Method and system for training a predictive model to generate a two-dimensional elemental representation of a mask pattern

Abstract

This specification describes a method and system for predicting a two-dimensional elemental representation of a mask pattern. An input mask pattern corresponding to a target pattern is given to a prediction model. The prediction model generates a two-dimensional elemental representation of an output mask pattern corresponding to the input mask pattern. The two-dimensional elemental representation includes multiple two-dimensional elements representing the mask features of the output mask pattern, each two-dimensional element defining a closed region. The mask feature contours of the output mask pattern are determined based on the two-dimensional elemental representation.

Description

Technical Field

[0001] Cross - reference to related applications

[0001] This application claims the priority of U.S. Patent Application No. 63 / 469,755, filed on May 30, 2023, which is hereby incorporated by reference in its entirety.

[0002]

[0002] The embodiments provided herein relate to semiconductor manufacturing, and more particularly to the design of mask patterns.

Background Art

[0003]

[0003] A lithography apparatus is a machine that applies a desired pattern to a target portion of a substrate. A lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, an IC chip of a smartphone can be as small as a human thumbnail and can contain more than two billion transistors. Manufacturing an IC involves different layers of circuit components and is a complex and time - consuming process involving hundreds of individual steps. An error in even one step can cause problems with the final IC and potentially lead to device failure. High process yield and high wafer throughput can be affected by the presence of defects.

Summary of the Invention

[0004]

[0004] In some aspects, the technology described herein relates to a method for determining a mask pattern used in a lithography process. The method includes providing an input mask pattern corresponding to a target pattern to a prediction model, and using the prediction model to generate a two - dimensional (2D) element representation of an output mask pattern corresponding to the input mask pattern, where the two - dimensional element representation includes a plurality of two - dimensional elements representing mask features of the output mask pattern, each two - dimensional element defining a closed region, generating, and determining a mask feature contour of the output mask pattern based on the two - dimensional element representation.

[0005]

[0005] In some embodiments, the techniques described herein relate to a method for training a predictive model to generate two-dimensional elemental representations of mask patterns used in a lithography process, the method comprising obtaining as training data a set of input mask patterns and a set of two-dimensional elemental representations of a set of output mask patterns corresponding to the set of input mask patterns, wherein the two-dimensional elemental representations of the set of two-dimensional elemental representations include a plurality of two-dimensional elements representing mask features of the mask patterns, each two-dimensional element defining a closed region, and training a predictive model using the training data to generate the two-dimensional elemental representations.

[0006]

[0006] In some embodiments, a non-temporary computer-readable medium is provided which, when executed by a computer, has instructions that cause the computer to perform the method described in any of the above embodiments.

[0007]

[0007] In some embodiments, a device is provided that includes a memory for storing a set of instructions and a processor configured to execute a set of instructions and cause the device to perform the method described in any of the above embodiments.

[0008]

[0008] Hereinafter, embodiments will be described simply as examples with reference to the attached drawings. [Brief explanation of the drawing]

[0009] [Figure 1]

[0009] A block diagram of various subsystems of a lithography projection apparatus according to one embodiment is shown. [Figure 2]

[0010] This is a schematic diagram of a lithography projection apparatus according to one embodiment. [Figure 3]

[0011] An exemplary flowchart for simulating lithography in a lithography projection apparatus according to one embodiment is shown. [Figure 4]

[0012] This document describes a method for arranging, associating, and adjusting two-dimensional (2D) elements that form a mask feature, consistent with various embodiments. [Figure 5]

[0013] This document describes a method for obtaining the contour of a mask feature based on two-dimensional elements, consistent with various embodiments. [Figure 6]

[0014] A diagram is shown of a 2D element representation using the positional information of the 2D elements of a mask feature, consistent with various embodiments. [Figure 7]

[0015] A set of images is shown representing a two-dimensional elemental representation of a mask pattern, consistent with various embodiments. [Figure 8]

[0016] This is a block diagram of an exemplary system for predicting the two-dimensional elemental representation of a mask pattern using a predictive model, consistent with various embodiments. [Figure 9]

[0017] This is a block diagram for generating an image representation of a mask pattern from a target pattern, consistent with various embodiments. [Figure 10]

[0018] This shows the contours of the mask features generated from the predicted 2D elemental representation of the mask features, consistent with various embodiments. [Figure 11]

[0019] This is a flowchart of a method for predicting the 2D elemental representation of a mask pattern using a predictive model, consistent with various embodiments. [Figure 12]

[0020] This is a block diagram of a system for training a predictive model to generate a two-dimensional elemental representation of a mask pattern that matches various embodiments. [Figure 13]

[0021] This is a flowchart of a method for training a predictive model to generate a two-dimensional elemental representation of a mask pattern that matches various embodiments. [Figure 14]

[0022] This demonstrates the generation of a two-dimensional elemental representation of a mask pattern as training data for training a predictive model, consistent with various embodiments. [Figure 15]

[0023] A block diagram showing a computer system that can assist in implementing the systems and methods disclosed herein.

Best Mode for Carrying Out the Invention

[0010]

[0024] Here, in order to enable those skilled in the art to implement the present disclosure, exemplary examples will be given and the embodiments of the present disclosure will be described in detail with reference to the drawings. In particular, the following drawings and examples are not intended to limit the scope to a single embodiment, and other embodiments are possible by exchanging some or all of the illustrated or described elements. Whenever convenient, the same reference numbers are used throughout the drawings to refer to the same or similar parts. Further, if specific elements of these embodiments can be implemented partially or fully using known components, only those parts of such known components necessary for understanding the embodiments are described, and detailed descriptions of other parts of such known components are omitted so as not to obscure the description of the embodiments. In this specification, embodiments showing a single component should not be considered limiting, unless explicitly stated otherwise herein. Rather, the scope is intended to include other embodiments including a plurality of the same components, and vice versa. Further, the applicants do not intend to ascribe any term in this specification or the claims to a special or particular meaning, unless it is explicitly described as such. Further, the scope includes current and future known equivalents to the components referred to herein by way of example.

[0011]

[0025] A lithography apparatus is a machine that applies a designed pattern to a target area on a substrate. This process of transferring the designed pattern to the substrate is called the patterning process or lithography process. The patterning process can include the patterning step of transferring the pattern from a patterning device (such as a mask) to the substrate. Various variability (e.g., variability in the patterning process or lithography apparatus) can potentially limit the implementation of lithography for high-volume manufacturing (HVM) of semiconductors. Optimal proximity effect correction (OPC) can be used in mask design to optimize the mask so that light is ultimately delivered to the substrate by the mask manufactured using the mask pattern, resulting in the formation of the desired design layout. Conventional mask optimization may involve starting with a target pattern polygon (e.g., representing the desired pattern to be manufactured) and extracting such a polygon to serve as the basis for the mask. However, such conventional mask feature optimization can be computationally expensive because there may be many elements that need to be adjusted to form the optimized mask feature. Furthermore, conventional OPC can sometimes produce mask features that violate Mask Rule Check (MRC) rules. Several methods can use machine learning (ML) models (e.g., neural networks) to predict a mask image (e.g., a level set φ image of the mask pattern), then extract polygons from the level set image, and use this level set image as input to an OPC optimization process to adjust the mask feature contours. Polygon extraction is highly sensitive to the values ​​in the φ image. Even slight changes in pixel values ​​can lead to large deviations in the contours. Conventional ML models may not provide sufficient predictive accuracy, and as a result, the initially extracted polygons may result in large deviations from ground truth, MRC violations, and ultimately, insufficient sography performance.

[0012]

[0026] Embodiments for predicting a two-dimensional element representation of a mask pattern using a prediction model (e.g., an ML model such as a neural network) are disclosed. In a two-dimensional (2D) element representation, each mask feature can be represented using a plurality of two-dimensional elements (e.g., circles, ellipses, semi-circles, parts of circles, etc.). Additional details regarding the two-dimensional element representation are described in PCT application No. PCT / EP2023 / 055028, which is hereby incorporated by reference in its entirety. The mask feature contour can be derived from the two-dimensional elements. Next, the derived mask feature contour can be provided to a mask optimization process (e.g., to further adjust the mask feature contour), which can generate an optimized mask pattern that can be used to manufacture a mask and print a target pattern on a substrate.

[0013]

[0027] In one embodiment, a predictive model predicts two-dimensional element representation data from which a two-dimensional element representation can be generated. The predicted two-dimensional element representation data may include a set of images that define the arrangement of two-dimensional elements in a grid. For example, a first image may indicate the presence or absence of a two-dimensional element at a particular grid position. A second image may indicate the displacement of a two-dimensional element from a particular grid position in the x-direction, and a third image may indicate the displacement of a two-dimensional element from a particular grid position in the y-direction. In another example, one or more images in the set of images may also define the associations between two-dimensional elements that define the shape of the mask feature contour. A two-dimensional element representation in which each mask feature of a mask pattern is represented using multiple two-dimensional elements may be generated using the set of images. The mask feature contour can then be generated from the two-dimensional elements. The resulting mask pattern can then be optimized using an OPC process. In some embodiments, a predictive model may be trained to predict the two-dimensional element representation of a mask pattern. The training data may include an input mask pattern that can be generated from a target pattern (e.g., a GDS design layout) and a set of images showing a 2D elemental representation of the optimized mask pattern corresponding to the input mask pattern. By having the predictive model predict the 2D elemental representation rather than the level set images, the mask feature contours derived using the prediction are less sensitive to prediction errors (as some errors may cause only minimal local contour shifts, in contrast to the large contour shifts of conventional prediction techniques), and therefore result in a more accurate prediction of the mask pattern. Furthermore, training such a predictive model is less complex compared to conventional prediction techniques, and the predictive model is fault-tolerant, converges faster, and suffers less from overfitting problems.

[0014]

[0028] While this disclosure may make specific references to the manufacture of ICs, it should be clearly understood that there are many other possible applications of the description herein. For example, the description herein may be used to manufacture integrated optical systems, induction 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 relation to such alternative applications, any use of the terms “rectil,” “wafer,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0015]

[0029] In this document, 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 5–100 nm). In this document, the terms “radiation source” or “source” are used to encompass all types of radiation sources, including laser sources, incandescent light sources, etc., and may include radiation processing between the radiation source and the target or other parts of the optical system, including filtering, collimating, focusing, etc.

[0016]

[0030] A patterning device may contain or form one or more design layouts. Design layouts can be generated using CAD (Computer-Aided Design) programs. This process is often referred to as EDA (Electronic Design Automation). Most CAD programs follow a set of design rules to create functional design layouts / patterning devices. These rules are set based on processing and design constraints. For example, design rules define space tolerances between devices (gates, capacitors, etc.) or between interconnection lines to ensure that devices or lines do not interact with each other in undesirable ways. One or more constraints of the design rules may be referred to as "critical dimensions" (CD). The critical dimensions of a device can be defined as the minimum width of a line or hole, or the minimum distance between two lines or two holes. Thus, the CD defines the overall size and density of the device being designed. One of the goals of device manufacturing is to faithfully reproduce the original design intent on a substrate (using patterning devices).

[0017]

[0031] The terms “mask” or “patterning device” as used in this document may be broadly interpreted to refer to any general patterning device that can be used to provide an incident radiation beam with a patterned cross section corresponding to a pattern formed on a target portion of a substrate. In this context, the term “light bulb” may also be used. In addition to classical masks (transmissive or reflective masks, 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) an addressed region of the reflective surface reflects the incident radiation as diffracted radiation, while an unaddressed region reflects the incident radiation as non-diffracted radiation. Using appropriate filters, non-diffracted radiation can be removed from the reflected beam, leaving only diffracted radiation, and thus the beam is patterned according to the addressable pattern of the matrix-addressable surface. The required matrix addressing can be performed using electronic means. Another example of such patterning devices is a programmable LCD array. An example of such a structure is shown in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0018]

[0032] As used herein, the term “projection optics” should be interpreted broadly to encompass various types of optical systems, including, for example, refractive optics, projection optics, apertures, and reflector-refractor optics. The term “projection optics” may also include components that operate according to any of these design types for guiding, shaping, or controlling a radiation projection beam collectively or individually. The term “projection optics” may include any optical components within a lithography projection apparatus, regardless of where the optical components are located in the optical path of the lithography projection apparatus. A projection optics may include optical components for shaping, adjusting, and / or projecting radiation from a radiation source before the radiation passes through a patterning device, and / or optical components for shaping, adjusting, and / or projecting radiation after the radiation passes through a patterning device. Generally speaking, a projection optics excludes the radiation source and the patterning device.

[0019]

[0033] Figure 1 shows a block diagram of various subsystems of a lithography projection apparatus 10A according to one embodiment. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of radiation sources including an extreme ultraviolet (EUV) source (the lithography projection apparatus itself does not require a radiation source); an illumination optical system, which may include, for example, partial coherence (shown as sigma) and shaping the radiation from the radiation source 12A, optical systems 14A, 16Aa, and 16Ab; a patterning device (or mask) 18A; and a transmission optical system 16Ac that projects an image of the pattern of the patterning device onto a substrate plane 22A.

[0020]

[0034] The pupil 20A may be included in the transmission optical system 16Ac. In some embodiments, one or more pupils may be present before and / or after the mask 18A. As will be described in more detail herein, the pupil 20A can provide patterning of light that ultimately reaches the substrate plane 22A. An adjustable filter or aperture in the pupil plane of the projection optical system may limit the range of beam angles that strike the substrate plane 22A, where the maximum possible angle defines the numerical aperture of the projection optical system NA = n sin(θmax), 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 strike the substrate plane 22A.

[0021]

[0035] In a lithography projection system, a radiation 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. This does not negate the fact that the radiation source itself does not perform pattern formation, guidance, or shaping of the radiation, or that pattern formation, guidance, or shaping does not occur between the radiation source and the projection optical system. For example, 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 model can be used to calculate a resist image from the spatial image, an example of which can be found in U.S. Patent Application Publication No. 2009-0157360, the entirety of which is incorporated herein by reference. The resist model is concerned only with the characteristics of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of a lithography projection system (e.g., the properties of the illumination, patterning device, and projection optics) determine the spatial image, and these optical properties can be defined by an optical model. Since the patterning device used in the lithography projection system can be changed, it is desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithography projection system, including at least the radiation source and projection optics. Details of the techniques and models used to convert design layouts into various lithographic images (e.g., spatial images, resist images, etc.), to apply OPC using these 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 their entirety.

[0022]

[0036] 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 by transmission and / or reflection patterning devices).

[0023]

[0037] Mask transparency functions can take on various different forms. One form is binary. A binary mask transparency function has one of two values ​​(e.g., zero and a positive constant) at a given position on the patterning device. A mask transparency function in binary form is sometimes called a binary mask. Another form is continuous. That is, the transmittance (or reflectance) of the patterning device is a continuous function of the position on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the position on the patterning device. A mask transparency function in continuous form is sometimes called a continuous tone mask or continuous transparency mask (CTM). For example, a CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of a binary value of 0 or 1. In one embodiment, the CTM may be a pixelated grayscale image, where each pixel has a value (for example, a value in the range [-255,255], a normalized value in the range [0,1] or [-1,1] or other appropriate range).

[0024]

[0038] To simplify the determination of the interaction between radiation and the patterning device, the thin-film mask approximation, also known as the Kirchhoff boundary condition, is widely used. The thin-film mask approximation assumes that the thickness of the structure on the patterning device is very small compared to the wavelength, and the width of the structure on the mask is very large compared to the wavelength. Therefore, the thin-film mask approximation assumes that the electromagnetic field after the patterning device is the product of the incident electromagnetic field and the mask transmission function. However, as lithography processes use radiation with increasingly shorter wavelengths and structures on the patterning device become increasingly smaller, the assumptions in the thin-film mask approximation can break down. For example, the interaction between radiation and structure (e.g., the edge between the top surface and the sidewall) can become significant due to the finite thickness ("mask 3D effect" or "M3D"). By including this scattering in the mask transmission function, the mask transmission function can better capture the interaction between radiation and the patterning device. The mask transmission function under the thin-film mask approximation is sometimes referred to as the thin-film mask transmission function. The mask transparency function that encompasses M3D is sometimes referred to as the M3D mask transparency function.

[0025]

[0039] Figure 2 schematically shows an exemplary lithography projection apparatus that can optimize the illumination source using the method described herein. - Includes an illumination system IL for adjusting the radiation beam B. In this particular case, the illumination system also includes the radiation source SO and - A first object table (e.g., mask table, patterning device table, or rectile stage) MT is provided, 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 or wafer stage) WT is provided, which includes a substrate holder for holding a substrate W (e.g., a resist-coated silicon wafer) and is connected to a second positioner for precisely positioning the substrate relative to an item PS. - The patterning device MA includes a projection system ("lens") PS (e.g., a refractive, reflective, or reflective-refractory optical system) for imaging the irradiated portion of the patterning device MA onto a target portion C of the substrate W (e.g., including one or more dies).

[0026]

[0040] As shown herein, the apparatus is transmissive (i.e., has a transmissive mask). However, generally speaking, the apparatus can also be reflective (having a reflective mask), for example. Alternatively, the apparatus may use another type of patterning device as an alternative to the use of classical masks, examples of which include programmable mirror arrays or LCD matrices.

[0027]

[0041] A radiation source SO (e.g., a mercury lamp or excimer laser) generates a radiation beam. This beam is supplied to an 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 intensity distribution within the beam (generally referred to as σ-outer and σ-inner, respectively). In addition, the illuminator IL generally includes various other components such as an integrator IN and a capacitor CO. Thus, the beam B that strikes the patterning device MA has the desired uniformity and intensity distribution in the cross-section of the radiation beam.

[0028]

[0042] Regarding Figure 2, it should be noted that while the radiation source SO may be located within the housing of the lithography projection apparatus (in most cases, when the radiation source SO is, for example, a mercury lamp), the radiation source SO may also be located away from the lithography projection apparatus, and the radiation beam generated by the radiation source SO may be guided into the apparatus (for example, with the help of appropriate guide mirrors). This latter scenario is often the case when the radiation source SO is an excimer laser (e.g., based on KrF, ArF, or F2 lathing).

[0029]

[0043] Subsequently, beam B intersects with the patterning device MA, which is held on the patterning device table MT. After crossing the patterning device MA, beam B passes through a lens PS that focuses beam B onto a target portion C of 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 PB. 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 11. However, in the case of a wafer stepper (as opposed to a step-and-scan tool), the patterning device table MT can be connected to or fixed only to short-stroke actuators.

[0030]

[0044] The illustration 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 one 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 area 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 moved simultaneously at velocity V=Mv in the same or opposite direction, where M is the magnification of the lens PS (typically M=1 / 4 or 1 / 5). In this way, a relatively large target area C can be exposed without having to compromise on resolution.

[0031]

[0045] Figure 3 shows an exemplary flowchart for simulating lithography in a lithography projection apparatus according to one embodiment. As recognized, the models may represent different patterning processes and do not necessarily include all the models described below. The radiation source model 300 represents the optical properties of illumination of the patterning device (including radiant intensity distribution, bandwidth, and / or phase distribution). The radiation source model 300 may, but is not limited to, represent the optical features of illumination including numerical aperture settings, illumination sigma (σ) settings, and any specific illumination shape (e.g., off-axis radiation shapes such as annular, quadrupole, and bipolar), where σ (i.e., sigma) is the outer radius range of the illuminator.

[0032]

[0046] Projection optics model 310 represents the optical characteristics of the projection optics (including changes in radiant intensity distribution and / or phase distribution caused by the projection optics). Projection optics model 310 can represent optical characteristics of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0033]

[0047] The patterning device / design layout model module 320 may include capturing how design features are laid out in the pattern of the patterning device and representing detailed physical properties of the patterning device, as described in, for example, U.S. Patent No. 7,587,704, which is incorporated by reference as a whole. In one embodiment, the patterning device / design layout model module 320 represents the optical features (including changes in radiant intensity distribution and / or phase distribution resulting from a given design layout) of a design layout (e.g., a device design layout corresponding to features such as an integrated circuit, memory, or electronic device), where the design layout is a representation of the arrangement of features on or formed by the patterning device. Since the patterning device used in the lithography projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the 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 can then be compared to the device design. Device designs are generally defined as OPC pre-patterned device layouts and provided in standardized digital file formats such as GDSII or OASIS.

[0034]

[0048] The spatial image 330 can be simulated from the radiation source model 300, the projection optics model 310, and the patterning device / design layout model module 320. 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.

[0035]

[0049] 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 350 can be simulated from the spatial image 330 using a resist model 340. A resist model can be used to calculate a resist image from a spatial image, an example of which can be found in U.S. Patent No. 8,200,468, the entire disclosure of which is incorporated herein by reference. The resist model 340 typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development to predict, for example, the contour of a resist feature 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 some embodiments, optical properties of the resist layer, such as refractive index, film thickness, propagation, and polarization effects, can be captured as part of a projection optical system model 310.

[0036]

[0050] Therefore, generally, the optical model and the resist model are linked by the simulated spatial image intensity within the resist layer, resulting from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (spatial image intensity) is converted into a potential "resist image" by the absorption of incident energy and further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full-chip applications approximate the realistic three-dimensional intensity distribution within the resist stack with a three-dimensional spatial (and resist) image.

[0037]

[0051] In one embodiment, the resist image 350 can be used as input to a post-pattern transfer process model module 360. The post-pattern transfer process model module 360 ​​defines the performance of one or more post-resist development processes (e.g., etching, development, etc.).

[0038]

[0052] By simulating the patterning process, it is possible to predict, for example, the contour, 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 ​​can be compared to the intended design for purposes such as correcting the patterning process and identifying locations where defects are expected to occur. The intended design is generally defined as an OPC pre-design layout, which can be provided in a standardized digital file format such as GDSII, OASIS, or other file formats.

[0039]

[0053] Therefore, the model formulation should ideally describe most, if not all, of the known physical and chemical properties of the entire process, with each model parameter corresponding to a different physical or chemical effect. The model formulation, therefore, sets an upper limit on how well the entire manufacturing process can be simulated using that model.

[0040]

[0054] The following paragraphs describe a system and method for predicting the two-dimensional elemental representation of a mask pattern. A prediction model (e.g., an ML model such as a neural network) is trained to predict the two-dimensional elemental representation based on an input mask pattern (e.g., generated from a target pattern printed on a substrate). The two-dimensional elemental representation predicted by the prediction model is a multi-channel output containing a set of images indicating the positional information of the two-dimensional elements representing the mask features (although it can be a single-channel output, as described below). Training data (e.g., ground truth), containing the input mask pattern and a set of images indicating the positional information of the two-dimensional elements, can be generated in many ways.

[0041]

[0055] Figures 4 and 5 provide a brief introduction to the 2D element representation of a mask feature and the generation of a mask feature contour from the 2D element representation, respectively.

[0042]

[0056] Figure 4 illustrates a method for arranging, associating, and aligning two-dimensional elements to form a mask feature, consistent with various embodiments. In some embodiments, determining the mask pattern (or portion thereof) used in the lithography process may include assigning the positions of the two-dimensional elements 410 based on the target pattern. As shown in the first (upper) portion 400A of Figure 4, the shape of the mask feature 401 can be represented by a collection of two-dimensional elements 410 (shown as a circle in this example). The two-dimensional elements are positioned at different locations to form the shape of the mask feature, as illustrated by a grid indicated by dots for reference. The dots at the grid locations may not be generated and are shown for illustrative purposes only. In some embodiments, the grid may be a collection of pixels in an image. Four of the two-dimensional elements are labeled 410a, 410b, 410c, and 410d. As will be further explained herein with reference to at least Figure 5, it can be seen that a contour formed around a two-dimensional element (for example, a circle having a diameter of at least the minimum width specified by the MRC rule) can inherently and automatically satisfy the MRC rule regardless of the position of the two-dimensional element.

[0043]

[0057] The next panel 400B in Figure 4 shows an example of associating 2D elements based on association criteria to form a cluster 430 representing a mask feature. Associations 420 are shown as line segments between the 2D elements. The associated 2D elements can be used to form a cluster 430 having a shape corresponding to the mask feature 401, as will be further described herein. In Figure 4, all of the illustrated 2D elements are part of cluster 430. Not all 2D elements in a cluster need to be associated with each other, as the associated elements depend on the optimization of the mask feature. For example, the upper left 2D element 410a is not associated with the lower right 2D element 410d, but 2D elements 410a and 410d are part of the same cluster 430 through associations with other 2D elements. In some embodiments, the association criteria may be rule-based criteria. For example, one association criterion may be distance-based, where two 2D elements can be associated with each other if they are within a specified distance range. The specified distance can be arbitrarily set by the user or manipulated by the system in another way, but in some embodiments, the specified distance may be based on MRC rules regarding the minimum width of the mask feature. In some embodiments, two 2D elements may be associated with each other based on predictions from a predictive model, as described with reference to at least Figures 7, 8 and 12-13.

[0044]

[0058] The central panel 400C in Figure 4 shows an exemplary contour 440 around the cluster 430. As will be described in more detail herein, for example with reference to Figure 5, the contour 440 can be generated to encompass the region formed by the two-dimensional elements and the region between the two-dimensional elements. Thus, the contour can be the outer contour of the cluster corresponding to the outer edge of the mask feature. Similarly, for mask features with an inner edge, such as a donut-shaped mask feature, the contour can be the inner contour of the cluster corresponding to the inner edge of the mask feature.

[0045]

[0059] The next panel, 400D, is similar to the central panel, and in this case also shows the 2D elements 410, associations 420, clusters 430, and contours 440, but does not show the lines forming the regions between the 2D elements or the mask feature 401. Here, the contours 440 are more clearly visible and surround the clusters of 2D elements.

[0046]

[0060] The bottom panel 400E in Figure 4 shows the adjustment of the 2D elements of cluster 430 to alter the mask features formed by cluster 430. In some embodiments, the adjustment of the mask features may be based on simulations associated with a lithography process, an OPC model, etc. (as described, for example, with reference to at least Figure 3). In other embodiments, the adjustment of the mask features may be based on the geometric properties of the mask pattern (e.g., width, spacing, etc.) and on rules defined with respect to OPC (e.g., adding serifs, biases, hammerheads, SRAFs, etc. to the main features). In some embodiments where the adjustment is based on simulation, the mask generation process in SMO or OPC, etc., can optimize the mask features by adjusting any combination of 2D elements of any of the clusters formed for the simulated mask. In this example, 2D element 450a is shown in a slightly different position, and 2D element 450b has been added (a nearby 2D element has also been moved slightly). As used herein, “adjusting” a 2D element means moving a 2D element, changing the shape of a 2D element, or adding / removing a 2D element. For example, the center of a circular 2D element can be moved as needed to optimize the mask. In other embodiments, the radius of a circular 2D element can be changed as part of the optimization process. When using such a method for determining / adjusting the contour of a mask feature, any of the disclosed methods may include manufacturing a mask from a mask pattern containing the contour generated from the adjusted 2D element.

[0047]

[0061] This disclosure intends that many types of two-dimensional elements are available. Since two-dimensional elements can be used to define at least certain dimensions (e.g., CD, minimum spacing between mask features) and, in some cases, certain regions (e.g., minimum region allowed for a mask feature), two-dimensional elements can define non-zero regions (e.g., different from points). In some embodiments, two-dimensional elements are two-dimensional (2D) elements. For example, two-dimensional elements can be circular or, more generally, elliptical. Two-dimensional elements can be the same size, or they can be different sizes within or between clusters. Two-dimensional elements do not have to be circular / elliptical. For example, two-dimensional elements can be polygonal (e.g., square, triangle, rectangle, hexagon, etc.) or any suitable shape. In such embodiments, contours can be drawn around vertices or along edges. Such two-dimensional elements can define closed regions (e.g., circular regions as shown), at least partially closed regions, or semi-closed regions (e.g., semicircles). While shapes such as circles and polygons are examples of closed regions, in some embodiments, two-dimensional elements can be effectively represented by arcs or other similar structures. For example, the same contour in the bottom panel of Figure 4 can be generated by positioning arc segments having the same center as the circle, where the arc segments are appropriately oriented and have sufficient length to generate the illustrated contour. Thus, other two-dimensional elements equivalent to those shown herein may be considered within the scope of this disclosure.

[0048]

[0062] Figure 5 illustrates a method for obtaining the contour of a mask feature based on two-dimensional elements, consistent with various embodiments. A cluster of two-dimensional elements can be contoured in any suitable way without departing from the scope of this disclosure, one embodiment of which is shown in Figure 5. The upper portion 500A of Figure 5 shows two exemplary related two-dimensional elements 510a and 510b. A virtual line segment 520 can connect the centers of the two-dimensional elements. The system does not need to generate the virtual line segment 520 (provided here for illustrative purposes). The virtual line segment 520 can be offset on both sides by a distance equal to the radius of the two-dimensional element with respect to the contour 530a around the two-dimensional element. This then allows for the formation of what is referred to herein as “subregions” (the region of the two-dimensional element and the region between the two-dimensional elements based on the offset line), one of which is shown as subregion 522a. In embodiments where the two-dimensional elements are not the same size, the offset can be made such that the offset distance shifts from one radius to the other. However, it will be recognized that this discussion is merely illustrative. The offset distance or subregion can be defined in any other suitable way, and a mask feature may have many such subregions. The region enclosed by contour 530a may be the region occupied by the subregion and any corresponding region inside the connected collection of subregions (e.g., the region of subregions around the perimeter of the mask feature, and the region that may be enclosed by such perimeter).

[0049]

[0063] The following section 500B extends the above example to include a two-dimensional element 510c. Another virtual line segment 520a is shown between 510b and 510c, along with a corresponding offset line segment that forms part of the contour 530b. Thus, in various embodiments, a process similar to that described above may include generating subregions of the contour (e.g., 522a and 522b) by applying a polygonal offset operation to a pair of associated two-dimensional elements (e.g., 510a / b and 510b / c). The process may then include calculating the union of the subregions, the contour 530b being the union of the subregions. Since the illustrated two-dimensional elements can form a cluster, the system can thereby generate a contour of the cluster based on the two-dimensional elements. In this example, the contour corresponds to the outer contour of all subregions within the cluster that form the perimeter of the cluster. This process can be extended to any number and configuration of two-dimensional elements, as shown by the lower section 500C, which shows the contour 530c.

[0050]

[0064] The examples in panels 500A-C of Figure 5 are provided to offer an exemplary stepwise method of contouring, but in some embodiments, contouring can be performed in substantially fewer steps. For example, once the two-dimensional elements forming the basis of the mask shape are determined, such two-dimensional elements can form a single shape (which may include any combination of polygons and line segments). This shape can then be treated as a "polygon" (which, in this case, may also have parts that are line segments and therefore does not need to be strictly a polygon), and this "polygon" can be contoured by performing a polygonal offset operation according to any of the examples herein, including some of which are described below.

[0051]

[0065] In some embodiments, a “polygon offset” operation can be performed, which allows the contouring polygon to be defined by selecting the position (e.g., center) of a 2D element corresponding to a desired mask feature. An example of such a polygon 540 is shown in bold in 500C, showing various line segments connecting specific centers of the 2D element. The polygon 540 (including an exemplary additional line segment 550) can then be offset (e.g., by the radius of the 2D element) to form the contour 530c shown. Although not shown in the example of Figure 5, any inner region (e.g., as seen in a “donut-shaped” mask feature) can similarly be defined, contoured, and shaped as described herein.

[0052]

[0066] The defined outer contour can be further processed with any suitable technique. As can be seen from the example of the circular two-dimensional element in Figures 4 and 5, some parts of the defined contour are naturally rounded based on the radius of the two-dimensional element. However, at some locations, such as the recesses of contours 530a-530c, the disclosed method may also include performing corner rounding or any other type of smoothing operation on the outer contour. One method of corner rounding may include performing spline interpolation between two points on either side of the corner. In some embodiments, spline interpolation may modify the contour to be smoother, but without the contour touching the two-dimensional element. Such deviations may be acceptable as they may further enhance compliance with the minimum width MRC rule.

[0053]

[0067] In some embodiments shown in panel 500D, the system generates “angular corners” 570 around the vertices of the contoured polygon such that intersecting segments, which would normally form sharp vertices rather than rounded corners 560, contact a third line segment (e.g., similar to a chamfer). Another option is to have the line segments contact each other so as to form “misered corners” 580, but in certain embodiments this may result in undesirable extension of the contour (e.g., exceeding a specified distance limit from the relevant vertex). In such cases, the system may make the mitered corners 580 square to form another angular corner 580a so that the contour does not extend beyond the specified limit. Additional details on generating 2D element representations or generating mask feature contours from 2D element representations are described in PCT application PCT / EP2023 / 055028, the entire disclosure of which is incorporated by reference.

[0054]

[0068] In some embodiments, a two-dimensional element representation may be represented using positional information of two-dimensional elements representing a mask feature. Figure 6 shows a diagram of a two-dimensional element representation using positional information of two-dimensional elements of a mask feature, consistent with various embodiments. For example, consider the two-dimensional element representation 600 of the mask feature 630 shown in Figure 6. In some embodiments, the two-dimensional element representation 600 is similar to the two-dimensional element representation in panel 400E of Figure 4. The two-dimensional element may be assigned a position in a grid (e.g., a collection of pixels), such as grid 625. Note that grid 625, shown as dots in Figure 6, is hypothetical and for illustrative purposes only, and is not generated by the system. Grid positions may correspond to one or more pixels in the image, and the resolution or size of the grid may be user-defined. For example, the grid may be a "10x10" or "25x25" grid position, and each grid position may correspond to one or more pixels. In some embodiments, grid 625 may be considered a two-dimensional matrix.

[0055]

[0069] Two-dimensional elements, such as the first two-dimensional element 603, can be represented using positional information. Two-dimensional elements may be assigned coordinates on a grid 625. In some embodiments, the grid coordinates assigned to a two-dimensional element depend on the geometric attributes of the two-dimensional element. In the example in Figure 6, the grid coordinates assigned to a two-dimensional element may be the grid coordinates closest to the center of the two-dimensional element. For example, for the first two-dimensional element 603, the grid coordinate (1,1) closest to the center 602 of the first two-dimensional element 603 is assigned as the position of the first two-dimensional element 603. Similarly, the grid coordinate (2,3) closest to the center 612 of the second two-dimensional element 605 is assigned as the position of the second two-dimensional element 605. Thus, positional information (e.g., grid coordinates) can be generated for all two-dimensional elements within the two-dimensional element representation 600. Note that while grid coordinates are used to indicate positional information, other parameters may be used as well. For example, (x,y) coordinates may be used instead of matrix-type coordinates.

[0056]

[0070] In some embodiments, location information may also include existence information, which may be a binary value indicating the presence or absence of a 2D element at a particular grid location. For example, for a first grid coordinate (1,1), existence information may include a value of "1" indicating the presence of a 2D element at the first grid coordinate (1,1). Similarly, for a second grid coordinate (1,2), existence information may include a value of "0" indicating the absence of a 2D element at the second grid coordinate (1,2). Thus, location information may include existence information for all grid coordinates. Binary values ​​can be represented in many ways (e.g., "0" or "1", "yes" or "no", "true" or "false", etc.).

[0057]

[0071] In some embodiments, the position information may also include the amount of deviation or displacement of a 2D element from a specific grid position. In some embodiments, the position information may separately provide deviation values ​​in different directions (e.g., x and y directions). For example, the position information may include the amount of deviation 652,a of a 2D element (e.g., a fifth 2D element 606) from grid coordinate (6,3) in the x direction. x This shows that the displacement was only ((6,3),a x ) may include displacement information such as. Similarly, position information may include a 2D element (e.g., a fifth 2D element 606) being a quantity 654,a in the y direction from the grid coordinate (6,3). y This shows that the displacement was only ((6,3),a y This may include displacement information such as )

[0058]

[0072] In some embodiments, the positional information may also include association information between two-dimensional elements. For example, the association information may indicate which two-dimensional elements are associated with which other two-dimensional elements. The association information can be shown in various ways. In the first example, associations 622, 623, and 624 may be shown as ((1,1),(2,1),(2,2)), indicating that a two-dimensional element at grid coordinate (1,1) (e.g., the first two-dimensional element 603) is associated with a two-dimensional element at grid coordinate (2,1) (e.g., the third two-dimensional element 608) and a two-dimensional element at grid coordinates (2,2) and (2,3) (e.g., the second two-dimensional element 605). In the second example, the association information may be shown separately with respect to the x and y directions. For example, x-direction association information for a 2D element at grid coordinate (2,1) can be represented as ((2,1),(2,2)), indicating that the 2D element at grid coordinate (2,1) (e.g., the third 2D element 608) is associated with another 2D element in the x-direction at grid coordinate (2,2). Similarly, y-direction association information for a 2D element at grid coordinate (2,1) can be represented as ((2,1),(1,1),(3,2)), indicating that the 2D element at grid coordinate (2,1) (e.g., the third 2D element 608) is associated with other 2D elements in the y-direction at grid coordinates (1,1) and (3,2) (e.g., the first 2D element 603) and (e.g., the fourth 2D element 610). In the third example, the association information can be represented as a binary value indicating whether a 2D element at a particular grid position is associated with 2D elements at adjacent positions in one or more directions. For example, x-direction association information for a 2D element at grid coordinate (2,1) can be expressed as ((2,1),1), indicating that the 2D element at grid coordinate (2,1) (e.g., a third 2D element 608) is associated with a 2D element in an adjacent grid at x-direction grid coordinate (2,2).Similarly, y-direction association information for a 2D element at grid coordinate (2,1) can be represented as ((2,1),0), indicating that the 2D element at grid coordinate (2,1) (e.g., the third 2D element 608) is not associated with a 2D element at an adjacent grid position in y-direction grid coordinate (3,1).

[0059]

[0073] In some embodiments, the above information, such as existence information, position information, displacement information, and association information, can be encoded into a set of images from which a two-dimensional element representation 600 can be derived. The above information can be used to generate a set of images, but in some embodiments, the set of images can be derived from a level set image of the mask pattern. Figure 7 shows a set of images representing a two-dimensional element representation of a mask pattern, consistent with various embodiments. In the example of Figure 7, the first image 715a may be a binary image in which each pixel value can indicate the presence or absence of a two-dimensional element at a corresponding grid position. For example, a white pixel may represent the presence of a two-dimensional element or a portion thereof at a corresponding grid position, and a black pixel may represent the absence of a two-dimensional element at a corresponding grid position.

[0060]

[0074] The second image 715b may show displacement information of a two-dimensional element in the first direction. For example, each pixel value in the second image 715b may indicate the amount of displacement of the two-dimensional element in the x-direction from the position of that pixel.

[0061]

[0075] The third image 715c may show displacement information of the two-dimensional element in the second direction. For example, each pixel value in the third image 715c may indicate the amount of displacement of the two-dimensional element in the y-direction from the position of that pixel.

[0062]

[0076] A set of images may contain fewer or more images than those shown in Figure 7. For example, a set of images may not include the first image 715a, in which case the existence information is derived from the second image 715b and the third image 715c. In some embodiments, a set of images may include additional images, such as images showing association information. One or more images may be generated to show associations in different directions. For example, the first association image may be a binary image showing an association in a first direction (e.g., the x-direction). Each pixel value may indicate whether a 2D element at a particular location is associated with a 2D element at an adjacent location in the x-direction. In another example, the second association image may be a binary image showing an association in a second direction (e.g., the y-direction). Each pixel value may indicate whether a 2D element at a particular location is associated with a 2D element at an adjacent location in the y-direction. In yet another example, the third association image may be a binary image showing an association in a third direction (e.g., the northeast (NE) direction). Each pixel value may indicate whether a 2D element at a particular location is associated with a 2D element at an adjacent location in the NE direction. For example, the pixel value of a pixel corresponding to grid coordinate (3,2) may indicate an association between a 2D element at grid coordinate (3,2) and a 2D element at grid coordinate (2,3). Other images may also be generated for associations in other directions (e.g., northwest, southeast, southwest).

[0063]

[0077] In some embodiments, training a predictive model to generate a set of images representing a two-dimensional elemental representation (e.g., one or more images in the set) is more efficient than training the predictive model to generate the mask pattern itself. For example, such an ML model may be fault-tolerant, converge faster, or consume fewer computing resources compared to training the ML model to generate the mask pattern itself. After the set of images is generated, the two-dimensional elemental representation can be derived or constructed from the set of images, and the mask feature contours can be constructed to generate the output mask pattern. Figures 8–11 illustrate generating or predicting a two-dimensional elemental representation of a mask pattern using an ML model.

[0064]

[0078] Figure 8 is a block diagram of an exemplary system for predicting the two-dimensional elemental representation of a mask pattern using a predictive model, consistent with various embodiments. Figure 11 is a flowchart of a method for predicting the two-dimensional elemental representation of a mask pattern using a predictive model, consistent with various embodiments.

[0065]

[0079] In process P1105 of Figure 11, the input mask pattern 805 is provided to the prediction model 850. In some embodiments, the prediction model 850 is an ML model (e.g., a neural network model) trained to predict a two-dimensional elemental representation of the mask pattern. Further details of training the prediction model 850 are described with reference to at least Figures 12 and 13.

[0066]

[0080] The input mask pattern 805 may be an image representation of an initial version of the mask pattern to be printed on the substrate. In some embodiments, the input mask pattern 805 may be generated from a target pattern (e.g., a GDS layout), as shown in Figure 9. Figure 9 is a block diagram for generating an image representation of the mask pattern from a target pattern, consistent with various embodiments. The imaging component 950 may generate the input mask pattern 805 from the target pattern 905, which is the design layout of the pattern to be printed on the substrate. The imaging component 950 may generate the input mask pattern 805 using any of many known methods. For example, the imaging component 950 may generate the input mask pattern 805 from the target pattern 905 using a rasterization process. In the rasterization process, the target pattern is decomposed into rectangles, and all rectangles are rasterized into a temporary buffer. Transmittance and phase are then applied to the buffer to generate an image of the input mask pattern 805. In some embodiments, the corners of the features in the target pattern 905 may be rounded, the edges may be smoothed (e.g., anti-aliased), and the pixel values ​​may be filled (e.g., converted to a grayscale image) as part of the rasterization process. In some embodiments, the generation of the input mask pattern 805 may not involve simulating a lithography process (e.g., as described with reference to at least Figure 3).

[0067]

[0081] Referring again to Figure 11, in process P1110, the prediction model 850 generates a set of images 815 representing a two-dimensional elemental representation of the output mask pattern (e.g., an intermediate optimized version of the input mask pattern). The set of images 815 may show positional information of the two-dimensional elements in the two-dimensional elemental representation. In some embodiments, the positional information includes information about the grid position assigned to the two-dimensional element and the displacement of the two-dimensional element from the assigned grid position. The set of images 815 may include at least one of the images described above with reference to Figure 7. For example, the set of images 815 may include a binary image (e.g., a first image 715a) indicating the presence or absence of a two-dimensional element at a given grid position. A set of images 815 may include a second image (e.g., a second image 715b) showing the displacement of a two-dimensional element in a first direction (e.g., the x-direction) from a specified grid position, and a third image (e.g., a third image 715c) showing the displacement of a two-dimensional element in a second direction (e.g., the y-direction) from a specified grid position. In some embodiments, a set of images 815 may not include the first image 715a, in which case the presence information may be derived from the second image 715b and the third image 715c.

[0068]

[0082] In some embodiments, a set of images 815 may also include images showing associations between 2D elements of a 2D element representation. For example, a first association image may be a binary image showing whether a 2D element at a particular location is associated with a 2D element at an adjacent location in a first direction (e.g., the x-direction). A second association image may be a binary image showing whether a 2D element at a particular location is associated with a 2D element at an adjacent location in a second direction (e.g., the y-direction). In some embodiments, association information may not be predicted by the prediction model. 2D elements may be associated based on association criteria. In some embodiments, the association criteria may be rule-based criteria. For example, one association criterion may be distance-based, as illustrated with reference to at least Figure 4, where two 2D elements can be associated with each other if they are within a specified distance range. In some embodiments, the prediction model 850 is referred to as a single-channel input and multi-channel output prediction model, since many images (e.g., a set of images 815) are produced as outputs for a single image (e.g., an input mask pattern 805) as input. In an embodiment in which the prediction model 850 outputs only existence information, such as the first image 715a, the prediction model 850 is referred to as a single-channel input and single-channel output prediction model.

[0069]

[0083] It should be noted that the prediction model can be trained to predict any number of images based on the desired information. For example, if only presence information for a 2D element is available, the prediction model can be trained to predict a single image (e.g., the first image 715a). In a single-channel output embodiment, displacement information (e.g., displacement of the 2D element from a particular grid position) may be considered "0". In another example, if only displacement information for a 2D element in two directions is available, the prediction model can be trained to predict two images (e.g., the second image 715b and the third image 715c). The presence information for the 2D element at various positions can be derived from the displacement information contained in the two images. In yet another example, if presence information and displacement information for a 2D element in two directions are available, the prediction model can be configured to generate three images (e.g., the first image 715a, the second image 715b, and the third image 715c). In yet another example, if existence information, displacement information of a 2D element in two directions, and association information of a 2D element in two directions are required, the prediction model may be configured to generate five images (e.g., a first image 715a, a second image 715b, a third image 715c, and two additional images) showing the association of the 2D element in two directions (e.g., x-direction - to the left of the 2D element and y-direction - downwards of the 2D element). In yet another example, if existence information, displacement information of a 2D element in two directions, and association information of a 2D element in four directions are required, the prediction model may be configured to generate seven images (e.g., a first image 715a, a second image 715b, a third image 715c, and a fourth additional image (e.g., two images showing the association of the 2D element to the left and right in the x-direction, and two images showing the association of the 2D element upwards and downwards in the y-direction)). Such a variety of outputs are possible.

[0070]

[0084] The two-dimensional element representation is generated based on a set of images 815. For example, the two-dimensional element representation may be similar to the two-dimensional element representation 600 of the mask feature 630, or the two-dimensional element representation in Figure 4 in the bottom panel 400E of the mask feature 401, and may be generated using various information derived from a set of images 815. In some embodiments, the two-dimensional element representation is generated for all mask features of the output mask pattern.

[0071]

[0085] In process P1115, mask feature contours are generated for mask features based on 2D elements in a 2D element representation. In some embodiments, mask feature contours may be constructed using polygonal offsets or clustering of 2D elements, as illustrated with reference to at least Figures 4 and 5. For example, a 2D element may be associated with one or more other 2D elements based on association criteria or association information obtained from a set of images predicted by a predictive model to generate one or more clusters of 2D elements to form the shape of a mask feature, and then mask feature contours may be generated from the 2D elements, as illustrated with reference to at least Figure 5. For example, as shown in Figure 10, mask feature contour 1005 may be generated for mask feature 630 based on 2D elements in a 2D element representation 600. Mask feature contours are generated for all mask features, thereby generating the output mask pattern.

[0072]

[0086] In some embodiments, in process P1120, the output mask pattern may be further optimized by performing a mask optimization process such as OPC to generate an optimized mask pattern 1120. The mask or patterning device may be manufactured based on the optimized mask pattern 1120 used in the lithography process to print a target pattern onto a substrate.

[0073]

[0087] Figures 12-14 show the training of a predictive model 850 for generating a two-dimensional elemental representation of a mask pattern. Figure 12 is a block diagram of the system for training a predictive model to generate a two-dimensional elemental representation of a mask pattern, consistent with various embodiments. Figure 13 is a flowchart of the method for training a predictive model to generate a two-dimensional elemental representation of a mask pattern, consistent with various embodiments.

[0074]

[0088] In process P1305, training data is obtained for training a predictive model. In some embodiments, the training data includes one set of input mask pattern images 1205 and several sets of images 1210, where each set of images represents a two-dimensional elemental representation of the output mask pattern of the corresponding input mask pattern. For example, the training data may include an input mask pattern 1205a and one set of images 1210a1 to 1210an corresponding to a two-dimensional elemental representation of the output mask pattern (e.g., an optimized version of the input mask pattern 1205a).

[0075]

[0089] In some embodiments, the input mask pattern 1205a is an image generated from a target pattern using, for example, an imaging component 950, as described with reference to at least Figure 9.

[0076]

[0090] In some embodiments, a set of images 1210a1-120an may be similar to a set of images 815 showing positional information, presence information, displacement information, association information, etc., of the 2D elements of a 2D element representation. A set of images 1210a1-1210an can be generated from a 2D element representation, which can be generated in many ways. In a first method, the 2D element representation of a mask pattern can be generated in an iterative manner, as illustrated at least in Figure 4. For example, mask features are obtained from an initial mask pattern, and the 2D element representation is generated by assigning positions to the 2D elements, associating the 2D elements, and adjusting the 2D elements to generate a 2D element representation of the output mask pattern. The adjustment of the 2D elements can be based on simulations associated with a lithography process, an OPC model, etc. (as illustrated, for example, with reference to Figure 3), or based on the geometric properties of the mask pattern (e.g., width, spacing, etc.) and rules defined with respect to OPC (e.g., adding serifs, biases, hammerheads, SRAFs, etc., to the main features).

[0077]

[0091] In the second method, the two-dimensional elemental representation of the mask pattern can be generated in a non-repeating manner, as shown in Figure 14. Figure 14 shows the generation of the two-dimensional elemental representation of the mask pattern used when training a predictive model, consistent with various embodiments. For example, the contour 1405 of the mask feature is obtained from the initial mask pattern. To generate the reduced contour 1435, the contour 1405 is reduced by a specified amount (e.g., shrunken). The specified amount may relate to geometric parameters associated with the two-dimensional element, such as the radius 1410 of the circle 1415. The two-dimensional element is then placed along the reduced contour 1435 at or near grid positions. In some embodiments, the contour 1405 is reduced by an amount equal to the radius of the 2D elements, and the 2D elements are placed along the reduced contour 1435 to generate a 2D element representation 1425, so that the contour 1454 reconstructed from the 2D element representation 1425 is almost the same size and shape as the original contour 1405 (for example, the reconstructed contour 1454 extends outward from the reduced contour 1435 by an amount equal to the radius of the circle 1415). In some embodiments, the number of 2D elements that can be placed along the reduced contour 1435 may depend on the resolution of the grid 1430. For example, the higher the resolution of the grid 1430, the more 2D elements that can be placed along the reduced contour, the finer the reconstructed contour 1454 becomes, and the more similar the reconstructed contour 1454 becomes to the original contour 1405. In some embodiments, the generation of the 2D element representation using the second method may be faster and consume fewer computing resources compared to the generation using the first method.

[0078]

[0092] After a two-dimensional element representation is generated (using either the first or second method), information such as existence information, position information, displacement information, and association information of the two-dimensional elements from the two-dimensional element representation can be used to generate a set of images 1210a1 to 1210an.

[0079]

[0093] Referring again to Figure 13, in process P1310, the prediction model 850 is executed by inputting training data (e.g., one set of input mask pattern images 1205 and one set of images 1210). The prediction model 850 generates one set of images 1215a1~1215an based on the input mask pattern 1205a. The predicted set of images 1215a1~1215an is compared with the input set of images 1210a1~1210an in the training data, and a cost function 1250 is calculated that shows the difference between the predicted set of images 1215a1~1215an and the input set of images 1210a1~1210an, respectively. A determination is made as to whether the cost function 1250 is minimized. If the cost function 1250 is not minimized, the parameters of the prediction model 850 (e.g., weights and biases) are adjusted, and the prediction model 850 is run again to predict a set of images 1215a1~1215an. The process of predicting a set of images, determining the cost function 1250, and adjusting the prediction model parameters to reduce the cost function 1250 is repeated until the cost function 1250 is minimized. After the cost function 1250 is minimized, the prediction model 850 is considered trained, and the trained prediction model can be used to generate a set of images (e.g., a set of images 815) representing a two-dimensional elemental representation of a mask pattern for an arbitrary input mask pattern (e.g., input mask pattern 805), as described with reference to at least Figures 8 and 11.

[0080]

[0094] Figure 15 is a block diagram showing a computer system 1500 capable of assisting in the implementation of various methods and systems disclosed herein. The computer system 1500 may be used to implement any of the entities, components, modules, or services shown in the example in the figure (and any other entities, components, modules, or services described herein). The computer system 1500 may be programmed to execute computer program instructions for performing any of the functions, methods, flows, or services described herein (e.g., any of the entities, components, or modules). The computer system 1500 may be programmed to execute computer program instructions by at least one of software, hardware, or firmware.

[0081]

[0095] The computer system 1500 includes a bus 1502 or other communication mechanism for communicating information, and a processor 1504 (or a plurality of processors 1504 and 1505) coupled to the bus 1502 for processing information. The computer system 1500 also includes main memory 1506, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 1502 for storing information and instructions executed by the processor 1504. The main memory 1506 may also be used to store temporary variables or other intermediate information during the execution of instructions executed by the processor 1504. The computer system 1500 further includes read-only memory (ROM) 1508 or other static storage device coupled to the bus 1502 for storing static information and instructions for the processor 1504. A storage device 1510, such as a magnetic disk or optical disk, is provided and coupled to the bus 1502 for storing information and instructions.

[0082]

[0096] The computer system 1500 may be coupled via a bus 1502 to a display 1512, such as a cathode ray tube (CRT) or a flat panel or touch panel display, for displaying information to the computer user. An input device 1514, including alphanumeric and other keys, is coupled to the bus 1502 for communicating information and command selections to the processor 1504. Another type of user input device is a cursor control 1516, such as a mouse, trackball, or cursor directional keys, for communicating directional information and command selections to the processor 1504 and for controlling the movement of a cursor on the display 1512. This input device typically has two degrees of freedom on two axes, namely a first axis (e.g., x) and a second axis (e.g., y), allowing the device to specify a position in a plane. A touch panel (screen) display may also be used as an input device.

[0083]

[0097] According to one embodiment, a portion of one or more methods described herein may be executed by a computer system 1500 in response to a processor 1504 executing one or more sequences of one or more instructions contained in main memory 1506. Such instructions may be read into main memory 1506 from another computer-readable medium, such as a storage device 1510. By executing the instruction sequence contained in main memory 1506, the processor 1504 performs the process steps described herein. One or more processors in a multiprocessing configuration may also be used to execute the instruction sequence contained in main memory 1506. In alternative embodiments, hardwired circuits may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuits and software.

[0084]

[0098] As used herein, the term “computer-readable medium” refers to any medium involved in providing instructions to the processor 1504 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 the storage device 1510. Volatile media include dynamic memory such as the main memory 1506. Transmission media include coaxial cables, copper wires, and optical fibers, including the wires that make up the bus 1502. Transmission media can also take the form of acoustic or optical 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, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media having a pattern of holes, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carriers as described below, or any other media from which a computer can read.

[0085]

[0099] Various forms of computer-readable media may be involved in transporting one or more sequences of one or more instructions to processor 1504 for execution. For example, the instructions may initially reside on a magnetic disk of a remote computer. The remote computer may load the instructions into dynamic memory and transmit them over a telephone line using a modem. A local modem of computer system 1500 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 1502 may receive the data transported by the infrared signal and place the data on bus 1502. Bus 1502 transports the data to main memory 1506, and processor 1504 retrieves the instructions from main memory 1506 and executes them. Instructions received by main memory 1506 may optionally be stored in storage device 1510 either before or after execution by processor 1504.

[0086]

[0100] The computer system 1500 may also preferably include a communication interface 1518 coupled to the bus 1502. The communication interface 1518 provides bidirectional data communication coupling to a network link 1520 connected to a local network 1522. For example, the communication interface 1518 may be an Integrated Services Digital Network (ISDN) card or modem for providing data communication connectivity to a corresponding type of telephone line. As another example, the communication interface 1518 may be a Local Area Network (LAN) card for providing data communication connectivity to a compatible LAN. Wireless links may also be implemented. In any such embodiment, the communication interface 1518 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0087]

[0101] Network link 1520 typically provides data communication to other data devices over one or more networks. For example, network link 1520 may provide connection to a host computer 1524 via a local network 1522 or to data equipment operated by an Internet service provider (ISP) 1526. The ISP 1526 then provides data communication services over a worldwide packet data communication network, now commonly referred to as the “Internet” 1528. Both the local network 1522 and the Internet 1528 use electrical, electromagnetic, or optical signals to carry digital data streams. Signals traversing various networks that carry digital data to and from computer system 1500, as well as signals on network link 1520 and signals traversing communication interface 1518, are exemplary forms of carrier waves that transmit information.

[0088]

[0102] The computer system 1500 can send messages and receive data, including program code, via a network, network link 1520, and communication interface 1518. In the example of the internet, server 1530 may send requested code for an application program via the internet 1528, ISP 1526, local network 1522, and communication interface 1518. One such downloaded application may, for example, perform lighting optimization as in the embodiment. The received code may be executed by processor 1504 upon receipt, or it may be stored in storage device 1510 or other non-volatile storage device for later execution. In this way, the computer system 1500 can obtain application code in carrier form.

[0089]

[0103] 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 conjunction with any type of lithography imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0090]

[0104] 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 result and / or process has more desirable features, such as a higher accuracy projection of the design layout onto the substrate, a larger process window, etc. Therefore, 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) in at least one relevant metric compared to an initial set of one or more values ​​of that parameter. “Optimal” and other relevant terms should be interpreted accordingly. In some embodiments, the optimization step can be applied iteratively to bring about further improvements in one or more metrics.

[0091]

[0105] Embodiments of the present invention can be implemented in any convenient form. For example, one embodiment can 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 can be implemented using a suitable apparatus that can specifically take the form of a programmable computer that runs a computer program configured to carry out the methods described herein. Thus, embodiments of the present disclosure can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure can also be implemented as instructions stored in a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium can include any mechanism for storing or transmitting information in a form that can be read by a machine (e.g., a computing device). For example, a machine-readable medium can include read-only memory (ROM), random access memory (RAM), magnetic disk storage medium, optical storage medium, flash memory device, propagating signals of electrical, optical, acoustic, or other forms (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Furthermore, firmware, software, routines, and instructions may be described herein as performing specific actions. However, such descriptions are merely for convenience, and it should be recognized that such actions are actually brought about by the execution of firmware, software, routines, instructions, etc., by computing devices, processors, controllers, or other devices.

[0092]

[0106] In the block diagram, the illustrated components are shown as individual functional blocks, but embodiments are not limited to systems in which the functions described herein are organized as illustrated. The functions provided by each component may be provided by software or hardware modules organized differently from those shown herein, for example, such software or hardware may be mixed, combined, replicated, divided, distributed, or otherwise organized (e.g., within a data center or geographically). 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 otherwise provided.

[0093]

[0107] Unless otherwise stated, as will be apparent from the discussion, throughout this specification, discussions using terms such as “process,” “calculate,” “calculate,” and “determine” refer to actions or processes of a specific device, such as a dedicated computer or similar dedicated electronic processing / computing device.

[0094]

[0108] Embodiments of this disclosure can be further described by the following clauses. 1. A method for determining a mask pattern used in a lithography process, wherein the method is: This involves providing the predictive model with an input mask pattern corresponding to the target pattern, The process involves generating a two-dimensional elemental representation of an output mask pattern corresponding to an input mask pattern using a predictive model, wherein the two-dimensional elemental representation includes multiple two-dimensional elements representing the mask features of the output mask pattern, and each two-dimensional element defines a closed region. Determining the mask feature contours of the output mask pattern based on a 2D element representation and Methods that include... 2. The method according to Clause 1, wherein the two-dimensional element representation includes a set of images showing the positional information of the two-dimensional elements in the two-dimensional element representation. 3. The method according to Clause 2, wherein the position information includes information about the grid position assigned to the 2D element and the displacement of the 2D element from the assigned grid position. 4. The method according to Clause 2, wherein one set of images includes a binary image indicating the presence or absence of a two-dimensional element at a specified grid position. 5. One set of images is: A first image showing the displacement of a 2D element in a first direction from a specified grid position, A second image showing the displacement of a 2D element in a second direction from a specified grid position, and The method described in Article 2, including the method described in Article 2. 6. One set of images is: A binary image indicating the presence or absence of a 2D element at a specified grid position, A first image showing the displacement of a 2D element in a first direction from a specified grid position, A second image showing the displacement of a 2D element in a second direction from a specified grid position, and The method described in Article 2, including the method described in Article 2. 7. The method according to clause 2, further comprising generating a two-dimensional elemental representation based on a set of images. 8. The method according to Clause 1, wherein each of the two-dimensional elements is circular. 9. The method according to Clause 1, wherein each of the two-dimensional elements is elliptical. 10. The method described in Clause 1, wherein each of the two-dimensional elements is the same size. 11. The method according to Clause 1, wherein the two-dimensional elements have different sizes. 12. Determining the mask feature contour of the output mask pattern from the 2D element representation is The process involves associating 2D elements based on association criteria to form clusters representing mask features, Generating cluster contours based on 2D elements and The method described in Clause 1, including the method described in Clause 1. 13. The association criteria are as described in Clause 12, including rule-based criteria. 14. Rule-based criteria include distance-based criteria that indicate the distance between two two-dimensional elements, as described in Clause 13. 15. The method according to Clause 12, wherein two-dimensional elements are associated based on association information derived from a binary image of the two-dimensional element representation, and the binary image indicates whether a two-dimensional element at a given position is associated with another two-dimensional element at an adjacent position. 16. The method according to clause 12, wherein the contour is the outer contour of the cluster corresponding to the outer edge of the mask feature. 17. The method according to clause 12, wherein the contour is the inner contour of the cluster corresponding to the inner edge of the mask feature. 18. Generating a contour subregion by applying a polygonal offset operation to a pair of associated 2D elements, The process involves calculating the union of subdomains, and the contour is the union of subdomains. The method described in Clause 12, further including the method described in Clause 12. 19. The method according to Clause 1, further comprising optimizing the output mask pattern using an optical proximity effect correction process. 20. The method according to clause 19, further comprising manufacturing a mask from an output mask pattern that includes mask feature contours generated from two-dimensional elements. 21. Providing an input mask pattern is, To obtain a representation of the target pattern, The process involves generating an image from a target pattern, where the image represents the input mask pattern. The predictive model is given an image of the input mask pattern. The method described in Clause 1, including the method described in Clause 1. 22. The method according to Clause 1, further comprising training a predictive model using training data to generate two-dimensional elemental representations, wherein the training data includes one set of input mask patterns and one set of output mask patterns corresponding to the one set of input mask patterns. 23. Training a predictive model is To obtain the first output mask pattern of a set of output mask patterns that corresponds to the first input mask pattern of a set of input mask patterns, To obtain a first two-dimensional element representation of the first output mask pattern, The predictive model is executed to generate a two-dimensional element representation of a specified first output mask pattern based on a first input mask pattern and a first two-dimensional element representation. The method described in Article 22, including the method described in Article 22. 24. Obtaining the first two-dimensional element representation is: Assigning the position of a collection of 2D elements based on a first input mask pattern, Associating a collection of 2D elements based on association criteria to form clusters representing the mask pattern of the specified first input mask pattern, Adjusting the collection of 2D elements of a cluster to change the specified mask feature and The method described in Article 23, including the method described in Article 23. 25. Adjustment is performed according to the method of Clause 24, based on the geometric characteristics of the first output mask pattern and based on the rules specified with respect to the optimal proximity effect correction (OPC) process. 26. Adjustment is to be made in accordance with the method described in Clause 24, based on simulations associated with the lithography process. 27. The method according to clause 24, further comprising generating a set of images showing positional information of a collection of two-dimensional elements in a first two-dimensional element representation. 28. Obtaining the first two-dimensional element representation is: This involves reducing the specified mask feature contour by a specified dimension associated with a 2D element to generate a reduced contour, and Assigning the positions of the 2D element collection along the reduced contour so that the contour generated from the collection of 2D elements approximates the contour of a specified mask feature. The method described in Article 23, including the method described in Article 23. 29. The method according to clause 23, wherein the first two-dimensional elemental representation of the first mask pattern is derived from the level set image of the first output mask pattern. 30. A method for training a predictive model to generate a two-dimensional elemental representation of a mask pattern used in a lithography process, wherein the method is: The method involves obtaining a set of 2D element representations of one set of input mask patterns and one set of output mask patterns corresponding to the input mask patterns, wherein each 2D element representation in the set of 2D element representations includes multiple 2D elements representing the mask features of the mask patterns, and each 2D element defines a closed region. Training a predictive model using training data to generate a 2D elemental representation Methods that include... 31. Training a predictive model is To obtain the first output mask pattern of a set of output mask patterns that corresponds to the first input mask pattern of a set of input mask patterns, To obtain a first two-dimensional element representation of the first output mask pattern, The predictive model is executed to generate a two-dimensional element representation of a specified first output mask pattern based on a first input mask pattern and a first two-dimensional element representation. The method described in Clause 30, including the method described in Clause 30. 32. Training a predictive model is The method according to Clause 31, comprising training a predictive model until the cost function is reduced, wherein the cost function represents the difference between (a) a specified two-dimensional element representation produced by the predictive model and (b) a first two-dimensional element representation. 33. Obtaining the first two-dimensional element representation is: Assigning the position of a collection of 2D elements based on a first input mask pattern, Associating a collection of 2D elements based on association criteria to form clusters representing the mask pattern of the specified first input mask pattern, Adjusting the collection of 2D elements of a cluster to change the specified mask feature and The method described in Article 31, including the method described in Article 31. 34. Adjustment is performed according to the method of Clause 33, based on the geometric characteristics of the first output mask pattern and based on the rules specified with respect to the optimal proximity effect correction (OPC) process. 35. Adjustment is to be made in accordance with the method described in Clause 33, based on simulations associated with the lithography process. 36. The method according to clause 33, further comprising generating a set of images showing positional information of a collection of two-dimensional elements in a first two-dimensional element representation. 37. Obtaining the first two-dimensional element representation is: This involves reducing the specified mask feature contour by a specified dimension associated with a 2D element to generate a reduced contour, and Assigning the positions of the 2D element collection along the reduced contour so that the contour generated from the collection of 2D elements approximates the contour of a specified mask feature. The method described in Article 33, including the method described in Article 33. 38. The method according to clause 31, wherein the first two-dimensional elemental representation of the first mask pattern is derived from the level set image of the first output mask pattern. 39. Providing the predictive model with an input mask pattern corresponding to the target pattern, Using a predictive model, generate a predicted 2D elemental representation of the output mask pattern, Determining the mask feature contours of the output mask pattern based on the predicted 2D element representation and The method described in clause 30, further including the following: 40. The method according to clause 39, further comprising optimizing the output mask pattern using an optical proximity effect correction process to generate a mask pattern. 41. The method according to clause 40, further comprising manufacturing a mask from a mask pattern that includes mask feature contours generated from two-dimensional elements. 42. A device, Memory that stores one set of instructions, A processor configured to execute a set of instructions to cause the device to perform any of the methods described in the above clauses, A device including a device. 43. 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 of the preceding clauses.

[0095]

[0109] Readers should be aware that this application describes several inventions. These inventions have been combined into a single document rather than separated into multiple independent patent applications because these related subjects are suitable for the economics of 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 of the inventions disclosed herein may not currently be included in the claims and may be included in subsequent applications, such as continuation applications, or by amending the current claims. Similarly, due to space constraints, neither the “Abstract” nor the “Summary” section of this document should be considered to contain a comprehensive list of all such inventions or all aspects of such inventions.

[0096]

[0110] It should be understood that this specification and drawings are not intended to limit this disclosure to any particular disclosed form, but rather to encompass all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention as defined by the appended claims.

[0097]

[0111] Various modifications and alternative embodiments of the present invention will be apparent to those skilled in the art in consideration of this description. Therefore, this description and drawings should be interpreted as illustrative only and are intended to teach those skilled in the art a general way of carrying out the present invention. It should be understood that the embodiments of the present invention shown and described herein should be interpreted as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be used independently, and embodiments or features of embodiments may be combined, as will become apparent to those skilled in the art after benefiting from this specification. Modifications to the elements described herein may be made without departing from the spirit and scope of the invention as described in the following claims. Titles used herein are for structural purposes only and are not intended to limit the scope of the description.

[0098]

[0112] Where used herein, unless otherwise specified, the term “or” encompasses all possible combinations, unless impossible. For example, if a component is stated to include A or B, unless otherwise specified or impossible, that component may include A, or B, or A and B. As a second example, if a component is stated to include A, B, or C, unless otherwise specified or impossible, that component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. Expressions such as “at least one” do not necessarily modify the entire list that follows, nor do they necessarily modify each element of the list; “at least one of A, B, and C” should be understood to include only A, only B, only C, or any combination of A, B, and C. The phrases "one of A and B" or "any one of A and B" shall be interpreted in their broadest sense as including either one of A or one of B.

[0099]

[0113] The descriptions herein are intended to be illustrative, not restrictive. It will therefore be apparent to those skilled in the art that modifications can be made to the extent described herein, without departing from the claims set forth below.

Claims

1. A non-temporary computer-readable medium on which instructions are recorded, wherein, when executed by a computer, the instructions carry out a method for determining a mask pattern used in a lithography process, and the method is This involves providing the predictive model with an input mask pattern corresponding to the target pattern, Using the prediction model, generate a two-dimensional elemental representation of an output mask pattern corresponding to the input mask pattern, wherein the two-dimensional elemental representation includes a plurality of two-dimensional elements representing the mask features of the output mask pattern, and each two-dimensional element defines a closed region. The mask feature contour of the output mask pattern is determined based on the two-dimensional element representation. Non-temporary computer-readable media, including [specific examples of such media].

2. The medium according to claim 1, wherein the two-dimensional element representation includes a set of images showing positional information of the two-dimensional elements in the two-dimensional element representation.

3. The medium according to claim 2, wherein the position information includes information relating to a grid position assigned to the two-dimensional element and the displacement of the two-dimensional element from the assigned grid position.

4. The medium according to claim 2, wherein the set of images includes a binary image indicating the presence or absence of a two-dimensional element at a specified grid position.

5. The aforementioned set of images is A first image showing the displacement of a two-dimensional element in a first direction from a specified grid position, A second image showing the displacement of the two-dimensional element in a second direction from the specified grid position, and Includes, The medium according to claim 2, further comprising generating the two-dimensional element representation based on the set of images.

6. The medium according to claim 1, wherein each of the two-dimensional elements is circular or elliptical, and each of the two-dimensional elements is the same size or different sizes.

7. Determining the mask feature contour of the output mask pattern from the two-dimensional element representation is: The two-dimensional elements are associated based on association criteria to form clusters representing the mask features, The process involves generating the contour of the cluster based on the two-dimensional elements, wherein the contour is either the outer contour of the cluster corresponding to the outer edge of the mask feature or the inner contour of the cluster corresponding to the inner edge of the mask feature. The medium according to claim 1, including the following:

8. The medium according to claim 7, wherein the association criterion relates to the distance between two two-dimensional elements.

9. The medium according to claim 7, wherein the two-dimensional elements are associated based on association information derived from a binary image of the two-dimensional element representation, and the binary image indicates whether a two-dimensional element at a specified position is associated with another two-dimensional element at an adjacent position.

10. The aforementioned method, The process involves generating a sub-region of the contour by applying a polygonal offset operation to the associated pair of two-dimensional elements, The calculation of the union of the sub-regions, wherein the contour is the union of the sub-regions, and the calculation The medium according to claim 7, further comprising:

11. Providing the aforementioned input mask pattern means, To obtain a representation of the aforementioned target pattern, The process involves generating an image from the target pattern, wherein the image represents the input mask pattern. The image of the input mask pattern is provided to the prediction model. The method includes, The medium according to claim 1, further comprising optimizing the output mask pattern using an optical proximity effect correction process.

12. The aforementioned method, The medium according to claim 1, further comprising training the predictive model using training data to generate two-dimensional elemental representations, wherein the training data includes a set of input mask patterns and two-dimensional elemental representations of a set of output mask patterns corresponding to the set of input mask patterns.

13. Training the aforementioned predictive model involves To obtain the first output mask pattern of the set of output mask patterns that corresponds to the first input mask pattern of the set of input mask patterns, To obtain a first two-dimensional element representation of the first output mask pattern, The prediction model is executed to generate a two-dimensional element representation of the first output mask pattern specification based on the first input mask pattern and the first two-dimensional element representation. Includes, Obtaining the first two-dimensional element representation means Assigning the position of a collection of two-dimensional elements based on the first input mask pattern, The set of two-dimensional elements is associated based on association criteria to form a cluster representing the mask pattern of the first input mask pattern specification, Adjusting the collection of two-dimensional elements of the cluster so as to change the specified mask feature. Includes, The medium according to claim 12, wherein the adjustment is based on the geometric characteristics of the first output mask pattern and on rules defined with respect to the optimal proximity effect correction (OPC) process, or the adjustment is based on a simulation associated with the lithography process.

14. The aforementioned method, The method further includes generating a set of images that show the positional information of the collection of two-dimensional elements in the first two-dimensional element representation, Obtaining the first two-dimensional element representation means This involves reducing the specified mask feature contour by a specified dimension associated with a 2D element to generate a reduced contour, and The position of the collection of two-dimensional elements along the reduced contour is assigned such that the contour generated from the collection of two-dimensional elements approximates the specified mask feature contour. The medium according to claim 13, including the following:

15. The medium according to claim 13, wherein the first two-dimensional element representation of the first mask pattern is derived from a level set image of the first output mask pattern.

Images