Method of training machine learning model for computational lithography

Abstract

Various methods of training a machine learning model associated with a patterning process are described herein. A method for training a machine learning model configured to predict a mask pattern is described herein. The method comprises obtaining: (i) a process model of a patterning process configured to predict a pattern on a substrate, wherein the process model comprises one or more trained machine learning models; and (ii) a target pattern; and training, by the hardware computer system, a machine learning model configured to predict the mask pattern based on the process model and a cost function that determines a difference between the predicted pattern and the target pattern.

Description

[0001] This application is a divisional application of ASML Netherlands GmbH's patent application No. 201980015018.X entitled "Method for Training a Machine Learning Model for Computational Lithography" (International Application Date: 20190220, International Application No.: PCT / EP2019 / 054246), which entered the Chinese national phase on August 24, 2020.

[0002] Cross-reference to related applications

[0003] This application claims priority to U.S. Application 62 / 634,523, filed February 23, 2018, the entire contents of which are incorporated herein by reference. Technical Field

[0004] This article describes, in general, the patterning process and the equipment and methods for determining patterns corresponding to a design layout using a pattern-forming apparatus. Background Technology

[0005] Photolithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning apparatus (e.g., a mask) can contain or provide a pattern corresponding to a single layer (“design layout”) of the IC, and this pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) that has already been coated with a layer of radiation-sensitive material (“resist”). Typically, a single substrate contains multiple adjacent target portions, and the pattern is sequentially transferred by the photolithography projection equipment onto these multiple adjacent target portions, one at a time. In one type of photolithography projection equipment, the entire pattern on the patterning apparatus is transferred onto one target portion at a time; such equipment is often referred to as a stepper. In alternative equipment (often referred to as a stepping and scanning apparatus), a projection beam scans across the patterning apparatus in a given reference direction (“scanning” direction) while moving the substrate parallel or antiparallel to that reference direction. Different portions of the pattern on the patterning apparatus are gradually transferred onto a target portion. Since photolithography projection apparatuses typically have a reduction ratio M (e.g., 4), the substrate movement speed F will be 1 / M of the speed of the projection beam scanning patterning apparatus. Further information regarding the photolithography apparatus described herein can be obtained, for example, from US 6046792, which is incorporated herein by reference.

[0006] Before a pattern is transferred from a patterning device to a substrate, the substrate can undergo various processes, such as applying an undercoat, coating with a resist, and soft baking. After exposure, the substrate can undergo other processes (“post-exposure processes”), such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred pattern. This series of processes serves as the basis for fabricating a single layer of a device (e.g., an IC). The substrate can then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all aimed at completing a single layer of the device. If multiple layers are required in the device, the entire process or its variations are repeated for each layer. Ultimately, a device appears in each target portion of the substrate. These devices are then separated from each other using techniques such as dicing or sawing, allowing individual devices to be mounted on a carrier, connected to pins, etc.

[0007] Therefore, manufacturing devices such as semiconductor devices typically involves processing a substrate (e.g., a semiconductor wafer) using several manufacturing processes to form various features of the device and to form multiple layers. These layers and features are typically fabricated and processed using processes such as deposition, photolithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on a substrate, and then the devices are separated into individual devices. This device manufacturing process can be considered a patterning process. A patterning process includes patterning steps, such as optical lithography and / or nanoimprint lithography using patterning apparatus in a photolithography device, to transfer a pattern from the patterning apparatus to the substrate, and typically, but optionally, includes one or more associated patterning processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching the pattern using an etching apparatus, etc.

[0008] As mentioned above, photolithography is a central step in the fabrication of devices such as integrated circuits (ICs), in which patterns formed on a substrate define the functional elements of the device, such as microprocessors and memory chips. Similar photolithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0009] As semiconductor manufacturing processes continue to advance, the size of functional components continues to shrink, while the number of functional components (such as transistors) in each device has steadily increased for decades, following a trend commonly known as "Moore's Law." At the current level of technology, layers of devices are fabricated using photolithography projection equipment. This equipment projects a design layout onto a substrate using irradiation from a deep ultraviolet source, thereby creating individual functional components with dimensions well below 100 nm (i.e., less than half the wavelength of radiation from the irradiation source, such as a 193 nm source).

[0010] According to the resolution formula CD = k1 × λ / NA (where λ is the wavelength of the radiation used (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithography projector, CD is the "critical size"—typically the smallest feature size to be printed—and k1 is an empirical resolution factor), the process of printing features smaller than the classical resolution limit of the lithography projector is often referred to as low-k1 lithography. Generally, the smaller k1 is, the more difficult it becomes to reproduce a pattern on a substrate that resembles the shape and size planned by the designer to achieve a specific electrical function and / or performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithography projector, design layout, or patterning apparatus. These steps include, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, the use of phase-shifting patterning devices, optical proximity correction terms (OPC, sometimes also referred to as "optical and process correction terms") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). As used herein, the term "projection optics" should be broadly interpreted to encompass various types of optical systems, including, for example, refractive optics, reflective optics, and aperture and reflective-refractive optics. The term "projection optics" may also include components that, according to the operation of any of these design types, guide, shape, or control a projected beam of radiation, either jointly or individually. The term "projection optics" can include any optical component in a lithographic projection apparatus, regardless of its location in the optical path of the apparatus. Projection optics can include optical components for shaping, modulating, and / or projecting radiation from a source before it passes through a patterning apparatus, and / or for shaping, modulating, and / or projecting radiation after it has passed through the patterning apparatus. Projection optics typically do not include a source or a patterning apparatus. Summary of the Invention

[0011] According to an embodiment, a method is provided for training a machine learning model configured to predict a mask pattern. The method includes obtaining: (i) a process model of a patterning process configured to predict a pattern on a substrate; and (ii) a target pattern; and training the machine learning model configured to predict the mask pattern by a hardware computer system based on the process model and a cost function that determines the difference between the predicted pattern and the target pattern.

[0012] Furthermore, according to an embodiment, a method is provided for training a process model for a patterning process to predict a pattern on a substrate. The method includes obtaining: (i) a first trained machine learning model for predicting mask transmission during the patterning process; and / or (ii) a second trained machine learning model for predicting the optical behavior of a device used in the patterning process; and / or (iii) a third trained machine learning model for predicting a resist process during the patterning process; and / or (iv) a printed pattern; concatenating the first trained model, the second trained model, and / or the third trained model to generate a process model; and training the process model configured to predict a pattern on a substrate by a hardware computer system based on a cost function, the cost function determining the difference between the predicted pattern and the printed pattern.

[0013] Furthermore, according to an embodiment, a method for determining an optical proximity correction term corresponding to a target pattern is provided. The method includes obtaining: (i) a trained machine learning model configured to predict the optical proximity correction term, and (ii) a target pattern to be printed on a substrate via a patterning process; and determining the optical proximity correction term by a hardware computer system based on the trained machine learning model configured to predict the optical proximity correction term corresponding to the target pattern.

[0014] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict a mask pattern based on defects. The method includes obtaining: (i) a process model of a patterning process configured to predict a pattern on a substrate, wherein the process model includes one or more trained machine learning models; (ii) a trained manufacturability model configured to predict defects based on the predicted pattern on the substrate; and (iii) a target pattern; and training the machine learning model configured to predict the mask pattern by a hardware computer system based on the process model, the trained manufacturability model, and a cost function, wherein the cost function is the difference between the target pattern and the predicted pattern.

[0015] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict mask patterns based on manufacturing violation probabilities. The method includes obtaining: (i) a process model of a patterning process configured to predict patterns on a substrate, wherein the process model includes one or more trained machine learning models; (ii) a trained mask rule checking model configured to predict manufacturing violation probabilities of the mask pattern; and (iii) a target pattern; and training the machine learning model configured to predict the mask pattern by a hardware computer system based on the trained process model, the trained mask rule checking model, and a cost function, wherein the cost function is based on manufacturing violation probabilities predicted by the mask rule checking model.

[0016] Furthermore, according to an embodiment, a method is provided for determining an optical proximity correction term corresponding to a target pattern. The method includes obtaining: (i) a trained machine learning model configured to predict the optical proximity correction term based on a mask manufacturing violation probability and / or based on defects on a substrate; and (ii) a target pattern to be printed on the substrate via a patterning process; and determining the optical proximity correction term by a hardware computer system based on the trained machine learning model and the target pattern.

[0017] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict a mask pattern. The method includes obtaining: (i) a set of reference images; and (ii) a mask image corresponding to a target pattern; and training the machine learning model configured to predict the mask pattern by a hardware computer system based on the reference images and a cost function that determines the difference between the predicted mask pattern and the reference pattern.

[0018] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict defects on a substrate. The method includes obtaining: (i) a resist image or an etched image; and / or (ii) a target pattern; and training a machine learning model configured to predict defect indices by a hardware computer system based on the resist image or etched image, the target pattern, and a cost function, wherein the cost function is the difference between the predicted defect indices and the true defect indices.

[0019] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict mask rule check violations of mask patterns. The method includes obtaining: (i) a set of mask rule checks; (ii) a set of mask patterns; and training the machine learning model configured to predict mask rule check violations by a hardware computer system based on the set of mask rule checks, the set of mask patterns, and a cost function based on mask rule check metrics, wherein the cost function is the difference between predicted mask rule check metrics and true mask rule check metrics.

[0020] Furthermore, according to an embodiment, a method for determining a mask pattern is provided. The method includes obtaining: (i) an initial image corresponding to a target pattern; (ii) a process model of a patterning process configured to predict patterns on a substrate; and (ii) a trained defect model configured to predict defects based on the pattern predicted by the process model; and a hardware computer system determining the mask pattern from the initial image based on the process model, the trained defect model, and a cost function including defect indices.

[0021] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict a mask pattern. The method includes obtaining: (i) a target pattern; (ii) an initial mask pattern corresponding to the target pattern; (iii) a resist image corresponding to the initial mask pattern; and (iv) a set of reference images; and training the machine learning model configured to predict the mask pattern by a hardware computer system based on the target pattern, the initial mask pattern, the resist image, the set of reference images, and a cost function that determines the difference between the predicted mask pattern and the reference images.

[0022] Furthermore, according to an embodiment, a method is provided for training a machine learning model configured to predict resist patterns. The method includes obtaining: (i) a process model of a patterning process configured to predict an etched image based on a resist image; and (ii) an etch target; and training the machine learning model configured to predict the resist image by a hardware computer system based on the etch model and a cost function, the cost determining the difference between the etched image and the etch target.

[0023] Furthermore, according to an embodiment, a computer program product is provided, the computer program product including a non-transitory computer-readable medium having instructions recorded thereon, the instructions performing any of the methods described above when executed by a computer. Attached Figure Description

[0024] Figure 1 A block diagram of the various subsystems of the photolithography system is shown.

[0025] Figure 2 A flowchart of a method for simulating images according to one embodiment is shown, in which M3D is taken into account.

[0026] Figure 3 A flowchart illustrating the use of a mask transmission function according to one embodiment is shown schematically.

[0027] Figure 4 A flowchart illustrating a method for training a neural network according to an embodiment is shown, the neural network determining the M3D of a structure on a pattern forming apparatus.

[0028] Figure 5 A flowchart illustrating a method for training a neural network according to an embodiment is shown, the neural network determining the M3D of a structure on a pattern forming apparatus.

[0029] Figure 6 It schematically shows that in Figure 4 or Figure 5 An example of a feature used in the design layout of the method.

[0030] Figure 7A A flowchart illustrating an embodiment is shown, showing how an M3D model can be exported for multiple patterning processes and stored in a database for future use.

[0031] Figure 7B A flowchart illustrating an embodiment of a process for retrieving M3D models from a database based on a patterning process is shown schematically.

[0032] Figure 8 This is a block diagram of a machine learning-based architecture for the patterning process according to an embodiment.

[0033] Figure 9 A flowchart illustrating a method for training a process model of a patterning process to predict patterns on a substrate, according to an embodiment, is shown schematically.

[0034] Figure 10A A flowchart illustrating a method for training a machine learning model according to one embodiment is shown, the machine learning model being configured to predict the mask pattern of a mask used in a patterning process.

[0035] Figure 10B A flowchart illustrating another method for training a machine learning model based on a benchmark image, according to one embodiment, is shown schematically. The machine learning model is configured to predict the mask pattern of the mask used in the patterning process.

[0036] Figure 10C A flowchart of another method for training a machine learning model according to one embodiment is illustrated, the machine learning model being configured to predict the mask pattern of a mask used in the patterning process.

[0037] Figure 11 A mask image with OPC generated according to a target pattern is shown according to one embodiment.

[0038] Figure 12 A curve mask image with OPC generated according to a target pattern is shown according to one embodiment.

[0039] Figure 13 This is a block diagram of a machine learning-based architecture for the patterning process according to an embodiment.

[0040] Figure 14A A flowchart illustrating a method for training a machine learning model, configured to predict defect data, is shown schematically according to one embodiment.

[0041] Figure 14BA flowchart illustrating a method for training a machine learning model based on predicted defects on a substrate, according to one embodiment, is shown schematically. The machine learning model is configured to predict mask patterns.

[0042] Figure 14C A flowchart of another method for training a machine learning model based on predicted defects on a substrate, according to one embodiment, is schematically shown. The machine learning model is configured to predict mask patterns.

[0043] Figure 15A , Figure 15B and Figure 15C An exemplary defect on a substrate according to an embodiment is shown.

[0044] Figure 16A A flowchart illustrating a method for training a machine learning model according to one embodiment is shown, the machine learning model being configured to predict the mask manufacturability of a mask pattern used in a patterning process.

[0045] Figure 16B A flowchart illustrating another method for training a machine learning model based on mask manufacturability according to one embodiment is shown, the machine learning model being configured to predict mask patterns.

[0046] Figure 16C A flowchart illustrating another method for training a machine learning model based on mask manufacturability according to one embodiment is shown, the machine learning model being configured to predict mask patterns.

[0047] Figure 17 This is a block diagram of an exemplary computer system according to an embodiment.

[0048] Figure 18 This is a schematic diagram of a photolithography projection apparatus according to an embodiment.

[0049] Figure 19 This is a schematic diagram of another photolithography projection device according to an embodiment.

[0050] Figure 20 According to the embodiments Figure 18 A more detailed view of the device.

[0051] Figure 21 According to the embodiments Figure 19 and Figure 20 A more detailed view of the device's source collector module SO. Detailed Implementation

[0052] While specific references may be made herein to the manufacture of ICs, it should be clearly understood that the description herein has many other possible applications. For example, the invention can be used in the manufacture of integrated optical systems, in guiding and detecting patterns for magnetic domain memories, in liquid crystal display panels, in thin-film magnetic heads, and so on. Those skilled in the art will understand that, in the context of these alternative applications, any use of the terms “mask,” “wafer,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” or “target portion,” respectively.

[0053] In this document, the terms “radiation” and “beam” are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., with wavelengths of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., with wavelengths in the range of about 5 nm to about 100 nm).

[0054] Patterning apparatuses can include or form one or more design layouts. Design layouts can be generated using CAD (Computer-Aided Design) programs, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a predetermined set of design rules to generate functional design layouts / patterning apparatuses. These rules are set by process and design constraints. For example, design rules define spatial tolerances between devices (such as gates, capacitors, etc.) or interconnects to ensure that devices or lines do not interact with each other in undesirable ways. One or more design rule constraints can be called “critical dimensions” (CDs). A device’s critical dimensions can be defined as the minimum width of a line or via, or the minimum space between two lines or vias. Therefore, CDs determine the overall size and density of the designed device. Of course, one of the goals in device fabrication (via patterning apparatuses) is to faithfully reproduce the initial design intent on the substrate.

[0055] Pattern layout design may include, for example, the application of resolution enhancement techniques such as Optical Proximity Correction (OPC). OPC addresses the fact that the final size and position of an image of the design layout projected onto a substrate will not be the same as, or simply depend on, the size and position of the design layout on the patterning apparatus. It should be noted that the terms “mask,” “mask plate,” and “patterning apparatus” are used interchangeably herein. Moreover, those skilled in the art will recognize that the terms “mask,” “patterning apparatus,” and “design layout” are used interchangeably, as in the RET context, a physical patterning apparatus is not necessarily used, but a design layout can be used to represent a physical patterning apparatus. For small feature sizes and high feature densities present on some design layouts, the position of a particular edge of a given feature will be influenced to some extent by the presence or absence of other adjacent features. These proximity effects are caused by minute radiation or non-geometric optical effects (e.g., diffraction and interference) connecting one feature to another. Similarly, proximity effects may be caused by diffusion and other chemical reactions during post-exposure baking (PEB), resist development, and etching, which typically occurs after photolithography.

[0056] To increase the likelihood that the projected image of a design layout is in accordance with the requirements of a given target circuit design, sophisticated numerical models, corrections, or pre-deformations of the design layout can be used to predict and compensate for proximity effects. The paper "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 current "model-based" optical proximity effect correction processes. In typical high-end designs, almost every feature of the design layout undergoes some modification to achieve high fidelity of the projected image relative to the target design. These modifications can include shifting or offsetting edge positions or linewidths, as well as the application of "auxiliary" features designed to assist the projection of other features.

[0057] The simplest form of OPC is selective bias. Given a CD versus pitch profile, all different pitches can be forced to produce the same CD, at least under optimal focus and exposure, by varying the CD at the horizontal plane of the patterning apparatus. Therefore, if a feature is printed too small at the horizontal plane of the substrate, the horizontal feature of the patterning apparatus will be biased slightly larger than the nominal value, and vice versa. Since the pattern transfer process from the horizontal plane of the patterning apparatus to the horizontal plane of the substrate is non-linear, the amount of bias is not simply the CD error measured under optimal focus and exposure multiplied by a reduction ratio, but rather an appropriate bias can be determined using modeling and experimentation. In particular, selective bias is an incomplete solution to the proximity effect problem if applied only under nominal process conditions. Although this bias can theoretically be applied to give a uniform CD versus pitch profile under optimal focus and exposure, once the exposure process changes from nominal conditions, the pitch profile for each bias will respond differently, resulting in different process windows for different features. A process window is a series of values ​​for two or more process parameters (such as focus and radiation dose in a lithography apparatus) under which features are created sufficiently accurately (e.g., the CD of the features is within a range such as ±10% or ±5%). Therefore, even the "optimal" bias for giving the same relationship between CD and pitch can negatively impact the overall process window, thereby reducing (rather than amplifying) the focus and exposure range for all target features to be printed on the substrate within the desired process tolerances.

[0058] Other, more sophisticated OPC techniques have been developed for applications beyond the one-dimensional bias example described above. Two-dimensional proximity effects are characterized by line tip shortening. Line tips tend to “pull back” from their desired endpoints as a function of exposure and focus. In many cases, the degree of tip shortening of long line tips can be several times greater than the corresponding line narrowing. This type of line tip pull-back can cause serious failures in the manufactured device if the line tip does not fully traverse the underlying layer it is intended to cover (e.g., the polysilicon gate layer above the source / drain regions). Because this type of pattern is highly sensitive to focus and exposure, simply biasing the line tip to grow longer than the design length is insufficient. This is because lines under optimal focus and exposure, or under insufficient exposure, can become too long, causing short circuits when the extended line tip contacts adjacent structures, or resulting in unnecessarily large circuit dimensions if more space is added between individual features in the circuit. Since one of the goals of integrated circuit design and manufacturing is to maximize the number of functional elements while minimizing the area required per chip, adding excessive spacing is an undesirable solution.

[0059] Two-dimensional OPC methods can help address line-end pullback issues. Additional structures such as “hammers” or “serifs” (also known as “auxiliary features”) can be added to the line end to effectively anchor it in place and provide reduced pullback across the entire process window. Even under optimal focus and exposure, these additional structures remain unresolved, altering the appearance of the primary feature without being fully resolved on their own. As used herein, “primary feature” refers to a feature intended to be printed onto the substrate under some or all conditions of the process window. Auxiliary features can take on more aggressive and diverse forms than simple hammers added to the line end, reaching a point where the pattern on the patterning apparatus is no longer simply a scaled-down version of the desired substrate pattern. Auxiliary features such as serifs can be applied to many situations beyond simply reducing line-end pullback. Internal or external serifs can be applied to any edge (especially two-dimensional edges) to reduce corner rounding or edge squeezing. With sufficient selective bias and auxiliary features of all sizes and polarizations, the similarity between the feature on the patterning apparatus and the desired final pattern at the substrate's horizontal plane decreases. Generally, the pattern forming apparatus patterns a pre-deformed form of a pattern on a horizontal plane of a substrate, wherein the deformation is intended to counteract or eliminate pattern deformation that will occur during the manufacturing process, so as to produce a pattern on the substrate that is as close as possible to the pattern intended by the designer.

[0060] Another OPC technique involves using completely independent and indistinguishable auxiliary features to replace or supplement those auxiliary features (such as wiring) connected to the main feature. Here, the term "independent" means that the edges of these auxiliary features are not connected to the edges of the main feature. These independent auxiliary features are not intended or expected to be printed as features on the substrate, but rather to modify the spatial image of the nearby main feature to improve its printability and process tolerance. These auxiliary features (often referred to as "scattering stripes" or "SBARs") can include sub-resolution auxiliary features (SRAFs) and sub-resolution inverse features (SRIFs). Sub-resolution auxiliary features are features outside the edges of the main feature, while sub-resolution inverse features are features extracted from within the edges of the main feature. The presence of SBARs adds another layer of complexity to the patterning apparatus. A simple example of using scattering stripes is drawing a regular, indistinguishable array of scattering stripes on either side of an isolation line feature. From a spatial image perspective, this has the effect of making the isolation line appear more representative of a single line within a dense line array, thus allowing the focus and exposure tolerances of the process window to more closely approximate those of a dense pattern. Compared to features drawn as isolations on the horizontal plane of the pattern-forming device, a shared process window between such decorative isolation features and dense patterns will have greater common tolerance for focus and exposure variations.

[0061] Auxiliary features can be viewed as the difference between features on the pattern-forming apparatus and features in the design layout. The terms "primary feature" and "auxiliary feature" do not imply that a particular feature on the pattern-forming apparatus must be labeled as one or the other.

[0062] As used herein, the terms "mask" or "patterning apparatus" can be broadly interpreted to refer to a general patterning apparatus that can be used to impart a patterned cross-section to an incident radiation beam, corresponding to a pattern to be generated in a target portion of a substrate; the term "optical valve" can also be used in this context. Examples of other such patterning apparatuses besides classic masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.) include:

[0063] - Programmable mirror array. An example of such a device is a matrix-addressable surface with a viscoelastic control layer and a reflective surface. The basic principle underlying this device is that, for example, the addressed regions of the reflective surface reflect incident radiation as diffracted radiation, while the unaddressed regions reflect incident radiation as non-diffracted radiation. With the use of appropriate filters, the non-diffracted radiation can be filtered out from the reflected beam, leaving only the diffracted radiation; thus, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The desired matrix addressing can be performed using appropriate electronics.

[0064] - Programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0065] As a brief introduction, Figure 1 An exemplary photolithography projection apparatus 10A is illustrated. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources, including extreme ultraviolet (EUV) sources (as mentioned above, the photolithography projection apparatus itself does not need to have a radiation source); illumination optics, which, for example, define local coherence (denoted as sigma), and may include optics 14A, 16Aa, and 16Ab for radiation shaping from source 12A; a pattern forming apparatus 18A; and a transmissive optics 16Ac that projects an image of a pattern from the pattern forming apparatus onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics can limit the range of beam angles incident on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA of the projection optics as n sin(Θmax), where n is the refractive index of the medium between the substrate and the last element of the projection optics, and Θmax is the maximum angle of the beam exiting the projection optics that can still be incident on the substrate plane 22A.

[0066] In a photolithography projection apparatus, a source provides illumination (i.e., radiation) to a patterning apparatus, and projection optics guide and shape the illumination onto a substrate via the patterning apparatus. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the distribution of radiation intensity at a horizontal plane of the substrate. A resist layer on the substrate is exposed, and the spatial image is transferred to the resist layer as a latent image therein, a “resist image” (RI). The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. Resist models can be used to calculate the resist image based on the spatial image, examples of which can be found in U.S. Patent Application Publication No. US2009-0157360, the entire disclosure of which is hereby incorporated herein by reference. The resist model relates only to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical characteristics of a photolithography projection apparatus (e.g., the characteristics of the source, patterning apparatus, and projection optics) determine the spatial image. Since the patterning apparatus used in a photolithography projection apparatus can be varied, it is desirable to separate the optical characteristics of the patterning apparatus from the optical characteristics of the rest of the photolithography projection apparatus, which includes at least the source and projection optics.

[0067] One aspect of understanding the photolithography process is understanding the interaction between radiation and the patterning apparatus. The electromagnetic field of the radiation after it has passed through the patterning apparatus can be determined based on the electromagnetic field of the radiation before it reaches the patterning apparatus and a function characterizing this interaction. This function can be called the mask transmission function (which can be used to describe the interaction between transmissive and / or reflective patterning apparatuses).

[0068] Mask transmission functions can take many different forms. One form is binary. A binary mask transmission function has either one of two values ​​(e.g., zero and a positive constant) at any given location on the patterning apparatus. A mask transmission function in the binary form can be called a binary mask. Another form is continuous. That is, the modulus of the transmittance (or reflectance) of the patterning apparatus is a continuous function of the location on the patterning apparatus. The phase of the transmittance (or reflectance) can also be a continuous function of the location on the patterning apparatus. A mask transmission function in the continuous form can be called a continuous transmission mask (CTM). For example, a CTM can be represented as a pixelated image where each pixel can be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.), rather than a binary value of 0 or 1. An exemplary CTM process and its details can be found in commonly assigned U.S. Patent No. 8,584,056, the entire disclosure of which is hereby incorporated herein by reference.

[0069] According to an embodiment, a design layout can be optimized as a continuous transmission mask (“CTM optimization”). In this optimization, the transmission at all locations of the design layout is not limited to a number of discrete values. Alternatively, the transmission can take any value within an upper and lower limit. Further details can be found in commonly assigned U.S. Patent No. 8,584,056, the entire disclosure of which is hereby incorporated herein by reference. Implementing a continuous transmission mask on a patterning apparatus is very difficult (if not impossible). However, a continuous transmission mask is a useful tool because it allows for faster optimization by not limiting the transmission to a number of discrete values. In EUV lithography projection apparatuses, the patterning apparatus can be reflective. The principle of CTM optimization also applies to design layouts to be produced on reflective patterning apparatuses, where the reflectivity at all locations of the design layout is not limited to a number of discrete values. Therefore, as used herein, the term “continuous transmission mask” can refer to a design layout to be produced on either a reflective or transmissive patterning apparatus. CTM optimization can be based on a three-dimensional mask model that takes into account the effects of a thick mask. The thick mask effect is caused by the vector nature of light and can be significant when the feature size in the design layout is smaller than the wavelength of light used in the photolithography process. The thick mask effect includes polarization dependence due to varying boundary conditions of electric and magnetic fields, transmittance, reflectance, and phase errors in smaller openings, edge diffraction (or scattering) effects, or electromagnetic coupling. Further details of the three-dimensional mask model can be found in commonly assigned U.S. Patent No. 7,703,069, the entire disclosure of which is hereby incorporated herein by reference.

[0070] In an embodiment, auxiliary features (sub-resolution auxiliary features and / or printable resolution auxiliary features) can be placed into the design layout based on a design layout optimized for a continuous transmission mask. This allows auxiliary features to be identified and designed according to the continuous transmission mask.

[0071] In embodiments, the thin mask approximation (also known as Kirchhoff boundary conditions) is widely used to simplify the determination of the interaction between radiation and the patterning apparatus. The thin mask approximation assumes that the thickness of the structure on the patterning apparatus is very small compared to the wavelength, and the width of the structure on the mask is very large compared to the wavelength. Therefore, the thin mask approximation assumes that the electromagnetic field after passing through the patterning apparatus is the product of the incident electromagnetic field and the mask transmission function. However, as the lithography process uses shorter radiation and shorter wavelengths, and the structures on the patterning apparatus become increasingly smaller, the assumptions of the thin mask approximation may fail. For example, due to the finite thickness of the structure (e.g., the edge between the top surface and the sidewalls), the interaction between radiation and said structure (“mask 3D effect” or “M3D”) can become significant. Including this scattering in the mask transmission function allows the mask transmission function to better capture the interaction between radiation and the patterning apparatus. The mask transmission function under the thin mask approximation can be called the thin mask transmission function. The mask transmission function that includes M3D can be called the M3D mask transmission function.

[0072] Figure 2 This is a flowchart of a method for determining an image (e.g., a spatial image, a resist image, or an etched image) according to an embodiment, the image being the result of a patterning process including a photolithography process taking into account M3D. In process 2008, the M3D mask transmission function 2006, the illumination source model 2005, and the projection optics model 2007 of the patterning apparatus are used to determine (e.g., simulate) the spatial image 2009. The spatial image 2009 and the resist model 2010 may be used in an optional process 2011 to determine (e.g., simulate) the resist image 2012. The resist image 2012 and the etch model 2013 may be used in an optional process 2014 to determine (e.g., simulate) the etched image 2015. The etched image can be defined as the spatial distribution of the amount of etching in the substrate after etching the substrate using a developed resist as an etch mask on the substrate.

[0073] As described above, the mask transmission function of a patterning apparatus (e.g., a thin mask or M3D mask transmission function) is a function that determines the electromagnetic field of the radiation after its interaction with the patterning apparatus based on the electromagnetic field of the radiation before the radiation interacts with the patterning apparatus. As mentioned above, the mask transmission function can describe the interaction between a transmissive patterning apparatus and a reflective patterning apparatus.

[0074] Figure 3A flowchart illustrating the use of a mask transmission function is shown schematically. The electromagnetic field 3001 of the radiation before its interaction with the patterning apparatus in process 3003 and the mask transmission function 3002 are used to determine the electromagnetic field 3004 of the radiation after its interaction with the patterning apparatus. The mask transmission function 3002 can be a thin mask transmission function. The mask transmission function 3002 can be an M3D mask transmission function. In general mathematical form, the relationship between electromagnetic fields 3001 and 3004 can be expressed by the formula: ,in It is the electric component of electromagnetic field 3004; It is the electric component of electromagnetic field 3001; and It is the mask transmission function.

[0075] The M3D of structures on a patterning apparatus (e.g., represented by one or more parameters of the M3D mask transmission function) can be determined by computational or empirical models. In one example, the computational model could include a rigorous simulation of the M3D of all structures on the patterning apparatus (e.g., using a Finite Discrete Time Domain (FDTD) algorithm or a Rigorous Coupled Waveguide Analysis (RCWA) algorithm). In another example, the computational model could include a rigorous simulation of the M3D of certain portions of structures tending to have a large M3D, and adding the M3D of these portions to the thin mask transmission function of all structures on the patterning apparatus. However, rigorous simulations are often computationally expensive.

[0076] In contrast, the empirical model does not simulate M3D; instead, the empirical model determines M3D based on the correlation between inputs to the empirical model (e.g., one or more characteristics of the design layout formed in or by the patterning apparatus, one or more characteristics of the patterning apparatus (such as its structure and material composition), and one or more characteristics of the irradiation used in the lithography process (such as wavelength)) and M3D.

[0077] An example of an empirical model is the neural network. A neural network, also known as an artificial neural network (ANN), is “a computational system consisting of many simple, highly interconnected processing elements that process information through dynamic responses to external inputs,” Neural Network Primer: Part I, Maureen Caudill, AI expert, February 1989. A neural network is a processing device (algorithm or actual hardware) that is roughly modeled after, but on a much smaller scale, the neuronal structure of the mammalian cerebral cortex. A neural network may have hundreds or thousands of processing units, while the mammalian brain has hundreds of millions of neurons, where the overall interaction and emergent behavior of these neurons are correspondingly amplified.

[0078] A neural network can be trained (i.e., its parameters are determined) using a set of training data. Training data can include a set of training samples or consist of a set of training samples. Each sample can be a pair consisting of an input object (typically a vector, which may be called a feature vector) and a desired output value (also called a supervision signal), or a pair consisting of said input object and desired output value. The training algorithm analyzes the training data and modulates the behavior of the neural network by adjusting its parameters (e.g., the weights of one or more layers) based on the training data. The trained neural network can then be used to map new samples.

[0079] When defining the M3D, the feature vector may include: one or more characteristics of the design layout included or formed by the patterning apparatus (e.g., shape, position, size, etc.), one or more characteristics of the patterning apparatus (e.g., one or more physical properties, such as size, reflectivity, material composition, etc.), and one or more characteristics of the irradiation used in the photolithography process (e.g., wavelength). The monitoring signal may include one or more characteristics of the M3D (e.g., one or more parameters of the M3D mask transmission function).

[0080] Given a set of forms N training samples, such that It is the feature vector of the i-th example, and It is the supervision signal of the i-th example, and the training algorithm seeks the neural network. ,in It is the input space and This is the output space. An eigenvector is an n-dimensional vector representing the numerical features of an object. The vector space associated with these vectors is usually called the feature space. Sometimes a scoring function is used. to indicate It is very convenient, making Defined as returning the highest score: of Value. Use Let's use this to represent the space of the scoring function.

[0081] when Using conditional probability model form or Using a joint probability model When in the form of , neural networks can be probabilistic.

[0082] There exists for selection or There are two basic approaches: empirical risk minimization and structural risk minimization. Empirical risk minimization seeks a neural network that best fits the training data. Structural risk minimization involves a penalty function that controls the trade-off between bias and variance. For example, in an embodiment, the penalty function could be based on a cost function, which could be the square of the error, the number of defects, EPE, etc. The function (or the weights within the function) can be modified to reduce or minimize the variance.

[0083] In both cases, it is assumed that the training set consists of independent pairs with the same distribution. One or more samples, or a combination of said samples. A loss function is defined to measure how well the function fits the training data. For training samples Predicted value The loss is .

[0084] function Risk Defined as The expected loss. This can be evaluated based on the training data. .

[0085] Figure 4A flowchart illustrating a method for training a neural network according to an embodiment is shown schematically. This neural network determines the M3D (e.g., represented by one or more parameters of an M3D mask transmission function) of one or more structures on a pattern forming apparatus. Values ​​of one or more properties 410 of a portion of a design layout are obtained. The design layout may be a binary design layout, a continuous design layout (e.g., rendered from a binary design layout), or other suitable forms of design layout. One or more properties 410 may include one or more geometric features (e.g., absolute position, relative position, and / or shape) of one or more patterns in the portion. One or more properties 410 may include statistical properties of one or more patterns in the portion. One or more properties 410 may include parameterization of the portion (e.g., function values ​​of one or more patterns in the portion), such as projections onto a basis function. One or more properties 410 may include (pixelated, binary, or continuous) images derived from the portion. Values ​​of one or more properties 430 of the M3D of the pattern forming apparatus that includes or forms the portion are determined using any suitable method. The values ​​of one or more characteristics 430 of M3D can be determined based on the portion or one or more characteristics 410 of the portion. For example, a computational model can be used to determine one or more characteristics 430 of M3D. For example, one or more characteristics 430 may include one or more parameters of the M3D mask transmission function of the patterning apparatus. The values ​​of one or more characteristics 430 of M3D can be derived from the result 420 of the patterning process using the patterning apparatus. The result 420 may be an image formed on a substrate by the patterning process (e.g., a spatial image, a resist image, and / or an etched image), or a characteristic of the image (e.g., CD, mask error enhancement factor (MEEF), process window, yield, etc.). The values ​​of one or more characteristics 410 of the portion of the design layout and the values ​​of one or more characteristics 430 of M3D are included as one or more samples in the training data 440. One or more characteristics 410 are feature vectors of the samples, and one or more characteristics 430 are supervision signals of the samples. In process 450, the training data 440 is used to train the neural network 460.

[0086] Figure 5A flowchart illustrating a method for training a neural network according to an embodiment is shown schematically. This neural network determines M3D (e.g., represented by one or more parameters of an M3D mask transmission function) of one or more structures on a pattern forming apparatus. Values ​​of one or more properties 510 for a portion of a design layout are obtained. The design layout may be a binary design layout, a continuous design layout (e.g., rendered from a binary design layout), or other suitable forms of design layout. One or more properties 510 may include one or more geometric features (e.g., absolute position, relative position, and / or shape) of one or more patterns in the portion. One or more properties 510 may include one or more statistical properties of one or more patterns in the portion. One or more properties 510 may include a parameterization of the portion (i.e., the values ​​of one or more functions of one or more patterns in the portion), such as a projection onto a basis function. One or more properties 510 may include an image derived from the portion (pixelated, binary, or continuous). Values ​​of one or more properties 590 of the patterning process are also obtained. One or more characteristics 590 of the patterning process may include one or more characteristics of the irradiation source of the lithography apparatus used in the photolithography process, one or more characteristics of the projection optics of the lithography apparatus used in the photolithography process, one or more characteristics of the post-exposure process (e.g., resist development, post-exposure baking, etching, etc.), or combinations thereof. The values ​​of one or more characteristics 580 of the result of the patterning process using a patterning apparatus that includes or forms the portion are determined. The values ​​of one or more characteristics 580 of the result may be determined based on the portion and the patterning process. The result may be an image (e.g., a spatial image, a resist image, and / or an etched image) formed on a substrate by the patterning process. One or more characteristics 580 may be CD, mask error enhancement factor (MEEF), processing window, or yield. One or more characteristics 580 of the result may be determined using a computational model. The values ​​of one or more characteristics 510 of the portion of the design layout, the values ​​of one or more characteristics 590 of the patterning process, and the values ​​of one or more characteristics 580 of the result are included as one or more samples in training data 540. One or more features 510 and one or more features 590 are feature vectors of the samples, and one or more features 580 are supervision signals of the samples. In process 550, training data 540 is used to train neural network 560.

[0087] Figure 6Examples of one or more features 410 and 510 are illustrated schematically and may include: a portion 610 of the design layout, parameterization 620 of the portion, one or more geometric portions 630 of the portion (e.g., one or more regions, one or more corners, one or more edges, etc.), continuous rendering of one or more geometric portions 640, and / or continuous rendering of the portion 650.

[0088] Figure 7A The flowchart schematically illustrates the process of exporting one or more M3D models for multiple patterning processes and storing the M3D models in a database for future use. In process 6002, patterning process 6001 (see...) Figure 7B One or more properties of ) are used to derive the M3D model 6003 of the patterning process 6001 (see Figure 7B M3D model 6003 can be obtained through simulation. M3D model 6003 is stored in database 6004.

[0089] Figure 7B A flowchart illustrating the retrieval of an M3D model from a database based on a patterning process is shown. In process 6005, one or more features of the patterning process 6001 are used to query the database 6004 and retrieve the M3D model 6003 for the patterning process 6001.

[0090] In an embodiment, an optical device model representing the optical characteristics of the projection optics of a lithography apparatus (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics) can be used. The projection optics model can represent the optical characteristics of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0091] In embodiments, a machine learning model (e.g., a CNN) can be trained to represent the resist process. In an example, a resist CNN can be trained based on a cost function representing the deviation of the resist CNN's output from a simulated value (e.g., obtained from a physics-based resist model, an example of which can be found in U.S. Patent Application Publication No. 2009-0157360). Such a resist CNN can predict a resist image based on a spatial image predicted by the optical device model discussed above. Typically, a resist layer on a substrate is exposed using a spatial image, and the spatial image is transferred to the resist layer as a latent image, the "resist image" (RI). The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. The resist image can be obtained from the spatial image using a resist CNN. Resist CNNs can be used to predict resist images based on spatial images; examples of training methods can be found in U.S. Patent Application No. 62 / 463560, the entire disclosure of which is hereby incorporated herein by reference. Resist CNNs can predict the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development to, for example, predict the profile of resist features formed on a substrate, and therefore are typically only related to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). In embodiments, optical properties of the resist layer (e.g., refractive index, film thickness, propagation, and polarization effects) can be captured as part of an optical device model.

[0092] Therefore, the correlation between the optical model and the resist model is typically the predicted spatial image intensity within the resist layer, which is caused by the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections within the resist film stack. By absorbing incident energy, the radiation intensity distribution (spatial image intensity) becomes a latent image, the "resist image," and is further modified through diffusion processes and various loading effects. For full-chip applications, sufficiently fast and efficient models and training methods can predict the true 3D intensity distribution within the resist stack.

[0093] In an embodiment, the resist image can be used as input to the patterned post-transfer process model module. The patterned post-transfer process model can be another CNN configured to predict the performance of one or more resist post-development processes (e.g., etching, development, etc.).

[0094] Training different machine learning models for the patterning process can, for example, predict contours, CD (color depth), edge positions (e.g., edge placement errors) in the resist and / or etched image. Therefore, the goal of training is to accurately predict, for example, the edge positions of the printed pattern and / or the spatial image intensity slope and / or CD. These values ​​can be compared to the expected design to, for example, correct the patterning process, identify where defects are predicted to occur, etc. The expected design (e.g., the target pattern to be printed on the substrate) is typically defined as a pre-design layout available in standardized digital file formats (such as GDSII or OASIS) or other file formats.

[0095] Modeling the patterning process is a crucial part of computational lithography applications. It typically involves creating several models corresponding to different aspects of the patterning process, including mask diffraction, optical imaging, resist development, and etching. These models are often a hybrid of physical and empirical models, with varying degrees of rigor or approximation. Models are fitted based on various substrate measurement data, typically collected using scanning electron microscopy (SEM) or other lithography-related measurement tools (e.g., HMI, YieldStar, etc.). Model fitting is a regression process where model parameters are adjusted to minimize the difference between the model output and the measurements.

[0096] Such models present challenges related to both runtime and the accuracy and consistency of results derived from them. The runtime requirements impose stringent constraints on the complexity of the algorithms implemented within the model due to the need to process massive amounts of data (e.g., related to hundreds of millions of transistors on a chip). Simultaneously, the accuracy requirements become increasingly stringent as the size of the patterns to be printed becomes smaller (e.g., less than 20 nm or even single-digit nm). When such problems involve inverse function calculations, models employ nonlinear optimization algorithms (such as Broyden–Fletcher–Goldfarb–Shanno (BFGS)), which typically require gradient calculations (i.e., the derivative of the cost function at the substrate level with respect to the variable corresponding to the mask). Such algorithms are often computationally intensive and may only be suitable for chip-level applications. A chip level refers to a portion of a substrate on which a selected pattern is printed; the substrate can have thousands of such dies. Therefore, not only are faster models needed, but models capable of producing more accurate results than existing models are required to print features and patterns of smaller dimensions (e.g., less than 20 nm to single-digit nm) on the substrate. On the other hand, according to this disclosure, machine learning-based process models or mask optimization models (i) provide a better fit compared to physics-based or empirical models due to the higher fitting ability of machine learning models (i.e., the ability to adjust a relatively larger number of parameters, such as weights and biases); and (ii) provide simpler gradient computation compared to traditional physics-based or empirical models. Furthermore, according to this disclosure, trained machine learning models (e.g., CTM models, LMC models (also known as manufacturability models), MRC models, other similar models, or combinations thereof, as discussed below in this disclosure) can provide benefits such as: (i) improved accuracy in predicting, for example, mask patterns or substrate patterns; (ii) significantly reduced runtime (e.g., by more than 10 times, more than 100 times, etc.) for any design layout for which a mask layout can be determined; and (iii) simpler gradient computation compared to physics-based models, which can also improve the computation time of the computer used in the patterning process.

[0097] According to this disclosure, machine learning models such as deep convolutional neural networks can be trained to model different aspects of the patterning process. Such trained machine learning models can provide significant speed improvements over nonlinear optimization algorithms, which are typically used in reverse lithography processes (e.g., iOPC) to determine mask patterns, and thus enable simulation or prediction for whole-chip applications.

[0098] Several deep learning models based on convolutional neural networks (CNNs) are proposed in U.S. patents 62 / 462337 and 62 / 463560. Such models are typically designed for various aspects of the lithography process (e.g., 3D mask diffraction or resist processes). Therefore, a hybrid of physical models, empirical or quasi-physical models, and machine learning models can be obtained. This disclosure provides a uniform model architecture and training method for machine learning-based modeling, which can potentially achieve additional accuracy increases throughout the patterning process.

[0099] In embodiments, machine learning models derived according to this disclosure can replace existing analytical models (e.g., physics-based or empirical models) associated with mask optimization processes such as optical proximity correction terms (or, in general, source mask optimization (SMO)). Compared to existing analytical models, machine learning models can provide faster time-to-market and better yield. For example, OPC determination based on empirical or physics-based models includes an inverse algorithm (e.g., inverse OPC (iOPC) and SMO) that solves for the optimal mask layout given a model and substrate target, i.e., gradient computation (which is highly complex, resource-intensive, and has a long runtime). According to this disclosure, machine learning models provide simpler gradient computation (compared to, for example, iOPC-based methods), thereby reducing the computational complexity and runtime of process models and / or models associated with mask optimization.

[0100] Figure 8 This is a block diagram of a machine learning-based architecture for a patterning process. The diagram illustrates different elements of the machine learning-based architecture, including: (i) a set of trained machine learning models (e.g., 8004, 8006, 8008) representing, for example, a lithography process; (ii) a machine learning model (e.g., 8002) representing or configured to predict a mask pattern (e.g., a CTM image or OPC); and (iii) cost functions 8010 (e.g., a first cost function and a second cost function) for the different machine learning models trained according to this disclosure. A mask pattern is a pattern of a patterning apparatus that, when used in the patterning process, produces a target pattern to be printed on a substrate. A mask pattern can be represented as an image. During the determination of the mask pattern, several related images, such as CTM images, binary images, OPC images, etc., can be generated. Such related images are also commonly referred to as mask patterns.

[0101] In embodiments, the machine learning architecture may be divided into several parts: (i) training individual process models (e.g., 8004, 8006, and 8008), as further discussed below in this disclosure; (ii) concatenating the individual process models and further training and / or fine-tuning the trained process models based on a first training dataset (e.g., a printed pattern) and a first cost function (e.g., the difference between the printed pattern and the predicted pattern), as in... Figure 9 Further discussed in the text; and (iii) using the trained process model to train another machine learning model (e.g., 8002) based on a second training dataset (e.g., the target pattern) and a second cost function (e.g., the EPE between the target pattern and the predicted pattern), which is configured to predict the mask pattern (e.g., including OPC), as in Figure 10A This will be discussed further. The training of the process model can be considered a supervised learning method, where the predicted pattern is compared with experimental data (e.g., a printed substrate). On the other hand, training of a model such as a CTM using a trained process model can be considered unsupervised learning, where the target pattern is compared with the predicted pattern based on a cost function (such as EPE).

[0102] In embodiments, the patterning process may include a photolithography process, which may be represented by one or more machine learning models, such as convolutional neural networks (CNNs) or deep CNNs. Each machine learning model (e.g., a deep CNN) may be pre-trained individually to predict the outcome of an aspect or process of the patterning process (e.g., mask diffraction, optics, resist, etching, etc.). Each such pre-trained machine learning model of the patterning process may be coupled together to represent the entire patterning process. For example, in Figure 8 In this model, the first trained machine learning model 8004 can be coupled to the second trained machine learning model 8006, and the second trained machine learning model 8006 can be further coupled to the third trained machine learning model 8008, such that the coupled model represents the lithography process model. Furthermore, in an embodiment, a fourth trained model (not shown) configured to predict the etching process can be coupled to the third trained model 8008, thereby further extending the lithography process model.

[0103] However, even if each model is optimized to accurately predict various aspects or process outputs, simply coupling the individual models may not produce accurate predictions of the lithography process. Therefore, the coupled model can be further fine-tuned to improve its predictions at the substrate level rather than specific aspects of the lithography process (e.g., diffraction or optics). Within this fine-tuned model, the individual trained models can have modified weights, thus preventing individual model optimization but resulting in a relatively more accurate overall coupled model compared to the individual trained models. The coupled model can be fine-tuned by adjusting the weights of one or more of the first trained model 8004, the second trained model 8006, and / or the third trained model 8008 based on a cost function.

[0104] The cost function (e.g., a first cost function) can be defined based on the difference between experimental data (i.e., the printed pattern on the substrate) and the output of a third model 8008. For example, the cost function can be an index (e.g., RMS, MSE, MXE, etc.) based on parameters of the patterning process (e.g., CD, overlap), which are determined based on the output of a third trained model (e.g., a trained resist CNN model predicting the outcome of the resist process). In an embodiment, the cost function can be an edge placement error, which can be determined based on the contour of the predicted pattern obtained from the third trained model 8008 and the printed pattern on the substrate. During the fine-tuning process, training can include modifying the parameters of the process model (e.g., weights, biases, etc.) such that the first cost function (e.g., RMS) decreases; in an embodiment, the first cost function is minimized. Therefore, training and / or fine-tuning the coupled model can produce a relatively more accurate lithography process model compared to an untuned model obtained by simply coupling the individual trained models of different processes / aspects of the patterning process.

[0105] In an embodiment, the first trained model 8004 may be a trained mask 3D CNN and / or a trained thin mask CNN model configured to predict the diffraction effects / behavior of the mask during the patterning process. The mask may include a target pattern (e.g., SRAF, wiring, etc.) corrected for an optical proximity correction term, enabling the target pattern to be printed onto a substrate via the patterning process. The first trained model 8004 may receive a continuous transmission mask (CTM) in the form of, for example, a pixelated image. Based on the CTM image, the first trained model 8004 may predict the mask image (e.g., Figure 6(640 in the original text). The mask image can also be a pixelated image, which can be further represented in vector form, matrix form, tensor form, etc., for further processing by other trained models. In embodiments, a deep convolutional neural network can be generated or a pre-trained model can be obtained. For example, as previously described for... Figures 2 to 6 The discussion focuses on training a first trained model 8004 for predicting 3D mask diffraction. The trained 3D CNN can then generate mask images that can be sent to a second trained model 8006.

[0106] In an embodiment, the second trained model 8006 may be a trained CNN model configured to predict the behavior of projection optics (e.g., including optical systems) of a lithography apparatus (also commonly referred to as a scanner or patterning apparatus). For example, the second trained model may receive a mask image predicted by the first trained model 8004 and may predict an optical image or a spatial image. In an embodiment, the second CNN model may be trained based on training data comprising multiple spatial images corresponding to multiple mask images, where each mask image may correspond to a selected pattern printed on a substrate. In an embodiment, the spatial images of the training data may be obtained from simulations of the optical model. Based on the training data, the weights of the second CNN model may be iteratively adjusted such that the cost function decreases, and in this embodiment, the cost function is minimized. After several iterations, the cost function may converge (i.e., no further improvement is observed in the predicted spatial images), at which point the second CNN model can be considered the second trained model 8006.

[0107] In an embodiment, the second trained model 8006 can be a non-machine learning model (e.g., a physics-based optical device model as previously discussed), such as the Abbe or Hopkins formula (typically extended via intermediate terms, transitive cross coefficients (TCC)). In the Abbe and Hopkins formulas, a mask image or near field is convolved with a series of kernels, then squared and summed to obtain an optical or spatial image. The convolution kernels can be directly carried over to other CNN models. Within such an optical device model, the squaring operation can correspond to the activation function in a CNN. Therefore, such an optical device model is directly compatible with other CNN models and thus can be coupled with them.

[0108] In an embodiment, the third trained model 8008 may be a CNN model configured to predict the behavior of the resist process, as previously discussed. In an embodiment, the training of the machine learning model (e.g., an ML-resist model) is based on: (i) one or more spatial images predicted by a spatial image model (e.g., a machine learning-based model or a physics-based model), and / or (ii) a target pattern (e.g., a mask image rendered based on a target layout). Furthermore, the training process may include reducing (in an embodiment, minimizing) a cost function that describes the difference between the predicted resist image and the experimentally measured resist image (SEM image). The cost function may be based on differences in image pixel intensity, differences between contours, or CD differences, etc. After training, the ML-resist model can predict resist images based on input images (e.g., spatial images).

[0109] This disclosure is not limited to the trained models discussed above. For example, in an embodiment, the third trained model 8008 may be a combination of resist and etching processes, or the third model 8008 may be further coupled to a fourth trained model representing the etching process. The output of such a fourth model (e.g., an etched image) can be used to train the coupled model. For example, parameters of the patterning process (e.g., EPE, overlap, etc.) can be determined based on the etched image.

[0110] Furthermore, the lithography model (i.e., the fine-tuned coupled model discussed above) can be used to train another machine learning model 8002 configured to predict optical proximity correction terms. In other words, a machine learning model (e.g., a CNN) for OPC prediction can be trained by forward simulation of the lithography model, where a cost function (e.g., EPE) is computed based on the pattern at the substrate level. Furthermore, training can include an optimization process based on a gradient-based approach, where local derivatives (or partial derivatives) are obtained through backpropagation through different layers of the CNN (similar to computing the partial derivatives of an inverse function). The training process can continue until the cost function (e.g., EPE) decreases, and in this embodiment, the cost function is minimized. In this embodiment, the CNN for OPC prediction can include a CNN for predicting continuous transmission masks. For example, a CTM-CNN model 8002 can be configured to predict a CTM image, which is also used to determine the structure corresponding to the optical proximity correction term of the target pattern. Therefore, machine learning models can perform optical proximity effect correction term predictions based on the target pattern to be printed on the substrate, thus taking into account multiple aspects of the patterning process (e.g., mask diffraction, optical behavior, resist processes, etc.).

[0111] On the other hand, typical OPC or typical inverse OPC methods are based on updating mask image variables (e.g., pixel values ​​of a CTM image), and updating these mask image variables is performed using a gradient-based approach. Gradient-based methods involve generating a gradient map based on the derivative of a cost function with respect to the mask variables. Furthermore, the optimization process may include multiple iterations, in which the cost function is computed until the mean squared error (MSE) or exponential deviation (EPE) decreases; in this embodiment, the MSE or EPE is minimized. For example, the gradient can be computed as dcost / dvar, where "cost" can be the square of the EPE (i.e., EPE...). 2 ), and var can be the pixel value of the CTM image. In an embodiment, the variable can be limited to var = var - alpha * gradient, where alpha can be a hyperparameter used to adjust the training process, and var can be used to update the CTM until the cost is minimized.

[0112] Therefore, using a machine learning-based lithography model allows for the definition of a cost function for the substrate plane, making it easily differentiable compared to cost functions in physics-based or empirical models. For example, CNNs with multiple layers (e.g., 5, 10, 20, 50, etc.) include simpler activation functions (e.g., linear forms such as ax+b) that are convolved several times to form the CNN. Determining the gradient of such a function in a CNN is computationally inexpensive compared to calculating gradients in a physics-based model. Furthermore, the number of variables (e.g., mask-related variables) in a physics-based model is limited compared to the number of weights and layers in a CNN. Therefore, CNNs can perform higher-order fine-tuning of the model, resulting in more accurate predictions, compared to physics-based models with a finite number of variables. Thus, according to this disclosure, methods based on machine learning architectures offer several advantages, such as improved prediction accuracy compared to conventional methods employing, for example, physics-based process models.

[0113] Figure 9This is a flowchart of a method 900 for training a process model for a patterning process to predict patterns on a substrate, as previously discussed. Method 900 illustrates the steps involved in training / fine-tuning / retraining a model for different aspects of the patterning process discussed above. According to embodiments, the process model PM trained with method 900 can be used not only to train additional models (e.g., machine learning model 8002) but also for several other applications. For example, in CTM-based mask optimization methods, this includes: forward lithography simulation and gradient-based updates of mask variables until the process converges; and / or any other applications requiring forward lithography simulation (such as LMC and / or MRC), which will be discussed below in this disclosure.

[0114] The training process 900 includes, in process P902, obtaining and / or generating multiple machine learning models and / or multiple trained machine learning models (as previously discussed) and training data. In an embodiment, the machine learning model may be (i) a first trained machine learning model 8004 for predicting mask transmission during the patterning process, (ii) a second trained machine learning model 8006 for predicting the optical behavior of the device used in the patterning process, and (iii) a third trained machine learning model for predicting the resist process during the patterning process. In an embodiment, the first trained model 8004, the second trained model 8006, and / or the third trained model 8008 are convolutional neural networks trained to individually optimize one or more aspects of the patterning process, as previously discussed in this disclosure.

[0115] Training data may include a printed pattern 9002 obtained from, for example, a printed substrate. In embodiments, multiple printed patterns may be selected from the printed substrate. For example, the printed pattern may be a pattern (e.g., including grids, contact holes, etc.) corresponding to a die of the printed substrate after the patterning process. In embodiments, the printed pattern 9002 may be part of an overall design pattern printed on the substrate. For example, the most representative pattern, a user-selected pattern, etc., may be used as the printed pattern.

[0116] The training method in process P904 includes connecting a first trained model 8004, a second trained model 8006, and / or a third trained model 8008 to generate an initial process model. In embodiments, connection means sequentially connecting the first trained model 8004 to the second trained model 8006, and connecting the second trained model 8006 to the third trained model 8008. Such sequential connection includes providing a first output of the first trained model 8004 as a second input to the second trained model 8004, and providing a second output of the second trained model 8006 as a third input to the third trained model 8008. Such connections for each model and the associated inputs and outputs have been discussed earlier in this disclosure. For example, in embodiments, the inputs and outputs may be pixelated images, such as a first output being a mask transmission image, a second output being a spatial image, and a third output being a resist image. Therefore, the sequential linking of models 8004, 8006, and 8008 generates an initial process model, which is then further trained or fine-tuned to produce a trained process model.

[0117] The training method in process P906 includes training an initial process model (i.e., including a coupled or connected model) configured to predict the pattern 9006 on the substrate based on a cost function (e.g., a first cost function) that determines the difference between the printed pattern 9002 and the predicted pattern 9006. In an embodiment, the first cost function corresponds to the determination of an index based on information at the substrate level (e.g., based on a third output (e.g., a resist image)). In an embodiment, the first cost function may be RMS, MSE, or other indices that define the difference between the printed pattern and the predicted pattern.

[0118] Training involves iteratively determining one or more weights corresponding to a first trained model, a second trained model, and / or a third trained model based on a first cost function. Training may include a gradient-based approach that determines: the derivative of the first cost function with respect to different variables associated with the mask or the weights of CNN model 8004; the derivative of the first cost function with respect to variables associated with the resist process or the weights of CNN model 8008; the derivative of the first cost function with respect to variables associated with optics or the weights of CNN model 8006; or the derivative of the first cost function with respect to other suitable variables, as previously discussed. Furthermore, a gradient map is generated based on the derivative of the first cost function, providing suggestions on increasing or decreasing the weights or parameters associated with the variables to reduce the value of the first cost function; in embodiments, the value of the first cost function is minimized. In embodiments, the first cost function may be the error between the predicted pattern and the printed pattern. For example, edge placement error between the printed pattern and the predicted pattern, mean square error, or other suitable measures for quantifying the difference between the printed pattern and the predicted pattern.

[0119] Furthermore, in process P908, it is determined whether the cost function decreases; in this embodiment, it is determined whether the cost function is minimized. A minimized cost function indicates that the training process has converged. In other words, additional training using one or more printed patterns does not lead to further improvement in the predicted pattern. For example, if the cost function is minimized, the process model is considered to have been successfully trained. In this embodiment, training may be stopped after a predetermined number of iterations (e.g., 50,000 or 100,000 iterations). Such a trained process model PM has unique weights, enabling it to predict patterns on the substrate with higher accuracy compared to a simply coupled or connected model without training or fine-tuning of weights, as described above.

[0120] In an embodiment, if the cost function is not minimized, a gradient map 9008 can be generated in process P908. In an embodiment, the gradient map 9008 can be a partial derivative of the cost function (e.g., RMS) with respect to the parameters of the machine learning model. For example, the parameters can be the biases and / or weights of one or more models 8004, 8006, and 8008. The partial derivatives can be determined in this order during backpropagation through models 8008, 8006, and / or 8004. As previously mentioned, since models 8004, 8006, and 8008 are CNN-based, calculating the partial derivatives is easier compared to calculating them for a physics-based process model. The gradient map 9008 can then suggest how to modify the weights of models 8008, 8006, and / or 8004 to reduce or minimize the cost function. After several iterations, when the cost function is minimized or converged, a fine-tuned process model PM can be considered to have been generated.

[0121] In embodiments, depending on the type of training dataset and cost function used, one or more machine learning models can be trained to predict CTM images. These one or more machine learning models can also be used to predict mask patterns or mask images including mask patterns. For example, this disclosure... Figure 10A , Figure 10B and Figure 10C The text discusses three different methods for training the first machine learning model (hereinafter referred to as the CTM1 model), the second machine learning model (hereinafter referred to as the CTM2 model), and the third machine learning model (hereinafter referred to as the CTM3 model). For example, target patterns (e.g., design layouts to be printed on a substrate, renderings of the design layouts, etc.) can be used (e.g., from...). Figure 9 The CTM1 model can be trained using a resist image (obtained from a trained process model or a model configured to predict resist images) and a cost function (e.g., EPE). The CTM2 model can be trained using a CTM baseline image (or ground truth image) (e.g., generated by SMO / iOPC) and a cost function (e.g., the root mean square error (RMS) between the CTM baseline image (or ground truth image) and the predicted CTM image). The CTM3 model can be trained using a mask image (e.g., obtained from a CTM1 model or another model configured to predict mask images), a simulated resist image (e.g., obtained from a physics-based or empirical model configured to predict resist images), a target pattern (e.g., a design layout to be printed on a substrate), and a cost function (e.g., EPE or a pixel-based cost function). In this embodiment, the simulated resist image is obtained via simulation using the mask image. Next, reference will be made to... Figure 10A , Figure 10B and Figure 10C We will discuss training methods for CTM1, CTM2, and CTM3 models.

[0122] Figure 10A This is a flowchart of a method 1001A for training a machine learning model 1010, which is configured to predict a CTM image or mask pattern (e.g., via a CTM image), the CTM image or mask pattern including, for example, an optical proximity correction term for the mask used in the patterning process. In an embodiment, the machine learning model 1010 may be a convolutional neural network (CNN). In an embodiment, the CNN 1010 may be configured to predict a continuous transmission mask (CTM), therefore, the CNN may be referred to as CTM-CNN. Without limiting the scope of this disclosure, the machine learning model 1010 is hereinafter referred to as CTM1 model 1010.

[0123] Training method 1001A includes obtaining, in process P1002,: (i) a trained process model PM for the patterning process (e.g., a trained process model PM generated by method 900 above), the process model PM being configured to predict patterns on a substrate, wherein the trained process model includes one or more trained machine learning models (e.g., 8004, 8006, and 8008); and (ii) a target pattern to be printed on the substrate. Typically, in the OPC process, a mask having a pattern corresponding to the target pattern is generated based on the target pattern. The OPC-based mask pattern includes additional structures (e.g., SRAF) and modifications to the edges of the target pattern (e.g., wiring) such that when the mask is used in the patterning process, the patterning process ultimately produces the target pattern on the substrate.

[0124] In an embodiment, one or more trained machine learning models include: a first trained model (e.g., model 8004) configured to predict mask diffraction during the patterning process; a second trained model (e.g., model 8006) coupled to the first trained model (e.g., 8004) and configured to predict the optical behavior of the device used in the patterning process; and a third trained model (e.g., 8008) coupled to the second trained model and configured to predict resist processes during the patterning process. Each of these models can be a CNN comprising multiple layers, each layer comprising a set of weights and activation functions, and these models are trained / assigned specific weights via a training process, e.g., as shown in... Figure 9 As discussed in the article.

[0125] In one embodiment, the first trained model 8004 includes a CNN configured to predict two-dimensional or three-dimensional mask diffraction during the patterning process. In another embodiment, the first trained machine learning model receives a CTM in image form and predicts the corresponding two-dimensional and / or three-dimensional mask diffraction images. During the first pass of the training method, the continuous transmission mask can be predicted by an initial or untrained CTM1 model 1010 configured to predict the CTM, for example, as part of an OPC process. Since the CTM1 model 1010 is untrained, the predictions may be suboptimal, resulting in relatively high errors relative to the target pattern to be printed on the substrate. However, after several iterations of the training process of the CTM1 model 1010, the error will gradually decrease, and in this embodiment, the error will be minimized.

[0126] The second trained model can receive a predicted mask transmission image (e.g., a 3D mask diffraction image from the first trained model) as input and predict a spatial image corresponding to the CTM. Furthermore, the third trained model can receive the predicted spatial image and predict a resist image corresponding to the CTM.

[0127] Such a resist image includes a predicted pattern that can be printed onto the substrate during the patterning process. As previously mentioned, in the first pass, the pattern generated on the resist image may differ from the target pattern because the initial CTM predicted by the CTM1 model 1010 may be imperfect or inaccurate. The difference between the predicted pattern and the target pattern (e.g., measured in terms of EPE) will be high compared to the difference after several iterations of training with CTM-CNN.

[0128] The training method in process P1004 includes training a machine learning model 1010 (e.g., a CTM1 model 1010), which is configured to predict CTM and / or further predict OPC based on a trained process model and a cost function that determines the difference between the predicted pattern and the target pattern. Training the machine learning model 1010 (e.g., the CTM1 model 1010) involves iteratively modifying the weights of the machine learning model 1010 based on gradient values, such that the cost function decreases; in this embodiment, the cost function is minimized. In this embodiment, the cost function may be the edge placement error between the target pattern and the predicted pattern. For example, the cost function may be expressed as: cost = f(PM-CNN(CTM-CNN(input, ctm_parameter), pm_parameter), target), where cost may be EPE (or EPE...). 2(or other suitable EPE-based metrics), the function f determines the difference between the predicted image and the target image. For example, the function f can first derive the contour from the predicted image and then compute the EPE relative to the target image. Furthermore, PM-CNN represents a trained procedural model, and CTM-CNN represents a trained CTM model. pm_parameter is the parameter of the PM-CNN determined during the training phase of the PM-CNN model. ctm_parameter is the optimized parameter determined during the training of the CTM-CNN using a gradient-based method. In an embodiment, the parameter can be the weights and biases of the CNN. Furthermore, the gradient corresponding to the cost function can be dcost / dparameter, where the parameter can be updated based on an equation (e.g., parameter = parameter + learning_rate * gradient). In an embodiment, parameter can be the weights and / or biases of a machine learning model (e.g., CNN), and learning_rate can be a hyperparameter used to tune the training process, and can be selected by the user or computer to improve the convergence of the training process (e.g., fast convergence).

[0129] After several iterations of the training process, a trained machine learning model 1020 (an example of the previously discussed model 8002) can be obtained, configured to predict CTM images directly based on the target pattern to be printed on the substrate. Furthermore, the trained model 1020 can be configured to predict OPCs. In embodiments, OPCs may include the placement of auxiliary features based on the CTM image. OPCs may be in image form, and training may be based on images or pixel data of images.

[0130] In process P1006, it can be determined whether the cost function decreases, and in this embodiment, whether the cost function is minimized. A minimized cost function indicates that the training process has converged. In other words, additional training using one or more target patterns does not lead to further improvement in the predicted pattern. For example, if the cost function is minimized, the machine learning model 1020 is considered to have been trained successfully. In this embodiment, training can be stopped after a predetermined number of iterations (e.g., 50,000 or 100,000 iterations). This trained model 1020 has unique weights that enable the trained model 1020 (e.g., CTM-CNN) to predict mask images (e.g., CTM images) with higher accuracy and speed based on the target patterns, as previously described.

[0131] In an embodiment, if the cost function is not minimized, a gradient map 1006 can be generated in process P1006. In an embodiment, the gradient map 1006 can be a representation of the partial derivative of the cost function (e.g., EPE) with respect to the weights of the machine learning model 1010. The gradient map 1006 can then suggest how to modify the weights of model 1010 to reduce or minimize the cost function. After several iterations, when the cost function is minimized or converged, model 1010 can be considered a trained model 1020.

[0132] In an embodiment, a trained model 1020 (an example of model 8002 previously discussed) can be obtained, and this model 1020 can be further used to directly determine optical proximity effect correction terms for the target pattern. Furthermore, a mask comprising structures corresponding to the OPC (e.g., SRAF, wiring) can be fabricated. Since the OPC takes into account several aspects of the patterning process via trained models such as 8004, 8006, 8008, and 8002, such a mask based on predictions from a machine learning model can be highly accurate, at least in terms of edge placement errors. In other words, when this mask is used during the patterning process, it will produce the desired pattern on the substrate with minimal error (e.g., in EPE, CD, overlap, etc.).

[0133] Figure 10B This is a flowchart of a method 1001B for training a machine learning model 1030 (also referred to as CTM2 model 1030) configured to predict CTM images. According to one embodiment, training can be performed based on a reference image (or ground truth image) generated, for example, by performing SMO / iOPC to pre-generate CTM ground truth images. The machine learning model can be further optimized based on a cost function that determines the difference between the reference CTM image and the predicted CTM image. For example, the cost function can be the root mean square error (RMS), which can be reduced by employing gradient-based methods (similar to those discussed previously).

[0134] Training method 1001B obtains a set of benchmark CTM images 1031 and an untrained CTM2 model 1030 configured to predict CTM images in process P1031. In an embodiment, the benchmark CTM images 1031 can be generated by SMO / iOPC-based simulation (e.g., using Tachyon software). In an embodiment, the simulation may include spatially shifting a mask image (e.g., a CTM image) during the simulation process to generate a set of benchmark CTM images 1031 corresponding to the mask pattern.

[0135] Furthermore, in process P1033, the method includes training a CTM2 model 1030 to predict CTM images based on the aforementioned set of benchmark CTM images 1031 and an evaluation of a cost function (e.g., RMS). The training process includes tuning the parameters of the machine learning model (e.g., weights and biases) to minimize (or maximize, depending on the metric used) the associated cost function. In each iteration of the training process, a gradient map 1056 of the cost function is computed, and this gradient map is also used to guide the direction of optimization (e.g., modification of the weights of the CTM2 model 1030).

[0136] For example, in process P1035, a cost function (e.g., RMS) is evaluated, and it is determined whether the cost function is minimized / maximized. In an embodiment, if the cost function is not reduced (in an embodiment, the cost function is minimized), a gradient map 1056 is generated by taking the derivative of the cost function with respect to the parameters of the CTM2 model 1030. After several iterations, in an embodiment, if the cost function is minimized, a trained CTM2 model 1040 is obtained, wherein the CTM2 model 1040 has unique weights determined according to the training process.

[0137] Figure 10C This is a flowchart of a method 1001C for training a machine learning model 1050 (also referred to as a CTM3 model 1060) configured to predict CTM images. According to one embodiment, training may be performed based on another training dataset and a cost function (e.g., EPE or RMS). The training data may include: a mask image corresponding to the target pattern (e.g., a CTM image obtained from a CTM1 model 1010 or a CTM2 model 1030); simulated process images corresponding to the mask image (e.g., resist images, spatial images, etched images, etc.); a reference image (or ground reality image) generated, for example, by performing SMO / iOPC to pre-generate a real CTM image; and the target pattern. The machine learning model may be further optimized based on a cost function that determines the difference between the reference CTM image and the predicted CTM image. For example, the cost function may be a mean squared error (MSE), higher-order error (MXE), root mean square error (RMS), or other suitable statistical metrics that can be reduced by employing gradient-based methods (similar to those discussed previously). The machine learning model can be further optimized based on a cost function that determines the difference between the target pattern and the pattern extracted from the resist image. For example, the cost function could be an EPE that can be reduced by employing a gradient-based method (similar to the methods discussed earlier). Those skilled in the art will understand that the machine learning model described herein can be trained using multiple sets of training data corresponding to different target patterns.

[0138] Training method 1001C obtains training data in process P1051, which includes: (i) a mask image 1052 (e.g., a CTM image obtained from CTM1 model 1010 or CTM2 model 1030), (ii) a simulated process image 1051 corresponding to the mask image 1052 (e.g., a resist image, spatial image, etched image, etc.), (iii) a target pattern 1053, and (iv) a set of reference CTM images 1054 and an untrained CTM3 model 1060 configured to predict CTM images. In embodiments, simulated resist images may be obtained in a manner different from, for example, simulations based on physics-based resist models, machine learning-based resist models, or other models discussed in this disclosure.

[0139] Furthermore, in process P1053, this method includes training a CTM3 model 1060 to predict CTM images based on training data and an evaluation of a cost function (e.g., EPE, pixel-based values, or RMS), similar to process P1033 discussed previously. Moreover, because this method uses additional input including simulated process images (e.g., resist images), the mask pattern (or mask image) obtained according to this method will predict a substrate profile that more closely matches (e.g., a match exceeding 99%) the target pattern compared to other methods.

[0140] Training the CTM3 model involves tuning the parameters of the machine learning model (e.g., weights and biases) to minimize / maximize the associated cost function. In each iteration of the training process, a gradient map 1056 of the cost function is computed, and this gradient map is also used to guide the direction of optimization (e.g., modifications to the weights of the CTM3 model 1060).

[0141] For example, in process P1055, a cost function (e.g., RMS) is evaluated, and it is determined whether the cost function is minimized / maximized. In an embodiment, if the cost function is not reduced (in an embodiment, the cost function is minimized), a gradient map 1056 is generated by taking the derivative of the cost function with respect to the parameters of the CTM3 model 1060. After several iterations, in an embodiment, if the cost function is minimized, a trained CTM3 model 1060 is obtained, wherein the CTM3 model 1060 has unique weights determined according to the training process.

[0142] In embodiments, based on defects observed in the patterned substrate (e.g., footing, necking, bridging, no-contact-hole, buckling of gratings, etc.), and / or based on the manufacturability of the mask with OPC, the above methods can be further extended to train one or more machine learning models (e.g., CTM4 models, CTM5 models, etc.) to predict mask patterns, mask optimization, and / or optical proximity effect correction terms (e.g., via CTM images). For example, it can be used... Figure 14A The method described herein is used to train a defect-based model (generally referred to in this disclosure as the LMC model). The LMC model can also be used for applications such as those targeting... Figure 14B The different methods discussed and for Figure 14C Another CTM generation process discussed is used to train machine learning models (e.g., CTM4 models). Furthermore, it is possible to use... Figure 16A The training methods described herein are used to train a mask manufacturability-based model (often referred to herein as an MRC model). The MRC model can also be used to train models targeting... Figure 16B The machine learning model discussed (e.g., the CTM5 model), or for Figure 16C Another CTM generation process discussed above. In other words, the machine learning model (or a new machine learning model) discussed above can also be configured to predict, for example, mask patterns (e.g., via CTM images) based on LMC and / or MRC models.

[0143] In embodiments, manufacturability can refer to the manufacturability of forming a pattern on a substrate with minimal to no defects via a patterning process (e.g., using a photolithography apparatus). In other words, a machine learning model (e.g., a CTM4 model) can be trained to predict, for example, OPC (e.g., via a CTM image) to reduce defects on the substrate, in embodiments, minimizing said defects.

[0144] In embodiments, manufacturability may refer to the ability to manufacture the mask itself (e.g., with OPC). Mask manufacturing processes (e.g., using an electron beam writer) may have limitations that restrict the fabrication of patterns of certain shapes and / or sizes on the mask substrate. For example, during a mask optimization process, OPC may produce mask patterns with, for example, Manhattan patterns or curved patterns (the corresponding masks are referred to as curved masks). In embodiments, mask patterns with Manhattan patterns typically include straight lines (e.g., modified edges of the target pattern) and SRAFs (e.g., lines of sight) arranged vertically or horizontally around the target pattern. Figure 11 (OPC-corrected mask 1108). This Manhattan pattern is relatively easier to manufacture compared to the curved pattern of a curved mask.

[0145] A curved mask is a mask with a pattern in which the edges of the target pattern are modified during OPC to form curved (e.g., polygonal) edges and / or curved SRAFs. Due to the larger process window, such curved masks can produce a more accurate and consistent pattern on the substrate during the patterning process (compared to Manhattan patterned masks). However, curved masks have several manufacturing limitations related to the geometry of the polygon, such as the radius of curvature, dimensions, curvature at corners, etc., that can be manufactured to produce the curved mask. Furthermore, the fabrication or fabrication process of a curved mask can include a "Manhattanization" process, which may involve breaking or fragmenting the shape into smaller rectangles and triangles and forcing a fit to the shape to simulate a curved pattern. Such a Manhattanization process can be time-intensive but produces a less accurate mask compared to a curved mask. Therefore, design-to-mask manufacturing time is increased, but accuracy may decrease. Therefore, the manufacturing limitations of the mask should be considered to improve accuracy and reduce design-to-manufacturing time; ultimately leading to increased yield of patterned substrates during the patterning process.

[0146] According to the method for determining OPC based on a machine learning model as disclosed herein (e.g., in... Figure 16B This approach can address issues related to defects and mask manufacturability. For example, in one embodiment, a defect-based cost function can be used to train a machine learning model (e.g., a CTM5 model) and configure that machine learning model to predict OPC (e.g., via a CTM image). In another embodiment, a cost function based on parameters of the patterning process (e.g., EPE) and mask manufacturability (e.g., mask rule checks or manufacturing requirement violation probabilities) can be used to train another machine learning model (e.g., a CTM5 model) and configure that other machine learning model to predict OPC (e.g., via a CTM image). Mask rule checks are defined as a set of rules or checks based on mask manufacturability, and such checks can be evaluated to determine whether a mask pattern (e.g., a curve pattern including OPC) can be manufactured.

[0147] In one embodiment, a multi-beam mask writer, for example, can be used to fabricate curved masks without a Manhattan process; however, the ability to fabricate curved or polygonal shapes may be limited. Therefore, such fabrication limitations or violations need to be considered during the mask design process to enable the fabrication of accurate masks.

[0148] Conventional methods for determining OPC based on physics-based process models can also take into account defect and / or manufacturing violation probability checks. However, such methods require gradient determination, which can be computationally time-intensive. Furthermore, since defect detection and manufacturability violation checks can be indistinguishable algorithms (e.g., including if-then-else conditional checks), determining gradients based on defect or mask rule check (MRC) violations may be infeasible. Therefore, gradient computation may be infeasible because such OPCs may not be accurately determined (e.g., via CTM images).

[0149] Figure 11 An exemplary OPC process for manufacturing a mask based on a target pattern is illustrated according to one embodiment. The process includes: obtaining a target pattern 1102; generating a CTM image 1104 (or a binary image) based on the target pattern 1102 to place SRAFs around the target pattern 1102; generating a binary image 1106 with SRAFs based on the CTM image 1104; and determining corrections for the edges of the target pattern 1102 to produce a mask 1108 with OPCs (e.g., with SRAFs and wiring). Furthermore, as discussed throughout this disclosure, conventional mask optimization, including complex gradient calculations based on physics-based models, can be performed.

[0150] In an embodiment, the target pattern 1102 may be a portion of a pattern to be printed on a substrate, multiple portions of a pattern to be printed on a substrate, or the entire pattern to be printed on a substrate. The target pattern 1102 is typically provided by the designer.

[0151] In embodiments, the CTM image 1104 can be generated using a machine learning model (e.g., CTM-CNN) trained according to embodiments of this disclosure. For example, a cost function based on EPE, a cost function based on defects, and / or a cost function based on manufacturability violations can be used, based on a fine-tuned process model (as previously discussed). Each such machine learning model can be different depending on the cost function used to train the machine learning model. The trained machine learning model (e.g., CTM-CNN) can also be different depending on additional process models (e.g., etching models, defect models, etc.) included in and / or coupled to the process model PM.

[0152] In embodiments, the machine learning model can be configured to directly generate a mask with OPC, such as the final mask 1108, from the target image 1102. Such a machine learning model can be generated using one or more training methods of this disclosure. Therefore, one or more machine learning models (e.g., CNNs) can be extended or generated, each model (e.g., CNN) configured to predict OPC (or CTM images) in different ways based on the training process, the process model used during training, and / or the training data used during training. The process model can refer to a model of one or more aspects of the patterning process, as discussed throughout this disclosure.

[0153] In an embodiment, a CTM+ process, which can be considered an extension of the CTM process, may include a curve mask function (also referred to as a phi function or level set function) that determines a polygon-based modification to the pattern profile, thereby achieving, according to the embodiment, as described above. Figure 12 The generation of the curve mask image 1208 is shown. Unlike Manhattan patterns, curve mask images comprise patterns with polygonal shapes. As previously described, such curve masks can produce more accurate patterns on the substrate compared to the final mask image 1108 (e.g., a Manhattan pattern). In embodiments, this CTM+ process can be part of mask optimization and OPC processes. However, the geometry of the curve SRAF, the position of the curve SRAF relative to the target pattern, or other relevant parameters can impose manufacturing limitations, as such curve shapes may not be manufacturable. Therefore, designers can consider these limitations during the mask design process. The limitations and challenges of manufacturing curve masks are discussed in detail in Spence et al., “Manufacturing Challenges for Curvilinear Masks” (Spence et al., Vol. 10451, Photomask Technology, 1045104 (October 16, 2017); Digital Object Identifier (doi): 10.1117 / 12.2280470), which is incorporated herein by reference.

[0154] Figure 13 This is a block diagram of a machine learning-based architecture for a patterning process according to an embodiment of a training method based on defects and / or mask manufacturability. The architecture includes a machine learning model 1302 (e.g., CTM-CNN or CTM+CNN) configured to predict OPC (or CTM / CTM+images) based on a target pattern. The architecture also includes a trained process model PM, which, as previously described, is designed for... Figure 8 and Figure 9It is configured and trained as discussed. Additionally, another trained machine learning model 1310 is configured to predict defects on the substrate (e.g., using the method discussed later). Figure 14A The machine learning model trained by the method can be coupled to the trained process model PM. Furthermore, the defects predicted by the machine learning model can be used as a cost function metric to further train model 1302 (e.g., Figure 14B and Figure 14C (Training method). In the following text, for better readability, the trained machine learning model 1310 will be referred to as the lithographic manufacturability check (LMC) model 1310, and this does not limit the scope of this disclosure. The LMC model can also generally be interpreted as a manufacturability model associated with a substrate (e.g., defects on the substrate).

[0155] In one embodiment, another trained machine learning model 1320 is configured to predict the MRC violation probability based on a curve mask image (e.g., generated by 1302). (e.g., using a model discussed later). Figure 16A The machine learning model trained by the method can be included in the training process. In the following text, for better readability, the trained machine learning model 1320 will be referred to as MRC model 1320, and this does not limit the scope of this disclosure. Furthermore, the MRC violations predicted by machine learning model 1320 can be used as a cost function metric to further train model 1302 (e.g., Figure 16B and Figure 16C (Training method). In an embodiment, the MRC model 1320 may not be coupled to the process model PM, but the predictions of the MRC model 1320 can be used to supplement the cost function (e.g., cost function 1312). For example, the cost function may include two condition checks, which include (i) based on EPE and (ii) the number of MRC violations (or the MRC violation probability). The cost function can then be used to compute a gradient map to modify the weights of the CTM+CNN model, thereby reducing the cost function (in an embodiment, the cost function is minimized). Thus, training the CTM+CNN model can overcome several challenges, including providing a model that is easier to obtain derivatives and compute gradients or gradient maps for optimizing the CTM+CNN images generated by the CTM+CNN model.

[0156] In an embodiment, Figure 13 The machine learning architecture can be broadly divided into two parts: (i) training a machine learning model (e.g., 1302, such as) using a trained process model PM, LMC model 1310 (discussed previously), and a defect-based cost function and / or other cost functions (e.g., EPE). Figure 14B(i) the CTM4 model in the example); and (ii) using the (previously discussed) trained process model PM, the trained MRC model 1320, and an MRC-based cost function and / or other cost functions (e.g., EPE) to train another machine learning model (e.g., 1302', such as...). Figure 16B (The CTM5 model in the example). In an embodiment, both the LMC model 1310 and the MRC model 1320, along with their respective cost functions, can be used simultaneously to train a machine learning model configured to predict CTM images. In an embodiment, each of the LMC and MRC models can also be used to combine a non-machine learning process model (e.g., a physics-based model) to train different machine learning models (e.g., the CTM4 and CTM5 models).

[0157] Figure 14A This is a flowchart for training a machine learning model 1440 (e.g., an LMC model), which is configured to predict defects (e.g., defect type, defect number, or other defect-related metrics) within an input image (e.g., a resist image obtained from a simulation of a process model (e.g., PM)). Training is based on training data, which includes: (i) defect data or true defect metrics (e.g., obtained from a printed substrate), (ii) a resist image corresponding to a target pattern, and (iii) (optionally) the target pattern, and a defect-based cost function. For example, depending on the defect type and / or the detector used to detect defects (e.g., a CD change detector), the target pattern may be used, for example, where the resist profile can be compared to the target pattern. Defect data may include a set of defects on the printed substrate. At the end of training, the machine learning model 1440 evolves into a trained machine learning model 1310 (i.e., LMC model 1310).

[0158] The training method in process P1431 includes obtaining training data, which includes defect data 1432, resist image 1431 (or etched image), and optional target pattern 1433. Defect data 1432 may include different types of defects that can be observed on the printed substrate. For example, Figure 15A , Figure 15B and Figure 15CDefects such as buckling of slat 1510, foot 1520, bridging 1530, and necking 1540 are illustrated. Such defects can be identified, for example, using simulation (e.g., via a Tachyon LMC device), experimental data (e.g., post-printing substrate data), SEM images, or other defect detection tools. Typically, SEM images can be input into a defect detection algorithm configured to identify different types of defects observable in patterns printed on a substrate (also known as a patterned substrate). The defect detection algorithm may include several if-then-else conditions or other suitable syntax, where defect conditions are encoded within said syntax and checked / evaluated when the algorithm is executed (e.g., by a processor, hardware computer system, etc.). A defect can be detected when one or more such defect conditions are evaluated as true. Defect conditions may be based on one or more parameters (e.g., CD, overlap, etc.) associated with the substrate in the patterning process. For example, necking is said to be detectable along the length of a gate strip where the CD (e.g., 10 nm) is less than 50% of the total CD or the desired CD (e.g., 25 nm) (see, for example, [link to relevant documentation]). Figure 15C (1540 in the example). Similarly, other geometric properties or other appropriate defect-related parameters can be evaluated. Such conventional algorithms may not be differentiable and therefore may not be used in gradient-based mask optimization processes. According to this disclosure, a trained LMC model 1310 (e.g., LMC-CNN) can provide a model with which derivatives can be determined, thereby enabling defect-based OPC optimization or mask optimization processes.

[0159] In an embodiment, the training data may include: a target pattern (e.g., Figure 11 The data includes 1102), a corresponding resist image 1431 with defects (or an etched image or outline of the resist image), and defect data (e.g., a pixelated image of one or more patterned substrates with defects). In embodiments, for a given resist image and / or target pattern, the defect data can have different formats: 1) the number of defects in the resist image; 2) a binary variable, i.e., whether a defect exists (yes or no); 3) the defect probability; 4) the defect size; 5) the defect type, etc. The defect data can include different types of defects occurring on the patterned substrate after the patterning process. For example, a defect can be a necking defect (e.g., Figure 15C 1540 in the middle), base defects (e.g. Figure 15B 1520 in the middle), bridging defects (e.g. Figure 15B 1530 in the middle) and buckling defects (e.g. Figure 15A(See 1510). Necking defects refer to a reduction in CD (e.g., less than 50% of the expected CD) along the length of a feature (e.g., a grating bar) at one or more locations. Foot defects (e.g., see 1510). Figure 15B (1520) can refer to the bottom (i.e., at the substrate) of a cavity or contact hole blocked by a resist layer where a through cavity or contact hole should exist. Bridging defects (e.g., see...) Figure 15B 1530 in the text can refer to the top surface of a blocking cavity or contact hole, thereby preventing the formation of a through cavity or contact hole from the top of the resist layer to the substrate. Buckling defects can refer to, for example, gratings in the resist layer due to a relatively large height relative to the width (see, for example, [reference needed]). Figure 15A buckling of 1510). In an embodiment, 1510 may buckle due to the weight of another patterned layer formed on top of the grating.

[0160] Furthermore, the method includes, in process P1433, training a machine learning model 1440 based on training data (e.g., 1431 and 1432). The training data can also be used to modify the weights (or biases or other relevant parameters) of model 1440 according to a defect-based cost function. The cost function can be a defect metric (e.g., the presence of a defect, defect probability, defect size, and other defect-related metrics). For each defect metric, different types of cost functions can be defined; for example, if for defect size, the cost function could be a function of the difference between the predicted defect size and the actual defect size. During training, the cost function can be iteratively reduced (in this embodiment, the cost function is minimized). In this embodiment, the trained LMC model 1310 can predict defect metrics, which are defined as, for example, defect size, defect quantity, a binary variable indicating the presence of a defect, defect type, and / or other appropriate defect-related metrics. During training, the metrics can be calculated and monitored until model 1440 can predict most defects within the defect data (in this embodiment, all defects). In an embodiment, the calculation of the cost function metric may include image segmentation (e.g., resist image or etched image) to identify distinct features and, based on this segmentation, to identify defects (or defect probabilities). Thus, the LMC model 1310 can establish a relationship between the target pattern and defects (or defect probabilities). Such an LMC model 1310 can now be coupled to a trained process model PM and can also be used to train model 1302 to predict OPC (e.g., including CTM images). In an embodiment, gradient methods may be used during the training process to tune the parameters of model 1440. In such gradient methods, gradients (e.g., dcost / dvar) can be computed relative to variables to optimize variables (e.g., the parameters of the LMC model 1310).

[0161] At the end of the training process, a trained LMC model 1310 can be obtained, which can predict defects based on resist images (or etched images) obtained, for example, from simulations of a process model (e.g., PM).

[0162] Figure 14B A flowchart illustrating a method 1401 for training a machine learning model 1410 according to one embodiment is shown schematically. The machine learning model 1410 is configured to predict mask patterns (e.g., including OPC or CTM images) based on defects on a substrate after a patterning process. In an embodiment, OPC prediction may include the generation of a CTM image. The machine learning model 1410 may be a convolutional neural network (CNN) configured to predict continuous transmission masks (CTMs), and the corresponding CNN may be referred to as CTM-CNN. As an exemplary model, model 1410 is referred to as CTM-CNN 1410 to clearly illustrate the training process and not to limit the scope of this disclosure. Further details previously discussed regarding... Figure 13 The training method is discussed in part. According to training method 1401, CTM-CNN 1410 can be trained to determine a mask pattern corresponding to the target pattern, such that the mask pattern includes a structure (e.g., SRAF) around the target pattern and modifications to the edges of the target pattern (e.g., wiring), such that when such a mask is used in the patterning process, the patterning process ultimately produces the target pattern on the substrate.

[0163] Training method 1401 includes obtaining in process P1402: (i) a trained process model PM of the patterning process (e.g., a trained process model PM generated by method 900 above), the process model PM being configured to predict patterns on a substrate; (ii) a trained LMC model 1310, the LMC model 1310 being configured to predict defects on a substrate after undergoing the patterning process; and (iii) a target pattern 1402 (e.g., target pattern 1102).

[0164] In an embodiment, the trained process model PM may include one or more trained machine learning models (e.g., for...). Figure 8 and Figure 9(Referring to models 8004, 8006, and 8008). For example, a first trained model (e.g., model 8004) can be configured to predict mask diffraction during the patterning process. A second trained model (e.g., model 8006) is coupled to the first trained model (e.g., 8004) and configured to predict the optical behavior of the device used in the patterning process. A third trained model (e.g., model 8008) is coupled to the second trained model 8006 and configured to predict the resist process during the patterning process.

[0165] The training method in process P1404 includes training a CTM-CNN 1410, which is configured to predict CTM images and / or further predict OPCs based on a trained process model. In the first iteration or first pass of the training method, the initial or untrained CTM-CNN 1410 can predict CTM images based on the target pattern 1402. Since the CTM-CNN 1410 may be untrained, the predictions may be suboptimal, resulting in relatively high errors relative to the target pattern 1402 expected to be printed on the substrate (e.g., in terms of EPE, overlap, number of defects, etc.). However, after several iterations of the training process of the CTM-CNN 1410, the error will gradually decrease, and in this embodiment, the error will be minimized. The process model PM (previously designed for...) then... Figure 8 and Figure 9 The internal workings of the PM (process model) are discussed. The PM receives a CTM image, and the process model can predict either a resist image or an etched image. Furthermore, the outline of the pattern in the predicted resist or etched image can be derived, and this outline is further used to determine parameters of the patterning process, and the corresponding cost function (e.g., EPE) can be evaluated.

[0166] The predictions from the process model PM can be received by a trained LMC model 1310, which is configured to predict defects within the resist (or etched) image. As previously mentioned, in the first iteration, the initial CTM predicted by the CTM-CNN may be suboptimal or inaccurate, thus the resulting pattern on the resist image may differ from the target pattern. The difference between the predicted and target patterns (e.g., measured in terms of EPE or defect number) will be high compared to the difference after several iterations of training with the CTM-CNN. After several iterations of the training process, the CTM-CNN 1410 can generate a mask pattern that will produce a reduced number of defects on the substrate after the patterning process, thereby achieving the desired productivity corresponding to the target pattern.

[0167] Furthermore, the training method in process P1404 may include a cost function for determining the difference between the predicted pattern and the target pattern. Training the CTM-CNN 1410 involves iteratively modifying the weights of the CTM-CNN 1410 based on gradient map 1406, such that the cost function decreases; in this embodiment, the cost function is minimized. In this embodiment, the cost function may be the number of defects on the substrate or the edge placement error between the target pattern and the predicted pattern. In this embodiment, the number of defects may be the total number of defects predicted by the trained LMC model 1310 (e.g., the sum of necking defects, foot defects, buckling defects, etc.). In this embodiment, the number of defects may be a set of individual defects (e.g., a set including foot defects, necking defects, buckling defects, etc.), and the training method may be configured to reduce (in this embodiment, minimize) one or more defects in the set of individual defects (e.g., minimize only foot defects).

[0168] After several iterations of the training process, a trained CTM-CNN 1420 (an example of the previously discussed model 1302) is reportedly generated, configured to predict CTM images directly from the target pattern 1402 to be printed on the substrate. Furthermore, the trained model 1420 can be configured to predict OPCs. In embodiments, OPCs may include auxiliary features and / or wiring placement based on the CTM image. OPCs may be in image form, and training may be based on images or pixel data of images.

[0169] In process P1406, it can be determined whether the cost function has decreased, or in this embodiment, whether the cost function has been minimized. A minimized cost function indicates that the training process has converged. In other words, additional training using one or more target patterns does not lead to further improvement in the predicted pattern. For example, if the cost function is minimized, the machine learning model 1420 is considered to have been trained successfully. In this embodiment, training can be stopped after a predetermined number of iterations (e.g., 50,000 or 100,000 iterations). This trained model 1420 has unique weights that enable the trained model 1420 (e.g., CTM-CNN) to predict a mask pattern that will produce minimized defects on the substrate during the patterning process, as previously described.

[0170] In an embodiment, if the cost function is not minimized, a gradient map 1406 can be generated in process P1406. In an embodiment, the gradient map 1406 can be a representation of the partial derivatives of the cost function (e.g., EPE, number of defects) with respect to the weights of CTM-CNN 1410. The partial derivatives can be determined in this order during backpropagation through different layers of LMC CNN model 1310, process model PM, and / or CTM-CNN 1410. Since models 1310, PM, and 1410 are CNN-based, the computation of partial derivatives during backpropagation can include the inverse transformation of a function representing different layers of the CNN with respect to the corresponding weights of the layers, which is more computationally efficient than computations involving the inverse transformation of physics-based functions, as previously described. The gradient map 1406 can then provide guidance on how to modify the weights of model 1410 to reduce or minimize the cost function. After several iterations, when the cost function is minimized or converged, model 1410 can be considered a trained model 1420.

[0171] In an embodiment, a trained model 1420 (model 1420 being an example of model 1302 previously discussed) can be obtained, and this model 1420 can be further used to directly determine optical proximity effect correction terms for the target pattern. Furthermore, a mask comprising a structure corresponding to the OPC (e.g., SRAF, wiring) can be fabricated. Since the OPC takes into account several aspects of the patterning process via trained models such as 8004, 8006, 8008, 1302, and 1310, such a machine learning model-based predictive mask can be highly accurate, at least in terms of the number (or yield) of defects on the substrate. In other words, when used during the patterning process, this mask will produce the desired pattern on the substrate with minimized defects.

[0172] In an embodiment, the cost function 1406 may include one or more conditions that can be simultaneously reduced (in this embodiment, simultaneously minimized). For example, in addition to the number of defects, it may include EPE, overlap, CD, or other parameters. Therefore, one or more gradient maps can be generated based on such a cost function, and the weights of the CTM-CNN can be modified based on such gradient maps. Thus, the pattern generated on the substrate not only produces high yield (e.g., minimized defects) but also high accuracy in, for example, EPE or overlap.

[0173] Figure 14CThis is a flowchart of another method for predicting OPC (or CTM / CTM+ images) based on the LMC model 1310. The method is an iterative process in which a model (which can be a machine learning model or a non-machine learning model) is configured to generate a CTM image (or CTM+ image) based on a cost function associated with the defects predicted by the LMC model 1310. The input to this method can be an initial image 1441 (e.g., a target pattern or mask image, i.e., a rendered result of the target pattern), which is used to generate the optimized CTM image or OPC pattern.

[0174] The method includes generating a CTM image 1442 based on an initial image (e.g., a binary mask image or an initial CTM image) in process P1441. In embodiments, the CTM image 1441 may be generated, for example, via simulation of a mask model (e.g., the mask layout model, thin mask, and / or M3D model discussed above).

[0175] Furthermore, in process P1443, the process model can receive CTM image 1442 and predict the process image (e.g., resist image). As previously discussed, the process model can be a combination of an optical device model, a resist model, and / or an etching model. In embodiments, the process model can be a non-machine learning model (e.g., a physics-based model).

[0176] Furthermore, in process P1445, a process image (e.g., a resist image) can be passed to LMC model 1310 to predict defects within the process image (e.g., the resist image). Additionally, process P1445 can be configured to evaluate a cost function based on the defects predicted by the LMC model. For example, the cost function can be limited to defect size, the number of defects, a binary variable indicating the presence of defects, a defect index indicating the type of defect, or other suitable defect-related indicators.

[0177] In process P1447, it can be determined whether the cost function is decreasing (in the embodiment, whether the cost function is minimized). In the embodiment, if the cost function is not minimized, the value of the cost function can be gradually (in an iterative manner) reduced by using a gradient-based method (similar to the method used throughout this disclosure).

[0178] For example, in process P1449, a gradient map can be generated based on the cost function, which is further used to determine the values ​​of the mask variables corresponding to the initial image (e.g., the pixel values ​​of the mask image) such that the cost function is reduced.

[0179] After several iterations, the cost function can be minimized, and the CTM image generated by process P1441 (e.g., a modified version of CTM image 1442 or 1441) can be considered an optimized CTM image. Furthermore, this optimized CTM image can be used to fabricate masks, thereby reducing defects.

[0180] Figure 16A This is a flowchart of a method for training a machine learning model 1640, which is configured to predict the probability of violations of mask manufacturing constraints (also known as mask rule checks) based on a curve mask image. In an embodiment, training may be performed based on training data including an input image 1631 (e.g., a curve mask), MRC 1632 (e.g., a set of mask rule checks), and a cost function based on the MRC violation probabilities. At the end of training, the machine learning model 1640 evolves into a trained machine learning model 1320 (i.e., MRC model 1320). The probability of a violation can be determined based on the violation of a specific feature of the mask pattern relative to the total number of all violations.

[0181] The training method includes obtaining training data in process P1631, which includes MRC 1632 (e.g., MRC violation probability, number of MRC violations, etc.) and mask image 1631 (e.g., a mask image with a curve pattern). In an embodiment, the curve mask image can be generated via simulation of the CTM+ process (as previously discussed).

[0182] Furthermore, the method includes training a machine learning model 1640 based on training data (e.g., 1631 and 1632) in process P1633. The training data can also be used to modify the weights (or biases or other relevant parameters) of model 1640 according to a defect-based cost function. The cost function can be an MRC metric, such as the number of MRC violations, a binary variable indicating MRC violations or no MRC violations, the probability of an MRC violation, or other suitable MRC-related metrics. During training, the MRC metric can be calculated and monitored until model 1640 can predict most MRC violations (in this embodiment, predicting all MRC violations). In this embodiment, the calculation of the metric of the cost function may include an evaluation of the MRC 1632 for image 1631 to identify different features with MRC violations.

[0183] In an embodiment, a gradient method can be used to tune the parameters of model 1640 during the training process. In this gradient method, gradients (e.g., dcost / dvar) can be computed relative to the variable to be optimized (e.g., the parameters of MRC model 1320). Therefore, MRC model 1320 can establish a relationship between the curve mask image and MRC violations or the probability of MRC violations. Such an MRC model 1320 can now be used to train model 1302 to predict OPCs (e.g., including CTM images). At the end of the training process, a trained MRC model 1320 is obtained, which can predict MRC violations based on, for example, the curve mask image.

[0184] Figure 16B A flowchart of a method 1601 for training a machine learning model 1610 according to one embodiment is schematically shown. The machine learning model 1610 is configured to predict OPC based on the manufacturability of a curve mask used in a patterning process. However, this disclosure is not limited to curve masks, and method 1601 can also be used for Manhattan-type masks. The machine learning model 1610 can be a convolutional neural network (CNN) configured to predict curve mask images. As previously discussed, in embodiments, a CTM+ process (an extension of the CTM process) can be used to generate curve mask images. Therefore, by way of example, the machine learning model 1610 is referred to as a CTM+CNN model 1610, and this does not limit the scope of this disclosure. Furthermore, the previously discussed methods will be described in further detail below. Figure 13 The training methods were partially discussed.

[0185] According to training method 1601, CTM+CNN 1610 is trained to determine a curve mask pattern corresponding to the target pattern, such that the curve mask pattern includes a curve structure (e.g., SRAF) around the target pattern and polygonal modifications (e.g., wiring) to the edges of the target pattern, such that when such a mask is used in the patterning process, the patterning process ultimately produces a more accurate target pattern on the substrate than the target pattern produced by a Manhattan patterned mask.

[0186] Training method 1601 in process P1602 includes obtaining: (i) a trained process model PM for the patterning process (e.g., a trained process model PM generated by method 900 above), the process model PM being configured to predict patterns on a substrate; and (ii) a trained MRC model 1320, the MRC model 1320 being configured to predict manufacturing violation probabilities (as previously stated for...). Figure 13 (iii) Target pattern 1602 (e.g., target pattern 1102). As previously discussed. Figure 8 and Figure 9The trained process model (PM) mentioned above may include one or more trained machine learning models (e.g., 8004, 8006, and 8008).

[0187] The training method in process P1604 includes training a CTM+CNN 1610, which is configured to predict curve mask images based on a trained process model. In the first iteration or first pass of the training method, the initial or untrained CTM+CNN 1610 can predict the curve mask image based on the CTM image corresponding to the target pattern 1602. Since the CTM+CNN 1610 may be untrained, the predicted curve mask image may be suboptimal, resulting in a relatively high error relative to the target pattern 1602 expected to be printed on the substrate (e.g., in EPE, overlap, manufacturing violations, etc.). However, after several iterations of the CTM+CNN 1610 training process, the error will gradually decrease, and in this embodiment, the error will be minimized. Then, the process model PM (previously designed for...) is used to... Figure 8 and Figure 9 The internal workings of the PM (process model) are discussed. The PM receives a predicted curve mask image, and can predict either a resist image or an etched image. Furthermore, the contours of the patterns in the predicted resist or etched images can be derived to determine parameters of the patterning process (e.g., EPE, overlap, etc.). The contours can be further used to evaluate the cost function to be reduced.

[0188] The curve mask image generated by the CTM+CNN model can also be passed to the MRC model 1320 to determine the probability of violating the manufacturing constraints / restrictions (also known as the MRC violation probability). In addition to the existing EPE-based cost function, the MRC violation probability can also be part of the cost function. In other words, the cost function can include at least two conditions: one based on EPE (as discussed throughout this disclosure) and the other based on the MRC violation probability.

[0189] Furthermore, the training method may include determining whether the cost function is reduced in procedure P1606, or in this embodiment, whether the cost function is minimized. If the cost function is not reduced (or minimized), the training of the CTM+CNN 1610 includes iteratively modifying the weights of the CTM+CNN 1610 based on the gradient map 1606 (in procedure 1604) such that the cost function is reduced, or in this embodiment, minimized. In this embodiment, the cost function may be the MRC violation probability predicted by the trained MRC model 1320. Therefore, the gradient map 1606 can provide guidance to simultaneously reduce the MRC violation probability and the EPE.

[0190] In an embodiment, if the cost function is not minimized, a gradient map 1606 can be generated in process P1606. In an embodiment, the gradient map 1606 can be a representation of the partial derivatives of the cost function (e.g., EPE and MRC violation probabilities) with respect to the weights of the CTM+CNN 1610. The partial derivatives can be determined in this order during backpropagation through the MRC model 1320, the process model PM, and / or the CTM+CNN 1610. Since models 1320, PM, and 1610 are CNN-based, the computation of partial derivatives during backpropagation can include the inverse transformation of functions representing different layers of the CNN with respect to their respective weights, which is more computationally efficient than computations involving the inverse transformation of physics-based functions, as previously described. The gradient map 1606 can then provide guidance on how to modify the weights of model 1610 to reduce or minimize the cost function. After several iterations, when the cost function is minimized or converged, model 1610 can be considered a trained model 1620.

[0191] After several iterations of the training process, it is said that a trained CTM+CNN 1620 (which is an example of the previously discussed model 1302) can be generated, which is ready to predict the curve mask image directly from the target pattern 1602 to be printed on the substrate.

[0192] In an embodiment, training can be stopped after a predetermined number of iterations (e.g., 50,000 or 100,000 iterations). This trained model 1620 has unique weights that enable it to predict a curve mask pattern that will satisfy manufacturing constraints for curve mask fabrication (e.g., via a multi-beam mask writer).

[0193] In an embodiment, a trained model 1620 can be obtained (model 1620 is an example of model 1302 discussed earlier), and this model 1620 can be further used to directly determine optical proximity effect correction terms for the target pattern. Furthermore, masks comprising structures corresponding to the OPC (e.g., SRAF, wiring) can be fabricated. Since the OPC takes into account several aspects of the patterning process via trained models such as 8004, 8006, 8008, 1602, and 1310, such a predictive mask based on a machine learning model can be highly accurate, at least in terms of the manufacturability (or yield) of the curved mask. In other words, when used during the patterning process, the mask will produce the desired pattern on the substrate with minimized defects.

[0194] In an embodiment, the cost function 1606 may include one or more conditions that can be simultaneously reduced (in this embodiment, simultaneously minimized). For example, in addition to the MRC violation probability, it may include the number of defects, EPE, overlap, CD difference (i.e., ΔCD), or other parameters, and all conditions may be reduced (or minimized) simultaneously. Therefore, one or more gradient maps can be generated based on such a cost function, and the weights of the CNN can be modified based on such gradient maps. Thus, the pattern generated on the substrate not only produces a high yield (i.e., minimized defects) of manufacturable curve masks, but also has high accuracy in, for example, EPE or overlap.

[0195] Figure 16C This is a flowchart of another method for predicting OPC (or CTM / CTM+ images) based on the MRC model 1320. This method is an iterative process where a model (which can be a machine learning model or a non-machine learning model) is configured to generate CTM (or CTM+) images based on a cost function associated with the MRC predicted by the MRC model 1320. Similar to... Figure 14C The method takes an initial image 1441 as input (e.g., a target pattern or mask image, i.e., the rendering result of the target pattern), which produces an optimized CTM image (or CTM+ image) or an OPC pattern.

[0196] The method includes, in process P1441 (discussed above), generating a CTM image 1442 (or a CTM+ image) based on an initial image (e.g., a binary mask image or an initial CTM image). In embodiments, the CTM image 1441 may be generated, for example, via simulation of a mask model (e.g., the thin mask and / or M3D model discussed above). In embodiments, the CTM+ image may be generated based on, for example, a level set function, from an optimized CTM image.

[0197] Furthermore, in process P1643, the process model can receive a CTM image (or CTM+ image) 1442 and predict a process image (e.g., a resist image). As previously discussed, the process model can be a combination of an optical device model, a resist model, and / or an etching model. In embodiments, the process model can be a non-machine learning model (e.g., a physics-based model). The process image (e.g., a resist image) can be used to determine a cost function (e.g., EPE).

[0198] Additionally, the CTM image 1442 can also be passed to the MRC model 1320 to determine MRC metrics such as the violation probability. Furthermore, process P1643 can be configured to evaluate a cost function based on the MRC violation probability predicted by the MRC model. For example, the cost function can be limited to a function of the EPE and / or the MRC violation probability. In an embodiment, if the output of the MRC model 1320 is the violation probability, the cost function can be the average of the differences between the predicted violation probabilities for all training samples and their corresponding ground truth values ​​(e.g., this difference could be (predicted MRC probability - true violation probability)). 2 ).

[0199] In process P1447, it can be determined whether the cost function is decreasing (in the embodiment, whether the cost function is minimized). In the embodiment, if the cost function is not minimized, the value of the cost function can be gradually (in an iterative manner) reduced by using a gradient-based method (similar to the method used throughout this disclosure).

[0200] For example, in process P1449, a gradient map can be generated based on the cost function, which is further used to determine the values ​​of the mask variables corresponding to the initial image (e.g., the pixel values ​​of the mask image) such that the cost function is reduced.

[0201] After several iterations, the cost function can be minimized, and the CTM image generated by process P1441 (e.g., a modified version of CTM image 1442 or 1441) can be considered an optimized and manufacturable CTM image.

[0202] In an embodiment, Figure 16C The method may also include process P1445, which determines the defects predicted by LMC model 1310, as previously discussed. Therefore, the cost function and gradient calculation can be modified to consider multiple conditions, including defect-based metrics, MRC-based metrics, and EPE.

[0203] In an embodiment, the OPC determined using the method described above includes structural features that can be Manhattan type or curved shape, such as SRAF, wiring, etc. A mask writer (e.g., an electron beam or multi-beam mask writer) can receive information associated with the OPC and further fabricate a mask.

[0204] Furthermore, in the embodiments, the predicted mask patterns from the different machine learning models discussed above can be further optimized. Optimization of the predicted mask patterns can include iteratively modifying the mask variables of the predicted mask patterns. Each iteration includes: predicting a mask transmission image based on the predicted mask patterns via a physics-based mask model simulation; predicting a resist image based on the mask transmission image via a physics-based resist model simulation; evaluating a cost function (e.g., EPE, sidelobe, etc.) based on the resist image; and modifying the mask variables associated with the predicted mask patterns based on the gradient of the cost function via simulation, thereby reducing the cost function.

[0205] Furthermore, in embodiments, the method for training the machine learning model is configured to predict a resist image based on an etched pattern (or derive a resist pattern from a resist image). The method includes obtaining: (i) a physics-based or machine learning-based process model of the patterning process (e.g., an etching model as previously discussed in this disclosure), configured to predict an etched image based on a resist image; and (ii) an etch target (e.g., in image form). In embodiments, the etch target may be an etched pattern on a printed substrate after an etching step in the patterning process, a desired etched pattern (e.g., a target pattern), or other reference etched patterns.

[0206] Furthermore, the method may include training a machine learning model configured to predict resist images by a hardware computer system based on an etching model and a cost function that determines the difference between the etched image and the etched target.

[0207] Figure 17 This is a block diagram illustrating a computer system 100, which can help implement the methods, processes, or apparatus disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or a plurality of processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing instructions and information to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0208] Computer system 100 can be coupled via bus 102 to a display 112 for displaying information to a computer user, such as a cathode ray tube (CRT), flat panel display, or touch panel display. Input device 114, including alphanumeric keys and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is a cursor controller 116, such as a mouse, trackball, or arrow keys, for communicating directional information and command selections to processor 104 and for controlling cursor movement on display 112. Such input devices typically have two degrees of freedom on two axes (a first axis, e.g., the x-axis, and a second axis, e.g., the y-axis), allowing the device to specify its position in a plane. Touch panel (screen) displays can also be used as input devices.

[0209] According to one embodiment, portions of one or more methods described herein can be executed by computer system 100 in response to processor 104 executing one or more sequences of instructions contained in main memory 106. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors arranged in a multiprocessor configuration may also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hard-wired circuitry may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0210] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing bus 102. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tapes, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carrier waves as described below, or any other media that can be read by a computer.

[0211] Various forms of computer-readable media may be involved when carrying one or more sequences of instructions to processor 104 for execution. For example, the instructions may initially be carried on the disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit the instructions via a telephone line using a modem. A modem local to computer system 100 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 fetches and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0212] Computer system 100 may also include a communication interface 118 coupled to bus 102. Communication interface 118 provides bidirectional data communication coupling to network link 120, which is connected to local area network 122. For example, communication interface 118 may be an Integrated Services Digital Network (ISDN) card or modem to provide data communication connectivity to a corresponding type of telephone line. As another example, communication interface 118 may be a Local Area Network (LAN) card to provide data communication connectivity to a compatible LAN. A wireless link may also be implemented. In any such implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0213] Network link 120 typically provides data communication to other data devices via one or more networks. For example, network link 120 may provide connectivity to host computer 124 or to data devices operated by Internet service provider (ISP) 126 via local area network 122. ISP 126, in turn, provides data communication services via a global packet data communication network (now commonly referred to as the "Internet") 128. Both local area network 122 and Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. Signals via various networks and signals on network link 120 and via communication interface 118 (which carry digital data to and from computer system 100) are exemplary carriers for transmitting information.

[0214] Computer system 100 can send messages and receive data (including program code) via a network, network link 120, and communication interface 118. In an Internet example, server 130 can transmit requested program code for an application via the Internet 128, ISP 126, local area network 122, and communication interface 118. For example, a downloadable application can provide all or part of the methods described herein. The received program code can be executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 can obtain application code in carrier form.

[0215] Figure 18 An exemplary photolithography projection apparatus that can be used in conjunction with the techniques described herein is schematically depicted. The apparatus includes:

[0216] - An illumination system IL, which is used to modulate the beam of radiation B. In this particular case, the illumination system also includes a radiation source SO;

[0217] - A first object stage (e.g., a pattern forming apparatus stage) MT, which is provided with a pattern forming apparatus holder for holding a pattern forming apparatus MA (e.g., a mask) and is connected to a first positioner for accurately positioning the pattern forming apparatus relative to an item PS;

[0218] - Second object stage (substrate stage) WT, which is provided with a substrate holder for holding the substrate W (e.g., a silicon wafer coated with resist) and connected to a second positioner for precisely positioning the substrate relative to item PS;

[0219] - A projection system (“lens”) PS (e.g., a refractive, reflective, or reflective-refractive optical system) for imaging a radiated portion of the pattern forming apparatus MA onto a target portion C of the substrate W (e.g., comprising one or more dies).

[0220] As described herein, the device is of the transmissive type (i.e., having a transmissive pattern forming apparatus). However, the device can also typically be of the reflective type, for example (having a reflective pattern forming apparatus). The device can employ a pattern forming apparatus of a different type than that of a conventional mask; examples include programmable mirror arrays or LCD matrices.

[0221] A source SO (e.g., a mercury lamp or excimer laser, LPP (laser-generated plasma) EUV source) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, either directly or after passing through a conditioning device such as a beam expander Ex. The illuminator IL may include a conditioning device AD, which sets the outer radial range and / or inner radial range (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. Additionally, the illuminator typically includes various other components, such as an integrator IN and a concentrator CO. In this way, the beam B incident on the pattern forming apparatus MA has the desired uniformity and intensity distribution in its cross-section.

[0222] against Figure 18 It should be noted that although the source SO can be inside the housing of the photolithography projection device (which is often the case when the source SO is, for example, a mercury lamp), the source SO can also be located away from the photolithography projection device, and the radiation beam generated by the source SO can be guided into the device (e.g., by means of a suitable directional mirror); the latter case is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 emitting laser).

[0223] Beam B is then truncated on the pattern forming apparatus MA held on the pattern forming apparatus stage MT. After traversing the pattern forming apparatus MA, beam B is passed through a lens PS, which focuses the beam B onto the target portion C of the substrate W. The substrate stage WT can be accurately moved by means of a second positioning device (and an interferometric measuring device IF) to, for example, position different target portions C within the path of beam B. Similarly, a first positioning device can be used to accurately position the pattern forming apparatus MA relative to the path of beam B, for example, after mechanically retrieving the pattern forming apparatus MA from a library of pattern forming apparatuses or during scanning. Typically, this will be achieved by means of a method not in... Figure 18 The long-stroke module (coarse positioning) and short-stroke module (fine positioning) are clearly described in the diagram to realize the movement of the object stage MT and WT. However, in the case of a stepper (as opposed to a stepping scanning tool), the pattern forming apparatus stage MT may be connected only to the short-stroke actuator, or it may be fixed.

[0224] The tools described can be used in two different modes:

[0225] - In step mode, the patterning apparatus stage MT is kept substantially stationary, and the entire patterning apparatus image is projected (i.e., a single "flash") onto the target portion C. Then, the substrate stage WT is shifted in the x and / or y directions so that different target portions C can be irradiated by the beam B;

[0226] In scanning mode, the same principle applies essentially, except that the given target portion C is not exposed in a single "flash". Alternatively, the pattern forming apparatus stage MT can move at a rate v in a given direction (the so-called "scanning direction", e.g., the y-direction) so that the projection beam B scans the pattern forming apparatus image; simultaneously, the substrate stage WT moves simultaneously in the same or opposite direction at a rate V = Mv, where M is the magnification of the lens PS (typically M = 1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without compromising resolution.

[0227] Figure 19 Another exemplary photolithography projection device 1000 that can be used in conjunction with the techniques described herein is illustrated.

[0228] The photolithography projection system 1000 includes:

[0229] - Source collector module SO;

[0230] - Irradiation system (irradiator) IL, which is configured to modulate the radiation beam B (e.g., EUV radiation).

[0231] - A support structure (e.g., a patterning device stage) MT, which is configured to support a patterning device (e.g., a mask or mask plate) MA and is connected to a first positioner PM configured to precisely position the pattern forming device;

[0232] - A substrate stage (e.g., a wafer stage) WT, configured to hold a substrate (e.g., a wafer coated with resist) W, and connected to a second positioner PW configured to precisely position the substrate; and

[0233] - A projection system (e.g., a reflective projection system) PS, which projects a pattern imposed on a radiation beam B by a patterning device MA onto a target portion C of a substrate W (e.g., comprising one or more dies).

[0234] As depicted here, device 1000 is of the reflective type (e.g., using a reflective patterning apparatus). It should be noted that because most materials are absorbent in the EUV wavelength range, the patterning apparatus can have a multilayer reflector comprising, for example, multiple layers of molybdenum and silicon. In one example, the multilayer reflector has 40 pairs of layers of molybdenum and silicon, where each layer is a quarter wavelength thick. Shorter wavelengths can be produced using X-ray lithography. Since most materials are absorbent at both EUV and X-ray wavelengths, a thin sheet of patterning absorbent material on the morphology of the patterning apparatus (e.g., a TaN absorber on top of the multilayer reflector) defines where features will be printed (positive resist) or not printed (negative resist).

[0235] Reference Figure 19 The irradiator IL receives an extreme ultraviolet (EUV) radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state, the material having at least one element (e.g., xenon, lithium, or tin) that has one or more emission lines in the EUV range. In such a method, commonly referred to as laser-generated plasma (“LPP”), the plasma can be generated by irradiating a fuel with a laser beam, the fuel being, for example, droplets, streams, or clusters of a material having a line-emitting element. The source collector module SO may be a laser comprising a laser beam for providing the excitation fuel. Figure 19 (Not shown) is part of an EUV radiation system. The resulting plasma emits output radiation, such as EUV radiation, which is collected by a radiation collector disposed in a source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and the source collector module can be separate entities.

[0236] In this case, the laser is not considered part of the lithography apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable directional mirrors and / or beam expanders. In other cases, such as when the source is a discharge-generated plasma EUV generator, commonly referred to as a DPP source, the source can be part of the source collector module.

[0237] An irradiator IL may include a modulator for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial range and / or inner radial range (often referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the irradiator can be adjusted. Additionally, the irradiator IL may include various other components, such as faceted field mirror assemblies and faceted pupil mirror assemblies. The irradiator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0238] A radiation beam B is incident on a pattern forming apparatus (e.g., a mask) MA held on a support structure (e.g., a pattern forming apparatus stage) MT and patterned by the pattern forming apparatus. After reflection from the pattern forming apparatus (e.g., the mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate stage WT can be accurately moved, for example, to position different target portions C within the path of the radiation beam B, by means of a second locator PW and a position sensor PS2 (e.g., an interferometer, a linear encoder, a capacitive sensor). Similarly, a first locator PM and another position sensor PS1 can be used to precisely position the pattern forming apparatus (e.g., the mask) MA relative to the path of the radiation beam B. The pattern forming apparatus (e.g., the mask) MA and the substrate W can be aligned using pattern forming apparatus alignment marks M1, M2 and substrate alignment marks P1, P2.

[0239] The depicted device 1000 can be used in at least one of the following modes:

[0240] 1. In step mode, the support structure (e.g., patterning apparatus stage) MT and substrate stage WT are kept substantially stationary (i.e., single static exposure) while the entire pattern to be applied to the radiation beam is projected onto the target portion C in one go. Then the substrate stage WT is shifted in the X and / or Y directions so that different target portions C can be exposed.

[0241] 2. In scanning mode, while the pattern to be applied to the radiation beam is projected onto the target portion C, the support structure (e.g., patterning apparatus stage) MT and the substrate stage WT are scanned simultaneously (i.e., single dynamic exposure). The speed and direction of the substrate stage WT relative to the support structure (e.g., patterning apparatus stage) MT can be determined by the magnification (reduction) and image inversion characteristics of the projection system PS.

[0242] 3. In another mode, while the pattern to be applied to the radiation beam is projected onto the target portion C, the support structure (e.g., the pattern forming apparatus stage) MT used to hold the programmable pattern forming apparatus essentially stationary, and the substrate stage WT is moved or scanned. In this mode, a pulsed radiation source is typically used, and the programmable pattern forming apparatus is updated as needed after each movement of the substrate stage WT or between successive radiation pulses during scanning. This mode of operation can be readily applied to maskless lithography utilizing programmable pattern forming apparatuses such as programmable mirror arrays of the type mentioned above.

[0243] Figure 20The apparatus 1000 is shown in more detail, comprising a source collector module SO, an irradiation system IL, and a projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained within the enclosed structure 220 of the source collector module SO. A plasma 210 emitting EUV radiation can be formed by a discharge-generated plasma source. EUV radiation can be generated from a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein an extremely hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. The extremely hot plasma 210 is generated, for example, by a discharge that causes at least partial ionization of the plasma. To effectively generate radiation, a partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In an embodiment, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0244] Radiation emitted from the thermal plasma 210 enters the collector cavity 212 from the source cavity 211 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or barrier trap) positioned in or behind an opening in the source cavity 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As known in the art, the contaminant trap or contaminant barrier 230 further illustrated herein includes at least a channel structure.

[0245] Collector cavity 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from a grating spectral filter 240 to be focused along the optical axis into a virtual source point IF, indicated by a dashed line 'O'. The virtual source point IF is often referred to as the intermediate focus, and the source-collector module is arranged such that the intermediate focus IF is located at or near an opening 221 in the enclosed structure 220. The virtual source point IF is an image of the plasma 210 emitting radiation.

[0246] Subsequently, the radiation passes through an illumination system IL, which may include a faceted field mirror assembly 22 and a faceted pupil mirror assembly 24, arranged to provide a desired angular distribution of the radiation beam 21 at the patterning apparatus MA and a desired uniformity of radiation intensity at the patterning apparatus MA. When the radiation beam 21 is reflected at the patterning apparatus MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS onto the substrate W held by the substrate stage WT via reflective elements 28 and 30.

[0247] The illumination optical unit IL and projection system PS can typically contain more elements than those shown. Depending on the type of photolithography equipment, a grating spectral filter 240 may optionally be present. Furthermore, more mirrors than are shown in the figures may be present; for example, the projection system PS may contain more than [number missing in original text]. Figure 20 The reflective element shown has 1 to 6 additional reflective elements.

[0248] like Figure 20 As shown, the collector optics CO is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, which are merely examples of collectors (or collector mirrors). The grazing incidence reflectors 253, 254, and 255 are arranged symmetrically about the optical axis O, and this type of collector optics CO can be used in conjunction with a discharge-generated plasma source (often referred to as a DPP source).

[0249] Alternatively, the source collector module SO can be as follows: Figure 21 This is part of the LPP radiation system shown. A laser LA is arranged to deposit laser energy into a fuel (e.g., xenon (Xe), tin (Sn), or lithium (Li)) to produce a highly ionized plasma 210 with an electron temperature of tens of eV. High-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a nearby normal-incident collector optics CO, and focused onto an opening 221 in a closed structure 220.

[0250] The embodiments can be further described using the following aspects:

[0251] 1. A method for training a machine learning model configured to predict mask patterns, the method comprising:

[0252] Obtain: (i) a process model of the patterning process configured to predict a pattern on a substrate; and (ii) the target pattern; and

[0253] The machine learning model, configured to predict mask patterns, is trained by a hardware computer system based on the process model and a cost function, wherein the cost function determines the difference between the predicted pattern and the target pattern.

[0254] 2. The method according to aspect 1, wherein training the machine learning model configured to predict the mask pattern comprises:

[0255] The parameters of the machine learning model are iteratively modified using a gradient-based method, thereby reducing the cost function.

[0256] 3. The method according to any one of aspects 1 to 2, wherein the gradient-based method generates a gradient graph indicating whether one or more parameters are modified to reduce the cost function.

[0257] 4. The method according to aspect 3, wherein the cost function is minimized.

[0258] 5. The method according to any one of aspects 1 to 4, wherein the cost function is the edge placement error between the target pattern and the predicted pattern.

[0259] 6. The method according to any one of aspects 1 to 5, wherein the process model comprises one or more trained machine learning models, the one or more trained machine learning models comprising:

[0260] (i) a first trained machine learning model configured to predict mask transmission during the patterning process; and / or

[0261] (ii) a second trained machine learning model, coupled to the first trained model, and configured to predict the optical behavior of the device used in the patterning process; and / or

[0262] (iii) A third trained machine learning model, which is coupled to the second trained model and configured to predict the resist process of the patterning process.

[0263] 7. The method according to aspect 6, wherein the first trained machine learning model includes a machine learning model configured to predict two-dimensional or three-dimensional mask transmission effects of the patterning process.

[0264] 8. The method according to any one of aspects 1 to 7, wherein the first trained machine learning model receives a mask image corresponding to the target pattern and predicts a mask transmission image.

[0265] The second trained machine learning model receives the predicted mask transmission image and predicts the spatial image, and

[0266] The third trained machine learning model receives the predicted spatial image and predicts the resist image, wherein the resist image includes the predicted pattern on the substrate.

[0267] 9. The method according to any one of aspects 1 to 8, wherein the machine learning model configured to predict the mask pattern, the first trained model, the second trained model, and / or the third trained model is a convolutional neural network.

[0268] 10. The method according to any one of aspects 8 to 9, wherein the mask pattern includes an optical proximity correction term, the optical proximity correction term including auxiliary features.

[0269] 11. The method according to aspect 10, wherein the optical proximity correction term is in the form of a mask image, and the training is based on the mask image or pixel data of the mask image and an image of the target pattern.

[0270] 12. The method according to any one of aspects 8 to 11, wherein the mask image is a continuous transmission mask image.

[0271] 13. A method for training a process model of a patterning process to predict patterns on a substrate, the method comprising:

[0272] Obtain: (i) a first trained machine learning model for predicting mask transmission during the patterning process; and / or (ii) a second trained machine learning model for predicting the optical behavior of the device used in the patterning process; and / or (iii) a third trained machine learning model for predicting the resist process during the patterning process; and / or (iv) a printed pattern.

[0273] Connect the first trained model, the second trained model, and / or the third trained model to generate the process model; and

[0274] The process model, configured to predict patterns on a substrate, is trained by a hardware computer system based on a cost function that determines the difference between the predicted pattern and the printed pattern.

[0275] 14. The method according to aspect 13, wherein the connection includes sequentially connecting the first trained model to the second trained model, and sequentially connecting the second trained model to the third trained model.

[0276] 15. The method according to aspect 14, wherein the sequential connection comprises:

[0277] Provide the first output of the first trained model as the second input of the second trained model; and

[0278] The second output of the second trained model is provided as the third input of the third trained model.

[0279] 16. The method according to aspect 15, wherein the first output is a mask transmission image, the second output is a spatial image, and the third output is a resist image.

[0280] 17. The method according to any one of aspects 13 to 16, wherein the training includes iteratively determining one or more parameters corresponding to the first trained model, the second trained model, and / or the third trained model based on the cost function, so as to reduce the cost function.

[0281] 18. The method according to aspect 17, wherein the cost function is minimized.

[0282] 19. The method according to any one of aspects 13 to 18, wherein the cost function is the difference between the mean square error, edge placement error and / or critical size between the printed pattern and the predicted pattern.

[0283] 20. The method according to any one of aspects 13 to 19, wherein the determination of the one or more parameters is performed according to a gradient-based method, wherein the local derivative of the cost function with respect to the parameters of the respective model is determined at the third trained model, the second trained model, and / or the first trained model.

[0284] 21. The method according to any one of aspects 13 to 20, wherein the first trained model, the second trained model and / or the third trained model are convolutional neural networks.

[0285] 22. A method for determining an optical proximity effect correction term for a target pattern, the method comprising:

[0286] To obtain (i) a trained machine learning model configured to predict optical proximity correction terms, and (ii) a target pattern to be printed on a substrate via a patterning process; and

[0287] The optical proximity correction term is determined by a hardware computer system based on the trained machine learning model, which is configured to predict the optical proximity correction term corresponding to the target pattern.

[0288] 23. The method according to aspect 22 further includes incorporating structural features corresponding to the optical proximity correction term into the data representing the mask.

[0289] 24. The method according to aspect 23, wherein the optical proximity effect correction term includes the setting of auxiliary features and / or contour modification.

[0290] 25. A computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions, when executed by a computer, implementing the method according to any one of aspects 1 to 24.

[0291] 26. A method for training a machine learning model configured to predict a defect based on a mask pattern, the method comprising:

[0292] Obtain: (i) a process model of the patterning process configured to predict a pattern on a substrate, wherein the process model includes one or more trained machine learning models; (ii) a trained manufacturability model configured to predict defects based on the predicted pattern on the substrate; and (iii) the target pattern; and

[0293] The machine learning model, configured to predict a mask pattern, is trained by a hardware computer system based on the process model, the trained manufacturability model, and a cost function, wherein the cost function is the difference between the target pattern and the predicted pattern.

[0294] 27. The method according to aspect 26, wherein the cost function includes the number of defects predicted by the manufacturability model and the edge placement error between the target pattern and the predicted pattern.

[0295] 28. The method according to any one of aspects 26 to 27, wherein the defect includes necking defects, footing defects, buckling defects and / or bridging defects.

[0296] 29. The method according to aspect 26, wherein training the machine learning model configured to predict the mask pattern comprises:

[0297] The machine learning model is iteratively modified using a gradient-based method to reduce the cost function, which includes the total number of defects and / or the edge placement error.

[0298] 30. The method according to aspect 29, wherein the total number of defects and the edge placement error are reduced simultaneously.

[0299] 31. The method according to any one of aspects 29 to 30, wherein the gradient-based method generates a gradient graph indicating whether the one or more parameters are modified to reduce the cost function.

[0300] 32. The method according to aspect 31, wherein the cost function is minimized.

[0301] 33. A method for training a machine learning model configured to predict mask patterns based on manufacturing violation probabilities, the method comprising:

[0302] Obtain: (i) a process model of the patterning process configured to predict a pattern on a substrate, wherein the process model includes one or more trained machine learning models; (ii) a trained mask rule checking model configured to predict the manufacturing violation probability of the mask pattern; and (iii) the target pattern; and

[0303] The machine learning model, configured to predict the mask pattern, is trained by a hardware computer system based on the process model, the trained mask rule checking model, and a cost function, wherein the cost function is based on the manufacturing violation probability predicted by the mask rule checking model.

[0304] 34. The method according to aspect 33, wherein the mask is a curved mask comprising a curved mask pattern.

[0305] 35. The method according to aspect 33, wherein training the machine learning model configured to predict the mask pattern comprises:

[0306] The parameters of the machine learning model are iteratively modified using a gradient-based method, such that the cost function, which includes the predicted manufacturing violation probability and / or edge placement error, is reduced.

[0307] 36. The method according to any one of aspects 33 to 35, wherein the predicted manufacturing violation probability and the edge placement error are reduced simultaneously.

[0308] 37. The method according to any one of aspects 35 to 36, wherein the gradient-based method generates a gradient graph indicating whether one or more parameters are modified to reduce the cost function.

[0309] 38. The method according to aspect 37, wherein the cost function is minimized.

[0310] 39. A method for determining an optical proximity effect correction term corresponding to a target pattern, the method comprising:

[0311] Obtain: (i) a trained machine learning model configured to predict optical proximity correction terms based on mask manufacturing violation probabilities, edge placement errors, and / or defects on the substrate; and (ii) a target pattern to be printed on the substrate via a patterning process; and

[0312] The optical proximity effect correction term is determined by a hardware computer system based on the trained machine learning model and the target pattern.

[0313] 40. The method according to aspect 39 further includes incorporating structural features corresponding to the optical proximity correction term into the data representing the mask.

[0314] 41. The method according to any one of aspects 38 to 40, wherein the optical proximity effect correction term includes the placement and / or contour modification of auxiliary features.

[0315] 42. The method according to any one of aspects 38 to 41, wherein the optical proximity effect correction term includes a structural feature of a curved shape.

[0316] 43. A method for training a machine learning model configured to predict defects on a substrate, the method comprising:

[0317] Obtain: (i) a resist image or an etched image; and / or (ii) a target pattern; and

[0318] The machine learning model, configured to predict defect metrics, is trained by a hardware computer system based on the resist image or the etched image, the target pattern, and a cost function, wherein the cost function is the difference between the predicted defect metrics and the actual defect metrics.

[0319] 44. The method according to aspect 43, wherein the defect index is the number of defects, defect size, a binary variable indicating the presence of a defect, and / or defect type.

[0320] 45. A method for training a machine learning model configured to predict mask pattern violations, the method comprising:

[0321] Obtain: (i) a set of mask rule checks; (ii) a set of mask patterns; and

[0322] The machine learning model, configured to predict mask rule check violations, is trained by a hardware computer system based on the set of mask rule checks, the set of mask patterns, and a cost function based on a mask rule check metric, wherein the cost function is the difference between the predicted mask rule check metric and the true mask rule check metric.

[0323] 46. ​​The method according to aspect 45, wherein the mask rule check metric includes a violation probability of the mask rule check, wherein the violation probability is determined based on the total number of violations for a specific feature of the mask pattern.

[0324] 47. The method according to any one of aspects 45 to 46, wherein the set of mask patterns is in the form of a continuous transmission mask image.

[0325] 48. A method for determining a mask pattern, the method comprising:

[0326] Obtain: (i) an initial image corresponding to the target pattern; (ii) a process model of the patterning process configured to predict the pattern on the substrate; and (ii) a trained defect model configured to predict defects based on the pattern predicted by the process model; and

[0327] The mask pattern is determined by a hardware computer system based on the process model, the trained defect model, and a cost function including defect indices, according to the initial image.

[0328] 49. The method according to aspect 48, wherein determining the mask pattern is an iterative process, the iteration comprising:

[0329] The pattern on the substrate is predicted based on the input image through simulation of the process model;

[0330] Defects in the predicted pattern are predicted by simulation of the trained defect model;

[0331] The cost function is evaluated based on the predicted defects; and

[0332] The pixel values ​​of the initial image are modified based on the gradient of the cost function.

[0333] 50. The method according to aspect 49, wherein the input image of the process model is an initial image for the first iteration, and the input image is a modified initial image for subsequent iterations.

[0334] 51. The method according to any one of aspects 48 to 50, wherein the defect index is the number of defects, defect size, a binary variable indicating the presence of defects, and / or defect type.

[0335] 52. The method according to any one of aspects 48 to 51, wherein the cost function further includes edge placement error.

[0336] 53. The method according to any one of aspects 48 to 52 further includes:

[0337] A trained mask rule checking model is obtained, the trained mask rule checking model being configured to predict the violation probability of a set of mask rule checks;

[0338] The violation probability is predicted by a hardware computer system based on the mask pattern; and

[0339] The mask pattern is modified by the hardware computer system based on a cost function that includes the predicted probability of violation.

[0340] 54. A method for training a machine learning model configured to predict mask patterns, the method comprising:

[0341] Obtain: (i) a target pattern; (ii) an initial mask pattern corresponding to the target pattern; (iii) a resist image corresponding to the initial mask pattern; and (iv) a set of reference images; and

[0342] The machine learning model, configured to predict the mask pattern, is trained by a hardware computer system based on the target pattern, the initial mask pattern, the resist image, the set of reference images, and a cost function that determines the difference between the predicted mask pattern and the reference images.

[0343] 55. The method according to aspect 54, wherein the initial mask pattern is a continuous transmission mask image obtained from simulation based on a trained machine learning model configured to predict the initial mask pattern.

[0344] 56. The method according to any one of aspects 54 to 55, wherein the cost function is the mean square error between the pixel intensity of the predicted mask pattern and the pixel intensity of the set of reference images.

[0345] 57. The method according to any one of aspects 1 to 12, aspects 26 to 32, 48 to 53, or aspects 54 to 56, further comprising optimizing the predicted mask pattern by iteratively modifying mask variables of the predicted mask pattern predicted by the trained machine learning model, the iteration comprising:

[0346] A mask transmission image is predicted based on the predicted mask pattern through simulation of a physics-based mask model or a machine learning-based mask model.

[0347] Optical images are predicted based on the mask transmission images through simulation using either a physics-based optical model or a machine learning-based optical model.

[0348] The resist image is predicted based on the optical image through simulation using a physics-based resist model or a machine learning-based resist model.

[0349] The cost function is evaluated based on the resist image; and

[0350] Through simulation, the mask variables associated with the predicted mask pattern are modified based on the gradient of the cost function, thereby reducing the cost function.

[0351] 58. A method for training a machine learning model configured to predict resist images, the method comprising:

[0352] Obtain: (i) a process model of the patterning process configured to predict the etched image based on the resist image; and (ii) the etched target; and

[0353] The machine learning model, configured to predict resist images, is trained by a hardware computer system based on the etching model and a cost function that determines the difference between the etched image and the etched target.

[0354] The concepts disclosed herein can be used to simulate or mathematically model any general imaging system for imaging sub-wavelength characteristics, and can be particularly applied to emerging imaging techniques capable of generating increasingly shorter wavelengths. Emerging techniques already in use include EUV (Extreme Ultraviolet) and DUV lithography, which can generate wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate photons in the range of 5 nm to 20 nm by using synchrotrons or by bombarding materials (solid-state or plasma) with high-energy electrons.

[0355] While the concepts disclosed herein can be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of lithography imaging system, such as those used for imaging on substrates other than silicon wafers.

[0356] The above description is intended to be illustrative and not restrictive. Therefore, it will be apparent to those skilled in the art that modifications can be made to the described invention without departing from the scope of the following claims.

Claims

1. A method for training a machine learning model configured to predict a mask pattern, the method comprising: obtaining: (i) a process model of a patterning process configured to predict a pattern on a substrate; and (ii) a target pattern; and training, by a hardware computer system, the machine learning model configured to predict a mask pattern based on the process model and a cost function that determines a difference between a predicted pattern and the target pattern, wherein the process model comprises one or more trained machine learning models comprising: (i) a first trained machine learning model configured to predict a mask transmission of the patterning process; and / or (ii) a second trained machine learning model coupled to the first trained machine learning model and configured to predict an optical behavior of a device used in the patterning process; and / or (iii) a third trained machine learning model coupled to the second trained machine learning model and configured to predict a resist process of the patterning process, wherein training the machine learning model configured to predict the mask pattern comprises: iteratively modifying parameters of the machine learning model according to a gradient-based method that produces a gradient map that is a partial derivative of the cost function with respect to the parameters of the machine learning model, such that the cost function decreases, the partial derivative being determined in that order during backpropagation through the third trained machine learning model, the second trained machine learning model, and the first trained machine learning model.

2. The method of claim 1, wherein, the gradient map indicates whether one or more parameters are modified such that the cost function decreases.

3. The method of claim 2, wherein, the cost function is minimized.

4. The method of claim 1, wherein, the cost function is an edge placement error between the target pattern and the predicted pattern.

5. The method of claim 1, wherein, the cost function is a mean square error between the target pattern and the predicted pattern, and / or a difference in a critical dimension.

6. The method of claim 1, wherein, the first trained machine learning model comprises a machine learning model configured to predict a two-dimensional mask transmission effect or a three-dimensional mask transmission effect of the patterning process.

7. The method of claim 1, wherein, the first trained machine learning model receives a mask image corresponding to the target pattern and predicts a mask transmission image, wherein the second trained machine learning model receives the predicted mask transmission image and predicts a space image, and wherein the third trained machine learning model receives the predicted space image and predicts a resist image, wherein the resist image comprises the predicted pattern on the substrate.

8. The method of claim 1, wherein, the machine learning model configured to predict the mask pattern, the first trained machine learning model, the second trained machine learning model, and / or the third trained machine learning model is a convolutional neural network.

9. The method of claim 7, wherein, The mask pattern includes optical proximity correction terms, the optical proximity correction terms including assist features.

10. The method of claim 9, wherein, The optical proximity correction terms are in the form of a mask image, and the training is based on the mask image or pixel data of the mask image and an image of the target pattern.

11. The method of claim 7, wherein, The mask image is a continuous transmission mask image.

12. The method of claim 1, further comprising optimizing the predicted mask pattern predicted by the trained machine learning model by iteratively modifying mask variables of the predicted mask pattern, the iterations comprising: predicting, via simulation of a physics-based mask model or a machine learning based mask model, a mask transmission image based on the predicted mask pattern; predicting, via simulation of a physics-based optical model or a machine learning based optical model, an optical image based on the mask transmission image; predicting, via simulation of a physics-based resist model or a machine learning based resist model, a resist image based on the optical image; evaluating the cost function based on the resist image; and modifying, via simulation, mask variables associated with the predicted mask pattern based on a gradient of the cost function such that the cost function is reduced.

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