Method of training machine learning model to determine optical proximity correction of mask

Abstract

Various training methods and a mask correction method are described. One of the methods is used to train a machine learning model configured to predict an optimized proximity effect correction (OPC) image for a mask. The method involves obtaining (i) a pre-optimization proximity effect corrected image associated with a design layout to be printed on a substrate, (ii) an image of one or more auxiliary features of the mask associated with the design layout, and (iii) a post-optimization proximity effect corrected reference image of the design layout; and training the machine learning model using the pre-optimization proximity effect corrected image and the image of the one or more auxiliary features as inputs such that a difference between the reference image and a predicted post-optimization proximity effect corrected image of the machine learning model is reduced.

Description

[0001] This application is a divisional application of the patent application with the invention title "Method for training a machine learning model to determine optical proximity correction of a mask" having application number 2020800152046, which entered the Chinese national phase on August 18, 2021, and the applicant is "ASML Netherlands B.V." (the international filing date is January 24, 2020, and the international application number is PCT / EP2020 / 051778).

[0002] Cross-reference to related applications

[0003] This application claims the priority of U.S. Application No. 62 / 808,410 filed on February 21, 2019, and the entire content of the said U.S. application is incorporated herein by reference. Technical field

[0004] The description herein relates to lithographic apparatus and processes, and more particularly to methods for determining corrections for patterning processes. Background art

[0005] A lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device (e.g., a mask) can contain or provide a circuit pattern ("design layout") corresponding to a single layer of the IC, and this circuit pattern can be transferred to a target portion (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a radiation-sensitive material ("resist") layer by irradiating the target portion through the circuit pattern on the patterning device. Typically, a single substrate contains a plurality of adjacent target portions, and the circuit pattern is transferred to the plurality of adjacent target portions successively, one target portion at a time, by the lithographic projection apparatus. In this type of lithographic projection apparatus, the entire circuit pattern on the patterning device is transferred to one target portion at once; such a device is commonly referred to as a wafer stepper. In an alternative device, commonly referred to as a step-and-scan device, the projection beam is scanned over the patterning device in a given reference direction ("scan" direction), while the substrate is moved synchronously parallel or anti-parallel to this reference direction. Different portions of the circuit pattern on the patterning device are transferred stepwise to one target portion. Typically, since the lithographic projection apparatus will have a magnification factor M (usually < 1), the speed F at which the substrate is moved will be a factor M times the speed at which the projection beam scans the patterning device. More information about lithographic apparatus as described herein can be gathered, for example, from US 6,046,792, which is incorporated herein by reference.

[0006] Before transferring the circuit pattern from the pattern forming apparatus to the substrate, the substrate may undergo various processes such as priming, applying a resist, and soft baking. After exposure, the substrate may be subjected to other processes such as post-exposure bake (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. This array of processes serves as the basis for fabricating a single layer of a device (e.g., an IC). The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical-mechanical polishing, etc., all of which are intended to complete a single layer of the device. If several layers are required in the device, the entire process or its variant is repeated for each layer. Eventually, there will be devices in each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, whereby the individual devices can be mounted on a carrier, connected to pins, etc.

[0007] As mentioned, lithographic etching is a central step in the fabrication of ICs, where the pattern formed on the substrate defines the functional elements of the IC, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0008] As semiconductor manufacturing processes continue to advance, over the decades, the sizes of the functional elements have been continuously decreasing, while the number of functional elements such as transistors per device has been steadily increasing, following a trend commonly referred to as "Moore's Law". Under current technology, lithographic projection equipment is used to fabricate layers of a device, which uses irradiation from a deep ultraviolet radiation source to project a design layout onto the substrate, thereby enabling the production of individual functional elements having dimensions sufficiently less than 100 nm, i.e., less than half the wavelength of the radiation from the radiation source (e.g., a 193 nm radiation source).

[0009] The process of printing features having dimensions smaller than the classical resolution limit of a lithographic projection apparatus is generally referred to as low-k1 lithography 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 lithographic projection apparatus, CD is the "critical dimension" (usually the smallest feature size printed), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce on the substrate a pattern similar in shape and size to that planned by the circuit designer in order to achieve a specific electrical function and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus and / or the design layout. These steps include (by way of example and not limitation) optimization of the NA and optical coherence settings, self-defined illumination schemes, use of phase-shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). As used herein, the term "projection optics" should be interpreted broadly to cover various types of optical systems, including (by way of example) refractive optics, reflective optics, apertures, and catadioptric optics. The term "projection optics" may also include components that operate according to any of these design types for jointly or individually guiding, shaping, or controlling a projection radiation beam. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located in the optical path of the lithographic projection apparatus. The projection optics may include optical components for shaping, conditioning, and / or projecting the radiation before it passes through the patterning device from the source, and / or for shaping, conditioning, and / or projecting the radiation after it passes through the patterning device. The projection optics generally excludes the source and the patterning device. SUMMARY OF THE INVENTION

[0010] In an embodiment, a method of training a machine learning model configured to predict an optimized optical proximity correction (OPC) image for a mask is provided. The method involves: obtaining (i) a pre-optimization optical proximity correction image associated with a design layout to be printed on a substrate, (ii) an image of one or more auxiliary features of the mask associated with the design layout, and (iii) an optimized optical proximity correction reference image of the design layout; and using the pre-optimization optical proximity correction image and the image of the one or more auxiliary features as inputs to train the machine learning model such that the difference between the reference image and the predicted optimized optical proximity correction image of the machine learning model is reduced.

[0011] In addition, in an embodiment, there is provided a method for training a machine learning model for predicting optimized proximity effect correction (OPC) for a mask. The method involves: obtaining (i) a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate, and (ii) a reference image of the optimized proximity effect correction of the design layout; and using the pre-optimization proximity effect correction image as an input to train the machine learning model such that the difference between the predicted optimized proximity effect correction image of the machine learning model and the reference image is reduced.

[0012] In addition, there is provided a method for determining an optimized proximity effect correction image for a mask. The method involves: obtaining a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate; determining a first optimized proximity effect correction image of the mask by simulating a trained first machine learning model using the pre-optimization proximity effect correction image, wherein the first optimized proximity effect correction image includes one or more auxiliary features of the mask; extracting geometries of the one or more auxiliary features of the first optimized proximity effect correction image; and determining a second optimized proximity effect correction image for the mask by simulating a trained second machine learning model using the pre-optimization proximity effect correction image of the design layout and the extracted geometries of the one or more auxiliary features of the first optimized proximity effect correction image.

[0013] In addition, in an embodiment, there is provided a method for determining a correction to a design layout. The method involves: (i) obtaining a predicted optimized proximity effect correction image via training a machine learning model, and obtaining (ii) the geometry of the design layout, the machine learning model using a pre-optimization proximity effect correction image of the design layout and an image of one or more auxiliary features associated with the design layout; segmenting the geometry of the design layout into a plurality of segments; and determining a correction to the plurality of segments such that the difference between an image of the design layout and the predicted optimized proximity effect correction image along the geometry is reduced.

[0014] In addition, there is provided a computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer, implement the methods as described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Embodiments will now be described by way of example only with reference to the accompanying drawings, in which:

[0016] Figure 1It is a block diagram of each subsystem of a lithography system according to an embodiment.

[0017] Figure 2 It is according to an embodiment and related to Figure 1 a block diagram of an analog model corresponding to the subsystem in

[0018] Figure 3 It is a flowchart of a method for training a machine learning model according to an embodiment, where the machine learning model is configured to predict an optimized proximity effect correction (OPC) image for a mask.

[0019] Figure 4A It is according to an embodiment Figure 3 an example of a training dataset and results of a training method of

[0020] Figure 4B It is according to an embodiment Figure 3 another example of a training dataset and results of a training method of

[0021] Figure 5 It is a flowchart of another method for training another machine learning model according to an embodiment, where the another machine learning model is configured to predict an optimized proximity effect correction (OPC) image for a mask.

[0022] Figure 6A 、 Figure 6B and Figure 6C 4 illustrate examples of a training set and results of a training method of Figure 5 according to an embodiment

[0023] Figure 7 It is a method according to an embodiment for using Figure 5 the trained first machine learning model and Figure 3 the trained second machine learning model to determine an optimized proximity effect correction image for a mask.

[0024] Figure 8 It is a flowchart of a method for determining a correction to a design layout according to an embodiment.

[0025] Figure 9 It is according to an embodiment Figure 7 exemplary results of a mask correction process of

[0026] Figure 10 It is a flowchart illustrating aspects of an exemplary method for joint optimization according to an embodiment.

[0027] Figure 11 It shows an embodiment of another optimization method according to an embodiment.

[0028] Figure 12A 、 Figure 12Band Figure 13 Exemplary flowcharts showing various optimization processes according to embodiments.

[0029] Figure 14 is a block diagram of an exemplary computer system according to an embodiment.

[0030] Figure 1� is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0031] Figure 16 is a schematic diagram of another lithographic projection apparatus according to an embodiment.

[0032] Figure 17 is according to an embodiment Figure 16 a more detailed view of the apparatus in

[0033] Figure 18 is according to an embodiment Figure 16 and Figure 17 a more detailed view of the source collector module SO of the apparatus of

[0034] Embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice the embodiments. It should be noted that the following figures and examples are not intended to limit the scope to a single embodiment, but rather to enable other embodiments by means of the interchange of some or all of the described or illustrated elements. Wherever convenient, the same reference numerals will be used throughout the figures to refer to the same or similar parts. In cases where some elements of these embodiments can be implemented using known components in part or in whole, only those parts of these known components that are necessary for understanding the embodiments will be described, and the detailed description of the other parts of these known components will be omitted so as not to obscure the description of the embodiments. In this specification, embodiments showing a single component should not be regarded as restrictive; rather, unless explicitly stated otherwise herein, the scope is intended to cover other embodiments including multiple identical components, and vice versa. Additionally, the applicant does not intend for any term in this specification to be construed in an uncommon or special sense, unless so explicitly set forth. Further, the scope covers current and future known equivalents of the components referred to herein by way of illustration. Detailed Description of the Invention

[0035] Although specific reference may be made in this text to IC manufacturing, it should be clearly understood that the description of the present invention has many other possible applications. For example, the description of the present invention can be used in the manufacture of integrated optical systems, guiding and detecting patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art should understand that in the context of these alternative applications, any use of the terms "reticle", "wafer" or "die" in this text should be considered to be interchangeable with the more general terms "mask", "substrate" and "target portion" respectively.

[0036] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of 5 nm to 20 nm).

[0037] As used herein, the term "optimizing / optimization" means: adjusting a lithographic projection apparatus such that the result and / or process of lithography has more desirable characteristics, such as, a higher accuracy of projection of a design layout onto a substrate, a larger process window, etc.

[0038] In addition, a lithographic projection apparatus may be of a type having two or more substrate tables (and / or two or more patterning device tables). In these "multi-platform" devices, additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are used for exposure. For example, a dual-platform lithographic projection apparatus is described in US 5,969,441 which is incorporated herein by reference.

[0039] The patterning device mentioned above includes or may form a design layout. A CAD (computer-aided design) program can be used to generate a design layout, and this process is often referred to as EDA (electronic design automation). Most CAD programs follow a set of predefined design rules in order to generate a functional design layout / patterning device. These rules are set by process and design constraints. For example, design rules define the space tolerances between circuit devices (such as gates, capacitors, etc.) or interconnect lines so as to ensure that circuit devices or lines do not interact with each other in an undesirable manner. Design rule limitations are usually referred to as "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or a hole or the minimum space between two lines or two holes. Thus, the CD determines the total size and density of the designed circuit. Of course, one of the objectives in integrated circuit manufacturing is to faithfully reproduce the original circuit design on a substrate (via the patterning device).

[0040] As used herein, the term "mask" or "patterning device" can be broadly interpreted as referring to a general patterning device that can be used to endow an incident radiation beam with a patterned cross-section corresponding to a pattern to be created in a target portion of a substrate; the term "light valve" can also be used in this context. In addition to classical masks (transmission or reflection; binary, phase-shift, hybrid, etc.), examples of such other patterning devices also include:

[0041] -programmable mirror arrays. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The underlying principle implicit in such a device is (for example) that the addressed areas of the reflective surface reflect the incident radiation as diffracted radiation, while the non-addressed areas reflect the incident radiation as non-diffracted radiation. With the use of an appropriate filter, the non-diffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronics. More information on such mirror arrays can be gathered, for example, from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0042] -programmable LCD arrays. An example of such a configuration is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0043] As a brief introduction, Figure 1 FIG. 10A illustrates an exemplary lithographic projection apparatus. The main components are: a radiation source 12A, which can be a deep ultraviolet excimer laser source or other types of sources including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have a radiation source); illumination optics that define partial coherence (represented as the mean square deviation) and can include optics 14A, 16Aa, and 16Ab for shaping the radiation from source 12A; a patterning device; and projection optics 16Ac that project an image of the pattern of the patterning device onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics can define the range of beam angles incident on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA = sin(Θ max )

[0044] In the optimization of a system, the quality factor of the system can be expressed as a cost function. The optimization process boils down to the process of finding a set of parameters (design variables) of the system that minimizes the cost function. The cost function can have any suitable form depending on the objective of the optimization. For example, the cost function can be the weighted root mean square (RMS) of the deviation of certain characteristics (evaluation points) of the system with respect to the expected values (e.g., ideal values) of these characteristics; the cost function can also be the maximum value of these deviations (i.e., the worst deviation). The term "evaluation point" in this document should be interpreted broadly to include any characteristic of the system. Due to the applicability of the implementation of the system, the design variables of the system can be restricted to a finite range and / or be interdependent. In the case of a lithographic projection apparatus, the constraints are often associated with the physical characteristics and properties of the hardware (such as the tunable range, and / or the manufacturability design rules of the patterning device), and the evaluation points can include physical points on the resist image on the substrate, as well as non-physical characteristics such as dose and focal length.

[0045] In a lithographic projection apparatus, a source provides illumination (i.e., light); the projection optics guides and shapes the illumination via a patterning device and directs the illumination onto a substrate. In this context, the term "projection optics" is broadly defined to include any optical component that can alter the wavefront of the radiation beam. For example, the projection optics can include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. The resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer to form a latent "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in co-pending U.S. Patent Application No. 12 / 315,849, which is hereby incorporated by reference in its entirety. The resist model is only associated with the properties of the resist layer (such as the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of the lithographic projection apparatus (such as the properties of the source, patterning device, and projection optics) define the aerial image. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the remainder of the lithographic projection apparatus, which at least includes the source and the projection optics.

[0046] Figure 2The figure shows an exemplary flow chart for simulating lithography in a lithographic projection apparatus. The source model 31 represents the optical characteristics of the source (including the radiation intensity distribution and / or phase distribution). The projection optics model 32 represents the optical characteristics of the projection optics (including the change in the radiation intensity distribution and / or phase distribution caused by the projection optics). The design layout model 35 represents the optical characteristics of the design layout (including the change in the radiation intensity distribution and / or phase distribution caused by the given design layout 33), where the design layout is a representation of the arrangement of features on or formed by the patterning device. The aerial image 36 can be simulated from the design layout model 35, the projection optics model 32, and the design layout model 35. The resist image 38 can be simulated from the aerial image 36 using the resist model 37. The simulation of lithography can, for example, predict the profiles and CDs in the resist image.

[0047] More specifically, it should be noted that the source model 31 can represent the optical characteristics of the source, which include but are not limited to the NA root mean square deviation (σ) setting, and any particular illumination source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical characteristics of the projection optics, which include aberration, distortion, refractive index, physical size, physical dimensions, etc. The design layout model 35 can also represent the physical properties of the physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is hereby incorporated by reference in its entirety. The goal of the simulation is to accurately predict (e.g.) edge placement, aerial image intensity slope, and CD, which can then be compared with the expected design. The expected design is typically defined as the pre-optimization proximity effect corrected design layout, which can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0048] From this design layout, one or more portions referred to as "clips" can be identified. In an embodiment, a set of clips is extracted, which represents complex patterns in the design layout (typically from about 50 to 1000 clips, but any number of clips can be used). As would be understood by those skilled in the art, these patterns or clips represent smaller portions of the design (i.e., circuits, cells, or patterns), and the clips in particular represent smaller portions that require special attention and / or verification. In other words, a clip can be a portion of the design layout, or can be similar, or have similar behavior to a portion of the design layout, in which key features are identified empirically (including clips provided by the customer), by trial and error, or by performing a full-chip simulation. Clips typically contain one or more test patterns or gauge patterns.

[0049] An initial larger set of clips can be provided a priori by a customer based on known critical feature regions in a design layout that require specific image optimization. Alternatively, in another embodiment, an initial larger set of clips can be extracted from the entire design layout by using some automation (such as machine vision) or a manual algorithm that identifies critical feature regions.

[0050] Optical proximity correction (OPC) is a lithography enhancement technique commonly used to compensate for image errors attributed to diffraction and process effects. Existing model-based OPC typically consists of several steps, including: (i) deriving a wafer target pattern including rule re-targeting, (ii) placing sub-resolution assist features (SRAFs), and (iii) performing iterative correction including model simulation (e.g., by computing an intensity map on the wafer). The most time-consuming part of the model simulation is model-based SRAF generation and clearing based on mask rule checking (MRC), as well as simulation of mask diffraction, optical imaging, and resist development.

[0051] One of the challenges in optimizing proximity correction simulation is runtime and accuracy. Generally, the more accurate the result, the slower the OPC process. To obtain a better process window, more model simulations under different conditions (nominal condition, defocus condition, under-dose condition) are required in each OPC iteration. In addition, the more patterning process-related models included, the more iterations are needed to converge the OPC result to the target pattern. Due to the large amount of data to be processed (billions of transistors on a chip), the runtime requirement imposes strict constraints on the complexity of OPC-related algorithms. Additionally, as the scaling of integrated circuits continues, the accuracy requirement becomes more stringent. Thus, new algorithms and techniques are needed to address these challenges. For example, different solutions are needed, such as for polygon-based OPC. For example, the present invention provides a method for determining an optimized proximity correction layout. The method provides high accuracy while maintaining high speed and simplification of the optimized proximity correction layout.

[0052] In an embodiment, the present invention discusses a method for generating a machine learning model to predict an optimized proximity correction image or an optimized proximity correction pattern extracted from an optimized proximity correction image. The method uses a pre-existing OPC process to obtain training patterns and collects data including target patterns, optimized proximity correction patterns, and SRAF / SERIF layouts for individual layers of a substrate. This data is used to train a machine learning model (such as a convolutional neural network (CNN)). In an embodiment, to generate a training data set, the OPC algorithm may be as complex as required to obtain high-accuracy data, since the number of training patterns is limited compared to a full chip.

[0053] The present invention provides several advantages. The trained model can be applied to predict the full-chip optimized post-proximity effect correction layout for any target layout / design layout. In an embodiment, the optimized post-proximity effect correction layout can be applied to polygon-based correction on a target (retargeted layer), where the correction is determined to substantially match the optimized post-proximity effect correction layout (determined by the trained model). The correction can also be used in an existing OPC process, which will require far fewer iterations.

[0054] Additional advantages of the method include a simpler mask layout. Since the optimized post-proximity effect correction is from polygon-based correction in both the initial step of mask rasterization and the subsequent existing OPC correction steps, it is easier to apply mask rule checking and the mask layout shape will be much simpler. In addition, compared with the existing OPC process, the trained machine learning model of the present invention results in faster OPC and SMO results.

[0055] Figure 3 is a flowchart of a method 300 for training a machine learning model configured to predict an optimized post-proximity effect correction (OPC) image for a mask. The training is based on an image or image data associated with a pre-optimized post-proximity effect correction layout and auxiliary features. In an embodiment, the pre-optimized post-proximity effect correction layout can be a design layout or a biased design layout. In an embodiment, the pre-optimized post-proximity effect correction data and the auxiliary feature data can be discrete (e.g., represented as two different images) or in a combined form (e.g., in the form of a single image). The model is trained to predict optimized post-proximity effect correction data (e.g., an optimized post-proximity effect correction image) that closely matches reference data (e.g., an optimized OPC image). According to an embodiment, an exemplary process of method 300 is described below.

[0056] In process P301, the method involves obtaining (i) a pre-optimized post-proximity effect correction image 302 associated with a design layout to be printed on a substrate, (ii) an image 304 of one or more auxiliary features of the mask associated with the design layout, and (iii) a reference image 306 of the optimized post-proximity effect correction of the design layout. In an embodiment, the pre-optimized post-proximity effect correction image 302, the image of the auxiliary features, the predicted optimized post-proximity effect correction image, and the reference image are pixelated images.

[0057] In an embodiment, obtaining the pre-optimization proximity effect corrected image 302 and the image 304 of one or more assist features involves obtaining the geometries of the design layout and the assist features (e.g., polygonal shapes such as square, rectangular, or circular shapes, etc.), and via image processing, generating the pre-optimization proximity effect corrected image 302 from the geometry of the design layout and generating another image from the geometry of the assist features. In an embodiment, the image processing includes a rasterization operation based on the geometry. For example, a rasterization operation that converts the geometry (e.g., in a vector graphics format) into a pixelated image. In an embodiment, rasterization may also involve applying a low-pass filter to clearly identify the feature shape and reduce noise.

[0058] In an embodiment, obtaining the geometry of the assist features involves determining the geometry of the assist features associated with the design layout via a rule-based method. In an embodiment, the geometry of the assist features associated with the design layout is determined via a model-based method. Exemplary ways for obtaining SRAF (e.g., rule-based or model-based) are discussed in U.S. Patent Application No. 14 / 282,754, filed May 20, 2014, and U.S. Patent No. 7,882,480, filed Jun. 4, 2007, which are hereby incorporated by reference in their entireties.

[0059] In an embodiment, obtaining the reference image involves performing a mask optimization process and / or a source mask optimization process using the design layout. In an embodiment, the mask optimization process uses an optical proximity effect correction process. Regarding Figures 10 to 13 exemplary OPC processes are further discussed.

[0060] In process P303, the method involves using the pre-optimization proximity effect corrected image 302 and the image 304 of one or more assist features as inputs to train a machine learning model such that the difference between the reference image and the predicted post-optimization proximity effect corrected image of the machine learning model is reduced. At the end of the training process, a trained machine learning model 310 (also referred to as the trained second model 310).

[0061] In an embodiment, the training of the machine learning model is an iterative process that involves: inputting the pre-optimization proximity effect corrected image 302 and the image 304 of one or more assist features into the machine learning model; simulating the machine learning model to predict the post-optimization proximity effect corrected image 302; determining the difference between the predicted post-optimization proximity effect corrected image and the reference image; and adjusting the weights of the machine learning model such that the difference between the predicted image and the reference image is reduced.

[0062] In an embodiment, weights are adjusted based on differential gradient descent. In an embodiment, weights may be adjusted based on other optimization methods that minimize the difference. Those skilled in the art will understand that the present invention is not limited to the gradient descent method, and other suitable methods that can guide how to adjust the weights such that the difference between the predicted image and the reference image is reduced may be used. In an embodiment, training is performed until the difference between the predicted image and the reference image is minimized.

[0063] Figure 4A An example of a training set and results of a training method 300 is illustrated, where a machine learning model (e.g., also referred to as a second machine learning model) is trained to determine / predict a predicted optimized proximity effect correction image (e.g., 420). In this example, the training set includes an image 402 that includes features 402a associated with the main features of the design layout, and assist features (SRAFs) 404a associated with the main features of the design layout. Thus, in this example, the image 402 is a combination of an image of the proximity effect correction image before optimization and the assist features. Additionally, a reference image 406 (e.g., an optimized optimized proximity effect correction image obtained via several iterations of a complex optimized proximity effect correction simulation) is used as the ground truth, which is used to modify the weights of the machine learning model during the training process.

[0064] During the training process, the weights are modified such that the difference 410 between the reference image 406 and the predicted optimized proximity effect correction image (e.g., 420) is iteratively reduced. In an embodiment, the weights are modified based on a gradient descent method (not illustrated), where a gradient map is calculated based on the differential of the difference 410. The gradient map of the difference 410 is used as a guide to modify the weights of the machine learning model such that the difference is reduced (minimized after several iterations in an embodiment). Thus, in an embodiment, when the difference between the reference image 406 and the predicted OPC image 420 is minimized, the model is considered a trained machine learning model 310. In other words, the training process (or simulation) converges and there is no further improvement in the difference 410, whereby the results of the trained model 310 closely match the reference image 406.

[0065] In an embodiment, the predicted optimized proximity effect corrected image may not match the reference image 406 exactly. For example, at location 407 in the reference image 406, a relatively large difference 417 is observed. This difference 417 indicates that at such a location, the predicted optimized proximity effect corrected image includes substantially different but not significantly different features. However, even in the presence of such a difference 417, the predicted optimized proximity effect corrected image 420 enables reducing the number of iterations of the optimized proximity effect correction simulation process (e.g., fewer than 10 iterations compared to 1000 iterations when only using the design layout) to further improve the optimized proximity effect corrected layout of the design layout. In other words, when the predicted optimized proximity effect corrected image 420 is used as the initial or starting point of the optimized proximity effect correction simulation, the optimized proximity effect correction simulation runs and converges in a faster manner, thereby saving computational time and resources.

[0066] Figure 4B Another example of the training set and results of the training method 300 is illustrated, where a machine learning model (e.g., a second machine learning model) is trained to determine / predict the predicted optimized proximity effect corrected image (e.g., 430). In this example, the pre-optimization proximity effect corrected image 422 and the assist feature image 424 are separate. In an embodiment, as discussed earlier, the pre-optimization proximity effect corrected image 422 can be obtained by rasterization of the design layout. The assist feature image 424 can be obtained via rasterization of the SRAF associated with the design layout (e.g., the geometry of the SRAF). In an embodiment, such an SRAF can be obtained via an SRAF guidance map, SRAF rules, or a model-based OPC method, as mentioned earlier. Additionally, the reference image 426 (e.g., the optimized optimized proximity effect corrected image obtained via several iterations of a complex optimized proximity effect correction simulation) is used as the ground truth for modifying the weights of the machine learning model during the training process. The training process is similar to the training process discussed above in Figure 3 and Figure 4A During the training process, the weights are modified such that the difference 430 between the reference image 426 and the predicted optimized proximity effect corrected image (e.g., 440) is reduced iteratively (minimized after several iterations in an embodiment).

[0067] Similar to the above discussion, the predicted optimized proximity effect corrected image 440 may not match the reference image 426 accurately. For example, at location 429 in the reference image 426, a relatively large difference 447 is observed. This difference 447 indicates that at such a location, the predicted optimized proximity effect corrected image 440 includes substantially different but not significantly different features. Even so, the predicted optimized proximity effect corrected image 440 enables reducing the number of iterations in the optimized proximity effect correction simulation process (e.g., fewer than 10 iterations compared to 1000 iterations when only using the design layout) to further improve the optimized proximity effect corrected layout of the design layout. In other words, the optimized proximity effect correction simulation runs and converges in a faster manner using the predicted image 420, thereby saving computational time and resources.

[0068] Return reference Figure 3 , method 300 may also involve a mask model correction process that involves determining a correction 316 to the design layout based on a trained machine learning model. For example, the method also involves processes P312 to P316 as discussed below. Process P312 involves obtaining the geometry 312 of the design layout. For example, the geometry 312 can be a rectangle with a desired CD value (e.g., length and width), a square with a desired CD value, a contact hole (e.g., circular) with a desired CD value (e.g., diameter), or other geometries. In an embodiment, such geometries can be in a GDS file for patterning process simulation.

[0069] Process P314 involves dividing the geometry 312 of the design layout (or generally the pre-optimized proximity effect corrected layout) into multiple segments 314. The division of the geometry refers to dividing the geometry into smaller segments or fragments such that the individual segments or fragments can be moved relative to other segments or fragments. For example, a line can be divided into 3 segments of similar length. The division of the geometry can be such that each segment has a similar length. However, the present invention is not limited to a particular division method (e.g., equal length or unequal length). The following Figure 9 shows an example of the divided geometry.

[0070] Process P316 involves determining a correction 316 for a plurality of segments 314 such that the difference between an image associated with a design layout and a predicted optimized proximity effect corrected image along a geometry is reduced. In an embodiment, the correction 316 involves geometric properties of the segments or relative properties with respect to other segments. For example, the correction can be an amount of distance by which a particular segment is moved relative to other segments (e.g., moved 2 nm in the upstream direction). In an embodiment, the correction can involve the angular position or curvature of the segments. In an embodiment, the correction (e.g., distance, angle, direction, radius of curvature) is associated with each segment that can be stored and further used during an optimization process (e.g., in OPC).

[0071] In an embodiment, determining the correction 316 is an iterative process that involves: adjusting a plurality of segments 314 of the geometry 312 (e.g., distance, length, radius of curvature, angle); generating an image from the adjusted geometry of the design layout (e.g., using a rasterization operation); and evaluating the difference between the generated image and a predicted optimized proximity effect corrected image along the geometry within the corresponding image.

[0072] In an embodiment, the image is a pixelated image, and the difference between the generated image and the predicted image is the difference in intensity values along the geometry. In an embodiment, pixel values along the geometry or relatively close to the geometry can be used to determine the difference.

[0073] In an embodiment, adjusting the plurality of segments 314 involves adjusting the shape and / or position of at least a portion of the plurality of segments such that the difference between the generated image and the predicted image is reduced. In an embodiment, the difference between the generated image and the predicted optimized proximity effect corrected image is minimized. In an embodiment, the adjustment or correction 316 may result in a substantial modification of the original geometry of the design layout. In other words, the original shape is not preserved.

[0074] In an embodiment, process P316 can involve placing one or more evaluation points on each of the plurality of segments. An evaluation point is a location within a segment where an indicator (e.g., EPE) is evaluated. In an embodiment, the sum of the values of the indicator at each evaluation point can be evaluated, and an adjustment to the segment can be performed such that the sum of the indicator is reduced (in an embodiment, minimized).

[0075] Method 300 can be further extended to perform an optimized proximity effect correction simulation using the trained model 310 and the correction 316. For example, process P320 involves determining a mask layout 320 to be used for manufacturing a mask for a patterning process via an optimized proximity effect correction simulation using a design layout and a correction 316 to the design layout.

[0076] In an embodiment, optimizing the proximity effect correction simulation involves: simulating a patterning process model via using the geometry 312 of a design layout and a correction 316 associated with a plurality of segments 314 to determine a simulated pattern to be printed on a substrate; and determining an optical proximity effect correction to the design layout such that the difference between the simulated pattern and the design layout is reduced.

[0077] In an embodiment, determining the optical proximity effect correction is an iterative process, and the iteration involves: adjusting the shape and / or size of polygons associated with the main features and / or auxiliary features of the design layout such that a performance metric of the patterning process is reduced. In an embodiment, the auxiliary features are extracted from the predicted optimized proximity effect correction image of a machine learning model. In an embodiment, the performance metric includes an edge placement error between the simulated pattern and the design layout, and / or a CD value of the simulated pattern. Other exemplary optimizing proximity effect correction simulation processes are subsequently discussed herein with reference to Figures 10 to 13 further discuss other exemplary optimizing proximity effect correction simulation processes.

[0078] Figure 5 is a method for training another machine learning model (also referred to as the first machine learning model) to predict an optimized proximity effect correction (OPC) for a design mask.

[0079] In process P501, the method involves obtaining (i) a pre-optimization proximity effect correction image 502 associated with a design layout to be printed on a substrate, and (ii) an optimized proximity effect correction reference image 506 of the design layout. In an embodiment, obtaining the pre-optimization proximity effect correction image is similar to that discussed in method 300, which involves: obtaining the geometry of the design layout; and generating an image from the geometry via image processing. In an embodiment, the image processing includes a rasterization operation of the geometry, as discussed earlier.

[0080] In an embodiment, obtaining the optimized proximity effect correction reference image 506 is similar to that discussed in method 300. For example, the reference image 506 is obtained by performing a mask optimization process and / or a source mask optimization process using the design layout. In an embodiment, the mask optimization process includes optical proximity effect correction.

[0081] In process P503, the method involves using the pre-optimization proximity effect correction image 502 as an input to train a machine learning model such that the difference between the predicted optimized proximity effect correction image of the machine learning model and the reference image 506 is reduced.

[0082] In an embodiment, the training of the machine learning model is an iterative process that involves: inputting the pre-optimization proximity effect corrected image 502 into the machine learning model; simulating the machine learning model to predict the post-optimization proximity effect corrected image; determining the difference between the predicted post-optimization proximity effect corrected image and the reference image; and adjusting the weights of the machine learning model such that the difference between the predicted image and the reference image is reduced (in an embodiment, minimized). In an embodiment, the weights are adjusted based on gradient descent of the difference.

[0083] Figure 6A , Figure 6B and Figure 6C FIG. illustrates an example of a training set and results of the training method 500, where a machine learning model (e.g., a first machine learning model) is trained to determine / predict the predicted post-optimization proximity effect corrected images (e.g., 607, 627, and 637). In this example, the training set includes pre-optimization proximity effect corrected images (e.g., 602, 622, and 632 in Figures 6A to 6C respectively), which include features associated with the main features of the design layout but do not include auxiliary features (e.g., SRAF). Additionally, reference images (e.g., reference images 604, 624, and 634 associated with 602, 622, and 632 respectively) are used as ground truth for modifying the weights of the machine learning model during the training process. In an embodiment, the reference image is an optimized post-optimization proximity effect corrected image obtained via several iterations of complex optimized proximity effect correction simulation using the design layout of interest.

[0084] During the training process (e.g., of method 500), the weights of the machine learning model (e.g., also referred to as the first machine learning model) are modified such that the difference (e.g., 605, 625, and 635) between the reference image (e.g., 604, 624, and 634) and the predicted post-optimization proximity effect corrected image (e.g., 607, 627, and 637) is reduced iteratively. In an embodiment, as previously mentioned, the weights are modified based on a gradient descent method (not shown). Thus, in an embodiment, when the difference between the reference image and the predicted OPC image is minimized, the model is considered the trained machine learning model 510. In other words, the training process (or simulation) converges and there is no substantial improvement in the difference (e.g., 605, 625, and 635).

[0085] In connection with the above discussion (regarding Figure 4A and Figure 4BSimilarly, the predicted optimized proximity effect corrected images 607 / 627 / 637 may not exactly match the reference images 604 / 624 / 634. For example, at locations 604a / 624a / 634a in the reference images 604 / 624 / 634, relatively large differences are observed. Such differences indicate that at such locations, the predicted optimized proximity effect corrected images include substantially (and in some cases significantly) different features. Nevertheless, the predicted optimized proximity effect corrected images 607 / 627 / 637 also enable reducing the number of iterations of the optimized proximity effect correction simulation process to further improve the optimized proximity effect corrected layout of the design layout. In other words, the optimized proximity effect correction simulation runs and converges in a faster manner using the predicted images 607 / 627 / 637, thereby saving computational time and resources. As mentioned above, the predicted optimized proximity effect corrected images 607 / 627 / 637 can be converted to, for example, GDS format by extracting the main features and auxiliary features from the image 440, and then this GDS file is used in the optimized proximity effect correction simulation.

[0086] In an embodiment, the trained machine learning model 510 generates a simpler SRAF, and such a simpler SRAF can be highly desirable because such a simpler SRAF is easier to fabricate. For example, at Figure 6C location 624a, several small and discrete SRAFs are placed relatively close to each other. On the other hand, at location 637a (corresponding to 624a), a straighter and less discrete and simpler SRAF is generated. From the perspective of mask fabrication, such a straighter SRAF is advantageous.

[0087] Referring to Figures 4A to 4B and Figures 6A to 6C , it can be observed that the predicted optimized proximity effect corrected images 607 / 627 / 637 (also referred to as the predicted first OPC images) are significantly different from the reference images 604 / 624 / 634. On the other hand, the predicted optimized proximity effect corrected images 420 / 430 match the reference images 406 / 426 more closely.

[0088] }In an embodiment, the first optimized proximity effect corrected images 607 / 627 / 637 include SRAFs associated with the main features. Such SRAFs can be extracted and further used as inputs to a trained second machine learning model (e.g., 310) to predict a second optimized proximity effect corrected image. Such a second optimized proximity effect corrected image can be further improved compared to SRAFs obtained via existing methods such as rule-based and model-based methods. Additionally, using the trained first machine learning model (e.g., 510) to obtain SRAFs can be much faster than existing methods. Below regardingFigure 7 An exemplary method of using the trained models 510 and 310 is described.

[0089] Figure 7 FIG. 700 is a flowchart of a method 700 for determining an optimized proximity effect correction image for a mask. In process P702, the method involves obtaining a pre-optimization proximity effect correction image 702 associated with a design layout. The pre-optimization proximity effect correction image 702 is obtained in a manner similar to that previously described in methods 300 and 500. In process P704, the method determines a first optimized proximity effect correction image 704 for the mask by using the pre-optimization proximity effect correction image 702 to execute a trained first machine learning model (e.g., 510), where the first optimized proximity effect correction image 704 includes auxiliary features for the mask. Additionally, process P706 involves extracting the geometry 706 of the auxiliary features of the first optimized proximity effect correction image.

[0090] In process P708, the method determines a second optimized proximity effect correction image 708 for the mask by simulating a trained second machine learning model (e.g., 310) using the pre-optimization proximity effect correction image 702 of the design layout and the extracted geometry 706 of the auxiliary features of the first optimized proximity effect correction image 704.

[0091] In an embodiment, method 700 can also be extended to determine a correction to the design layout as earlier discussed in Figure 3 In an embodiment, process P710 involves determining a correction 710 to the design layout based on the second optimized proximity effect correction image 708 and the design layout.

[0092] In an embodiment, as earlier discussed, determining the correction 710 is an iterative process that involves: obtaining the geometry of the design layout; dividing the geometry of the design layout into multiple segments; adjusting the multiple segments; generating an image from the adjusted geometry of the design layout; and evaluating the difference between the generated image and the second optimized proximity effect correction image 708 along the geometry of the corresponding image.

[0093] In an embodiment, adjusting the multiple segments involves adjusting the shape and / or position of at least a portion of the multiple segments such that the difference between the generated image and the second optimized proximity effect correction image 708 along the geometry of the corresponding image is reduced (minimized in an embodiment).

[0094] Method 700 can be further extended to perform optimized proximity effect correction simulations. For example, process P712 involves: determining a mask layout 720 to be used for manufacturing a mask for a patterning process via an optimized proximity effect correction simulation using a design layout and a correction 710 of the design layout.

[0095] Figure 8 Exemplary method 800 for determining a correction to a design layout, exemplary method 800 is similar to the method discussed above with respect to Figure 3 as discussed.

[0096] In process P802, the method involves obtaining (i) a predicted optimized proximity effect correction image 802 via training a machine learning model, and obtaining (ii) the geometry of a design layout 804, where the machine learning model is trained using a pre-optimized proximity effect correction image of the design layout and an image of one or more auxiliary features associated with the design layout.

[0097] In process P804, the method involves segmenting the geometry of the design layout into a plurality of segments. Additionally, as discussed below, the method involves determining a correction 810 for the plurality of segments such that the difference between an image of the design layout and the predicted optimized proximity effect correction image along the geometry is reduced.

[0098] In process P805, the method places one or more evaluation points on each of the plurality of segments, as earlier discussed with respect to method 300.

[0099] In an embodiment, determining the correction 810 is an iterative process that involves processes P806, P808, and P810.

[0100] Process P806 involves adjusting the plurality of segments via one or more evaluation points. Process P808 involves generating an image from the adjusted geometry of the design layout. Process P810 involves evaluating the difference between the generated image 808 and the predicted optimized proximity effect correction image 802 at one or more evaluation points on the plurality of segments of the geometry. In an embodiment, the difference between the generated image and the predicted image is the difference in intensity values at one or more evaluation points. In an embodiment, process P812 determines whether the difference is minimized. If the difference is not minimized, the process continues to adjust the segments in process P806.

[0101] In an embodiment, in process P806, adjusting the plurality of segments involves adjusting the shape and / or position of at least a portion of the plurality of segments such that the difference between the generated image and the predicted image is reduced.

[0102] In an embodiment, when process P812 determines that the difference between the generated image and the predicted optimized proximity effect corrected image is minimized, the correction process stops. At the end of the iteration, correction 810 is obtained for each of the plurality of segments.

[0103] Figure 9 is an example of a result mask correction process as discussed in method 700 (this example can also be applied to methods 300 and 500). For example, feature 901 is part of a design layout, where the feature 901 has a rectangular geometry. In an embodiment, the geometry is divided (or segmented) into a plurality of segments S1, S2, S3, S4, S5, S6, S7, and S8. These segments S1 through S8 are modified based on the predicted optimized proximity effect corrected image (e.g., the first or second predicted optimized proximity effect corrected image mentioned earlier) or the geometry of the features therein. For example, segments S1, S2, and S3 of feature 901 of the design layout are moved upward in different ways. For example, S1 and S3 are moved relatively farther than segment S2. Similarly, segments S4 through S7 are also moved independently.

[0104] Each movement of segments S1 through S7 results in a different geometry that, when used to generate an image (e.g., via rasterization), will have different pixel intensities along the geometry. This generated image is compared with the predicted optimized proximity effect corrected image (as discussed in method 700) to reduce the difference between the images. After several iterations, as discussed in method 700, the final positions of segments S1 through S7 are obtained and the corresponding geometry 910 can be used as part of a mask layout, which is further used to generate a mask to be used in the patterning process for printing the design layout.

[0105] Since the correction of the design layout is performed relative to the predicted optimized proximity effect corrected image rather than the existing optimized proximity effect correction simulation process, the generated mask layout is obtained in a manner that is many orders of magnitude faster than the existing optimized proximity effect correction simulation process. Thus, compared to the existing optimized proximity effect correction simulation method, such correction not only provides an accurate solution for designing the mask layout but also reduces the computation time and resources.

[0106] In an embodiment, method 800 can also be extended to perform an optimized proximity effect correction simulation (e.g., process P320) using the correction 810 determined above at a much faster rate to further improve the optimized proximity effect correction result of the optimized proximity effect correction simulation, since the simulation process is initialized with a correction that is already close to the final optimized proximity effect correction result (e.g., the predicted optimized proximity effect correction). In an embodiment, the method involves determining a mask layout 820 via an optimized proximity effect correction simulation that uses a design layout and a correction to the design layout. In an embodiment, the optimized proximity effect correction simulation involves: simulating a patterning process via using the geometry of the design layout and corrections associated with multiple segments of the geometry to determine a simulated pattern that will be printed on a substrate; and determining an optical proximity effect correction to the design layout such that the difference between the simulated pattern and the design layout is reduced.

[0107] In an embodiment, determining the optical proximity effect correction is an iterative process that involves: adjusting the shape and / or size of polygons associated with primary features and / or auxiliary features of the design layout such that a performance metric of the patterning process is reduced. In an embodiment, auxiliary features are extracted from a predicted optimized proximity effect correction image of a machine learning model.

[0108] In an embodiment, the performance metric includes an edge placement error between the simulated pattern and the design layout, and / or a CD value of the simulated pattern.

[0109] In an embodiment, the corrections and the predicted optimized proximity effect correction images determined according to methods 300, 500, 700, and / or 800 can be used to optimize a patterning process or adjust parameters of the patterning process. As an example, OPC addresses the fact that the final size and arrangement of an image of a design layout projected onto a substrate will not be the same as or simply depend only on the size and arrangement of the design layout on a patterning device. It should be noted that the terms "mask", "reticle", "patterning device" can be used interchangeably herein. In addition, those skilled in the art should recognize that, especially in the case of lithography simulation / optimization, the terms "mask" / "patterning device" and "design layout" can be used interchangeably because: in lithography simulation / optimization, it is not necessary to use a physical patterning device, but a design layout can be used to represent a physical patterning device. For smaller feature sizes and higher feature densities present in a certain design layout, the position of a particular edge of a given feature will be affected to some extent by the presence or absence of other neighboring features. These proximity effects are caused by a small amount of radiation coupled from one feature to another and / or non-geometric optical effects such as diffraction and interference. Similarly, proximity effects can be caused by diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching, which typically follow lithography.

[0110] To ensure that the projected image of a design layout meets the requirements of a given target circuit design, complex numerical models, corrections, or pre-deformations of the design layout are needed 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 a review of the current "model-based" optical proximity correction process. In a typical high-end design, almost every feature of the design layout has some modification to achieve a higher fidelity of the projected image to the target design. These modifications can include shifts or biases in edge positions or line widths, and the application of "assist" features intended to aid in the projection of other features.

[0111] In the case of typically having millions of features in a chip design, applying model-based OPC to a target design involves good process models and significant computational resources. However, applying OPC is usually not an "exact science" but an empirical iterative process that does not always compensate for all possible proximity effects. Therefore, it is necessary to verify the effects of OPC (e.g., the design layout after applying OPC and any other RET) through design inspection (i.e., intensive full-chip simulation using a calibrated numerical process model) to minimize the likelihood of creating design defects in the pattern on the patterning device. This is driven by the following: the huge cost in the range of millions of dollars for manufacturing high-end patterning devices; and the impact on turnaround time of reworking or repairing an actual patterning device once it has been manufactured.

[0112] Both OPC and full-chip RET verification can be based on numerical modeling systems and methods such as those described in, for example, U.S. Patent Application No. 10 / 815,573 and the paper "Optimized Hardware and Software For Fast, Full Chip Simulation" by Y. Cao et al. (Proc. SPIE, Vol. 5754, 405 (2005)).

[0113] A RET involves adjusting a global bias of a design layout. The global bias is the difference between the pattern in the design layout and the pattern intended to be printed on a substrate. For example, a circular pattern with a diameter of 25 nm can be printed on the substrate by a pattern with a diameter of 50 nm in the design layout or by a pattern with a diameter of 20 nm in the design layout but with a higher dose.

[0114] In addition to the optimization of the design layout or the patterning device (e.g., OPC), the illumination source can also be optimized jointly or separately with the patterning device optimization to strive for improving the overall lithography fidelity. The terms "illumination source" and "source" can be used interchangeably in this document. Since the 1990s, many off-axis illumination sources such as annular, quadrupole, and dipole have been introduced, and the off-axis illumination sources have provided more degrees of freedom for OPC design, thereby improving the imaging results. As is known, off-axis illumination is a proven way for resolving fine structures (i.e., target features) included in the patterning device. However, compared with the conventional illumination source, the off-axis illumination source generally provides a smaller radiation intensity for the aerial image (AI). Therefore, it is desirable to attempt to optimize the illumination source to achieve an optimal balance between finer resolution and reduced radiation intensity.

[0115] For example, numerous illumination source optimization methods can be found in the paper by Rosenbluth et al., titled "Optimum Mask and Source Patterns to Print A Given Shape" (Journal of Microlithography, Microfabrication, Microsystems 1(1), pp. 13-20 (2002)). The source is segmented into a number of regions, each of which corresponds to a certain region of the pupil spectrum. Then, the source distribution is assumed to be uniform in each source region, and the intensity of each region is optimized for the process window. However, the assumption that the source distribution is uniform in each source region is not always valid, and as a result, the effectiveness of this method is impaired. In another example described in the paper by Granik, titled "Source Optimization for Image Fidelity and Throughput" (Journal of Microlithography, Microfabrication, Microsystems 3(4), pp. 509-522 (2004)), a number of existing source optimization methods are reviewed, and an illuminator pixel-based method that transforms the source optimization problem into a series of non-negative least squares optimizations is proposed. Although these methods have proven to be somewhat successful, they generally require multiple complex iterations to converge. Additionally, it may be difficult to determine the appropriate / optimal values for some additional parameters, such as γ in the Granik method, which determines the trade-off between optimizing the source for substrate image fidelity and the smoothness requirements of the source.

[0116] For low-k1 lithography, optimization of both the source and the patterning device helps ensure a viable process window for the projection of critical circuit patterns. Some algorithms (e.g., Proc. SPIE, Vol. 5853, 2005, p. 180 by Socha et al.) discretize the illumination into independent source points and the mask into diffraction orders in the spatial frequency domain, and formulate a cost function (the cost function being defined as a function of selected design variables) separately based on process window metrics (such as exposure latitude) that can be predicted from the source point intensities and the diffraction orders of the patterning device through an optical imaging model. As used herein, the term "design variables" includes the set of parameters of a lithographic projection apparatus or a lithographic process, e.g., parameters that can be adjusted by a user of the lithographic projection apparatus, or image characteristics that the user can adjust by adjusting those parameters. It should be understood that any characteristic of the lithographic projection process (including characteristics of the source, the patterning device, the projection optics, and / or the resist) can be among the design variables in the optimization. The cost function is often a non-linear function of the design variables. Standard optimization techniques are then used to minimize the cost function.

[0117] Correspondingly, the pressure to continuously reduce design rules has driven semiconductor chip manufacturers deeper into the low-k1 lithography era in the context of existing 193nm ArF lithography. Lithography towards lower k1 places high demands on RET, exposure tools, and the need for lithography-friendly designs. Future 1.35 ArF extreme numerical aperture (NA) exposure tools may be used. To help ensure that circuit designs can be produced onto a substrate using a process window that can function, source-patterning device optimization (referred to herein as source-mask optimization or SMO) is becoming a significant RET for the 2x nanometer node.

[0118] An international patent application number PCT / US2009 / 065359, titled "Fast Freeform Source and Mask Co-Optimization Method", filed on November 20, 2009 and published as WO2010 / 059954, which is commonly assigned, describes a source and patterning device (design layout) optimization method and system that allows the use of a cost function to simultaneously optimize the source and the patterning device without constraints and within an executable amount of time, the entire text of which patent application is hereby incorporated by reference.

[0119] Another source and mask optimization method and system for optimizing a source by adjusting pixels of the source are described in the commonly assigned U.S. Patent Application No. 12 / 813456, titled "Source-Mask Optimization in Lithographic Apparatus", filed on June 10, 2010 and published as U.S. Patent Application Publication No. 2010 / 0315614, the entire text of which is incorporated herein by reference.

[0120] In a lithographic projection apparatus, by way of example, the cost function is expressed as: (Equation 1)

[0121] where are N design variables or values of design variables. can be a function of the design variable , such as the difference between the actual value and the expected value of the characteristics at the evaluation point for a set of values of the design variable . is a weight constant associated with . Higher values can be assigned to evaluation points or patterns that are more critical than other evaluation points or patterns. Higher values can also be assigned to patterns and / or evaluation points with a greater number of occurrences. Examples of evaluation points can be any physical point or pattern on the substrate, any point on the virtual design layout, or the resist image, or the aerial image, or a combination thereof. can also be a function of one or more random effects such as LWR, the one or more random effects being a function of the design variable . The cost function can represent any suitable characteristic of the lithographic projection apparatus or the substrate, such as the failure rate of features, focal length, CD, image shift, image distortion, image rotation, random effects, throughput, CDU, or a combination thereof. CDU is the local CD variation (e.g., three times the standard deviation of the local CD distribution). CDU can be interchangeably referred to as LCDU. In one embodiment, the cost function represents CDU, throughput, and random effects (i.e., is a function of CDU, throughput, and random effects). In one embodiment, the cost function represents EPE, throughput, and random effects (i.e., is a function of EPE, throughput, and random effects). In one embodiment, the design variable includes dose, global bias of the patterning device, shape of the illumination from the source, or a combination thereof. Since the resist image often defines the circuit pattern on the substrate, the cost function often includes a function representing some characteristic of the resist image. For example, for such an evaluation point can be just the distance between a point in the resist image and the expected position of the point (i.e., the edge placement error ). The design variables can be any adjustable parameters, such as adjustable parameters of the source, the patterning device, the projection optics, the dose, the focal length, etc. The projection optics can include components commonly referred to as "wavefront manipulators", which can be used to adjust the shape and intensity distribution and / or the phase shift of the wavefront of the irradiation beam. The projection optics can preferably adjust the wavefront and intensity distribution at any location along the optical path of the lithographic projection apparatus (such as before the patterning device, near the pupil plane, near the image plane, near the focal plane). The projection optics can be used to correct or compensate for certain deformations of the wavefront and intensity distribution caused by, for example, the source, the patterning device, temperature variations in the lithographic projection apparatus, and thermal expansion of the components of the lithographic projection apparatus. Adjusting the wavefront and intensity distribution can change the values of the evaluation points and the cost function. These changes can be simulated from a model or actually measured. Of course, is not limited to the form in Equation 1. can take any other suitable form.

[0122] It should be noted that the normal weighted root mean square (RMS) of is defined as , so minimizing the weighted RMS of is equivalent to minimizing the cost function defined in Equation 1 . Therefore, for the sake of simplicity of notation in this article,

[0123] and the weighted RMS of Equation 1 can be used interchangeably.

[0124]

[0125] (Equation 1')

[0126] where is the value of under the u-th PW condition . When When it is EPE, minimizing the above cost function is equivalent to minimizing the edge shift under various PW conditions. Therefore, this leads to maximizing PW. Specifically, if PW also consists of different mask biases, minimizing the above cost function also includes minimizing the MEEF (Mask Error Enhancement Factor), which is defined as the ratio between the substrate EPE and the induced mask edge bias.

[0127] The design variables can have constraints, which can be expressed as , where Z is the set of possible values of the design variables. A possible constraint can be imposed on the design variables by the desired production volume of the lithographic projection apparatus. The desired production volume can limit the dose and thus have an impact on the stochastic effects (e.g., imposing a lower limit on the stochastic effects). A higher production volume generally results in a lower dose, a shorter or longer exposure time, and larger stochastic effects. The consideration of minimizing the substrate production volume and the stochastic effects can constrain the possible values of the design variables because the stochastic effects are a function of the design variables. Without this constraint imposed by the desired production volume, the optimization may yield a set of values of the design variables that are unrealistic. For example, if the dose is among the design variables, without such a constraint, the optimization can yield dose values that make the production volume economically impossible. However, the usefulness of the constraint should not be interpreted as a necessity. The production volume may be affected by the failure rate-based adjustment of the parameters of the patterning process. It is desired to have a lower failure rate of the features while maintaining a high production volume. The production volume can also be affected by the resist chemical reaction. A slower resist (e.g., a resist that requires a higher amount of light to be properly exposed) results in a lower production volume. Therefore, an optimization process based on the failure rate of the features due to resist chemical reactions or fluctuations and the dose requirements for a higher production volume can determine the appropriate parameters of the patterning process.

[0128] Therefore, the optimization process will find the set of values of the design variables that minimizes the cost function subject to the constraint , that is, find:

[0129]

[0130] (Equation 2)

[0131] Figure 10The figure illustrates a general method of optimizing a lithographic projection apparatus according to an embodiment. This method includes a step S1202 of defining a multi-variable cost function of a plurality of design variables. The design variables may include any suitable combination selected from characteristics of an illumination source (1200A) (e.g., a pupil filling ratio, i.e., the percentage of radiation of the source passing through a pupil or aperture), characteristics of a projection optical device (1200B), and characteristics of a design layout (1200C). For example, the design variables may include characteristics of an illumination source (1200A) and characteristics of a design layout (1200C) (e.g., global biasing), but not characteristics of a projection optical device (1200B), which results in SMO. Alternatively, the design variables may include characteristics of an illumination source (1200A), characteristics of a projection optical device (1200B), and characteristics of a design layout (1200C), which results in source-mask-lens optimization (SMLO). In step S1204, the design variables are simultaneously adjusted such that the cost function moves towards convergence. In step S1206, it is determined whether a predetermined termination condition is satisfied. The predetermined termination condition may include various possibilities, i.e., the cost function may be minimized or maximized (as required by the numerical technique used), the value of the cost function has become equal to or exceeded a threshold, the value of the cost function has reached within a preset error range, or a preset number of iterations has been reached.If any of the conditions in step S1206 is satisfied, the method ends. If none of the conditions in step S1206 is satisfied, steps S1204 and S1206 are iteratively repeated until a desired result is obtained. The optimization does not necessarily result in a single set of values for the design variables, because there may be physical constraints caused by factors such as failure rates, pupil filling factors, resist chemical reactions, production volumes, etc. The optimization may provide multiple sets of values for the design variables and associated performance characteristics (e.g., production volume), and allows a user of the lithographic apparatus to pick one or more sets.

[0132] In a lithographic projection apparatus, the source, the patterning device, and the projection optical device may be alternately optimized (which is referred to as alternate optimization), or the source, the patterning device, and the projection optical device may be simultaneously optimized (which is referred to as simultaneous optimization). As used in the present invention, the terms "simultaneous", "simultaneously", "joint", and "jointly" mean that the design variables of the characteristics of the source, the patterning device, the projection optical device, and / or any other design variables are allowed to change simultaneously. As used in the present invention, the terms "alternate" and "alternately" mean that not all design variables are allowed to change simultaneously.

[0133] In Figure 11 the optimization of all design variables is performed simultaneously. Such a process may be referred to as a simultaneous process or a co-optimization process. Alternatively, the optimization of all design variables is performed alternately, as in Figure 11As shown. In such a process, at each step, while fixing some design variables, other design variables are optimized to minimize the cost function; then, in the next step, while fixing a different set of variables, other sets of variables are optimized to minimize the cost function. These steps are alternately executed until a convergence condition or some termination condition is met.

[0134] As Figure 11 shown in the non - limiting exemplary flowchart of, first, a design layout is obtained (step S1302), and then, in step S1304, a source optimization step is performed, where while optimizing all design variables of the illumination source (SO) to minimize the cost function, all other design variables are fixed. Then, in the next step S1306, mask optimization (MO) is performed, where while optimizing all design variables of the patterning device to minimize the cost function, all other design variables are fixed. These two steps are alternately executed until some termination condition is met in step S1308. Various termination conditions can be used, such as the value of the cost function becomes equal to a threshold, the value of the cost function exceeds a threshold, the value of the cost function reaches within a preset error range, or a preset number of iterations is reached, etc. It should be noted that SO - MO - alternating - optimization is used as an example of the alternative process. The alternative process can take many different forms, such as: SO - LO - MO - alternating - optimization, where SO, LO (lens optimization), and MO are alternately and iteratively executed; or SMO can be performed once first, and then LO and MO are alternately and iteratively executed; etc. Finally, in step S1310, the output of the optimized result is obtained and the process stops.

[0135] The pattern selection algorithm as previously discussed can be formed integrally with simultaneous optimization or alternating optimization. For example, when alternating optimization is adopted, first, full - chip SO can be performed to identify "hot spots" and / or "warm spots", and then MO is performed. Given the present invention, numerous permutations and combinations of sub - optimizations are possible to achieve the desired optimization result.

[0136] Figure 12AAn exemplary optimization method is shown, in which a cost function is minimized. In step S502, an initial value of a design variable is obtained, including a tuning range (if any) of the design variable. In step S504, a multi-variable cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood near the starting value of the design variable for the first iteration step (i = 0). In step S508, standard multi-variable optimization techniques are applied to minimize the cost function. It should be noted that constraints, such as a tuning range, can be imposed during the optimization process in S508 or at a subsequent stage in the optimization process. Step S520 indicates that each iteration is completed for a given test pattern (also referred to as a "gauge") for the identified evaluation points that have been selected for optimizing the lithography process. In step S510, the lithography response is predicted. In step S512, the result of step S510 is compared with the desired or ideal lithography response value obtained in step S522. If the termination condition is satisfied in step S514, that is, the optimization yields a lithography response value that is sufficiently close to the desired value, then in step S518, the final value of the design variable is output. The output step may also include using the final value of the design variable to output other functions, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized source map, and an optimized design layout, etc. If the termination condition is not satisfied, then in step S516, the value of the design variable is updated using the result of the i-th iteration, and the process returns to step S506. The process described below is elaborated in detail Figure 12A hereafter.

[0137] In an exemplary optimization process, no assumptions or approximations are made about the relationship between the design variables, except that the cost function is sufficiently smooth (e.g., there is a first derivative )) and is otherwise valid in a lithographic projection apparatus ). Algorithms such as the Gauss - Newton algorithm, the Levenberg - Marquardt algorithm, the gradient descent algorithm, simulated annealing, and genetic algorithms can be applied to find the .

[0138] Here, the Gauss - Newton algorithm is used as an example. The Gauss - Newton algorithm is an iterative method applicable to general non - linear multi - variable optimization problems. In the i - th iteration where the design variable takes the value [[ID=2i22]], the Gauss - Newton algorithm linearizes near , and then calculates near that gives the minimum value of ). The design variable Takes on a value during the (i + 1)-th iteration ). This iteration continues until convergence is reached (i.e., no longer decreases) or a preset number of iterations is reached.

[0139] Specifically, during the i-th iteration, near ),

[0140]

[0141] (Equation 3)

[0142] Based on the approximation of Equation 3, the cost function becomes:

[0143]

[0144] (Equation 4)

[0145] Equation 4 is a quadratic function of the design variable ). Except for the design variable ), all terms are constant.

[0146] If the design variable is not subject to any constraints, then can be derived by solving N linear equations:

[0147] , where .

[0148] If the design variable is subject to constraints in the form of J inequalities (e.g., tuning range) where ); and is subject to constraints in the form of K equalities (e.g., interdependencies between design variables) where ); then the optimization process becomes a classical quadratic programming problem, where , , , are constants. Additional constraints can be imposed for each iteration. For example, a "damping factor" can be introduced to limit the difference between and such that the approximation of Equation 3 holds. Such a constraint can be expressed as . It is possible to use, for example, the method described in Numerical Optimization (2nd Edition) by Jorge Nocedal and Stephen J. Wright (Berlin New York: Vandenberghe. Cambridge University Press) to derive ).

[0149] Instead of minimizing the RMS, the optimization process can minimize the magnitude of the maximum deviation (worst defect) among the evaluation points to its expected value. In such a method, alternatively, the cost function can be expressed as

[0150] (Equation 5),

[0151] where is the maximum allowable value for . This cost function represents the worst defect among the evaluation points. Optimization using this cost function minimizes the magnitude of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0152] The cost function of Equation 5 can be approximated as:

[0153] (Equation 6),

[0154] where q is an even positive integer, such as at least 4, preferably at least 10. While Equation 6 mimics the behavior of Equation 5, it allows the optimization to be performed analytically and accelerated by using methods such as the steepest descent method, conjugate gradient method, etc.

[0155] Minimizing the size of the worst defect can also be combined with the linearization of . Specifically, as in Equation 3, approximate . Then, the constraint on the size of the worst defect is written as the inequality where and are two constants specifying the minimum and maximum allowable deviations for

[0156]

[0157] (Equation 6')

[0158] and

[0159]

[0160] (Equation 6'')

[0161] Since Equation 3 is generally only valid in the vicinity of if the desired constraints cannot be achieved in this vicinity (which can be determined by any conflict among the said inequalities), the constants and can be relaxed until the said constraints can be achieved. This optimization process minimizes the magnitude of the worst defect in the vicinity of

[0162] Another way to minimize the worst defect is to adjust the weights in each iteration. For example, after the i-th iteration, if the r-th evaluation point is the worst defect, then can be increased in the (i + 1)-th iteration so that a higher priority is given to reducing the magnitude of the defect towards the said evaluation point.

[0163] In addition, the cost functions in Equation 4 and Equation 5 can be modified by introducing Lagrange multipliers to achieve a trade-off between optimizing the RMS of the magnitude of the defect and optimizing the magnitude of the worst defect, i.e.:

[0164]

[0165] (Equation 6''')

[0166] where λ is a preset constant specifying the trade-off between optimizing the RMS of the magnitude of the defect and optimizing the magnitude of the worst defect. Specifically, if λ = 0, the equation becomes Equation 4 and only the RMS of the magnitude of the defect is minimized; if λ = 1, the equation becomes Equation 5 and only the magnitude of the worst defect is minimized; if 0 < λ < 1, both cases are considered in the optimization. Multiple methods can be used to solve this optimization. For example, similar to the method described previously, the weighting in each iteration can be adjusted. Alternatively, similar to minimizing the magnitude of the worst defect from the inequalities, the inequalities in Equation 6' and 6'' can be regarded as constraints on the design variables during the solution of the quadratic programming problem. Then, the bounds on the magnitude of the worst defect can be incrementally relaxed, or the weights for the magnitude of the worst defect can be incrementally increased for the bounds on the magnitude of the worst defect, the cost function values for each achievable magnitude of the worst defect can be calculated, and the design variable values that minimize the total cost function can be selected as the initial points for the next step. By performing this operation iteratively, the minimization of this new cost function can be achieved.

[0167] Optimizing a lithographic projection apparatus can extend the process window. A larger process window provides more flexibility in process design and chip design. The process window can be defined as a set of focal length and dose values that keep the resist image within a certain range of the design target of the resist image. It should be noted that all methods discussed here can also be extended to generalized process window definitions, which can be established by different or additional base parameters other than the exposure dose and defocus. These base parameters can include, but are not limited to, optical settings such as NA, root mean square deviation, aberration, polarization, or the optical constants of the resist layer. For example, as described earlier, if the PW also consists of different mask biases, the optimization includes minimizing the Mask Error Enhancement Factor (MEEF), which is defined as the ratio between the substrate EPE and the induced mask edge bias. The process window defined for the focal length and dose values is only used as an example herein. Methods for maximizing the process window according to embodiments are described below.

[0168] In a first step, starting from the known conditions in the process window (where f0 is the nominal focal length and ε0 is the nominal dose), minimize one of the cost functions below the vicinity:

[0169] (Equation 7).

[0170] or

[0171] (Equation 7')

[0172] or

[0173]

[0174] (Equation 7'')

[0175] If the nominal focal length f0 and the nominal dose ε0 are allowed to change, the nominal focal length f0 and the nominal dose ε0 can be jointly optimized with the design variables . In the next step, if a set of can be found such that the cost function is within a preset range, accept as part of the process window.

[0176] Alternatively, if the focal length and dose are not allowed to change, optimize the design variables with the focal length and dose fixed at the nominal focal length f0 and the nominal dose ε0. In an alternative embodiment, if a set of values of can be found such that the cost function is within a preset range, accept as part of the process window.

[0177] The methods described earlier in this document can be used to minimize the corresponding cost functions of Equation 7, 7', or 7''. If the design variables are characteristics of the projection optical device, such as Zernike coefficients, minimizing the cost functions of Equation 7, 7', or 7'' results in maximizing the process window based on projection optical device optimization (i.e., LO). If the design variables are characteristics of the source and pattern formation device other than those of the projection optical device, minimizing the cost functions of Equation 7, 7', or 7'' results in maximizing the process window based on SMLO, as Figure 11 illustrated. If the design variables are characteristics of the source and pattern formation device, minimizing the cost functions of Equation 7, 7', or 7'' results in maximizing the process window based on SMO. The cost functions of Equation 7, 7', or 7'' can also include at least one , such as in Equation 7 or Equation 8, and at least one is a function of one or more random effects such as LWR or local CD variation of 2D features and production volume.

[0178] Figure 13 Shows a specific example of how a simultaneous SMLO process can use the Gauss-Newton algorithm for optimization. In step S702, the starting values of the design variables are identified. The tuning range for each variable can also be identified. In step S704, the cost function is defined using the design variables. In step S706, the cost function is expanded near the starting values for all the evaluation points in the design layout. In an optional step S710, full-chip simulation is performed to cover all the critical patterns in the full-chip design layout. The desired lithography response metrics (such as CD or EPE) are obtained in step S714, and the desired lithography response metrics are compared with the predicted values of those quantities in step S712. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to the corresponding steps S514, S516, and S518 as described with respect to Figure 12A . As mentioned earlier, the final output can be a wavefront aberration map in the pupil plane, which is optimized to produce the desired imaging performance. The final output can also be an optimized source map and / or an optimized design layout.

[0179] Figure 12B Shows an exemplary method for optimizing the cost function, in which the design variables include design variables that can only take discrete values. <0,

[0180] The method begins by defining pixel groups of the illumination source and patterning device type pattern blocks of the patterning device (step S802). Generally, the pixel groups or patterning device type pattern blocks may also be referred to as division portions of the lithography process components. In one exemplary method, the illumination source is divided into 117 pixel groups, and 94 patterning device type pattern blocks are defined for the patterning device (substantially as described above), resulting in a total of 211 division portions.

[0181] In step S804, a lithography model is selected as the basis for lithography simulation. The lithography simulation generates results for calculating lithography metrics or responses. A specific lithography metric is defined as the performance metric to be optimized (step S806). In step S808, initial (pre-optimization) conditions are set for the illumination source and the patterning device. The initial conditions include the initial states of the pixel groups of the illumination source and the patterning device type pattern blocks of the patterning device, such that the initial illumination shape and the initial pattern of the patterning device can be referenced. The initial conditions may also include mask bias, NA, and focus slope range. Although steps S802, S804, S806, and S808 are depicted as consecutive steps, it should be understood that in other embodiments of the present invention, these steps may be performed in other orders.

[0182] In step S810, the pixel groups and the patterning device type pattern blocks are ranked. The pixel groups and the patterning device type pattern blocks may be interleaved in the ranking. Various ranking methods may be used, including: consecutively (e.g., from the 1st pixel group to the 117th pixel group and from the 1st patterning device type pattern block to the 94th patterning device type pattern block), randomly, according to the physical locations of the pixel groups and the patterning device type pattern blocks (e.g., ranking higher the pixel groups closer to the center of the illumination source), and according to how changes to the pixel groups or patterning device type pattern blocks affect the performance metric.

[0183] Once the pixel groups and the pattern forming device type pattern blocks are ranked, the illumination source and the pattern forming device are adjusted to improve the performance metrics (step S812). In step S812, each of the pixel groups and the pattern forming device type pattern blocks is analyzed in the order of ranking to determine whether a change to a pixel group or a pattern forming device type pattern block will result in an improvement in the performance metrics. If it is determined that the performance metrics will be improved, the corresponding pixel group or pattern forming device type pattern block is changed accordingly, and the resulting improved performance metrics and the modified illumination shape or the modified pattern forming baseline of the pattern forming device are obtained for comparison and thus for subsequent analysis of lower ranked pixel groups and pattern forming device type pattern blocks. In other words, the changes that improve the performance metrics are retained. As the changes to the states of the pixel groups and the pattern forming device type pattern blocks are made and retained, the initial illumination shape and the initial pattern of the pattern forming device are changed accordingly, such that the modified illumination shape and the modified pattern of the pattern forming device are caused by the optimization process in step S812.

[0184] In other methods, polygon shape adjustment and paired polling of the pattern forming device of the pixel groups and / or the pattern forming device type pattern blocks are also performed within the optimization process of S812.

[0185] In an alternative embodiment, the interleaved simultaneous optimization process may include changing the pixel groups of the illumination source and, in the case where an improvement in the performance metrics is found, gradually increasing and decreasing the dose to find further improvement. In a further alternative embodiment, the gradual increase and gradual decrease of the dose or intensity may be replaced by changing the bias of the pattern of the pattern forming device to find further improvement in the simultaneous optimization process.

[0186] In step S814, a determination is made as to whether the performance metrics have converged. For example, if little or no improvement in the performance metrics has been demonstrated in the last few iterations of steps S810 and S812, the performance metrics may be considered to have converged. If the performance metrics have not converged, steps S810 and S812 are repeated in the next iteration, where the modified illumination shape and the modified pattern forming device from the current iteration are used as the initial illumination shape and the initial pattern forming device for the next iteration (step S816).

[0187] The optimization method described above can be used to increase the throughput of a lithographic projection apparatus. For example, the cost function may include that is a function of the exposure time. Optimization of such a cost function is preferably constrained or influenced by a measure of random effects or other measures. Specifically, a computer-implemented method for increasing the throughput of a lithographic process may include optimizing a cost function that is a function of one or more random effects of the lithographic process and a function of the exposure time of a substrate in order to minimize the exposure time.

[0188] In one embodiment, the cost function includes at least one that is a function of one or more random effects . The random effects can include failures of features, such as measurement data (e.g., SEPE) determined in the method of Figure 3 , LWR of 2D features, or local CD variations. In one embodiment, the random effects include random variations in the properties of the resist image. For example, these random variations can include the failure rate of features, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU). Including the random variations in the cost function allows finding the values of the design variables that minimize the random variations, thereby reducing the risk of defects due to random effects.

[0189] Figure 14 FIG. is a block diagram of a computer system 100 that can assist in implementing the optimization methods and processes disclosed by the present invention. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106 coupled to the bus 102 for storing information and instructions to be executed by the processor 104, such as random access memory (RAM) or other dynamic storage devices. 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 further 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 the storage device 110 is coupled to the bus 102 for storing information and instructions.

[0190] The computer system 100 can be coupled by the 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. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116 for communicating direction information and command selections to the processor 104 and for controlling the movement of a cursor on the display 112, such as a mouse, trackball, or cursor direction keys. Such input devices typically have two degrees of freedom in two axes - a first axis (e.g., x) and a second axis (e.g., y), and the two degrees of freedom allow the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0191] In accordance with one embodiment, portions of the optimization process may be performed by a computer system 100 in response to one or more sequences of one or more instructions contained in main memory 106 being executed by a processor 104. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the instruction sequences contained in main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multiprocessing arrangement may also be used to execute the instruction sequences contained in main memory 106. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Accordingly, the description of the present invention is not limited to any specific combination of hardware circuitry and software.

[0192] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 110. Volatile media includes volatile memory, such as main memory 106. Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, a hard disk, a magnetic tape, any other magnetic medium, a CD-ROM, a DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and an EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[0193] Various forms of computer-readable media may be used to carry one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 either before or after being executed by processor 104.

[0194] Computer system 100 also preferably includes a communication interface 118 coupled to bus 102. The communication interface 118 provides a two-way data communication coupling to a network link 120, which is connected to a local area network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 118 transmits and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0195] The network link 120 typically provides data communication to other data devices via one or more networks. For example, the network link 120 can provide a connection through the local area network 122 to a main computer 124 or to a data device operated by an Internet service provider (ISP) 126. The ISP 126 in turn provides data communication services via the global packet data communication network (now commonly referred to as the "Internet") 128. Both the local area network 122 and the Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. Signals via the various networks and signals on the network link 120 and via the communication interface 118, which carry digital data to and from the computer system 100, are exemplary forms of carriers that convey information.

[0196] The computer system 100 can send messages and receive data (including program code) via one or more networks, the network link 120, and the communication interface 118. In the Internet example, a server 130 may transmit the requested program code for an application via the Internet 128, the ISP 126, the local area network 122, and the communication interface 118. One such downloaded application can provide, for example, the irradiation optimization of the embodiments. The received code can be executed by the processor 104 when it is received, and / or stored in the storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 can obtain application code in the form of a carrier wave.

[0197] Figure 15 Schematically depicts an exemplary lithographic projection apparatus that can optimize an irradiation source using the method described in the present invention. The apparatus includes:

[0198] - An illumination system IL for conditioning a radiation beam B. In such a particular case, the illumination system also includes a radiation source SO;

[0199] - A first object table (e.g., a mask table) MT, the first object table being provided with a patterning device holder for holding a patterning device MA (e.g., a reticle), and the first object table being connected to a first positioner for accurately positioning the patterning device relative to an object PS;

[0200] - A second object table (substrate table) WT, the second object table being provided with a substrate holder for holding a substrate W (e.g., a silicon wafer coated with resist), and the second object table being connected to a second positioner for accurately positioning the substrate relative to an object PS;

[0201] - A projection system ("lens") PS (e.g., a refractive, reflective or catadioptric optical system), the projection system being configured to image an irradiated portion of a patterning device MA onto a target portion C (e.g., including one or more dies) of a substrate W.

[0202] As depicted herein, the apparatus is of the transmissive type (i.e., has a transmissive mask). However, in general, the apparatus can also be of, for example, the reflective type (having a reflective mask). Alternatively, the apparatus can use another type of patterning device as an alternative to the use of a classical mask; examples include a programmable mirror array or an LCD matrix.

[0203] A source SO (e.g., a mercury lamp or an excimer laser) generates a radiation beam. For example, such a beam is fed directly or after having traversed an adjustment device such as a beam expander Ex into an illumination system (illuminator) IL. The illuminator IL can include adjustment devices AD for setting an outer radial range and / or an inner radial range of the intensity distribution in the beam (commonly referred to as σ - outer and σ - inner, respectively). Additionally, the illuminator IL will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B incident on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0204] Regarding Figure 15 It should be noted that the source SO can be within the housing of the lithographic projection apparatus (this is often the case when the source SO is, for example, a mercury lamp), but the source SO can also be remote from the lithographic projection apparatus, and the radiation beam generated by the source SO is directed into the apparatus (e.g., by means of a suitable steering mirror); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 excimer laser).

[0205] The beam PB then intercepts the patterning device MA held on the patterning device table MT. After having traversed the patterning device MA, the beam B passes through the lens PL which focuses the beam B onto the target portion C of the substrate W. By means of the second positioning device (and the interferometric device IF), the substrate table WT can be accurately moved, for example, so as to position different target portions C in the path of the beam PB. Similarly, the first positioning device can be used, for example, to accurately position the patterning device MA relative to the path of the beam B after having mechanically retrieved the patterning device MA from the patterning device library or during scanning. Generally, the movement of the object tables MT, WT will be realized by means of long stroke modules (coarse positioning) and short stroke modules (fine positioning) not explicitly depicted in Figure 15 However, in the case of a wafer stepper (relative to a step-and-scan tool), the patterning device table MT can be connected only to a short stroke actuator or can be fixed.

[0206] The tool depicted can be used in two different modes:

[0207] - In the step mode, the patterning device table MT is held substantially stationary and the entire image of the patterning device is projected in one go (i.e., a single "flash") onto the target portion C. The substrate table WT is then displaced in the x-direction and / or y-direction so that different target portions C can be irradiated by the beam PB;

[0208] - In the scan mode, substantially the same situation applies except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT can be moved at a speed v in a given direction (the so-called "scan direction", e.g., the y-direction) such that the projection beam B scans over the entire image of the patterning device; simultaneously, the substrate table WT is moved at a speed V = Mv in the same or opposite direction, where M is the magnification of the lens PL (usually, M = 1 / 4 or = 1 / 5). In this way, a relatively large target portion C can be exposed without having to compromise on the resolution.

[0209] Figure 16 Another exemplary lithographic projection apparatus 1000 which can optimize an illumination source by using the method described in the present invention is schematically depicted.

[0210] The lithographic projection apparatus 1000 comprises:

[0211] - A source collector module SO;

[0212] - An illumination system (illuminator) IL which is configured to condition a radiation beam B (e.g., EUV radiation);

[0213] - A support structure (e.g., a mask table) MT configured to support a patterning device (e.g., a mask or a reticle) MA, and the support structure is connected to a first positioner PM configured to accurately position the patterning device;

[0214] - A substrate table (e.g., a wafer table) WT configured to hold a substrate (e.g., a wafer coated with a resist) W, and the substrate table is connected to a second positioner PW configured to accurately position the substrate; and

[0215] - A projection system (e.g., a reflective projection system) PS configured to project a pattern imparted to a radiation beam B by the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W.

[0216] As depicted herein, the apparatus 1000 is of the reflective type (e.g., using a reflective mask). It should be noted that since most materials are absorptive in the EUV wavelength range, the mask can have a multilayer reflector including, for example, multiple stacks of molybdenum and silicon. In one example, the multilayer reflector has 40 layer pairs of molybdenum and silicon, with the thickness of each layer being a quarter wavelength. X-ray lithography can be utilized to generate smaller wavelengths. Since most materials are absorptive at EUV and x-ray wavelengths, a thin film of patterned absorptive material on the topography of the patterning device (e.g., a TaN absorber on top of the multilayer reflector) defines where features will be printed (positive resist) or not printed (negative resist).

[0217] Reference Figure 16 , the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include but are not limited to: converting a material having at least one element (e.g., xenon, lithium, or tin) into a plasma state using one or more emission spectral lines in the EUV range. In one such method (often referred to as laser-produced plasma "LPP"), a plasma can be generated by irradiating a fuel (such as droplets, streams, or clusters of a material having a spectral emission element) with a laser beam. The source collector module SO can be a part of an EUV radiation system including a laser ( Figure 16 not shown in the figure) that provides a laser beam for exciting the fuel. The resulting plasma emits output radiation, e.g., EUV radiation, and the output radiation is collected using a radiation collector disposed in the 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.

[0218] In these cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the laser to the source collector module by means of a beam delivery system including, for example, suitable directing mirrors and / or beam expanders. In other cases, for example, when the source is a discharge-produced plasma EUV generator (often referred to as a DPP source), the source can be an integral part of the source collector module.

[0219] The illuminator IL may include a conditioner for conditioning the angular intensity distribution of the radiation beam. In general, at least the outer radial extent and / or the inner radial extent of the intensity distribution in the pupil plane of the illuminator can be conditioned (commonly referred to as σ-outer and σ-inner respectively). Additionally, the illuminator IL may include various other components such as faceted field mirror devices and faceted pupil mirror devices. The illuminator can be used to condition the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0220] The radiation beam B is incident on a patterning device (e.g., a mask) MA which is held on a support structure (e.g., a mask table) MT, and is patterned by the patterning device. After reflection from the patterning device (e.g., a mask) MA, the radiation beam B passes through the projection system PS which focuses the beam onto a target portion C of the substrate W. By means of a second positioning stage PW and a position sensor PS2 (e.g., an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example, so as to position different target portions C in the path of the radiation beam B. Similarly, a first positioning stage PM and another position sensor PS1 can be used to accurately position the patterning device (e.g., a mask) MA relative to the path of the radiation beam B. Alignment marks M1, M2 on the patterning device (e.g., a mask) MA and alignment marks P1, P2 on the substrate can be used to align the patterning device and the substrate W.

[0221] The depicted apparatus 1000 can be used in at least one of the following modes:

[0222] 1. In step mode, while projecting the entire pattern to be imparted to the radiation beam onto the target portion C in one go, the support structure (e.g., the mask table) MT and the substrate table WT are kept substantially stationary (i.e., single static exposure). Subsequently, the substrate table WT is displaced in the X and / or Y direction such that different target portions C can be exposed.

[0223] 2. In scan mode, while projecting the pattern to be imparted to the radiation beam onto the target portion C, the support structure (e.g., the mask table) MT and the substrate table WT are scanned synchronously (i.e., single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g., the mask table) MT can be determined by the magnification (reduction ratio) and image inversion characteristics of the projection system PS.

[0224] 3. In another mode, when the pattern to be imparted to the radiation beam is projected onto the target portion C, the support structure (e.g., the mask table) MT is kept substantially stationary, thus holding the programmable patterning device, and the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is typically used, and the programmable patterning device is updated as needed after each movement of the substrate table WT or between successive radiation pulses during the scan. This operating mode can be readily applied to maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0225] Figure 17 Device 1000 is shown in more detail, the device comprising a source collector module SO, an illumination 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 enclosure 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 by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), with a very hot plasma 210 being generated in the gas or vapor to emit radiation in the EUV range of the electromagnetic spectrum. For example, the very hot plasma 210 is generated by causing a discharge in at least a partially ionized plasma. A partial pressure of, for example, 10 pascals of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required for efficient generation of the radiation. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0226] The radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or foil trap) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 can include a channel structure. The contaminant trap 230 can also include a gas barrier, or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0227] The collector chamber 211 may include a radiation collector CO which may be a so-called grazing-incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused in a virtual source point IF along the optical axis indicated by the dotted line "O". The virtual source point IF is generally referred to as the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near the opening 221 in the enclosure structure 220. The virtual source point IF is an image of the plasma 210 emitting radiation.

[0228] Subsequently, the radiation traverses the illumination system IL, which may include a faceted field mirror device 22 and a faceted pupil mirror device 24. The faceted field mirror device 22 and the faceted pupil mirror device 24 are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of the radiation intensity at the patterning device MA. After reflection at the patterning device MA held by the support structure MT of the radiation beam 21, a patterned beam 26 is formed, and the patterned beam 26 is imaged onto a substrate W held by the substrate table WT via the projection system PS and the reflecting elements 28, 30.

[0229] More elements than those shown may generally be present in the illumination optical unit IL and the projection system PS. Depending on the type of lithographic apparatus, the grating spectral filter 240 may optionally be present. Additionally, there may be more mirrors than those shown in each figure. For example, in the projection system PS, there may be 1 to 6 additional reflecting elements more than the Figure 17 reflecting elements shown.

[0230] As Figure 17 illustrated, 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 axially symmetrically about the optical axis O, and this type of collector optics CO is preferably used in combination with a discharge-generated plasma source (a discharge-generated plasma source is often referred to as a DPP source).

[0231] Alternatively, the source collector module SO may be as Figure 18Components of the LPP radiation system shown. The laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 having an electron temperature of several tens of electron volts. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma and collected by the near-normal incidence collector optics CO, and focused onto the opening 221 in the enclosure structure 220.

[0232] The concepts disclosed herein can be simulated or mathematically modeled for any general imaging system capable of imaging sub-wavelength features, and in particular can be used in emerging imaging technologies capable of generating increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography capable of generating a wavelength of 193 nm by using an ArF laser and even capable of generating a wavelength of 157 nm by using a fluorine laser. In addition, EUV lithography can generate wavelengths in the range of 5 nm to 20 nm by using a synchrotron or by bombarding a material (solid or plasma) with high-energy electrons in order to generate photons in this range.

[0233] The embodiments can be further described in terms of the following:

[0234] 1. A method of training a machine learning model configured to predict an optimized proximity effect correction (OPC) image for a mask, the method comprising:

[0235] obtaining (i) a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate, (ii) an image of one or more auxiliary features of the mask associated with the design layout, and (iii) an optimized proximity effect correction reference image of the design layout; and

[0236] using the pre-optimization proximity effect correction image and the image of the one or more auxiliary features as inputs to train the machine learning model such that the difference between the reference image and the predicted optimized proximity effect correction image of the machine learning model is reduced.

[0237] 2. The method according to aspect 1, wherein obtaining the pre-optimization proximity effect correction image and the image of the one or more auxiliary features comprises:

[0238] obtaining the geometries of the design layout and the one or more auxiliary features; and

[0239] generating the pre-optimization proximity effect correction image from the geometry of the design layout and generating another image from the geometries of the one or more auxiliary features via image processing.

[0240] 3. The method according to aspect 2, wherein the image processing includes a rasterization operation based on the geometric shape.

[0241] 4. The method according to aspect 2, wherein obtaining the geometric shape of the one or more auxiliary features includes:

[0242] determining, via a rule-based method, the geometric shape of the one or more auxiliary features associated with the design layout; and / or

[0243] determining, via a model-based method, the geometric shape of the one or more auxiliary features associated with the design layout.

[0244] 5. The method according to any one of aspects 1 to 4, wherein obtaining the reference image includes:

[0245] performing a mask optimization process and / or a source mask optimization process using the design layout.

[0246] 6. The method according to aspect 5, wherein the mask optimization process uses an optical proximity effect correction process.

[0247] 7. The method according to any one of aspects 1 to 6, wherein training the machine learning model is an iterative process, and the iteration includes:

[0248] inputting the pre-optimization proximity effect correction image and the image of the one or more auxiliary features into the machine learning model;

[0249] predicting the post-optimization proximity effect correction image by simulating the machine learning model;

[0250] determining the difference between the predicted post-optimization proximity effect correction image and the reference image; and

[0251] adjusting the weights of the machine learning model such that the difference between the predicted image and the reference image is reduced.

[0252] 8. The method according to aspect 7, wherein the weights are adjusted based on the gradient descent of the difference.

[0253] 9. The method according to any one of aspects 7 to 8, wherein the difference is minimized.

[0254] 10. The method according to any one of aspects 1 to 9, the method further includes:

[0255] obtaining the geometric shape of the design layout;

[0256] segmenting the geometric shape of the design layout into a plurality of segments; and

[0257] Determine a correction for the plurality of sections such that the difference between the image associated with the design layout and the predicted optimized proximity effect corrected image along the geometry is reduced.

[0258] 11. The method according to aspect 10, the method further comprising:

[0259] Place one or more evaluation points on each of the plurality of sections.

[0260] 12. The method according to any one of aspects 10 to 11, wherein determining the correction is an iterative process, the iteration comprising:

[0261] Adjust the plurality of sections of the geometry;

[0262] Generate an image from the adjusted geometry of the design layout; and

[0263] Evaluate the difference between the generated image and the predicted optimized proximity effect corrected image along the geometry within the corresponding image.

[0264] 13. The method according to aspect 12, wherein the difference between the generated image and the predicted image is the difference in intensity values along the geometry.

[0265] 14. The method according to any one of aspects 12 to 13, wherein adjusting the plurality of sections comprises:

[0266] Adjust the shape and / or position of at least a portion of the plurality of sections such that the difference between the generated image and the predicted image is reduced.

[0267] 15. The method according to any one of aspects 12 to 14, wherein the difference between the generated image and the predicted optimized proximity effect corrected image is minimized.

[0268] 16. The method according to any one of aspects 12 to 15, the method further comprising:

[0269] Determine a mask layout to be used for manufacturing the mask for the patterning process via an optimized proximity effect correction simulation using the design layout and the correction to the design layout.

[0270] 17. The method according to aspect 16, wherein the optimized proximity effect correction simulation comprises:

[0271] Determining a simulated pattern to be printed on a substrate by simulating a patterning process model using the geometry of the design layout and the correction associated with the plurality of sections; and

[0272] Determining an optical proximity effect correction for the design layout such that the difference between the simulated pattern and the design layout is reduced.

[0273] 18. The method according to aspect 17, wherein the determining the optical proximity effect correction is an iterative process, the iteration comprising:

[0274] Adjusting the shape and / or size of the geometry of the main features and / or the one or more auxiliary features of the design layout such that a performance metric of the patterning process is reduced.

[0275] 19. The method according to aspect 18, wherein the one or more auxiliary features are extracted from the predicted optimized proximity effect correction image of the machine learning model.

[0276] 20. The method according to any one of aspects 18 to 19, wherein the performance metric includes an edge placement error between the simulated pattern and the design layout, and / or a CD value of the simulated pattern.

[0277] 21. The method according to any one of aspects 1 to 20, wherein the pre-optimization proximity effect correction image, the image of the auxiliary features, the predicted optimized proximity effect correction image, and the reference image are pixelated images.

[0278] 22. A method for training a machine learning model to predict an optimized proximity effect correction (OPC) for a mask, the method comprising:

[0279] Obtaining (i) a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate, and (ii) a reference image of an optimized proximity effect correction of the design layout; and

[0280] Using the pre-optimization proximity effect correction image as an input to train the machine learning model such that the difference between the predicted optimized proximity effect correction image of the machine learning model and the reference image is reduced.

[0281] The method according to aspect 22, wherein obtaining the pre-optimization proximity effect correction image comprises:

[0282] Obtaining the geometry of the design layout; and

[0283] Generating an image from the geometry via image processing.

[0284] 24. The method according to aspect 23, wherein the image processing includes a rasterization operation using the geometry.

[0285] 25. The method according to any one of aspects 22 to 24, wherein obtaining the reference image includes:

[0286] Performing a mask optimization process and / or a source mask optimization process using the design layout.

[0287] 26. The method according to aspect 25, wherein the mask optimization process includes optical proximity effect correction.

[0288] 27. The method according to any one of aspects 22 to 26, wherein training the machine learning model is an iterative process, the iteration including:

[0289] Inputting the pre-optimization proximity effect correction image into the machine learning model;

[0290] Predicting the post-optimization proximity effect correction image by simulating the machine learning model;

[0291] Determining the difference between the predicted post-optimization proximity effect correction image and the reference image; and

[0292] Adjusting the weights of the machine learning model such that the difference between the predicted image and the reference image is reduced.

[0293] 28. The method according to aspect 27, wherein the weights are adjusted based on gradient descent of the difference.

[0294] 29. The method according to any one of aspects 22 to 27, wherein the difference is minimized.

[0295] 30. A method for determining a post-optimization proximity effect correction image for a mask, the method comprising:

[0296] Obtaining a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate;

[0297] Determining a first post-optimization proximity effect correction image of the mask by simulating a trained first machine learning model using the pre-optimization proximity effect correction image, wherein the first post-optimization proximity effect correction image includes one or more assist features of the mask;

[0298] Extracting the geometry of the one or more assist features of the first post-optimization proximity effect correction image; and

[0299] Determining a second optimized proximity effect corrected image for the mask by simulating a trained second machine learning model with the extracted geometries of one or more auxiliary features of the pre-optimization proximity effect corrected image and the first optimized proximity effect corrected image of the design layout.

[0300] 31. The method according to aspect 30, the method further comprising:

[0301] Determining a correction to the design layout based on the second optimized proximity effect corrected image and the design layout.

[0302] 32. The method according to aspect 31, wherein determining the correction is an iterative process, the iteration comprising:

[0303] Obtaining the geometry of the design layout;

[0304] Segmenting the geometry of the design layout into a plurality of segments;

[0305] Adjusting the plurality of segments;

[0306] Generating an image from the adjusted geometry of the design layout; and

[0307] Evaluating the difference between the generated image and the second optimized proximity effect corrected image along the geometry of the corresponding image.

[0308] 33. The method according to aspect 32, wherein adjusting the plurality of segments comprises:

[0309] Adjusting the shape and / or position of at least a portion of the plurality of segments such that the difference between the generated image and the second optimized proximity effect corrected image along the geometry of the corresponding image is reduced.

[0310] 34. The method according to any one of aspects 30 to 33, further comprising:

[0311] Determining a mask layout to be used for manufacturing the mask for the patterning process via an optimized proximity effect correction simulation using the design layout and the correction to the design layout.

[0312] 35. A method for determining a correction to a design layout, the method comprising:

[0313] Obtaining (i) a predicted optimized proximity effect corrected image and (ii) the geometry of the design layout via a trained machine learning model using a pre-optimization proximity effect corrected image of the design layout and an image of one or more auxiliary features associated with the design layout;

[0314] Divide the geometry of the design layout into a plurality of segments; and

[0315] Determine a correction for the plurality of segments such that the difference between the image of the design layout and the predicted optimized proximity effect corrected image along the geometry is reduced.

[0316] 36. The method according to aspect 35, the method further comprising:

[0317] Place one or more evaluation points on each of the plurality of segments.

[0318] 37. The method according to aspect 36, wherein determining the correction is an iterative process, the iteration comprising:

[0319] Adjust the plurality of segments via the one or more evaluation points;

[0320] Generate an image from the adjusted geometry of the design layout; and

[0321] Evaluate the difference between the generated image and the predicted optimized proximity effect corrected image at the one or more evaluation points on the plurality of segments of the geometry.

[0322] 38. The method according to aspect 37, wherein the difference between the generated image and the predicted image is the difference in intensity values at the one or more evaluation points.

[0323] 39. The method according to aspect 37, wherein adjusting the plurality of segments comprises:

[0324] Adjust the shape and / or position of at least a portion of the plurality of segments such that the difference between the generated image and the predicted image is reduced.

[0325] 40. The method according to any one of aspects 35 to 39, wherein the difference between the generated image and the predicted optimized proximity effect corrected image is minimized.

[0326] 41. The method according to any one of aspects 35 to 40, the method further comprising:

[0327] Determine a mask layout via an optimized proximity effect correction simulation using the design layout and the correction to the design layout.

[0328] 42. The method according to aspect 41, wherein the optimized proximity effect correction simulation comprises:

[0329] Simulating a patterning process by using the geometry of the design layout and the correction associated with the plurality of sections of the geometry to determine a simulated pattern to be printed on a substrate; and

[0330] Determining an optical proximity effect correction for the design layout such that the difference between the simulated pattern and the design layout is reduced.

[0331] 43. The method according to aspect 42, wherein the determining of the optical proximity effect correction is an iterative process, the iteration comprising:

[0332] Adjusting the shape and / or dimensions of the geometry of the main features and / or the one or more auxiliary features of the design layout such that a performance metric of the patterning process is reduced.

[0333] 44. The method according to aspect 43, wherein the one or more auxiliary features are extracted from the predicted optimized proximity effect correction image of the machine learning model.

[0334] 45. The method according to any one of aspects 43 to 44, wherein the performance metric comprises an edge placement error between the simulated pattern and the design layout, and / or a CD value of the simulated pattern.

[0335] 46. 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 the above aspects.

[0336] Although the concepts disclosed herein can be used for imaging on a substrate such as a silicon wafer, it should be understood that the disclosed concepts can be used with any type of lithographic imaging system, e.g., a lithographic imaging system for imaging on a substrate different from a silicon wafer.

[0337] The above description is intended to be illustrative, not restrictive.

Claims

1. A method for training a machine learning model configured to predict an optimized proximity effect correction (OPC) image for a mask, the method comprising: obtaining (i) a pre-optimization proximity effect correction image associated with a design layout to be printed on a substrate, (ii) an image of one or more assist features of the mask associated with the design layout, and (iii) an optimized proximity effect correction reference image of the design layout; and when using the pre-optimization proximity effect correction image and the image of the one or more assist features as inputs to train the machine learning model, adjusting the weights of the machine learning model by the optimized proximity effect correction reference image such that the difference between the optimized proximity effect correction reference image and the predicted optimized proximity effect correction image of the machine learning model is reduced.

2. The method according to claim 1, wherein obtaining the pre-optimization proximity effect correction image and the image of the one or more assist features comprises: obtaining the geometries of the design layout and the one or more assist features; and via image processing, generating the pre-optimization proximity effect correction image from the geometry of the design layout and generating another image from the geometries of the one or more assist features.

3. The method according to claim 2, wherein the image processing comprises a rasterization operation based on the geometries.

4. The method according to claim 2, wherein obtaining the geometries of the one or more assist features comprises: determining, via a rule-based method, the geometries of one or more assist features associated with the design layout; and / or determining, via a model-based method, the geometries of one or more assist features associated with the design layout.

5. The method according to any one of claims 1 to 4, wherein obtaining the optimized proximity effect correction reference image comprises: performing a mask optimization process and / or a source mask optimization process using the design layout.

6. The method according to claim 5, wherein the mask optimization process uses an optical proximity effect correction process.

7. The method according to claims 1 to 4 and 6, wherein training the machine learning model is an iterative process, the iteration comprising: inputting the pre-optimization proximity effect correction image and the image of the one or more assist features into the machine learning model; predicting the optimized proximity effect correction image by simulating the machine learning model; and determining the difference between the predicted optimized proximity effect correction image and the optimized proximity effect correction reference image.

8. The method according to claim 1, wherein the weights are adjusted based on the gradient descent of the difference.

9. The method according to claim 7, wherein the difference is minimized.

10. The method according to any one of claims 1 to 4, 6, 8, 9, the method further comprising: obtaining the geometry of the design layout; segmenting the geometry of the design layout into a plurality of segments; and Determine the correction for the plurality of sections such that the difference between the image associated with the design layout and the predicted optimized proximity effect corrected image along the geometry is reduced.

11. The method according to claim 10, the method further comprising: Placing one or more evaluation points on each of the plurality of sections.

12. The method according to claim 10, wherein determining the correction is an iterative process, the iteration comprising: Adjusting the plurality of sections of the geometry; Generating an image from the adjusted geometry of the design layout; And Evaluating the difference between the generated image and the predicted optimized proximity effect corrected image along the geometry within the corresponding image.

13. The method according to claim 12, wherein the difference between the generated image and the predicted optimized proximity effect corrected image is the difference in intensity values along the geometry.

14. The method according to any one of claims 12 to 13, wherein adjusting the plurality of sections comprises: Adjusting the shape and / or position of at least a portion of the plurality of sections such that the difference between the generated image and the predicted optimized proximity effect corrected image is reduced.

15. The method according to any one of claims 12 to 13, wherein the difference between the generated image and the predicted optimized proximity effect corrected image is minimized.

16. The method according to any one of claims 12 to 13, the method further comprising: Determining a mask layout to be used for manufacturing the mask for the patterning process via an optimized proximity effect correction simulation using the design layout and the correction to the design layout.

17. The method according to claim 16, wherein the optimized proximity effect correction simulation comprises: Determining a simulated pattern to be printed on a substrate via simulating a patterning process model using the geometry of the design layout and the correction associated with the plurality of sections; And Determining an optical proximity effect correction to the design layout such that the difference between the simulated pattern and the design layout is reduced.

18. The method according to claim 17, wherein determining the optical proximity effect correction to the design layout is an iterative process, the iteration comprising: Adjusting the shape and / or size of the geometry of the main features and / or the one or more auxiliary features of the design layout such that a performance metric of the patterning process is reduced.

19. The method according to claim 18, wherein the one or more auxiliary features are extracted from the predicted optimized proximity effect corrected image of the machine learning model.

20. The method according to any one of claims 18 to 19, wherein the performance metric comprises an edge placement error between the simulated pattern and the design layout, and / or a CD value of the simulated pattern.

21. The method according to any one of claims 1 to 4, 6, 8, 9, 11 to 13, 17 to 19, wherein the pre-optimization proximity effect correction image, the image of the auxiliary feature, the predicted post-optimization proximity effect correction image, and the post-optimization proximity effect correction reference image are pixelated images.

22. A computer program product, the 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 the above claims.

Images