Method and system for mask prediction using diffusion model

Abstract

Described herein is a method and system for generating a mask pattern representation using a diffusion model. A noise image is input to the diffusion model along with a target pattern representation, and the diffusion model is executed to generate a mask pattern representation corresponding to the target pattern representation. The diffusion model predicts the mask pattern representation by removing the noise from the noise image iteratively using the target pattern representation as guidance data. The diffusion model is trained using (a) a set of noise images corresponding to a representation of a set of ground truth mask patterns, and (b) a representation of a set of target patterns to which the set of ground truth mask patterns correspond.

Description

METHOD AND SYSTEM FOR MASK PREDICTION USING DIFFUSION MODELCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 681,137 which was filed on August 8, 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 mask pattern design for a lithography process. The method includes: inputting a noise image and a target pattern representation (e.g., target polygons, pixelated images rendered from target polygons) to a diffusion model, wherein the target pattern representation can be input as guidance data to the diffusion model, and wherein the diffusion model is trained using representations of a set of target patterns and representations of a corresponding set of mask patterns (e.g., mask contours, mask contour polygons, mask images); and generating a mask pattern representation corresponding to the target pattern representation by executing the diffusion model.

[0005] In some embodiments, the mask pattern design method includes: inputting a noise image and a target pattern representation to a diffusion model, wherein the target pattern representation can be input as guidance data to the diffusion model, and wherein the diffusion model can be trained using representations of a set of target patterns and representations of a corresponding set of mask patterns; and obtaining a defective mask pattern representation from a second diffusion model that is trained to generate representations of a set of defective mask patterns, wherein the defective mask pattern representation includes a defect; inputting the defective mask pattern representation to the diffusion model; and generating a mask pattern representation corresponding to the target pattern representation by executing the diffusion model, wherein the mask pattern representation is generated based on thedefective mask pattern representation to avoid the defect. Embodiments of the present disclosure also include training of the diffusion models.

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

[0014] Figure 6 illustrates prediction of a mask pattern representation by a mask prediction model using a boundary constraint, consistent with various embodiments.

[0015] Figures 7 and 8 illustrate prediction of a mask pattern representation by a mask prediction model using a defect-aware constraint, consistent with various embodiments.

[0016] Figure 9 is a flow diagram of a method for generating a mask pattern representation using a diffusion model, consistent with various embodiments.

[0017] Figure 10 is a block diagram that illustrates a computer system which can assist in implementing various methods and systems disclosed herein.

[0018] 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 illustrated elements. 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 arenecessary 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

[0019] 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. A mask pattern typically includes several types of features. For example, a mask pattern includes “main” features of a target pattern, which are features to be printed on a substrate, and sub-resolution assist features (SRAFs), which are features that do not print on the substrate but aids in printing of the main features. Various methods are used to generate a mask pattern. For example, a machine learning (ML) model is used to generate a mask pattern for a given target pattern. Such conventional methods have drawbacks or limitations. For example, some of the conventional ML-based mask prediction techniques suffer from training data inconsistency due to which the resulting mask patterns may be inaccurate. Accordingly, such ML models are less reliable. Additionally, some post processing may have to be performed on the predicted mask pattern for further modification or adjustment of mask features, and such post processing may not only be time consuming or compute-intensive but also challenging. These and other drawbacks exist.

[0020] Disclosed are embodiments for predicting a mask pattern representation using a prediction model that is based on a diffusion model. A diffusion model typically is trained by first corrupting original data (e.g., ground truth data) with noise in a controlled manner to generate a noise image and then learning to reverse this process to generate or predict new, realistic data from the generated noise image. In some embodiments, a mask prediction model implemented using a diffusion model may be trained to generate a mask pattern representation by gradually denoising a noise input (e.g., random noise image or other images with different amounts of pattern information like a transformation of the target pattern such as an aerial image, or noisy versions of the target pattern, aerial image, optical or forward simulation or any other simulation of the target pattern) over several steps guided by an input target pattern representation to predict the mask pattern representation that corresponds to the target pattern representation. The training process includes a noise addition process in which the prediction model starts with an image of a ground truth mask pattern (e.g., a mask image) and gradually adds noise (e.g., Gaussian) to the mask image over severalsteps, creating a sequence of increasingly noisy versions of the ground truth mask pattern to result in a final noise image (e.g., random noise image). The training process further includes 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. The training process may be repeated until a difference between a ground truth mask pattern and the predicted mask pattern representation is reduced (e.g., minimized). A target pattern representation to which the ground truth mask pattern corresponds may be supplied as another input to the diffusion model, e.g., as guidance data, during the training to guide the mask prediction model during the denoising process to generate a predicted image corresponding to the target pattern.

[0021] In some embodiments, the guidance data is another input to a diffusion model used to guide or steer the generative process towards a targeted output (e.g., a mask pattern representation corresponding to the target pattern representation). During training, when a target pattern representation is input as guidance data to the mask prediction model, the denoising of a noise image is conditioned on the target pattern representation, which causes the denoising process to generate a mask pattern representation similar to the ground-truth mask pattern representation corresponding to the target pattern representation. That is, the conditioned denoising process learns a relationship between the ground truth mask pattern representation and the corresponding guidance target pattern representation, which enables the mask prediction model to generate a mask pattern representation for the given guidance target representation. After training the mask prediction model with several ground truth mask pattern representations for the same target pattern representation and / or different target pattern representations, the conditioned denoising process can be used to generate a mask pattern representation any given target pattern representation.

[0022] The trained mask prediction model may be used to generate a mask pattern representation for any target pattern representation. In some embodiments, the model can be used to predict a mask image which is then used to extract a corresponding mask pattern. The input to the model can be a noise image and a target pattern representation as guidance data. For example, the target pattern representation may be an image (e.g., a target image) that may be generated by rendering the target pattern into a pixelated image using an image processing technique without involving simulating the lithography process, and the noise image may be a noisy version of the target pattern. In the inference stage, the mask prediction model can remove the noise from the noise image iteratively to generate the mask pattern representation.

[0023] 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 additionprocess can advantageously act as data augmentation, helping the diffusion model generalize better and handle inconsistencies. The adding of noise and denoising process can further advantageously help in regularization, preventing the diffusion model from overfitting to noisy or inconsistent data.

[0024] In some embodiments, the mask prediction model may be configured to predict representations of mask patterns based on various constraints. In some embodiments, the mask prediction model may be subjected to a “boundary” constraint in predicting mask images during an inference stage such that a predicted mask feature near the boundary of one predicted pattern representation matches a predicted mask feature near the boundary of a neighboring predicted pattern representation. In OPC, when two mask patches (e.g., two portions of the mask pattern or two mask patterns) are combined (e.g., “stitched”), a first portion of a mask feature from a first patch and a second portion of the mask feature from a reference patch along a boundary of the two patches may not match (e.g., the portions may be misaligned, disconnected, or not continuous across the boundary). The boundary may correspond to the border region of the two adjacent or neighboring patches of the mask pattern representation, or is a region of the mask pattern representation separating two adjacent patches. Typically, some post processing may be required to adjust the mask features so that they match across the boundary when two pattern representations are stitched. According to embodiments of the present disclosure, by constraining the mask prediction model with a boundary constraint during the inference stage, the mask prediction model predicts a mask pattern representation (e.g., a “first patch”) such that feature portions from the predicted mask pattern and the feature portions of a neighboring reference mask pattern representation (e.g., “reference patch”) located along the boundary match (e.g., are continuous or connected across the boundary, or a misalignment is reduced) when the first patch is stitched with the reference patch. In some embodiments, by applying the boundary constraint in predicting a first portion of a feature in a first patch, the mask prediction model uses information regarding a second portion of the feature from the reference patch during a denoising phase to cause the first portion to be predicted in such a way that the first portion matches with the second portion when the two patches are stitched along the boundary. For example, the value of the first portion of the feature near the boundary from the first patch may be interpolated with the second portion of the feature near the boundary from the reference patch so that the feature portions match across the boundary. In some embodiments, a combination of the interpolation result and the gradient computed during the generation of the first patch may be used to predict the first feature portion near the boundary. The boundary constraint facilitates pattern stitching with minimal to none post processing of the patches as would be required, thereby reducing the time and computing resources that may be consumed in post processing of the mask pattern representation.

[0025] In some embodiments, the mask prediction model may be subject to a “defect-aware” constraint in predicting the mask images during an inference stage to avoid defects in the prediction. The defect-aware constraint can advantageously cause the mask prediction model to predictrepresentations of mask patterns by avoiding known defects (e.g., defects that are identified from defective mask patterns in an OPC verification process and / or mask inspection or metrology process). In some embodiments, a representation of a defective mask pattern (e.g., a mask pattern representation that is known to have defects) may be generated using information gathered from wafer defects, an OPC verification process and / or mask inspection, or metrology process. In some embodiments, a “defective-mask prediction model” implemented using a diffusion model may be trained using a target pattern representation as guidance data and representations of a set of defective mask patterns as ground truth to predict defective mask pattern representations. During the inference stage, a defective mask pattern representation (e.g., a defective mask pattern predicted by the defective-mask prediction model for a given target pattern) is input as a constraint to the mask prediction model, which is trained to predict a mask pattern representation for the given target pattern representation from a given noise image. The mask prediction model may use information from the defective mask pattern representation to cause a prediction of a mask pattern representation avoid to those one or more defects. In some embodiments, the mask prediction model causes the denoising process to generate the mask pattern representation such that the one or more defects from the defective mask pattern representation are avoided during the generation of the mask pattern representation. In some embodiments, the mask prediction model may use a gradient from the defective-mask prediction model (e.g., at a particular time step during the denoising process), which is indicative of how the model parameters are to be changed so that a loss function associated with the defective maskprediction model is reduced. The mask prediction model may also use a gradient associated with the mask prediction model (e.g., at the corresponding particular time step), which is indicative of how the model parameters are to be changed so that a loss function associated with the mask prediction model is reduced. In some embodiments, a difference between a first gradient from the mask prediction model and a second gradient from the defective-mask prediction model may be used to control the prediction of the mask pattern representation either towards or away from the defective mask pattern representation. For example, a weight may be associated with the second gradient to control a direction of the prediction of the mask pattern representation to either towards or away from the defective mask pattern representation. In some embodiments, by increasing the weight, the prediction can be directed away from the defective mask pattern representation, causing the predicted mask pattern representation to be less similar to the defective mask pattern representation so that the one or more defects that are identified from the defective mask pattern representation are avoided. In another example, by decreasing the weight, the prediction can be directed towards the defective mask pattern representation, causing the predicted mask pattern representation to be more similar to the defective mask pattern representation. By subjecting the mask prediction model to a “defect-aware” constraint, not only the accuracy and reliability of the mask prediction model in predicting the mask pattern representations is improved by avoiding known defects, also the time and computing resources thatmay be consumed in any post processing of (e.g., to remove the defects or other types of repairing the mask pattern representation) the mask pattern representation is reduced.

[0026] In some embodiments, the mask prediction model may be subjected to a “location-aware” constraint that causes the mask prediction model to restrict a prediction a particular portion of the mask pattern representation. In some embodiments, this could be used in the procedure of local repair (e.g., remove defects), or modification of a mask pattern representation. For example, by providing location coordinates of an area in which the mask pattern representation has to be repaired, the mask prediction model restricts the prediction, repair (e.g., remove defects), or modification of the mask pattern representation to the specified area of the mask pattern representation and does not process the portion outside that area, thereby minimizing time and computing resources consumed in repairing the mask pattern representation.

[0027] 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.

[0028] 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.

[0029] A patterning device can comprise, or can form, one or more design layouts. The design layout 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).

[0030] 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.

[0031] 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.

[0032] 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) 18 A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A.

[0033] 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 adjustablefilter 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.

[0034] 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.

[0035] 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).

[0036] 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 thepaterning device. The phase of the transmitance (or reflectance) may also be a continuous function of the location on the paterning 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). In a level set process, an initial image (e.g., enhanced image, level set image initialized from a CTM image, etc.) can be progressively modified to generate different types of images to eventually generate information of mask paterns or an image (e.g., a level set image or CTM+ image corresponding to a final curvilinear mask) further used to fabricate / manufacture a mask. CTM optimization with grayscale image may be transitioned to to CTM+ optimization with curvilinear mask and may be simplified by replacing the level set process and the thresholding process by a different process where a sigmoid transformation is applied to the enhanced image and corresponding change in gradient computation is performed. The sigmoid transformation of the enhanced image generates a transformed image that gradually evolve into a curvilinear patern during an optimization process (e.g., minimizing cost function). During an iteration or a step of optimization, variables (e.g., steepness and / or a threshold) related to sigmoid function may be modified based on the gradient computation. Through iterations, a gradual transition from the CTM image to a final CTM+ image may be achieved allowing improved results in the final CTM+ optimization with curvilinear mask paterns. Details of various embodiments of CTM images and CTM+ images are described in U.S. Patent Application Publication No. 20220121804A1, the disclosure of each which is hereby incorporated by reference in its entirety.

[0037] 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 paterning device. The thin-mask approximation assumes that the thickness of the structures on the paterning 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 paterning 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 paterning 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 scatering in the mask transmission function may enable the mask transmission function to beter capture the interaction of the radiation with the paterning 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.

[0038] 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, the illumination 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.

[0039] 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.

[0040] 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 c -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.

[0041] 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).

[0042] 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 bemoved 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 realized with 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.

[0043] 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.

[0044] 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.

[0045] 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.

[0046] 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 electronic device, 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.

[0047] 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.

[0048] 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.

[0049] 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 therealistic 3 -dimensional intensity distribution in the resist stack by a 3 -dimensional aerial (and resist) image.

[0050] 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.).

[0051] 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 the simulation 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.

[0052] 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.

[0053] The following paragraphs describe a system and a method for predicting a mask pattern representation 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 file, 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, sub-resolution assist features (SRAF), curvilinear patterns, Manhattan patterns, etc. Further, a representation of a defective mask pattern (e.g., a mask pattern representation that has defects) may be generated using defects information gathered from wafer defects, an OPC verification process, mask inspection, metrology process, etc., and may include one or more of a mask image, a mask contour, mask polygons (polygonised mask contours), CTM, CTM+, etc.

[0054] 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 reverseprocess, 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.

[0055] 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.

[0056] 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 5, 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.

[0057] 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, anyinconsistency 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 of the mask prediction model 450 in predicting a mask image is significantly improved by implementing the mask prediction model 450 using a diffusion model.

[0058] 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 such as an aerial image, or noisy versions of the target pattern, aerial image, optical or forward simulation or any other simulation of the target pattern. 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.

[0059] In some embodiments, the constraint 412 may be a boundary constraint that constraints the mask prediction model 450 in predicting mask images such that a predicted mask image and a reference mask image match in a boundary region (e.g., additional details are described at least with reference to Figure 6 below). In some embodiments, the constraint 412 may be defect-aware constraint that causes the mask prediction model 450 to predict mask image by avoiding known defects (e.g., additional details are described at least with reference to Figures 7 and 8 below). 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 image to a particular portion of the mask image (e.g., additional details are described at least with reference to Figures 7 and 8 below).

[0060] Figure 5 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 504), which is used as guidance data, and a representation of a set of ground truth mask pattern, such as mask image 502, corresponding to the target image 504. The ground truth mask image 502 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 502 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 image.

[0061] The training process may include two sub processes - (i) a forward process, noise addition process or a diffusion process 525, and (ii) a reverse process or denoising process 550, as illustrated in Figure 5. 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 525, a forward diffusion component 451 of the mask prediction model 450 starts with ground truth mask image 502 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 506a, 506b- 506n) to result in a random noise image (e.g., image 506n). 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.

[0062] In the denoising process 550, a reverse diffusion component 452 of the mask prediction model 450 reverses the noise-adding process by starting from the random noise image (e.g., image 506n) and gradually removing the noise, step by step, creating a sequence of less noisy images (e.g., images 516a, 516b-516n) until it generates a predicted mask image 516n, which is a reconstructed version of the ground truth mask image 502. The reverse diffusion component 452 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. At each step, a loss that is indicative of a difference between the predicted mask image (e.g., mask image 516n) in the corresponding step and the ground truth mask image 502 may be determined. Further, a gradient of the loss function 540 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 540. After the denoising process is executedat a particular time step, the loss function 540 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 540 is computed. The model parameters (e.g., weights and biases) are adjusted using the gradient to optimize (e.g., reduce or minimize) the loss function 540. 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 540 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 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 540 may be a sum of the loss in all the steps, and a gradient of the loss function 540 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 540.

[0063] Note that the target image 504 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 504. 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 504 is input as guidance data to the mask prediction model 450, the denoising of the noise image is conditioned on the target image 504 to cause the generated mask image 516n to be similar to a ground-truth mask image 502 corresponding to the target image 504. That is, the conditioned denoising process learns a relationship between the ground truth mask image 502 and the corresponding guidance target image 504, 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 504 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 540 associated with the mask prediction model 450 is used to guide the denoising process to generate the mask image 516n such that it matches the ground-truth mask image 502. 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 516n towards the ground-truth mask image 502, the denoising process learns the model parameters to predict a mask image for the corresponding guidance target image.

[0064] In some embodiments, the use of gradients, especially in guided diffusion, allows for fine-tuning the generative process to meet the given condition. Additionally, the mask prediction model 450 may be subject to a constraint 512 (e.g., similar to the constraint 412 described at least with reference to Figure 4 above) during the training.

[0065] Figure 6 illustrates prediction of a mask pattern representation by a mask prediction model using a boundary constraint, consistent with various embodiments. When two mask patches (e.g., two portions of the mask pattern representations) are combined (e.g., “stitched”), a first portion of a mask feature from a first patch and a second portion of the mask feature from a reference patch along a boundary of the two patches may differ, or not match (e.g., the portions may be misaligned, disconnected, or not continuous across the boundary). The boundary may correspond to the border region of the two adjacent or neighboring patches of the mask image, or is a region of the mask image separating two adjacent patches. In some embodiments, the mask prediction model 450 may be subjected to a “boundary” constraint during the inference stage, which causes the mask prediction model 450 to generate a mask image such that feature portions in a predicted mask image (e.g., “a first patch”) and feature portions in a reference mask pattern (e.g., “reference patch”) match in the boundary. The two patches may be stitched together seamlessly as the mask features near the boundary from each of the patches match with each other (e.g., are continuous, or connected to each other, across the boundary).

[0066] Consider that the mask prediction model 450 predicts a mask pattern 602 as multiple portions or “patches,” such as a first patch 604 and a second patch 606. A first stitched image 612 shows a result of stitching the patches that are generated by the mask prediction model 450 without any boundary constraint. It can be seen in the first stitched image 612 that the mask features along the boundary 610 do not match (e.g., are misaligned, discontinuous or disconnected across the boundary). For example, the first portion 636a of the mask feature from the first patch 604 and a second portion 636b of the mask feature from the second patch 616 do not match (e.g., are disconnected or discontinuous across the boundary 610).

[0067] A second stitched image 622 shows a result of stitching the patches that are generated by the mask prediction model 450 with a constraint 412 such as a boundary constraint. It can be seen in the second stitched image 622 that the mask features from each of the patches along the boundary 610 match (e.g., are continuous or connected across the boundary region). For example, the first portion 636a of a mask feature from the first patch 604 and the second portion 636b of the mask feature from a second patch 626 match with each other (e.g., are continuous, or connected to each other across the boundary 610).

[0068] In some embodiments, by constraining the mask prediction model 450 with a boundary constraint, the mask prediction model 450 predicts a mask image such that mask features of the predicted mask image (e.g., second patch 626) match with mask features of a reference mask image (e.g., first patch 604) near the boundary (e.g., boundary 610). That is, when a first image having thepredicted mask image (e.g., second patch 626) is stitched with another image having a reference mask image (e.g., first patch 604), the mask features from the predicted mask image and the reference mask image match (e.g., are continuous or connected along the boundary).

[0069] In some embodiments, the boundary constraint may be defined using pixel values. For example, the boundary constraint may indicate that pixel values in a first region of the predicted mask image (e.g., second patch 626) match with pixel values in a second region of a reference mask image (e.g., first patch 604), where the first region and the second region are areas adjacent to the boundary 610. In some embodiments, the pixel values are considered to match when their similarity is within a specified range. When the mask prediction model 450 is executed with the boundary constraint, the denoising process removes the noise from the noise image (e.g., noise input 402 in Figure 4) to generate the mask image (e.g., second patch 626) such that pixel values in the first region of the predicted mask image match with pixel values with the second region of the reference mask image (e.g., first patch 604) in each iteration of the denoising process. For example, the pixel value of the second portion 636b of the feature near the boundary 610 from the second patch 626 may be interpolated with the first portion 636a of the feature near the boundary form the first patch 604 so that the feature portions match across the boundary 610. In some embodiments, a combination of the interpolation result and the gradient computed during the generation of the second patch 626 may be used to predict the second feature portion 636b near the boundary 610. The feature portions of the second patch 626 at the boundary 610 are forced to follow the feature portions in the first patch 604 at the patch boundary 610. In some embodiments, when the mask prediction model 450 is subjected to a boundary constraint, the reference mask image (e.g., first patch 604) may be provided as an input to the generation process so that the mask prediction model 450 may use the reference mask image as a constraint to predict the mask image such that the mask features of the predicted mask image match with the mask features of the reference mask image along the boundary.

[0070] In some embodiments, by using the boundary constraint in the prediction of a mask image, the mask prediction model 450 advantageously facilitates pattern stitching with minimal to no post processing of the mask images, thereby reducing any time and computing resources that may be consumed in post processing of the mask image.

[0071] Figures 7 and 8 illustrate prediction of a mask pattern representation by a mask prediction model using a defect-aware constraint, consistent with various embodiments. In some embodiments, the mask prediction model 450 may be subjected to a “defect-aware” constraint that causes the mask prediction model 450 to predict mask images by avoiding known defects (e.g., defects that are detected in defective mask pattern representations). During the inference stage, for predicting a mask image for a given target image from a given noise image by a mask prediction model 450, a defective mask image (e.g., a mask pattern representation with defects) is input as a constraint to the mask prediction model 450. The mask prediction model 450 may use information from the defective mask image to cause a prediction of a mask image to avoid those one or more defects.

[0072] In some embodiments, a defective mask image may be generated using information gathered from wafer defects, an OPC verification process, mask inspection, metrology process or other such processes. In some embodiments, a defective mask image, such as a first defective mask image 702, may be generated using another mask prediction model, referred to as a “defective-mask” prediction model, which is also implemented using a diffusion model. The defective-mask prediction model may be trained to generate examples of defective mask images (e.g., mask images with defects such as the first defective mask image 702). In some embodiments, the defective-mask prediction model may also be implemented using a diffusion model, and trained using a set of defective-mask images as ground truth to generate defective mask images for any given target image from a noise image (e.g., in a way similar to training the mask prediction model to generate mask images as described at least with reference to Figures 4 and 5). The ground truth defective mask images may be obtained in a number of ways, for example, using known mask pattern generation techniques (e.g., using information gathered from wafer defects, an OPC verification process, mask inspection, metrology process or other such processes). Once trained, the defective-mask prediction model may be used to generate a defective mask image for any given target image. For example, the defectivemask prediction model may be executed with a specified target image as guidance data to obtain an output of the first defective mask image 702 corresponding to the specified target image. The first defective mask image 702 includes a number of defects that, when printed on a substrate, the resulting pattern on the substrate can cause a device failure. For example, the first defective mask image 702 shows a first defect 704, such as bridging, which may occur when two mask features that are not supposed to be connected are connected, which may result in a resist being removed from a particular location where it is supposed to remain. The first defective mask image 702 also shows a second defect 706, such as pinching, at various locations. In some embodiments, pinching may occur when mask features that are supposed to be connected are disconnected, which may result in a resist remaining in a particular location where it is supposed to be removed.

[0073] The first predicted mask image 802 is a mask image predicted by the mask prediction model 450 for the specified target image without any defect-aware constraint. As shown in Figure 8, the first predicted mask image 802 includes defects at various locations - a first location 806a (e.g., bridging) and a third location 806c (e.g., pinching) in the mask image.

[0074] In some embodiments, by subjecting the mask prediction model 450 to a defect-aware constraint, the known defects (e.g., defects such as those detected in the first defective mask image 702) may be avoided in prediction of the first predicted mask image 802. For the defect-aware prediction of the first predicted mask image 802, the first defective mask image 702 may be provided as an input to the mask prediction model 450 as part of the defect-aware constraint. In some embodiments, the mask prediction model 450 causes the denoising process to generate a mask image such that the one or more defects detected in the defective mask image are avoided during the generation of the mask image. For example, the defect-aware constraint may cause the maskprediction model 450 to use (a) a first gradient associated with a loss function of the mask prediction model 450 computed in the generation of the first predicted mask image 802 and (b) a second gradient associated with a loss function of the defective-mask prediction model computed in the generation of first defective mask image 702 to avoid the defects detected in the first defective mask image 702 in generation of the first predicted mask image 802. In some embodiments, a difference between the first gradient from the mask prediction model 450 and the second gradient from the defective-mask prediction model may be used in avoiding the defects. For example, a weight may be associated with the second gradient to control a direction of the prediction of the mask pattern to either towards or away from the first defective mask image 702. In some embodiments, by adjusting a weight associated with the second gradient the prediction of the first predicted mask image 802 may be adjusted (e.g., control a direction of the prediction) either towards or away from the first defective mask image 702. For example, by increasing a weight associated with the second gradient, the prediction of the first predicted mask image 802 can be directed away from the first defective mask image 702, causing a second predicted mask image 812 generated to be less similar to the first defective mask image 702, thereby having none or fewer defects from the first defective mask image 702. As illustrated in the second predicted mask image 812, the defects are removed at locations 806a and 806c. In another example, by decreasing a weight associated with the second gradient, the prediction of the first predicted mask image 802 can be directed towards the first defective mask image 702, causing a third predicted mask image 822 to be more similar to the first defective mask image 702, thereby having more defects from the first defective mask image 702. For example, by decreasing the weight associated with the second gradient, not only the defects at the first and third locations 806a and 806c in the first predicted mask image 802 (e.g., defects arising without defect- aware constraint) are retained, but also new defects may be introduced in the generated mask image, as illustrated in a third predicted mask image 822 at a second location 806b and a fourth location 806d which were free from defects in the first predicted mask image 802. Accordingly, the mask prediction model 450 may control the weight appropriately so that not only defects detected from the first defective mask image 702 are avoided, but also no new defects are introduced in prediction of the mask image. Thus, by subjecting the mask prediction model 450 to a “defect-aware” constraint, the mask prediction model 450 can be configured to predict mask images by avoiding defects that are detected from a defective mask image that is input as a constraint.

[0075] In some embodiments, by constraining the mask prediction model 450 to predict mask images by avoiding detected defects, not only accuracy and reliability of the mask prediction model 450 in predicting the mask images is improved, also the time and computing resources that may otherwise be consumed in any post processing (e.g., to remove the defects or other types of repairing the mask image) the mask image is reduced.

[0076] While the above paragraphs discussing using two separate diffusion models - a mask prediction model 450 to generate a “non-defective” or “normal” mask image (e.g., the first predictedmask image 802) and a defective-mask prediction model to generate a defective mask image (e.g., the first defective mask image 702), in some embodiments, a single diffusion model may be configured to predict both types of mask images. In some embodiments, a control parameter may be used with the mask prediction model 450 to indicate what type of mask image (e.g., normal mask image or a defective mask image) should be generated. For example, by setting the control parameter to a first value (e.g., “1”), the mask prediction model 450 can be configured to generate normal mask patterns after a specified number of denoising steps, and by setting the control parameter to a second value (e.g., “0”) the mask prediction model 450 can be configured to generate defective mask images after the specified number of denoising steps. In some embodiments, while the entire number of denoising steps may not have to be actually executed to generate any defective patterns, during each step of the denoising process, the gradient from the mask prediction model 450 (from the normal mask image generation stage) and the gradient from the mask prediction model 450 (from the defective mask image generation stage) may be used to generate the normal mask image away from (e.g., less similar to) the defective mask image.

[0077] While the above paragraphs discuss generation or prediction of new mask image using the defect-aware constraint, the defect-aware constraint may also be used in repairing a mask image (e.g., removing defects from, or modifying features, in a mask image). In some embodiments, a noise image may be generated based on the first predicted mask image 802 (e.g., a noisy version of the first predicted mask image 802) and provided as input to the mask prediction model 450, and the specified target image as the guidance data. If the repair is for removing the defects, a defect-aware constraint including the first defective mask image 702 may also be provided as input to the mask prediction model 450, which may serve as an example for the defects to be avoided. The mask prediction model 450 executes the denoising process to predict a mask image (e.g., the second predicted mask image 812 or the third predicted mask image 822) by removing one or more of the known defects.

[0078] Further, in some embodiments, the repairing of a mask image may be restricted to a particular area of the mask image. For example, the mask prediction model 450 may be configured to repair or modify only a specified area 804 of the first predicted mask image 802 by executing the mask prediction model 450 with a “location-aware” constraint. With the location-aware constraint, the mask prediction model 450 restricts the prediction, modification, or repair of the first predicted mask image 802 to the specified area 804 and does not consider the portion outside of the specified area 804 (e.g., for repair or modification), thereby reducing time and computing resources consumed in repairing or modifying the first predicted mask image 802. The location-aware constraint may be defined using location coordinates of an area in which the mask image has to be repaired or modified. For example, the location-aware constraint may be defined using location coordinates of four comers of the square representing the specified area 804.

[0079] The mask prediction model 450 may be subjected to various such constraints in predicting the mask image. Another example of a constraint includes a frequency constraint, which causes themask prediction model to remove a set of frequency components from the images (e.g., noise input 402 or noise images 406a-406f) during the denoising process to generate the mask image 408. The frequency constraint may be defined using at least one of a high-pass filter, low-pass filter, or a bandpass filter.

[0080] Figure 9 is a flow diagram of a method for generating a mask pattern using a diffusion model, consistent with various embodiments. The method of Figure 9 is described at least with reference to Figure 4 above.

[0081] At process P902, a noise image and a target image representative of a target pattern is provided as an input to a mask prediction model that is trained to generate a mask image (e.g., a representation of a mask pattern). For example, a noise input 402 (e.g., image with random noise, a transformation of the target pattern such as an aerial image, or noisy versions of the target pattern, aerial image, optical or forward simulation or any other simulation of the target pattern) and a target image 404 is input to the mask prediction model 450. The mask prediction model 450 may be implemented using a diffusion model. The mask prediction model 450 uses the target image 404 as guidance data for generating the corresponding 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 images, and (b) a set of target images to which the set of ground truth mask image correspond (e.g., as described at least with reference to Figure 5 above).

[0082] At process P904, the mask prediction model is executed to generate a mask image representative of a mask pattern corresponding to the target image. The mask prediction model predicts or generates the mask image by removing the noise (referred to as “denoising” process) from the noisy data iteratively using the target image. For example, the mask prediction model 450 predicts a mask image 408 by removing the noise from the noise input 402 iteratively using the target image 404. This may involve estimating both the mean and variance of the noise distribution at each step. As described at least with reference to Figure 4, the mask prediction model 450 constructs the mask image 408 over “7” iterations or steps, 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 pattern 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. The target image 404 may be used as a guidance in every step of the denoising process. 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 to generate a mask image corresponding to the target image. In some embodiments, thenumber 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).

[0083] 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.

[0084] 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.

[0085] 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.

[0086] 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 process steps 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 alternativeembodiment, 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.

[0087] 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. Nonvolatile 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.

[0088] 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.

[0089] 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.

[0090] 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 network122 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.

[0091] 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.

[0092] Embodiments of the present disclosure can be further described by the following clauses.1. A method of generating a mask pattern for a lithography process, the method comprising: inputting a noise image and a target pattern representation to a diffusion model, wherein the target pattern representation is input as guidance data to the diffusion model, and wherein the diffusion model is trained using representations of a set of target patterns and a representations of a corresponding set of mask patterns; and generating a mask pattern representation by executing the diffusion model, wherein the mask pattern representation corresponds to the target pattern representation.2. 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) images, or levelset CTM images (CTM+).3. The method of clause 1, wherein the generating the mask pattern representation includes: denoising the noise image using the target pattern representation iteratively to generate a mask image.4. The method of clause 3, wherein denoising the noise image using the target pattern representation includes: using a gradient associated with a loss function of the diffusion model to generate the mask image corresponding to the target pattern representation.5. The method of clause 1, wherein inputting the noise image includes: applying a constraint in generating the noise image.6. The method of clause 5, wherein applying the constraint includes:applying a symmetry constraint that is indicative of a symmetry of the target pattern representation, and generating the noise image based on the symmetry constraint to distribute noise in the noise image based on the symmetry of the target pattern representation.7. The method of clause 5, wherein applying the constraint includes: adding noise to the target pattern representation to generate a noisy target image, and inputting the noisy target image as the noise image.8. The method of clause 5, wherein applying the constraint includes: generating a transformation of the target pattern representation, and inputting the transformation of the target pattern representation as the noise image.9. The method of clause 1, wherein generating the mask pattern representation includes: executing the diffusion model with a constraint to generate the mask pattern representation that satisfies the constraint.10. The method of clause 9, wherein the constraint includes a boundary constraint, wherein the boundary constraint indicates that a first portion of a mask feature from the mask pattern representation matches a second portion of the mask feature from a reference mask pattern representation near a specified boundary region.11. The method of clause 9, wherein executing the diffusion model with the constraint includes: obtaining a reference mask pattern representation; applying a boundary constraint to the diffusion model, wherein the boundary constraint indicates that pixel values in a first region of the mask pattern representation match with pixel values in a second region of the reference mask pattern representation, wherein the first region and the second region are adjacent to a specified boundary region; and executing the diffusion model to generate the mask pattern representation, wherein the executing includes: denoising the noise image iteratively to generate the mask pattern representation, wherein the boundary constraint causes pixel values in the first region of the mask pattern representation and the second region of the reference mask pattern representation to match in each iteration.12. The method of clause 11, wherein denoising the noise image iteratively includes: obtaining, for a given time step of the denoising process, the mask pattern representation and the corresponding reference mask pattern representation ,and interpolating pixel values of a first feature portion of a feature from the first region with pixel values of a second feature portion of the feature from the second region to cause the first feature portion and the second feature portion to match.13. The method of clause 11 further comprising:stitching the mask pattern representation with the reference mask pattern representation at the specified boundary region to generate a combined mask pattern representation, wherein the mask pattern representation includes a first portion of the combined mask pattern representation, and wherein the reference mask pattern representation includes a second portion of the combined mask pattern representation.14. The method of clause 9, wherein the constraint includes a symmetry constraint that is indicative of a symmetry of the target pattern representation, and wherein the executing includes: adjusting a gradient of the diffusion model in the generation of the mask pattern representation to satisfy the symmetry of the target pattern representation.15. The method of clause 9, wherein the constraint includes a frequency constraint that causes a set of frequency components to be removed from the noise image during generation of the mask pattern representation by the diffusion model.16. The method of clause 15, wherein the frequency constraint is specified using at least one of a high-pass filter, a low-pass filter, or a band-pass filter.17. The method of clause 1 further comprising: training the diffusion model by using training data that includes representation of a set of target patterns as guidance data, wherein the diffusion model is configured to generate a predicted mask pattern for an input guidance target pattern representation.18. The method of clause 17, wherein the training includes: executing a diffusion process that adds noise to a ground truth mask pattern corresponding to the input guidance target pattern representation iteratively to generate a first noise image; and executing a denoising process that iteratively removes the noise from the first noise image using the input guidance target pattern representation to generate the predicted mask pattern representation.19. The method of clause 1 further comprising: modifying a portion of the mask pattern representation by executing the diffusion model.20. The method of clause 19, wherein modifying the portion of the mask pattern representation includes: specifying location coordinates of a specified portion of the mask pattern representation to be adjusted as a constraint; and executing the diffusion model with the constraint, wherein the constraint restricts modifying of the mask pattern representation to the specified portion of the mask pattern representation.21 . The method of clause 1, wherein generating the mask pattern representation includes: obtaining a defective mask pattern representation from a second diffusion model that is trained to generate a representation of a set of mask patterns, wherein the defective mask pattern representation includes a defect; andgenerating the mask pattern representation based on the defective mask pattern representation to avoid the defect.22. The method of clause 21, wherein generating the mask pattern representation based on the defective mask pattern representation includes: obtaining a first gradient from the diffusion model used in generating the mask pattern representation; obtaining a second gradient from the second diffusion model used in generating the defective mask pattern representation; and generating the mask pattern representation based on the first gradient and the second gradient.23. The method of clause 22, wherein generating the mask pattern representation based on the first gradient and the second gradient includes: generating the mask pattern representation based on a difference between the first gradient and the second gradient.24. The method of clause 22, wherein generating the mask pattern representation based on the first gradient and the second gradient includes: adjusting a weight associated with the second gradient to vary the generation of the mask pattern representation.25. The method of clause 24, wherein adjusting the weight includes: increasing the weight to generate the mask pattern representation with a decreased similarity with the defective mask pattern representation.26. The method of clause 24, wherein adjusting the weight includes: decreasing the weight to generate the mask pattern representation with an increased similarity with the defective mask pattern representation.27. The method of clause 21, wherein generating the mask pattern representation based on the defective mask pattern representation includes: modifying a portion of the mask pattern representation to avoid the defect.28. The method of clause 21 further comprising: training the second diffusion model by using training data that includes a representation of a set of target patterns as guidance data, wherein the second diffusion model is configured to generate a predicted mask pattern representation for an input guidance target pattern representation, wherein the predicted mask pattern representation includes a defect.29. A method of generating a mask pattern representation in a lithography process, the method comprising: inputting a noise image and a target pattern representation to a diffusion model, wherein the target pattern representation is input as guidance data to the diffusion model, and wherein the diffusion model is trained using a representation of a set of target patterns and a representation of a corresponding set of mask patterns;obtaining a defective mask pattern representation from a second diffusion model that is trained to generate a representation of a set of defective mask patterns, wherein the defective mask pattern representation includes a defect; inputting the defective mask pattern representation to the diffusion model; and generating a mask pattern representation by executing the diffusion model, wherein the mask pattern representation corresponds to the target pattern representation, wherein the mask pattern representation is generated based on the defective mask pattern representation to avoid the defect.30. The method of clause 29, wherein generating the mask pattern representation includes: obtaining a first gradient from the diffusion model used in generating the mask pattern representation; obtaining a second gradient from the second diffusion model used in generating the defective mask pattern representation; and generating the mask pattern representation based on the first gradient and the second gradient.31. The method of clause 30, wherein generating the mask pattern representation based on the first gradient and the second gradient includes: generating the mask pattern representation based on a difference between the first gradient and the second gradient.32. The method of clause 30, wherein generating the mask pattern representation based on the first gradient and the second gradient includes: adjusting a weight associated with the second gradient to vary the generation of the mask pattern representation.33. The method of clause 32, wherein adjusting the weight includes: increasing the weight to generate the mask pattern representation with a decreased similarity with the defective mask pattern representation.34. The method of clause 32, wherein adjusting the weight includes: decreasing the weight to generate the mask pattern representation with an increased similarity with the defective mask pattern representation.35. The method of clause 29, wherein generating the mask pattern representation includes: modifying a portion of the mask pattern representation to avoid the defect.36. 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.37. 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.

[0093] 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.

[0094] 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.

[0095] 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.

[0096] 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 or hardware 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.

[0097] 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.

[0098] 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.

[0099] 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.

[0100] 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 departing from 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.

[0101] 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 includesA 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.

[0102] 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 generating a mask pattern for a lithography process, the method comprising: inputting a noise image and a target pattern representation to a diffusion model, wherein the target pattern representation is input as guidance data to the diffusion model, and wherein the diffusion model is trained using representations of a set of target patterns and a representations of a corresponding set of mask patterns; and generating a mask pattern representation by executing the diffusion model, wherein the mask pattern representation corresponds to the target pattern representation.

2. The method of claim 1, wherein the generating the mask pattern representation includes: denoising the noise image using the target pattern representation iteratively to generate a mask image, wherein denoising the noise image using the target pattern representation includes: using a gradient associated with a loss function of the diffusion model to generate the mask image corresponding to the target pattern representation.

3. The method of claim 1, wherein inputting the noise image includes: applying a constraint in generating the noise image, and wherein applying the constraint includes: applying a symmetry constraint that is indicative of a symmetry of the target pattern representation, and generating the noise image based on the symmetry constraint to distribute noise in the noise image based on the symmetry of the target pattern representation.

4. The method of claim 1, wherein the noise image is generated by applying a constraint, and wherein applying the constraint includes: adding noise to the target pattern representation to generate a noisy target image, and inputting the noisy target image as the noise image.

5. The method of claim 1, wherein the noise image is generated by applying a constraint, and wherein applying the constraint includes: generating a transformation of the target pattern representation, and inputting the transformation of the target pattern representation as the noise image.

6. The method of claim 1, wherein generating the mask pattern representation includes: executing the diffusion model with a constraint to generate the mask pattern representation that satisfies the constraint; wherein the constraint includes a boundary constraint, wherein the boundary constraint indicates that a first portion of a mask feature from the mask pattern representation matches a second portion of the mask feature from a reference mask pattern representation near a specified boundary region.

7. The method of claim 1, wherein executing the diffusion model includes: obtaining a reference mask pattern representation; applying a boundary constraint to the diffusion model, wherein the boundary constraint indicates that pixel values in a first region of the mask pattern representation match with pixel values in a second region of the reference mask pattern representation, wherein the first region and the second region are adjacent to a specified boundary region; and executing the diffusion model to generate the mask pattern representation, wherein the executing includes: denoising the noise image iteratively to generate the mask pattern representation, wherein the boundary constraint causes pixel values in the first region of the mask pattern representation and the second region of the reference mask pattern representation to match in each iteration.

8. The method of claim 7, wherein denoising the noise image iteratively includes: obtaining, for a given time step of the denoising process, the mask pattern representation and the corresponding reference mask pattern representation ,and interpolating pixel values of a first feature portion of a feature from the first region with pixel values of a second feature portion of the feature from the second region to cause the first feature portion and the second feature portion to match.

9. The method of claim 7 further comprising: stitching the mask pattern representation with the reference mask pattern representation at the specified boundary region to generate a combined mask pattern representation, wherein the mask pattern representation includes a first portion of the combined mask pattern representation, and wherein the reference mask pattern representation includes a second portion of the combined mask pattern representation.

10. The method of claim 1, wherein the executing a diffusion model is performed by applying a constraint, and wherein the constraint includes a symmetry constraint that is indicative of a symmetry of the target pattern representation, and wherein the executing includes:adjusting a gradient of the diffusion model in the generation of the mask pattern representation to satisfy the symmetry of the target pattern representation.

11. The method of claim 1, wherein the executing a diffusion model is performed by applying a constraint, and wherein the constraint includes a frequency constraint that causes a set of frequency components to be removed from the noise image during generation of the mask pattern representation by the diffusion model.

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

13. The method of claim 12, wherein the training includes: executing a diffusion process that adds noise to a ground truth mask pattern corresponding to the input guidance target pattern representation iteratively to generate a first noise image; and executing a denoising process that iteratively removes the noise from the first noise image using the input guidance target pattern representation to generate the predicted mask pattern representation.

14. 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) image, or CTM+ image, and further comprising: modifying a portion of the mask pattern representation by executing the diffusion model.

15. The method of claim 14, wherein modifying the portion of the mask pattern representation includes: specifying location coordinates of a specified portion of the mask pattern representation to be adjusted as a constraint; and executing the diffusion model with the constraint, wherein the constraint restricts modifying of the mask pattern representation to the specified portion of the mask pattern representation.

Images