The pattern is selected based on a representation of the pattern characterized by the lithographic equipment or process characteristics

Abstract

A method and apparatus for selecting patterns for training or calibrating a model related to semiconductor manufacturing is described herein. The method includes obtaining a first set of patterns, representing each pattern in the first set of patterns in a representation domain, the representation domain corresponding to an electromagnetic function, and selecting a second set of patterns from the first set of patterns based on the representation domain.

Description

Technical Field

[0001] The present disclosure generally relates to improving lithography and lithography-related processes, and more particularly, to apparatus, methods, and computer program products for selecting informational patterns for training models used in lithography and lithography-related processes. Background Art

[0002] Lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device (e.g., a mask) can contain or provide a pattern corresponding to a single layer of the IC (a "design layout"), and this pattern can be transferred to a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the pattern on the patterning device. Typically, a single substrate includes multiple adjacent target portions, to which the pattern is transferred sequentially, one target portion at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the entire pattern on the patterning device is transferred to a target portion at a time; such apparatuses are often referred to as steppers. In an alternative apparatus, often referred to as a stepper-scan apparatus, a projection beam is scanned over the patterning device along a given reference direction (the "scanning" direction) while the substrate is synchronously moved parallel or antiparallel to the reference direction. Different portions of the pattern on the patterning device are transferred incrementally to a target portion. Since, typically, the lithographic projection apparatus will have a demagnification ratio M (e.g. 4), the speed F at which the substrate is moved will be 1 / M of the speed at which the projection beam scans the patterning device. More information on lithographic apparatus can be found, for example, in US 6,046,792, which is incorporated herein by reference.

[0003] Before the pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various processes, such as primer coating, resist coating and soft baking. After exposure, the substrate may undergo other processes ("post-exposure processes"), such as post-exposure baking (PEB), development, hard baking and measurement / inspection of the transferred pattern. An array of such processes is used as the basis for making a single layer of a device (e.g., an IC). The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to ultimately complete a single layer of the device. If multiple layers are required in the device, all processes or variations thereof are repeated for each layer. Ultimately, a device will be present in each target portion on the substrate. These devices are then separated from each other by techniques such as sawing or cutting, whereby individual devices can be mounted on a carrier, connected to pins, etc.

[0004] Therefore, manufacturing devices (such as semiconductor devices) typically involves processing a substrate (e.g., a semiconductor wafer) using multiple preparation processes to form multiple features and multiple layers of the device. These layers and features are typically manufactured and processed using, for example, deposition, photolithography, etching, chemical mechanical polishing, ion implantation. Multiple devices can be made on multiple dies on a substrate, and then the multiple devices are separated into individual devices. This device manufacturing process can be considered a patterning process. The patterning process involves a patterning step (such as optical and / or nanoimprint lithography) using a patterning device in a lithographic apparatus to transfer the pattern on the patterning device to the substrate, and the patterning process typically but optionally involves one or more related pattern processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching from the pattern using an etching apparatus, etc. Summary of the Invention

[0005] In an embodiment, a method is provided for generating a training data set for computing a lithography machine learning model. In order to obtain a model that can accurately predict a wide range of future pattern instances or model generality, sufficient pattern coverage in the training process is critical. The training data is selected based on a set of patterns in a representation domain. For example, the set of patterns can be patterns within a target layout. The target layout can have hundreds of millions of patterns, so that it is desirable to select a small number of the most informative patterns overall for training purposes. In an embodiment, the selection of a subset of patterns is performed based on the data points in the representation domain and also based on an information metric that characterizes the amount of information in the pattern subset. This selection process can enable the selection of informative patterns without involving additional patterned process models or machine learning models, such as pattern classification and selection processes based on autoencoders. In this way, the selection can be applied directly to the target layout, which can also save a lot of computing resources and time.

[0006] According to one aspect of the present disclosure, pattern selection is based on maximizing the system entropy of the selected pattern as a whole. The total entropy depends on the mutual information of the selected patterns, for example, the distance between each pattern in the representation domain. In an embodiment, each pattern is represented as a pixel embedding information cloud in the representation domain. In an embodiment, each pattern is projected into a Hilbert space for linear pattern representation, for example, where the basis functions are Hermite Gaussian moduli, Zernike polynomials, or Bessel functions. The method herein has several advantages. For example, the method herein does not need to be trained as a machine learning model (such as an autoencoder). It handles pixel offsets well. Good performance results based on RMS and LMC.

[0007] According to one aspect of the present disclosure, a method for selecting patterns based on interaction information between patterns for training a machine learning model related to semiconductor manufacturing is provided. The method includes: obtaining a pattern set including a first pattern and a second pattern, each pattern in the pattern set including one or more features; representing each pattern in the pattern set as a group of data points in a representation domain, the first pattern being represented as a first group of data points in the representation domain, and the second pattern being represented as a second group of data points in the representation domain, each data point in the first group indicating information associated with a feature within a portion of the first pattern, and each data point in the second group indicating information associated with a feature within a portion of the second pattern; determining a set of distance values ​​for a distance indicator corresponding to the pattern set, the set of distance values ​​including a first distance value determined between the first group of data points and another group of data points and a second distance value determined between the second group of data points and the another group of data points, the distance indicator indicating an amount of interaction information between a given pattern in the pattern set and the another pattern; and selecting a subset of patterns from the pattern set based on a value of the distance indicator that exceeds a distance threshold.

[0008] In an embodiment, the representation domain is a linear representation domain or a Hilbert space domain.

[0009] According to another aspect, a method for selecting representative patterns for training a machine learning model is provided. The method comprises: obtaining a set of patterns; representing each pattern in the set of patterns as a set of data points in a representation domain; and selecting a subset of patterns from the set of patterns based on the set of data points as a guide for interaction information between a given pattern and another pattern in the set of patterns. In an embodiment, the representation domain is a linear representation domain or a Hilbert space domain.

[0010] In an embodiment, the indicator indicates the non-uniformity of each image in the plurality of patterns. Thus, for example, the indicator can guide the selection of the most informative pattern from among billions of patterns from a target layout.

[0011] In an embodiment, the selected subset of patterns may be provided as training data for training a model associated with the patterning process (eg, OPC).

[0012] Although a linear representation of a pattern is provided by projecting the pattern onto a Hilbert space as described in the previous paragraph, embodiments of the present disclosure describe projecting the pattern into a representation domain using basis functions that represent characteristics of a lithographic apparatus or process, such as characteristics of an illumination source of the lithographic apparatus. For example, pattern information quality is significantly dependent on optical system diffraction (e.g., illumination source response to the pattern). In some embodiments, such characteristics of an optical system can be described using transmission cross coefficients (TCCs), which can be determined using a Hopkin imaging model. The TCCs can then be decomposed into a discrete set of coherent systems (e.g., summation of coherent systems (SOCS) TCCs) that represent electromagnetic field (EMF) transfer functions of separate coherent systems. The pattern can be projected onto a Hilbert space using the TCC functions as basis functions. For example, each pixel of a pattern can be projected onto a TCC set (N) to generate an N-dimensional vector. The vectors provide information about how the pattern pixels are represented in the optical system. For example, the vectors represent the EMF excitation of the pixels based on their proximity (e.g., how the proximity of the pixels affects the EMF excitation of the pixels). A pattern can be represented as a collection of pixels, and therefore, each pixel in the pattern can be represented as a vector, thereby generating a set of vectors or a vector cloud representing the pattern. The vector clouds associated with different patterns can be analyzed for pattern similarity, and a set of patterns having indicators that meet a criteria (e.g., meet one or more of the distance thresholds described above, information entropy that meets a specified criteria, etc.) can be selected as representative patterns (e.g., to calibrate or train a model for determining characteristics of a lithographic apparatus or process, or for other purposes). In some embodiments, the above embodiments can also be modified to include resist characteristics (e.g., photoresist response to the pattern) in addition to or instead of the optical system characteristics that represent the pattern in the representation domain.

[0013] This projection of the pattern (e.g., using TCC) into the representation domain is easy to compute (e.g., once the configuration of the illumination source is known), more accurate than conventional representations, and thus provides improved pattern similarity analysis for better selection of representative patterns. Such projections advantageously do not require any training as in autoencoding techniques and thus can achieve faster pattern selection.

[0014] According to an embodiment, a computer system is provided that includes a non-transitory computer-readable medium having instructions recorded thereon. The instructions, when executed by a computer, implement the above method steps. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain aspects of the subject matter disclosed herein and, together with the description, help explain some of the principles associated with the disclosed embodiments.

[0016] Figure 1 Figure shows a block diagram of various subsystems of a lithographic projection apparatus according to an embodiment.

[0017] Figure 2 The figure shows a flow chart of an exemplary method for simulating lithography in a lithographic projection apparatus according to an embodiment.

[0018] Figure 3 The transformation of the pattern into pixel embedded information in a representation domain with reduced dimensionality compared to the dimensionality of the input image is pictorially depicted, using a convolution operation of a bounding box around the pixel of interest.

[0019] Figure 4 is a flow chart of an exemplary method for selecting a pattern from a target layout based on data points associated with the pattern in a representation domain, according to an embodiment.

[0020] Figure 5A is an example depicting transformation of a pattern into a representation domain (eg, coefficients of orthogonal basis functions), according to an embodiment.

[0021] Figure 5B The diagram illustrates groups of data points in the representation domain, wherein a first group (bright dots) represents a first pattern and a second group (dark dots) represents a second pattern, according to an embodiment.

[0022] Figure 6 The diagram illustrates exemplary selection of a pattern from a plurality of patterns of a portion of a design layout according to an embodiment of the present disclosure.

[0023] Figure 7 is a block diagram of an exemplary computer system according to an embodiment.

[0024] Figure 8 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0025] Figure 9 is a schematic diagram of another lithographic projection apparatus according to an embodiment.

[0026] Figure 10 is a detailed view of the lithographic projection apparatus according to an embodiment.

[0027] Figure 11 is a detailed view of the source collector module of the lithographic projection apparatus according to an embodiment.

[0028] Figure 12is a flow chart of an exemplary method for selecting a pattern from a target layout based on a pattern representation in a representation domain of a source, according to an embodiment. DETAILED DESCRIPTION

[0029] Although this document has been specifically referenced to the manufacture of ICs, it should be clearly understood that the description herein has many other possible applications. For example, it can be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, and the like. The skilled person will understand that in the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" herein should be considered interchangeable with the more general terms "mask," "substrate," and "target portion," respectively.

[0030] In this document, the terms "radiation" and "beam" may be used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5 nm to 100 nm).

[0031] The pattern forming device may include or may constitute one or more design layouts. A CAD (computer-aided design) program can be used to generate a design layout, a process often referred to as EDA (electronic design automation). Most CAD programs follow a predetermined set of design rules to generate a functional design layout / pattern forming device. These rules are set by processing and design constraints. For example, the design rules limit the spacing tolerance between devices (such as gates, capacitors, etc.) or interconnects to ensure that the devices or lines do not interact with each other in an undesirable manner. One or more of the design rule constraints may be referred to as a "critical dimension" (CD). The critical dimension of a device can be defined as the minimum width of a line or hole, or the minimum spacing between two lines or two holes. Therefore, the CD determines the overall size and density of the designed device. Of course, one of the goals in device manufacturing is to faithfully reproduce the original design intent on the substrate (via the pattern forming device).

[0032] As used herein, the terms "mask" or "patterning device" should be broadly interpreted to refer to a general patterning device that can be used to impart an incident radiation beam with a patterned cross-section that corresponds to the pattern to be produced in a target portion of the substrate; in this context, the term "light valve" may also be used. In addition to classical masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0033] An example of a programmable mirror array can be a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle underlying such a device is that, for example, addressed areas of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as undiffracted radiation. Using appropriate filters, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; the beam then becomes patterned according to the addressing pattern of the matrix-addressable surface. Appropriate electronics can be used to perform the required matrix addressing.

[0034] An example of a programmable LCD array is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0035] Figure 1 The figure shows a block diagram of various subsystems of a lithographic projection apparatus 10A according to an embodiment. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or another type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have such a radiation source); illumination optics, which, for example, define partial coherence (denoted as sigma) and may include optics 14A, 16Aa, and 16Ab that shape the radiation from the source 12A; a patterning device 18A; and transmission optics 16Ac that project an image of the patterned device pattern onto a substrate plane 22A. An adjustable filter or hole or aperture 20A at the pupil plane of the projection optical device can limit the range of beam angles incident on the substrate plane 22A, wherein the largest possible angle defines the numerical aperture NA=n sin(Θmax) of the projection optical device, wherein n is the refractive index of the medium between the substrate and the final element of the projection optical device, and Θmax is the maximum angle of the beam emitted from the projection optical device that can still be incident on the substrate plane 22A.

[0036] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device, and projection optics direct and shape the illumination onto a substrate via the patterning device. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) is the radiation intensity distribution at substrate level. The resist image can be calculated from the aerial image using a resist model, an example of which can be found in U.S. Patent Application Publication No. US 20090157630, the entire contents of which are hereby incorporated by reference. The resist model is solely dependent on the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure bake (PEB), and development). The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, the patterning device, and the projection optics) dictate the aerial image and can be defined within the optical model. Because the patterning device used in the lithographic projection apparatus can be varied, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and the projection optics. Techniques and models for transforming a design layout into various lithographic images (e.g., aerial images, resist images, etc.), applying OPC using those techniques and models, and evaluating performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the entire disclosure of each of which is hereby incorporated by reference herein.

[0037] According to embodiments of the present disclosure, one or more images may be generated using various types of signals corresponding to the pixel value (e.g., intensity value) of each pixel. Depending on the relative values ​​of the pixels within the image, the signal may be referred to as, for example, a weak signal or a strong signal, as would be understood by one of ordinary skill in the art. The terms "strong" and "weak" are relative terms based on the intensity values ​​of the pixels within the image, and the specific intensity values ​​may not limit the scope of the present disclosure. In embodiments, strong and weak signals may be identified based on a selected threshold. In embodiments, the threshold may be fixed (e.g., the midpoint between the highest intensity and the lowest intensity of the pixels within the image). In embodiments, a strong signal may refer to a signal having a value greater than or equal to the average signal value across the entire image, and a weak signal may refer to a signal having a value less than the average signal value. In embodiments, the relative intensity values ​​may be based on percentages. For example, a weak signal may be a signal having an intensity less than 50% of the highest intensity of the pixels within the image (e.g., the pixels corresponding to the target pattern may be considered to be the pixels with the highest intensity). Furthermore, each pixel within an image may be considered a variable. According to this embodiment, a derivative or partial derivative can be determined for each pixel in the image, and the value of each pixel can be determined or modified based on an estimate based on a cost function and / or a gradient-based calculation of the cost function. For example, a CTM image may include a plurality of pixels, where each pixel is a variable that can take any real value.

[0038] Figure 2 The figure shows an exemplary flow chart for simulating lithography in a lithographic projection apparatus according to an embodiment. A source model 31 represents the optical properties of the source (including the radiation intensity distribution and / or phase distribution). A projection optics model 32 represents the optical properties of the projection optics (including changes in the radiation intensity distribution and / or the phase distribution caused by the projection optics). A design layout model 35 represents the optical properties of a design layout (including changes in the radiation intensity distribution and / or the phase distribution caused by the design layout 33), which is a representation of the arrangement of features on or formed by a patterning device. An aerial image 36 can be simulated based on the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated based on the aerial image 36 using a resist model 37. The simulation of lithography can, for example, predict the profile and CD in the resist image.

[0039] More specifically, it should be noted that the source model 31 can represent the optical properties of the source, including but not limited to the numerical aperture setting, the illumination sigma (σ) setting, and any specific illumination shape (e.g., an off-axis radiation source such as a toroidal, quadrupole, dipole, etc.). The projection optics model 32 can represent the optical properties of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc. The design layout model 35 can represent one or more physical properties of a physical pattern forming device, such as that described in U.S. Patent No. 7,587,704, the entire contents of which are incorporated herein by reference. The purpose of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and / or CD, which can then be compared to the intended design. The intended design is typically interpreted as a pre-OPC design layout, which can be provided in a standardized digital file format (such as GDSII or OASIS, or other file formats).

[0040] Based on this design layout, one or more portions referred to as "snippets" may be identified. In an embodiment, a set of snippets is extracted that represents complex patterns in the design layout (typically on the order of 50 to 1000 snippets, but any number of snippets may be used). These patterns or snippets represent smaller portions of the design (i.e., circuits, cells, or patterns), and more specifically, the snippets typically represent smaller portions that require special attention and / or verification. In other words, a snippet may be a portion of a design layout, or may be similar or have similar behavior to a portion of the design layout, where one or more key features are identified empirically (including snippets provided by a customer), by trial and error, or by running a full-chip simulation. A snippet may contain one or more test patterns or gauge patterns.

[0041] The initial large set of segments can be provided a priori by the customer based on one or more known key feature areas in the design layout that require specific image optimization. Alternatively, in another embodiment, the initial large set of segments can be extracted from the entire design layout using some automated (such as machine vision) or manual algorithm that identifies the one or more key feature areas.

[0042] In a lithographic projection apparatus, as an example, the cost function may be expressed as:

[0043]

[0044] Among them, (z1, z2, ..., z N ) are N design variables or their values. p (z1,z2,…,z N) can be the design variables (z1, z2, ..., z N ), such as for (z1, z2, ..., z N ) is the difference between the actual value and the expected value of the characteristic of the set of values ​​of the design variable. p is with f p (z1,z2,…,z N ) is a weight constant associated with the edge of the image. For example, the characteristic may be the position of the edge measured at a given point on the edge of the image. Different f p (z1,z2,…,z N ) can have different weights w p For example, if a particular edge has a narrow range of allowed positions, then f, which represents the difference between the actual position and the expected position of the edge, p (z1,z2,…,z N ) weight w p Can be assigned a larger value. p (z1,z2,…,z N ) can also be a function of the intermediate layer characteristics, which are in turn the design variables (z1, z2, ..., z N ) function. Of course, CF(z1, z2, ..., z N ) is not limited to the form in Equation 1. CF(z1, z2, ..., z N ) may be in any other suitable form.

[0045] The cost function may represent any one or more suitable characteristics of the lithographic projection apparatus, the lithographic process, or the substrate, such as focal length, CD, image offset, image deformation, image rotation, random variation, throughput, local CD variation, process window, intermediate layer characteristics, or a combination thereof. In one embodiment, the design variables (z1, z2, ..., z N ) includes one or more selected from dose, global bias of the patterning device, and / or shot shape. Since it is often the resist image that dictates or determines the image on the substrate, the cost function may include a function representing one or more characteristics of the resist image. For example, f p (z1,z2,…,z N ) may simply be the distance between a point in the resist image and the expected position of the point (ie, the edge placement error EPE p (z1,z2,…,z N )). The design variables may include any adjustable parameters, such as adjustable parameters of the source, the patterning device, the projection optics, dose, focal length, etc.

[0046] The lithographic apparatus may include components collectively referred to as "wavefront manipulators", which may be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the radiation beam. In an embodiment, the lithographic apparatus may adjust the wavefront and intensity distribution at any address along the optical path of the lithographic projection apparatus (such as before the pattern forming device, near the pupil plane, near the image plane, and / or near the focal plane). The wavefront manipulator may be used to correct or compensate for certain distortions of the wavefront and intensity distribution and / or phase shift, such as those caused by temperature changes in the source, the pattern forming device, the lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, etc. Adjusting the wavefront and intensity distribution and / or phase shift may change the value of the characteristic represented by the cost function. Such changes may be simulated according to a model or actually measured. The design variables may include parameters of the wavefront manipulator.

[0047] The design variables may have constraints, which may be expressed as (z1, z2, ..., z N )∈Z, where Z is the set of possible values ​​of the design variables. One possible constraint on the design variables may be imposed by the desired throughput of the lithographic projection apparatus. In the absence of a constraint imposed by the desired throughput, the optimization may produce a set of unrealistic values ​​for the design variables. For example, if the dose is a design variable, but there is such a constraint, the optimization may produce dose values ​​that make the throughput economically impossible. However, the usefulness of a constraint should not be interpreted as a necessity. For example, the throughput may be affected by the pupil fill ratio. For some illumination designs, a lower pupil fill ratio may discard radiation, resulting in lower throughput. Throughput may also be affected by the chemical properties of the resist. Slower resists (e.g., resists that require a higher amount of radiation to be properly exposed) result in lower throughput.

[0048] As used herein, the term "patterning process" generally refers to a process that produces an etched substrate by applying a specified pattern of light as part of a photolithography process. However, "patterning process" may also include plasma etching, as many of the features described herein may provide benefits for using plasma processing to form printed patterns.

[0049] As used herein, the term "target pattern" means an idealized pattern to be etched onto a substrate. The term "target layout" refers to a design layout that includes one or more target patterns.

[0050] As used herein, the term "printed pattern" or "patterned substrate" refers to a physical pattern on a substrate that is imaged and / or etched based on a target pattern. The printed pattern may include, for example, grooves, channels, recesses, edges, or other two-dimensional and three-dimensional features produced by a photolithographic process.

[0051] As used herein, the term "process model" means a model that includes one or more models that simulate a patterning process. For example, a process model may include an optical model (e.g., the optical model models the lens system / projection system used to transmit light in the lithography process and may include modeling the final optical image of the light onto the photoresist), a resist model (e.g., the resist model models the physical effects of the resist (such as chemical effects caused by the light)), and an OPC model (e.g., the OPC model may be used to modify the target pattern to include sub-resolution resist features (SRAF), etc.).

[0052] In order to improve the patterning process and patterning accuracy, a process model is trained using a target pattern, a mask pattern, a substrate image, etc. For example, the process model includes one or more training models used in the OPC process to generate a better mask pattern. For example, OPC assisted by machine learning significantly improves the accuracy of full-chip auxiliary feature (e.g., SRAF) placement while keeping the consistency and run time of the mask design under control. A deep convolutional neural network (CNN) is trained using the target layout or the target pattern therein, and the corresponding continuous transmission mask (CTM) images. These CTM images are optimized using an inverse mask optimization simulation process. The CNN generated by the SRAF guided mapping is then used to place the SRAF on the full-chip design layout.

[0053] When selecting a set of patterns for training, it is desirable to select patterns that will be the most informative or provide the most useful information for the model. Currently, several methods can be used for pattern selection. For example, pattern hashing techniques may be faster, but work best in exact matching rather than in capturing pattern similarity. In another example, pattern imaging techniques based on unmanaged images (e.g., pattern imaging techniques based on autoencoders) can capture pattern similarity in a higher multidimensional latent space, but require training and are data-dependent. In pattern classification and selection techniques based on model simulation, spatial images or resist image parameter spaces that consider similarity from a model simulation perspective can be used. However, the parameter space may be limited and may not clearly distinguish different design patterns.

[0054] In this embodiment, a method for selecting a pattern for training a machine learning model, for example, based on a design layout, is provided. The pattern selection method herein employs a transformation operation that results in embedding information around pixels of interest in a pattern in a representation domain. This embedding of the information can be represented as a set of data points in the representation domain characterized by a mathematical operation. For example, the set of data points with embedded information indicates pixel values ​​associated with features that can be obtained around the pixel of interest. Compared to machine learning-based methods for pattern selection, the transformations discussed herein are less computationally intensive. Furthermore, the set of data points that guide the selection of a pattern based on a design layout can be used to determine an information metric (e.g., information entropy).

[0055] Some machine learning-based methods tend to fail pixel shift tests, in which after slightly shifting a pattern, the shifted pattern may be mistakenly perceived as very different or greatly different. On the other hand, using the method disclosed herein, the pixel shift test results show better pattern selection. For example, by shifting the window by a certain number of pixels, some patterns may be evaluated as similar but not having enough distinguishing information. In this way, the present method can select fewer but most representative patterns with less unnecessary information. That is, a smaller training data set can be used to achieve higher model quality.

[0056] According to the present disclosure, transforming a pattern into a representation domain and determining an information metric (such as the entropy of the target layout) significantly improves the pattern selection process by saving significant computational time and resources. For example, according to the present disclosure, the need for expensive physics-based calculations to generate a CTM used in error-based methods can be eliminated. Furthermore, the information metric can help eliminate multiple forward computations of a neural network that can be performed in uncertainty-based methods.

[0057] Figure 3 The figure shows an exemplary transformation of a portion 301 of a pattern of interest using a convolution operation (e.g., via a convolutional network such as an autoencoder). For example, proximity information 303 is transformed into network weights using progressive convolution of a portion 301 of the pattern to produce pixels 305 with embedded proximity information. Thus, the pattern can be represented as a collection of pixel embeddings. However, such machine learning-based convolution operations require cumbersome training, especially when trained on a pixel-by-pixel basis.

[0058] According to the present disclosure, a method for selecting a pattern does not require machine learning or other patterning process simulation. For example, the pattern selection process involves transforming the pattern into a representation domain using a set of basis functions to generate a pattern representation (e.g., a linear pattern representation) for any input graphic. In particular, the pattern can be identified as a combination (e.g., a linear combination) of basis functions with respective weights or coefficients. Such a transformation advantageously does not require any training as in autoencoding techniques, and thus can achieve faster pattern selection.

[0059] Figure 4 4 is a flow chart of an exemplary method 400 for selecting a pattern or portion of a pattern from an input (e.g., a target layout including a target pattern for patterning a substrate) according to an embodiment. In embodiments, the input may be represented as an image, a vector, or the like. The selected pattern may be used as training data for training a model associated with a patterning process. The method involves processes P401, P403, P405, and P407.

[0060] Process P401 includes obtaining a pattern set 402 including a first pattern and a second pattern, each pattern in the pattern set including one or more features. In an embodiment, the pattern set 402 can be obtained from a design layout to be printed on a substrate; a simulation image associated with a patterning process; or an image associated with a patterned substrate. In an embodiment, the simulation image can be an aerial image, a mask image, a resist image, or a method (e.g., as described with respect to FIG. 1 ) to obtain a pattern set 402. Figure 2 In an embodiment, the image of the patterned substrate may be a scanning electron microscope (SEM) image of the patterned substrate simulated or captured by a SEM system.

[0061] In an embodiment, the pattern set 402 may be represented as an image. In this case, the pattern set 402 may be referred to as an image 402. In an embodiment, the image 402 may be an image of a design layout including a pattern to be printed onto a substrate; or an SEM image of a patterned substrate acquired via a scanning electron microscope (SEM). In an embodiment, the image 402 may be a binary image, a grayscale image, or an n-channel image, where n refers to the number of colors used in the image 402 (e.g., a 3-channel image has red, green, and blue (RGB) colors). For example, a binary image may include pixels assigned a value of 1 (1 indicates that a feature is present at the pixel address) and pixels assigned a value of 0 (0 indicates that a feature is not present at the pixel address). Similarly, the grayscale image may include pixel intensities indicating the presence or absence of features of a pattern. In an embodiment, the n-channel image may include RGB color channels, which may indicate the presence or absence of features of a pattern. In an embodiment, the RGB colors may indicate a collection of specific features in a pattern.

[0062] In an embodiment, the patterns of the pattern set 402 may include one or more features (e.g., lines, holes, etc.) that are desired to be printed on a substrate. In an embodiment, the one or more features are arranged relative to each other according to circuit design specifications. In an embodiment, the patterns of the pattern set 402 may include one or more features (e.g., lines, holes, etc.) printed on a substrate. The present disclosure is not limited to a particular image or pattern, or features therein.

[0063] Process P403 includes representing the patterns of the pattern set 402 as a group of data points 404 in a representation domain. In an embodiment, each pattern can be represented as a group of data points 404 in the representation domain. For example, the first pattern can be represented as a first group of data points in the representation domain. The second pattern can be represented as a second group of data points in the representation domain. In an embodiment, each data point of the first group can indicate information associated with a feature within a portion of the first pattern, and each data point of the second group can indicate information associated with a feature within a portion of the second pattern. In an embodiment, the information associated with the feature within a portion of a given pattern in the pattern set 402 includes pixel values ​​or pixel intensities within the portion of the given pattern. In an embodiment, the pixel values ​​or pixel intensities are associated with the feature within the portion. For example, a higher intensity value can indicate a portion of the feature. In an embodiment, the term "given pattern" is used generally to refer to any pattern under consideration from the pattern set 402.

[0064] In an embodiment, representing each pattern as the set of data points 404 in the representation domain includes transforming the given pattern through a set of basis functions that characterize the representation domain. In an embodiment, when transformed, the set of data points 404 is a set of coefficients associated with the set of basis functions. In an embodiment, the set of coefficients associated with the set of basis functions corresponds to a set of pixel addresses of the given pattern in the representation domain.

[0065] In an embodiment, the basis function set is a set of orthogonal functions. In an embodiment, the basis function set may be a Hermite-Gaussian module, a Zernike polynomial, a Bessel function or other functions.

[0066] In an embodiment, the transformation comprises projecting the given pattern of the pattern set 402 into a linear representation domain. In an embodiment, the projection comprises determining a linear combination of the set of orthogonal functions that represents the given pattern in the pattern set 402. In an embodiment, the representation domain is a Hilbert space domain. Embodiments of the present disclosure are described in detail with respect to a linear representation domain or a Hilbert space. It will be understood that the present disclosure is not limited to any specific combination of basis functions or any specific set of basis functions.

[0067] Figure 5A An exemplary transformation of a pattern into a representation domain according to an embodiment of the present disclosure is depicted in a pictorial manner. In an embodiment, the function projection in Hilbert space can be represented as in, represents the pattern to be represented in the representation domain, and ψ i Denotes the i-th order basis function to be used in the representation. For such a Hilbert space, the projection coefficients can be calculated as

[0068] Therefore, the projection coefficient set C = {c0, c1, ... c n} can be used as the representation field (e.g., In this case, the representation is a vector of individual coefficients. However, this discussion is merely exemplary. Pattern representations may use various mathematical forms of projection coefficients without departing from the scope of this disclosure. Furthermore, the projection of the pattern onto Hilbert space may be implemented using any suitable projection technique well known in the art.

[0069] Process P405 determines a set of distance values ​​for a distance metric corresponding to the pattern set 402, the set of distance values ​​including a first distance value determined between the first data point group and another data point group (e.g., the second, third, fourth, fifth, sixth, etc. data point groups), and a second distance value determined between the second data point group and the another data point group (e.g., the third, fourth, fifth, sixth, etc. data point groups). According to an embodiment of the present disclosure, the distance metric indicates an amount of mutual information between a given pattern in the pattern set 402 and the another pattern.

[0070] In an embodiment, the amount of mutual information, , between the given pattern and the other pattern indicates how much information the given pattern shares with the other pattern. A higher amount of mutual information, , indicates a higher amount of shared information between the given pattern and the other pattern. In an embodiment, the distance metric comprises a Kullback-Leibler divergence calculated using data points within the groups in the representation domain; or a k-means of nearest neighbors calculated using data points within the groups in the representation domain. A larger distance between the groups indicates a lower amount of mutual information between the two patterns. For example, the further the groups are from each other, the less mutual information there is between the groups.

[0071] Process P407 includes selecting a pattern subset 410 from the pattern set 402 using the data point group 404 as a guide for the interaction information between a given pattern and another pattern in the pattern set 402. In an embodiment, the selection of the pattern subset may be based on a value of the distance indicator that exceeds a distance threshold. For example, when two data point groups (e.g., Figure 5B When groups G1 and G2 in the dataset are far away from each other (e.g., greater than the distance threshold), these groups are generally considered to be more informative or provide more useful information in terms of machine learning training compared to groups that are closer to each other (e.g., less than the distance threshold).

[0072] In an embodiment, selecting the subset of patterns includes selecting a plurality of patterns from the set of patterns 402 based on a total entropy of the selected patterns. In an embodiment, the selecting includes determining the total entropy as a combination of information entropies associated with each group of data points corresponding to each pattern in the set of patterns 402. In an embodiment, due to sparse high-dimensional problems, the information entropy may be calculated directly on the groups of data points, where the calculation may fail as the unit volume of the bounding box approaches zero as the dimensionality increases.

[0073] In an embodiment, selecting the pattern subset from the pattern set 402 includes selecting multiple groups from the group representing the pattern set 402. For example, each selected group has a value of the distance indicator that breaks through the distance threshold. For the selected group, it can be determined whether the information entropy in the representation domain meets a certain standard, for example, maximization. However, the standard can be in any form with respect to the total entropy without departing from the scope of this disclosure. For example, in response to the information entropy not being maximized, one or more groups (previously not selected) are added to the selected multiple groups or one group is removed from the selected multiple groups. The addition or removal of groups can be repeated until the information entropy is maximized (or within a specific range) and the final selected group is obtained. Then, multiple patterns in the pattern subset are selected corresponding to the selected multiple groups.

[0074] There are many ways to calculate entropy in different representation domains. In some embodiments, the Hilbert space coefficients (also referred to as data points) are used to calculate the total entropy. In some embodiments, pixel values ​​in different representation domains can be used to calculate entropy. In some embodiments, the entropy associated with a pattern can be determined based on the pixel intensity within a portion of the image 402 representing the pattern subset. In an embodiment, the entropy indicates the unevenness of each pattern in the plurality of patterns 402. For example, the unevenness of the pattern indicates that these patterns are substantially different from each other and are thus more informative for training purposes. In an embodiment, the entropy is at least one of information entropy, Renyi entropy, or differential entropy.

[0075] In an embodiment, the information entropy comprises the sum of the products of the probability of a result among a plurality of possible results associated with a portion of an image and the logarithmic function of the probability of the result. In an embodiment, the information entropy is calculated by the following equation:

[0076]

[0077] In the above equation, H(X) is the entropy of the portion of the image, x i represents the possible outcomes associated with the pattern subset 410, each outcome having a probability P X (x i ). For example, in a binary image, the possible outcomes xi are x1 and x2, where x1 is a white pixel (e.g., a pixel intensity value of 0) and x2 is a black pixel (e.g., a pixel intensity value of 1). In an embodiment, the pattern subset 410 may be a grayscale image, in which case the possible outcomes xi, wherein, may vary from 0 to 255.

[0078] For example, the probability P X (xi ) is calculated as follows: P X (x i ) = (number of pixels with intensity level i in the sliding window) / (number of pixels in the sliding window). The associated entropy value is then typically assigned to the center pixel in the sliding window. Thus, for the binary image example, if 50% of the pixels are white and 50% of the pixels are black (i.e., P X (x1)=P X (x2) = 0.5), then the entropy expression is the largest, and when there is only a single color in the entire sliding window (i.e., P X (x1)=1 and P X (x2) = 0 or vice versa) the entropy expression is minimum.

[0079] In an embodiment, possible results include at least one of: a binary value assigned to a pixel of the image, a first value indicating that a pattern is present within the image and a second value indicating that a pattern is not present within the image; a grayscale value assigned to a pixel of the image; or a number of colors assigned to a pixel of the image 402.

[0080] In an embodiment, the entropy can be calculated for each channel, and the entropies for each channel can be compared to select a pattern. In an embodiment, the multi-channel image can be a collection of SEM images at the same location but with different SEM settings. The information index can be calculated for each channel. The entropy can be combined as a weighted average across all channels, or selected as the worst case of the index among different channels.

[0081] In an embodiment, the determination of the distance metric or information entropy need not include simulating one or more of the plurality of patterns 402, a process model associated with the patterning process, or simulating using the plurality of patterns 402, a machine learning model associated with the patterning process. The metric can be applied directly to the target layout, a portion of the target layout, or a pattern in the target layout. In an embodiment, the target layout can be provided in a GDS format.

[0082] Figure 6 The figure shows an example of a subset of multiple patterns selected from an exemplary design layout. For example, according to the method 400 discussed above, several portions of the design layout can be transformed into grouped data points or groups of data points in a representation domain (e.g., see Figure 5A and Figure 5B ). Based on the distances between groups of data points, a subset of patterns can be selected based on the total entropy (e.g., corresponding to the maximum entropy). Figure 6The features within boxes PAT1, PAT2, and PAT3 represent multiple patterns, from which subsets PAT1 and PAT3 can be selected based on groups of data points in the representation domain that correspond to the patterns PAT1, PAT2, and PAT3. In this example, a first group of data points (not shown) can correspond to pattern PAT1, and a second group of data points (not shown) can correspond to pattern PAT2. The distance between the first and second groups can be less than a distance threshold or may not correspond to maximizing the information entropy between patterns PAT1 and PAT2. Thus, pattern PAT2 can be omitted or not selected as a pattern subset.

[0083] In an embodiment, the method may further include a process for providing the selected pattern subset 410 as training data for training a model associated with the patterning process. The present disclosure is not limited to a specific use of the output sub-pattern. In an embodiment, the pattern subset may be used to improve one or more aspects of the patterning process, including but not limited to improving the training of an aerial image model, a mask model, a resist model, an OPC process, a metrology-related model, or other models related to the patterning process.

[0084] In an embodiment, the method 400 may further include a step for training a model associated with the patterning process using the pattern subset 410 as training data. In an embodiment, the training includes training a model configured to generate an optical proximity correction structure associated with the plurality of patterns 402 of the design layout. For example, the optical proximity correction structure includes a main feature corresponding to the plurality of patterns 402 of the design layout; or an auxiliary feature surrounding the plurality of patterns 402 of the design layout.

[0085] In an embodiment, another variation of a method for selecting patterns and generating training data from the patterns can be implemented as follows. In an embodiment, the method includes: obtaining a set of patterns; representing each pattern in the set as a set of data points in a representation domain; and, based on the set of data points, selecting a subset of patterns from the set of patterns to serve as a guide for determining the interaction information between a given pattern and another pattern in the set of patterns. As discussed above, the patterns can be represented in the representation domain using a set of basis functions. For example, the patterns can be represented in a Hilbert space.

[0086] In an embodiment, a method for representing patterns in a representation domain is provided. The method includes obtaining a set of patterns, each pattern including one or more features, and converting each pattern in the set of patterns into a set of data points in the representation domain, each data point indicating information associated with a feature within a portion of a given pattern in the set of patterns.

[0087] In an embodiment, representing each pattern as the set of data points in the representation domain comprises transforming the given pattern through a set of basis functions, the set of basis functions characterizing the representation domain. In an embodiment, the set of basis functions is a set of orthogonal functions. In an embodiment, when transformed, the set of data points is a set of coefficients associated with the set of basis functions. In an embodiment, the set of coefficients associated with the set of basis functions corresponds to a set of addresses of pixels of the given pattern in the representation domain.

[0088] In an embodiment, the transforming comprises projecting the given pattern of the pattern set into a linear representation domain. In an embodiment, the projecting comprises determining a linear combination of the set of orthogonal functions that represents the given pattern of the pattern set. In an embodiment, the set of basis functions comprises at least one of: a Hermite-Gaussian module; a Zernike polynomial; or a Bessel function.

[0089] In an embodiment, the methods discussed herein may be provided as one or more computer program products or non-transitory computer-readable media having instructions recorded thereon that, when executed by a computer, implement the operations according to the method 400 discussed above. For example, Figure 7 The exemplary computer system CS in includes a non-transitory computer-readable medium (e.g., memory) including instructions that, when executed by one or more processors (e.g., 104), result in operations for selecting a pattern from a target layout. In an embodiment, the instructions include: obtaining a set of patterns; representing each pattern in the set of patterns as a set of data points in a representation domain; and selecting a subset of patterns from the set of patterns based on the set of data points as guidance for interaction information between a given pattern in the set of patterns and another pattern.

[0090] In an embodiment, the instructions include: obtaining a set of patterns including a first pattern and a second pattern, each pattern in the set of patterns including one or more features; representing each pattern in the set of patterns as a group of data points in a representation domain; determining a set of distance values ​​for a distance metric corresponding to the set of patterns (e.g., the set of distance values ​​including a first distance value determined between the first group of data points and another group of data points and a second distance value determined between the second group of data points and the another group of data points); and selecting a subset of patterns from the set of patterns based on a value of the distance metric that exceeds a distance threshold. In an embodiment, the distance metric indicates an amount of mutual information between a given pattern in the set of patterns and the another pattern. In an embodiment, the first pattern is represented as a first group of data points in the representation domain, and the second pattern is represented as a second group of data points in the representation domain. In an embodiment, each data point of the first group may indicate information associated with a feature within a portion of the first pattern, and each data point of the second group may indicate information associated with a feature within a portion of the second pattern.

[0091] According to the present disclosure, combinations and subcombinations of the disclosed elements or components constitute discrete embodiments. For example, a first combination includes determining groups of data points and selecting patterns based on the groups of data points. The subcombination may include determining a distance metric between the groups. The subcombination may include determining the information entropy associated with a subset of patterns (e.g., using the entropy equation discussed above). In another combination, a selected image may be used during an inspection process to train a machine learning model related to the patterning process, and the selected pattern may be used to determine the OPC or SMO.

[0092] Figure 7 is a block diagram of an exemplary computer system CS according to an embodiment.

[0093] The computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processors) coupled to the bus BS for processing information. The computer system CS also includes a main memory MM (such as a random access memory (RAM) or other dynamic memory) coupled to the bus BS for storing information and instructions to be executed by the processor PRO. The main memory MM can also be used to store temporary variables or other intermediate information during the execution of the instructions to be executed by the processor PRO. The computer system CS also includes a read-only memory (ROM) ROM or other static storage device coupled to the bus BS for storing static information and instructions for the processor PRO. A storage device SD such as a magnetic disk or optical disk is provided and coupled to the bus BS for storing information and instructions.

[0094] The computer system CS can be coupled to a display DS for displaying information to the computer user via a bus BS, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display. An input device ID comprising alphanumeric keys and other keys is coupled to the bus BS for communicating information and command selections to the processor PRO. Another type of user input device is a cursor controller CC (such as a mouse, a trackball or cursor direction keys), which is used to communicate direction information and command selections to the processor PRO and to control cursor movement on the display DS. Such an input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0095] According to one embodiment, the parts of one or more methods described in the present disclosure can be executed by the computer system CS in response to the processor PRO executing one or more sequences of one or more instructions contained in the main memory MM. Such instructions can be read into the main memory MM from another computer-readable medium (such as a storage device SD). The execution of the instruction sequence contained in the main memory MM causes the processor PRO to perform the process steps described herein. One or more processors in a multi-processing arrangement can also be used to execute the instruction sequence contained in the main memory MM. In an alternative embodiment, a hard-wired circuit can be used to replace a software instruction or to be combined with a software instruction. Therefore, the description herein is not limited to any specific combination of hardware circuits and software.

[0096] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to the processor PRO for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage devices SD. Volatile media include dynamic memory, such as main memory MM. Transmission media include coaxial cables, copper wires, and optical fibers, including the wires comprising the bus BS. Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Computer-readable media can be non-transitory, such as floppy disks, disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical media with a pattern of holes, RAM, PROMs, and EPROMs, FLASH-EPROMs, any other memory chips, or cassette memory. Non-transitory computer-readable media can have instructions recorded thereon. When executed by a computer, these instructions can implement any of the features described above. Transitory computer readable media may include carrier waves or other propagated electromagnetic signals.

[0097] Various forms of computer-readable media may involve carrying one or more sequences of one or more instructions to the processor PRO for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions via a telephone line using a modem. The local modem of the computer system CS may receive data on the telephone line and convert the data into infrared signals using an infrared transmitter. An infrared detector coupled to the bus BS may receive the data carried in the infrared signal and place the data on the bus BS. The bus BS carries the data to the main memory MM, from which the processor PRO retrieves and executes the instructions. The instructions received by the main memory MM may optionally be stored on a storage device SD before or after being executed by the processor PRO.

[0098] The computer system CS may also include a communication interface CI coupled to the bus BS. The communication interface CI provides bidirectional data communication coupled to a network link NDL, which is connected to a local area network LAN. For example, the communication interface CI may be an integrated services digital network (ISDN) card or a modem for providing a data communication connection to a corresponding type of telephone line. As another example, the communication interface CI may be a local area network (LAN) card for providing a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such embodiment, the communication interface CI sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0099] The network link NDL typically provides data communications to other data devices via one or more networks. For example, the network link NDL may provide a connection to a host computer HC via a local area network LAN. This may include data communications services provided by the global packet data communications network now commonly referred to as the "Internet" INT. Both the local area network LAN (and the Internet) use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network data link NDL and through the communication interface CI (which carry digital data to and from the computer system CS) are exemplary forms of carrier waves that transmit the information.

[0100] The computer system CS can send messages and receive data, including program code, via one or more networks, network data links NDL, and communication interfaces CI. In the example of the Internet, a host computer HC can transmit request code for an application program via the Internet INT, the network data link NDL, the local area network LAN, and the communication interface CI. For example, such a downloaded application can provide all or part of the method described herein. The received code can be executed by the processor PRO upon receipt and / or stored in a storage device SD or other non-volatile memory for later execution. In this way, the computer system CS can obtain application code in the form of a carrier wave.

[0101] Figure 8 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0102] The lithographic projection apparatus may comprise an illumination system IL, a first stage MT, a second stage WT and a projection system PS.

[0103] The illumination system IL may condition the radiation beam B. In this particular case, the illumination system further comprises a radiation source SO.

[0104] A first stage (eg, patterning device table) MT may be provided with a patterning device holder for holding a patterning device MA (eg, a reticle) and connected to a first positioner to accurately position the patterning device relative to the article PS.

[0105] A second work table (substrate table) WT may be provided with a substrate holder for holding a substrate W (eg a resist-coated silicon wafer) and connected to a second positioner to accurately position the substrate relative to the item PS.

[0106] A projection system ("lens") PS (e.g., a refractive, reflective, or catadioptric optical system) may project the irradiated portion of the patterning device MA onto a target portion C of the substrate W (e.g., comprising one or more dies).

[0107] As depicted herein, the device may be of the transmissive type (i.e., having a transmissive patterning device). However, in general, the device may also be, for example, of the reflective type (i.e., having a reflective patterning device). The device may employ patterning devices of a different kind than a classical mask; examples include a programmable mirror array or an LCD matrix.

[0108] The source SO (e.g., a mercury lamp or an excimer laser, LPP (laser produced plasma) EUV source) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, for example, directly or after having traversed a conditioning device such as a beam expander Ex. The illuminator IL may include an adjustment device AD ​​for setting the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. In addition, the illuminator IL will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B incident on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0109] In some embodiments, although the source SO may be within the housing of the lithographic projection apparatus (which is often the case when the source SO is, for example, a mercury lamp), the source SO may also be remote from the lithographic projection apparatus, the radiation beam generated by the source SO being directed into the apparatus (for example, with the aid of suitable directional reflectors); the latter case may be the case when the source SO is an excimer laser (for example, based on KrF, ArF or F2 laser action).

[0110] The beam PB may then be intercepted by the patterning device MA which is held on the patterning device table MT. Having traversed the patterning device MA, the radiation beam B may pass through the lens PL which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning device (and the interferometric measurement device IF), the substrate table WT can be accurately moved, for example, to position a different target portion C in the path of the radiation beam PB. Similarly, the first positioning device may be used to accurately position the patterning device MA relative to the path of the radiation beam B, for example after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. Typically, movement of the stage MT, WT will be achieved with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning). However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to a short-stroke actuator only, or may be fixed.

[0111] The depicted tool can be used in two different modes, a step mode and a scan mode. In the step mode, the patterning device table MT is held substantially stationary and an image of the entire patterning device is projected at once (i.e., a single "flash") onto a target portion C. The substrate table WT can be shifted in the x-direction and / or y-direction so that a different target portion C can be irradiated by the beam PB.

[0112] In scan mode, essentially the same situation applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT can be moved in a given direction (the so-called "scanning direction", e.g., the y-direction) at a velocity v, such that the projection beam B is scanned across the patterning device image; while the substrate table WT is simultaneously moved in the same or opposite direction at a velocity V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without having to compromise resolution.

[0113] Figure 9 is a schematic diagram of another lithographic projection apparatus (LPA) according to an embodiment.

[0114] The LPA may comprise a source collector module SO, an illumination system (illuminator) IL, a support structure MT, a substrate table WT and a projection system PS, the illumination system being configured to condition a radiation beam B (eg EUV radiation).

[0115] The support structure (e.g., patterning device table) MT may be constructed to support a patterning device (e.g., mask or reticle) MA and be connected to a first positioner PM configured to accurately position the patterning device;

[0116] The substrate table (eg, wafer stage) WT is constructed to hold a substrate (eg, a resist-coated wafer) W and is connected to a second positioner PW configured to accurately position the substrate.

[0117] A projection system (eg, a reflective projection system) PS may be configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0118] As depicted here, the LPA can be of the reflective type (e.g., using a reflective patterning device). It should be noted that because most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector comprising multiple stacks of, for example, molybdenum and silicon. In one example, the multilayer reflector has 40 layers of paired molybdenum and silicon, each of which is a quarter wavelength thick. X-ray lithography can be used to produce even smaller wavelengths. Since most materials are absorptive at EUV and x-ray wavelengths, the patterned thin sheets of absorbing material on the topography of the patterning device (e.g., a TaN absorber on top of a multilayer reflector) define areas where features will be printed (positive resist) or not printed (negative resist).

[0119] The illuminator IL can receive an extreme ultraviolet radiation beam from a source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) with one or more emission lines in the EUV range. In one such method, often referred to as laser produced plasma ("LPP"), a plasma can be generated by irradiating a fuel, such as a droplet, stream, or cluster of a material having a line-emitting element, with a laser beam. The source collector module SO can be a laser (e.g., a laser) of an EUV radiation system including a laser beam for providing a laser beam to excite the fuel. Figure 9 The resulting plasma emits output radiation, such as EUV radiation, which is collected by a radiation collector disposed in the source collector module. For example, when a CO2 laser is used to provide the laser beam for fuel excitation, the laser and the source collector module may be separate entities.

[0120] In such cases, the laser may not be considered to form part of the lithographic apparatus, and the radiation beam may be delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, such as when the source is a discharge produced plasma EUV generator (often referred to as a DPP source), the source may be an integral part of the source collector module.

[0121] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam PB. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator can be used to adjust the radiation beam so as to have a desired uniformity and intensity distribution in its cross-section.

[0122] The radiation beam B can be incident on and patterned by the patterning device (e.g., mask) MA, which is held on the support structure (e.g., patterning device table) MT. After reflecting from the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position sensor PS2 (e.g., an interferometer device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0123] The depicted device LPA can be used in at least one of the following modes, namely a stepping mode, a scanning mode and a stationary mode.

[0124] In step mode, the support structure (e.g. patterning device table) MT and the substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam is projected at one time onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0125] In scan mode, the support structure (e.g. patterning device table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam B is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (e.g. patterning device table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0126] In stationary mode, the support structure (e.g., patterning device table) MT is held substantially stationary so as to hold a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography using a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0127] Figure 10 is a detailed view of the lithographic projection apparatus according to an embodiment.

[0128] As shown, the LPA may include the source collector module SO, the illumination system IL and the projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained in the enclosure 220 of the source collector module SO. The plasma 210 that emits EUV radiation can be formed by a discharge-generated plasma source. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor or tin vapor, in which an extremely high temperature plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, a very hot plasma 210 is generated by causing a discharge of a partially ionized plasma. In order to effectively generate radiation, a Xe, Li, Sn vapor or any other suitable gas or vapor with a partial pressure of, for example, 10 Pa may be required. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0129] Radiation emitted by the high temperature plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or fin trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230 further illustrated herein includes at least a channel structure.

[0130] The collector chamber 211 may include a radiation collector CO which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation passing through the collector CO may be reflected off the grating spectral filter 240 and then focused along the optical axis indicated by the dotted line "O" at a virtual source point IF. The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near an opening 221 in the enclosure structure 220. The virtual source point IF is an image of the plasma 210 emitting the radiation.

[0131] The radiation then traverses the illumination system IL, which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the radiation beam 21 at the patterning device MA, which is held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by the substrate table WT.

[0132] Typically, more elements than shown may be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, the grating spectral filter 240 may optionally be present. Additionally, more mirrors than shown may be present, for example, more than one mirror may be present in the projection system PS. Figure 10 1 to 6 additional reflective elements other than the reflective element shown in .

[0133] Collector optics CO (eg Figure 10 ) is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are arranged axially symmetrically about the optical axis O, and this type of collector optics CO can be used in conjunction with a discharge produced plasma source (often referred to as a DPP source).

[0134] Figure 11 is a detailed view of a source collector module SO of a lithographic projection apparatus LPA according to an embodiment.

[0135] The source collector module SO can be part of the LPA radiation system. The laser LA can be arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of tens of eV. The high-energy radiation generated during the deexcitation and recombination of these ions is emitted by the plasma, collected by the near normal incidence collector optics CO, and focused onto the opening 221 in the enclosure 220.

[0136] According to the present disclosure, a method for selecting a pattern involves transforming the pattern into a representation domain (such as an optical system based on the domain of an illumination source) via a set of basis functions to produce a pattern representation (e.g., a linear pattern representation) for any input pattern. In particular, the pattern can be represented using a set of transmission cross coefficients (TCCs) that represent the optical properties of the illumination source of the lithographic apparatus, such as electromagnetic field (EMF) excitation of multiple portions of the pattern. This transformation is easy to compute (e.g., once the configuration of the illumination source is known), is more accurate than conventional representations, and therefore provides an improved pattern similarity analysis for better selection of representative patterns. Such a transformation advantageously does not require any training as in auto-encoding techniques, and therefore can achieve faster pattern selection.

[0137] Figure 12 Flowchart of an exemplary method for selecting a pattern from a target layout based on a pattern representation in a source-based representation domain, according to an embodiment. In an embodiment, the input may be represented as an image, a vector, or the like. The selected pattern may be used for various purposes, for example, as training data for training or calibrating a model associated with a patterning process.

[0138] In process P1201, a first pattern set 1202 is obtained. In some embodiments, the first pattern set 1202 can be obtained from a design layout to be printed on a substrate; a simulation image associated with a patterning process; or an image associated with a patterned substrate. In some embodiments, the simulation image can be an aerial image, a mask image, a resist image, or a process (e.g., as described with respect to FIG. 1 ). Figure 2 In some embodiments, the image of the patterned substrate may be an SEM image of the patterned substrate simulated or captured by a SEM system.

[0139] In some embodiments, the first pattern set 1202 can be represented as an image. In this case, the first pattern set 1202 can be referred to as an image 1202. In some embodiments, the image 1202 can be an image of a design layout including a pattern to be printed onto a substrate; or an SEM image of a patterned substrate acquired via an SEM. In some embodiments, the image 1202 can be a binary image, a grayscale image, or an n-channel image, where n refers to the number of colors used in the image 1202 (e.g., a 3-channel image has red, green, and blue colors (RGB)). For example, a binary image can include pixels assigned a value of "1" (indicating a feature at the pixel's address) and pixels assigned a value of "0" (indicating the absence of a feature at the pixel's address). Similarly, the grayscale image can include pixel intensities indicating the presence or absence of a feature of the pattern. In some embodiments, the n-channel image can include RGB color channels, which can indicate the presence or absence of a feature of the pattern. In some embodiments, the RGB colors can indicate a collection of specific features in the pattern.

[0140] In some embodiments, the patterns of the first pattern set 402 may include one or more features (e.g., lines, holes, etc.) that are desired to be printed on the substrate. The features may be arranged relative to each other according to circuit design specifications. The present disclosure is not limited to a particular image or pattern, or features therein.

[0141] In process P1203, the patterns of the first pattern set 402 can be represented in a representation domain. For example, the patterns can be represented in a Hilbert space domain, such as an electromagnetic field (EMF) domain. In some embodiments, representing the patterns in the representation domain includes representing the patterns as a set of data points 1204. In some embodiments, the data points indicate information associated with features within a portion of the pattern. In some embodiments, representing a given pattern as the set of data points 1204 in the representation domain includes transforming the given pattern through a set of basis functions that characterize the representation domain. When transformed, the set of data points 1204 can be a set of coefficients associated with the set of basis functions. In some embodiments, the set of basis functions is a set of orthogonal functions. In an embodiment, the transformation includes projecting the given pattern into a linear representation domain, which includes determining a linear combination of the set of orthogonal functions that represents the given pattern. For example, the pattern can be projected into the EMF domain using SOCS TCC as a basis function. When converted, each pixel of the pattern is represented using a vector representing the EMF excitation at the pixel (e.g., an N-dimensional vector of TCC), and the pattern is represented as a vector group (data point group 1204). Figure 5Ato describe the details of representing patterns in a linear representation domain or Hilbert space. Figure 5A where ψ represents the basis function of order i to be used in the representation i It may include TCC basis functions, such as TCCi. The projection coefficient set C = {c0, c1, ...c n This representation of} can be used as a pattern representation in the representation domain, and the set of projection coefficients can contain the necessary information about how the pattern-pixels are represented in the EMF domain. The image of the pattern can be reconstructed using the coefficients (but lossy - lossy representing the diffraction loss of the illumination source). The reconstruction can be expressed as:

[0142]

[0143] (Equation A)

[0144] where c i is the i-th order coefficient, TCC i is the i-th order basis function, and (x, y) is the address of the pixel.

[0145] The following paragraphs describe additional details of projecting a pattern into an illumination source-based representation domain that describes the characteristics of the source relative to the pattern (e.g., the source response to the pattern). In some embodiments, the pattern from the first pattern set 1202 can be represented as a source-based representation domain, such as an EMF domain, using a summation of coherent systems (SOCS) TCCs as basis functions. The TCC describes the EMF excitation of a portion of the pattern. For example, the source characteristics of the lithographic apparatus can be modeled using the Hopkin imaging formula, which calculates the TCC of a partially coherent source. The TCC can then be decomposed into a discrete set of coherent systems (e.g., N-dimensional SOCS TCCs) with orthogonal transfer functions. The set of SOCSTCCs represents the EMF transfer functions of individual coherent systems, where the final imaging intensity (e.g., the spatial image intensity associated with the pattern) can be determined as the sum of the individual intensities. The calculation of the spatial image intensity can be expressed as follows:

[0146]

[0147] (Equation A)

[0148] Where i: pixel order

[0149] TCC k : k-th order (source-dependent) spatial SOCS TCC

[0150] λ k : TCC kth order eigenvalue (source dependent)

[0151] M: spatial mask clipped at the TCC size

[0152] In some embodiments, projecting a pattern into the EMF domain using the SOCS TCC as a basis function includes representing pixels of the pattern using a set of TCCs (e.g., an N-dimensional vector of SOCS TCCs). The vector represents an EMF excitation at the pixel based on the proximity of the pixel. That is, the vector indicates how the proximity of the pixel affects the EMF excitation at the pixel. Each element of the vector corresponds to a projection of a pixel onto the TCC of the N-dimensional SOCS TCC.

[0153] Since a pattern can be represented by its pixels, and each pixel can be represented using a vector of SOCS TCCs, the pattern can be represented as a vector group or vector cloud, e.g. as represented by Figure 5B For example, group G1 may represent a first pattern vector group, and group G2 may represent a second pattern vector group from the first pattern set 1202 , and the axis may correspond to a representation domain (eg, EMF value).

[0154] After representing the patterns as vector groups or data point groups 1204, at process P1205, a second pattern set 1206 can be selected as representative patterns from the first pattern set 1202 based on one or more criteria. In some embodiments, the vector groups of the first pattern set 1204 can be analyzed for pattern similarity, and one or more indicators indicative of the pattern similarity can be determined, such as a distance indicator between two vector groups. If the indicator meets the criteria (e.g., the distance indicator meets (e.g., exceeds) a distance threshold), the pattern group can be considered sufficiently different from the pattern group whose indicator does not meet the criteria to be selected as a representative pattern. In some embodiments, the second pattern set 1206 can be selected based on the total entropy of the selected patterns. At least the above with respect to Figure 4 (e.g., processes P405 and P407), Figure 5B and Figure 6 Additional details regarding selecting the second set of patterns 1206 are described.

[0155] The second pattern set 1206 can be used for various purposes. For example, as at least Figure 4As described, the second pattern set 1206 can be used to configure (e.g., train or calibrate) a model associated with the patterning process. The present disclosure is not limited to the specific use of the second pattern set 1206 selected. The second pattern set 1206 can be used to improve one or more aspects of the patterning process, such as improving the performance of an aerial image model, a mask model, a resist model, an OPC process, a metrology-related model, or other models related to the patterning process.

[0156] Note that although Figure 12 The description represents the pattern in a representation domain characterized by the optical system or illumination source of the lithographic apparatus (e.g., the source response to the pattern), but the representation domain is not limited to the optical system. The representation domain can be characterized based on any lithographic apparatus or process characteristics, such as a photoresist domain (e.g., the photoresist response to the pattern).

[0157] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features and can be used in particular with emerging imaging technologies that can produce shorter and shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography, which can produce wavelengths of 193 nm by using ArF lasers and even 157 nm by using fluorine lasers. In addition, to generate photons in this range, EUV lithography can produce wavelengths in the range of 20 nm to 50 nm by using synchrotrons or by applying high-energy electrons to bombard materials (solid or plasma).

[0158] The embodiments of the present disclosure may also be described by the following aspects:

[0159] 1. A non-transitory computer-readable medium configured to select patterns based on interaction information between the patterns for training a machine learning model related to semiconductor manufacturing, the medium comprising instructions stored therein that, when executed by one or more processors, result in operations comprising:

[0160] obtaining a pattern set comprising a first pattern and a second pattern, each pattern in the pattern set comprising one or more features;

[0161] representing each pattern in the set of patterns as a group of data points in a representation domain, the first pattern being represented as a first group of data points in the representation domain, and the second pattern being represented as a second group of data points in the representation domain, each data point in the first group indicating information associated with a feature within a portion of the first pattern, and each data point in the second group indicating information associated with a feature within a portion of the second pattern;

[0162] determining a set of distance values ​​for a distance metric corresponding to the set of patterns, the set of distance values ​​comprising a first distance value determined between the first group of data points and another group of data points and a second distance value determined between the second group of data points and the another group of data points, the distance metric indicating an amount of mutual information between a given pattern in the set of patterns and the another pattern; and

[0163] A subset of patterns is selected from the set of patterns based on a value of the distance indicator that breaks through a distance threshold.

[0164] 2. The medium of clause 1, wherein the set of patterns comprises patterns obtained from:

[0165] the design layout that is expected to be printed on the substrate;

[0166] a simulated image associated with the patterning process; or

[0167] An image associated with a patterned substrate.

[0168] 3. The medium according to aspect 2, wherein

[0169] The simulation image includes at least one of an aerial image, a mask image, a resist image, or an etch image.

[0170] 4. The medium according to aspect 2, wherein

[0171] The image of the patterned substrate includes a scanning electron microscope (SEM) image of the patterned substrate.

[0172] 5. The medium according to any one of aspects 1 to 4, wherein

[0173] The information associated with features within a portion of the given pattern in the set of patterns comprises:

[0174] A pixel value within the portion of the given pattern indicates an intensity associated with a feature within the portion.

[0175] 6. The medium according to any one of aspects 1 to 5, wherein

[0176] The amount of mutual information between the given pattern and the other pattern indicates how much information in the given pattern is in common with the other pattern, with a higher amount of mutual information indicating a higher amount of common information between the given pattern and the other pattern.

[0177] 7. The medium according to any one of aspects 1 to 6, wherein

[0178] Representing each pattern as the set of data points in the representation domain comprises:

[0179] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0180] 8. The medium according to aspect 7, wherein

[0181] During conversion, each pixel of the given image corresponds to a set of coefficients associated with the set of basis functions.

[0182] 9. The medium according to aspect 8, wherein

[0183] The set of coefficients associated with the set of basis functions corresponds to a set of TCCs.

[0184] 10. The medium according to aspect 8, wherein

[0185] The basis function set includes a TCC function set.

[0186] 11. The medium according to aspect 7, wherein

[0187] When converted, the set of data points corresponds to the set of coefficients associated with the set of basis functions.

[0188] 12. The medium according to aspect 11, wherein

[0189] The set of coefficients associated with the set of basis functions corresponds to the set of addresses of pixels of the given pattern in the representation domain.

[0190] 13. The medium according to any one of aspects 7 to 12, wherein

[0191] The basis function set is an orthogonal function set.

[0192] 14. The medium according to any one of aspects 7 to 13, wherein

[0193] The conversion includes:

[0194] The given pattern in the set of patterns is projected into a linear representation domain.

[0195] 15. The medium according to aspect 14, wherein

[0196] The projection includes:

[0197] A linear combination of the set of orthogonal functions representing the given pattern in the set of patterns is determined.

[0198] 16. The medium according to any one of aspects 7 to 15, wherein

[0199] The basis function set includes at least one of the following:

[0200] Hermite Gaussian module;

[0201] Zernike polynomials; or

[0202] Bessel function.

[0203] 17. The medium according to any one of aspects 1 to 16, wherein

[0204] The representation domain is the Hilbert space domain.

[0205] 18. The medium according to any one of aspects 1 to 16, wherein

[0206] Selecting the subset of patterns includes selecting a plurality of patterns from the set of patterns based on a total entropy of the selected patterns.

[0207] 19. The medium of clause 18, wherein selecting comprises:

[0208] The total entropy is determined as a combination of information entropies associated with each group of data points corresponding to each pattern of the set of patterns.

[0209] 20. The medium of clause 19, wherein selecting the subset of patterns from the set of patterns comprises:

[0210] selecting a plurality of groups from the group representing the set of patterns, each selected group having a value of the distance indicator that exceeds the distance threshold; and

[0211] For the selected group, determining whether the information entropy of the representation domain meets a specified standard;

[0212] In response to the information entropy not meeting the specified criteria, adding another group to the selected plurality of groups or removing a group from the selected plurality of groups, and repeating these steps; and

[0213] A plurality of patterns corresponding to the selected plurality of groups are selected.

[0214] 21. The medium of any one of aspects 1 to 20, wherein the distance indicator comprises:

[0215] the Kullback-Leibler divergence calculated using data points within the group in the representation domain; or

[0216] The nearest neighbor k-means are calculated using the data points within the group in the representation domain.

[0217] 22. The medium according to any one of aspects 1 to 21, further comprising:

[0218] A machine learning model configured to determine characteristics of the patterning process is trained based on the subset of patterns.

[0219] 23. The medium according to any one of aspects 1 to 22, wherein

[0220] The machine learning model is configured to determine characteristics of an illumination source of a lithographic apparatus, a mask pattern of a mask, a projection system of the lithographic apparatus, or a resist used to print a pattern on a substrate.

[0221] 24. The medium according to any one of aspects 1 to 23, wherein

[0222] Representing each pattern as the data point in the representation domain does not include using a machine learning model.

[0223] 25. The method according to aspect 1, wherein:

[0224] The representation domain corresponds to electromagnetic functions.

[0225] 26. The medium of aspect 25, wherein

[0226] The electromagnetic function is a set of transmission cross coefficient (TCC) functions associated with an illumination source of a lithographic apparatus used to print a first set of patterns onto a substrate.

[0227] 27. The medium of clause 26, wherein representing each pattern comprises:

[0228] Pixels of a pattern in the set of patterns are represented as pattern vectors, wherein each element in the pattern vector corresponds to a projection of a pixel at a TCC of the set of TCC functions.

[0229] 28. The medium of clause 27, wherein the pattern vectors are indicative of EMF excitations of corresponding pixels.

[0230] 29. The medium of clause 27, wherein the pattern vector indicates an effect of proximity of the respective pixels on EMF excitation of the respective pixels.

[0231] 30. The medium of aspect 1, wherein the set of data points associated with each pattern in the set of patterns comprises a set of pattern vectors, wherein each pattern vector corresponds to a pixel of a plurality of pixels of the respective pattern.

[0232] 31. The medium of aspect 1, wherein each pattern in the set of patterns is represented as a plurality of components in the representation domain, wherein each component corresponds to a pixel of the pattern.

[0233] 32. A non-transitory computer-readable medium representing a pattern in a representation domain, the medium comprising instructions stored therein that, when executed by one or more processors, result in operations comprising:

[0234] obtaining a set of patterns, each pattern comprising one or more features; and

[0235] Each pattern in the set of patterns is converted into a set of data points in a representation domain, each data point indicating information associated with a feature within a portion of a given pattern in the set of patterns.

[0236] 33. The medium of clause 32, wherein representing each pattern as the set of data points in the representation domain comprises:

[0237] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0238] 34. The medium of clause 33, wherein, when converted, the set of data points is a set of coefficients associated with the set of basis functions.

[0239] 35. The medium of clause 34, wherein the set of coefficients associated with the set of basis functions corresponds to a set of addresses in the representation domain of pixels of the given pattern.

[0240] 36. The medium of clause 33, wherein the set of basis functions is a set of orthogonal functions.

[0241] 37. The medium of any one of aspects 33 to 36, wherein the converting comprises:

[0242] The given pattern in the set of patterns is projected into a linear representation domain.

[0243] 38. The medium of clause 37, wherein the projecting comprises determining a linear combination of the set of orthogonal functions that represents the given pattern in the set of patterns.

[0244] 39. The medium of any of clauses 33 to 38, wherein the set of basis functions comprises at least one of:

[0245] Hermite Gaussian module;

[0246] Zernike polynomials; or

[0247] Bessel function.

[0248] 40. The medium of any of clauses 32 to 39, wherein the representation domain is a Hilbert space domain.

[0249] 41. A non-transitory computer-readable medium configured to select a representative pattern for training a machine learning model, the medium comprising instructions stored therein that, when executed by one or more processors, result in operations comprising:

[0250] Get a pattern collection;

[0251] representing each pattern in the set of patterns as a set of data points in a representation domain; and

[0252] Based on the set of data points, a subset of patterns is selected from the set of patterns as a guide for interaction information between a given pattern and another pattern in the set of patterns.

[0253] 42. The medium of clause 41, wherein each data point represents the information associated with a feature within a portion of the given pattern in the set of patterns.

[0254] 43. The medium of clause 42, wherein the information associated with the feature comprises pixel values ​​within the portion of the given pattern.

[0255] 44. A medium according to any one of aspects 41 to 43, wherein the amount of mutual information between the given pattern and the other pattern indicates how much information in the given pattern is shared with the other pattern, and a higher amount of mutual information indicates a higher amount of shared information between the given pattern and the other pattern.

[0256] 45. The medium of any one of clauses 41 to 44, wherein representing each pattern as the set of data points in the representation domain comprises:

[0257] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0258] 46. ​​The medium of clause 45, wherein, when converted, the set of data points is a set of coefficients associated with the set of basis functions.

[0259] 47. The medium of clause 46, wherein the set of coefficients associated with the set of basis functions corresponds to a set of addresses in the representation domain of pixels of the given pattern.

[0260] 48. The medium of any one of clauses 45 to 47, wherein the set of basis functions is a set of orthogonal functions.

[0261] 49. The medium of any one of aspects 45 to 48, wherein the converting comprises:

[0262] The given pattern in the set of patterns is projected into a linear representation domain.

[0263] 50. The medium of clause 49, wherein the projecting comprises determining a linear combination of the set of orthogonal functions that represents the given pattern in the set of patterns.

[0264] 51. The medium of any one of clauses 45 to 50, wherein the set of basis functions comprises at least one of:

[0265] Hermite Gaussian module;

[0266] Zernike polynomials; or

[0267] Bessel function.

[0268] 52. The medium of any of clauses 41 to 51, wherein the representation domain is a Hilbert space domain.

[0269] 53. The medium of any of aspects 41 to 52, wherein selecting the subset of patterns comprises selecting a plurality of patterns from the set of patterns based on a total entropy of the selected patterns.

[0270] 54. The medium of clause 53, wherein selecting comprises:

[0271] The total entropy is determined as a combination of information entropies associated with each group of data points corresponding to each pattern in the set of patterns.

[0272] 55. The medium of clause 54, wherein selecting the subset of patterns from the set of patterns comprises:

[0273] selecting a plurality of groups from the group representing the set of patterns, each selected group having a value of a distance indicator that exceeds a distance threshold, the distance indicator indicating a distance between the selected group and another group from the group representing the set of patterns; and

[0274] For the selected group, determining whether the information entropy in the representation domain is maximized;

[0275] In response to the information entropy not being maximized, adding another group to the plurality of groups or removing a group from the plurality of groups, and repeating steps until the information entropy is maximized; and

[0276] A plurality of patterns corresponding to the selected plurality of groups are selected.

[0277] 56. The medium of clause 55, wherein the distance indicator comprises:

[0278] the Kullback-Leibler divergence calculated using data points within the group in the representation domain; or

[0279] The nearest neighbor k-means are calculated using the data points within the group in the representation domain.

[0280] 57. The medium of any one of aspects 41 to 56, wherein the set of patterns comprises patterns obtained from:

[0281] the design layout that is expected to be printed on the substrate;

[0282] a simulated image associated with the patterning process; or

[0283] An image associated with a patterned substrate.

[0284] 58. The medium of any one of aspects 41 to 57, wherein the simulated image comprises at least one of an aerial image, a mask image, a resist image, or an etch image.

[0285] 59. The medium of clause 58, wherein the image of the patterned substrate comprises a scanning electron microscope (SEM) image of the patterned substrate.

[0286] 60. The medium of any one of aspects 41 to 59, further comprising:

[0287] A machine learning model configured to determine characteristics of the patterning process is trained based on the subset of patterns.

[0288] 61. The medium of aspect 60, wherein the machine learning model is configured to determine characteristics of an illumination source of a lithographic apparatus, a mask pattern of a mask, a projection system of the lithographic apparatus, or a resist used to print a pattern on a substrate.

[0289] 62. The medium of any one of aspects 41 to 61, wherein representing each pattern as the data point in the representation domain does not include using a machine learning model.

[0290] 63. A method for selecting patterns based on interaction information between patterns for training a machine learning model related to semiconductor manufacturing, the method comprising:

[0291] obtaining a pattern set comprising a first pattern and a second pattern, each pattern in the pattern set comprising one or more features;

[0292] representing each pattern in the set of patterns as a group of data points in a representation domain, the first pattern being represented as a first group of data points in the representation domain, and the second pattern being represented as a second group of data points in the representation domain, each data point in the first group indicating information associated with a feature within a portion of the first pattern, and each data point in the second group indicating information associated with a feature within a portion of the second pattern;

[0293] determining a set of distance values ​​for a distance metric corresponding to the set of patterns, the set of distance values ​​comprising a first distance value determined between the first group of data points and another group of data points and a second distance value determined between the second group of data points and the another group of data points, the distance metric indicating an amount of mutual information between a given pattern in the set of patterns and the another pattern; and

[0294] A subset of patterns is selected from the set of patterns based on a value of the distance indicator that breaks through a distance threshold.

[0295] 64. A method according to clause 63, wherein the set of patterns comprises patterns obtained from:

[0296] the design layout that is expected to be printed on the substrate;

[0297] a simulated image associated with the patterning process; or

[0298] An image associated with a patterned substrate.

[0299] 65. The method of clause 64, wherein the simulated image comprises at least one of an aerial image, a mask image, a resist image, or an etch image.

[0300] 66. The method of clause 64, wherein the image of the patterned substrate comprises a scanning electron microscope (SEM) image of the patterned substrate.

[0301] 67. A method according to any one of clauses 63 to 66, wherein the information associated with features within a portion of the given pattern in the set of patterns comprises:

[0302] A pixel value within the portion of the given pattern indicates an intensity associated with a feature within the portion.

[0303] 68. A method according to any one of aspects 63 to 67, wherein the amount of mutual information between the given pattern and the other pattern indicates how much information in the given pattern is shared with the other pattern, and a higher amount of mutual information indicates a higher amount of shared information between the given pattern and the other pattern.

[0304] 69. The method of any one of clauses 63 to 68, wherein representing each pattern as the set of data points in the representation domain comprises:

[0305] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0306] 70. The medium of clause 69, wherein, upon conversion, each pixel of the given image corresponds to a set of coefficients associated with the set of basis functions.

[0307] 71. A method according to clause 70, wherein the set of coefficients associated with the set of basis functions corresponds to a set of TCCs.

[0308] 72. A method according to clause 70, wherein the set of basis functions comprises a set of TCC functions.

[0309] 73. The method of clause 69, wherein, when converted, the set of data points is a set of coefficients associated with the set of basis functions.

[0310] 74. A method according to clause 73, wherein the set of coefficients associated with the set of basis functions corresponds to a set of addresses in the representation domain of pixels of the given pattern.

[0311] 75. A method according to any one of aspects 69 to 74, wherein the set of basis functions is a set of orthogonal functions.

[0312] 76. The method of any one of aspects 69 to 75, wherein the converting comprises:

[0313] The given pattern in the set of patterns is projected into a linear representation domain.

[0314] 77. The medium of clause 76, wherein the projection comprises:

[0315] A linear combination of the set of orthogonal functions representing the given pattern in the set of patterns is determined.

[0316] 78. A method according to any one of clauses 69 to 74, wherein the set of basis functions comprises at least one of:

[0317] Hermite Gaussian module;

[0318] Zernike polynomials; or

[0319] Bessel function.

[0320] 79. A method according to any one of clauses 63 to 78, wherein the representation domain is a Hilbert space domain.

[0321] 80. The method of any one of clauses 63 to 79, wherein selecting the subset of patterns comprises selecting a plurality of patterns from the set of patterns based on a total entropy of the selected patterns.

[0322] 81. The method of clause 80, wherein selecting comprises:

[0323] The total entropy is determined as a combination of information entropies associated with each group of data points corresponding to each pattern in the set of patterns.

[0324] 82. The method of clause 81, wherein selecting the subset of patterns from the set of patterns comprises:

[0325] selecting a plurality of groups from the group representing the set of patterns, each selected group having a value of the distance indicator that exceeds the distance threshold; and

[0326] For the selected group, determining whether the information entropy in the representation domain is maximized;

[0327] In response to the information entropy not being maximized, adding another group to the plurality of groups or removing a group from the plurality of groups, and repeating steps until the information entropy is maximized; and

[0328] A plurality of patterns corresponding to the selected plurality of groups are selected.

[0329] 83. A method according to any one of aspects 63 to 82, wherein the distance indicator comprises:

[0330] the Kullback-Leibler divergence calculated using data points within the group in the representation domain; or

[0331] The nearest neighbor k-means are calculated using the data points within the group in the representation domain.

[0332] 84. The method of any one of aspects 63 to 83, further comprising:

[0333] A machine learning model configured to determine characteristics of the patterning process is trained based on the subset of patterns.

[0334] 85. A method according to any one of aspects 63 to 84, wherein the machine learning model is configured to determine characteristics of an illumination source of a lithographic device, a mask pattern of a mask, a projection system of the lithographic device, or a resist used to print a pattern on a substrate.

[0335] 86. A method according to any one of aspects 63 to 85, wherein representing each pattern as the data point in the representation domain does not include using a machine learning model.

[0336] 87. The method of clause 63, wherein the representation domain corresponds to an electromagnetic function.

[0337] 88. A method according to clause 87, wherein the electromagnetic function is a set of transmission cross coefficient (TCC) functions associated with an illumination source of a lithographic apparatus used to print the first set of patterns onto the substrate.

[0338] 89. The method of clause 88, wherein representing each pattern comprises:

[0339] Pixels of a pattern in the set of patterns are represented as pattern vectors, wherein each element in the pattern vector corresponds to a projection of a pixel at a TCC of the set of TCC functions.

[0340] 90. The method of clause 89, wherein the pattern vectors are indicative of EMF excitations of corresponding pixels.

[0341] 91. The method of clause 89, wherein the pattern vector indicates an effect of the proximity of the respective pixels on the EMF excitation of the respective pixels.

[0342] 92. The method of clause 63, wherein the set of data points associated with each pattern in the set of patterns comprises a set of pattern vectors, wherein each pattern vector corresponds to a pixel of a plurality of pixels of the respective pattern.

[0343] 93. The method of clause 63, wherein each pattern in the set of patterns is represented as a plurality of components in the representation domain, wherein each component corresponds to a pixel of the pattern.

[0344] 94. A method for representing a pattern in a representation domain, the method comprising:

[0345] obtaining a set of patterns, each pattern comprising one or more features; and

[0346] Each pattern in the set of patterns is converted into a set of data points in a representation domain, each data point indicating information associated with a feature within a portion of a given pattern in the set of patterns.

[0347] 95. The method of clause 94, wherein representing each pattern as the set of data points in the representation domain comprises:

[0348] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0349] 96. A method according to clause 95, wherein, when converted, the set of data points is a set of coefficients associated with the set of basis functions.

[0350] 97. A method according to clause 96, wherein the set of coefficients associated with the set of basis functions corresponds to a set of addresses in the representation domain of pixels of the given pattern.

[0351] 98. The method of clause 95, wherein the set of basis functions is a set of orthogonal functions.

[0352] 99. The method of any one of aspects 95 to 98, wherein the converting comprises:

[0353] The given pattern in the set of patterns is projected into a linear representation domain.

[0354] 100. The method of clause 99, wherein the projecting comprises determining a linear combination of the set of orthogonal functions that represents the given pattern in the set of patterns.

[0355] 101. A method according to any one of clauses 95 to 100, wherein the set of basis functions comprises at least one of:

[0356] Hermite Gaussian module;

[0357] Zernike polynomials; or

[0358] Bessel function.

[0359] 102. A method according to any one of clauses 94 to 101, wherein the representation domain is a Hilbert space domain.

[0360] 103. A method for selecting representative patterns for training a machine learning model, the method comprising:

[0361] Get a pattern collection;

[0362] representing each pattern in the set of patterns as a set of data points in a representation domain; and

[0363] Based on the set of data points, a subset of patterns is selected from the set of patterns as a guide for interaction information between a given pattern and another pattern in the set of patterns.

[0364] 104. The method of clause 103, wherein each data point represents the information associated with a feature within a portion of the given pattern in the set of patterns.

[0365] 105. A method according to clause 104, wherein the information associated with the feature comprises pixel values ​​within the portion of the given pattern.

[0366] 106. A method according to any one of aspects 103 to 105, wherein the amount of mutual information, , between the given pattern and the other pattern indicates how much information in the given pattern is shared with the other pattern, and a higher amount of mutual information, , indicates a higher amount of shared information, , between the given pattern and the other pattern.

[0367] 107. The method of any one of clauses 103 to 106, wherein representing each pattern as the set of data points in the representation domain comprises:

[0368] The given pattern is transformed by a set of basis functions, the set of basis functions characterizing the representation domain.

[0369] 108. The method of clause 107, wherein, when converted, the set of data points is a set of coefficients associated with the set of basis functions.

[0370] 109. A method according to clause 108, wherein the set of coefficients associated with the set of basis functions corresponds to a set of addresses in the representation domain of pixels of the given pattern.

[0371] 110. The method of any one of clauses 107 to 109, wherein the set of basis functions is a set of orthogonal functions.

[0372] 111. The method of any one of aspects 107 to 110, wherein the converting comprises:

[0373] The given pattern in the set of patterns is projected into a linear representation domain.

[0374] 112. The method of clause 111, wherein the projecting comprises determining a linear combination of the set of orthogonal functions that represents the given pattern in the set of patterns.

[0375] 113. A method according to any one of clauses 107 to 112, wherein the set of basis functions comprises at least one of:

[0376] Hermite Gaussian module;

[0377] Zernike polynomials; or

[0378] Bessel function.

[0379] 114. A method according to any one of clauses 103 to 113, wherein the representation domain is a Hilbert space domain.

[0380] 115. The method of any one of clauses 103 to 114, wherein selecting the subset of patterns comprises selecting a plurality of patterns from the set of patterns based on a total entropy of the selected patterns.

[0381] 116. The method of clause 115, wherein selecting comprises:

[0382] The total entropy is determined as a combination of information entropies associated with each group of data points corresponding to each pattern in the set of patterns.

[0383] 117. The method of clause 116, wherein selecting the subset of patterns from the set of patterns comprises:

[0384] selecting a plurality of groups from the group representing the set of patterns, each selected group having a value of a distance indicator that exceeds a distance threshold, the distance indicator indicating a distance between the selected group and another group from the group representing the set of patterns; and

[0385] For the selected group, determining whether the information entropy in the representation domain is maximized;

[0386] In response to the information entropy not being maximized, adding another group to the plurality of groups or removing a group from the plurality of groups, and repeating steps until the information entropy is maximized; and

[0387] A plurality of patterns corresponding to the selected plurality of groups are selected.

[0388] 118. The method of clause 117, wherein the distance indicator comprises:

[0389] the Kullback-Leibler divergence calculated using data points within the group in the representation domain; or

[0390] The nearest neighbor k-means are calculated using the data points within the group in the representation domain.

[0391] 119. The medium of any one of aspects 103 to 118, wherein the set of patterns comprises patterns obtained from:

[0392] the design layout that is expected to be printed on the substrate;

[0393] a simulated image associated with the patterning process; or

[0394] An image associated with a patterned substrate.

[0395] 120. The method of any one of aspects 103 to 119, wherein the simulated image comprises at least one of an aerial image, a mask image, a resist image, or an etch image.

[0396] 121. The method of clause 120, wherein the image of the patterned substrate comprises a scanning electron microscope (SEM) image of the patterned substrate.

[0397] 122. The method according to any one of aspects 103 to 121, further comprising:

[0398] A machine learning model configured to determine characteristics of the patterning process is trained based on the subset of patterns.

[0399] 123. A method according to aspect 122, wherein the machine learning model is configured to determine characteristics of an illumination source of a lithographic device, a mask pattern of a mask, a projection system of the lithographic device, or a resist used to print a pattern on a substrate.

[0400] 124. A method according to any one of aspects 103 to 123, wherein representing each pattern as the data point in the representation domain does not include using a machine learning model.

[0401] 125. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for selecting a pattern for training or calibrating a model related to semiconductor manufacturing, the method comprising:

[0402] Obtaining a first pattern set;

[0403] representing each pattern in the first set of patterns in a representation domain, the representation domain corresponding to an electromagnetic function; and

[0404] A second set of patterns is selected from the first set of patterns based on the representation domain.

[0405] 126. The computer-readable medium of clause 125, wherein the electromagnetic function is a set of transmission cross coefficient (TCC) functions associated with an illumination source of a lithographic apparatus used to print the first set of patterns onto the substrate.

[0406] 127. The computer-readable medium of clause 126, wherein representing each pattern comprises:

[0407] Pixels of a pattern in the first set of patterns are represented as pattern vectors, wherein each element in the pattern vector corresponds to a projection of a pixel at a TCC of the set of TCC functions.

[0408] 128. The computer-readable medium of clause 127, wherein the pattern vectors indicate EMF excitations of corresponding pixels.

[0409] 129. The computer-readable medium of clause 127, wherein the pattern vector indicates an effect of proximity of the respective pixels on EMF excitation of the respective pixels.

[0410] 130. The computer-readable medium of clause 125, wherein each pattern in the first set of patterns is represented as a set of pattern vectors, wherein each pattern vector corresponds to a pixel of a plurality of pixels of the respective pattern.

[0411] 131. The computer-readable medium of clause 125, wherein each pattern in the first set of patterns is represented as a plurality of components in the representation domain, wherein each component corresponds to a pixel of the pattern.

[0412] 132. The computer-readable medium of clause 125, wherein selecting the second set of patterns comprises selecting a plurality of patterns from the first set of patterns based on a total entropy of the second set of patterns.

[0413] 133. The computer-readable medium of clause 132, wherein selecting the second set of patterns comprises:

[0414] The total entropy is determined as a combination of information entropies associated with each group of pattern vectors corresponding to each pattern in the first set of patterns.

[0415] 134. The computer-readable medium of clause 133, wherein selecting the second set of patterns from the first set of patterns comprises:

[0416] selecting a plurality of groups from the group representing a set of patterns, each selected group having a value of the distance indicator that satisfies a distance threshold;

[0417] For the plurality of groups, determining whether the information entropy of the representation domain meets a specified standard;

[0418] In response to the information entropy not meeting the specified criteria, adding another group to the plurality of groups or removing a group from the plurality of groups, and repeating steps; and

[0419] A plurality of patterns corresponding to the plurality of groups are selected.

[0420] 135. The computer-readable medium of clause 134, wherein the distance indicator comprises:

[0421] the Kullback-Leibler divergence computed using pattern vectors within a group in the representation domain; or

[0422] The nearest neighbor k-means are calculated using the pattern vectors within the group in the representation domain.

[0423] 136. The computer-readable medium of clause 125, the method further comprising:

[0424] A machine learning model configured to determine characteristics of a patterning process is trained based on the second set of patterns.

[0425] 137. A computer-readable medium according to aspect 136, wherein the machine learning model is configured to determine characteristics of at least one of an illumination source of a lithographic device, a mask pattern of a mask, a projection system of the lithographic device, or a resist used to print the pattern on a substrate.

[0426] 138. The computer-readable medium of clause 125, wherein representing each pattern in the representation domain comprises:

[0427] The given pattern in the first set of patterns is transformed by a set of basis functions that characterize the representation domain.

[0428] 139. The computer-readable medium of clause 138, wherein, upon conversion, each pixel of the given pattern corresponds to a set of coefficients associated with the set of basis functions.

[0429] 140. The computer-readable medium of clause 139, wherein the set of coefficients associated with the set of basis functions corresponds to a set of TCCs.

[0430] 141. A computer-readable medium according to 138, wherein the set of basis functions is a set of orthogonal functions.

[0431] 142. The computer-readable medium of clause 138, wherein converting the given pattern comprises:

[0432] The given pattern is projected into a linear representation domain.

[0433] 143. The computer-readable medium of clause 138, wherein the set of basis functions comprises a set of TCC functions.

[0434] 144. The computer-readable medium of clause 125, wherein the representation domain is a Hilbert space domain.

[0435] 145. A method of selecting a pattern for training or calibrating a model related to semiconductor manufacturing, the method comprising:

[0436] Obtaining a first pattern set;

[0437] representing each pattern in the first set of patterns in a representation domain, the representation domain corresponding to an electromagnetic function; and

[0438] A second set of patterns is selected from the first set of patterns based on the representation domain.

[0439] 146. A method according to clause 145, wherein the electromagnetic function is a set of transmission cross coefficient (TCC) functions associated with an illumination source of a lithographic apparatus used to print the first set of patterns onto the substrate.

[0440] 147. The method of clause 146, wherein representing each pattern comprises:

[0441] Pixels of a pattern in the first set of patterns are represented as pattern vectors, wherein each element in the pattern vector corresponds to a projection of a pixel at a TCC of the set of TCC functions.

[0442] 148. A method according to clause 147, wherein the pattern vector indicates the EMF excitation of the corresponding pixel.

[0443] 149. A method according to aspect 147, wherein the pattern vector indicates the effect of the proximity of the corresponding pixels on the EMF excitation of the corresponding pixels.

[0444] 150. The method of clause 145, wherein each pattern in the first set of patterns is represented as a set of pattern vectors, wherein each pattern vector corresponds to a pixel of a plurality of pixels of the respective pattern.

[0445] 151. A method according to clause 145, wherein each pattern in the first set of patterns is represented as a plurality of components in the representation domain, wherein each component corresponds to a pixel of the pattern.

[0446] 152. The method of clause 145, wherein selecting the second set of patterns comprises selecting a plurality of patterns from the first set of patterns based on a total entropy of the second set of patterns.

[0447] 153. A method according to clause 152, wherein selecting the second set of patterns comprises:

[0448] The total entropy is determined as a combination of information entropies associated with each group of pattern vectors corresponding to each pattern in the first set of patterns.

[0449] 154. A method according to clause 153, wherein selecting the second set of patterns from the first set of patterns comprises:

[0450] selecting a plurality of groups from the group representing a set of patterns, each selected group having a value of the distance indicator that satisfies a distance threshold;

[0451] For the plurality of groups, determining whether the information entropy of the representation domain meets a specified standard;

[0452] In response to the information entropy not meeting the specified criteria, adding another group to the plurality of groups or removing a group from the plurality of groups, and repeating steps; and

[0453] A plurality of patterns corresponding to the plurality of groups are selected.

[0454] 155. The method of aspect 154, wherein the distance indicator comprises:

[0455] the Kullback-Leibler divergence computed using pattern vectors within a group in the representation domain; or

[0456] The nearest neighbor k-means are calculated using the pattern vectors within the group in the representation domain.

[0457] 156. The method of aspect 145, further comprising:

[0458] A machine learning model configured to determine characteristics of a patterning process is trained based on the second set of patterns.

[0459] 157. A method according to aspect 156, wherein the machine learning model is configured to determine characteristics of at least one of an illumination source of a lithographic device, a mask pattern of a mask, a projection system of the lithographic device, or a resist used to print the pattern on a substrate.

[0460] 158. A method according to clause 145, wherein representing each pattern in the representation field comprises:

[0461] The given pattern in the first set of patterns is transformed by a set of basis functions that characterize the representation domain.

[0462] 159. A method according to clause 158, wherein, upon conversion, each pixel of the given pattern corresponds to a set of coefficients associated with the set of basis functions.

[0463] 160. A method according to clause 159, wherein the set of coefficients associated with the set of basis functions corresponds to a set of TCCs.

[0464] 161. A method according to 158, wherein the set of basis functions is a set of orthogonal functions.

[0465] 162. The method of clause 158, wherein converting the given pattern comprises:

[0466] The given pattern is projected into a linear representation domain.

[0467] 163. A method according to clause 158, wherein the set of basis functions comprises a set of TCC functions.

[0468] 164. The method of clause 145, wherein the representation domain is a Hilbert space domain.

[0469] While the concepts disclosed herein can be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of lithographic imaging system, for example, a lithographic imaging system for imaging on substrates other than silicon wafers. The description herein is intended to be illustrative and not restrictive. Accordingly, those skilled in the art will appreciate that modifications may be made as described without departing from the scope of the claims set forth below.

Claims

1. A pattern selection method for simulating a patterning process in semiconductor manufacturing, comprising: Get a pattern collection; representing each pattern in the set of patterns as a set of data points in a representation domain, wherein each data point represents information associated with a feature within a portion of a given pattern in the set of patterns; and Based on the set of data points, a subset of patterns is selected from the set of patterns as a guide for interaction information between a given pattern and another pattern in the set of patterns.

2. The pattern selection method according to claim 1, wherein: The information associated with the feature includes pixel values ​​within the portion of the given pattern.

3. The pattern selection method according to claim 1, wherein: The amount of mutual information between the given pattern and the other pattern indicates an amount of information in the given pattern that is common to the other pattern.

4. The pattern selection method according to claim 1, wherein: Representing each pattern as the set of data points in the representation domain comprises: The given pattern is transformed using a set of basis functions, the set of basis functions characterizing the representation domain.

5. The pattern selection method according to claim 4, wherein: When transformed, the set of data points corresponds to the set of coefficients associated with the set of basis functions.

6. The pattern selection method according to claim 5, wherein: The set of coefficients associated with the set of basis functions corresponds to the set of addresses of pixels of the given pattern in the representation domain.

7. The pattern selection method according to claim 4, wherein: The conversion involves: The given pattern in the set of patterns is projected in a linear representation domain, wherein the projecting comprises determining a linear combination of a set of orthogonal functions representing the given pattern in the set of patterns.

8. The pattern selection method according to claim 4, wherein: The set of basis functions includes at least one of the following: Hermite Gaussian module; Zernike polynomials; or Bessel function.

9. The pattern selection method according to claim 1, wherein: The representation domain is the Hilbert space domain.

10. The pattern selection method according to claim 1, wherein: Selecting the subset of patterns includes selecting a plurality of patterns from the set of patterns based on a total entropy of the selected patterns; and determining the total entropy as a combination of information entropies associated with each group of data points corresponding to each pattern in the set of patterns.

11. The pattern selection method according to claim 10, wherein: Selecting the subset of patterns from the set of patterns comprises: selecting a plurality of groups from the set of data points representing the set of patterns, each selected group having a value for a distance indicator that exceeds a distance threshold, the distance indicator indicating a distance between the selected group and another of the groups representing the set of patterns; and For the selected group, determining whether the information entropy in the representation domain is maximized; In response to the information entropy not being maximized, adding another group to the selected plurality of groups or removing a group from the selected plurality of groups, and repeating these steps until the information entropy is maximized; and A plurality of patterns corresponding to the selected plurality of groups are selected.

12. The pattern selection method according to claim 1, further comprising: training a machine learning model configured to determine characteristics of a patterning process based on the subset of patterns; calibrating a non-machine learning model using the subset of patterns; or Metrology or inspection measurements are performed on the subset of patterns.

13. The pattern selection method according to claim 1, wherein: The representation domain corresponds to electromagnetic functions.

14. The pattern selection method according to claim 13, wherein: The electromagnetic functions are a set of transmission cross coefficient (TCC) functions associated with an illumination source of a lithographic apparatus used to print a first set of patterns onto a substrate. 15 . A non-transitory computer-readable medium having instructions, which, when executed by a computer, cause the computer to perform the pattern selection method according to claim 1 .

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