Using physical process window trend to constrain nominal condition machine learning model behavior

Abstract

A method for training a machine learning model associated with a lithography process is disclosed. More particularly, a method for training a machine learning model associated with a lithography process to generate process window trend predictions for an imaging characteristic with improved accuracy is disclosed. The disclosed method provides a universal machine learning model that can group training data based on an imaging characteristic variation across a varied lithography process condition and use the grouped training data to train the model and generate a predicted variation trend. A loss function may be used to evaluate and minimize an overlapping area between the predicted variation trend and the reference variation trend, a distance between the predicted variation trend and the reference variation trend, or a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.

Description

2025P00004WQ 01 1USING PHYSICAL PROCESS WINDOW TREND TO CONSTRAIN NOMINAL CONDITION MACHINE LEARNING MODEL BEHAVIORCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of PCT application PCT / CN2025 / 075607 which was filed on January 29, 2025, and which is incorporated herein in its entirety by its reference.FIELD

[0002] The embodiments provided herein disclose a method of training a machine learning model associated with a lithography process to improve prediction accuracy.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). 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 may potentially result in problems with the final IC and may cause device failure. Therefore, in manufacturing processes of ICs, unfinished or finished circuit components are inspected to ensure that they are manufactured according to design and are free of defects. Inspection systems utilizing optical microscopes or charged particle (e.g., electron) beam microscopes, such as a scanning electron microscope (SEM) can be employed. As the physical sizes of IC components continue to shrink, accuracy and yield in IC inspection become increasingly important. High process yield and high wafer throughput can be impacted by the presence of defects, especially if operator intervention is required for reviewing the defects. Therefore, modeling lithographic conditions that may accurately predict the formation of defects in ICs before fabrication occurs is desired.SUMMARY

[0004] The embodiments provided herein disclose a method of training a machine learning model associated with a lithography process and predicting an imaging characteristic trend over varied lithography process conditions.

[0005] Some embodiments of the present disclosure provide a method for training a machine learning model associated with a lithography process. The method comprises obtaining training data from a plurality of varying process conditions, grouping the training data, wherein a group of the training data comprises data of an imaging characteristic obtained from the plurality of varying process conditions, and training the machine learning model to generate a predicted variation trend of the imaging characteristic with the plurality of varying process conditions, wherein the training2025P00004WQ 01 2comprises comparing the predicted variation trend to a reference variation trend of the imaging characteristic with the plurality of varying process conditions.

[0006] In some embodiments, a non-transitory computer readable medium comprising a set of instructions that is executable by one or more processors of a computing device to cause the computing device to perform operations for training a machine learning model associated with a lithography process is provided. The operation comprise obtaining training data from a plurality of varying process conditions, grouping the training data, wherein a group of the training data comprises data of an imaging characteristic obtained from the plurality of varying process conditions, and training the machine learning model to generate a predicted variation trend of the imaging characteristic with the plurality of varying process conditions, wherein the training comprises comparing the predicted variation trend to a reference variation trend of the imaging characteristic with the plurality of varying process conditions.

[0007] Other advantages of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of the present disclosure.BRIEF DESCRIPTION OF FIGURES

[0008] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0009] FIG. 1 illustrates an example lithographic projection assembly to fabricate an IC, consistent with some embodiments of the present disclosure.

[0010] FIG. 2 illustrates an example flowchart for simulating lithography in a lithographic projection apparatus, consistent with some embodiments of the present disclosure.

[0011] FIG. 3 illustrates an example flowchart for source and mask optimization of a patterning process, consistent with some embodiments of the present disclosure.

[0012] FIG. 4 illustrates an example artificial intelligence architecture, consistent with some embodiments of the present disclosure.

[0013] FIG. 5 illustrates an example flowchart for training a model associated with a lithography process.

[0014] FIG. 6 illustrates an example flowchart for obtaining data to train a model associated with a lithography process, consistent with some embodiments of the present disclosure.

[0015] FIG. 7 illustrates an example diagram for grouping training data to train a model associated with a lithography process, consistent with some embodiments of the present disclosure.

[0016] FIG. 8 illustrates example grouped training data to use for training a model associated with a lithography process, consistent with embodiments of the present disclosure.

[0017] FIG. 9 illustrates an example predicted variation trend compared to a reference variation trend, consistent with some embodiments of the present disclosure.2025P00004WQ 01 3

[0018] FIG. 10 illustrates and example flowchart for training a model associated with a lithography process to predict a trend for an imaging characteristic with a varied lithography process condition, consistent with some embodiments of the present disclosure.

[0019] FIG. 11 illustrates an example block diagram of a system for obtaining training data or training a model associated with a lithography process, consistent with some embodiments of the present disclosure.DETAILED DESCRIPTION

[0020] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations consistent with the disclosure. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the disclosure as recited in the appended claims.

[0021] The enhanced computing power of electronic devices, while reducing the physical size of the devices, can be accomplished by significantly increasing the packing density of circuit components such as transistors, capacitors, diodes, etc. on an IC chip. Semiconductor IC manufacturing is a complex and time-consuming process, with hundreds of individual steps. Errors in even one step have the potential to dramatically affect the functioning of the final product. Even one “killer defect” can cause device failure. The goal of the manufacturing process is to improve the overall yield of the process.

[0022] ICs may be manufactured using lithography, which is a fabrication process involving creating complex circuit patterns drawn on a mask deposited onto a substrate. Lithography may be performed by a lithographic apparatus, which is a machine that applies a source of radiation (e.g., light or X-ray) onto a target portion of the substrate to form a desired pattern. The target portion of the substrate may be covered with a pattern device (e.g., mask) that may be either eliminated or developed after exposure to the radiation source. This process of transferring the desired pattern to the substrate is called a patterning process. The patterning process may include a patterning step to transfer a pattern from a pattern device (e.g., a mask) to the substrate. There can also be one or more related pattern processing steps, such as mask development by a development apparatus, baking of the substrate using a bake tool, etching the pattern onto the substrate using an etch apparatus, or other chemical and physical processing steps involved in fabricating a pattern onto the substrate. Variations in experimental parameters (e.g., stochastic variations, errors, or noise due to an inspection tool or pattern processing tool) can potentially limit lithography implementation for high volume manufacturing (HVM), or process yield, of ICs and introduce defects into IC structures.2025P00004WQ 01 4

[0023] In the manufacture of ICs using a lithographic apparatus, typically many lithographic patterning steps are performed, thereby forming functional features in successive layers on the substrate. A critical aspect of performance of the lithographic apparatus is therefore the ability to place the applied pattern correctly and accurately in relation to features laid down in previous layers. For this purpose, the substrate is provided with one or more sets of alignment marks. Each mark is a structure having a position that can be measured later using, for example, an electron beam inspection tool. Defects may occur in which an applied pattern structure or pattern layer is incorrectly placed in relation to a reference mark, or when the fabrication conditions are suboptimal. A reference mark or layout defines the desired structure, structure dimensions, and the distance between IC structures (such as gates, capacitors, etc.) or interconnect lines. This may ensure that the IC devices or lines do not interact with one another in an undesirable way. The structure limitations provided by the reference layouts are typically referred to as critical dimensions. A critical dimension of a circuit can be defined as the smallest width of a line or hole or the smallest space between two lines or two holes. Thus, the critical dimension determines the overall size and packing density of the designed IC. A goal in IC fabrication is to faithfully reproduce the original IC design on the substrate. If an error occurs during fabrication where the created IC design pattern does not match the reference design, this may result in a defect in the IC structure and render the IC inoperable.

[0024] As semiconductor manufacturing processes continue to advance, the dimensions of functional elements have continually been reduced while the number of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as “Moore's law.” At the current state of technology, layers of devices are manufactured using lithographic projection apparatuses that project a design layout onto a substrate using illumination from a deep-ultraviolet illumination source, creating individual functional elements having dimensions well below 100 nm, i.e., less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source). This process in which features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus are printed, is commonly known as low-ki lithography, according to the resolution formula critical dimension (CD)=kix / NA, where / . is the wavelength of radiation employed (currently in most cases 248 nm or 193 nm), NA is the numerical aperture of projection optics in the lithographic projection apparatus and ki is an empirical resolution factor. In general, the smaller ki the more difficult it becomes to reproduce a pattern on the substrate that resembles the shape and dimensions planned by a designer in order to achieve particular electrical functionality and performance. To overcome these difficulties, simulated or computational lithography models are applied to the lithographic projection apparatus, the design layout, or the patterning device. These include, for example, but not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as “optical2025P00004WQ 01 5and process correction”) in the design layout, or other methods generally defined as “resolution enhancement techniques” (RET).

[0025] In computational lithography, patterning process models related to different aspects of the patterning process such as a mask model, an optical model, a resist model, or an etch model may be employed to predict a pattern that will be printed on the substrate. The patterning process models when properly trained (e.g., using measurement data associated with a printed wafer) can produce accurate prediction of patterns dimensions output from the patterning processes. For example, a patterning process model of lithography processes may be trained based on processed wafers. In practice, faster and more accurate models may serve to improve lithography performance (e.g., yield), enhance process windows, patterning recipes, or enabled increased complexity of a design pattern.

[0026] A lithography patterning process is a complex process and not all aspects may be modeled based on physics / chemistry involved in the lithography patterning process. For example, some effects of lithography processes are well understood and can be modelled with mathematical expressions of physical terms (e.g., parameters associated with a resist process) that describe the physics / chemistry of the process. For example, an acid-base diffusion after the exposure can be modelled by a Gaussian filter on the aerial image. Additionally, some of physical terms (e.g., associated with dose, focus, bias, intensity, pupil, etc.) are associated with and tunable via tunable parameters (e.g., tunable knobs) of the lithographic apparatus, thereby enabling real-time control of the patterning process. Some physical terms may not be directly tunable via tuning knobs but may be explained by the physics / chemistry of a process (e.g., aerial image formation, resist image formation, etc.). For example, a resist model may comprise a Gaussian filter on the aerial image for modelling an acid-base diffusion in the resist after the exposure. This sigma term is generally not tunable via tunable knobs. Even so, the values of such physical terms (e.g., sigma) may be determined based on empirical equations or physics-based equations that model effects of a process (e.g., resist formation).

[0027] However, several aspects or effects of a lithography patterning process are not well understood, and thus difficult to model using physics / chemistry-based equations. Conventional modeling methods and systems train a lithography model using training data from the same process condition (e.g., nominal process conditions). Thus, a trained lithography model (e.g., a trained resist model) is specific to only one process condition (e.g., a first focus / dose condition) and may not be as accurate in predictions for other process conditions (e.g., a second focus / dose condition), and lack robustness in process window trend predictions. The trained lithography model may be suitable for use in some simulation and optimization procedures such as optical proximity correction (OPC) and lithography model calibration (EMC) application. However, using such a trained lithography model can be challenging simulation and optimization procedures which need accurate prediction results for a range of process conditions (or other conditions associated with data generation), such as source mask optimization (SMO). Existing methods to train a lithography model may overfit process window trend predictions as a result of poor pattern coverage in non-nominal conditions, and are thus not2025P00004WQ 01 6suitable for lithography optimization applications. A method that can train a lithography process model to enable process window trend prediction accuracy for applications requiring strict process window control (e.g., optimization) is thus desired.

[0028] Embodiments of the present disclosure provide a method to train a lithography patterning process model using training data from a plurality of conditions, including lithography process conditions or other conditions associated with the physical characteristics of the data, to improve model robustness and enable process window trend prediction accuracy. In some embodiments, the training data is grouped based on a variation of an imaging characteristic and a lithography process condition from the plurality of lithography process conditions. In some embodiments, the training data may be measured data or simulated data across a process window. In some embodiments, the training data may be added to existing data representing a lithography process trend. In some embodiments, the training method comprises grouping the training data based on a variation of an imaging characteristic (e.g., CD, EPE, hinge, etc.) of a pattern with a process condition across a process window. In some embodiments, the training method comprises evaluating a loss function to guide predictions from the trained machine learning model towards known physical trends (e.g., pitch, draw CD, focus, dose, or mask bias). In some embodiments, each known physical trend is indicated by a corresponding data group including data associated with a range of conditions (e.g., the focus values across a process window) in a particular physical property (e.g., CD) for a certain pattern (e.g., a ID pattern). Iteratively, the loss function may be used to evaluate a deviation of a predicted process window trend against a simulated or ground truth process window trend, and accordingly the neural network is adjusted to reduce the deviation. The trained machine learning model may then be used to predict process window variation for a lithography process and be suitable for further optimization applications (e.g., SMO or OPC). Thus, some embodiments of the present disclosure may increase throughput of IC manufacturing and confidence in predicting lithographic fabrication conditions with a goal of manufacturing defect-free ICs.

[0029] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings the same or like reference numbers refer to the same or like components or entities, and only the differences with respect to the individual embodiments are described. 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 database can include A or B, then, unless specifically stated otherwise or infeasible, the database can include A, or B, or A and B. As a second example, if it is stated that a database can include A, B, or C, then, unless specifically stated otherwise or infeasible, the database can include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0030] FIG. 1 illustrates an example lithographic projection apparatus 100. Lithographic projection apparatus 100 may include an emission source 101, which may be a charged-particle emission source, deep-ultraviolet excimer laser source or other type of source including an extreme2025P00004WQ 01 7ultraviolet (EUV) source, and emits a beam 108. Illumination optics which may include illumination optics components 102 and 103 that shape radiation from the radiation source 101; a patterning device 104; and transmission optics 105 that project an image of the patterning device pattern onto a substrate 106. An adjustable filter or aperture 107 at the pupil plane of the projection optics may restrict the range of beam angles that impinge on substrate 106, where the largest possible angle defines the numerical aperture of the projection optics NA=sin(0maxbstrate 106 where beam 108 impacts is called a target portion 109, in which the beam impacts the top layer or mask (not shown).

[0031] Illumination optics components 102 and 103 may direct and shape beam 108 via patterning device 104 onto substrate 106 and may include any optical component that may alter the wavefront of beam 108. A resist layer on substrate 106 may be exposed and a radiation intensity distribution at substrate 106 (i.e., an aerial image) may be transferred to the resist layer. Optical properties of the lithographic projection apparatus (e.g., properties of the source, the patterning device, and the projection optics) dictate this process. The resist layer may be removed and the applied pattern from beam 108 may then be applied to the substrate as discussed above.

[0032] A resist model can be used to calculate a resist image from the aerial image. The resist model is related to properties of the resist layer (e.g., effects of chemical processes that 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, or the projection optics) may 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 the source and the projection optics. Details of techniques and models that may be used to transform a design layout into various lithographic images (e.g., an aerial image or a resist image), to apply OPC using those techniques and models, and to evaluate performance 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 being hereby incorporated herein by reference in their entireties.

[0033] It may be desirable to use one or more tools to produce results that, for example, can be used to design, control, monitor, etc. the patterning process. One or more tools used in computationally controlling, designing, etc. one or more aspects of the patterning process, such as the pattern design for a patterning device (including, for example, adding sub-resolution assist features or optical proximity corrections), the illumination for the patterning device, etc., may be provided. Accordingly, in a system for computationally controlling, designing, etc. a manufacturing process involving patterning, the manufacturing system components or processes can be described by various functional modules or models. In some embodiments, one or more electronic (e.g., mathematical, parameterized, etc.) models may be provided that describe one or more steps or apparatuses of the patterning process (e.g., etching). In some embodiments, a simulation of the patterning process can be2025P00004WQ 01 8performed using one or more electronic models to simulate how the patterning process forms a patterned substrate using a pattern provided by a patterning device.

[0034] Although reference may be made in the present disclosure to ICs, it is appreciated that the present disclosure may be applicable to other possible applications or designs. For example, the present disclosure may be applied to integrated optical systems, magnetic domain memories, liquidcrystal display panels, thin-film magnetic heads, and other nanoscale structures. It is further appreciated that the terms “reticle”, “wafer”, or “die” may be used interchangeably with the terms “mask”, “substrate” or “sample”, and “target portion”, respectively.

[0035] FIG. 2 illustrates an example flowchart for simulating lithography in a lithographic projection apparatus. An illumination model 231 represents optical characteristics (including radiation intensity distribution or phase distribution) of the illumination. A projection optics model 232 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by the projection optics) of the projection optics. A design layout model 235 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by a given design layout) of a design layout, which is the representation of an arrangement of features on or formed by a patterning device. An aerial image 236 can be simulated using the illumination model 231, the projection optics model 232, and the design layout model 235. A resist image 238 can be simulated from the aerial image 236 using a resist model 237. Simulation of lithography can, for example, predict contours or CDs in the resist image.

[0036] More specifically, illumination model 231 can represent the optical characteristics of the illumination that include, but are not limited to, NA-sigma (o) settings as well as any particular illumination shape (e.g., off-axis illumination such as annular, quadrupole, dipole, etc.). The projection optics model 232 can represent the optical characteristics of the of the projection optics, including, for example, aberration, distortion, a refractive index, a physical size or dimension, etc. The design layout model 235 can also represent one or more physical properties of a physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. Optical properties associated with the lithographic projection apparatus (e.g., properties of the illumination, the patterning device, and the projection optics) dictate the aerial image. 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 (hence design layout model 235).

[0037] The resist model 237 can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent No. 8,200,468, which is hereby incorporated herein by reference in its entirety. The resist model is typically related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake or development).

[0074] One of the objectives of the full simulation is to accurately predict, for example, edge2025P00004WQ 01 9placements, aerial image intensity slopes or CDs, which can then be compared against an intended design. The intended design is generally defined as a pre-OPC design layout which can be provided in a standardized digital file format such as GDS, GDSII, OASIS, or other file formats.

[0075] From the design layout, one or more portions may be identified, which are referred to as “clips.” In some embodiments, a set of clips is extracted, which represents the complicated patterns in the design layout (typically about 50 to 1000 clips, although any number of clips may be used). It is appreciated that these patterns or clips represent small portions (e.g., circuits, cells, etc.) of the design and especially the clips represent small portions for which particular attention or verification is needed. In other words, clips may be the portions of the design layout or may be similar or have a similar behavior of portions of the design layout where critical features are identified either by experience (including clips provided by a customer), by trial and error, or by running a full-chip simulation. Clips often contain one or more test patterns or gauge patterns. An initial larger set of clips may be provided a priori by a customer based on known critical feature areas in a design layout that require particular image optimization. Alternatively, in some embodiments, the initial larger set of clips may be extracted from the entire design layout by using an automated (such as, machine vision) or manual algorithm that identifies the critical feature areas.

[0038] For example, the simulation and modeling can be used to configure one or more features of the patterning device pattern (e.g., performing optical proximity correction), one or more features of the illumination (e.g., changing one or more characteristics of a spatial / angular intensity distribution of the illumination, such as change a shape), or one or more features of the projection optics (e.g., numerical aperture, etc.). Such a configuration can be generally referred to as, respectively, mask optimization, source optimization, and projection optimization. Such optimization can be performed on their own or combined in different combinations. One such example is sourcemask optimization (SMO), which involves the configuring of one or more features of the patterning device pattern together with one or more features of the illumination. The optimization techniques may focus on one or more of the clips. The optimizations may use the machine learning model described herein to predict values of various parameters (including images, etc.).

[0039] Similar modelling techniques may be applied for optimizing an etching process, for example, or other processes. In some embodiments, illumination model 231, projection optics model 232, design layout model 235, resist model 237, or other models may be used in conjunction with an etch model, for example. For example, output from an after-development inspection (ADI) model (e.g., included as some or all of design layout model 235, resist model 237, or other models) may be used to determine an ADI contour, which may be provided to an effective etch bias (EEB) model to generate a predicted after etch inspection (AEI) contour.

[0040] In some embodiments, an optimization process of a system may be represented as a cost function. The optimization process may comprise finding a set of parameters (design variables, process variables, etc.) of the system that minimizes the cost function. The cost function can have any2025P00004WQ 01 10suitable form depending on the goal of the optimization. For example, the cost function can be weighted root mean square (RMS) of deviations of certain characteristics (evaluation points) of the system with respect to the intended values (e.g., ideal values) of these characteristics. The cost function can also be the maximum of these deviations (e.g., worst deviation). The term “evaluation points” should be interpreted broadly to include any characteristics of the system or fabrication method. The design or process variables of the system can be confined to finite ranges or be interdependent due to practicalities of implementations of the system or method. In the case of a lithographic projection apparatus, the constraints are often associated with physical properties and characteristics of the hardware such as tunable ranges, or patterning device manufacturability design rules. The evaluation points can include physical points on a resist image on a substrate, as well as non-physical characteristics such as one or more etching parameters, dose and focus, etc., for example.

[0041] In some embodiments, illumination model 231, projection optics model 232, design layout model 235, resist model 237, an etch model, or other models associated with or included in an integrated circuit manufacturing process may be an empirical or other simulation model that performs at least some of the operations of the method described herein. The empirical model may predict outputs based on correlations between various inputs (e.g., one or more characteristics of a pattern such as curvature, one or more characteristics of the patterning device, one or more characteristics of the illumination used in the lithographic process such as the wavelength, etc.). As an example, the empirical model may be a machine learning model or any other parameterized model. In some embodiments, the machine learning model (for example) may be or include mathematical equations, algorithms, plots, charts, networks (e.g., neural networks), or other tools and machine learning model components. For example, the machine learning model may be or include one or more neural networks having an input layer, an output layer, and one or more intermediate or hidden layers. In some embodiments, the one or more neural networks may be or include deep neural networks (e.g., neural networks that have one or more intermediate or hidden layers between the input and output layers). As an example, the one or more neural networks may be based on a large collection of neural units (or artificial neurons). The one or more neural networks may loosely mimic the manner in which a biological brain works (e.g., via large clusters of biological neurons connected by axons). Each neural unit of a neural network may be connected with many other neural units of the neural network. Such connections can be enforcing or inhibitory in their effect on the activation state of connected neural units. In some embodiments, each individual neural unit may have a summation function that combines the values of all its inputs together. In some embodiments, each connection (or the neural unit itself) may have a threshold function such that a signal must surpass the threshold before it is allowed to propagate to other neural units. These neural network systems may be self-learning and trained, rather than explicitly programmed, and can perform significantly better in certain areas of problem solving, as compared to traditional computer programs. In some embodiments, the one or2025P00004WQ 01 11more neural networks may include multiple layers (e.g., where a signal path traverses from front layers to back layers). In some embodiments, back propagation techniques may be utilized by the neural networks, where forward stimulation is used to reset weights on the “front” neural units. In some embodiments, stimulation and inhibition for the one or more neural networks may be freer flowing, with connections interacting in a more chaotic and complex fashion. In some embodiments, the intermediate layers of the one or more neural networks include one or more convolutional layers, one or more recurrent layers, or other layers.

[0042] The one or more neural networks may be trained (e.g., parameters are determined) using a set of training information. The training information may include a set of training samples. Each sample may be a pair comprising an input object (typically a vector, which may be called a feature vector) and a desired output value (also called the supervisory signal). A training algorithm analyzes the training information and adjusts the behavior of the neural network by adjusting the parameters (e.g., weights of one or more layers) of the neural network based on the training information. For example, given a set of N training samples of the form { (xi, y i), (x2, yz), ... ,(XN,YN) } such that Xi is the feature vector of the i-th example and y; is its supervisory signal, a training algorithm seeks a neural network g: X -> Y, where X is the input space and Y is the output space. A feature vector is an n-dimensional vector of numerical features that represent some object (e.g., a simulated aerial image, a wafer design, a clip, etc.). The vector space associated with these vectors is often called the feature space. After training, the neural network may be used for making predictions using new samples.

[0043] In some embodiments, the present systems and methods include (or use) an empirical simulation model that comprises one or more algorithms. The one or more algorithms comprise one or more non-linear, linear, or quadratic functions representative of the physical parameters of a lithography patterning process. In some embodiments, the one or more algorithms comprise a curvature term configured to, alone or in combination with other algorithm terms, correlate curvatures with bias amounts or directions.

[0044] As one example practical application of the present disclosure, optical proximity correction involves adjusting a desired or target pattern or placing appropriate assist features around the desired pattern such that a difference between a predicted pattern and a desired pattern is reduced. Optical proximity correction often requires an optical model, a mask model, a resist model, and an etch model to the simulate the lithography process for mask design optimization. The resist model is configured to generate a resist image. The etch model (e.g., an effective etch bias model) is configured to simulate etch effects and generate an etch contour determined based on a resist contour. In some embodiments, the etch model calculates after-etching- image (AEI) contours by directly biasing after development image (ADI) contours. During etch model calibration, an etch biasing value and an etch bias direction are determined and used to configure the model. The etch bias value (e.g., a scalar magnitude) is determined for a location of interest on a contour. An etch bias direction may be2025P00004WQ 01 12determined based on an ADI feature characteristic (e.g., a curvature) or pattern density of the ADI contour.

[0045] Metrology data may be collected and provided to embodiments of the present disclosure (e.g., a simulation model) using any number of metrology tools or measurements. Embodiments of the present disclosure are not limited to the metrology tool used to collect metrology. Non-limiting examples of metrology tools include a charged particle beam tool (e.g., electron beam tool), an aerial imaging measurement tool, an optical microscope, or any other metrology tool may be used to collect metrology measurements.

[0046] Although reference may be made in the present disclosure to ICs, it is appreciated that the present disclosure may be applicable to other possible applications or designs. For example, the present disclosure may be applied to integrated optical systems, magnetic domain memories, liquidcrystal display panels, thin-film magnetic heads, and other nanoscale structures. It is further appreciated that the terms “die”, “structure”, and “IC structure” are used interchangeably in this disclosure.

[0047] In some embodiments, a machine learning model may comprise a neural network. For example, a model may be a deep neural network with a set of weights that model according to the data that it has been fed to train it.

[0048] Neural networks typically consist of multiple layers, and the signal path traverses from front to back. The goal of the neural network is to solve problems in the same way that the human brain would, although several neural networks are much more abstract. Modern neural network projects typically work with a few thousand to a few million neural units and millions of connections. The neural network may have any suitable architecture and / or configuration known in the art.

[0049] A neural network, as used herein, may refer to a computing model for analyzing underlying relationships in a set of input data by way of mimicking human brains. Similar to a biological neural network, the neural network may include a set of connected units or nodes (referred to as “neurons”), structured as different layers, where each connection (also referred to as an “edge”) may obtain and send a signal between neurons of neighboring layers in a way similar to a synapse in a biological brain. The signal may be any type of data (e.g., a real number). Each neuron may obtain one or more signals as an input and output another signal by applying a non-linear function to the inputted signals. Neurons and edges may typically be weighted by corresponding weights to represent the knowledge the neural network has acquired. During a training process (similar to a learning process of a biological brain), the weights may be adjusted (e.g., by increasing or decreasing their values) to change the strengths of the signals between the neurons to improve the performance accuracy of the neural network. Neurons may apply a thresholding function (referred to as an “activation function”) to its output values of the non-linear function such that a signal is outputted only when an aggregated value (e.g., a weighted sum) of the output values of the non-linear function exceeds a threshold determined by the thresholding function. Different layers of neurons may2025P00004WQ 01 13transform their input signals in different manners (e.g., by applying different non-linear functions or activation functions). The output of the last layer (referred to as an “output layer”) may output the analysis result of the neural network, such as, for example, a categorization of the set of input data (e.g., as in image recognition cases), a numerical result, or any type of output data for obtaining an analytical result from the input data.

[0050] During the training of a neural network, a loss function may be used to evaluate the output data. The loss function, as used herein, may map output data of a machine learning model (e.g., the neural network) onto a real number (referred to as a “loss”) that intuitively represents a loss or an error (e.g., representing a difference between the output data and target output data) associated with the output data. The training of the neural network may seek to maximize or minimize the loss function (e.g., by pushing the loss towards a local maximum or a local minimum in a loss curve). For example, one or more parameters of the neural network may be adjusted or updated purporting to maximize or minimize the loss function. After adjusting or updating the one or more parameters, the neural network may obtain new input data in a next iteration of its training. When the loss function is maximized or minimized, the training of the neural network may be terminated.

[0051] FIG. 3 illustrates an example flowchart of a method 300 for source and mask optimization of a patterning process, consistent with embodiments of the present disclosure. In a typical high-end design, almost every feature edge can benefit from some modification to achieve printed patterns that come sufficiently close to the target design. These modifications can include shifting or biasing of edge positions or line widths as well as application of “assist” features that are not intended to print themselves, but can affect the properties of an associated primary feature.Furthermore, optimization techniques applied to the source of illumination can have different effects on different edges and features. Optimization of illumination sources can include the use of pupils to restrict source illumination to a selected pattern of light. Embodiments of the present disclosure provide optimization methods that can be applied to both source and mask configurations.

[0052] A method of performing source and mask optimization (SMO) can allow full chip pattern coverage while lowering the computation cost by intelligently selecting a small set of critical design patterns from the full set of clips to be used in SMO. SMO can be performed on these selected patterns to obtain an optimized source. The optimized source can then be used to optimize the mask (e.g., using OPC and local mechanical-stress control) for the full chip, and the results can be compared. Various methods are provided for iteratively converging on an optimal result. Method 300 is an example SMO method.

[0053] A target design 301 (e.g., comprising a layout in a standard digital format such as OAIS, GDSII, etc.) for which a lithographic process is to be optimized can include memory, test patterns, and logic. From this design, a full set of clips 302 can be extracted, which represents complex patterns in design 301 (e.g., about 50 to 1000 clips). It is to be appreciated that these clips represent small portions (i.e., circuits, cells, or patterns) of the design for which particular attention or verification is2025P00004WQ 01 14of interest. At operation 304, a small subset of clips 306 (e.g., 15 to 50 clips) can be selected from full set of clips 302. As will be explained in more detail below, the selection of clips can be performed such that the process window of the selected patterns matches the process window for the full set of critical patterns as close as possible. The effectiveness of the selection can be measured by the total run time (pattern selection and SMO) reduction.

[0054] At operation 308, SMO can be performed with the selected patterns (15 to 50 patterns) of subset of clips 306. In particularly, an illumination source can be optimized for the selected patterns of subset of clips 306. Examples of other source optimization methods can be found in, for example, U.S. Patent Application Publication No. 2004 / 0265707, the contents of which are incorporated herein by reference in their entirety.

[0055] At operation 310, manufacturability verification of the selected patterns of subset of clips 306 can be performed with the source obtained in operation 308. In particular, verification can include performing an aerial image simulation of the selected patterns of subset of clips 306 and the optimized source and verifying that the patterns will print across a sufficiently wide process window. An example verification process can be found in U.S. Patent No. 7,342,646, the contents of which are incorporated herein by reference in their entirety. If the verification at operation 310 is satisfactory, as determined in operation 312, then processing can advance to full chip optimization (e.g., advanced to operations using optimized source 314). Otherwise, processing can return to operation 308, where SMO is performed again but with a different source or set of patterns. For example, the process performance as estimated by the verification tool can be compared against thresholds for certain process window parameters such as exposure latitude and depth of focus. These thresholds can be predetermined or set by a user.

[0056] After the selected patterns meet lithography performance specification as determined in step 312, the optimized source 314 can be used for optimization of the full set of clips 316 (e.g., originating from full set of clips 302).

[0057] At operation 318, model-based sub-resolution assist feature placement (MB-SRAF) and optical proximity correction (OPC) for all the patterns in the full set of clips 316 can be performed. Examples of MB-SRAF and OPC can be found in U.S. Patent Nos. 5,663,893; 5,821,014; 6,541,167; and 6,670,081, the contents of which are incorporated herein by reference in their entirety.

[0058] At operation 320, using processes similar to step 310, full pattern simulation based manufacturability verification can be performed with the optimized source 414 and the full set of clips 316 as corrected in step 318.

[0059] At operation 322, the performance (e.g., process window parameters such as exposure latitude and depth of focus) of the full set of clips 316 can be compared against subset of clips 306. For example, the pattern selection can be considered complete or the source is fully qualified for the full chip when the similar (<10%) lithography performances are obtained for both selected patterns of subset of clips 306 and critical patterns of full set of clips 316.2025P00004WQ 01 15

[0060] Otherwise, at operation 324, hotspots can be extracted. At operation 326, the hotspots can be added to subset of clips 306 and the process starts over. For example, hotspots (e.g., features among the full set of clips 316 that limit process window performance) identified during verification step 320 can be used for further source tuning or to run SMO of operation 308 again. The source can be considered fully converged when the process window of the full set of clips 316 are the same between the last run and the run before the last run of operation 322.

[0061] OPC calibration can be performed by modeling or simulation. For example, for the desired yield, the total number of features, and their respective probabilities of failure, simulation can be performed to optimize OPC for a lowest yielding feature. OPC addresses the fact that, in addition to any demagnification by the lithographic projection apparatus, the final size and placement of an image of the patterning device pattern projected on the substrate will not be identical to, or simply depend only on the size and placement of, the corresponding patterning device pattern features on the patterning device.

[0062] In some embodiments, the measurement data (e.g., stochastic variations) related to the printed pattern can be employed in optimizing the patterning process or adjusting parameters of the patterning process. For small feature sizes and high feature densities present on some design layouts, the position of a particular edge of a given feature can be influenced to a certain extent by the presence or absence of other adjacent features. These proximity effects arise from minute amounts of radiation coupled from one feature to another or non-geometrical optical effects such as diffraction and interference. Similarly, proximity effects can arise from diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching that generally follow lithography.

[0063] To ensure that the projected image of the patterning device pattern is in accordance with tolerances of a given target design, proximity effects should be predicted and compensated for using sophisticated numerical models, corrections, or pre-distortions of the patterning device pattern. The article “Full-Chip Lithography Simulation and Design Analysis — How OPC Is Changing IC Design,” C. Spence, Proc. SPIE, Vol. 5751, pp 1-14 (2005) provides an overview of “model-based” optical proximity correction processes, the contents of which are incorporated herein by reference in their entirety. In a typical high-end design, almost every feature of the patterning device pattern has some modification to achieve high fidelity of the projected image to the target design. These OPC modifications can include shifting or biasing of edge positions or line widths or application of “assist” features that are intended to assist projection of other features.

[0064] Application of model-based OPC to a target design can involve good process models and considerable computational resources, given the many millions of features typically present in a device design. However, applying OPC is generally an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the effect of OPC, e.g., patterning device patterns after application of OPC and any other resolution enhancement technique (RET), should be verified by design inspection, e.g., intensive full-chip simulation using calibrated numerical2025P00004WQ 01 16process models, to reduce or minimize the possibility of design flaws being built into the patterning device pattern. This is driven by the enormous cost of making high-end patterning devices, as well as by the impact on turn-around time by reworking or repairing existing patterning devices once they have been manufactured. OPC and full-chip RET verification can be based on numerical modelling systems and methods. Examples of such methods can be found in U.S. Pat. No. 7,003,758 and an article titled “Optimized Hardware and Software For Fast, Full Chip Simulation”, by Y. Cao et al., Proc. SPIE, Vol. 5754, 405 (2005), the contents of which are incorporated herein by reference in their entirety.

[0065] The illumination source can also be optimized, either jointly with patterning device optimization or separately, to improve the overall lithography fidelity. The terms “illumination source” and “source” can be used interchangeably in this disclosure. Off-axis illumination (e.g., annular, quadrupole, dipole, or the like) can be used to resolve fine structures (e.g., target features) contained in the patterning device. However, when compared to a traditional illumination source, an off-axis illumination source usually provides less radiation intensity for the aerial image. Thus, it is desirable to optimize the illumination source to achieve balance between finer resolution (relevant to yield) and reduced radiation intensity (relevant to throughput).

[0066] In the manufacturing of integrated circuits, an illumination source is designed or optimized by computation lithography to achieve improved performance (e.g., improved image quality, larger process window, etc.).

[0067] FIG. 4 illustrates an example artificial intelligence architecture, consistent with some embodiments of the present disclosure. For example, FIG. 4 illustrates a neural network 400. Neural network 400 may include an input layer 420 that receives inputs, including input 410-1, . . ., input 410-m (m being an integer). For example, an input of neural network 400 may include any structure or unstructured data (e.g., an image). In some embodiments, neural network 400 may obtain a plurality of inputs simultaneously. For example, in FIG. 4, neural network 400 may obtain m inputs simultaneously. In some embodiments, input layer 420 may obtain m inputs in succession such that input layer 420 receives input 410-1 in a first cycle (e.g., in a first inference) and pushes data from input 410-1 to a hidden layer (e.g., hidden layer 430-1), then receives a second input in a second cycle (e.g., in a second inference) and pushes data from the second input to the hidden layer, and so on. Input layer 420 may obtain any number of inputs in the simultaneous manner, the successive manner, or any manner of grouping the inputs.

[0068] Input layer 420 may include one or more nodes, including node 420-1, node 420-2, . . ., node 420-a (a being an integer). A node (also referred to as a “machine perceptron” or a “neuron”) may model the functioning of a biological neuron. Each node may apply an activation function to received inputs (e.g., one or more of input 410-1, . . ., input 410-m). An activation function may include a Heaviside step function, a Gaussian function, a multiquadratic function, an inverse multiquadratic function, a sigmoidal function, a rectified linear unit (ReEU) function (e.g., a ReEU52025P00004WQ 01 17function or a Leaky ReLU function), a hyperbolic tangent (“tanh”) function, or any non-linear function. The output of the activation function may be weighted by a weight associated with the node. A weight may include a positive value between 0 and 1, or any numerical value that may scale outputs of some nodes in a layer more or less than outputs of other nodes in the same layer.

[0069] Neural network 400 may include multiple hidden layers, including hidden layer 430-1, . . ., hidden layer 430-n (n being an integer). When neural network 400 includes more than one hidden layer, it may be referred to as an “artificial neural network” (ANN). An ANN encompasses a “deep neural network” (DNN) and a “recurrent neural network” (RNN). Each hidden layer may include one or more nodes. For example, in FIG.4, hidden layer 430-1 includes node 430-1-1, node 430-1-2, node 430-1-3, . . ., node 430-1-b (b being an integer), and hidden layer 430-n includes node 430-n- 1, node 430-n-2, node 430-n-3, . . ., node 430-n-c (c being an integer). Similar to nodes of input layer 420, nodes of the hidden layers may apply the same or different activation functions to outputs from connected nodes of a previous layer, and weight the outputs from the activation functions by weights associated with the nodes.

[0070] As further depicted in FIG.4, neural network 400 may include an output layer 440 that finalizes outputs, including output 450-1, output 450-2, . . ., output 450-d (d being an integer). Output layer 440 may include one or more nodes, including node 440-1, node 440-2, . . ., node 440-d. Similar to nodes of input layer 420 and of the hidden layers, nodes of output layer 440 may apply activation functions to outputs from connected nodes of a previous layer and weight the outputs from the activation functions by weights associated with the nodes.

[0071] Although nodes of each hidden layer of neural network 400 are depicted in FIG.4 to be connected to each node of its previous layer and next layer (referred to as “fully connected”), the layers of neural network 400 may use any connection scheme. For example, one or more layers (e.g., input layer 420, hidden layer 430-1, . . ., hidden layer 430-n, or output layer 440) of neural network 400 may be connected using a convolutional scheme, a sparsely connected scheme, or any connection scheme that uses fewer connections between one layer and a previous layer than the fully connected scheme as depicted in FIG.4.

[0072] Moreover, although the inputs and outputs of the layers of neural network 400 are depicted as propagating in a forward direction (e.g., being fed from input layer 420 to output layer 440, referred to as a “feedforward network”) in FIG.4, neural network 400 may additionally or alternatively use backpropagation (e.g., feeding data from output layer 440 towards input layer 420) for other purposes. In some embodiments, neural network 400 may use backpropagation to evaluate and minimize a loss function. Neural network 400 may evaluate and minimize a loss function to improve a weight or bias of neutral network 400 to improve a feedforward network. In some embodiments, neural network 400 may minimize a loss function by applying a mean squared error loss function, a cross-entropy loss function, a mean absolute percentage error loss function, or a stability related loss function (e.g., a grid dependency loss or a trend loss). Accordingly, although2025P00004WQ 01 18neural network 400 is depicted similar to a deep neural network (DNN), neural network 400 may include a recurrent neural network (RNN) or any other neural network.

[0073] FIG. 5 illustrates a flowchart of an example method 500 to train a model for a lithography patterning process. Step S501 involves obtaining (i) image data 502 associated with a desired pattern, (ii) measured pattern data 504 of the substrate, associated with the desired pattern, (iii) a first model associated with an aspect (e.g., having effects that can be accurately modelled by physics / chemistry based equations) of the patterning process, the first model comprising a first set of parameters 507, and (iv) a machine learning model associated with another aspect (e.g., having effects that may not be accurately modelled by physics / chemistry based equations) of the patterning process, the machine learning model comprising a second set of parameters 508.

[0074] Image data 502 may refer to any input to the patterning process model configured to predict effects of an aspect of the patterning process or a final pattern that will be printed on the substrate. Image data 502 may be digital or analog data representing an aerial image, a mask image, a resist image, or other outputs related to one or more aspects of the patterning process. Obtaining the aerial image, mask image, resist image, etc. may comprise simulating a patterning process, as discussed in reference to FIG. 2.

[0075] The patterning process model comprises the first model coupled to a second model (e.g., a machine learning model). The first model may be connected to the machine learning model in a series or in a parallel combination. A series combination of the models involves providing output of the first model as an input to the machine learning model. A series combination of the models involves providing output of the machine learning model as an input to the first model. A parallel combination of the models involves providing the same input to the first model and the machine learning model, combining output of the first model and the machine learning model, and determining the predicted printed pattern based on the combined outputs of the respective models. The patterning process model may be configured to include both series and parallel arrangement of the first model, a machine learning model, or another physics-based or machine learning model.

[0076] The first model is an empirical model comprising physical terms that accurately describes effects of a first aspect of the patterning process. In some embodiments, the first model may correspond to a first aspect related to an acid-based diffusion after exposure of the substrate. In some embodiments, a first model is a resist model. The first set of parameters of the resist model may correspond to at least one of the following physical terms: an initial acid distribution; an acid diffusion; an image contrast; a long range pattern loading effect; a long range pattern loading effect; an acid concentration after neutralization; a base concentration after neutralization; a diffusion due to high acid concentration; a diffusion due to high base concentration; a resist shrinkage; a resist development; or two-dimensional convex curvature effects.

[0077] The machine learning model may be a neural network that models a second aspect of the patterning process having a relatively less physics-based understanding. The second set of parameters2025P00004WQ 01 19includes weights and bias of one or more layers of the neural network. During the training process (e.g., involving processes S503, S507), the weights and biases are adjusted in cooperation with the first set of parameters such that a difference between the predicted pattern and the measured pattern is reduced. The patterning process model may correspond to the second aspect of a post-exposure process of the patterning process.

[0078] Method 500 further involves iteratively determining values of the first set of parameters 507 and the second set of parameters 508 to train the patterning process model. The iteration involves executing steps S503, S505, and S507.

[0079] Step S503 involves executing, using the image data 502, the first model and the machine learning model to cooperatively predict a pattern of the substrate. Step S505, involves determining a difference between the measured pattern 504 and the predicted pattern 505 of the patterning process model and further determining whether the difference is reduced or minimized. Step S507 involves modifying the values of the first set of parameters 507 and the second set of parameters 508 such that a difference between the measured pattern 504 and the predicted pattern 505 of the patterning process model is reduced.

[0080] The modified values are determined based on an optimization technique such as a gradient descent method that guides how to modify the values of the first set of parameters and the second set of parameters such that a gradient of the difference with respect to the respective parameters is reduced. After several iterations, a global or a local optimum value of the parameters is obtained such that the difference in prediction and measurements is minimized Thus, the patterning process model is calibrated (or trained) and can be further employed for improving the patterning process via OPC, defect detection, hot spot ranking, or other known applications of the patterning process model.

[0081] Existing machine learning models for a lithography process can be trained to predict imaging characteristics for a pattern on a sample according to one process condition. Specifically, training data for a machine learning lithography process model are typically from a single process condition (e.g., one focus / dose in a lithography process). However, due to low pattern coverage provided by limited off-nominal process condition training data, existing machine learning models tend to overfit, and predictions from the trained model deviate from physical trends that characterize the patterning process with respect to a pattern variation across process conditions (e.g., a process window). Accurate process window prediction control (e.g., how EPE or CD of a pattern varies across a range of focus values) is desirable for optimization applications (e.g., SMO), so existing machine learning training methods may not enable use of existing lithography process models for accurate SMO applications.

[0082] In contrast, embodiments of the present disclosure provide a method for training a machine learning lithography process model using training data from a range of process conditions (e.g., a plurality of focus and dose conditions). The training data may be measured data or simulated2025P00004WQ 01 20data across a process window. In some embodiments, training data may be augmented (e.g., added to existing data when the existing data representing a lithography process trend is insufficient). In some embodiments, the training method comprises grouping the training data based on a variation of an imaging characteristic (e.g., CD, EPE, hinge, etc.) of a pattern with a process condition across a process window. In some embodiments, the training method comprises evaluating a loss function to guide predictions from the trained machine learning model towards known physical trends (e.g., pitch, draw CD, focus, dose, or mask bias). The loss function may evaluate and minimize a deviation of a predicted process window trend against a simulated or ground truth process window trend. The trained machine learning model may then be used to predict process window variation for a lithography process and be suitable for further optimization applications (e.g., SMO or OPC).

[0083] Reference is now made to FIG.6, which illustrates an example method 600 for obtaining training data, consistent with some embodiments of the present disclosure. The training data may be augmented (e.g., additional measured or simulated data added to available data) to train a machine learning lithography process model. The training data may be determined based on a physical trend associated with a set of patterns on a sample and a process variation across a process window resulting from a lithography process.

[0084] In step 601, a trend of one or more imaging characteristics with respect to a certain pattern variation on a substrate across a plurality of process conditions is obtained or otherwise determined, where the imaging characteristics are associated with a patterning process. The patterning process may be a lithography process, a mask diffraction process, an etching process, or other processes. In some embodiments, the one or more imaging characteristics comprise a critical dimension (CD), an edge placement location, a curvature, a pitch, a symmetry, a rotation, an aspect ratio, an offset, or other imaging characteristics.

[0085] A trend may be a physics-based indication or tendency that an imaging characteristic may change with different process conditions (e.g., different focus / dose conditions). A trend may describe how the imaging characteristics may respond or change in reality according to physical principles, when the pattern design or process conditions change. The trend may be associated with, for example, pattern design variation (e.g., variation in imaging characteristics such as CD, pitch, etc.) or patterning process variation (e.g., changes in the imaging characteristics caused by variation in dose, focus, etc.; etching process variation such as source power, bias power, etching time, gas chemistry, gas flow, etc.). The trend may be obtained based on data for a first set of patterns and patterning process conditions across a process window. In some embodiments, the data for the first set of patterns and patterning process conditions comprises simulated data or measured data.

[0086] In step 602, training data is obtained. The training data may be obtained (e.g., generated) based on the trend (determined at step 601), or other information. The training data comprises data that conforms to the trend and is derived based on the data for the set of patterns and the patterning process described above. In other words, the training data is not random or uncontrolled. In some2025P00004WQ 01 21embodiments, training data is obtained by applying a bias to the trend (simulated or measured data) from step 601. The training data may therefore be added to any existing data (simulated or measured) for a pattern across a process window of lithography process conditions.

[0087] In step 603, the training data is grouped based on an imaging characteristic obtained under varied lithography process conditions.

[0088] Reference is now made to FIG.7, which is an example workflow for grouping training data based on an imaging characteristic obtained under varied lithography process conditions, consistent with some embodiments of the present disclosure. FIG. 7 illustrates training data 701 comprising image data of patterns 702 and 703, where each of pattern 702 and 703 corresponds to a pattern resulting from a different lithography process condition (e.g., a different focus). Pattern 702 comprises feature 704 and pattern 703 comprises feature 705. Pattern 702 may correspond to a first process condition (e.g., a first focus) and pattern 703 may correspond to a second process condition (e.g., a second focus). In some embodiments, training data 701 may be grouped into an imaging characteristic varied with a process condition of a certain process parameter, e.g., for a certain feature or pattern. For example, training data 701 may be grouped into a CD varied over a process condition group or an EP varied over a process condition group. In some embodiments, a contour gauge 707 may be determined for feature 704 and a contour gauge 709 may be determined for feature 705. In some embodiments, a CD gauge 706 may be determined for feature 704 and a CD gauge 708 may be determined for feature 705. Because pattern 702 and pattern 703 correspond to varying process conditions (e.g., focus), CD gauge 706 and CD gauge 708 may be grouped into a CD varied through focus trend group and contour gauge 707 and contour gauge 709 may be grouped into an EP varied through focus trend group. It is appreciated that the groups for an imaging characteristic or lithography process condition are not so limited and may correspond to any imaging characteristic of a pattern or feature and any lithography process condition. Training data 701 may include any number of patterns or features and is not limited to only pattern 702 and 703 as illustrated in FIG.7.Additionally, training data 701 may be grouped based on a trend of an imaging characteristic varied over a plurality of different lithography process conditions (e.g., varied dose, slit position, mask bias, pitch, draw CD, etc.).

[0089] In addition to grouping training data 701 into trend groups, embodiments of the present disclosure also include grouping training data into gauge groups. For example, FIG.7 shows that CD gauge 706 has a left gauge point 706b and a right gauge point 706c, and CD gauge 708 has a left gauge point 708b and a right gauge point 708c. CD gauge 706 and CD gauge 708 may be split into the left and right gauge points, respectively, and grouped, and contour gauge 707 and contour gauge 709 may be grouped. The grouped CD and contour gauges may be used for evaluating a total loss function, which is described further below.

[0090] Reference is now made to FIG.8, which is an example diagram illustrating grouped training data obtained for training a lithography process machine learning model, consistent with2025P00004WQ 01 22some embodiments of the present disclosure. FIG.8 illustrates a predicted imaging characteristic 801 (e.g., CD) across a lithography process window 802 (e.g., for defocus). Embodiments of the present disclosure may use modeled trend 803 representing a variation of predicted imaging characteristic 801 over lithography process condition 802 to obtain and group training data as described above. Modeled trend 803 may be simulated data obtained from a calibrated non-machine learning lithography model, e.g., a rigorous physical model, an empirical physical model, a termed physical model, or a semi-empirical model. FIG.8 also illustrates target data 804, which may represent data to be used to predict a process window trend for predicted imaging characteristic 801. In some embodiments, training data 804 may be insufficient to predict an accurate process window trend. In some embodiments, a bias may be applied to modeled trend 803 to obtain training data 805, such that training data 805 augments target data 804 and increases the amount of data for predicting a process window trend. As seen in FIG.8, training data 805 has been grouped based on an imaging characteristic varied with a process condition (e.g., CD trend through focus). As an illustrative example, training data point 806 may correspond to grouped trend CD gauge data from a training feature at a more negative focus value (e.g., feature 704 in FIG. 7) and training data point 807 may correspond to a grouped trend CD gauge data point from a training feature at a more positive focus value (e.g., feature 705 in FIG. 7). FIG.8 illustrates a first group of training data for embodiments of the present disclosure. A plurality of grouped training data may be obtained as described above for other imaging characteristics (e.g., EP, pitch, etc.) of a pattern (e.g., ID or 2D pattern) over a focus condition, or other lithography process conditions (e.g., as described above). It is appreciated that FIG.8 is for illustrative purposes, and embodiments of the present disclosure may obtain and group training data for a plurality of lithography process windows (e.g., focus, dose, draw CD, pitch, mask bias, or slit position), and the training data may be used to train a universal machine learning lithography process model.

[0091] In some embodiments, training the disclosed machine learning lithography process model comprises evaluating a predicted variation trend of an imaging characteristic (e.g., CD) with the process condition (e.g., focus) against a reference variation trend. The reference variation trend may be a ground truth variation trend of the imaging characteristic (e.g., CD) with the process condition (e.g., focus). The predicted variation trend of the imaging characteristic with the process condition may be evaluated by using a loss function to guide the predictions towards the known physical trend (e.g., the reference variation trend).

[0092] Reference is now made to FIG.9, which is an illustration of an example predicted variation trend compared to a reference variation trend, consistent with some embodiments of the present disclosure. FIG. 9 shows a predicted variation trend 901 and a reference variation trend 902 for an imaging characteristic 903 over a lithography process condition 904, where predicted variation trend 901 does not align with reference variation trend 902. Accordingly, FIG.9 illustrates that further iterations of training the disclosed machine learning lithography process may be needed. In2025P00004WQ 01 23some embodiments, predicted variation trend 901 may be evaluated against reference variation trend 902 by comparing an overlapping area, a distance between predicted variation trend 901 and reference variation trend 902, or a slope between a first point and a second point on both predicted variation trend 901 and reference variation trend 902.

[0093] In some embodiments, predicted variation trend 901 may be evaluated against reference variation trend 902 by a slope between a first point and a second point on predicted variation trend 901 at a point and variation trend 902. For example, FIG. 9 illustrates that at point 905 on predicted variation trend 901 and reference variation trend 902, there is a distance dj between predicted variation trend 901 and reference variation trend 902. At point 906, there is a distance dj+1 between predicted variation trend 901 and reference variation trend 902. If a difference between distance dj+1 and distance dj is minimized, then the machine learning lithography process model may be sufficiently trained. Point 905 on predicted variation trend 901 may correspond to a data point in the grouped training data (e.g., training data point 807 in FIG.8) and point 906 on predicted variation trend 901 may correspond to a neighboring data point in the grouped training data. It will be appreciated that any other methods of calculating a difference between two trends can be used without departing from the scope of the present disclosure.

[0094] In some embodiments, predicted variation trend 901 may be evaluated against reference variation trend 902 by an overlapping area between predicted variation trend 901 and reference variation trend 902. FIG. 9 illustrates an overlapping area 907 between predicted variation trend 901 and reference variation trend 902. Overlapping area 907 may correspond to an area resulting from overlap between predicted variation trend 901 and reference variation trend 902 at a first point and a second point. Overlapping area 907 may comprise an edge length 908. In some embodiments, if overlapping area 907 is minimized, then the machine learning lithography process model may be sufficiently trained. In some embodiments, if a ratio of an overlapping area to an edge length across all of predicted variation trend 901 and reference variation trend 902 is minimized, then the machine learning lithography process model may be sufficiently trained. In some embodiments, if a distance between predicted variation trend 901 and reference variation trend 902 is minimized, then the machine learning lithography process model may be sufficiently trained.

[0095] Evaluating predicted variation trend 901 may comprise using a trend loss component in a loss function, which may be represented by Equation 1 below:(Eq. 1), trend loss = f(area) + f (slope)where f(area) describes a function evaluating an overlapping area between a target trend (e.g., reference variation trend 902) and a predicted trend (e.g., predicted variation trend 901) and where f (slope) describes a function to evaluate a slope between two points on the target trend and the2025P00004WQ 01 24predicted trend. In some embodiments, (area) may describe a function evaluating a maximum or an average overlapping area between a target trend and a predicted trend for an imaging characteristic over a varied lithography process condition. In some embodiments, f {slope) may describe a function evaluating a maximum or an average slope between points on a target trend and a predicted trend for an imaging characteristic over a varied lithography process condition.

[0096] In some embodiments, evaluating predicted variation trend 901 may comprise using a trend loss component in a loss function, which may be represented by Equation 2 below:| area; |trend loss = a * max — - - + (1 — a) .\edgei\. (Eq. 2), <where d is a distance between two segments and a is a loss coefficient.

[0097] In addition to the above, a trend loss value may be determined (e.g., calculated) for other predicted trends of an imaging characteristic (e.g., CD trend or EP trend) for a pattern across different process windows of lithography process conditions. Thus, a total trend loss value may be determined based on Equation 3 provided below:where xtrend is a tunable weight factor, and M is the total number of training points in one iteration.

[0098] A total loss may be evaluated by incorporating the total trend loss value in Equation 3 into a machine learning loss function architecture, as shown in Equation 4 below:. - (Eq- 4), Lossau = / hinge2+ gd2+ err2+ trend2where hinge and grid dependency (gd) are associated with a predicted image-based loss and err is calculated based on gauge signal (e.g., CD gauge 706, contour gauge 707, CD gauge 708, and contour gauge 709 in FIG. 7). Each may be calculated based on Equations 5-7:2025P00004WQ 01 25(Eq. 6), gd2= xgd * xgd * 10000 *— / gd)2>where hinge2 is associated with a contour gauge signal (e.g., contour gauge 707 and contour gauge 709 in FIG.7), and where xhinge, xhinge2, xgd, and xerr are tunable weight factors.

[0099] For the CD and contour groups, only hinge, gd, and error loss are relevant, and the trend groups (e.g., CD trend or EP trend) are associated with trend loss. The tunable weight factors in Equations 3 and 5-7 may be tuned to guard against convergence during training of the machine learning model. The tunable weight factors may also improve stability of the disclosed training method by adding additional physical constraints to the machine learning model. For the CD gauges (e.g., CD gauge 706 and CD gauge 708), loss components are handled separately. Therefore, disclosed training methods may have improved capability to model information from individual CD gauges or from a CD trend group.

[0100] In some embodiments, a total loss function (e.g., Equation 4) may be minimized and used to evaluate a predicted variation trend to a reference variation trend. The trained universal machine learning model associated with a lithography process may then be used to predict an imaging characteristic trend (e.g., CD trend or EP trend) for a pattern across different process windows with a desired accuracy for, e.g., SMO or OPC applications.

[0101] In some embodiments, the machine learning lithography process model comprises a mask model, an optical model, a resist model, an etch model, or any other model that describes or predicts a lithography process. In some embodiments, the machine learning lithography process model comprises a mask model configured to predict a mask image based on polygon data, and the training data comprises a plurality of polygon representations of a mask contour or a mask pattern. In some embodiments, the mask model may be a thin mask model or a thick mask model. In some embodiments, the machine learning lithography process model comprises a thin mask model and the training data comprises a plurality of polygon representations of a thin mask contour or a thin mask pattern (e.g., does not consider a thickness of a mask contour or a mask pattern). In some embodiments, the machine learning lithography process model comprises a thick mask model and the training data comprises a plurality of polygon representations of a thick mask contour or a thick mask pattern (e.g., a 3D representation of a mask contour or a mask pattern).

[0102] In some embodiments, the machine learning lithography process model comprises an optical model configured to predict an aerial image from mask data, and the training data comprises a plurality of mask images or mask patterns. In some embodiments, the machine learning lithography process model comprises a resist model configured to predict a resist image from aerial data, and the2025P00004WQ 01 26training data comprises a plurality of aerial images or aerial patterns. In some embodiments, the machine learning lithography process model comprises an etch model configured to predict an etch image from resist data, and the training data comprises a plurality of resist images or resist patterns.

[0103] Reference is now made to FIG. 10, which is an example workflow illustrating a method 1000 of training a machine learning associated with a lithography process model to predict a trend for an imaging characteristic with a lithography process condition, consistent with embodiments of the present disclosure. It is appreciated that the illustrated method 1000 may be altered to modify the order of steps and to include the additional steps.

[0104] In step 1001, training data from different process conditions is obtained. The training data may be obtained (e.g., generated) based on simulated data or measured data. The training data may comprise data that conforms to a simulated trend and is derived based on the data for the set of patterns and the patterning process. The training data may be obtained by applying a bias to the simulated or measured data, thus augmenting any existing data (simulated or measured) for a pattern across a process window of lithography process conditions. The process conditions may be different focus conditions, different dose conditions, different mask biases, different slit positions, different draw CD values, different capture pitch values, or other process conditions associated with a lithography process.

[0105] In step 1002, the training data is grouped based on an imaging characteristic obtained from a varied process condition. The imaging characteristic may be a CD, a contour (e.g., EP), pitch, or any other imaging characteristic associated with a pattern or feature in a lithography process. The process condition may be as described above.

[0106] In step 1003, the machine learning model is trained using the grouped training data by comparing a predicted variation trend of an imaging characteristic with a varied process condition to a reference variation trend of the imaging characteristic with the varied process condition. The training may involve multiple iterations using the grouped training data and evaluating a loss function for the predicted variation trend. The predicted variation trend may be trained by evaluating an overlapping area between the predicted variation trend and the reference variation trend, a distance between the predicted variation trend and the reference variation trend, or a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.

[0107] Benefits of the present disclosure include providing a method to train a machine learning model associated with a lithography process to accurately predict process window variation. Trend information for lithography process parameters such as CD or EP across varying focus, dose, capture pitch, draw CD, mask bias, or slit position may be accurately determined and used to guide and improve lithography modeling. In some embodiments, the disclosed method can capture trends for unseen patterns with less accurate CD information and improve model stability. In at least a specific case, embodiments of the present disclosure reduce model error root-mean-square (RMS) loss compared to existing machine learning training methods and improve process window prediction2025P00004WQ 01 27accuracy. Thus, embodiments of the present disclosure may be suitable for desired simulation and optimization procedures which need accurate prediction results for, e.g., a range of process conditions that existing machine learning training methods are unable to reliably provide.

[0108] In some embodiments, an offline computing system (e.g., offline from high volume manufacturing) may be used to obtain training data (e.g., as described in FIG. 6), group training data, evaluate a loss function for a imaging characteristic trend over a varied process condition, or train a machine learning model associated with a lithography process (e.g., as described in FIG.8).

[0109] FIG. 11 illustrates a block diagram of an example computing system for training a machine learning model associated with a lithography process, consistent with embodiments of the present disclosure. For example, computing system 1104 may be a preprocessor, an encoder, or a decoder. In some embodiments, computing system 1104 may comprise a memory 1106 storing a set of instructions and at least one processor 1105 configured to execute the set of instructions to cause computing system 1104 to perform operations or manipulations on data for processing. As shown in FIG. 11, computing system 1104 can include processor 1105. When processor 1105 executes instructions described herein, computing system 1104 can become a specialized machine for preprocessing, encoding, or decoding image data. Processor 1105 can be any type of circuitry capable of manipulating or processing information. For example, processor 1105 can include any combination of any number of a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), a neural processing unit (“NPU”), a microcontroller unit (“MCU”), an optical processor, a programmable logic controller, a microcontroller, a microprocessor, a digital signal processor, an intellectual property (IP) core, a Programmable Logic Array (PLA), a Programmable Array Logic (PAL), a Generic Array Logic (GAL), a Complex Programmable Logic Device (CPLD), a Field-Programmable Gate Array (FPGA), a System On Chip (SoC), an Application-Specific Integrated Circuit (ASIC), or the like. In some embodiments, processor 1105 can also be a set of processors grouped as a single logical component. For example, as shown in FIG. 11, processor 1105 can include multiple processors, including processor 1105a, processor 1105b, and processor 1105n.

[0110] Computing system 1104 can also include memory 1106 configured to store data (e.g., a set of instructions, computer codes, intermediate data, or the like). For example, as shown in FIG. 11, the stored data can include program instructions (e.g., program instructions for calibrating a tuning engine) and data for processing (e.g., metrology data). Processor 1105 can access the program instructions and data for processing (e.g., via bus 1107), and execute the program instructions to perform an operation or manipulation on the data for processing. Memory 1106 can include a highspeed random-access storage device or a non-volatile storage device. In some embodiments, memory 1106 can include any combination of any number of a random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or the like. Memory 1106 can also be a group of memories (not shown in FIG. 11) grouped as a single logical component.2025P00004WQ 01 28

[0111] Bus 1107 can be a communication device that transfers data between components included in computing system 1104, such as an internal bus (e.g., a CPU-memory bus), an external bus (e.g., a universal serial bus port, a peripheral component interconnect express port), or the like.

[0112] For ease of explanation without causing ambiguity, processor 1105 and other data processing circuits are collectively referred to as a “data processing circuit” in this disclosure. The data processing circuit can be implemented entirely as hardware, or as a combination of software, hardware, or firmware. In addition, the data processing circuit can be a single independent module or can be combined entirely or partially into any other component of computing system 1104.

[0113] Computing system 1104 can further include network interface 1108 to provide wired or wireless communication with a network (e.g., the Internet, an intranet, a local area network, a mobile communications network, or the like). In some embodiments, network interface 1108 can include any combination of any number of a network interface controller (NIC), a radio frequency (RF) module, a transponder, a transceiver, a modem, a router, a gateway, a wired network adapter, a wireless network adapter, a Bluetooth adapter, an infrared adapter, a near-field communication (“NFC”) adapter, a cellular network chip, or the like.

[0114] In some embodiments, optionally, computing system 1104 can further include peripheral interface 1109 to provide a connection to one or more peripheral devices. As shown in FIG. 11, the peripheral device can include, but is not limited to, a cursor control device (e.g., a mouse, a touchpad, or a touchscreen), a keyboard, a display (e.g., a cathode -ray tube display, a liquid crystal display, or a light-emitting diode display), an input device (e.g., a computing device), or the like.

[0115] A non-transitory computer readable medium may be provided that may store instructions for a processor of a lithographic projection apparatus (e.g., lithographic projection apparatus 100 of FIG. 1), a computing device (e.g., computing system 1104 of FIG. 11) to train or apply a tuning engine, method 600 of FIG. 6, method 1000 of FIG. 10, and other executable functions relating to the training of a machine learning model associated with a lithography process. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read Only Memory (PROM), and Erasable Programmable Read Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0116] The embodiments of the present disclosure may further be described using the following clauses:1. A method for training a machine learning model associated with a lithography process, the method comprising:obtaining training data from a plurality of varying process conditions;2025P00004WQ 01 29grouping the training data, wherein a group of the training data comprises data of an imaging characteristic obtained from the plurality of varying process conditions; andtraining the machine learning model to generate a predicted variation trend of the imaging characteristic with the plurality of varying process conditions, wherein the training comprises comparing the predicted variation trend to a reference variation trend of the imaging characteristic with the plurality of varying process conditions.2. The method of clause 1, wherein the training data comprises simulated or measured data of a feature associated with the lithography process.3. The method of clause 1 or 2, wherein the imaging characteristic comprises a critical dimension, an edge placement, or a pitch of a feature associated with the lithography process.4. The method of any one of clauses 1 to 3, wherein the plurality of varying process conditions comprises a varying focus, a varying dose, a varying mask bias, a varying slit position, a varying draw CD, or a varying capture pitch.5. The method of any one of clauses 1 to 4, wherein the training of the machine learning model comprises comparing an overlapping area between the predicted variation trend and the reference variation trend.6. The method of any one of clauses 1 to 5, wherein the training of the machine learning model comprises comparing a distance between the predicted variation trend and the reference variation trend.7. The method of any one of clauses 1 to 6, wherein the training of the machine learning model comprises comparing a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.8. The method of any one of clauses 1 to 7, wherein the training of the machine learning model comprises evaluating a loss function of the predicted variation trend, wherein the loss function comprises a function evaluating an overlapping area the predicted variation trend and the reference variation trend.9. The method of any one of clauses 1 to 8, wherein the training of the machine learning model comprises evaluating a loss function of the predicted variation trend, wherein the loss function comprises a function evaluating a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.10. The method of clause 8 or 9, wherein the loss function is minimized.11. The method of any one of clauses 1 to 10, wherein the training data comprises augmented data across a process window.12. The method of any one of clauses 1 to 11, wherein the reference variation trend is a user-defined reference variation trend.13. The method of any one of clauses 1 to 12, wherein the reference variation trend is a previously simulated variation trend.2025P00004WQ 01 3014. The method of any one of clauses 1 to 13, wherein the machine learning model comprises a mask model, an optical model, a resist model, or an etch model.15. The method of any one of clauses 1 to 14, wherein the machine learning model comprises a neural network architecture.16. The method of any one of clauses 1 to 15, wherein the predicted variation trend comprises a predicted process window of the imaging characteristic across the plurality of varying process conditions.17. The method of any one of clauses 1 to 16, wherein the predicted variation trend is derived from a plurality of generated predictions of the machine learning model in a plurality of training iterations.18. The method of any one of clauses 1 to 17, wherein the machine learning model is trained using an offline server or system.19. A non-transitory computer readable medium comprising a set of instructions that is executable by one or more processors of a computing device to cause the computing device to perform operations for training a machine learning model associated with a lithography process, the operations comprising the method of any one of clauses 1-18.

[0117] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof. The present disclosure has been described in connection with various embodiments, other embodiments of the disclosure will be apparent from consideration of the specification and practice of the technology disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims

2025P00004WQ 01 31CLAIMS1. A method for training a machine learning model associated with a lithography process, the method comprising:obtaining training data from a plurality of varying process conditions;grouping the training data, wherein a group of the training data comprises data of an imaging characteristic obtained from the plurality of varying process conditions; andtraining the machine learning model to generate a predicted variation trend of the imaging characteristic with the plurality of varying process conditions, wherein the training comprises comparing the predicted variation trend to a reference variation trend of the imaging characteristic with the plurality of varying process conditions.

2. The method of claim 1, wherein the training data comprises simulated or measured data of a feature associated with the lithography process.

3. The method of claim 1, wherein the imaging characteristic comprises a critical dimension, an edge placement, or a pitch of a feature associated with the lithography process.

4. The method of claim 1, wherein the plurality of varying process conditions comprises a varying focus, a varying dose, a varying mask bias, a varying slit position, a varying draw CD, or a varying capture pitch.

5. The method of claim 1, wherein the training of the machine learning model comprises comparing an overlapping area between the predicted variation trend and the reference variation trend.

6. The method of claim 1, wherein the training of the machine learning model comprises comparing a distance between the predicted variation trend and the reference variation trend.

7. The method of claim 1, wherein the training of the machine learning model comprises comparing a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.

8. The method of claim 1, wherein the training of the machine learning model comprises evaluating a loss function of the predicted variation trend, wherein the loss function comprises a function evaluating an overlapping area the predicted variation trend and the reference variation trend.2025P00004WQ 01 329. The method of claim 1, wherein the training of the machine learning model comprises evaluating a loss function of the predicted variation trend, wherein the loss function comprises a function evaluating a slope between a first point and a second point on both the predicted variation trend and the reference variation trend.

10. The method of claim 1, wherein the training data comprises augmented data across a process window.

11. The method of claim 1, wherein the reference variation trend is a user-defined reference variation trend.

12. The method of claim 1, wherein the reference variation trend is a previously simulated variation trend.

13. The method of claim 1, wherein the machine learning model comprises a mask model, an optical model, a resist model, or an etch model.

14. The method of claim 1, wherein the predicted variation trend comprises a predicted process window of the imaging characteristic across the plurality of varying process conditions.

15. The method of claim 1, wherein the predicted variation trend is derived from a plurality of generated predictions of the machine learning model in a plurality of training iterations.

Images