signal at one or more control points. 51. Mask points are initially obtained based on the target polygon design of the feature, as described in Clause 44. 52. The mask point is obtained first based on the design resulting from the segment-based OPC process, in the medium described in Clause 44. 53. The segment-based OPC process is a CTM freeform OPC process, a machine learning OPC process, or an ILT process, as described in Clause 52. 54. This method is, Establishing an association between control points and mask points, Disconnecting the control point and the mask point, The medium described in Clause 44 further includes establishing an association between a control point and another mask point. 55. Deactivating and / or re-establishing a feature is based on a comparison of the feature's target polygon with the modified design, as described in Clause 54. 56. The mask feature is a primary feature or SRAF in the medium as described in Clause 44. 57. The medium described in Clause 44, further including determining the process window based on the adjusted design of the mask feature. 58. A non-temporary, tangible, computer-readable medium (CRM) that, when executed by a processor, stores instructions causing the processor to perform a radiation source mask optimization (SMO) method, This method modifies the design of a mask feature by obtaining the mask points of the mask feature design and optimizing the process window by adjusting the position of the mask points according to the SMO process, thereby creating a non-temporary, tangible computer-readable medium (CRM). 59. Adjusting the position of mask points to generate a modified design includes generating the modified design as a polygonal pattern in computer-readable media as described in Clause 1. 60. A polygonal pattern is a computer-readable medium as described in Clause 59, which includes a pattern in which the angle between the straight lines of the pattern and the horizontal axis is 45 * n degrees (where n is an integer). 61. A polygonal pattern is a computer-readable medium as described in Clause 59, which includes a pattern in which the angle between the straight lines of the pattern and the horizontal axis is 90 * n degrees (where n is an integer). 62. Generating a modified design by adjusting the position of mask points includes generating the modified design as a curved pattern in computer-readable media as described in Clause 1. 63. Adjusting the position of a mask point includes adjusting the position of one of several mask points by moving that mask point in any direction relative to a control point on a target feature, as described in the computer-readable media of Clause 62. 64. The modified design is generated as a polygonal or curved pattern based on a cost function associated with the optical proximity effect correction process or the radiation source mask optimization process, in a computer-readable medium as described in any one of clauses 59 to 63. 65. The computer-readable media described in Clause 64, wherein the modified design is generated as a polygonal pattern, based on the determination that the cost function is more optimized when the modified design is generated as a curved pattern than when it is generated as a curved pattern. 66. If the modified design is generated as a curved pattern, the modified design is generated as a polygonal pattern in the computer-readable media described in Clause 64, based on the determination that the mask rule check constraints are not met. 67. Adjusting the position of mask points to generate a modified design includes generating the modified design as a combination of polygonal and curved patterns in a computer-readable medium as described in Clause 1. 68. The modified design is generated as a curved pattern in the computer-readable media described in Clause 67, for portions adjacent to one or more vertices of the target feature. 69. The modified design is generated as a polygonal pattern for portions of the target feature other than those adjacent to one or more vertices of the target feature, in a computer-readable medium as described in Clause 67. 70. The modified design is generated as a curved pattern for the first portion of the target feature and as a polygonal pattern for the second portion of the target feature in a computer-readable medium as described in Clause 67. 71. The first portion of the target feature includes portions adjacent to one or more vertices of the target feature, as described in the computer-readable media of Clause 70. 72. The computer-readable medium described in Clause 70, which includes the second portion of the target feature other than the portion adjacent to one or more vertices of the target feature.

[0123]

[0149] In the block diagrams, the illustrated components are depicted as separate functional blocks, but embodiments are not limited to systems in which the functions described herein are configured as illustrated. The functions provided by each component may be provided by software or hardware modules configured in a manner different from those currently depicted, for example, such software or hardware may be mixed, combined, duplicated, divided, distributed (e.g., within a data center or geographically), or otherwise configured differently. The functions described herein may be provided by one or more processors of one or more computers executing code stored in tangible, non-temporary, machine-readable media. In some cases, a third-party content distribution network may host some or all of the information transmitted over the network, in which case the information (e.g., content) may be provided by sending commands to retrieve the information from the content distribution network, to the extent that the information is said to be supplied or provided.

[0124]

[0150] Unless otherwise specified, as will be evident from the discussion, throughout this specification, any discussion using terms such as “process,” “calculate,” “calculate,” or “determine” should be understood to refer to the operation or process of a specific device, such as a special-purpose computer or similar special-purpose electronic processing / calculating equipment.

[0125]

[0151] Readers should understand that this application describes several inventions. These inventions are combined into a single document rather than being separated into multiple independent patent applications because the relevant subject matter of these inventions is economical in the filing process. However, the unique advantages and aspects of such inventions should not be confused. While in some cases embodiments address all of the shortcomings described herein, it should be understood that the inventions are useful independently, and some embodiments address only a subset of such problems or provide other unmentioned advantages that would be obvious to those skilled in the art considering this disclosure. Due to cost constraints, some inventions disclosed herein may not be claimed here and may be claimed in a later application, such as a continuation application, or by amending these claims. Similarly, due to space constraints, neither the abstract nor the summary chapter of the inventions in this document should be construed as containing a comprehensive enumeration of all such inventions or all aspects of such inventions.

[0126]

[0152] The description and drawings are not intended to limit the invention to any particular form disclosed herein, but rather to cover all modifications, equivalents, and alternative forms that fall within the spirit and scope of the invention as defined by the appended claims.

[0127]

[0153] Various modifications and alternative embodiments of the present invention will be apparent to those skilled in the art in light of this specification. Accordingly, this description and drawings should be construed as illustrative only and are intended to teach those skilled in the art a general method for carrying out the invention. It should be understood that the embodiments of the present invention illustrated and described herein should be construed as examples of embodiments. Elements and materials may be replaced with those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be used independently, or features of embodiments or embodiments may be combined, as will be obvious to those skilled in the art after benefiting from this specification. Modifications to the elements described herein can be made without departing from the spirit and scope of the invention as set forth in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the description.

[0128]

[0154] When used throughout this application, the phrase "may be" is used in an optional sense (i.e., possible) rather than a required sense (i.e., must be). Words such as "include," "including," and "includes" mean that they include but are not limited to. When used throughout this application, the singular forms "a," "an," and "the" include multiple referents unless otherwise specified. Thus, for example, a reference to an element "an" or an element "a" includes combinations of two or more elements, even if other terms or phrases are used for one or more elements, such as "one or more." The term "or" is non-exclusive unless otherwise specified, i.e., encompasses both "and" and "or." When used herein, unless otherwise specified, the term "or" encompasses all possible combinations unless impossible. For example, if it is stated that a component may include A or B, then unless otherwise specified or impossible, that 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 otherwise specified or impossible to achieve, that component may include A, B, or C, or A and B, or A and C, or B and C, or A, B and C. Terms describing conditional relationships, such as "in response to X, Y," "when X, Y," "if X, Y," and "when X, Y," encompass causal relationships in which the preceding term is either a required causal condition, a sufficient causal condition, or a causal condition that contributes to the result. For example, "State X occurs when condition Y is met" is a general term for "X occurs only in response to Y" and "X occurs in response to Y and Z." Such conditional relationships are not limited to results that follow immediately after the preceding term is met, because some results may be delayed, and in conditional descriptions, the preceding term is linked to the result, for example, the preceding term relates to the possibility of the result occurring.Unless otherwise specified, a description that associates multiple attributes or functions with multiple objects (e.g., one or more processors performing steps A, B, C, and D) includes both the case where all such attributes or functions associate with all such objects, and the case where a subset of attributes and functions associates with a subset of objects (e.g., each of the processors performs steps A through D, and the case where processor 1 performs step A, processor 2 performs steps B and part of step C, and processor 3 performs part of step C and step D). Furthermore, unless otherwise specified, a description that one value or behavior "based on" another condition or value includes both the case where that condition or value is the sole factor, and the case where that condition or value is one of several factors. Unless otherwise specified, a description that "each" part of any set has a certain property should not be interpreted as excluding the case where any other identical or similar element of the larger set does not have that property; i.e., each does not necessarily mean all of them. A reference to a selection from a range includes the endpoints of that range.

[0129]

[0155] In the above description, any process, description, or block in the flowchart should be understood to represent a module, segment, or portion of code containing one or more executable instructions for performing a particular logical function or step in the process, and as those skilled in the art will understand, alternative embodiments are included within the scope of the exemplary embodiments of this advance, in which functions may be performed in an order different from that shown or considered, including substantially simultaneously or in reverse order, depending on the functions involved.

[0130]

[0156] To the extent that specific U.S. patents, U.S. patent applications, or other materials (e.g., articles) are incorporated by reference, the text of such U.S. patents, U.S. patent applications, and other materials is incorporated by reference only to the extent that it does not create a conflict between such materials and the descriptions and drawings contained herein. Where such a conflict exists, the conflicting text in the U.S. patents, U.S. patent applications, and other materials incorporated by reference is not incorporated herein by reference in particular.

[0131]

[0157] While specific embodiments have been described, these embodiments are presented merely as examples and are not intended to limit the scope of this disclosure. In fact, the novel methods, apparatus, and systems described herein can be embodied in a variety of other forms. Furthermore, various omissions, substitutions, and modifications can be made in the forms of the methods, apparatus, and systems described herein without departing from the spirit of this disclosure. The appended claims and their equivalents are intended to cover such forms or modifications as being included within the scope and spirit of this disclosure.

Claims

1. A non-temporary, tangible, computer-readable medium (CRM) that, when executed by a processor, stores instructions causing the processor to perform a method, The aforementioned method, Obtaining the mask points of the mask feature design, The control points located on the target features of the mask feature are obtained, each control point is functionally associated with one or more mask points, and the simulated signal or cost function determined at the control point is affected by the positional adjustment of the associated one or more mask points. By performing optical proximity correction (OPC) and adjusting the position of the mask points, the design of the mask feature is modified. Non-temporary, tangible, computer-readable media, including [specific examples of such media].

2. The computer-readable medium according to claim 1, wherein generating a modified design by adjusting the position of the mask points includes generating the modified design as a polygonal pattern.

3. The aforementioned method, The modified design is used to perform a simulation, and the resist image signal or etching image signal is obtained as the simulated signal. Determining the simulated signal for each control point It further includes, The aforementioned modification includes fitting a curve to the mask points to obtain the modified design of the mask feature. The computer-readable medium according to claim 1, wherein the adjustment includes adjusting a plurality of mask points collectively or individually to optimize the simulated signal at one or more control points.

4. The computer-readable medium according to claim 2, wherein the polygonal pattern includes a pattern in which the angle between the straight lines of the pattern and the horizontal axis is 45 * n degrees or 90 * n degrees (where n is an integer).

5. The computer-readable medium according to claim 1, wherein generating a modified design by adjusting the position of the mask points includes generating the modified design as a curved pattern.

6. The computer-readable medium according to claim 5, wherein adjusting the position of the mask point includes adjusting the position of one of a plurality of mask points by moving that mask point in any direction with reference to a control point on a target feature.

7. The computer-readable medium according to any one of claims 1 to 6, wherein the modified design is generated as a polygonal pattern or a curved pattern based on a cost function associated with a optical proximity effect correction process.

8. The computer-readable medium according to claim 7, wherein the modified design is generated as a polygonal pattern based on the determination that the cost function is more optimized when the modified design is generated as a curved pattern than when it is generated as a curved pattern.

9. The computer-readable medium according to claim 7, wherein the modified design is generated as a polygonal pattern based on the determination that the mask rule check (MRC) constraints are not satisfied when the modified design is generated as a curved pattern.

10. The computer-readable medium according to claim 1, wherein generating a modified design by adjusting the position of the mask points includes generating the modified design as a combination of polygonal patterns and curved patterns.

11. The computer-readable medium according to claim 10, wherein the modified design is generated as a curved pattern in portions adjacent to one or more vertices of the target feature.

12. The computer-readable medium according to claim 10, wherein the modified design is generated as a polygonal pattern for portions of the target feature other than those adjacent to one or more vertices of the target feature.

13. The computer-readable medium according to claim 10, wherein the modified design is generated as a curved pattern for a first portion of the target feature and as a polygonal pattern for a second portion of the target feature.

14. The computer-readable medium according to claim 13, wherein the first portion of the target feature includes portions adjacent to one or more vertices of the target feature.

15. The computer-readable medium according to claim 13, wherein the second portion of the target feature includes portions other than those adjacent to one or more vertices of the target feature.

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