Method and system for pattern coverage determination and pattern selection using diffusion model

Abstract

Described herein is a method and system for pattern coverage determination and pattern selection based on a variance of mask pattern representations generated using a diffusion model. Multiple mask pattern representations are generated for a target pattern representation by inputting multiple noise images to the diffusion model. A variance of the mask pattern representations is computed and represented using a variance map. The variance map may be used for various applications such as determining a pattern coverage of the diffusion model, or for pattern selection process to select a target pattern representation for further training the diffusion model to improve the pattern coverage.

Description

METHOD AND SYSTEM FOR PATTERN COVERAGE DETERMINATION AND PATTERN SELECTION USING DIFFUSION MODELCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 690,520 which was filed on September 4, 2024 and which is incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] The embodiments provided herein relate to semiconductor manufacturing, and more particularly to mask pattern design through computational lithography.BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. The lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, an IC chip in a smart phone, can be as small as a person’s thumbnail, and may include over 2 billion transistors. Making an IC is a complex and time-consuming process, with circuit components in different layers and including hundreds of individual steps. Errors in even one step have the potential to result in problems with the final IC and can cause device failure. High process yield and high wafer throughput can be impacted by the presence of defects.BRIEF SUMMARY

[0004] In some embodiments, the techniques described herein relate to a method of determining a pattern coverage of a mask prediction model. The method includes: inputting multiple noise images to a mask prediction model; generating a mask image representative of a mask pattern for each of the noise images by executing the mask prediction model with a target image having a target pattern, wherein the target pattern is input as guidance data to the mask prediction model, and wherein the mask prediction model is implemented using a diffusion model, and wherein the mask prediction model is trained by using a set of target patterns; determining a variance of the mask patterns; and determining a pattern coverage of the mask prediction model based on the variance.

[0005] In some embodiments, the techniques described herein relate to a method of pattern selection for training a mask prediction model. The method includes: inputting multiple noise images to a mask prediction model; generating a mask image representative of a mask pattern for each of the noise images by executing the mask prediction model with a target image having a target pattern, wherein the target pattern is input as guidance data to the mask prediction model, and wherein the mask prediction model is implemented using a diffusion model, and wherein the mask prediction model is trained by using a set of target patterns; determining a variance of the mask patterns; and determining a portion of the target pattern to be selected for training of the mask prediction model based on thevariance.

[0006] In some embodiments, there is provided a non-transitory computer readable medium having instructions that, when executed by a computer, cause the computer to execute a method of any of the above embodiments.

[0007] In some embodiments, there is provided an apparatus that includes a memory storing a set of instructions and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above embodiments.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Embodiments will now be described, by way of example only, with reference to the accompanying drawings in which:

[0009] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus, according to an embodiment.

[0010] Figure 2 is a schematic diagram of a lithographic projection apparatus, according to an embodiment.

[0011] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment.

[0012] Figure 4 is a block diagram for generating a mask pattern representation using a diffusion model, consistent with various embodiments.

[0013] Figure 5A shows a variance map generated for a set of mask pattern representations, consistent with various embodiments.

[0014] Figure 5B illustrates different predictions of a mask pattern representation in a high variance area for a given target pattern representation, consistent with various embodiments.

[0015] Figure 6 illustrates different predictions of a mask pattern representation in a high variance area for a given target pattern representation, consistent with various embodiments.

[0016] Figure 7 illustrates pattern selection using a variance map, consistent with various embodiments.

[0017] Figure 8 is a block diagram for training a mask prediction model to generate a mask pattern representation, consistent with various embodiments.

[0018] Figure 9 is a flow diagram of a method for pattern coverage determination or pattern selection using a diffusion model, consistent with various embodiments.

[0019] Figure 10 is a block diagram that illustrates a computer system which can assist in implementing various methods and systems disclosed herein.

[0020] Embodiments will now be described in detail with reference to the drawings, which are provided as illustrative examples so as to enable those skilled in the art to practice the embodiments. Notably, the figures and examples below are not meant to limit the scope to a single embodiment, but other embodiments are possible by way of interchange of some or all of the described or illustratedelements. Wherever convenient, the same reference numbers will be used throughout the drawings to refer to same or like parts. Where certain elements of these embodiments can be partially or fully implemented using known components, only those portions of such known components that are necessary for an understanding of the embodiments will be described, and detailed descriptions of other portions of such known components will be omitted so as not to obscure the description of the embodiments. In the present specification, an embodiment showing a singular component should not be considered limiting; rather, the scope is intended to encompass other embodiments including a plurality of the same component, and vice-versa, unless explicitly stated otherwise herein. Moreover, applicants do not intend for any term in the specification or claims to be ascribed an uncommon or special meaning unless explicitly set forth as such. Further, the scope encompasses present and future known equivalents to the components referred to herein by way of illustration.DETAILED DESCRIPTION

[0021] A lithographic apparatus is a machine that applies a designed pattern onto a target portion of a substrate. This process of transferring the designed pattern to the substrate is called a patterning process. The patterning process can include a patterning step to transfer a pattern from a patterning device (such as a mask) to the substrate. Various methods are used to design a mask pattern. For example, a machine learning (ML) model is used to generate a mask pattern for a given target pattern. In some embodiments, an accuracy of the ML model in predicting mask patterns may depend on the coverage of the training data with reference to all possible target patterns used in the inference stage (“pattern coverage”), e.g., a diversity of patterns. Typically, the higher the pattern coverage, the more likely the predicted mask pattern for any given target pattern is accurate. In some embodiments, the pattern coverage of the ML model may be improved by a pattern selection process. In some embodiments, pattern selection is a process of selecting diverse patterns from a number of patterns, e.g., as training data to calibrate or train models (e.g., physical model, ML model, empirical model, rule-based model, etc.) to predict corresponding results that further facilitates a patterning process. Selecting an appropriate set of patterns is one of the important factors in improving the pattern coverage of a model. Conventional pattern coverage metrics do not correlate well with, or are not descriptive of, the ML model performance. Further, conventional pattern selection methods such as image-based pattern selection method or uncertainty-based pattern selection method, which selects patterns based on prediction variance (“uncertainty”) from multiple models, have drawbacks or limitations. For example, the uncertainty-based pattern selection method is a complex method because it requires results from multiple models to perform the pattern selection. The implementation of such models may require significant time and computing resources as generation of training data and the training process have to be performed for multiple models. Further, the method depends on the model accuracy of each of the models, which makes the pattern selection more vulnerable. These and other drawbacks exist.

[0022] Disclosed are embodiments for determining a pattern coverage of a model (e.g., an ML model) and a pattern selection process using a single model, such as a diffusion model. For example, a mask prediction model implemented using a diffusion model may be used to generate a mask pattern representation for a given target pattern representation by providing a noise input (e.g., a random noise image) and the target pattern representation (e.g., as guidance data) to the mask prediction model. Several such noise images may be input to the mask prediction model for the given target pattern representation to obtain multiple mask pattern representations for the same target pattern representation. A variance of the mask pattern representations is determined. For example, a variance map, which is an image having pixel values that is indicative of a variance of the mask pattern representations, may be generated. In another example, the variance may be determined based on a range of pixel values of a corresponding pixel from the multiple mask pattern representations. The variance among model predictions may be used for several applications. In some embodiments, the variance map may be used to evaluate pattern coverage of the mask prediction model. The pattern coverage may be quantified using a metric. For example, the pattern coverage may be determined based on at least one of a minimum variance, a maximum variance, or an average variance in the variance map. In another example, the pattern coverage may be determined as a percentage of an area in the variance map that is indicative of the variance below a specified threshold. In some embodiments, the variance map may be used to identify a location in a mask pattern representation where the prediction is not reliable. For example, a first location in the variance map in which the variance is above a specified threshold is determined and a corresponding location in the predicted mask pattern representation is identified as a location where the prediction by the mask prediction model is not accurate, or varies across various mask pattern representations. In some embodiments, the variance map may be used for pattern selection, e.g., for selecting target pattern representations that are either not used in, or different from the target pattern representations used in, training of the mask prediction model. For example, a first portion of the variance map in which the variance is above a specified threshold (e.g., which implies that the prediction of mask pattern representation for the corresponding portion of the input target pattern representation is inaccurate or not consistent) is determined, and the corresponding portion of the input target pattern representation may be identified as the portion of the target pattern representation that is either not used in, or different from the target patterns used in, training of the mask prediction model. Such portions of the target pattern representation (e.g., and their corresponding ground truth mask pattern representations) may be selected as training data for further training of the mask prediction model, e.g., to improve the pattern coverage, and therefore, the prediction accuracy for a diverse set of target pattern representations. In some embodiments, instead of selecting portions of the target pattern representation for training the mask prediction model, the entire target pattern representation and its corresponding ground truth mask pattern representation may be used to further train the mask prediction model.

[0023] By using the variance generated from the prediction results of a single model, such as the diffusion model, the complexity and consumption of time and computing resources in the pattern coverage determination and pattern selection process is reduced compared to the conventional methods as the need for using results from multiple models is eliminated. Further, by using the diffusion model in prediction of mask pattern representations, any inconsistency that may exist in the training data may be overcome. Advantageously, the diffusion model may be robust to certain types of optical proximity correction (OPC) pattern inconsistencies as would be produced in other types of machine learning models, such as label noise or noisy features, as it is trained to reconstruct clean data from noise inputs. In another example, the noise addition process may act as data augmentation, helping the diffusion model generalize better and handle inconsistencies. In another example, the adding of noise and denoising process may help in regularization, preventing the diffusion model from overfitting to noisy or inconsistent data, thereby making the prediction of mask patterns more accurate. Typically, the diffusion model generates a mask pattern representation by gradually denoising a noise input (e.g., random noise image) over several steps guided by an input target pattern representation to predict a mask pattern representation that corresponds to the target pattern representation. The training process of the diffusion model includes (i) a noise addition process in which the prediction model starts with an image of a ground truth mask pattern (e.g., an image) and gradually adds noise (e.g., Gaussian) to the mask pattern representation over several steps, creating a sequence of increasingly noisy versions of the ground truth mask pattern representation to result in a random noise image, and (ii) a denoising process in which the prediction model is trained to reverse the noise-adding process by starting from the random noise image and gradually removing the noise, step by step, until it reconstructs the ground truth mask pattern representation.

[0024] In the present disclosure, although specific reference may be made to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle”, “wafer” or “die” in this text should be considered as interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0025] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range of about 5-100 nm). In the present document, the term “radiation source” or “source” is used to encompass all types of sources of radiation, including laser sources, incandescent sources, etc. which may include treatment of the radiation between the radiation source and the target or other parts of the optics, including filtering, collimating, focusing, etc.

[0026] A patterning device can comprise, or can form, one or more design layouts. The designlayout can be generated utilizing CAD (computer-aided design) programs. This process is often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts / patteming devices. These rules are set based processing and design limitations. For example, design rules define the space tolerance between devices (such as gates, capacitors, etc.) or interconnect lines, to ensure that the devices or lines do not interact with one another in an undesirable way. One or more of the design rule limitations may be referred to as a “critical dimension” (CD). A critical dimension of a device can be defined as the smallest width of a line or hole, or the smallest space between two lines or two holes. Thus, the CD regulates the overall size and density of the designed device. One of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0027] The term “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation. Using an appropriate filter, the said undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. Examples of other such patterning devices also include a programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0028] The term “projection optics” as used herein should be broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping, or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting and / or projecting radiation from the source before the radiation passes the patterning device, and / or optical components for shaping, adjusting and / or projecting the radiation after the radiation passes the patterning device. The projection optics generally exclude the source and the patterning device.

[0029] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus 10A, according to an embodiment. Major components are a radiation source 12A, which may be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (the lithographic projection apparatus itself need not have the radiation source), illumination optics which, e.g., define the partial coherence (denoted as sigma) and which may include optics 14A, 16Aa and 16Ab that shape radiation from the source 12A; a patterning device (or mask) 18A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A.

[0030] A pupil 20A can be included with transmission optics 16Ac. In some embodiments, there can be one or more pupils before and / or after mask 18A. As described in further detail herein, pupil 20A can provide patterning of the light that ultimately reaches substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics may restrict the range of beam angles that impinge on the substrate plane 22A, where the largest possible angle defines the numerical aperture of the projection optics NA= n sin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics, and ©max is the largest angle of the beam exiting from the projection optics that can still impinge on the substrate plane 22A.

[0031] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device and projection optics direct and shape the illumination, via the patterning device, onto a substrate. This is not to disclaim that the source does not itself provide patterning, directing, or shaping to the radiation or that patterning, directing, or shaping does not occur between the source and the projection optics. The projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB) and development). Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image and can be defined in an optical model. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics. Details of techniques and models used to transform a design layout into various lithographic images (e.g., an aerial image, a resist image, etc.), apply optical proximity correction (OPC) using those techniques and models and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosure of each which is hereby incorporated by reference in its entirety.

[0032] One aspect of understanding a lithographic process is understanding the interaction of the radiation and the patterning device. The electromagnetic field of the radiation after the radiation passes the patterning device may be determined from the electromagnetic field of the radiation before the radiation reaches the patterning device and a function that characterizes the interaction. This function may be referred to as the mask transmission function (which can be used to describe the interaction by a transmissive patterning device and / or a reflective patterning device).

[0033] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in the binary form may be referred to as a binary mask. Another form is continuous. Namely, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the location on the patterning device. A mask transmission function in the continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, the CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of binary value of either 0 or 1. In an embodiment, CTM may be a pixelated gray scale image, where each pixel has values (e.g., within a range [-255, 255], normalized values within a range [0, 1] or [-1, 1] or other appropriate ranges).

[0034] The thin-mask approximation, also called the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction of the radiation and the patterning device. The thin-mask approximation assumes that the thickness of the structures on the patterning device is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin-mask approximation assumes the electromagnetic field after the patterning device is the multiplication of the incident electromagnetic field with the mask transmission function. However, as lithographic processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device become smaller and smaller, the assumption of the thin-mask approximation can break down. For example, interaction of the radiation with the structures (e.g., edges between the top surface and a sidewall) because of their finite thicknesses (“mask 3D effect” or “M3D”) may become significant. Encompassing this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of the radiation with the patterning device. A mask transmission function under the thin-mask approximation may be referred to as a thin-mask transmission function. A mask transmission function encompassing M3D may be referred to as a M3D mask transmission function.

[0035] Figure 2 schematically depicts an exemplary lithographic projection apparatus whose illumination source could be optimized utilizing the methods described herein. The apparatus comprises:- an illumination system IL, to condition a beam B of radiation. In this particular case, theillumination system also comprises a radiation source SO;- a first object table (e.g., mask table, patterning device table or reticle stage) MT provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS;- a second object table (substrate table or wafer stage) WT provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS;- a projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) to image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0036] As depicted herein, the apparatus is of a transmissive type (i.e., has a transmissive mask). However, in general, it may also be of a reflective type, for example (with a reflective mask). Alternatively, the apparatus may employ another kind of patterning device as an alternative to the use of a classic mask; examples include a programmable mirror array or LCD matrix.

[0037] The source SO (e.g., a mercury lamp or excimer laser) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AD for setting the outer or inner radial extent (commonly referred to as <j-outcr and n-inner, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0038] It should be noted with regard to Figure 2 that the source SO may be within the housing of the lithographic projection apparatus (as is often the case when the source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam that it produces being led into the apparatus (e.g., with the aid of suitable directing mirrors); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[0039] The beam B subsequently intercepts the patterning device MA, which is held on a patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PS, which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the beam B. Similarly, the first positioning means can be used to accurately position the patterning device MA with respect to the path of the beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT will be realizedwith the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in Figure 2. However, in the case of a wafer stepper (as opposed to a step-and-scan tool) the patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[0040] The depicted tool can be used in two different modes:- In step mode, the patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x or y directions so that a different target portion C can be irradiated by the beam B;- In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single “flash”. Instead, the patterning device table MT is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that the projection beam B is caused to scan over a patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, in which M is the magnification of the lens PS (typically, M = 1 / 4 or 1 / 5). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0041] Figure 3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment. As will be appreciated, the models may represent a different patterning process and need not comprise all the models described below. A source model 300 represents optical characteristics (including radiation intensity distribution, bandwidth and / or phase distribution) of the illumination of a patterning device. The source model 300 can represent the optical characteristics of the illumination that include, but not limited to, numerical aperture settings, illumination sigma (o) settings as well as any particular illumination shape (e.g., off-axis radiation shape such as annular, quadrupole, dipole, etc.), where o (or sigma) is outer radial extent of the illuminator.

[0042] A projection optics model 310 represents optical characteristics (including changes to the radiation intensity distribution and / or the phase distribution caused by the projection optics) of the projection optics. The projection optics model 310 can represent the optical characteristics of the projection optics, including aberration, distortion, one or more refractive indexes, one or more physical sizes, one or more physical dimensions, etc.

[0043] The patterning device / design layout model module 320 captures how the design features are laid out in the pattern of the patterning device and may include a representation of detailed physical properties of the patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In an embodiment, the patterning device / design layout model module 320 represents optical characteristics (including changes to the radiation intensity distribution and / or the phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to a feature of an integrated circuit, a memory, an electronicdevice, etc.), which is the representation of an arrangement of features on or formed by the patterning device. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the illumination and the projection optics. The objective of the simulation is often to accurately predict, for example, edge placements and CDs, which can then be compared against the device design. The device design is generally defined as the pre-OPC patterning device layout, and will be provided in a standardized digital file format such as GDSII or OASIS.

[0044] An aerial image 330 can be simulated from the source model 300, the projection optics model 310 and the patterning device / design layout model module 320. An aerial image (Al) is the radiation intensity distribution at substrate level. Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image.

[0045] A resist layer on a substrate is exposed by the aerial image and the aerial image is transferred to the resist layer as a latent “resist image” (RI) therein. The resist image (RI) can be defined as a spatial distribution of solubility of the resist in the resist layer. A resist image 350 can be simulated from the aerial image 330 using a resist model 340. The resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model 340 typically describes the effects of chemical processes which occur during resist exposure, post exposure bake (PEB) and development, in order to predict, for example, contours of resist features formed on the substrate and so it typically related only to such properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake and development). In an embodiment, the optical properties of the resist layer, e.g., refractive index, film thickness, propagation, and polarization effects — may be captured as part of the projection optics model 310.

[0046] So, in general, the connection between the optical and the resist model is a simulated aerial image intensity within the resist layer, which arises from the projection of radiation onto the substrate, refraction at the resist interface and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) is turned into a latent “resist image” by absorption of incident energy, which is further modified by diffusion processes and various loading effects. Efficient simulation methods that are fast enough for full -chip applications approximate the realistic 3- dimensional intensity distribution in the resist stack by a 3-dimensional aerial (and resist) image.

[0047] In an embodiment, the resist image 350 can be used as an input to a post-pattern transfer process model module 360. The post-pattern transfer process model module 360 defines performance of one or more post-resist development processes (e.g., etch, development, etc.).

[0048] Simulation of the patterning process can, for example, predict contours, CDs, edge placement (e.g., edge placement error), etc. in the resist and / or etched image. Thus, the objective of thesimulation is to accurately predict, for example, edge placement, and / or aerial image intensity slope, and / or CD, etc. of the printed pattern. These values can be compared against an intended design to, e.g., correct the patterning process, identify where a defect is predicted to occur, etc. The intended design is generally defined as a pre-OPC design layout which can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0049] Thus, the model formulation describes most, if not all, of the known physics and chemistry of the overall process, and each of the model parameters desirably corresponds to a distinct physical or chemical effect. The model formulation thus sets an upper bound on how well the model can be used to simulate the overall manufacturing process.

[0050] The following paragraphs describe a system and a method for pattern coverage determination and pattern selection using a machine learning (ML) model, such as a diffusion model. Note that while the embodiments in the following paragraphs describe the pattern representations as being images of the pattern, the embodiments are applicable to other pattern representations as well. For example, a target pattern representation may include one or more target polygons, target image such as a pixelated image rendered from target polygons, an image from a GDS fde, etc. Similarly, the mask pattern representation may include one or more of a mask image (e.g., an image rendered from a mask pattern that is to be printed on a mask), a mask contour, mask polygons (polygonised mask contours), CTM, CTM+, etc. The mask pattern representation may correspond to mask features, subresolution assist features (SRAF), curvilinear patterns, Manhattan patterns, etc.

[0051] Figure 4 is a block diagram for generating a mask pattern representation using a diffusion model, consistent with various embodiments. A mask prediction model 450 generates a representation of a mask pattern (e.g., a mask image 408) for a given target pattern representation (e.g., target image 404) from a noise input 402 (e.g., image with random noise). The mask prediction model 450 is configured using a diffusion model which may be constructed using any suitable type of neural networks (e.g., convolutional neural network (CNN), deep learning CNN (DCNN), U-NET, etc.). The diffusion model consists of three major components: the forward process, the reverse process, and the sampling procedure. The diffusion model may be trained by first corrupting or destroying original data (e.g., ground truth data) with noise in a controlled manner and then learning to reverse this process to generate or predict new, realistic data. In some embodiments, the mask prediction model 450 implemented using a trained diffusion model can generate a mask image 408 by gradually denoising a noise input 402 over several steps to predict the mask image 408. In some embodiments, the mask prediction model 450 is implemented as a guided diffusion model, where the mask prediction model 450 is conditioned on an additional data (“guidance data”) to “guide” the mask prediction model 450 to generate predictions that align with desired characteristics or conditions specified by the guidance data. For example, the mask prediction model 450 may be conditioned using a target image 404, which guides the mask prediction model 450 to generate the mask image 408 corresponding to the target image 404.

[0052] The mask prediction model 450 predicts the mask image 408 by removing the noise (referred to as “denoising” process) from the noise input iteratively using the target image 404. This may involve estimating both the mean and variance of the noise distribution at each step. In the example of Figure 4, the mask prediction model 450 constructs the mask image 408 over several iterations or steps (e.g., “7”), by gradually removing the noise from the image of the previous step generating a sequence of images (e.g., images 406a, 406b, 406c, 4 06d, 406e, and 406f) until the mask image 408 is generated. For example, in a first step, the mask prediction model 450 constructs a first image 406a by removing the noise from the noise input 402 (e.g., random noise image), then in a second step, constructs a second image 406b by removing the noise from the first image 406a, and so on until it generates the mask image 408. In some embodiments, the number of steps in the denoising process may be predefined and the removal of noise may involve estimating both the mean and variance of the noise distribution at each step (which may be learnt during the training process). In some embodiments, mask contour 410 shows feature contours extracted from the mask image 408.

[0053] The target image 404 may be used as a guidance in every step of the denoising process to generate an image having a pattern corresponding to the target image 404. In some embodiments, the guidance data is another input to a diffusion model used to guide or steer the generative process towards a desired outcome. The denoising process is conditioned on the guidance data to direct the generation of the predicted output towards the targeted output. For example, when the target image is input as guidance data to the mask prediction model, the denoising of the noise image is conditioned on the target image to cause the mask prediction model 450 to generate a mask image corresponding to the target image. As described below at least with reference to Figure 8, by training the mask prediction model 450 with guidance target image, the denoising process of the mask prediction model 450 is conditioned on an input target image, and can generate a mask image for any given target image.

[0054] Such a method predicting a mask image using a diffusion model has several advantages. By using the diffusion model-based mask prediction model 450 in prediction of mask images, any inconsistency that may exist in the training data may be overcome. Advantageously, the diffusion model may be robust to certain types of OPC pattern inconsistencies as would be produced in other types of machine learning models, such as label noise or noisy features, as it is trained to reconstruct clean data from noise inputs. In another example, the noise addition process may act as data augmentation, helping the diffusion model generalize better and handle inconsistencies. In another example, the adding of noise and denoising process may help in regularization, preventing the diffusion model from overfitting to noisy or inconsistent data. In another example, the multi-step nature of the denoising process means that the diffusion model learns to progressively refine its predictions and each step provides an opportunity to correct errors introduced in previous steps, helping to mitigate the impact of inconsistent training data. As such, the reliability and accuracy ofthe mask prediction model 450 in predicting a mask image is significantly improved by implementing the mask prediction model 450 using a diffusion model.

[0055] While the above embodiment describes the noise input 402 to the mask prediction model 450 as a random noise image, the noise input 402 may take many forms. For example, the noise input 402 may be a transformation of the target pattern representation such as an aerial image, or noisy versions of the target pattern representation, aerial image, optical or forward simulation or any other simulation of the target pattern representation. In some embodiments, the noise input 402 may be noise with some constraint 412. For example, the constraint 412 may include a symmetry constraint, which indicates that the noise may have to be distributed symmetrically in the noise input 402 (e.g., noise image in which the noise is distributed symmetrically). In some embodiments, if the target image 404 is symmetrical (e.g., along a specified axis), then a symmetry constraint may be imposed on generating the noise input 402, which causes the noise to spread symmetrically across the specified axis in the noise image. Further, during the generation of the mask image 408, by adjusting a gradient associated with a loss function of the mask prediction model 450, the noise from the images is removed symmetrically (e.g., to satisfy the symmetry of the target image 404). Such a constraint helps in generating the mask image 408 that is symmetrical across the specified axis, like the target image 404, thereby improving the accuracy of the prediction. In some embodiments, the constraint 412 may be a “location-aware” constraint that causes the mask prediction model 450 to restrict the prediction, repair (e.g., remove defects), or modification of a mask pattern representation to a particular portion of the mask pattern representation.

[0056] Figure 5A shows a variance map generated for a set of mask pattern representations, consistent with various embodiments. In some embodiments, the variance map is an image indicative of the variance between a number of mask pattern representations. For example, a pixel value at a particular location in the variance map may be indicative of the variance between the different mask pattern representations at the corresponding location. A number of mask pattern representations (e.g., mask images) may be generated for a target pattern representation (e.g., a target image) using the mask prediction model 450. For example, as described at least with reference to Figure 4, multiple mask images, such as the mask image 408, may be generated for a given target image (e.g., target image 404) by inputting different noise images (e.g., the random noise image) and the given target image to the mask prediction model 450. The variance is computed by comparing the different mask images and a variance map, such as the variance map 502, may be generated based on the computed variance. In another example, the variance may also be determined based on a range of pixel values of a corresponding pixel from the multiple mask pattern representations. For example, if the size of a mask image is x*y pixels, then for each pixel (xf, a value of the pixel is obtained from each of the mask images generated for the target image to obtain a range of values (vminto vmax) for the pixel. If the range is outside of a specified range, the variance of the mask images is considered to be above a specified threshold.

[0057] The variance map 502 may be used for several applications. As an example of a first application, the variance map 502 may be used for determining a pattern coverage of the mask prediction model 450. In some embodiments, pattern coverage is indicative of the prediction accuracy of the mask prediction model 450 for any given target image. In some embodiments, the prediction accuracy of the model may depend on the coverage of the training data (“pattern coverage”), e.g., a variety of patterns, used to train the model. Typically, the higher the pattern coverage, the more accurate the predicted mask image for any given target image. The pattern coverage of the mask prediction model 450 may be determined using the variance map in various ways. For example, the pattern coverage may be determined based on percentage of “high-variance area,” which is an area or a portion of the variance map indicative of a variance above a specified threshold. In some embodiments, the higher the percentage of high-variance area, the lower the pattern coverage of the mask prediction model. In other words, the higher the percentage of an area indicative of a variance below the specified threshold, the greater the pattern coverage of the mask prediction model 450. In the example of Figure 5 A, the high-variance area is shown in locations such as a first location 504a, a second location 504b, a third location 504c, a fourth location 504d, and a fifth location 506. The pattern coverage may also be determined based on one or more metrics. For example, the pattern coverage may be determined based on at least one of a minimum variance, a maximum variance, or an average variance. Such metric may be computed for a patch (e.g., mask pattern corresponding to a portion of an entire target pattern) or across a number of patches.

[0058] As a second example of the application of variance map, the variance map may be used to identify or determine locations of a mask image where the prediction result may be (a) inaccurate, or (b) different for different mask image for the same target image. Figure 5B illustrates different predictions of a mask pattern in a high variance area for a given target pattern, consistent with various embodiments. The composite image 522 may be generated by overlapping multiple mask images (e.g., contours of the mask patterns) predicted by the mask prediction model 450. As illustrated, the locations in the composite image 522 corresponding to the high variance locations 504a-504d in the variance map shows different prediction results across different mask images. In some embodiments, if the prediction result is consistent or same across mask images, then a given mask feature would not have different shapes or sizes across different mask images. For example, as illustrated in the composite image 522, a mask feature 510, at a location corresponding to the first location 504a of the high variance area, has a first shape or size 511 in a first mask image and a second shape or size 512 in a second mask image. Such a variance may indicate that either the first and second mask images are inaccurate, or that they are different possible solutions for the same target image. Figure 6 illustrates different predictions of a mask pattern representation in a high variance area for a given target pattern representation, consistent with various embodiments. Figure 6 shows another example of a variance map, such as a variance map 602, having high variance in a portion 604. A composite image 622 may be generated by overlapping multiple mask patterns (e.g., contours of the maskpaterns) predicted by the mask prediction model 450 for a particular target patern. As illustrated, the composite image 622, which is an enlarged image of a portion of the mask image corresponding to the high variance portion 604, shows different prediction results across different mask images generated for the same target image.

[0059] The variance may occur for various reasons. For example, the variance may be due to a poor patern coverage, which may mean that the target image for which the mask prediction model 450 generated the mask images may be a new or unseen target image (e.g., a target patern representation that is not used in training the mask prediction model 450 or in generating a prediction in the inference stage). In another example, the variance may occur due to inconsistent training data. The training data used to train the mask prediction model 450 may have two or more different ground truth mask images for the same target image. Such inconsistency, or conflicting ground truth, may also result in high prediction variance. Regardless of the reason for variance, such high variance areas may be used to identify locations of a mask image where the prediction results are different. Based on the identification of the high variance areas, one or more actions may be performed, either automatically or based on user input. As an example of a first action, the portion of the mask image corresponding to the high variance area may be repaired, corrected, adjusted, modified, fine-tuned, optimized, etc. to improve the accuracy of the mask image (e.g., so that when a patern is printed on a substrate using the mask image in a lithography process, the dimensions and / or shape of the printed patern conforms to a defined specification). The adjustment may be made in various ways. For example, the adjustment may be made based on a predefined set of rules, or heuristics. As an example of a second action, a message or notification may be generated for a user. The notification may include the location of the high variance area and possible actions that may be taken by a user.

[0060] As a third example of the application of the variance map, the variance map be used to aid the patern selection process. As mentioned above, patern selection is a process of selecting paterns (e.g., diverse, or different paterns) from a number of paterns, e.g., as training data to calibrate or train models (e.g., physical model, ML model, empirical model, rule-based model, etc.) to predict corresponding results that further facilitates a paterning process. Selecting an appropriate set of paterns is one of the important factors in improving the patern coverage of a model. Figure 7 illustrates patern selection using a variance map, consistent with various embodiments. The variance map may be used to select paterns. For example, consider the variance map 602 indicates the variance across a set of mask patern representations predicted by the mask prediction model 450 for a specified target patern representation, e.g., target image 702. The high variance portion in the variance map 602, such as a high variance portion 604, is identified. In some embodiments, identifying the high variance portion 604 includes determining the smallest box such as a bounding box 606 that encloses the high variance portion 604. A portion 704 of the target image 702 corresponding to the high variance portion 604 is identified as the target image for which the patern coverage is low. That is, the portion 704 of the target image 702 may be identified as a new or unseentarget pattern (e.g., a target pattern that was not used in training the mask prediction model 450). For example, the features such as a first feature 706, a second feature 708, and athird feature 710 in the portion 704 may be considered as new target features since the variance is high for those features when compared to other features such as a fourth feature 714. Accordingly, the portion 704 of the target image 702 may be selected as a target pattern representation to be used for further training the mask prediction model 450, e.g., to improve the pattern coverage, thereby improving the prediction accuracy of the mask prediction model 450. The training may involve obtaining the ground truth mask image corresponding to the portion 704 of the target image 702 and using the ground truth mask image along with the portion 704 of the target image 702 as training data to train the mask prediction model 450. As described with reference to Figure 8 below, the ground truth mask image may be generated in a number of ways (e.g., via ML model prediction, via rigorous simulation, a physical or semi-physical model prediction, or other such processes). In some embodiments, the ground truth mask image is in the form of a CTM image. The variance map may be used to select such unseen pattern representations, which may be used to continuously train the mask prediction model 450 to improve the pattern coverage.

[0061] In some embodiments, the training process is continued with one or more target images until a training condition is satisfied. For example, the mask prediction model 450 may be incrementally, or iteratively, trained until the pattern coverage of the mask prediction model 450 satisfies a specified threshold coverage metric. In some embodiments, in each iteration, a pattern coverage of the mask prediction model 450 is determined based on a variance of the mask images generated for a given target image of the target images (e.g., using a variance map as described above), and if the pattern coverage is below a specified threshold coverage, the given target image and a ground truth mask image corresponding to the given target image are added to the training data to further train the mask prediction model 450.

[0062] While the above paragraphs describe pattern selection and training the mask prediction model 450 using portions of the target image for which the variance is above a specified threshold, the training may be performed using an entire target image in which case a ground truth mask pattern corresponding to the entire target image may be used in the training. For example, instead of using the portion 704 of the target image, the entire target image 702 and a ground truth mask image corresponding to the target image 702 may be used for training the mask prediction model 450. In some embodiments, a pattern selection process, which identifies portions of the target image for which the variance is above a specified threshold as training data for further training the mask prediction model 450, may select an entire target image 702 to be used in further training of the mask prediction model 450. For example, the pattern coverage of the mask prediction model 450 may be determined based on variance maps generated for a number of target images, and one or more target images for which the variance is above a specified threshold, such as the target image 702, may be selected as training data for further training the mask prediction model 450.

[0063] Figure 8 is a block diagram for training a mask prediction model to generate a mask pattern representation, consistent with various embodiments. Figure 8 is a block diagram for training a mask prediction model to generate a mask pattern representation, consistent with various embodiments. The mask prediction model 450 is trained using a training dataset that includes a target pattern representation (e.g., target image 804), which is used as guidance data, and a set of ground truth mask pattern representation, such as mask image 802, corresponding to the target image 804. The ground truth mask image 802 may be generated in a number of ways, e.g., via rigorous simulation, a physical or semi -physical model prediction, or other such processes. In some embodiments, the ground truth mask image 802 is in the form of a CTM image. In some embodiments, the training dataset may include more than one target image and each target image may be associated with a corresponding set of ground truth mask images.

[0064] The training process may include two sub processes - (i) a forward process, noise addition process or a diffusion process 825, and (ii) a reverse process or denoising process 850, as illustrated in Figure 8. The forward diffusion process in a diffusion model is a well-defined mathematical procedure that transforms original data into noise through a series of incremental steps. It sets the foundation for the reverse diffusion process by creating a structured noise representation that the model can learn to invert, enabling high-quality data generation. In the noise addition process 825, a forward diffusion component 851 of the mask prediction model 450 starts with ground truth mask image 802 and gradually adds prescribed noise (e.g., Gaussian) over several time steps, creating a sequence of increasingly noisy versions of the ground truth mask image (e.g., images 806a, 806b- 806n) to result in a random noise image (e.g., image 806n). In some embodiments, the number of time steps may be specified as an input. The noise added is typically parameterized by a variance schedule [3t, which controls the amount of noise added at each step. The variance schedule [3t is designed to ensure a smooth transition from the original data to pure noise. The variance schedule can be linear, cosine, or follow other forms to balance the trade-off between diffusion speed and reconstruction quality.

[0065] In the denoising process 850, a reverse diffusion component 852 of the mask prediction model 450 reverses the noise-adding process by starting from the random noise image (e.g., image 806n) and gradually removing the noise, step by step, creating a sequence of less noisy images (e.g., images 816a, 816b-816n) until it generates a predicted mask image 816n, which is a reconstructed version of the ground truth mask image 802. The reverse diffusion component 852 is implemented using a neural network, often a UNet or another convolutional architecture, which is trained to reverse the forward diffusion process. This network iteratively refines the noisy data back into a coherent form. The removal of noise may involve estimating both the mean and variance of the noise distribution at each step. After the denoising process is executed at a particular time step, the loss function 840 is computed as a difference between the predicted mask image and the ground-truth mask image mixed with noise at the corresponding time step, and a gradient of the loss function 840 iscomputed with respect to each model parameter may also be calculated. The gradient calculation may involve determining how changing each model parameter would increase or decrease the loss function 840. The model parameters (e.g., weights and biases) are adjusted using the gradient to optimize (e.g., reduce or minimize) the loss function 840. The training process is repeated, with the same ground truth mask image or different ground truth mask image, or for random time steps until a training criterion is satisfied (e.g., the loss function 840 is optimized or a specified number of iterations of training is performed). After the training criterion is satisfied, the mask prediction model 450 is considered to be trained. The trained mask prediction model 450 may be used to predict a mask image for any unseen target image (e.g., a target pattern representation that is not used in training the mask prediction model or in generating a prediction in the inference stage) using a noise image as an input (e.g., as described at least with reference to Figure 4). While the above embodiment describes the loss function being computed for a single timestep, in some embodiments, the loss function 840 may be a sum of the loss in all the steps, and a gradient of the loss function 840 is also computed as a sum of all the gradients, and the model parameters are adjusted using the accumulated gradient to optimize the loss function 840.

[0066] Note that the target image 804 may be provided as guidance data, which guides the mask prediction model 450 in each step of the denoising process in removing the noise from the noise image to generate a mask pattern corresponding to the target image 804. In some embodiments, the guidance data is another input to a diffusion model used to guide or steer the generative process towards a desired outcome. The denoising process is conditioned on the guidance data to direct the generation of the predicted output towards the targeted output (e.g., a mask image corresponding to the target image). For example, when the target image 804 is input as guidance data to the mask prediction model 450, the denoising of the noise image is conditioned on the target image 804 to cause the generated mask image 816n to be similar to a ground-truth mask image 802 corresponding to the target image 804. That is, the conditioned denoising process learns a relationship between the ground truth mask image 802 and the corresponding guidance target image 804, which enables the mask prediction model 450 to generate a mask image for the given guidance target image. After training the mask prediction model 450 with several ground truth mask images for the same target image 804 and / or different target image, the conditioned denoising process can be used to generate a mask image for any given target image. For example, a gradient of a loss function 840 associated with the mask prediction model 450 is used to guide the denoising process to generate the mask image 816n such that it matches the ground-truth mask image 802. In each iteration of the training, by adjusting the mask prediction model parameters (e.g., weights and biases) based on the gradient to steer the generation of the mask image 816n towards the ground-truth mask image 802, the denoising process learns the model parameters to predict a mask image for the corresponding guidance target image. In some embodiments, the use of gradients, especially in guided diffusion, allows for finetuning the generative process to meet the given condition. Additionally, the mask prediction model450 may be subject to a constraint 812 (e.g., similar to the constraint 412 described at least with reference to Figure 4 above) during the training.

[0067] Figure 9 is a flow diagram of a method for pattern coverage determination or pattern selection using a diffusion model, consistent with various embodiments. The method of Figure 9 is described at least with reference to Figures 4-7 above.

[0068] At process P902, a noise input and a target pattern representation are provided as inputs to a mask prediction model that is trained to generate a mask pattern representation. For example, a noise input 402 (e.g., image with random noise, a transformation of the target pattern representation such as an aerial image, or noisy versions of the target pattern representation, aerial image, optical or forward simulation or any other simulation of the target pattern representation) and a target image 404 are input to the mask prediction model 450. In some embodiments, the mask prediction model 450 is implemented using a diffusion model. The mask prediction model 450 uses the target image 404 as guidance data for generating the corresponding mask pattern representation (e.g., mask image). The mask prediction model 450 may be trained using (a) a set of noise images corresponding to a set of ground truth mask pattern representations, and (b) a set of target pattern representations to which the set of ground truth mask pattern representations correspond (e.g., as described at least with reference to Figure 8 above).

[0069] At process P904, the mask prediction model is executed to generate a mask pattern representation corresponding to the target pattern representation. The mask prediction model predicts or generates the mask pattern representation by removing the noise (referred to as “denoising” process) from the noisy data iteratively using the target pattern representation. For example, the mask prediction model 450 predicts a mask image 408 by iteratively removing the noise from the noise input 402 using the target image 404. This may involve estimating both the mean and variance of the noise distribution at each iteration. As described at least with reference to Figure 4, the mask prediction model 450 constructs the mask image 408 over several iterations or steps (e.g., “7”), by gradually removing the noise from the image of the previous step generating a sequence of images (e.g., images 406a-406f) until the mask image 408 is generated. For example, in a first step, the mask prediction model 450 constructs a first image 406a by removing the noise from the noise input 402, then in a second step, constructs a second image 406b by removing the noise from the first image 406a, and so on until it generates the mask image 408. The target image 404 may be used as a guidance in every step of the denoising process. In some embodiments, the number of steps in the denoising process may be predefined and the removal of noise may involve estimating both the mean and variance of the noise distribution at each step (which may be learnt during the training process).

[0070] In some embodiments, multiple mask pattern representations may be obtained for the same target pattern representation. For example, the processes P902-P904 may be repeated for multiple noise inputs (e.g., noise images with different noise data) with the same target image to obtain multiple mask images for the target image.

[0071] At process P906, a variance of the mask pattern representations is determined. In some embodiments, the variance between the mask pattern representations is represented as a variance map, which is an image whose pixel values are indicative of a variance between the mask pattern representations at the corresponding pixel. Some examples of the variance map, such as the variance map 502 and variance map 602, are illustrated in Figure 5A and Figure 6, respectively. The variance may be used for various applications. For example, the variance may be used for pattern coverage determination and pattern selection process (as described at least with reference to Figures 5A-7 above and the processes P908 and P910 below.

[0072] At process P908, the variance may be used to determine a pattern coverage of the mask prediction model 450. For example, as described at least with reference to Figure 5A above, the pattern coverage may be determined based on a percentage of the high-variance area in the variance map, which is the area indicative of a variance above a specified threshold. In some embodiments, the higher the percentage of high-variance area, the lower the pattern coverage of the mask prediction model. In the example of Figure 5A, the high-variance area is shown in locations such as a first location 504a, a second location 504b, a third location 504c, a fourth location 504d, and a fifth location 506. In some embodiments, the pattern coverage may be determined as a value between “0”- “100.” For example, if the percentage of high variance area in the variance map 502 is “2%,” then the pattern coverage may be determined as “98%” or “0.98”(which is a difference between the percentage total area of the variance map 502 and percentage of the high variance area). The pattern coverage may also be determined based on one or more metrics. For example, the pattern coverage may be determined based on at least one of a minimum variance, a maximum variance, or an average variance. Such metric may be computed for a patch (e.g., mask pattern representation corresponding to a portion of an entire target pattern representation) or across a number of patches.

[0073] At process P910, the variance may be used for pattern selection, which is a process for selecting a particular target pattern representation for further training of the mask prediction model to improve the pattern coverage. As described at least with reference to Figure 5 A above, the variance map may be used to select pattern representations. For example, consider the variance map 602 indicates the variance across a set of mask pattern representations predicted by the mask prediction model 450 for a specified target pattern representation (e.g., target image 702). The high variance portion in the variance map 602, such as the portion 604, which corresponds to the locations in the mask images at which the predictions are inaccurate or inconsistent, is identified. A portion of the target image 702 corresponding to the high variance portion 604 is identified as the target pattern representation for which the pattern coverage is low. That is, the portion 704 of the target image 702 may be identified as a new or unseen target pattern representation (e.g., a target pattern that was not used in training the mask prediction model 450). For example, the features such as a first feature 706, a second feature 708, and a third feature 710 in the portion 704 may be considered as new target features since the variance is high for those features when compared to other features such as a fourthfeature 714. Accordingly, the portion 704 of the target image 702 may be selected as a target pattern representation to be used for further training the mask prediction model 450, e.g., to improve the pattern coverage, thereby improving the prediction accuracy of the mask prediction model 450.

[0074] Note that while the method of Figure 9 shows both processes P908 and P910, the method may execute one or both of the processes.

[0075] Figure 10 is a block diagram that illustrates a computer system 100 which can assist in implementing various methods and systems disclosed herein. The computer system 100 may be used to implement any of the entities, components, modules, or services depicted in the examples of the figures (and any other entities, components, modules, or services described in this specification). The computer system 100 may be programmed to execute computer program instructions to perform functions, methods, flows, or services (e.g., of any of the entities, components, or modules) described herein. The computer system 100 may be programmed to execute computer program instructions by at least one of software, hardware, or firmware.

[0076] Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled with bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 104. Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0077] Computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is cursor control 116, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0078] According to one embodiment, portions of one or more methods described herein may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the processsteps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In an alternative embodiment, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0079] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may 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 device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[0080] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 either before or after execution by processor 104.

[0081] Computer system 100 also preferably includes a communication interface 118 coupled to bus 102. Communication interface 118 provides a two-way data communication coupling to a network link 120 that is connected to a local network 122. For example, communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0082] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. ISP 126 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet” 128. Local network 122 and Internet 128 both use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0083] Computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, a server 130 might transmit a requested code for an application program through Internet 128, ISP 126, local network 122 and communication interface 118. One such downloaded application may provide for the illumination optimization of the embodiment, for example. The received code may be executed by processor 104 as it is received, or stored in storage device 110, or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[0084] While the concepts disclosed herein may be used for imaging on a substrate such as a silicon wafer, it shall be understood that the disclosed concepts may be used with any type of lithographic imaging systems, e.g., those used for imaging on substrates other than silicon wafers.

[0085] The terms “optimizing” and “optimization” as used herein refers to or means adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc. such that results and / or processes have more desirable characteristics, such as higher accuracy of projection of a design pattern on a substrate, a larger process window, etc. Thus, the term “optimizing” and “optimization” as used herein refers to or means a process that identifies one or more values for one or more parameters that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for those one or more parameters. "Optimum" and other related terms should be construed accordingly. In an embodiment, optimization steps can be applied iteratively to provide further improvements in one or more metrics.

[0086] Embodiments of the present disclosure can be further described by the following clauses.1. A method of determining a pattern coverage of a mask prediction model, the method comprising: inputting multiple noise images to a mask prediction model, wherein the mask prediction model comprises a diffusion model; generating a mask pattern representation for each of the noise images by executing the mask prediction model with a target pattern representation, wherein the target pattern representation is inputas guidance data to the mask prediction model, and wherein the mask prediction model is trained by using a set of target pattern representations; determining a variance among mask pattern representations that are generated by executing the mask prediction model in response to the multiple noise images; and determining a pattern coverage of the mask prediction model based on the variance.2. The method of clause 1, wherein determining the variance includes: generating a variance map, wherein the variance map comprises an image whose pixel values are indicative of the variance among the mask pattern representations.3. The method of clause 2, wherein determining the pattern coverage includes: determining a percentage of an area in the variance map that is indicative of the variance below a specified threshold; and determining the pattern coverage based on the percentage of the area.4. The method of clause 2, wherein determining the pattern coverage includes: determining, using the variance map, a metric associated with the variance; and determining the pattern coverage based on the metric.5. The method of clause 4, wherein the metric includes at least one of a minimum variance, a maximum variance, or an average variance.6. The method of clause 1, wherein determining the variance includes: for each pixel, obtaining a value of the pixel from each of the mask pattern representations, determining a range of the values for each pixel, and determining the variance based on the range of values.7. The method of clause 2 further comprising: determining a first portion of the variance map in which the variance is above a specified threshold; and identifying a portion of the target pattern representation corresponding to the first portion as the portion of the target pattern representation for which the pattern coverage is below a threshold coverage.8. The method of clause 2 further comprising: determining that the pattern coverage is below a threshold coverage based on the variance map; obtaining a ground truth mask pattern representation corresponding to the target pattern representation; and further training the mask prediction model with the target pattern representation and the ground truth mask pattern representation.9. The method of clause 8, wherein training the mask prediction model includes: training the mask prediction model for a plurality of training pattern representations iteratively until a training condition is satisfied, wherein each iteration includes:computing the variance map based on a set of mask pattern representations generated for a given target pattern representation of the training pattern representations; determining the pattern coverage of the mask prediction model based on the variance map; determining that the pattern coverage is below a threshold coverage; and training the mask prediction model with a given ground truth mask representation corresponding to the given target pattern representation.10. The method of clause 9, wherein the training condition includes the pattern coverage satisfying a threshold coverage.11. The method of clause 8, wherein further training the mask prediction model includes: determining portions of the target pattern representation for which the variance is above a specified threshold; obtaining a set of ground truth mask pattern representations corresponding to the portions of the target pattern representations; and training the mask prediction model with the portions of target pattern representation and the set of ground truth mask pattern representations.12. The method of clause 2 further comprising: determining a first portion in the variance map in which the variance is above a specified threshold; obtaining a first mask pattern representation of the mask pattern representations; and modifying the first mask pattern representation at a portion corresponding to the first portion.13. The method of clause 2 further comprising: selecting one of a plurality of target pattern representations based on the pattern coverage of the mask prediction model for further training of the mask prediction model.14. The method of clause 13, wherein selecting one of the target pattern representations for further training the mask prediction model includes: generating a plurality of variance maps for the plurality of target pattern representations, wherein the plurality of variance maps includes a first variance map generated for a first target pattern representation of the plurality of target representations, wherein the first variance map is generated based on a set of mask pattern representations generated by the mask prediction model for the first target pattern representation; determining that the pattern coverage of the mask prediction model is below a threshold coverage for the first target pattern representation based on the first variance map; and selecting the first target pattern representation for further training of the mask prediction model.15. The method of clause 1, wherein the mask pattern representation is at least one of a mask image, mask pattern contours, mask polygons, a continuous transmission mask (CTM), or CTM+.16. The method of clause 15, wherein generating the mask pattern representation by executing the mask prediction model includes: denoising a first noise image of the noise images using the target pattern representation iteratively to generate a first mask image.17. The method of clause 1, wherein inputting the noise images includes: adding noise to the target pattern representation to generate a noisy target image, and inputting the noisy target image as a first noise image of the noise images.18. The method of clause 1, wherein inputting the noise images includes: generating a transformation of the target pattern representation, and inputting the transformation of the target pattern representation as a first noise image of the noise images.19. The method of clause 1 further comprising: training the mask prediction model by using training data that includes a set of target pattern representations as guidance data, wherein the mask prediction model is configured to generate a predicted mask pattern representation for an input guidance target pattern representation.20. The method of clause 19, wherein the training includes: executing a diffusion process that adds noise to a ground truth mask pattern representation corresponding to the input guidance target pattern representation iteratively to generate a training noise image; and executing the diffusion model to perform a denoising process that iteratively removes the noise from the training noise image using the input guidance target pattern representation to generate the predicted mask pattern representation.21. A method of pattern selection for training a mask prediction model, the method comprising: inputting multiple noise images to a mask prediction model, wherein the mask prediction model is implemented using a diffusion model; generating a mask pattern representation for each of the noise images by executing the mask prediction model with a target pattern representation, wherein the target pattern representation is input as guidance data to the mask prediction model, and wherein the mask prediction model is trained by using a set of target pattern representations; determining a variance of the mask pattern representations; and determining a portion of the target pattern representation to be selected for training of the mask prediction model based on the variance.22. The method of clause 21, wherein determining the variance includes: generating a variance map, wherein the variance map is an image whose pixel values are indicative of the variance.23. The method of clause 22, wherein determining a portion of the target pattern representation to be selected includes:determining a first portion of the variance map in which the variance is above a specified threshold; and identifying the portion of the target pattern representation corresponding to the first portion as the portion of the target pattern representation for which the mask prediction model is not trained on.24. The method of clause 22 further comprising: obtaining a ground truth mask pattern representation corresponding to the portion of the target pattern representation; and training the mask prediction model with the target pattern representation and the ground truth mask pattern representation.25. The method of clause 22 further comprising: determining a first portion of the variance map in which the variance is above a specified threshold; obtaining a first mask pattern representation of the mask pattern representations; and modifying the first mask pattern representation at a portion corresponding to the first portion.26. The method of clause 22 further comprising: determining a percentage of an area in the variance map that is indicative of the variance below a specified threshold; and determining a pattern coverage of the mask prediction model based on the percentage of the area.27. The method of clause 22 further comprising: determining, using the variance map, a metric associated with the variance; and determining a pattern coverage of the mask prediction model based on the metric.28. The method of clause 27, wherein the metric includes at least one of a minimum variance, a maximum variance, or an average variance.29. The method of clause 21, wherein determining the variance includes: for each pixel, obtaining a value of the pixel from each of the mask pattern representations, determining a range of the values for each pixel, and determining the variance based on the range of values.30. The method of clause 21, wherein the mask pattern representation is at least one of a mask image, mask pattern contours, mask polygons, a continuous transmission mask (CTM), or CTM+.31. The method of clause 30, wherein generating the mask pattern representation includes: denoising a first noise image of the noise images using the target pattern representation iteratively to generate a first mask image.32. The method of clause 21 further comprising:training the mask prediction model by using training data that includes a set of target pattern representations as guidance data, wherein the mask prediction model is configured to generate a predicted mask pattern representation for an input guidance target pattern representation.33. The method of clause 32, wherein the training includes: executing a diffusion process that adds noise to a ground truth mask pattern representation corresponding to the input guidance target pattern representation iteratively to generate a training noise image; and executing a denoising process that iteratively removes the noise from the training noise image using the input guidance target pattern representation to generate the predicted mask pattern representation.34. An apparatus, the apparatus comprising: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above clauses.35. A non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above clauses.

[0087] Aspects of the invention can be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs which may be carried on an appropriate carrier medium which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communications signal). Embodiments of the invention may be implemented using suitable apparatus which may specifically take the form of a programmable computer running a computer program arranged to implement a method as described herein. Thus, embodiments of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[0088] In block diagrams, illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each of the components may be provided by software orhardware modules that are differently organized than is presently depicted, for example such software or hardware may be intermingled, conjoined, replicated, broken up, distributed (e.g., within a data center or geographically), or otherwise differently organized. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium. In some cases, third party content delivery networks may host some or all of the information conveyed over networks, in which case, to the extent information (e.g., content) is said to be supplied or otherwise provided, the information may be provided by sending instructions to retrieve that information from a content delivery network.

[0089] Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing / computing device.

[0090] The reader should appreciate that the present application describes several inventions. Rather than separating those inventions into multiple isolated patent applications, these inventions have been grouped into a single document because their related subject matter lends itself to economies in the application process. But the distinct advantages and aspects of such inventions should not be conflated. In some cases, embodiments address all of the deficiencies noted herein, but it should be understood that the inventions are independently useful, and some embodiments address only a subset of such problems or offer other, unmentioned benefits that will be apparent to those of skill in the art reviewing the present disclosure. Due to cost constraints, some inventions disclosed herein may not be presently claimed and may be claimed in later filings, such as continuation applications or by amending the present claims. Similarly, due to space constraints, neither the Abstract nor the Summary sections of the present document should be taken as containing a comprehensive listing of all such inventions or all aspects of such inventions.

[0091] It should be understood that the description and the drawings are not intended to limit the present disclosure to the particular form disclosed, but to the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the inventions as defined by the appended claims.

[0092] Modifications and alternative embodiments of various aspects of the inventions will be apparent to those skilled in the art in view of this description. Accordingly, this description and the drawings are to be construed as illustrative only and are for the purpose of teaching those skilled in the art the general manner of carrying out the inventions. It is to be understood that the forms of the inventions shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and embodiments or features of embodiments may be combined, all as would be apparent to one skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departingfrom the spirit and scope of the invention as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description.

[0093] As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component includes A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component includes A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. Expressions such as “at least one of’ do not necessarily modify an entirety of a following list and do not necessarily modify each member of the list, such that “at least one of A, B, and C” should be understood as including only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase “one of A and B” or “any one of A and B” shall be interpreted in the broadest sense to include one of A, or one of B.

[0094] The descriptions herein are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made as described without departing from the scope of the claims set out below.

Claims

CLAIMS1. A method of pattern selection for training a mask prediction model, the method comprising: inputting multiple noise images to a mask prediction model, wherein the mask prediction model is implemented using a diffusion model; generating a mask pattern representation for each of the noise images by executing the mask prediction model with a target pattern representation, wherein the target pattern representation is input as guidance data to the mask prediction model, and wherein the mask prediction model is trained by using a set of target pattern representations; determining a variance of the mask pattern representations; and determining a portion of the target pattern representation to be selected for training of the mask prediction model based on the variance.

2. The method of claim 1, wherein determining the variance includes: generating a variance map, wherein the variance map is an image whose pixel values are indicative of the variance.

3. The method of claim 2, wherein determining a portion of the target pattern representation to be selected includes: determining a first portion of the variance map in which the variance is above a specified threshold; and identifying the portion of the target pattern representation corresponding to the first portion as the portion of the target pattern representation for which the mask prediction model is not trained on.

4. The method of claim 2 further comprising: obtaining a ground truth mask pattern representation corresponding to the portion of the target pattern representation; and training the mask prediction model with the target pattern representation and the ground truth mask pattern representation.

5. The method of claim 2 further comprising: determining a first portion of the variance map in which the variance is above a specified threshold; obtaining a first mask pattern representation of the mask pattern representations; and modifying the first mask pattern representation at a portion corresponding to the first portion.

6. The method of claim 2 further comprising:determining a percentage of an area in the variance map that is indicative of the variance below a specified threshold; and determining a pattern coverage of the mask prediction model based on the percentage of the area.

7. The method of claim 2 further comprising: determining, using the variance map, a metric associated with the variance; and determining a pattern coverage of the mask prediction model based on the metric.

8. The method of claim 7, wherein the metric includes at least one of a minimum variance, a maximum variance, or an average variance.

9. The method of claim 1, wherein determining the variance includes: for each pixel, obtaining a value of the pixel from each of the mask pattern representations, determining a range of the values for each pixel, and determining the variance based on the range of values.

10. The method of claim 1, wherein the mask pattern representation is at least one of a mask image, mask pattern contours, mask polygons, a continuous transmission mask (CTM), or CTM+.

11. The method of claim 10, wherein generating the mask pattern representation includes: denoising a first noise image of the noise images using the target pattern representation iteratively to generate a first mask image.

12. The method of claim 1 further comprising: training the mask prediction model by using training data that includes a set of target pattern representations as guidance data, wherein the mask prediction model is configured to generate a predicted mask pattern representation for an input guidance target pattern representation.

13. The method of claim 2, wherein the training includes: executing a diffusion process that adds noise to a ground truth mask pattern representation corresponding to the input guidance target pattern representation iteratively to generate a training noise image; and executing a denoising process that iteratively removes the noise from the training noise image using the input guidance target pattern representation to generate the predicted mask pattern representation.

14. An apparatus, the apparatus comprising: a memory storing a set of instructions; and a processor configured to execute the set of instructions to cause the apparatus to perform a method of any of the above claims.

15. A non-transitory computer-readable medium having instructions recorded thereon, the instructions when executed by a computer implementing the method of any of the above claims.

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