Systems, methods, and products for determining a print probability of an auxiliary feature and applications thereof

Abstract

A method for determining a likelihood that an assist feature of a mask pattern will be printed on a substrate is described herein. The method includes obtaining (i) a plurality of images of a pattern printed on a substrate, and (ii) variance data, the plurality of images of the pattern; determining a model configured to produce variance data associated with the mask pattern based on the variance data; and determining a likelihood that an assist feature of a given mask pattern will be printed on the substrate based on variance data produced by the model for the given mask pattern, and a resist image or etch image associated with the given mask pattern. The likelihood can be applied to adjust one or more parameters related to a patterning process or a pattern formation apparatus to reduce the likelihood that the assist feature will be printed on the substrate.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to PCT application PCT / CN2020 / 098166, filed on June 24, 2020, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The description in this article relates to photolithography equipment and patterning processes, and more particularly to printing methods for determining the features of patterning apparatus and improvements related to the patterning process. Background Technology

[0004] Photolithography projection equipment can be used, for example, in the fabrication of integrated circuits (ICs). In such cases, a patterning apparatus (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 onto target portions (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) coated with a radiation-sensitive material (“resist”) layer via the circuit pattern on the patterning apparatus. Typically, a single substrate contains multiple adjacent target portions, and the circuit pattern is sequentially transferred by the photolithography projection equipment to these adjacent target portions, one target portion at a time. In this type of photolithography projection equipment, the entire circuit pattern on the patterning apparatus is transferred onto a single target portion at once; such equipment is commonly referred to as a wafer stepper. In an alternative equipment, commonly referred to as a step-scanning apparatus, a projection beam scans across the patterning apparatus in a given reference direction (“scanning” direction) while the substrate is moved synchronously parallel to or antiparallel to this reference direction. Different portions of the circuit pattern on the patterning apparatus are progressively transferred onto a single target portion. Because photolithography projection apparatuses typically have a magnification factor M (usually < 1), the rate at which the substrate is moved, F, will be a factor M times the rate at which the projection beam scans the pattern forming apparatus. Further information regarding photolithography apparatuses as described herein can be obtained, for example, from US 6,046,792, which is incorporated herein by reference.

[0005] Before transferring the circuit pattern from the patterning apparatus to the substrate, the substrate may undergo various processes, such as primer application, resist coating, and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. This array of processes forms the basis for the monolayer used to manufacture devices (e.g., ICs). The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all intended to refine the monolayer of the device. If several layers are required in the device, the entire process or its variations are repeated for each layer. Ultimately, a device will be present in each target portion of the substrate. These devices are then separated from each other using techniques such as dicing or sawing, thereby allowing individual devices to be mounted on carriers, connected to pins, etc.

[0006] As mentioned, microlithography is a central step in IC manufacturing, in which patterns formed on a substrate define the functional elements of the IC, such as microprocessors and memory chips. Similar lithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007] As semiconductor manufacturing processes continue to advance, the size of functional components has shrunk steadily over the decades, while the number of functional components, such as transistors, per device has steadily increased, following a trend commonly known as "Moore's Law." With current advanced technology, device layers are fabricated using photolithography projection equipment. This equipment projects a design layout onto a substrate using illumination from a deep ultraviolet irradiation source, resulting in individual functional components with dimensions sufficiently below 100 nm—that is, smaller than half the wavelength of the radiation from the irradiation source (e.g., a 193 nm irradiation source). This process for printing features smaller than the classical resolution limits of photolithography projection equipment is commonly referred to as low-k1 lithography, based on 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 photolithography projection equipment, CD is the "critical size" (typically the smallest feature size that can be printed), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce patterns on the substrate that resemble the shape and size planned by the circuit designer to achieve specific electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithography projection apparatus and / or design layout. These steps include, for example, but not limited to, optimization of NA and optical coherence settings, custom 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 encompass various types of optical systems, including, for example, refractive optics, reflective optics, apertures or aperture stops, and reflective-refractive optics. The term “projection optics” may also include components that operate according to any of these design types for guiding, shaping, or controlling the projected radiation beam, either jointly or individually. The term “projection optics” can include any optical component in the lithography projection apparatus, regardless of where the optical component is positioned on the optical path of the lithography projection apparatus. Projection optics may include optical components for shaping, adjusting, and / or projecting radiation from a source before it passes through a patterning apparatus, and / or optical components for shaping, adjusting, and / or projecting radiation after it has passed through the patterning apparatus. Projection optics typically exclude the light source and the patterning apparatus. Summary of the Invention

[0008] In an embodiment, a method is provided for determining the likelihood that an auxiliary feature of a mask pattern will be printed on a substrate. The method includes: obtaining (i) a plurality of images of a pattern printed on a substrate, and (ii) variance data associated with pixels of the plurality of images of the pattern, the images being formed using the mask pattern; determining, based on the variance data, a model configured to generate variance data associated with the mask pattern; and determining, based on the variance data generated by the model for a given mask pattern, and a resist image or etch image associated with the given mask pattern, the likelihood that an auxiliary feature of the given mask pattern will be printed on the substrate, the likelihood being applied to adjust one or more parameters associated with a patterning process or patterning apparatus to reduce the likelihood that the auxiliary feature will be printed on the substrate.

[0009] Furthermore, in an embodiment, a method for generating a model associated with a mask pattern is provided. The method includes: obtaining (i) a plurality of images of a pattern printed on a substrate using the mask pattern, and (iii) variance data associated with each pixel of the plurality of images of the pattern; and generating, based on the variance data, a model configured to predict variance data associated with the mask pattern, the variance data being used to determine the probability that auxiliary features of the mask pattern will be printed on the substrate.

[0010] Furthermore, in an embodiment, a method for generating optical proximity correction (OPC) data for a mask pattern is provided. The method includes: obtaining (i) a mask image or spatial image associated with the mask pattern, and (ii) a resist image associated with the mask pattern; executing a model configured to predict variance data associated with the mask pattern, the model using the mask image or the spatial image to predict the variance data; determining, based on the variance data and the resist image, the probability that auxiliary features of the mask pattern will be printed on a substrate; and generating the OPC data for modifying one or more main features or one or more auxiliary features of the mask pattern based on the probability that the auxiliary features will be printed.

[0011] Furthermore, in an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions that, when executed by one or more processors, cause operations including: obtaining (i) a plurality of images of a pattern printed on a substrate, the images having been formed using a mask pattern, and (ii) variance data associated with pixels of the plurality of images of the pattern; determining, based on the variance data, a model configured to generate variance data associated with the mask pattern; and determining, based on the variance data generated by the model for a given mask pattern, and a resist image or etched image associated with the given mask pattern, the probability being applied to adjust one or more parameters associated with the patterning process or patterning apparatus to reduce the probability that the auxiliary feature will be printed on the substrate.

[0012] Furthermore, in an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions that, when executed by one or more processors, cause operations including: obtaining (i) a plurality of images of a pattern printed on a substrate using the mask pattern, and (iii) variance data associated with each pixel of the plurality of images of the pattern; and generating, based on the variance data, a model configured to predict variance data associated with the mask pattern, the variance data being used to determine the probability that auxiliary features of the mask pattern will be printed on the substrate.

[0013] Furthermore, in an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions that, when executed by one or more processors, cause operations including: obtaining (i) a mask image or spatial image associated with the mask pattern, and (ii) a resist image associated with the mask pattern; executing a model configured to predict variance data associated with the mask pattern, the model using the mask image or the spatial image to predict the variance data; determining, based on the variance data and the resist image, the probability that an auxiliary feature of the mask pattern will be printed on a substrate; and generating, based on the probability that the auxiliary feature will be printed, optical proximity correction (OPC) data for modifying one or more main features or one or more auxiliary features of the mask pattern.

[0014] Furthermore, in an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions for generating a printable mapping associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including: obtaining (i) a plurality of images of a patterned substrate, (ii) a plurality of improved images based on the plurality of images, and (iii) a simulated improved image based on the mask pattern; labeling each of the plurality of images based on the plurality of improved images, the simulated improved image, and the intensity of pixels within each of the plurality of images; and generating the printable mapping associated with the mask pattern based on the labeling.

[0015] Furthermore, in an embodiment, a method is provided for generating one or more parameters for a patterning process. The method includes: obtaining (i) a plurality of images of a patterned substrate, (ii) a plurality of improved images based on the plurality of images, and (iii) a simulated improved image based on the mask pattern; labeling each of the plurality of images based on the plurality of improved images, the simulated improved image, and the intensity of pixels within each of the plurality of images; and generating the printability map associated with the mask pattern based on the labeling.

[0016] Furthermore, in an embodiment, a method for generating a printability map associated with a mask pattern is provided. The method includes: obtaining a plurality of binary images of a patterned substrate based on features of the mask pattern; aligning the plurality of binary images and summing the intensities of the plurality of binary images; and dividing the summed image intensities by the total number of binary images to generate the printability map associated with the mask pattern, wherein the intensity of each pixel of the printability map indicates the probability that features of the mask pattern will be printed onto the substrate.

[0017] Furthermore, in an embodiment, a non-transitory computer-readable medium is provided, the non-transitory computer-readable medium including instructions for generating a printable map associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including: obtaining a plurality of binary images of a patterned substrate based on features of the mask pattern; aligning the plurality of binary images and summing the intensities of the plurality of binary images; and dividing the summed image intensities by the total number of binary images to generate the printable map associated with the mask pattern, wherein the intensity of each pixel of the printable map indicates the probability that features of the mask pattern will be printed on the substrate. Attached Figure Description

[0018] Embodiments will now be described by way of example only with reference to the accompanying drawings, in which:

[0019] Figure 1 This is a block diagram of the various subsystems of the lithography system according to an embodiment;

[0020] Figure 2 According to the embodiments and Figure 1 A block diagram of the simulation model corresponding to the subsystems in the diagram;

[0021] Figure 3A This is a flowchart of a process for determining the likelihood that auxiliary features of a mask pattern can be printed on a substrate, according to an embodiment.

[0022] Figure 3B This is a flowchart of a process for determining the likelihood that auxiliary features of a given mask pattern can be printed on a substrate, according to an embodiment.

[0023] Figure 3C The variance data (in the model generated according to the embodiment) is used in the example. Figure 3A A flowchart illustrating the process of establishing a correlation between the resist image and the resist image;

[0024] Figure 4A and Figure 4C The illustration shows exemplary average data obtained from SEM images of a first pattern and a second pattern, respectively, according to an embodiment.

[0025] Figure 4B and Figure 4D The illustration shows exemplary variance data obtained from SEM images of a first pattern and a second pattern, respectively, according to an embodiment.

[0026] Figure 5 The illustration shows resist image intensity data according to an embodiment, and for example in... Figure 3A Exemplary correlations between variance data identified in the data;

[0027] Figure 6A An exemplary image showing a resist pattern imaged on a substrate according to an embodiment;

[0028] Figure 6B Exemplary variance data according to the embodiments and Figure 6A The curve of resist image intensity data;

[0029] Figure 7A Another exemplary image showing a resist pattern imaged on a substrate according to an embodiment;

[0030] Figure 7B This is another exemplary variance data according to the embodiments and Figure 7AThe curve of resist image intensity data;

[0031] Figure 8A Another exemplary image showing a resist pattern imaged on a substrate according to an embodiment;

[0032] Figure 8B This is yet another exemplary variance data according to the embodiments and Figure 8A The curve of resist image intensity data;

[0033] Figure 9A Another exemplary image showing a resist pattern imaged on a substrate according to an embodiment;

[0034] Figure 9B This is yet another exemplary variance data according to the embodiments and Figure 9A The curve of resist image intensity data;

[0035] Figure 10 This is a flowchart of a process for generating a model associated with a mask pattern to determine variance data associated with the mask pattern, according to an embodiment.

[0036] Figure 11 This is a flowchart of a process for generating optical proximity correction data for a mask pattern according to an embodiment;

[0037] Figure 12A This is a flowchart of a process for generating a printability map according to an embodiment;

[0038] Figure 12B This is another flowchart of the process for generating a printability map according to an embodiment;

[0039] Figure 12C This is yet another flowchart of a process for generating a printable map according to an embodiment;

[0040] Figure 13 The illustrations show exemplary original SEM images of a patterned substrate according to embodiments, denoised SEM images of the original SEM images, and improved SEM images of the original SEM images.

[0041] Figure 14 The illustrations show a simulated image associated with a mask pattern, a ridge-highlighted image of the simulated image, and a simulated improved image of the simulated image, according to an embodiment.

[0042] Figure 15A The illustration is based on an embodiment. Figure 13 An exemplary segmentation of an SEM image and another improved image associated with the segmented image;

[0043] Figure 15BThe illustration is based on an embodiment. Figure 15A An exemplary printability map determined by the improved image;

[0044] Figure 16 An embodiment of a scanning electron microscope (SEM) according to an example is schematically depicted;

[0045] Figure 17 An embodiment of an electron beam inspection apparatus according to an embodiment is schematically depicted;

[0046] Figure 18 This is a flowchart illustrating aspects of an example method for joint optimization according to an embodiment;

[0047] Figure 19 An embodiment of another optimization method according to the embodiments is shown;

[0048] Figure 20A , Figure 20B and Figure 21 Example flowcharts illustrating various optimization processes according to embodiments are shown;

[0049] Figure 22 This is a block diagram of an example computer system according to an embodiment;

[0050] Figure 23 This is a schematic diagram of a photolithography projection apparatus according to an embodiment;

[0051] Figure 24 This is a schematic diagram of another photolithography projection device according to an embodiment;

[0052] Figure 25 According to the embodiments Figure 24 A more detailed view of the device;

[0053] Figure 26 According to the embodiments Figure 24 and Figure 25 A more detailed view of the device's source collector module SO.

[0054] 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 is important to note that the following figures and examples are not intended to limit the scope to a single embodiment, but rather to make other embodiments possible by means of interchange of some or all of the described or illustrated elements. Where it is convenient, the same reference numerals will be used throughout the drawings to refer to the same or similar parts or components. Where some components of these embodiments can be implemented partially or completely using known components, only those portions of these known components necessary for understanding the embodiments will be described, and detailed descriptions of other portions of these known components will be omitted to avoid obscuring the description of the embodiments. In this specification, embodiments showing a singular number of components should not be considered limiting; rather, unless expressly stated otherwise herein, the scope is intended to cover other embodiments including a plurality of identical components, and vice versa. Furthermore, the applicant does not intend for any terminology in this specification or claims to be relegated to an uncommon or particular meaning unless so expressly stated. Additionally, the scope covers current and future known equivalents of components mentioned herein by means of illustrations. Detailed Implementation

[0055] While specific references may be made herein to the manufacture of ICs, it should be clearly understood that the descriptions herein have many other possible applications. For example, the embodiments described can be used to manufacture integrated optical systems, guide and detection patterns for magnetic domain memories, liquid crystal display panels, thin-film magnetic heads, etc. Those skilled in the art will understand that, in the context of such alternative applications, any use of the terms “mask,” “wafer,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0056] In this document, the terms “radiation” and “beam” are used to cover 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 extreme ultraviolet radiation (EUV, e.g., having wavelengths in the range of 5 nm to 20 nm).

[0057] As used in this article, “optimizing” means adjusting the lithography projection equipment to give the lithography results and / or process more desirable characteristics, such as higher accuracy of the projection of the design layout onto the substrate, a larger process window, etc.

[0058] Additionally, photolithography projection apparatus can be of the type having two or more substrate stages (and / or two or more pattern forming apparatus stages). In these "multi-platform" apparatuses, additional stages can be used in parallel, or preparatory steps can be performed on one or more stages while one or more other stages are used for exposure. For example, a dual-platform photolithography projection apparatus is described in US 5,969,441, which is incorporated herein by reference.

[0059] The patterning apparatus mentioned above includes or can form design layouts. Design layouts can be generated using computer-aided design (CAD) processes, often referred to as electronic design automation (EDA). Most CAD processes follow a predetermined set of design rules to produce a functional design layout / patterning apparatus. These rules are set through processing and design constraints. For example, design rules define the space tolerances between circuit devices (such as gates, capacitors, etc.) to ensure that the circuit devices or lines do not interact with each other in undesirable ways. Design rule constraints are often called "critical dimensions (CD)." The critical dimension of a circuit can be defined as the minimum width of a line or via, or the minimum space between two lines or two vias. Therefore, CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit manufacturing is (via the patterning apparatus) to faithfully reproduce the original circuit design on a substrate.

[0060] As used herein, the terms "mask" or "patterning apparatus" can be broadly interpreted to refer to a general patterning apparatus that can be used to impart a patterned cross-section to an incident radiation beam, the patterned cross-section corresponding to a pattern to be generated in a target portion of a substrate; the term "optical valve" can also be used in this context. Examples of other patterning apparatuses besides classic masks (transmission or reflection; binary, phase-shifting, hybrid, etc.) include:

[0061] - 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 of such a device is (for example): addressable regions of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed regions reflect incident radiation as non-diffracted radiation. Using appropriate filters, the non-diffracted radiation can be filtered out from 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. Suitable electronics can be used to perform the desired matrix addressing. More information about such mirror arrays can be found, for example, from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0062] - Programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0063] As a brief introduction, Figure 1 The illustration shows an exemplary photolithography projection apparatus 10A. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including extreme ultraviolet (EUV) sources (as discussed above, the photolithography projection apparatus itself does not need to have a radiation source); an illumination optics that define partial coherence (denoted as sigma) and may include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a pattern forming apparatus 14A; and a transmissive optics 16Ac that projects an image of a pattern from the pattern forming apparatus onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics can define the range of beam angles illuminating the substrate plane 22A, wherein the maximum possible angle defines the numerical aperture NA of the projection optics as sin(Θ). max ).

[0064] In the optimization process of a system, the quality factor of the system can be represented as a cost function. The optimization process boils down to finding the set of system parameters (design variables) that minimize the cost function. The cost function can have any suitable form depending on the optimization objective. For example, the cost function can be the weighted root mean square (RMS) of the deviations of certain characteristics (evaluation points) of the system from 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 suitability of the system implementation, the design variables of the system can be limited to a finite range and / or be interdependent. In the case of photolithography projection equipment, constraints are often associated with the physical properties and characteristics of the hardware (such as tunability range, and / or manufacturability design rules for patterning apparatus), and 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.

[0065] In a photolithography projection apparatus, a source provides illumination (i.e., light); a projection optics guides and shapes the illumination via a patterning apparatus, and directs and shapes the illumination onto a substrate. In this context, the term "projection optics" is broadly defined as any optical component that can modify the wavefront of the radiation beam. For example, a projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the distribution of radiation intensity at the substrate level. A resist layer on the substrate is exposed, and the spatial image is transferred to the resist layer as a potential "resist image" (RI). A 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 spatial image; examples of such a case can be found in commonly assigned U.S. Patent Application No. 12 / 315,849, which is incorporated herein by reference in its entirety. The resist model only considers the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a photolithographic projection apparatus (e.g., the properties of the source, pattern forming apparatus, and projection optics) define the spatial image. Since the pattern forming apparatus used in a photolithographic projection apparatus can be modified, it is desirable to separate the optical properties of the pattern forming apparatus from the optical properties of the rest of the photolithographic projection apparatus, which includes at least the source and projection optics.

[0066] Figure 2 The diagram illustrates an exemplary flowchart for simulating lithography in a lithographic projection apparatus. Source model 31 represents the optical characteristics of a source (including radiation intensity distribution and / or phase distribution). Projection optics model 32 represents the optical characteristics of a projection optics (including changes in radiation intensity distribution and / or phase distribution caused by the projection optics). Design layout model 35 represents the optical characteristics of a design layout (including changes in radiation intensity distribution and / or phase distribution caused by a given design layout 33), which is a representation of the arrangement of features formed on or by a patterning apparatus. A spatial image 36 can be simulated from design layout model 35, projection optics model 32, and design layout model 35. A resist image 38 can be simulated from the spatial image 36 using resist model 37. The lithography simulation can, for example, predict the contours and CDs in the resist image.

[0067] More specifically, it should be noted that source model 31 can represent the optical characteristics of a source, including but not limited to the NA standard deviation (σ) setting, and any particular illumination source shape (e.g., off-axis radiation sources such as ring, quadrupole, and bipolar sources). Projection optics model 32 can represent the optical characteristics of a projection optics, including aberrations, distortion, refractive index, physical size, physical dimensions, etc. Design layout model 35 can also represent the physical properties of a solid pattern forming apparatus, such as those described, for example, in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. The goal of the simulation is to accurately predict, for example, edge placement, spatial image intensity slope, and CD, which can then be compared to a desired design. A desired design is typically defined as a pre-designed layout that can be provided in a standardized digital file format, such as GDSII or OASIS or other file formats.

[0068] From this design layout, one or more portions referred to as "segments" can be identified. In embodiments, a set of segments is extracted, representing complex patterns in the design layout (typically about 50 to 1000 segments, but any number of segments can be used). As those skilled in the art will understand, these patterns or segments represent small portions of the design (i.e., circuits, cells, or patterns), and in particular, the segments represent small portions that require special attention and / or verification. In other words, a segment can be a part of the design layout, or a part of the design layout that exhibits similar or critical characteristics and is identified through experience (including segments provided by the customer), through trial and error, or by running full-chip simulations. Segments typically contain one or more test patterns or gauge patterns.

[0069] An initial, larger set of fragments can be provided a priori by the user based on known critical feature regions in the design layout, which requires specific image optimization. Alternatively, in another embodiment, an initial, larger set of fragments can be extracted from the entire design layout using some automated (e.g., machine vision) or manual algorithm that identifies critical feature regions.

[0070] As discussed above, semiconductor manufacturing involves imaging a target pattern (e.g., a desired circuit such as DRAM) onto a substrate using a mask that includes a mask pattern. The mask pattern includes main features corresponding to the target pattern and auxiliary features designed to make the printed pattern match the target pattern as closely as possible. These auxiliary features are not intended to be printed onto the substrate. Thus, the geometry of the auxiliary features is designed to be small enough that they are not printed under the various focused exposure conditions used during semiconductor manufacturing.

[0071] Existing technologies employ methods to determine whether auxiliary features (e.g., SRAFs) of the mask pattern can be printed onto a substrate. These technologies can be divided into two parts—metrology and lithography—which are typically used together in semiconductor manufacturing. For example, metrology tools can be used to collect data related to the printed pattern on the substrate. The metrology data can also be used, through one or more models, to adjust the lithography equipment or related processes to improve the accuracy of the printed pattern relative to the target pattern.

[0072] On the measurement side, the measurement tool can capture an image of the printed substrate. Based on the image, a contour extraction algorithm can extract the contours of features printed on the substrate. The extracted contours can be compared with a target pattern to determine whether auxiliary features (e.g., SRAF) have been printed. In an embodiment, user input can be used to identify the contours from the image captured by the measurement tool.

[0073] On the lithography side, models based on spatial image (AI) intensity can be used to predict the probability that auxiliary features will be printed onto the substrate. These probability values ​​can also be incorporated into cost functions, such as those used in optical proximity correction (OPC) processes. The cost function guides the OPC process to modify the shape and size of auxiliary or primary features, making the auxiliary features less likely to be printed onto the substrate. For example, the cost function could be a function of AI intensity and the printing probability of the auxiliary feature. In another lithography-related application, lithographic manufacturability inspection (LMC) can identify additional contours (e.g., SRAF) by comparing the design with a target pattern.

[0074] Existing technologies face several challenges. For example, on the measurement side, contour extraction based on noisy SEM images may produce incorrect contours of highly variable areas of the printed pattern on the substrate. Since contour extraction may involve some thresholding, i.e., thresholding segmentation, for example to identify the edges of features or filter out noise, it can introduce random truncation errors due to noise in the original SEM image. On the lithography side, errors can be introduced from calibrated models (e.g., calibrated based on measurement data) because residual errors from the model remain even after calibration.

[0075] According to this disclosure, a method is provided to determine the probability (also referred to as likelihood) that an auxiliary feature can be printed on a substrate based on contourless data associated with the feature being printed on the substrate. In other words, the contour is not extracted from measurement data, thereby reducing the inaccuracies related to contour extraction that can be introduced into model predictions. Part of the advantage of the method discussed herein is the improved data quality and the development of very high-resolution models (e.g., reaching nanopixel-level resolution). In other words, for example, model predictions can be 1,000 times more accurate in predicting the location of the auxiliary feature on the substrate. Therefore, several lithography and measurement-related applications can be improved using the probability values ​​determined based on the method described herein. For example, the method described herein can be employed in conjunction with OPC (e.g., a cost function via OPC) to determine modifications to the mask pattern.

[0076] Figure 3A This is a flowchart of an exemplary process 300 for determining the likelihood that auxiliary features of a mask pattern can be printed onto a substrate, according to embodiments of the present disclosure. Unlike prior art, process 300 does not involve contour extraction herein, but instead uses, for example, grayscale values ​​of a cumulative measurement image of the substrate. An exemplary implementation of method 300 includes the following steps.

[0077] Step P301 includes obtaining (i) a plurality of images 301 of a pattern printed on a substrate, the images having been formed using a mask pattern, and (ii) variance data 302 associated with the pixels of the plurality of images 301 of the pattern. Optionally, in an embodiment, average data associated with each pixel of the plurality of images 301 of the pattern may be obtained. In an embodiment, average data may be used in addition to variance data 302.

[0078] In an embodiment, multiple images 301 can be received via a measurement tool. In an embodiment, the multiple images 301 can be captured by exposing the substrate using a measurement tool and a pattern printed on the substrate. In an embodiment, the measurement tool can be a scanning electron microscope (SEM) (e.g., regarding...). Figure 16 (As discussed). In an embodiment, the image is a pixelated image having a grayscale value associated with each pixel.

[0079] In an embodiment, variance data 302 is represented as a pixelated image, with each pixel assigned a variance value based on the grayscale values ​​of each pixel in the plurality of images 301. Optionally, in an embodiment, average data is represented as a pixelated image, with each pixel assigned an average based on the average of the grayscale values ​​of each pixel in the plurality of images 301. According to an embodiment, Figures 4A to 4D The diagram illustrates examples of variance and mean data.

[0080] Figure 4B and Figure 4D Exemplary variance data 410 and 420 (example of variance data 302) obtained from SEM images of a first pattern and a second pattern are illustrated. The first pattern includes five contact holes, and the second pattern includes an array of lines and contact holes. Figure 4B In this example, variance data 410 of the first pattern shows the variance associated with the main features (such as the five contact holes) and the variance associated with each of the four SRAFs surrounding each contact hole. For example, variance data 410 shows the variance associated with the first contact hole H1 and the variance associated with each of SRAFs A1, A2, A3, and A4, respectively. Variance data 410 is represented as an image, where each pixel has a grayscale value obtained from the variance between multiple SEM images of, for example, the first pattern. In this example, the grayscale values ​​associated with H1 and A1 through A4 indicate the amount of variance. For example, SRAFs A2 and A3 have relatively higher variances compared to SRAFs A1 and A3. This can indicate a higher probability, or likelihood, that SRAFs A2 and A3 are printed on the substrate. The process of determining the probability that auxiliary features (e.g., A2 and A3) are printed is further discussed below and illustrated in the example. Figures 6A to 6B to Figures 9A to 9B The diagram in the middle shows this. Similarly, the variance data is 420 (in...). Figure 4D The variance (in Chinese) represents the variance associated with the main feature (such as lines and contact holes) and the auxiliary features that may exist around the main feature.

[0081] Figure 4A and Figure 4C The illustrations show exemplary average data 405 and 415 obtained from SEM images of a first pattern and a second pattern, respectively. The average data is represented as another image, where each pixel has values ​​based on, for example, the first pattern (…). Figure 4A The grayscale value is determined by averaging multiple SEM images of the first and second patterns. In this example, the average values ​​405 and 415 are obtained by averaging the grayscale values ​​of multiple SEM images of the first and second patterns, respectively. These average values ​​405 and 415 may optionally be used in the different processes described herein.

[0082] Step P303 includes determining a model 303 configured to generate variance data associated with the mask pattern based on variance data 302. In an embodiment, average data other than variance data 302 can be used to determine model 303. Thus, for example, model 303 can generate both variance data and average data for use as input patterns. In an embodiment, model 303 can receive a mask image (MI), resist image (RI), etched image (EI), or other images associated with a photolithography or metrology process as input. In an embodiment, MI, RI, or EI can be obtained from metrology tools; for example, RI can be captured after the pattern is imaged in resist on the substrate, and EI can be captured after an etching process is performed on the imaged pattern on the substrate. In an embodiment, the model can be obtained via a photolithography process (e.g., as... Figure 2 The relevant simulation models (e.g., resist models or etching models) discussed in the literature are used to obtain images MI, RI, or EI.

[0083] In an embodiment, the model 303 is at least one of the following: a convolutional neural network (CNN) including weights and biases as model parameters; a linear model including a combination of linear term correlation coefficients, the coefficients being model parameters; and a polynomial model including a combination of polynomial term correlation coefficients, the coefficients being model parameters.

[0084] In an embodiment, determining model 303 includes inputting (i) a spatial image or mask image associated with the mask pattern, and (ii) variance data 302 associated with the mask pattern into model 303; executing model 303 using initial values ​​of model parameters to generate initial variance data 302; determining the difference between the initial variance data and the input variance data 302; and adjusting the initial values ​​of the model parameters based on the difference so that model 303 generates variance data within a specified threshold of the input variance data 302. In an embodiment, the spatial image or mask image may be obtained, for example, through simulation (e.g., Figure 2 (or SEM tools)

[0085] In this embodiment, the determination of model 303 is an iterative process. In each iteration, steps such as the step of determining the difference and the step of adjusting can be repeated until the variance data generated by the model falls within a specified threshold (e.g., 0 to 5%) of the input variance data 302. Thus, the variance data generated by the model will closely match the input variance data 302. In this embodiment, the initial values ​​of the model parameters are adjusted based on the gradient of the difference between the output variance map and the input variance, the gradient guiding the values ​​of the model parameters towards decreasing or minimizing the difference. Once model 303 is determined, it can be used to generate variance data for any input image.

[0086] Step P305 includes determining the likelihood 305 of the probability that auxiliary features of a given mask pattern can be printed onto the substrate, based on variance data generated from a model for a given mask pattern and a resist image or etch image associated with the given mask pattern. In embodiments, likelihood 305 may be applied to adjust one or more parameters associated with the patterning process or patterning apparatus to reduce the likelihood 305 that auxiliary features can be printed onto the substrate. Additional examples of how likelihood 305 can be used in lithography-related applications (e.g., OPC, source and / or mask optimization (SMO)) will be discussed later in this disclosure.

[0087] In an embodiment, Figure 3B This is an exemplary flowchart of process P305 for determining the likelihood 305 that auxiliary features of a given mask pattern 311 can be printed on a substrate. In an embodiment, process P305 includes the following steps. Step P311 includes obtaining the resist image 312 associated with the given mask pattern 311. For example, this can be simulated via a patterning process (e.g., Figure 2 The resist image 312 is obtained using a measurement tool (e.g., SEM). Step P313 includes establishing a correlation 313 between the variance data 315 generated by the model and the resist image 312. Step P315 includes identifying areas of mask patterns or target layouts corresponding to mask patterns with relatively high likelihood of auxiliary features being printed on the substrate based on the correlation 313.

[0088] In an embodiment, Figure 3CThis is an exemplary flowchart of process P313 for establishing a correlation 313 between variance data 315 generated by the model and resist image 312. Process P313 includes the following steps: Step P321 includes identifying intensity values ​​from resist image 312 along a selected line on resist image 312. Step P323 includes identifying variance values ​​from variance data 315 generated by the model corresponding to the selected line. Step P325 includes correlating the variance values ​​identified along the selected line on resist image 312 with the identified intensity values ​​of resist image 312. Figure 5 and Figures 6A to 9B Further illustration shows how the correlation between variance data and resist images can be used to determine regions of the resist image with auxiliary features that have a higher likelihood of being printed onto the substrate.

[0089] In an embodiment, the step P323 of identifying regions with relatively high likelihood of auxiliary features being printed on a substrate includes: determining, for one or more regions of the resist image 312, whether an intensity value exceeds a printing threshold associated with the resist layer on the substrate where the feature is printed; determining, based on correlation 313, whether a variance value corresponding to one or more regions exceeds a specified variance threshold range; in response to exceeding the specified variance threshold range, assigning a relatively high printing probability to a portion of the one or more regions; in response to exceeding the specified variance threshold range and not exceeding the printing threshold, assigning a relatively low printing probability to a portion of the one or more regions; in response to not exceeding the specified variance threshold range and not exceeding the printing threshold, assigning a zero printing probability to a portion of the one or more regions; and identifying from the one or more regions a region with a printing probability greater than zero, the region being located around the main pattern of the mask pattern. Figure 5 and Figures 6A to 9B The diagram also illustrates how the correlation between variance data and resist images can be used to determine regions of the resist image with auxiliary features that have a higher likelihood of being printed onto a substrate.

[0090] In embodiments, the printing threshold refers to an upper threshold indicating that the feature should be printed within the resist layer, and a lower threshold indicating that the feature should not be printed within the resist layer. For example, in Figure 5 In the diagram, the upper threshold PTU indicates the resist strength, where a value higher than the resist strength indicates that the feature is printed with over 90% certainty. The lower threshold PTL indicates the resist strength, where a value lower than the resist strength indicates that the feature is indeed printed on the resist layer. In embodiments, the printing threshold may depend on the focused exposure conditions, the type of resist, the critical size of the feature to be imaged on the resist, or other resist or lithography-related properties.

[0091] In an embodiment, values ​​within the specified variance threshold range indicate that the feature is not printed, and values ​​outside the specified variance threshold range indicate that the feature is printed. For example, in Figure 5 In this embodiment, the variance threshold range can be a variance value higher than VT1. Assuming that for an auxiliary feature, the variance is higher than VT1, and the resist strength is between the printing threshold PTL and PTU, it can be determined that the auxiliary feature can be printed on the substrate. In other words, based on the variance data, it can be determined that the auxiliary feature has a high probability of being printed, even if the resist strength may not indicate printing of the auxiliary feature. It is understood that this disclosure is not limited to a constant threshold for the variance, and this example does not limit the scope of this disclosure. In embodiments, the variance threshold can be specified as a function. In embodiments, the variance threshold can also depend on the resist type, dose-focusing conditions, and process conditions associated with the patterning process.

[0092] Figures 6A to 6B , Figures 7A to 7B , Figures 8A to 8B ,and Figures 9A to 9B The illustration shows how to combine resist image or etch image intensity values ​​with variance data associated with the resist image to determine the printing of auxiliary features onto the substrate. Figure 6A , Figure 7A , Figure 8A and Figure 9A An exemplary image showing a resist pattern imaged on the substrate is shown. Figure 6B , Figure 7B , Figure 8B and Figure 9B Show along Figure 6A , Figure 7A , Figure 8A and Figure 9A The resist image intensity data (e.g., RI1, RI2, RI3, and RI4) and exemplary variance data (e.g., VA1, VA2, VA3, and VA3) for selected lines L1 in each resist image are used. In embodiments, the original SEM image, simulated image, or averaged SEM image of the resist pattern or the etched pattern (e.g., unit cell averaging can be performed on the original image data to produce an averaged SEM image) can be used to determine the likelihood of feature printing. It is understood that this embodiment is not limited to the original SEM image or the averaged SEM image, and does not limit the scope of this disclosure.

[0093] exist Figure 6AIn the resist image of the substrate, features F1, F2, F3, and F4 are included. The dashed outlines (drawn for reference) surrounding features F1 to F4 correspond to mask features, such as primary and secondary features. For example, features F1 and F2 correspond to primary features, and features F3 and F4 correspond to secondary features. An example line L1 passing through features F1 to F4 is drawn on the resist image. Intensity data (e.g., RI1) is extracted from the resist image along line L1. The resist image intensity data RI1 is plotted on... Figure 6B For visualization and observation. In an embodiment, variance data can be generated by using a mask image (used to generate the resist image) as input to the model (e.g., model 303). From the variance data generated by the model, variance data VA1 associated with line L1 can be extracted. The variance data VA1 is plotted above the resist image intensity data RI1 for visualization and observation.

[0094] refer to Figure 6B The resist image intensity data RI1 is represented as a curved profile, i.e., a curved feature curve. Viewed from left to right along line L1, the resist intensity profile, i.e., the resist intensity feature curve RI1, shows two peaks corresponding to features F1 and F2 (e.g., primary features), and two relatively smaller or narrower peaks corresponding to features F3 and F4 (e.g., secondary features). In this example, the two peaks corresponding to features F1 and F2 are above the printing threshold Th1. This indicates that features F1 and F2 will be printed on the substrate. On the other hand, the smaller peaks corresponding to features F3 and F4 are relatively below the printing threshold Th1. This indicates that features F3 and F4 will not be printed on the substrate. In an embodiment, the printing threshold Th1 corresponds to an upper limit (e.g., Figure 5 (PTU in the middle).

[0095] exist Figure 6B Viewed from left to right, the variance data VA1 along line L1 also shows two peaks corresponding to the locations of the peaks in the resist characteristic curve RI1, and a relatively flat characteristic curve pointing to the right corresponding to the smaller peak in the resist characteristic curve RI1. In an embodiment, a relatively high variance in the variance data VA1 indicates that the feature can be printed on the substrate, while a relatively low variance in the variance data VA1 indicates that the feature can not be printed on the substrate. For example, based on the VA1 data, the first two peaks (i.e., the relatively high variance) correspond to features F1 and F2, and the relatively low variance corresponds to features F3 and F4. In an embodiment, a variance threshold (e.g., such as...) can be used as a basis for... Figure 5A specified threshold (such as VT1) or a variance threshold range is used to determine relatively high and low variance. Therefore, resist image intensity data RI1 and variance data VA1 can be correlated and used to determine the probability that a feature can be printed on the substrate.

[0096] Figure 7A and Figure 7B This is another example of obtaining the resist image under different process conditions. Figure 7B This is shown in relation to what has been discussed above. Figure 6B Similar behavior. As discussed above, the resist image intensity data RI2 and variance data VA2 show two peaks on the left and a relatively flat portion on the right. The two peaks on the left of the resist image intensity data RI2 and the corresponding peaks in the variance data VA2 indicate that features F1 and F2 can be printed. Furthermore, the relatively flat portion in VA2 and RI2 on the right indicates that features F3 and F4 will not be printed.

[0097] In one embodiment, regions on the resist image where the resist image intensity data (or feature curve) is above a threshold Th1 are assigned a probability value of 1 or 100%, indicating an approximate 100% chance that the feature can be printed onto the substrate. Conversely, regions on the resist image where the resist image intensity data is significantly below the threshold Th1 are assigned a probability value of 0 or 0%, indicating an approximate 0% chance that the feature can be printed onto the substrate.

[0098] However, if a region has resist image intensity data that is close to or within a specified range of the threshold Th1 (e.g., corresponding to...), Figure 5 If the PTL and PTU are given, then the probability that a feature (e.g., an auxiliary feature) can be printed at the location can be any value between 0 and 1 (or 0% and 100%). In such cases, the variance data VA1 can be referenced to determine the probability that a feature (e.g., an auxiliary feature) can be printed on the substrate. Figures 8A to 9B The text also discusses examples where resist characteristic curve data are supported by the variance data to determine the probability that a feature (e.g., an auxiliary feature) can be printed on the substrate.

[0099] Figures 8A to 8B as well as Figures 9A to 9B Examples of resist images obtained under different process conditions are shown. As discussed above, intensity data can be extracted from the resist image along line L1, and variance data can be extracted from the variance data generated by the model. Figure 8B and Figure 9BIn the meantime, the variance along lines L1, VA3, and VA4 is relatively high, and the resist image intensity feature curves RI3 and RI4 are relatively close to the threshold Th1. For example, in Figure 8B In the image, the resist image intensity feature curve RI3 shows four peaks. The two peaks on the upper left are approximately above the threshold Th1. These two peaks correspond to features F1 and F2 (in... Figure 8A (in the middle). However, the two peaks on the right side of RI3 are close to but below the threshold Th1. These two peaks in RI3 correspond to features F3 and F4 (in Figure 8A (In the middle). Currently, referring to the variance data VA3, there are four peaks with approximately equal amplitudes. The first two peaks (on the upper left) correspond to the peaks in RI3, both indicating a 100% probability that features F1 and F2 can be printed. On the other hand, the two peaks in RI3 below the threshold Th1 may indicate that features F3 and F4 may not be printed. However, the corresponding peaks in the variance data VA3 indicate a relatively high probability that features F3 and F4 are printed on the substrate, due to the relatively high variance.

[0100] Similarly, refer to Figure 9B The resist image intensity data RI4 and the variance data VA4 indicate that RI4 has a peak value close to the threshold Th1. Corresponding to the peak value in RI4, the variance data VA4 also indicates features F1 to F4 (in... Figure 9A (The middle) has a relatively high probability of peaks being printed on the substrate.

[0101] In an embodiment, Figures 6A to 9B The above examples illustrate that the variance data (or variance image) can be used as a guide map, which, combined with a resist image or etched image, determines the probability that a feature (e.g., an auxiliary feature) can be printed onto the substrate. Therefore, for a given mask pattern, locations or auxiliary features with a relatively high probability of being printed onto the substrate can be identified. Furthermore, the identified auxiliary features can be modified so that they are not printed onto the substrate. For example, during an optical proximity correction (OPC) process, the variance data and the resist image intensity data can be used to determine locations on the mask pattern. Depending on the probability of printing the auxiliary feature, the identified locations can be penalized more or less. The penalty function can be implemented via the cost function of the OPC process discussed herein. For example, locations with higher variance indicate a higher probability of printing, so the OPC process can penalize those locations or features (e.g., SRAF) relatively more than other locations, such that the OPC-processed features are adjusted to minimize the probability of printing those features (e.g., SRAF). Exemplary OPC processes and example cost functions are described below. Figures 14 to 17 Let's discuss this.

[0102] In an embodiment, resist models for generating the resist image or etched image are trained based on the principal features printed with 100% probability (e.g., in...). Figure 2 (In the middle) or etching model. The resist model may not be calibrated for data related to features that may not be printed on the substrate or have a relatively low printing probability. Thus, this disclosure can be used in conjunction with existing photolithography simulation processes to better predict the probability that features can be printed and improve the yield of the patterning process. Additional examples of this process 300 are further discussed below.

[0103] Return to reference Figure 3A Process 300 has several applications. Process 300 can be modified to optionally include subsequent processes P307, P309, or P311 as needed.

[0104] In an embodiment, step P307 includes generating optical proximity correction (OPC) data based on the model 303 and the likelihood 305 that the auxiliary features can be printed on the substrate to adjust one or more main features, or one or more auxiliary features, of the mask pattern. In an embodiment, the generation of OPC data includes an OPC simulation process associated with the patterning process (e.g., Figures 14 to 17 The shape and / or size of one or more main features or one or more auxiliary features of the mask pattern are adjusted. The adjusted shape and / or size reduces the likelihood that the auxiliary features can be printed on the substrate, i.e., likelihood 305. In an embodiment, the OPC process may remove one or more auxiliary features of the mask pattern.

[0105] In an embodiment, step P309 includes determining a source and / or mask pattern based on the likelihood 305 of the model 303 and the possibility that auxiliary features can be printed on the substrate, in order to reduce the likelihood 305 of the possibility that auxiliary features can be printed on the substrate. The determination of the source and / or mask pattern includes adjusting source parameters and / or mask parameters via a source mask optimization (SMO) process to reduce the likelihood 305 of the possibility that auxiliary features of the mask pattern can be printed on the substrate.

[0106] In an embodiment, step P311 includes adjusting one or more parameters of the patterning process used to pattern the substrate based on the model 303 and the likelihood 305 that the auxiliary feature can be printed. Adjusting one or more parameters of the patterning process includes using a mask image or spatial image of the pattern to be printed on the substrate as input to the model 303 to determine the likelihood 305 that the auxiliary feature can be printed on the substrate; and adjusting one or more parameters of the patterning process to reduce the likelihood 305 that the auxiliary feature can be printed on the substrate. In an embodiment, the one or more parameters include (but are not limited to) the scanner dose, the scanner focus, and / or the substrate stage height.

[0107] Figure 10 This is a flowchart of a process 1400 for generating a model associated with a mask pattern to determine variance data associated with said mask pattern. As previously mentioned, the process does not involve contour extraction, but rather uses grayscale values ​​from, for example, a cumulative measurement image of a substrate. An example implementation of process 1400 includes the following steps.

[0108] Step P1401 includes obtaining (i) a plurality of images 1401 of a pattern printed on a substrate using the mask pattern, and (ii) variance data 1402 associated with each pixel of the plurality of images 1401 of the pattern. Optionally, in an embodiment, mean data associated with each pixel of the plurality of images 1401 of the pattern may be obtained. In an embodiment, the mean data may be used in conjunction with the variance data 1402. In an embodiment, the plurality of images 1401 are SEM images obtained via a SEM tool. Optionally, in an embodiment, the mean data associated with each pixel of the plurality of images 1401 of the pattern may be determined and used as training data for generating the model.

[0109] In this embodiment, the variance data 1402 is represented as a pixelated image, where each pixel is assigned a variance value of the grayscale values ​​of each pixel in the image 1401. For example, the variance data is represented as... Figure 4B and Figure 4D The image in the image. Similarly, optionally, the average data is represented as a pixelated image, where each pixel is assigned the average grayscale value of each pixel in multiple images.

[0110] Step P1403 includes generating a model 1410 based on the variance data 1402, configured to predict variance data associated with the mask pattern, which is being used to determine the likelihood that auxiliary features of the mask pattern can be printed on the substrate. In embodiments, model 1410 is at least one of: a convolutional neural network including weights and biases as model parameters; a linear model including a combination of linear term correlation coefficients, where the coefficients are the model parameters; and a polynomial model including a combination of polynomial term correlation coefficients, where the coefficients are the model parameters.

[0111] In an embodiment, generating model 1410 includes inputting (i) a spatial image or mask image associated with the mask pattern and (ii) variance data 1402 associated with the mask pattern into model 1410; executing model 1410 using initial values ​​of model parameters to generate initial variance data; determining the difference between the initial variance data and the input variance data 1402; and adjusting the initial values ​​of the model parameters based on the difference so that model 1410 generates variance data within a specified threshold of the input variance data 1402.

[0112] In an embodiment, the generation of model 1410 is an iterative process in which the values ​​of the model parameters are adjusted until the variance data generated by the model is within a specified threshold of the input variance data 1402.

[0113] In this embodiment, the initial values ​​of the model parameters are adjusted based on the gradient of the difference between the output variance mapping and the input variance, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

[0114] Figure 11 This is a flowchart of a process 1500 for generating optical proximity correction data for a mask pattern. An example implementation of method 1500 includes the following steps.

[0115] Process P1501 includes obtaining (i) a mask image 1501 or spatial image 1502 associated with the mask pattern, and (ii) a resist image or etched image associated with the mask pattern. In an embodiment, obtaining the mask image 1501 or the spatial image 1502 includes using the mask pattern to simulate one or more process models to generate the mask image 1501 or the spatial image 1502.

[0116] Step P1503 includes executing a model (e.g., 303 or 1410) configured to predict variance data 1505 associated with the mask pattern. The model (e.g., 303 or 1410) is configured to take the mask image 1501 or the spatial image 1502 as input and output variance data 1505 associated with the mask pattern. Step P1505 includes determining the likelihood, or probability, that auxiliary features of the mask pattern can be printed onto the substrate based on the variance data 1505 generated by the model and the resist image 1501 or etched image 1502.

[0117] Step P1507 includes generating Optical Proximity Correction (OPC) data 1510 for modifying one or more main features or one or more auxiliary features of the mask pattern based on the likelihood that auxiliary features can be printed. In an embodiment, generating OPC data 1510 includes adjusting the shape and / or size of one or more main features or one or more auxiliary features of the mask pattern via an OPC simulation process. The adjusted shape and / or size reduces the likelihood that the auxiliary features can be printed. In an embodiment, OPC data 1510 involves removing one or more auxiliary features of the mask pattern via an OPC simulation process. In an embodiment, the OPC data can be applied via a patterning apparatus modification tool to modify the mask pattern on the mask.

[0118] As previously discussed, semiconductor manufacturing involves imaging a mask pattern onto a substrate to form the desired circuitry for a chip. The mask pattern includes auxiliary features (e.g., SRAF) to form a printed pattern on the substrate that closely matches the design pattern. In an embodiment, the printed pattern is examined to determine whether any auxiliary features have been printed on the substrate. Such printing of auxiliary features is not required. In an embodiment, an SEM image of the printed pattern on the substrate is examined to determine the printing quality of the pattern based on whether auxiliary features have been printed. The SEM image and data within the SEM image (e.g., pixel intensity, feature information, etc.) can be used to train one or more process models to improve the yield of the patterning process.

[0119] However, SEM images that include auxiliary features (e.g., SRAFs) can typically have poor image quality (e.g., blurry or noisy). Such SEM images can make identifying auxiliary features challenging, for example, due to blurring or noise around the areas of the auxiliary features. When these SEM images are used to train one or more process models (e.g., configured to determine a printed pattern on a substrate, or to determine whether an SRAF can be printed), the models may not produce accurate results. For example, the process model could be a resist model that generates a resist image. The resist model is a simplified model used to determine whether a resist image can be formed on a substrate. Based on the resist image, the patterning process can be adjusted. Adjustments can be made to, for example, dosage, focus, or resist parameters to result in the desired pattern on the substrate. Thus, the resist model should be configured to determine whether, for example, an SRAF can be printed, so that adjustments can be performed more accurately to remove the SRAF features.

[0120] In this disclosure, a printability map (also referred to as a probability map) is generated to determine the probability that an auxiliary feature can be printed onto the substrate. A printability map can be generated for any mask pattern that needs to be printed onto the substrate. The printability map can be used as a guide to determine one or more parameters of the patterning process to prevent the auxiliary feature from being printed onto the substrate. The printability map can be considered as a two-dimensional (2D) map, distinct from one-dimensional (1D) gauge data (e.g., CD). In an embodiment, the printability map includes SRAF printing probability values, which are values ​​between 0% and 100% (or real numbers between 0 and 1) associated with each pixel in the 2D plane of the image.

[0121] Figure 12 is an exemplary flowchart of a method 1600 for generating a printability map associated with a mask pattern. In an embodiment, for example, method 1600 includes the step of acquiring a patterned substrate image including SRAF data of the mask pattern. For example, multiple SEM images from different substrate dies of the same mask pattern can be acquired via a SEM tool. These raw SEM images can be aligned using, for example, a die-to-die alignment tool. For each aligned image, image segmentation can be performed. Based on the segmented images, improved images such as binary images can be generated. The binary images provide information about whether auxiliary features can be printed for each pixel. These binary images are stacked to generate a probability map, where each pixel in the probability map is a printing probability. The printing probability is determined, for example, by dividing the number of binary images by the total number of binary maps.

[0122] In this embodiment, the accuracy of the printability mapping depends on the accuracy of image segmentation of the SEM image. Compared to existing contour extraction methods, such as ridge or crest detection, the problem is that the individual SEM images used for image segmentation have more noise than the averaged images used for ridge detection. Furthermore, this method 1600 provides a different identifier-based image segmentation as discussed herein, compared to general image segmentation methods. Method 1600 is implemented as example procedures P1601, P1603, and P1605, which are discussed in detail below.

[0123] Process P1601 includes obtaining (i) a plurality of images 1601 of a patterned substrate, (ii) a plurality of improved images 1603 based on the plurality of images 1601, and (iii) a simulated improved image 1605 based on a mask pattern. In an embodiment, obtaining the plurality of images 1601 includes receiving the plurality of images 1601 of the pattern printed on the substrate via a measurement tool. In an embodiment, obtaining the plurality of images 1601 includes capturing the plurality of images 1601 of the pattern printed on the substrate via a measurement tool. As discussed herein, the plurality of images 1601 of the patterned substrate can be obtained via scanning electron microscopy (SEM) (see [link to documentation]). Figure 16 and Figure 17 Therefore, each of the plurality of images 1601 is an SEM image.

[0124] In an embodiment, one or more of the plurality of improved images 1603 are one or more binary images. For example, a portion of a feature (e.g., a primary feature or an auxiliary feature) is assigned a value of 1, and pixels surrounding the feature have a value of 0. The simulated improved image 1605 may also be another binary image where each pixel has a value of 0 or 1. For example, a portion of a feature (e.g., a primary feature or an auxiliary feature) has a value of 1, and pixels in the region surrounding the feature have a value of 0.

[0125] In an embodiment, obtaining a plurality of improved images 1603 includes denoising each of the plurality of images 1601. For example, denoising the original SEM image of the pattern on the substrate. In an embodiment, each of the denoised plurality of images 1601 is further converted into an improved image via an adaptive thresholding algorithm. The adaptive thresholding algorithm can be any algorithm other than adaptively finding an optimal threshold to distinguish between printed and unprinted areas within an image (e.g., an SEM image). In an embodiment, the adaptive thresholding algorithm is an Otsu thresholding algorithm configured to receive the plurality of images 1601 or the denoised plurality of images 1601 and the identifiers within each of the plurality of images 1601 as input, and output the improved image.

[0126] In an embodiment, denoising the plurality of images 1601 includes applying a first median filter and a Gaussian filter to each of the plurality of images 1601 such that the ridge edge accuracy associated with each of the plurality of images 1601 is maintained, the first median filter being characterized by a first kernel size; applying a second median filter to enhance the image contrast of each of the plurality of images 1601, the image contrast being between printed and unprinted areas, the second median filter being characterized by a second kernel size, the second kernel size being larger than the first kernel size; and applying a third filter to further reduce noise in the plurality of images 1601, the third filter being characterized by a third kernel size.

[0127] Figure 13 An example of generating an improved image 1320 from a raw SEM image 1301 on a patterned substrate is illustrated. The raw SEM image 1302 is noisy, making it difficult to identify the contours or profiles of features within the image based on pixel intensity. In an embodiment, one or more filters may be applied to reduce or remove noise within the raw image 1302. In an embodiment, a first median filter and a Gaussian filter may be applied to perform denoising on the raw image 1301 to make the raw image 1301 relatively smooth. For example, the first median filter may be a nonlinear noise filter characterized by a first kernel size (e.g., 3×3). The Gaussian filter may be a blur filter configured to reduce the blur of the raw image 1301 while preserving the blur of ridges within the image. For example, the ridges within the image are characterized by local maxima (e.g., maximum intensity) around features of interest (e.g., holes, lines, etc.) in the raw image 1301. After applying the first filter and the Gaussian filter, a denoised image (not shown) is obtained.

[0128] Furthermore, a second median filter is applied to the denoised image to enhance image contrast. Image contrast is the difference in pixel intensity between the printed and unprinted areas of the substrate. For example, image contrast is enhanced around the main and secondary features within the denoised image. The second median filter may have a second kernel size larger than the first kernel size. Applying the second filter yields a denoised image 1310. Compared to the original image 1301, the denoised image 1310 has relatively less noise around the features, steeper edges, and better contrast. Furthermore, a third filter may be applied to the denoised image 1310 to further reduce noise. The third filter may be referred to as a minimum filter with a kernel size similar to or smaller than the first filter. An adaptive thresholding algorithm is then applied to the denoised image 1301 to produce an improved image 1320. The improved image 1320 is used to guide the image segmentation process as discussed herein. In an embodiment, the improved image 1320 may be a binary image. In an embodiment, the adaptive thresholding algorithm may be the Otsu algorithm, which converts the denoised image 1310 into a binary image 1320. In the adaptive thresholding algorithm, thresholds are calculated for multiple parts, for example, based on features of the denoised image (e.g., primary features and secondary features). Thus, adaptive thresholding differs from simple thresholding, where a single threshold is applied globally to the image. As a result of adaptive thresholding, a more improved image 1302 can be obtained that highlights features within the original image 1301. In an embodiment, the highlighted features (e.g., white areas in 1320) correspond to primary features (e.g., lines and holes) and secondary features surrounding the primary features.

[0129] Additionally, some unknown features may exist in the improved image 1320. These unknown features may not be readily visible in the original image 1301, the denoised image 1302, or even the mask pattern used to generate the patterned substrate. These unknown features may not be expected and can be distinguished by comparing them with the simulated improved image (see [link to image 1320]). Figure 14 The simulated improved image (see 1420) is compared to remove it. In this embodiment, unknown features can be removed because they are not the expected principal features or SRAF features, but rather unknown features that may originate from SEM noise or erroneous signals generated during the process of generating the improved image. Figure 14 1420 in the diagram is used as a guide to identify features associated with the mask pattern and to ignore unknown features. The process of obtaining the simulated improved image and further comparing it with the improved image is discussed below (e.g., 1320).

[0130] Referring back to Figure 12, at process P1601, obtaining the simulated improved image 1605 includes performing one or more process models of the patterning process using process conditions and mask patterns corresponding to each of the plurality of images 1601 to generate a simulated image of a pattern to be printed on a substrate; and applying a selected threshold intensity value to the simulated image to generate the simulated improved image 1605.

[0131] Figure 14 An example of generating an improved simulated image 1420 is illustrated. In an embodiment, one or more process models (e.g., such as...) are performed using the mask pattern (not shown) used for patterning a substrate. Figure 2 (as discussed in the text) to generate the analog image 1401. For example, the analog image 1401 can be generated by performing the patterning process (e.g., as...). Figure 2 The spatial images or resist images generated by the optical device model or resist model (discussed in the text). Figure 14 In the simulation, image 1401 is superimposed on the contours of the target and auxiliary features for reference. A ridge magnitude image 1410 of the simulation image 1401 is shown to highlight features within the simulation image 1401. In an embodiment, intensity thresholding may be applied to the simulation image 1401 to produce an improved image, also referred to as the simulated improved image 1420. In an embodiment, intensity thresholding may be applied generally to the simulation image 1401. In an embodiment, adaptive thresholding may be applied to the simulation image 1401 to produce the simulated improved image 1420. In an embodiment, the simulated improved image 1420 is a binary image as shown, where features have values ​​of 1 and the features are surrounded by values ​​of 0. Thus, the simulated improved image 1420 clearly identifies the locations of the primary and auxiliary features associated with the mask pattern.

[0132] In this embodiment, the main and auxiliary features of the simulated improved image 1420 are compared with those of the improved image 1320 of the original SEM image (see [link]). Figure 13 The corresponding principal and auxiliary features of the image are aligned. Therefore, the improved image 1320 (see [link to image 1320]) can be ignored. Figure 13 The image segmentation process involves identifying any unknown features in the image based on the aligned and improved image (e.g., ...). Figure 13 The image segmentation process involves identifying features within the original image 1301 or the denoised image 1310, and placing identifiers around those features. This image segmentation process is discussed in further detail below.

[0133] Referring back to Figure 12, process P1603 includes labeling each of the plurality of improved images 1601 based on the plurality of improved images, the simulated improved image 1605, and the intensity of pixels within each of the plurality of images 1601. This labeling produces a plurality of labeled images 1613 corresponding to the plurality of images 1601.

[0134] In an embodiment, labeling of each of the plurality of images 1601 includes aligning an improved image of the plurality of improved images with a simulated improved image 1605; identifying features within the improved image that correspond to features within the simulated improved image 1605; aligning the images of the plurality of images with the aligned improved image; and placing a marker on the aligned image based on the identified features, each marker being placed at a location associated with a local minimum of intensity within the image surrounding the identified feature.

[0135] In an embodiment, the placement of the markers includes determining the contour of the identified feature within the improved image; aligning the contour with a corresponding feature in the images of the plurality of images 1601; identifying portions of the markers around the contour in the normal direction of the contour; and generating multiple pairs of markers. A pair of markers includes a first marker located inside the contour of the corresponding feature in the image, and a second marker located outside the contour of the corresponding feature in the image. In an embodiment, the contour of the feature in the image 1601 may also be a portion of the marker.

[0136] In an embodiment, the generation of multiple pairs of identifiers includes determining the first identifier at a local minimum of the intensity of the image within the contour. In an embodiment, the local minimum can be determined along the normal direction of the contour. Furthermore, the second identifier is determined at another local minimum of the intensity of the image, where the intensity is at a local maximum value outside the contour and spans the entire image. In an embodiment, the second local minimum or local maximum can be determined along the normal direction of the contour. Therefore, a marked image 1613 corresponding to the images of the plurality of images 1601, including the first and second identifiers, is generated. In an embodiment, the marked image 1613 also includes a contour of features.

[0137] Figure 15AThe illustration shows an example of generating a segmented image 1501 corresponding to an SEM image (e.g., the original image 1301 or the denoised image 1310) and another improved image 1510. In an embodiment, the segmented image 1501 is generated by placing identifiers (e.g., points) within the image (e.g., the original image 1301 or the denoised image 1310). In an embodiment, the identifiers indicate information associated with a specific location within a given image (e.g., 1301 or 1310). In an embodiment, the information linked to the identifiers may be a location relative to a feature or design layout of interest, the intensity associated with said location, or other information directly available or derived therefrom.

[0138] In an embodiment, the placement of the identifier includes determining the improved image (e.g., Figure 13 The contour of the identified feature within the improved image 1320 is used. The contour is aligned with the contour of the corresponding feature Fe1 in a given image 1501 (e.g., images 1301 or 1310). A normal (not shown) is drawn to the contour of feature Fe1 in the given image 1501 (e.g., 1301 or 1310). Along the normal, locations of identifiers Mi1, Me1, Mi2, and Me2 are determined. In an embodiment, the identifiers are a pair, including a first identifier Mi1 (or Mi2) located inside the contour of the corresponding feature Fe1 in image 1501, and a second identifier Me1 (or Me2) located outside the contour of the corresponding feature Fe1 in image 1501.

[0139] In an embodiment, a local minimum of the image intensity within the contour of feature Fe1 is determined. This local minimum is the location of the first identifier Mi1 (or Mi2). Similarly, another local minimum of the intensity feature curve that represents the local maximum intensity across the entire image (e.g., at the contour (dashed line)) towards the outside of the contour of feature Fe1 is determined. This other local minimum is the location of the second identifier Mei1 (or Mei2). In an embodiment, the local minimum can be determined in a specified direction, for example, along the normal direction of the contour.

[0140] In embodiments, the segmented image 1501 may be represented as a pixelated image, matrix, or other data format that can be read by a computer-readable medium and imported and / or exported by a program implemented on the computer-readable medium. The segmented image 1501 is transformed into another improved image 1510 for further determination of printability mapping, as discussed below. For example, the segmented image 1501 is transformed into the improved image 1510 using a watershed algorithm.

[0141] Referring back to Figure 12, process P1605 includes generating a printability map 1615 associated with the mask pattern based on the markers. In an embodiment, generating the printability map 1615 includes inputting the markers of the plurality of images 1601 into an algorithm configured to generate a plurality of other modified images corresponding to each of the plurality of images 1601. In an embodiment, the printability map 1615 is a spatial distribution of probability values ​​indicating the likelihood that features of the pattern will be printed onto a substrate.

[0142] In one embodiment, the algorithm for generating other improved images is a watershed algorithm configured to perform image segmentation based on identifiers placed within the plurality of images 1601. In another embodiment, the watershed algorithm is configured to generate binary images as improved images.

[0143] In embodiments, the model can be used to generate other improved images, such as a convolutional neural network (CNN) including weights and biases as model parameters. The CNN is configured to generate improved images based on the plurality of images 1601 and the identifiers within the plurality of images 1601. In embodiments, such a CNN can be trained using a training dataset including a spatial image or resist image of the mask pattern, and a reference printability map 1615 (as the true valid value, i.e., the ground truth). For example, training the CNN includes determining the values ​​of the model parameters such that the CNN produces a printability map that closely matches the reference printability map 1615 when the spatial image or resist image of the mask pattern is input to the CNN.

[0144] Furthermore, the process P1605 includes aligning a plurality of other improved images relative to each other; and generating a printability map 1615 of at least one of the plurality of other improved images based on the intensity values ​​of the aligned plurality of other improved images.

[0145] In an embodiment, the generation of the printability map 1615 includes determining the probability value of each pixel of the printability map 1615 by: summing the image intensities of other improved images of the plurality of improved images 1603; and dividing the image intensity of the summed image by the total number of improved images 1603.

[0146] Figure 15BAn exemplary printability map 1520 (discussed previously) generated based on a plurality of modified images 1603, such as image 1510, is illustrated. In an embodiment, the printability map 1520 is generated by summing the image intensities of other modified images (e.g., 1510) of the plurality of modified images; and dividing the image intensity of the summed image by the total number of modified images 1603.

[0147] In an embodiment, the method 1600 further includes a process P1607 for generating values ​​1617 of one or more parameters of the patterning process based on the printability map 1615.

[0148] In an embodiment, the generation of value 1617 includes inputting a printability map 1615 associated with the mask pattern into an optical proximity correction (OPC) process; determining from the printability map 1615 a probability associated with an auxiliary feature of the mask pattern, the probability indicating whether the auxiliary feature will be printed on the substrate; and generating OPC data based on the probability of the auxiliary feature to adjust one or more main features or one or more auxiliary features of the mask pattern to minimize the probability that the auxiliary feature will be printed on the substrate.

[0149] In an embodiment, the generation of OPC data includes adjusting the shape and / or size of one or more primary features or one or more auxiliary features of the mask pattern via an OPC simulation process associated with the patterning process, wherein the adjusted shape and / or size reduces the probability that the auxiliary features will be printed on the substrate; or removing one or more auxiliary features of the mask pattern via an OPC simulation process associated with the patterning process.

[0150] In one embodiment, the generation of the parameter values ​​1617 in the patterning process includes determining parameters associated with the source and / or mask pattern based on the printability map 1615 to reduce the probability of printing auxiliary features. In another embodiment, the determination of the source and / or mask pattern includes adjusting the source parameters and / or mask parameters via a source mask optimization (SMO) process to reduce the probability that auxiliary features of the mask pattern will be printed on the substrate.

[0151] In an embodiment, generating values ​​1617 for one or more parameters of the patterning process includes adjusting one or more parameters associated with the patterning apparatus for patterning the substrate based on the printability map 1615, resulting in a reduced probability that auxiliary features will be printed on the substrate. In an embodiment, the one or more parameters include: scanner dose, scanner focus, and / or substrate stage height.

[0152] In the embodiment, reference Figure 12BFurther flowcharts are provided for method 1700 for generating a printability mapping associated with a mask pattern. Method 1700 includes subsequent processes P1701, P1703, and P1705, which are discussed in detail below.

[0153] Process P1701 includes obtaining a plurality of improved images 1701 of a patterned substrate based on labels of a plurality of images 1601 of the patterned substrate. The label for each of the plurality of images 1601 is associated with the intensity of a pixel in that image. In an embodiment, the acquisition of the plurality of improved images 1701 is similar to that described in method 1600. For example, the plurality of improved images 1701 are obtained by inputting the labels of the plurality of images 1601 into an algorithm configured to generate a plurality of improved images 1701 corresponding to each of the plurality of images 1601. In an embodiment, the algorithm is configured to perform a watershed algorithm for image segmentation based on identifiers placed within the plurality of images 1601.

[0154] As discussed herein, labeling each of the plurality of images 1601 includes aligning a binary image of the plurality of images 1601 with a simulated improved image; identifying features within the binary image corresponding to features within the simulated improved image; aligning the images of the plurality of images with the aligned binary image; and placing identifiers on the aligned image based on the identified features, each identifier being placed at a location associated with a local minimum of intensity within the image surrounding the identified feature. In embodiments, the binary image can be obtained via a denoising process and a thresholding process as discussed above.

[0155] In an embodiment, the placement of the markers includes determining the contour of the identified feature within the binary image; aligning the contour with corresponding features in the images of the plurality of images 1601; and identifying locations of a pair of markers around the contour, the first marker being located at a local minimum of image intensity inside the contour, and the second marker being located at another local minimum of image intensity outside the contour.

[0156] In an embodiment, the identification of the pair of identifiers includes determining that the first identifier is located at a local minimum of the intensity of the image in a specified direction toward the interior of the contour; and determining that the second identifier is located at another local minimum of the intensity of the image in a specified direction and across the entire image in a specified direction toward the exterior of the contour.

[0157] Process P1703 includes summing the image intensities of the plurality of improved images 1701. Process P1705 includes dividing the summed image intensities by the total number of improved images 1701 to produce a printability map 1615 associated with the mask pattern. For example, the plurality of improved images 1701 may be stacked, and each corresponding pixel of the stacked images may be summed. The summed intensity associated with each pixel may be divided by the total number of the plurality of images 1601.

[0158] In addition, the method 1700 may include a process P1607 for determining the value 1617 of one or more parameters (e.g., OPC data, dose, focus, source parameters, pupil parameters, etc.) associated with the patterning process as discussed above.

[0159] In the embodiment, reference Figure 12C Further flowcharts are provided for method 1700 for generating a printability mapping associated with a mask pattern. Method 1700 includes the following processes P1801, P1803, and P1805, which are discussed in detail below.

[0160] Process P1801 includes obtaining a plurality of binary images 1801 of the patterned substrate based on features of the mask pattern. In an embodiment, the plurality of binary images 1801 are obtained by applying a binaryization algorithm to each of the plurality of images 1601 of the patterned substrate. In an embodiment, the binaryization algorithm is configured to generate a binary image of a given image based on features in a given image of the plurality of images 1601 that correspond to the features of the mask pattern. In an embodiment, features corresponding to the features of the mask pattern within each of the plurality of images 1601 are identified based on a simulated image of the patterned substrate, for example, as per [reference to...]. Figure 15A The discussion.

[0161] In an embodiment, the binary algorithm includes thresholding each of a plurality of images 1601 of a patterned substrate, the thresholding being based on features corresponding to the mask pattern. In an embodiment, the thresholding can be adaptive thresholding or single-valued thresholding. In an embodiment, thresholding refers to applying a threshold associated with pixel intensity to a given image. Thus, if a pixel intensity of a given image is below an intensity threshold, the pixel is assigned a value of 0 (e.g., indicating no printing), and if the pixel intensity is above the intensity threshold, the pixel is assigned a value of 1 (e.g., indicating printing), or vice versa. Thus, a binary image is obtained. In an embodiment, thresholding can be applied to a portion of the image surrounding a feature corresponding to the mask pattern. For the remaining portion, pixels can simply be assigned a value of 0 (e.g., indicating no printing), regardless of whether the threshold intensity is exceeded.

[0162] In an embodiment, the binary algorithm is configured to perform a watershed algorithm for image segmentation based on identifiers placed within a plurality of images 1601. In this embodiment, the identifiers include a first identifier and a second identifier. The first identifier may be located at a local minimum of the image intensity in a specified direction, towards the interior of the contour. The second identifier may be located at another local minimum of the image intensity, in a specified direction, towards the exterior of the contour, spanning the entire image, where a local maximum of the intensity is located. For example, Figure 15A The illustration shows example identifiers Me1, Mi1, and Mi2 surrounding the feature Fe1 as previously discussed.

[0163] It is understood that the identifiers or markers based on local minima discussed herein are merely exemplary to illustrate the concepts of this disclosure. Those skilled in the art may specify different identifiers based on, for example, user-defined locations, feature contours, metrics derived from image intensity, or other markers related to image segmentation.

[0164] Process P1803 includes aligning a plurality of binary images 1801 and summing the intensities of the plurality of binary images 1801. Process P1805 includes dividing the summed image intensities by the total number of binary images to produce a printability map 1605 associated with the mask pattern. In an embodiment, the intensity of each pixel in the printability map 1605 indicates the probability that a feature of the mask pattern will be printed on the substrate.

[0165] In addition, the method 1800 may include a process P1607 for determining the value 1617 of one or more parameters (e.g., OPC data, dose, focus, source parameters, pupil parameters, etc.) associated with the patterning process as discussed above.

[0166] In an embodiment, the process of method 1600 may be included in a non-transitory computer-readable medium. In an embodiment, a non-transitory computer-readable medium is provided, comprising instructions for generating a printability map associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including: obtaining (i) a plurality of images of a patterned substrate, (ii) a plurality of improved images based on the plurality of images, and (iii) a simulated improved image based on the mask pattern; labeling each of the plurality of images based on the plurality of improved images, the simulated improved image, and the intensity of pixels within each of the plurality of images; and generating a printability map associated with the mask pattern based on the labeling. In an embodiment, the printability map is a spatial distribution of probability values ​​indicating the likelihood that features of the pattern will be printed onto the substrate.

[0167] In an embodiment, acquiring the plurality of images includes instructions to receive, via a measurement tool, the plurality of images of the pattern printed on the substrate; or to capture, via the measurement tool, the plurality of images of the pattern printed on the substrate. In an embodiment, one or more of the plurality of improved images are one or more binary images. In an embodiment, the simulated improved image is a binary image. In an embodiment, the plurality of images are obtained via scanning electron microscopy (SEM) of a patterned substrate. In an embodiment, each of the plurality of images is an SEM image.

[0168] In one embodiment, obtaining the plurality of improved images includes denoising the plurality of images; and converting each of the denoised plurality of images into an improved image via an adaptive thresholding algorithm, the adaptive thresholding algorithm adaptively finding an optimal threshold to distinguish printed and unprinted regions within the image. In another embodiment, the adaptive thresholding algorithm is an Otsu thresholding algorithm configured to receive the plurality of images or the denoised plurality of images and an identifier within each of the plurality of images as input, and output the improved image.

[0169] In an embodiment, the denoising of the plurality of images includes applying a first median filter and a Gaussian filter to each of the plurality of images to maintain the ridge edge accuracy associated with each of the plurality of images, the first median filter being characterized by a first kernel size; applying a second median filter to enhance the image contrast of each of the plurality of images, the image contrast being between printed and unprinted areas, the second median filter being characterized by a second kernel size, the second kernel size being larger than the first kernel size; and applying a third filter to further reduce noise in the plurality of images, the third filter being characterized by a third kernel size.

[0170] In an embodiment, obtaining the simulated improved image includes: performing one or more process models of the patterning process using process conditions and mask patterns corresponding to each of the plurality of images to generate the simulated image of the pattern to be printed on a substrate; and applying a selected threshold intensity value to the simulated image to generate the simulated improved image.

[0171] In an embodiment, labeling each of the plurality of images includes aligning one of the plurality of improved images with a simulated improved image; identifying features in the improved image that correspond to features in the simulated improved image; aligning the images of the plurality of images with the aligned improved image; and placing a marker on the aligned image based on the identified features, each marker being placed at a location associated with a local minimum of intensity in the image surrounding the identified features.

[0172] In one embodiment, the placement of the markers includes determining the contour of the identified features within the improved image; aligning the contour with corresponding features in the images of the plurality of images; and identifying locations of a pair of markers around the contour, for example, in the normal direction of the contour. The first marker is located at a local minimum of image intensity inside the contour, and the second marker is located at a local minimum of the image feature curve found outside the contour along, for example, the normal direction.

[0173] In an embodiment, the generation of multiple pairs of identifiers includes determining that the first identifier is located at a local minimum of the intensity of the image along the normal direction toward the interior of the contour; and determining that the second identifier is located at another local minimum of the intensity of the image along the normal direction and across the entire image along the exterior of the contour.

[0174] In an embodiment, the generation of a printability map includes inputting the markers of the plurality of images into an algorithm configured to generate a plurality of other improved images corresponding to each of the plurality of images; aligning the plurality of other improved images relative to each other; and generating a printability map of at least one of the plurality of other improved images based on the intensity values ​​of the aligned plurality of other improved images.

[0175] In one embodiment, the algorithm is configured to perform a watershed algorithm for image segmentation based on identifiers placed within the plurality of images. Alternatively, a model such as a convolutional neural network may be used. The convolutional neural network is configured to generate an improved image based on the plurality of images and the identifiers within those images.

[0176] In an embodiment, the generation of a printable map includes determining the probability value of each pixel of the printable map by: summing the image intensities of other improved images of the plurality of improved images; and dividing the summed image intensities by the total number of improved images.

[0177] In an embodiment, the computer-readable medium includes instructions for generating values ​​for one or more parameters of the patterning process based on a printability map.

[0178] In an embodiment, the generation of values ​​includes inputting a printability map associated with the mask pattern into an optical proximity correction (OPC) process; determining from the printability map a probability associated with an auxiliary feature of the mask pattern, the probability indicating whether the auxiliary feature will be printed on the substrate; and generating OPC data based on the probability of the auxiliary feature to adjust one or more main features or one or more auxiliary features of the mask pattern to minimize the probability that the auxiliary feature will be printed on the substrate.

[0179] In an embodiment, the generation of OPC data includes adjusting the shape and / or size of one or more primary features or one or more auxiliary features of the mask pattern via an OPC simulation process associated with the patterning process, wherein the adjusted shape and / or size reduces the probability that the auxiliary features will be printed on the substrate; or removing the one or more auxiliary features of the mask pattern via an OPC simulation process associated with the patterning process.

[0180] In one embodiment, the generation includes determining parameters associated with the source and / or mask pattern based on a printability mapping to reduce the probability that auxiliary features will be printed. In another embodiment, determining the source and / or mask pattern includes adjusting source and / or mask parameters via a source mask optimization (SMO) process to reduce the probability that auxiliary features of the mask pattern will be printed on the substrate.

[0181] In one embodiment, the generation includes adjusting one or more parameters associated with the patterning apparatus used to pattern the substrate based on a printability map, resulting in a reduced probability that auxiliary features will be printed on the substrate. In another embodiment, one or more parameters include: scanner dose, scanner focus, and / or substrate stage height.

[0182] In an embodiment, a non-transitory computer-readable medium is further provided, comprising instructions for generating a printable map associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including: obtaining a plurality of improved images of a patterned substrate based on labels of a plurality of images of the patterned substrate, each image's label being associated with the intensity of a pixel in each image; summing the image intensities of the plurality of improved images; and dividing the summed image intensities by the total number of improved images to generate a printable map associated with the mask pattern. The plurality of improved images are obtained, for example, via a watershed algorithm, as discussed above. Furthermore, the process of labeling multiple images of the patterned substrate (e.g., SEM images) is discussed above.

[0183] In some embodiments, the inspection or measurement equipment may be a scanning electron microscope (SEM) that produces images of structures (e.g., some or all of the structures of a device) exposed or transferred onto the substrate. Figure 16 An embodiment of the SEM tool is described. The primary electron beam EBP emitted from the electron source ESO is converged by the condenser lens CL and then passed through the beam deflector EBD1, the E×B deflector EBD2, and the objective lens OL to illuminate the substrate PSub on the substrate stage ST at the focal length.

[0184] When the substrate PSub is irradiated with an electron beam EBP, secondary electrons are generated by the substrate PSub. These secondary electrons are deflected by an E×B deflector EBD2 and detected by a secondary electron detector SED. A two-dimensional electron beam image can be obtained by simultaneously detecting electrons generated from the sample, for example, by performing a two-dimensional scan of the electron beam by a beam deflector EBD1 in the X or Y direction, or by repeatedly scanning the electron beam EBP by a beam deflector EBD1, and by continuously moving the substrate PSub in the other direction (X or Y) by a substrate stage ST.

[0185] The signal detected by the secondary electronic detector (SED) is converted into a digital signal by an analog-to-digital (A / D) converter (ADC), and the digital signal is sent to the image processing system (IPU). In an embodiment, the image processing system (IPU) may have a memory (MEM) to store all or part of the digital image for processing by a processing unit (PU). The processing unit (PU) (e.g., specially designed hardware, or a combination of hardware and software) is configured to convert or process the digital image into a dataset representing the digital image. Furthermore, the image processing system (IPU) may have a storage medium (STOR) configured to store the digital image and the corresponding dataset in a reference database. A display device (DIS) may be connected to the image processing system (IPU), allowing an operator to perform necessary operations of the equipment using a graphical user interface.

[0186] As mentioned above, SEM images can be processed to extract contours that describe the edges of objects representing device structures in the image. These contours are then quantized via metrics such as CD. Therefore, images of device structures are typically compared and quantified via oversimplified metrics such as distance between edges (CD) or simple pixel differences between images. Typical contour models for detecting the edges of objects in an image to measure CD use image gradients. In practice, those models rely on strong image gradients. However, in practice, images are often noisy and have discontinuous boundaries. Techniques such as smoothing, adaptive thresholding, edge detection, abrasion, and dilation can be used to process the results of image gradient contour models to address noisy and discontinuous images, but ultimately result in low-resolution quantization of high-resolution images. Thus, in most instances, mathematical operations—i.e., mathematical transformations—on images of device structures to reduce noise and automated edge detection lead to a loss of image resolution, resulting in a loss of information. Therefore, the result is low-resolution quantization equivalent to an oversimplified representation of a complex high-resolution structure.

[0187] Therefore, a mathematical representation of the general shape of a structure (e.g., circuit features, alignment marks, or measurement target portions (e.g., grating features), etc.) that can retain resolution and describe the structure produced or anticipated using a patterning process is needed, regardless of whether the structure is in a potential resist image, a developed resist image, or a layer transferred onto the substrate, for example, by etching. In the context of photolithography or other patterning processes, the structure may be a device being manufactured or a portion thereof, and the image may be a SEM image of the structure. In some cases, the structure may be a feature of a semiconductor device (e.g., an integrated circuit). In such cases, the structure may be referred to as a pattern or desired pattern comprising multiple features of the semiconductor device. In some cases, the structure may be an alignment mark, or a portion thereof (e.g., a grating of the alignment mark), used in alignment measurement processes to determine the alignment of an object (e.g., a substrate) with another object (e.g., a patterning apparatus), or a measurement target, or a portion thereof (e.g., a grating of the measurement target), used to measure parameters of the patterning process (e.g., overlap, focus, dose, etc.). In one embodiment, the measurement target is used to measure, for example, overlapping diffraction gratings.

[0188] Figure 17 Another embodiment of the inspection apparatus is illustrated schematically. The system is used to inspect a sample 90 (such as a substrate) on a sample platform 88 and includes a charged particle beam generator 81, a condenser lens module 82, a probe forming objective module 83, a charged particle beam deflection module 84, a secondary charged particle detector module 85, and an image forming module 86.

[0189] Charged particle beam generator 81 generates a primary charged particle beam 91. A condenser lens module 82 focuses the generated primary charged particle beam 91. A probe forming objective module 83 focuses the focused primary charged particle beam into a charged particle beam probe 92. A charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the surface of the region of interest on a sample 90 secured to a sample platform 88. In embodiments, the charged particle beam generator 81, the condenser lens module 82, and the probe forming objective module 83, or equivalent designs, alternatives, or any combination thereof, together form a charged particle beam probe generator that generates the scanning charged particle beam probe 92.

[0190] The secondary charged particle detector module 85 detects secondary charged particles 93 emitted from the sample surface immediately after being bombarded by the charged particle beam probe 92 (and may also include other reflected or scattered charged particles from the sample surface) to generate a secondary charged particle detection signal 94. An image forming module 86 (e.g., a computing device) is coupled to the secondary charged particle detector module 85 to receive the secondary charged particle detection signal 94 from the secondary charged particle detector module 85 and accordingly forms at least one scanned image. In embodiments, the secondary charged particle detector module 85 and the image forming module 86, or their equivalents, alternatives, or any combination thereof, together form an image forming apparatus that forms a scanned image based on the detected secondary charged particles emitted from the sample 90 bombarded by the charged particle beam probe 92.

[0191] In an embodiment, the monitoring module 87 is coupled / linked to the image forming module 86 of the image forming apparatus to monitor, control, etc., the patterning process, and / or to derive parameters for patterning process design, control, monitoring, etc., using scanned images of the sample 90 received from the image forming module 86. Therefore, in an embodiment, the monitoring module 87 is configured or programmed to perform the methods described herein. In an embodiment, the monitoring module 87 includes a computing device. In an embodiment, the monitoring module 87 includes a computer program for providing the functionality described herein and encoded on a computer-readable medium forming or disposed within the monitoring module.

[0192] In an embodiment, a probe may be used to inspect the substrate. Figure 16 Electron beam inspection tools, Figure 17 The electronic current in the system compared to, for example, such as Figure 16The CD SEM described herein is significantly larger, resulting in a sufficiently large probe spot for faster inspection speeds. However, due to the large probe spot, the resolution may not be as high as that of the CD SEM. In embodiments, without limiting the scope of this disclosure, the inspection apparatus discussed above can be a single-beam or multi-beam apparatus.

[0193] It can process from, for example Figure 16 and / or Figure 17 The system uses SEM images to extract contours that describe the edges of objects representing device structures. These contours are then typically quantified using metrics such as CD at user-defined cut lines. Thus, images of device structures are typically compared and quantified using metrics such as the distance between edges (CD) measured on the extracted contours or simple pixel differences between images.

[0194] In embodiments, one or more steps of processes 300, 1400, and / or 1500 may be implemented as instructions (e.g., program code) in a processor of a computer system (e.g., process 104 of computer system 100). In embodiments, multiple steps may be distributed across multiple processors (e.g., parallel computing) to improve computational efficiency. In embodiments, instructions are recorded on a computer program product including a non-transitory computer-readable medium, the instructions being combined with, when executed by a computer hardware system, […]. Figure 2 and Figures 14 to 17 The relevant methods are used to implement methods 300, 1400, or 1500.

[0195] According to this disclosure, combinations and sub-combinations of the disclosed elements constitute multiple individual embodiments. For example, a first combination includes determining the likelihood of printing an auxiliary feature (e.g., SRAF) onto a substrate. A sub-combination may include determining a model configured to predict variance data associated with a given mask image, which includes the auxiliary feature. In another example, the combination includes determining OPC or SMO based on the variance data generated by the model. In yet another example, the combination includes determining process adjustments for a lithography process, resist process, or etching process based on the variance data, such that the probability of printing the auxiliary feature (SRAF) is minimized.

[0196] In embodiments, the corrected and OPC-post-image determined using the results of methods 300 and 1400 (e.g., variance data) can be used to optimize the patterning process or adjust the parameters of the patterning process. As an example, OPC addresses the fact that the final size and placement of the image of the design layout projected onto the substrate will not be the same as or simply depend only on the size and placement of the design layout on the patterning apparatus. It should be noted that the terms “mask,” “patterning plate,” and “patterning apparatus” can be used interchangeably herein. Furthermore, those skilled in the art will recognize that, particularly in the context of lithography simulation / optimization, the terms “mask” / “patterning apparatus” and “design layout” can be used interchangeably because: in lithography simulation / optimization, it is not necessary to use a physical patterning apparatus, but rather a design layout can be used to represent a physical patterning apparatus. For a small feature size and high feature density present on a given 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 arise from small amounts of radiation coupled from one feature to another and / or non-geometric optical effects such as diffraction and interference. Similarly, proximity effects can result from diffusion and other chemical effects during post-exposure baking (PEB), resist development, and etching in typical photolithography processes.

[0197] To ensure that the projected image of the design layout is accurate to the requirements of a given target circuit design, complex numerical models, corrections, or pre-distortions 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 an overview of current “model-based” optical proximity effect correction processes. In typical high-end designs, almost every feature of the design layout is modified in some way to achieve high fidelity in the projected image to the target design. These modifications can include offsets or biases of edge positions or linewidths, as well as the application of “auxiliary” features intended to assist the projection of other features.

[0198] In chip design, where millions of features are typically present, applying model-based OPC to the target design involves well-developed process models and considerable computational resources. However, applying OPC is often not an "exact science" but rather an empirical iterative process that doesn't always compensate for all possible proximity effects. Therefore, the effects of OPC need to be validated through design checks, such as using intensive full-chip simulations with calibrated numerical process models, for example, in the design layout after applying OPC and any other RETs, to minimize the possibility of building design flaws into the patterning device pattern. This is driven by the enormous cost of manufacturing high-end patterning devices, ranging in the millions of dollars; and the impact on turnaround time, which is caused by reworking or repairing actual patterning devices (once they have been manufactured).

[0199] Both OPC and full-chip RET verification can be based on numerical modeling systems and methods, as described, for example, in U.S. Patent Application No. 10 / 815,573, which is incorporated herein by reference in its entirety, and in Y. Cao et al.’s paper entitled “Optimized Hardware and Software For Fast, Full Chip Simulation” (Proc. SPIE, Vol. 5754, 405 (2005)).

[0200] One type of RET relates to the adjustment of global deviations in the design layout. Global deviation is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, a circular pattern with a diameter of 25 nm can be printed onto the substrate using a pattern with a diameter of 50 nm in the design layout, or it can be printed onto the substrate with a large dose using a pattern with a diameter of 20 nm in the design layout.

[0201] In addition to optimizing the design layout or patterning apparatus (e.g., OPC), the illumination source can also be optimized, either in conjunction with the patterning apparatus optimization or separately, with the aim of improving overall lithographic fidelity. In this document, the terms "illumination source" and "source" are used interchangeably. Since the 1990s, numerous off-axis illumination sources (such as toroidal, quadrupole, and bipolar sources) have been introduced, providing greater freedom in OPC design and thus improving imaging results. Off-axis illumination is a proven method for resolving fine structures (i.e., target features) contained within a patterning apparatus. However, off-axis illumination sources typically provide lower light intensity for spatial imaging (AI) compared to conventional illumination sources. Therefore, there is a need to optimize the illumination source to achieve an optimal balance between finer resolution and reduced light intensity.

[0202] For example, in the article "Optimum Mask and Source Patterns to PrintA Given Shape" by Rosenbluth et al., Journal of Microlithography, Microfabrication, Microsystems 1(1), pp.13-20, (2002), numerous methods for optimizing illumination sources can be found. The source is subdivided into multiple regions, each corresponding to a specific region of the pupil spectrum. Then, it is assumed that the source distribution is uniform in each source region, and the brightness of each region is optimized for the process window. However, such an assumption that "the source distribution is uniform in each source region" is not always valid, thus affecting the effectiveness of this method. In another example described in Granik's article "Source Optimization for Image Fidelity and Throughput", Journal of Microlithography, Microfabrication, Microsystems 3(4), pp.509-522, (2004), several existing source optimization methods are reviewed, and a method based on illuminator pixels is proposed, which transforms the source optimization problem into a series of non-negative least-squares optimizations. While these methods have demonstrated some success, they typically require multiple complex iterations to converge. Furthermore, it can be difficult to determine suitable / optimized values ​​for certain additional parameters (such as γ in the Granik method), which dictate a trade-off between optimizing the source for substrate image fidelity and the smoothness requirements of the source.

[0203] For low-k1 lithography, optimization of the source and patterning apparatus is very useful for ensuring a feasible process window for 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 independently express the cost function (defined as a function of selected design variables) based on process window metrics (such as exposure latitude), which can be predicted by an optical imaging model from the source point intensity and the diffraction order of the patterning apparatus. The term “design variables” as used herein includes a set of parameters of the lithographic projection apparatus or the lithographic process, such as parameters of the lithographic projection apparatus that can be adjusted by the user, or image characteristics that the user can adjust by adjusting those parameters. It should be recognized that any characteristics of the lithographic projection apparatus (including those of the source, patterning apparatus, projection optics, and / or resist) can be included in the design variables during optimization. The cost function is typically a nonlinear function of the design variables. Standard optimization techniques are then used to minimize the cost function.

[0204] Correspondingly, the pressure of ever-decreasing design rules has driven semiconductor chip manufacturers deeper into the era of low-k1 lithography, building upon the existing 193nm ArF lithography. This shift towards lower k1 lithography places high demands on resolution enhancement techniques (RETs), exposure tools, and lithography-friendly design. In the future, ultra-high numerical aperture (NA) exposure tools at 1.35ArF may be used. To help ensure that the circuit design can be printed onto the substrate using a working process window, source-patterning device optimization (referred to herein as source-mask optimization or SMO) has become a crucial RET required for the 2x nm node.

[0205] A method and system for optimizing source and pattern forming apparatus (design layout) allows for the simultaneous optimization of source and pattern forming apparatus using a cost function without constraint and within a practically feasible timeframe. This is described in commonly assigned International Patent Application No. PCT / US2009 / 065359, filed November 20, 2009, and Publication No. WO2010 / 059954, entitled "FastFreeform Source and Mask Co-Optimization Method," the entire contents of which are incorporated herein by reference.

[0206] Another source and mask optimization method and system relates to optimizing the source by adjusting the source pixels, which is described in commonly assigned U.S. Patent Application No. 12 / 813456, filed June 10, 2010, and U.S. Patent Application Publication No. 2010 / 0315614, entitled “Source-Mask Optimization in Lithographic Apparatus,” the entire contents of which are incorporated herein by reference.

[0207] In a photolithography projection device, as an example, the cost function is expressed as:

[0208]

[0209] Where (z1, z2, ..., z N ) represents N design variables or their values. p (z1,z2,...,z N ) can be design variables (z1, z2, ..., z N Functions such as (z1, z2, ..., z) N The difference between the actual and expected values ​​of the characteristic at the evaluation point of the set of design variable values. p Is with f p (z1,z2,...,z N The associated weighting constant. Higher weights can be assigned to evaluation points or patterns that are more critical than other evaluation points or patterns. p Value. Higher w values ​​can also be assigned to patterns and / or evaluation points that occur more frequently. p Value. Examples of evaluation points can be any solid point or pattern on the substrate, any point on a virtual design layout, a resist image, a spatial image, or a combination thereof. p (z1,z2,...,z N It can also be a function of one or more random effects, such as LWR, where the one or more random effects are the design variables (z1, z2, ..., z...). NThe cost function can represent any suitable characteristic of the photolithography projection device or substrate, such as feature failure rate, focal length, CD, image shift, image distortion, image rotation, random effects, production volume, 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, production volume, and random effects (i.e., a function of CDU, production volume, and random effects). In another embodiment, the cost function represents EPE, production volume, and random effects (i.e., a function of EPE, production volume, and random effects). In one embodiment, the design variables (z1, z2, ..., z...) N This includes dosage, global deviations of the patterning apparatus, the shape of the irradiation from the source, or combinations thereof. Since the resist pattern often defines the circuit pattern on the substrate, the cost function often includes functions representing some characteristics of the resist pattern. For example, f at such evaluation points... p (z1,z2,...,z N It can simply be the distance between a point in the resist image and the expected location of that point (i.e., edge placement error EPE). p (z1,z2,...,z N The design variables can be any adjustable parameters, such as those of the source, patterning apparatus, projection optics, dose, focal length, etc. The projection optics may include components commonly referred to as "wavefront manipulators," which can be used to adjust the shape of the wavefront and intensity distribution and / or phase shift of the illumination beam. The projection optics are preferably capable of adjusting the wavefront and intensity distribution at any location along the optical path of the lithography projection apparatus (e.g., before the patterning apparatus, 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, temperature variations in the source, patterning apparatus, lithography projection apparatus, or thermal expansion of components of the lithography projection apparatus. Adjusting the wavefront and intensity distribution can change the values ​​of the evaluation point and the cost function. These changes can be simulated from a model or actually measured. Of course, CF(z1,z2,...,z...) N (This is not limited to the form in Equation 1.) CF(z1,z2,...,z) N It can be in any other suitable form.

[0210] It should be noted that f p (z1,z2,...,z N The normal weighted root mean square (RMS) of ) is defined as Therefore, minimize f p (z1, z2, ..., z NThe weighted RMS is equivalent to minimizing the cost function defined in Equation 1. Therefore, for the sake of simplicity in the notation used in this article, equation 1 and f can be used interchangeably. p (z1,z2,...,z N The weighted RMS of ).

[0211] Furthermore, if we consider maximizing the process window (PW), the same entity part from different PW conditions can be regarded as different evaluation points of the cost function in (Equation 1). For example, if we consider N PW conditions, the evaluation points can be classified according to the PW conditions of the evaluation points, and the cost function can be written as:

[0212]

[0213] Under the u-th PW condition u = 1, ..., U, f pu (z1,z2,...,z N ) is f p (z1,z2,...,z N The value of f. p (z1,z2,...,z N When the substrate EPE is 0, minimizing the above cost function is equivalent to minimizing the edge shift under various PW conditions, thus leading to maximizing the PW. Specifically, if the PW is also composed of different mask deviations, minimizing the above cost function also includes minimizing the mask error enhancement factor (MEEF), which is defined as the ratio between the substrate EPE and the induced mask edge deviation.

[0214] Design variables can have constraints, which can be expressed as (z1, z2, ..., z...). NLet Z be the set of possible values ​​for the design variables. A possible constraint on the design variables can be imposed by the expected production rate of the photolithography projection equipment. The expected production rate may limit the dose and thus have an effect on random effects (e.g., imposing a lower limit on random effects). Higher production rates generally result in lower doses, shorter exposure times, and larger random effects. Considerations of minimizing substrate production rate and random effects can constrain the possible values ​​of the design variables because random effects are a function of the design variables. Without such a constraint imposed by the expected production rate, the optimization may yield an unrealistic set of values ​​for the design variables. For example, if the dose is among the design variables, the optimization may yield dose values ​​that make production economically impossible without such a constraint. However, the usefulness of the constraint should not be interpreted as its necessity. Production rate may be affected by failure rate-based adjustments to the parameters of the patterning process. It is desirable to maintain a characteristic low failure rate while maintaining a high production rate. Production rate may also be affected by the resist chemistry. Slower resists (e.g., resists requiring a higher amount of light for proper exposure) result in lower production yields. Therefore, appropriate parameters for the patterning process can be determined based on the failure rate of features involving characteristics due to resist chemistry or fluctuations, and an optimized process for higher production yields.

[0215] Therefore, the optimization process is performed under the constraints (z1, z2, ..., z). N Find the set of design variable values ​​that minimize the cost function under the z-axis, i.e., find:

[0216]

[0217] Figure 18The figure illustrates a general method for optimizing the photolithography projection apparatus according to an embodiment. This method includes step S1202, which defines a multivariate cost function of multiple design variables. The design variables may include any suitable combination selected from characteristics of the illumination source (1200A) (e.g., pupil fill ratio, i.e., the percentage of radiation from the source that passes through the pupil or aperture), characteristics of the projection optics (1200B), and characteristics of the design layout (1200C). For example, the design variables may include characteristics of the illumination source (1200A) and characteristics of the design layout (1200C) (e.g., global bias), but not characteristics of the projection optics (1200B), a situation leading to SMO. Alternatively, the design variables may include characteristics of the illumination source (1200A), characteristics of the projection optics (1200B), and characteristics of the design layout (1200C), a situation leading to Source-Mask-Lens Optimization (SMLO). In step S1204, the design variables are simultaneously adjusted such that the cost function moves toward convergence. In step S1206, it is determined whether a predefined termination condition is met. The predefined termination condition can include various possibilities, namely, the cost function can be minimized or maximized (as required by the numerical technique used), the value of the cost function is equal to or exceeds a threshold, the value of the cost function is within a preset error limit, or a preset number of iterations has been reached. If any of the conditions in step S1206 are met, the method terminates. If none of the conditions in step S1206 are met, steps S1204 and S1206 are iteratively repeated until the desired result is obtained. Optimization does not necessarily result in a single set of values ​​for the design variables because physical inhibitions can exist due to factors such as failure rate, pupil fill factor, resist chemistry, production volume, etc. The optimization can provide multiple sets of values ​​for the design variables and associated performance characteristics (e.g., production volume), allowing the user of the lithography equipment to select one or more sets.

[0218] In photolithography projection equipment, the source, patterning apparatus, and projection optics can be optimized alternately (referred to as alternating optimization) or simultaneously (referred to as simultaneous optimization). As used herein, the terms "simultaneous," "simultaneously," "jointly," and "jointly" mean that design variables of the characteristics of the source, patterning apparatus, and projection optics, and / or any other design variables, are allowed to change simultaneously. As used herein, the terms "alternating" and "alternatingly" mean that not all design variables are allowed to change simultaneously.

[0219] exist Figure 19 In this approach, optimization of all design variables is performed simultaneously. This process can be called a simultaneous process or a common optimization process. Alternatively, optimization of all design variables can be performed alternately, such as... Figure 19The diagram illustrates this process. In this flow, at each step, some design variables are fixed while others are optimized to minimize the cost function; then, in the next step, a different set of variables is fixed while other sets are optimized to minimize the cost function. These steps are performed alternately until convergence or some termination condition is met.

[0220] like Figure 19 As shown in the non-limiting example flowchart, firstly, a design layout is obtained (step S1302). Then, in step S1304, a source optimization step is performed, where all design variables of the illumination source (SO) are optimized to minimize the cost function, while all other design variables are fixed. Next, in the next step S1306, mask optimization (MO) is performed, where all design variables of the pattern forming apparatus are optimized to minimize the cost function, while all other design variables are fixed. These two steps are performed alternately until certain termination conditions are met in step S1308. Various termination conditions can be used, such as the cost function becoming equal to a threshold, the cost function exceeding a threshold, the cost function reaching a preset error threshold, or reaching a preset number of iterations, etc. It should be noted that alternating SO-MO optimization is an example used as an alternative process. The alternative process can take many different forms, such as: alternating SO-LO-MO optimization, where SO, LO (lens optimization), and MO are performed alternately and iteratively; or a first SMO can be performed once, followed by alternating and iterative LO and MO; etc. Finally, the optimization result is output in step S1310, and the process stops.

[0221] The pattern selection algorithm discussed earlier can be integrated with simultaneous or alternating optimization. For example, when using alternating optimization, a full-chip SO can be performed first to identify "hot spots" and / or "warm spots," followed by MO. Given this disclosure, numerous permutations and combinations of sub-optimizations are possible to achieve the desired optimization results.

[0222] Figure 20AAn exemplary optimization method is shown, in which a cost function is minimized. In step S502, initial values ​​for design variables are obtained, including the tuning range of the design variables (if any). In step S504, a multivariate cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting value of the design variable used for the first iteration step (i = 0). In step S508, standard multivariate optimization techniques are applied to minimize the cost function. It should be noted that constraints, such as the tuning range, may be imposed on the optimization problem during the optimization process in S508 or later in the optimization process. Step S520 indicates that each iteration is performed for a given test pattern (also referred to as a “gauge”) for the identified evaluation points that have been selected for optimization of the lithography process. In step S510, the lithography response is predicted. In step S512, the result of step S510 is compared with the expected or ideal lithography response value obtained in step S522. If the termination condition is met in step S514, i.e., the optimized lithographic response value is sufficiently close to the desired value, then the final value of the design variable is output in step S518. The output step may also include using the final value of the design variable to output other functions, such as outputting the wavefront aberration adjustment mapping at the pupil plane (or other planes), the optimized source mapping, and the optimized design layout, etc. If the termination condition is not met, 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. This will be explained in detail below. Figure 20A The process.

[0223] In the exemplary optimization process, no assumptions or approximations were made regarding the design variables (z1, z2, ..., z). N ) and f p (z1,z2,...,z N The relationship between ) except for f p (z1,z2,...,z N Sufficiently smooth (e.g., having a first derivative) In addition, it is typically effective in photolithography projection equipment. Algorithms such as the Gauss-Newton algorithm, the Levenberg-Marquardt algorithm, gradient descent, simulated annealing, and genetic algorithms can be applied to find...

[0224] Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newton algorithm is an iterative method applicable to general nonlinear multivariable optimization problems. In the design variables (z1, z2, ..., z...),... N ) value (z 1i ,z 2i ,...,z NiIn the i-th iteration of ), the Gauss-Newton algorithm reaches (z) 1i ,z 2i ,...,z Ni Linearization of f in the neighborhood of ) p (z1,z2,...,z N ), and then calculate (z) 1i ,z 2i ,...,z Ni The minimum CF(z1, z2, ..., z) in the neighborhood of ) is given. N The value of (z) 1(i+1) ,z 2(i+1) ,...,z N(i+1) Design variables (z1, z2, ..., z) N The value of z is taken in the (i+1)th iteration. 1(i+1) ,z 2(i+1) ,...,z N(i+1) This iteration continues until convergence (i.e., CF(z1,z2,...,z)). N ()) until it no longer decreases) or until the preset number of iterations is reached.

[0225] Specifically, in the i-th iteration, in (z 1i ,z 2i ,...,z Ni In the neighborhood of ),

[0226]

[0227] Under the approximation of Equation 3, the cost function becomes:

[0228]

[0229] It is the design variable (z1, z2, ..., z N A quadratic function of (z1, z2, ..., z). Except for the design variables (z1, z2, ..., z...). N Apart from ), all terms are constants.

[0230] If the design variables are (z1, z2, ..., z...) N If (z) is not under any constraints, then (z) 1(i+1) ,z 2(i+1) ,...,z N(i+1) This can be derived by solving N linear equations:

[0231]

[0232] If the design variables are (z1, z2, ..., z...) N ) is in the form of J inequalities (for example, (z1, z2, ..., z...).N Under the constraint of the tuning range Where j = 1, 2, ..., J); and under the constraints of K equations (e.g., the interdependencies between design variables). Where k = 1, 2, ..., K); then the optimization process becomes a classic quadratic programming problem, where A nj B j C nk D k It is a constant. Additional constraints can be imposed for each iteration. For example, a "damping factor" Δ can be introduced. D To limit (z) 1(i+1) ,z 2(i+1) ,...,z N(i+1) ) and (z 1i ,z 2i ,...,z Ni The difference between z and z makes the approximation of equation 3 hold. This constraint can be expressed as z ni -Δ D ≤z n ≤z ni +Δ D The method described, for example, in Jorge Nocedal and Stephen J. Wright's *Numerical Optimization* (2nd edition), can be used to derive (z). 1(i+1) ,z 2(i+1) ,...,z N(i+1) )).

[0233] The substitution makes f p (z1,z2,...,z N The optimization process minimizes the RMS of the evaluation points, reducing the magnitude of the maximum deviation (worst-case defect) to their expected value. In such a method, the cost function can alternatively be expressed as:

[0234]

[0235] Among them CL p It is aimed at f p (z1,z2,...,z N The maximum allowable value of the worst defect. This cost function represents the worst defect among the evaluation points. Optimization using this cost function minimizes the magnitude of the worst defect. Iterative greedy algorithms can be used for this optimization.

[0236] The cost function of Equation 5 can be approximated as:

[0237]

[0238] Where q is an even positive integer, such as at least 4, preferably at least 10. Equation 6 mimics the behavior of Equation 5, while allowing for analytical optimization and speeding up the optimization by using methods such as the deepest descent method, the conjugate gradient method, etc.

[0239] Minimizing the worst-case defect size can also be related to f p (z1,z2,...,z N A linearized combination of f. Specifically, as in Equation 3, the approximation of f. p (z1,z2,...,z N Next, the constraint on the worst-case defect size is written as inequality E. Lp ≤f p (z1,z2,...,z N )≤E Up E Lp and E Up Is it specified f p (z1,z2,...,z N These are two constants representing the minimum and maximum permissible deviations. Inserting Equation 3, these constraints are transformed into the following equation: (where p = 1, ..., P),

[0240]

[0241] and

[0242]

[0243] Because equation 3 is usually only in (z) 1i ,z 2i ,...,z Ni It is valid in the neighborhood of ), so the desired constraint E cannot be achieved in such a neighborhood. Lp ≤f p (z1,z2,...,z N )≤E Up In cases where (it can be determined by any conflict in the inequalities stated above), the constant E can be relaxed. Lp and E Up This continues until the constraints can be met. This optimization process minimizes (z... 1i ,z 2i ,...,z Ni The worst-case defect size in the neighborhood is determined. Then, each step progressively reduces the worst-case defect size, and each step is performed iteratively until certain termination conditions are met. This process leads to an optimal reduction in the worst-case defect size.

[0244] Another way to minimize the worst defect is to adjust the weights w in each iteration.p For example, after the i-th iteration, if the r-th evaluation point is the worst defect, then w can be increased in the (i+1)-th iteration. r This gives higher priority to reducing the size of defects at the evaluation points.

[0245] Alternatively, the cost functions in Equations 4 and 5 can be modified by introducing Lagrange multipliers to achieve a trade-off between optimizing the RMS of defect size and optimizing the worst-case defect size.

[0246]

[0247] Here, λ is a preset constant specifying the trade-off between optimizing the RMS of the defect size and optimizing the worst-case defect size. Specifically, if λ = 0, the equation becomes Equation 4, minimizing only the RMS of the defect size; if λ = 1, the equation becomes Equation 5, minimizing only the worst-case defect size; if 0 < λ < 1, both cases are considered in the optimization. This optimization can be solved using various methods. For example, similar to the previously described method, the weights in each iteration can be adjusted. Alternatively, similar to minimizing the worst-case defect size from inequalities, the inequalities in Equations 6' and 6" can be viewed as constraints on the design variables during the solution of the quadratic programming problem. Then, the bounds on the worst-case defect size can be incrementally relaxed, or the weights for the worst-case defect size can be incrementally increased, the cost function value for each achievable worst-case defect size can be calculated, and the design variable value that minimizes the overall cost function can be selected as the initial point for the next step. By performing this operation iteratively, the minimization of this new cost function can be achieved.

[0248] Optimizing photolithography projection equipment can extend the process window. A larger process window provides greater flexibility in process and chip design. A process window can be defined as a set of focal length and dose values ​​that keep the resist image within certain limits of the design goals for the resist image. It should be noted that all the methods discussed herein can also be extended to a generalized process window definition that can be established by different or additional basis parameters besides exposure dose and defocus. These basis parameters can include (but are not limited to) optical settings such as NA, mean square deviation, aberrations, polarization, or optical constants of the resist layer. For example, as previously described, if the PW also consists of different mask deviations, 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 deviation. The process window defined for focal length and dose values ​​is used only as an example in this disclosure. A method for maximizing the process window according to the example is described below.

[0249] In the first step, starting from the known conditions (f0, ε0) in the process window (where f0 is the nominal focal length and ε0 is the nominal dose), minimize one of the cost functions below in the neighborhood (f0 ± Δf, ε0 ± Δε):

[0250]

[0251] or

[0252]

[0253] or

[0254]

[0255] If the nominal focal length f0 and nominal dose ε0 are allowed to shift, they can be used with the design variables (z1, z2, ..., z). N Joint optimization. In the next step, if we can find (z1, z2, ..., z...) N If the set of values ​​of f, ε is given, then (f0±Δf, ε0±Δε) is accepted as part of the process window, so that the cost function is within the preset limit.

[0256] Alternatively, if shifts in focal length and dose are not permitted, the design variables (z1, z2, ..., z) are optimized while keeping the focal length and dose fixed at the nominal focal length f0 and nominal dose ε0, respectively. N In an alternative embodiment, if (z1, z2, ..., z) can be found... N If the set of values ​​of ) is given, then (f0±Δf, ε0±Δε) is accepted as part of the process window, so that the cost function is within the preset limit.

[0257] The methods described above can be used to minimize the corresponding cost functions of equations 7, 7', or 7"". If the design variables are characteristics of the projection optics, such as Zernike coefficients, minimizing the cost function of equations 7, 7', or 7" leads to maximization of the process window based on projection optics optimization (i.e., LO). If the design variables are characteristics of the source and patterning apparatus other than the characteristics of the projection optics, minimizing the cost function of equations 7, 7', or 7" leads to maximization of the process window based on SMLO, such as... Figure 19 As illustrated in the figure. If the design variables are characteristics of the source and pattern forming apparatus, minimizing the cost function of Equations 7, 7', or 7" will result in maximization of the SMO-based process window. The cost function of Equations 7, 7', or 7" may also include at least one f p (z1,z2,...,z N ), such as f in equation 7 or equation 8 p (z1,z2,...,zN This is a function of one or more random effects, such as LWR or local CD variations in 2D features and production output.

[0258] Figure 21 This illustrates a specific example of how the Gauss-Newton algorithm can be used for optimization in a simultaneous SMLO process. In step S702, initial values ​​for the design variables are identified. Tuning ranges for each variable may also be identified. In step S704, a cost function is defined using the design variables. In step S706, the cost function is expanded around the initial values ​​for all evaluation points in the design layout. In an optional step S710, a full-chip simulation is performed to cover all critical patterns in the full-chip design layout. In step S714, desired lithographic response metrics (such as CD or EPE) are obtained, and in step S712, the desired lithographic response metrics are compared with the predicted values ​​of those metrics. In step S716, a process window is determined. Steps S718, S720, and S722 are similar to those described above. Figure 20A The corresponding steps S514, S516, and S518 are described. 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.

[0259] Figure 20B An exemplary method for optimizing the cost function is shown, wherein the design variables (z1, z2, ..., z) N This includes design variables that can take only discrete values.

[0260] The method begins by defining pixel groups of the irradiation source and pattern blocks of the pattern forming apparatus (step S802). Typically, pixel groups or pattern blocks of the pattern forming apparatus can also be referred to as divisions of photolithography process components. In an exemplary method, the irradiation source is divided into 117 pixel groups, and 94 pattern blocks of the pattern forming apparatus are defined for the pattern forming apparatus (generally as described above), resulting in a total of 211 divisions.

[0261] In step S804, a lithography model is selected as the basis for lithography simulation. The lithography simulation produces results for calculating lithography parameters or responses. Specific lithography parameters are defined as performance parameters to be optimized (step S806). In step S808, initial (pre-optimized) conditions are set for the illumination source and the pattern forming apparatus. The initial conditions include the initial states of the pixel group of the illumination source and the pattern blocks of the pattern forming apparatus, such that the initial illumination shape and the initial pattern forming apparatus pattern can be referenced. The initial conditions may also include mask deviation, NA, and focus ramp range (or focus gradient range). Although steps S802, S804, S806, and S808 are depicted as consecutive steps, it should be understood that in other embodiments of the invention, these steps may be performed in a different order.

[0262] In step S810, the pixel groups and pattern blocks of the pattern forming apparatus are sorted. The pixel groups and pattern blocks can be staggered during sorting. Various sorting methods can be used, including: sequentially (e.g., from pixel group 1 to pixel group 117 and from pattern block 1 to pattern block 94), randomly, according to the physical location of the pixel groups and pattern blocks (e.g., sorting pixel groups closer to the center of the illumination source higher), and according to how changes to the pixel groups or pattern blocks affect performance indicators.

[0263] Once the pixel groups and pattern forming apparatus pattern blocks are sorted, the illumination source and pattern forming apparatus are adjusted to improve performance metrics (step S812). In step S812, each of the pixel groups and pattern forming apparatus pattern blocks is analyzed in sorting order to determine whether a change in the pixel group or pattern forming apparatus pattern block will result in improved performance metrics. If it is determined that the performance metrics will be improved, the pixel group or pattern forming apparatus pattern block is changed accordingly, and the resulting improved performance metrics and the modified illumination shape or modified pattern forming apparatus pattern form a baseline for comparison in subsequent analysis of lower-ranked pixel groups and pattern forming apparatus pattern blocks. In other words, the change to improve performance metrics is maintained. As the changes to the state of the pixel groups and pattern forming apparatus pattern blocks are made and maintained, the initial illumination shape and the initial pattern forming apparatus pattern are changed accordingly, such that the modified illumination shape and the modified pattern forming apparatus pattern are caused by the optimization process in step S812.

[0264] In other methods, the polygon shape adjustment and pairwise polling of the pattern forming apparatus polygons of the pixel group and / or pattern forming apparatus pattern blocks are also performed within the optimization process of S812.

[0265] In an alternative embodiment, the staggered simultaneous optimization process may include changing the pixel group of the irradiation source and, if an improvement in performance is observed, gradually increasing and decreasing the dose to seek further improvement. In another alternative, the gradual increase and decrease of dose or intensity may be replaced by changes in the pattern of the pattern forming apparatus to seek further improvement in the simultaneous optimization process.

[0266] In step S814, it is determined whether the performance metric has converged. For example, if little or no improvement in the performance metric has been observed in the last few iterations of steps S810 and S812, the performance metric can be considered converged. If the performance metric has not yet converged, steps S810 and S812 are repeated in the next iteration, wherein the modified irradiation shape and modified pattern forming apparatus from the current iteration are used as the initial irradiation shape and initial pattern forming apparatus for the next iteration (step S816).

[0267] The optimization methods described above can be used to increase the production volume of photolithography projection equipment. For example, the cost function can include f as a function of exposure time. p (z1,z2,...,z N The optimization of this cost function is preferably constrained or influenced by the measurement of random effects or other indicators. Specifically, a computer-based method for increasing the productivity of the lithography process may include optimizing a cost function that is a function of one or more random effects of the lithography process and a function of the substrate exposure time, in order to minimize the exposure time.

[0268] In one embodiment, the cost function includes at least one f, which is a function of one or more random effects. p (z1,z2,...,z N Random effects can include feature failures, such as in Figure 3A The method identifies measurement data (e.g., SEPE), LWR of 2D features, or local CD variations. In one embodiment, random effects include random variations in the characteristics of the resist image. For example, these random variations may include the failure rate of characteristics, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU). Including random variations in the cost function allows finding values ​​for design variables that minimize random variations, thereby reducing the risk of defects due to random effects.

[0269] Figure 22The block diagram illustrating computer system 100 is intended to assist in executing the optimization methods and processes disclosed herein. Computer system 100 includes: a bus 102 or other communication mechanism for information communication; and a processor 104 (or multiple processors 104 and 105) connected to the bus 102 for processing information. Computer system 100 also includes main memory 106 (such as random access memory (RAM) or other dynamic storage device), connected to the bus 102 for storing information and instructions executed by processor 104. Main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions executed by processor 104. Computer system 100 also includes a read-only memory (ROM) 108 or other static storage device connected to the bus 102 for storing static information and instructions for processor 104. Storage device 110 (such as a magnetic disk or optical disk) is provided and connected to the bus 102 for storing information and instructions.

[0270] Computer system 100 can be connected to display 112 (such as a cathode ray tube (CRT) or flat panel or touch panel display) via bus 102 for displaying information to the computer user. Input device 114 (including alphanumeric keys and other keys) is connected to bus 102 for communicating information and command selections with processor 104. Another type of user input device is cursor controller 116 (such as a mouse, trackball, or arrow keys) for communicating directional information and command selections with processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), which allows the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

[0271] According to one embodiment of the invention, a portion of the optimization process may be executed by a processor 104 of a computer system 100 in response to a sequence or more of instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the method steps described herein. In a multiprocessor arrangement, one or more processors may also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0272] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires comprising bus 102. Transmission media can also take the form of sound waves 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, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tapes, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or tapes, carrier waves as described below, or any other media that a computer can read.

[0273] Various forms of computer-readable media may involve transmitting one or more sequences of instructions to processor 104 for execution. For example, the instructions may initially appear on the disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit the instructions over a telephone line using a modem. A modem local to computer system 100 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 transmits the data to main memory 106, from which processor 104 fetches and executes instructions. Instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0274] Computer system 100 may also preferably include a communication interface 118 connected to bus 102. Communication interface 118 provides bidirectional data communication to network link 120, which is connected to local network 122. For example, communication interface 118 may be an Integrated Services Digital Network (ISDN) card or a modem for providing data communication connectivity to a corresponding type of telephone line. As another example, communication interface 118 may be a Local Area Network (LAN) card for providing data communication connectivity to a compatible LAN. A wireless link may also be implemented. In any such implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0275] Typically, network link 120 provides data communication to other data devices via one or more networks. For example, network link 120 may provide connection to host 124 or data devices operated by network service provider (ISP) 126 via local network 122. ISP 126, in turn, provides data communication services via global packet data communication network (now commonly referred to as the "Internet") 128. Both local network 122 and Internet 128 use electrical, electromagnetic, or optical signals carrying digital data streams. The transmission of digital data to and from computer system 100 via signals from various networks and on network link 120 and via communication interface 118 is an exemplary form of carrier wave for transporting information.

[0276] Computer system 100 can send and receive information, including program code, via a network, network link 120, and communication interface 118. In the example of the Internet, server 130 can send request codes for applications via the Internet 128, ISP 126, local area network 122, and communication interface 118. Such a downloaded application can provide illumination optimization for, for example, the embodiments described. The received code can be executed by processor 104 when it is received and / or stored in storage device 110 or other non-volatile storage for subsequent execution. Thus, computer system 100 can obtain application codes in carrier form.

[0277] Figure 23 An exemplary photolithography projection apparatus (LA) is schematically described, wherein the illumination source can be optimized using the methods described herein. The apparatus includes:

[0278] - Irradiation system IL, which is used to modulate the radiation beam B. In this particular case, the irradiation system also includes a radiation source SO;

[0279] - A first stage (e.g., a mask stage) MT, the first stage being provided with a pattern forming apparatus holder for holding a pattern forming apparatus MA (e.g., a mask), and connected to a first positioner for accurately positioning the pattern forming apparatus relative to an apparatus PS;

[0280] - Second stage (substrate stage) WT, the second stage is provided with a substrate holder for holding the substrate W (e.g., a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the device PS;

[0281] - A projection system (“lens”) PS (e.g., a refractive, reflective, or reflective-refractive optical system) for imaging an illuminated portion of the pattern forming apparatus MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0282] As depicted in this invention, the device is of the transmissive type (i.e., having a transmissive mask). However, it can also typically be of the reflective type, for example (having a reflective mask). Alternatively, the device can be used as an alternative to using a classic mask to employ another class of pattern forming apparatus; examples include programmable mirror arrays or LCD matrices.

[0283] A source SO (e.g., a mercury lamp or excimer laser) generates a radiation beam. This beam is fed, for example, directly or after passing through an adjustment member such as a beam expander Ex into an irradiation system (irradiator) IL. The irradiator IL may include an adjustment member AD for setting the outer radial range and / or inner radial range (typically referred to as σ_outer and σ_inner, respectively) of the intensity distribution in the beam. Additionally, the irradiator IL typically includes various other components, such as an integrator IN and a concentrator CO. Thus, the beam B irradiating the pattern forming apparatus MA has the desired uniformity and intensity distribution in its cross-section.

[0284] about Figure 23 It should be noted that the source SO can be inside the housing of the photolithography projection device (which is usually the case when the source SO is, for example, a mercury lamp), but it can also be located away from the photolithography projection device, with the radiation beam it generates being guided into the device (e.g., by means of a suitable guiding mirror); the latter case is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF, or F2 laser action).

[0285] The beam PB then intercepts the pattern forming apparatus MA held on the pattern forming apparatus stage MT. Having traversed the pattern forming apparatus MA, the beam B is passed through the lens PL, which focuses the beam B onto the target portion C of the substrate W. The substrate stage WT can be accurately moved, for example, to position the different target portions C within the path of the beam PB, by means of a second positioning member (and an interferometry member IF). Similarly, the first positioning member can be used to accurately position the pattern forming apparatus MA relative to the path of the beam B, for example, after it has been mechanically acquired from the pattern forming apparatus library or during scanning. Typically, this will be achieved by means of... Figure 23 The long-stroke module (coarse positioning) and short-stroke module (fine positioning) are clearly described in the text to realize the movement of the stage MT and WT. However, in the case of a wafer stepper (as opposed to a stepping scanning tool), the pattern forming apparatus stage MT may only be connected to the short-stroke actuator, or it may be fixed.

[0286] The depicted tools can be used in two different modes:

[0287] - In step mode, the pattern forming apparatus stage MT is kept substantially stationary, and the entire pattern forming apparatus image is projected (i.e., a single "flash") onto the target portion C. The substrate stage WT is then shifted in the x and / or y directions so that different target portions C can be illuminated by the beam PB;

[0288] In scanning mode, the same principle applies, but the given target portion C is not exposed in a single "flash." Instead, the pattern forming apparatus stage MT moves at a speed v in a given direction (the so-called "scanning direction," such as the y-direction), causing the projection beam B to scan the pattern forming apparatus image; simultaneously, the substrate stage WT moves simultaneously in the same or opposite directions at a speed V = Mv, where M is the magnification of the lens PL (typically M = 1 / 4 or 1 / 5). This allows for the exposure of a relatively large target portion C without compromising resolution.

[0289] Figure 24 Another exemplary photolithography projection device LA is schematically depicted, whose illumination source can be optimized using the methods described herein.

[0290] Photolithography projection equipment (LA) includes:

[0291] -Source collector module SO;

[0292] - Irradiation system (irradiator) IL, the irradiation system being configured to modulate the radiation beam B (e.g., EUV radiation);

[0293] - A support structure (e.g., a mask stage) MT, the support structure being configured to support a pattern forming apparatus (e.g., a mask or a mask plate) MA and connected to a first positioning device PM configured for precisely positioning the pattern forming apparatus;

[0294] - A substrate stage (e.g., a wafer stage) WT, the substrate stage being configured to hold a substrate (e.g., a wafer coated with resist) W and connected to a second positioning device PW configured for precise positioning of the substrate; and

[0295] - A projection system (e.g., a reflective projection system) PS, the projection system PS being configured to project a pattern given by a radiation beam B by a pattern forming apparatus MA onto a target portion C (e.g., comprising one or more dies) of a substrate W.

[0296] As shown here, the device LA is reflective (e.g., employing a reflective mask). It should be noted that since most materials are absorbent in the EUV wavelength range, the mask can have multiple layers of reflectors, including, for example, multiple stacks of molybdenum and silicon. In one example, the multi-layer reflector has 40 pairs of molybdenum and silicon layers, each layer being a quarter wavelength thick. Even smaller wavelengths can be produced using X-ray lithography. Because most materials are absorbent in both EUV and X-ray wavelengths, the thin sheets of absorbent material patterned on the morphology of the patterning apparatus (e.g., a TaN absorber on top of a multi-layer reflector) define the areas where features will be printed (positive resist) or not printed (negative resist).

[0297] Reference Figure 24 The irradiator IL receives an extreme ultraviolet (EUV) radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state, the material having at least one element with one or more emission lines in the EUV range, such as xenon, lithium, or tin. In one such method, commonly referred to as laser-generated plasma (“LPP”), the desired plasma can be generated by irradiating a fuel, such as a droplet, beam, or cluster of a material having an emission line element, using a laser beam. Figure 24 (Not shown) is part of an EUV radiation system. The resulting plasma emits output radiation, such as EUV radiation, which is collected by a radiation collector disposed in a source collector module. The laser and the source collector module can be separate entities, for example, when a CO2 laser is used to provide a laser beam for fuel excitation.

[0298] In this case, the laser is not considered part of the photolithography apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable directional mirrors and / or beam expanders. In other cases, the source may be part of the source collector module, for example when the source is a discharge-generated plasma EUV generator, commonly referred to as a DPP source.

[0299] The irradiator IL may include a modulator for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial ranges of the intensity distribution in the pupil plane of the irradiator (generally referred to as σ-outer and σ-inner, respectively) can be adjusted. Furthermore, the irradiator IL may include various other components, such as faceted field mirror devices and faceted pupil mirror devices. The irradiator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0300] The radiation beam B is incident on the pattern forming apparatus (e.g., mask) MA held on a support structure (e.g., mask stage) MT, and a pattern is formed by the pattern forming apparatus. After being reflected by the pattern forming apparatus (e.g., mask) MA, the radiation beam B is focused onto a target portion C of the substrate W by a projection system PS. With the aid of a second positioning device PW and a position sensor system PS2 (e.g., an interferometer, a linear encoder, or a capacitive sensor), the substrate stage WT can be precisely moved, for example, to position different target portions C in the path of the radiation beam B. Similarly, the first positioning device PM and another position sensor system PS1 can be used to precisely position the pattern forming apparatus (e.g., mask) MA relative to the path of the radiation beam B. Pattern shape alignment marks M1, M2 and substrate alignment marks P1, P2 can be used to align the pattern forming apparatus (e.g., mask) MA and the substrate W.

[0301] The depicted device LA can be used in at least one of the following modes:

[0302] 1. In step mode, while keeping the support structure (e.g., mask stage) MT and substrate stage WT substantially stationary, the entire pattern imparting the radiation beam is projected onto the target portion C in one pass (i.e., single static exposure). The substrate stage WT is then moved along the X and / or Y directions, allowing exposure of different target portions C.

[0303] 2. In the scanning mode, while the support structure (e.g., mask stage) MT and the substrate stage WT are scanned synchronously, a pattern imparting the radiation beam is projected onto the target portion C (i.e., single dynamic exposure). The velocity and direction of the substrate stage WT relative to the support structure (e.g., mask stage) MT can be determined by the (reduced) magnification and image inversion features of the projection system PS.

[0304] 3. In another mode, the support structure (e.g., mask stage) MT used to hold the programmable patterning apparatus is kept substantially stationary, and the pattern imparted by the radiation beam is projected onto the target portion C while the substrate stage WT is moved or scanned. In this mode, a pulsed radiation source is typically used, and the programmable patterning apparatus is updated as needed after each movement of the substrate stage WT or between consecutive radiation pulses during scanning. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning apparatus (e.g., a programmable mirror array of the type described above).

[0305] Figure 25The apparatus LA is shown in more detail, including a source collector module SO, an irradiation system IL, and a projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment is maintained within the enclosing structure 220 of the source collector module SO. A plasma 210 for emitting EUV radiation can be formed by generating a plasma source through a discharge. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein an extremely high-temperature plasma 210 is formed to emit radiation in the EUV range of the electromagnetic radiation spectrum. The extremely high-temperature plasma 210 is formed, for example, by a discharge that causes at least partial ionization of the plasma. For example, efficient radiation generation may require a partial pressure of 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor. In one embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0306] Radiation emitted by the high-temperature plasma 210 is transferred from the source cavity 211 to the collector cavity 212 via a gas barrier or contaminant trap 230 (in some cases referred to as a contaminant barrier or vane trap) optionally positioned within or behind an opening in the source cavity 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further shown herein includes at least a channel structure, as known in the prior art.

[0307] Collector cavity 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation passing through the collector CO may be reflected off the grating spectral filter 240 to be focused along the optical axis indicated by the dashed line 'O' onto a virtual source point IF. The virtual source point IF is commonly 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 surrounding structure 220. The virtual source point IF is an image of the plasma 210 used for emitting radiation.

[0308] The radiation then passes through an illumination system IL, which may include a faceted field mirror assembly 22 and a faceted pupil mirror assembly 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning apparatus MA and a desired uniformity of radiation intensity at the patterning apparatus MA. As the radiation beam 21 is reflected at the patterning apparatus MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged via a projection system PS onto a substrate W held by a substrate stage WT through reflective elements 28 and 30.

[0309] The illumination optical unit IL and projection system PS can typically contain more components than those shown in the figure. The grating spectral filter 240 can be optionally provided, depending on the type of photolithography equipment. Furthermore, more mirrors than are shown in the figure, for example, in the projection system PS. Figure 25 In addition to the element shown, there are 1-6 additional reflective elements.

[0310] Collector optical device CO, such as Figure 25 As shown in the figure, a nested collector with grazing incidence reflectors 253, 254, and 255 is presented only as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are arranged symmetrically about the optical axis O. This type of collector optics CO is preferably used in conjunction with a plasma source generated by discharge, commonly referred to as a DPP source.

[0311] Alternatively, the source collector module SO can be as follows: Figure 26 This is part of the LPP radiation system shown. A laser LA is arranged to incident laser energy onto a fuel, such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of tens of eV. High-energy radiation generated during the deexcitation and recombination of these ions is emitted by the plasma, collected by a near-normal incident collector optics CO, and focused onto an opening 221 surrounding the structure 220.

[0312] The concepts disclosed herein can be used to model or mathematically model any general imaging system for enabling subwavelength characteristic imaging, and may be particularly useful with the advent of imaging techniques capable of generating increasingly shorter wavelengths. Existing techniques already in use include EUV (Extreme Ultraviolet) lithography, which can generate wavelengths of 193 nm using ArF lasers, and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate wavelengths in the 20–5 nm range by using synchrotrons or by bombarding materials (solid-state or plasma) with high-energy electrons, thus generating photons within this range.

[0313] While the concepts disclosed herein can be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of lithography imaging system, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0314] The embodiments can be further described using the following aspects:

[0315] 1. A method for determining the likelihood that auxiliary features of a mask pattern will be printed on a substrate, the method comprising:

[0316] Obtain (i) multiple images of a pattern printed on a substrate, and (ii) variance data associated with the pixels of the multiple images of the pattern, the images being formed using the mask pattern;

[0317] Based on the variance data, a model configured to generate variance data associated with the mask pattern is determined; and

[0318] Based on variance data generated from a model for a given mask pattern, and a resist image or etched image associated with the given mask pattern, the likelihood that an auxiliary feature of the given mask pattern will be printed on the substrate is determined. This likelihood is applied to adjust one or more parameters associated with the patterning process or patterning apparatus to reduce the likelihood that the auxiliary feature will be printed on the substrate.

[0319] 2. The method according to aspect 1, wherein obtaining the plurality of images comprises:

[0320] The plurality of images of the pattern printed on the substrate are received via a measuring tool; or

[0321] The plurality of images of the pattern printed on the substrate are captured via the measurement tool.

[0322] 3. The method according to aspect 1, wherein:

[0323] The variance data is represented as another pixelated image, where each pixel is assigned the variance value of the grayscale value of each pixel in the plurality of images.

[0324] 4. The method according to any one of aspects 1 to 3, wherein determining the model comprises:

[0325] Input (i) the spatial image or mask image associated with the mask pattern, and (ii) the variance data associated with the mask pattern into the model;

[0326] The model is executed using the initial values ​​of the model parameters to generate initial variance data;

[0327] Determine the difference between the initial variance data and the input variance data; and

[0328] The initial values ​​of the model parameters are adjusted based on the difference so that the model produces variance data within a specified threshold of the input variance data.

[0329] 5. The method according to aspect 4, wherein determining the model is an iterative process, wherein the adjustment of the values ​​of the model parameters is performed until the variance data generated by the model is within the specified threshold of the input variance data.

[0330] 6. The method according to aspect 5, wherein the adjustment of the initial values ​​of the model parameters is based on the gradient of the difference between the output variance mapping and the input variance, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

[0331] 7. The method according to any one of aspects 1 to 6, wherein the model is at least one of the following:

[0332] A convolutional neural network, comprising weights and biases as model parameters.

[0333] A linear model, comprising a combination of correlation coefficients of linear terms, wherein the coefficients are model parameters, and

[0334] A polynomial model, wherein the polynomial model comprises a combination of correlation coefficients of polynomial terms, and the coefficients are the model parameters.

[0335] 8. The method according to any one of aspects 1 to 7, wherein determining the probability that the auxiliary feature of the given mask pattern will be printed on the substrate includes:

[0336] The resist image associated with the given mask pattern is obtained through patterning process simulation or measurement tools;

[0337] Establish the correlation between the variance data generated by the model and the resist image; and

[0338] Based on the correlation, identify areas of the mask pattern that have a relatively high probability of having the auxiliary features printed on the substrate, or target layouts corresponding to the mask pattern.

[0339] 9. The method according to aspect 8, wherein the correlation between the variance data generated by establishing the model and the resist image includes:

[0340] Identify the intensity value along a selected line on the resist image from the resist image;

[0341] Identify the variance value corresponding to the selected line from the variance data generated by the model; and

[0342] The identified variance value is correlated with the identified intensity value of the resist image along the selected line.

[0343] 10. The method according to aspect 9, wherein identifying the region having a relatively high probability that the auxiliary feature is printed on the substrate comprises:

[0344] For one or more regions of the resist image, determine whether the intensity value exceeds a printing threshold associated with the printing of features within the resist layer on the substrate;

[0345] Based on the correlation, determine whether the variance value corresponding to the one or more regions exceeds a specified variance threshold range;

[0346] In response to exceeding the specified variance threshold range, a relatively higher printing probability is assigned to a portion of the one or more regions;

[0347] In response to exceeding the specified variance threshold range or not exceeding the printing threshold, a relatively lower printing probability is assigned to a portion of the one or more zones;

[0348] In response to not exceeding the specified variance threshold range and not exceeding the printing threshold, a zero printing probability is assigned to a portion of the one or more zones; and

[0349] Identify regions with a printing probability greater than zero from the one or more regions, said regions being located around the main pattern of the mask pattern.

[0350] 11. The method according to aspect 10, wherein the printing threshold includes:

[0351] Upper threshold, the upper threshold indicator feature being printed within the resist layer, and

[0352] A lower threshold, which indicates that the feature has not been printed on the resist layer.

[0353] 12. The method according to aspect 11, wherein values ​​within the specified variance threshold range indicate that the feature is not printed, and values ​​outside the specified variance threshold range indicate that the feature is printed.

[0354] 13. The method according to any one of aspects 1 to 12, further comprising:

[0355] Based on the model and the possibility of printing the auxiliary features, optical proximity correction (OPC) data is generated to adjust one or more main features or one or more auxiliary features of the mask pattern.

[0356] 14. The method according to aspect 13, wherein generating the OPC data comprises:

[0357] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via an OPC simulation process associated with the patterning process. The adjusted shape and / or size reduces the likelihood that the auxiliary features will be printed onto the substrate; or

[0358] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process associated with the patterning process.

[0359] 15. The method according to any one of aspects 1 to 12, further comprising:

[0360] Based on the model and the probability that the auxiliary feature will be printed, a source and / or mask pattern is determined to reduce the probability that the auxiliary feature will be printed.

[0361] 16. The method according to aspect 15, wherein determining the source and / or the mask pattern comprises:

[0362] The source parameters and / or mask parameters are adjusted via a source mask optimization (SMO) process to reduce the likelihood that the auxiliary features of the mask pattern will be printed.

[0363] 17. The method according to any one of aspects 1 to 12, further comprising:

[0364] Based on the model and the possibility of printing using the auxiliary features, one or more parameters of the patterning process used to pattern the substrate are adjusted.

[0365] 18. The method according to any one of aspects 17, wherein adjusting the one or more parameters of the patterning process comprises:

[0366] Using a mask image or spatial image of a pattern printed on the substrate as input to the model, the likelihood that auxiliary features will be printed on the substrate is determined; and

[0367] Adjust one or more parameters of the patterning process to reduce the likelihood that the auxiliary features will be printed on the substrate.

[0368] 19. The method according to aspect 18, wherein the one or more parameters include: the scanner dose, the scanner focus, and / or the substrate stage height.

[0369] 20. A method for generating a model associated with a mask pattern, the method comprising:

[0370] Obtain (i) multiple images of a pattern printed on a substrate using the mask pattern, and (iii) variance data associated with each pixel of the multiple images of the pattern; and

[0371] A model is generated based on the variance data, configured to predict variance data associated with the mask pattern, the variance data being used to determine the likelihood that auxiliary features of the mask pattern will be printed on the substrate.

[0372] 21. The method according to aspect 20, wherein generating the model comprises:

[0373] Input (i) the spatial image or mask image associated with the mask pattern, and (ii) the variance data associated with the mask pattern into the model;

[0374] The model is executed using the initial values ​​of the model parameters to generate initial variance data;

[0375] Determine the difference between the initial variance data and the input variance data; and

[0376] The initial values ​​of the model parameters are adjusted based on the difference so that the model produces variance data within a specified threshold of the input variance data.

[0377] 22. The method according to aspect 21, wherein generating the model is an iterative process, wherein the adjustment of the values ​​of the model parameters is performed until the variance data generated by the model is within the specified threshold of the input variance data.

[0378] 23. The method according to aspect 22, wherein the adjustment of the initial values ​​of the model parameters is based on the gradient of the difference between the output variance mapping and the input variance, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

[0379] 24. The method according to any one of aspects 20 to 23, wherein:

[0380] The variance data is represented as another pixelated image, where each pixel is assigned the variance value of the grayscale value of each pixel in the plurality of images.

[0381] 25. The method according to any one of aspects 20 to 24, wherein the model is at least one of the following:

[0382] A convolutional neural network, comprising weights and biases as model parameters.

[0383] A linear model, comprising a combination of correlation coefficients of linear terms, wherein the coefficients are model parameters, and

[0384] A polynomial model, wherein the polynomial model comprises a combination of correlation coefficients of polynomial terms, and the coefficients are the model parameters.

[0385] 26. A method for generating optical proximity correction data for a mask pattern, the method comprising:

[0386] Obtain (i) a mask image or spatial image associated with the mask pattern, and (ii) a resist image associated with the mask pattern;

[0387] Execute a model configured to predict variance data associated with the mask pattern, the model using the mask image or the spatial image to predict the variance data;

[0388] The probability that auxiliary features of the mask pattern will be printed on the substrate is determined based on the variance data and the resist image; and

[0389] Based on the possibility of printing the auxiliary features, optical proximity correction (OPC) data is generated for modifying one or more main features or one or more auxiliary features of the mask pattern.

[0390] 27. The method according to aspect 26, wherein generating the OPC data comprises:

[0391] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via an OPC simulation process. The adjusted shape and / or size reduces the likelihood that the auxiliary features will be printed.

[0392] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process.

[0393] 28. The method according to any one of aspects 26 to 27, wherein obtaining the mask image or the spatial image comprises:

[0394] The mask pattern is used to simulate one or more process models to generate the mask image or the spatial image.

[0395] 29. The method according to any one of aspects 26 to 28, wherein the OPC data is used by a pattern forming apparatus modification tool to modify the mask pattern on the mask.

[0396] 30. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause operations including:

[0397] Obtain (i) multiple images of a pattern printed on a substrate, the images having been formed using a mask pattern, and (ii) variance data associated with the pixels of the multiple images of the pattern;

[0398] Based on the variance data, a model configured to generate variance data associated with the mask pattern is determined; and

[0399] Based on variance data generated from a model for a given mask pattern, and a resist image or etched image associated with the given mask pattern, the likelihood that an auxiliary feature of the given mask pattern will be printed on the substrate is determined. This likelihood is applied to adjust one or more parameters associated with the patterning process or patterning apparatus to reduce the likelihood that the auxiliary feature will be printed on the substrate.

[0400] 31. The non-transitory computer-readable medium according to aspect 30, wherein obtaining the plurality of images comprises:

[0401] The plurality of images of the pattern printed on the substrate are received via a measuring tool; or the plurality of images of the pattern printed on the substrate are captured via the measuring tool.

[0402] 32. The non-transitory computer-readable medium according to aspect 30, wherein:

[0403] The variance data is represented as another pixelated image, where each pixel is assigned the variance value of the grayscale value of each pixel in the plurality of images.

[0404] 33. The non-transitory computer-readable medium according to any one of aspects 30 to 32, wherein determining the model comprises:

[0405] Input (i) the spatial image or mask image associated with the mask pattern, and (ii) the variance data associated with the mask pattern into the model;

[0406] The model is executed using the initial values ​​of the model parameters to generate initial variance data;

[0407] Determine the difference between the initial variance data and the input variance data; and adjust the initial values ​​of the model parameters based on the difference so that the model produces variance data within a specified threshold of the input variance data.

[0408] 34. The non-transitory computer-readable medium according to aspect 32, wherein determining the model is an iterative process, wherein the adjustment of the values ​​of the model parameters is performed until the variance data generated by the model is within the specified threshold of the input variance data.

[0409] 35. The non-transitory computer-readable medium according to aspect 34, wherein the adjustment of the initial values ​​of the model parameters is based on the gradient of the difference between the variance mapping of the output and the variance of the input, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

[0410] 36. The non-transitory computer-readable medium according to any one of aspects 30 to 35, wherein the model is at least one of the following:

[0411] A convolutional neural network, comprising weights and biases as model parameters.

[0412] A linear model, comprising a combination of correlation coefficients of linear terms, wherein the coefficients are model parameters, and

[0413] A polynomial model, wherein the polynomial model comprises a combination of correlation coefficients of polynomial terms, and the coefficients are the model parameters.

[0414] 37. The non-transitory computer-readable medium according to any one of aspects 30 to 36, wherein the possibility of determining that the auxiliary feature of the given mask pattern will be printed on the substrate includes:

[0415] The resist image associated with the given mask pattern is obtained through patterning process simulation or measurement tools;

[0416] Establish the correlation between the variance data generated by the model and the resist image; and

[0417] Based on the correlation, identify areas of the mask pattern that have a relatively high probability of having the auxiliary features printed on the substrate, or target layouts corresponding to the mask pattern.

[0418] 38. The non-transitory computer-readable medium according to aspect 37, wherein the correlation between the variance data generated from establishing the model and the resist image includes:

[0419] Identify the intensity value along a selected line on the resist image from the resist image;

[0420] Identify the variance value corresponding to the selected line from the variance data generated by the model; and

[0421] The identified variance value is correlated with the identified intensity value of the resist image along the selected line.

[0422] 39. The non-transitory computer-readable medium according to aspect 38, wherein identifying the region having a relatively high probability that the auxiliary feature is printed on the substrate comprises:

[0423] For one or more regions of the resist image, determine whether the intensity value exceeds a printing threshold associated with the printing of features within the resist layer on the substrate;

[0424] Based on the correlation, determine whether the variance value corresponding to the one or more regions exceeds a specified variance threshold range;

[0425] In response to exceeding the specified variance threshold range, a relatively higher printing probability is assigned to a portion of the one or more regions;

[0426] In response to exceeding the specified variance threshold range or not exceeding the printing threshold, a relatively lower printing probability is assigned to a portion of the one or more zones;

[0427] In response to not exceeding the specified variance threshold range and not exceeding the printing threshold, a zero printing probability is assigned to a portion of the one or more zones; and

[0428] Identify regions with a printing probability greater than zero from the one or more regions, said regions being located around the main pattern of the mask pattern.

[0429] 40. The non-transitory computer-readable medium according to aspect 39, wherein the printing threshold includes:

[0430] Upper threshold, the upper threshold indicator feature being printed within the resist layer, and

[0431] A lower threshold, which indicates that the feature has not been printed on the resist layer.

[0432] 41. The non-transitory computer-readable medium according to aspect 40, wherein values ​​within the specified variance threshold range indicate that the feature is not printed, and values ​​outside the specified variance threshold range indicate that the feature is printed.

[0433] 42. The non-transitory computer-readable medium according to any one of aspects 30 to 41 further comprises:

[0434] Based on the model and the possibility of printing the auxiliary features, optical proximity correction (OPC) data is generated to adjust one or more main features or one or more auxiliary features of the mask pattern.

[0435] 43. The non-transitory computer-readable medium according to aspect 42, wherein generating the OPC data comprises:

[0436] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via an OPC simulation process associated with the patterning process. The adjusted shape and / or size reduces the likelihood that the auxiliary features will be printed onto the substrate; or

[0437] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process associated with the patterning process.

[0438] 44. The non-transitory computer-readable medium according to any one of aspects 30 to 42 further comprises:

[0439] Based on the model and the probability that the auxiliary feature will be printed, a source and / or mask pattern is determined to reduce the probability that the auxiliary feature will be printed.

[0440] 45. The non-transitory computer-readable medium according to aspect 44, wherein determining the source and / or the mask pattern comprises:

[0441] The source parameters and / or mask parameters are adjusted via a source mask optimization (SMO) process to reduce the likelihood that the auxiliary features of the mask pattern will be printed.

[0442] 46. ​​The non-transitory computer-readable medium according to any one of aspects 30 to 42 further comprises:

[0443] Based on the model and the possibility of printing using the auxiliary features, one or more parameters of the patterning process used to pattern the substrate are adjusted.

[0444] 47. The non-transitory computer-readable medium according to aspect 46, wherein adjusting the one or more parameters of the patterning process includes:

[0445] Using a mask image or spatial image of a pattern printed on the substrate as input to the model, the likelihood that auxiliary features will be printed on the substrate is determined; and

[0446] Adjust one or more parameters of the patterning process to reduce the likelihood that the auxiliary features will be printed on the substrate.

[0447] 48. The non-transitory computer-readable medium according to aspect 47, wherein the one or more parameters include: the dose of the scanner, the focus of the scanner, and / or the substrate stage height.

[0448] 49. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause operations including:

[0449] Obtain (i) multiple images of a pattern printed on a substrate using the mask pattern, and (iii) variance data associated with each pixel of the multiple images of the pattern; and

[0450] A model is generated based on the variance data, configured to predict variance data associated with the mask pattern, the variance data being used to determine the likelihood that auxiliary features of the mask pattern will be printed on the substrate.

[0451] 50. The non-transitory computer-readable medium according to aspect 49, wherein generating the model comprises:

[0452] Input (i) the spatial image or mask image associated with the mask pattern, and (ii) the variance data associated with the mask pattern into the model;

[0453] The model is executed using the initial values ​​of the model parameters to generate initial variance data;

[0454] Determine the difference between the initial variance data and the input variance data; and adjust the initial values ​​of the model parameters based on the difference so that the model produces variance data within a specified threshold of the input variance data.

[0455] 51. The non-transitory computer-readable medium according to aspect 50, wherein generating the model is an iterative process, wherein the adjustment of the values ​​of the model parameters is performed until the variance data generated by the model is within the specified threshold of the input variance data.

[0456] 52. The non-transitory computer-readable medium according to aspect 51, wherein the adjustment of the initial values ​​of the model parameters is based on the gradient of the difference between the variance mapping of the output and the variance of the input, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

[0457] 53. The non-transitory computer-readable medium according to any one of aspects 49 to 52, wherein:

[0458] The variance data is represented as another pixelated image, where each pixel is assigned the variance value of the grayscale value of each pixel in the plurality of images.

[0459] 54. The non-transitory computer-readable medium according to any one of aspects 49 to 53, wherein the model is at least one of the following:

[0460] A convolutional neural network, comprising weights and biases as model parameters.

[0461] A linear model, comprising a combination of correlation coefficients of linear terms, wherein the coefficients are model parameters, and

[0462] A polynomial model, wherein the polynomial model comprises a combination of correlation coefficients of polynomial terms, and the coefficients are the model parameters.

[0463] 55. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause operations including:

[0464] Obtain (i) a mask image or spatial image associated with the mask pattern, and (ii) a resist image associated with the mask pattern;

[0465] Execute a model configured to predict variance data associated with the mask pattern, the model using the mask image or the spatial image to predict the variance data;

[0466] The probability that auxiliary features of the mask pattern will be printed on the substrate is determined based on the variance data and the resist image; and

[0467] Based on the possibility of printing the auxiliary features, optical proximity correction (OPC) data is generated for modifying one or more main features or one or more auxiliary features of the mask pattern.

[0468] 56. The non-transitory computer-readable medium according to aspect 55, wherein generating the OPC data comprises:

[0469] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via an OPC simulation process. The adjusted shape and / or size reduces the likelihood that the auxiliary features will be printed.

[0470] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process.

[0471] 57. The non-transitory computer-readable medium according to any one of aspects 55 to 56, wherein obtaining the mask image or the spatial image comprises:

[0472] The mask pattern is used to simulate one or more process models to generate the mask image or the spatial image.

[0473] 58. The non-transitory computer-readable medium according to any one of aspects 55 to 57, wherein the OPC data is used by a pattern forming apparatus modification tool to modify the mask pattern on the mask.

[0474] 59. A non-transitory computer-readable medium comprising instructions for generating a printable mapping associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including:

[0475] Obtain (i) multiple images of a patterned substrate, (ii) multiple improved images based on the multiple images, and (iii) a simulated improved image based on the mask pattern;

[0476] Each of the plurality of improved images is labeled based on the plurality of improved images, the simulated improved images, and the intensity of pixels within each of the plurality of images; and

[0477] The printability mapping associated with the mask pattern is generated based on the marker.

[0478] 60. The non-transitory computer-readable medium according to aspect 59, wherein the marker for each of the plurality of images comprises:

[0479] Align the improved image of the plurality of improved images with the simulated improved image;

[0480] Identify features within the improved image that correspond to features within the simulated improved image;

[0481] Align the images of the plurality of images with the aligned and improved image; and

[0482] Identifiers are placed on the aligned image based on the identified features, with each identifier placed at a location associated with a local minimum of the intensity within the image surrounding the identified feature.

[0483] 61. The non-transitory computer-readable medium according to aspect 60, wherein placing the identifier comprises:

[0484] Determine the contours of the identified features within the improved image;

[0485] Align the contour with corresponding features in the plurality of images; and

[0486] Identify locations of a pair of markers around the contour, with the first marker located at a local minimum of image intensity inside the contour and the second marker located at another local minimum of image intensity outside the contour.

[0487] 62. The non-transitory computer-readable medium according to aspect 61, wherein identifying the pair of identifiers comprises:

[0488] The first identifier is located at the local minimum of the intensity of the image, in a specified direction, towards the interior of the contour; and

[0489] Oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, the second identifier is determined to be located at another local minimum value of the intensity of the image.

[0490] 63. The non-transitory computer-readable medium according to any one of aspects 59 to 62, wherein generating the printability mapping comprises:

[0491] The labels of the plurality of images are input into an algorithm configured to generate a plurality of other improved images corresponding to each of the plurality of images;

[0492] Align the plurality of other improved images relative to each other; and

[0493] The printability mapping of at least one of the plurality of other improved images is generated based on the intensity values ​​of the aligned plurality of other improved images.

[0494] 64. The non-transitory computer-readable medium according to aspect 63, wherein generating the printability mapping comprises:

[0495] The probability value for each pixel of the printability map is determined by the following operation:

[0496] Summing the image intensities of the other improved images of the plurality of improved images; and

[0497] Divide the summed image intensity by the total number of improved images.

[0498] 65. A non-transitory computer-readable medium according to any one of aspects 62 to 64, wherein the algorithm is a watershed algorithm configured to perform image segmentation based on the identifier placed within the plurality of images.

[0499] 66. The non-transitory computer-readable medium according to any one of aspects 59 to 65, wherein obtaining the plurality of images comprises:

[0500] The plurality of images of the pattern printed on the substrate are received via a measuring tool; or

[0501] The plurality of images of the pattern printed on the substrate are captured via the measurement tool.

[0502] 67. The non-transitory computer-readable medium according to any one of aspects 59 to 66, wherein obtaining the plurality of improved images comprises:

[0503] Denoise the multiple images; and

[0504] Each of the denoised images is transformed into an improved image via an adaptive thresholding algorithm, which adaptively finds the optimal threshold to distinguish between printed and unprinted regions within the image.

[0505] 68. The non-transitory computer-readable medium according to aspect 67, wherein the adaptive thresholding algorithm is an Otsu thresholding algorithm configured to receive the plurality of images or the denoised plurality of images and the identifier within each of the plurality of images as input, and output an improved image.

[0506] 69. The non-transitory computer-readable medium according to any one of aspects 66 to 68, wherein the denoising of the plurality of images comprises:

[0507] A first median filter and a Gaussian filter are applied to each of the plurality of images to maintain the ridge edge accuracy associated with each of the plurality of images, wherein the first median filter is characterized by a first kernel size;

[0508] A second median filter is applied to enhance the image contrast of each of the plurality of images, the image contrast being between the printed and unprinted areas. The second median filter is characterized by a second kernel size, which is larger than the first kernel size.

[0509] A third filter is applied to further reduce noise in the plurality of images, the third filter being characterized by a third kernel size.

[0510] 70. The non-transitory computer-readable medium according to any one of aspects 59 to 69, wherein obtaining the simulated improved image comprises:

[0511] One or more process models of the patterning process are performed using the mask pattern and process conditions corresponding to each of the plurality of images to generate the simulated image of the pattern to be printed on a substrate; and

[0512] A selected threshold intensity value is applied to the simulated image to produce the simulated improved image.

[0513] 71. The non-transitory computer-readable medium according to any one of aspects 59 to 70 further includes generating values ​​for one or more parameters of the patterning process based on the printability mapping.

[0514] 72. The non-transitory computer-readable medium according to aspect 71, wherein the generation comprises:

[0515] The printability map associated with the mask pattern is input into the optical proximity correction process;

[0516] The probability associated with an auxiliary feature of the mask pattern is determined from the printability map, the probability indicating whether the auxiliary feature will be printed on the substrate; and

[0517] Optical proximity correction (OPC) data is generated based on the probability of the auxiliary features to adjust one or more main features or one or more auxiliary features of the mask pattern to minimize the probability that the auxiliary features will be printed on the substrate.

[0518] 73. The non-transitory computer-readable medium according to aspect 72, wherein generating the OPC data comprises:

[0519] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via the OPC simulation process associated with the patterning process. The adjusted shape and / or size reduces the probability that the auxiliary features will be printed on the substrate; or

[0520] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process associated with the patterning process.

[0521] 74. The non-transitory computer-readable medium according to aspect 71, wherein the generation comprises:

[0522] Based on the printability mapping, parameters associated with the source and / or mask pattern are determined to reduce the probability that auxiliary features will be printed.

[0523] 75. The non-transitory computer-readable medium according to aspect 74, wherein determining the source and / or the mask pattern comprises:

[0524] The source parameters and / or mask parameters are adjusted via a source mask optimization (SMO) process to reduce the probability that the auxiliary features of the mask pattern will be printed on the substrate.

[0525] 76. The non-transitory computer-readable medium according to aspect 71, wherein the generation comprises:

[0526] Based on the printability mapping, one or more parameters associated with the patterning apparatus used to pattern the substrate are adjusted to reduce the probability that auxiliary features will be printed on the substrate.

[0527] 77. The non-transitory computer-readable medium according to aspect 76, wherein the one or more parameters include: the dose of the scanner, the focus of the scanner, and / or the substrate stage height.

[0528] 78. The non-transitory computer-readable medium according to any one of aspects 59 to 77, wherein one or more of the plurality of improved images is one or more binary images.

[0529] 79. The non-transitory computer-readable medium according to any one of aspects 59 to 78, wherein the simulated improved image is a binary image.

[0530] 80. The non-transitory computer-readable medium according to any one of aspects 59 to 79, wherein the printability mapping is a spatial distribution of probability values ​​indicating the likelihood that features of the pattern will be printed on a substrate.

[0531] 81. The non-transitory computer-readable medium according to any one of aspects 59 to 80, wherein the plurality of images are obtained via scanning electron microscopy (SEM) of a patterned substrate.

[0532] 82. The non-transitory computer-readable medium according to aspect 81, wherein each of the plurality of images is a SEM image.

[0533] 83. A method for generating a printability mapping associated with a mask pattern, the method comprising:

[0534] Obtain (i) multiple images of a patterned substrate, (ii) multiple improved images based on the multiple images, and (iii) a simulated improved image based on the mask pattern;

[0535] Each of the plurality of improved images is labeled based on the plurality of improved images, the simulated improved images, and the intensity of pixels within each of the plurality of images; and

[0536] The printability mapping associated with the mask pattern is generated based on the marker.

[0537] 84. The method according to aspect 83, wherein the marker for each of the plurality of images comprises:

[0538] Align the improved image of the plurality of improved images with the simulated improved image;

[0539] Identify features within the improved image that correspond to features within the simulated improved image;

[0540] Align the images of the plurality of images with the aligned and improved image; and place identifiers on the aligned image based on the identified features, each identifier being placed at a location associated with a local minimum of the intensity within the image surrounding the identified features.

[0541] 85. The method according to aspect 84, wherein placing the identifier comprises:

[0542] Determine the contours of the identified features within the improved image;

[0543] Align the contour with corresponding features in the images of the plurality of images; and identify locations of a pair of markers around the contour, the first marker being located at a local minimum of image intensity inside the contour, and the second marker being located at another local minimum of image intensity outside the contour.

[0544] 86. The method according to aspect 84, wherein identifying the pair of identifiers comprises:

[0545] The first identifier is located at the local minimum of the intensity of the image, in a specified direction, towards the interior of the contour; and

[0546] Oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, the second identifier is determined to be located at another local minimum value of the intensity of the image.

[0547] 87. The method according to any one of aspects 83 to 86, wherein generating the printability map comprises:

[0548] The labels of the plurality of images are input into an algorithm configured to generate a plurality of other improved images corresponding to each of the plurality of images;

[0549] Align the plurality of other improved images relative to each other; and

[0550] The printability mapping of at least one of the plurality of other improved images is generated based on the intensity values ​​of the aligned plurality of other improved images.

[0551] 88. The method according to aspect 63, wherein generating the printability map comprises:

[0552] The probability value for each pixel of the printability map is determined by the following operation:

[0553] Summing the image intensities of the other improved images of the plurality of improved images; and

[0554] Divide the summed image intensity by the total number of improved images.

[0555] 89. The method according to any one of aspects 86 to 88, wherein the algorithm is a watershed algorithm, the watershed algorithm being configured to perform image segmentation based on the identifier placed within the plurality of images.

[0556] 90. The method according to any one of aspects 83 to 89, wherein obtaining the plurality of images comprises:

[0557] The plurality of images of the pattern printed on the substrate are received via a measuring tool; or

[0558] The plurality of images of the pattern printed on the substrate are captured via the measurement tool.

[0559] 91. The method according to any one of aspects 83 to 90, wherein obtaining the plurality of improved images comprises:

[0560] Denoise the multiple images; and

[0561] Each of the denoised images is transformed into an improved image via an adaptive thresholding algorithm, which adaptively finds the optimal threshold to distinguish between printed and unprinted regions within the image.

[0562] 92. The method according to aspect 91, wherein the adaptive thresholding algorithm is an Otsu thresholding algorithm configured to receive the plurality of images or the denoised plurality of images and the identifier within each of the plurality of images as input, and output an improved image.

[0563] 93. The method according to any one of aspects 90 to 92, wherein the denoising of the plurality of images comprises:

[0564] A first median filter and a Gaussian filter are applied to each of the plurality of images to maintain the ridge edge accuracy associated with each of the plurality of images, wherein the first median filter is characterized by a first kernel size;

[0565] A second median filter is applied to enhance the image contrast of each of the plurality of images, the image contrast being between the printed and unprinted areas. The second median filter is characterized by a second kernel size, which is larger than the first kernel size.

[0566] A third filter is applied to further reduce noise in the plurality of images, the third filter being characterized by a third kernel size.

[0567] 94. The method according to any one of aspects 83 to 93, wherein obtaining the simulated improved image comprises:

[0568] One or more process models of the patterning process are performed using the mask pattern and process conditions corresponding to each of the plurality of images to generate the simulated image of the pattern to be printed on a substrate; and

[0569] A selected threshold intensity value is applied to the simulated image to produce the simulated improved image.

[0570] 95. The method according to any one of aspects 83 to 94 further includes generating values ​​for one or more parameters of the patterning process based on the printability mapping.

[0571] 96. The method according to aspect 95, wherein the generation comprises:

[0572] The printability map associated with the mask pattern is input into the optical proximity correction process;

[0573] The probability associated with an auxiliary feature of the mask pattern is determined from the printability map, the probability indicating whether the auxiliary feature will be printed on the substrate; and

[0574] Optical proximity correction (OPC) data is generated based on the probability of the auxiliary features to adjust one or more main features or one or more auxiliary features of the mask pattern to minimize the probability that the auxiliary features will be printed on the substrate.

[0575] 97. The method according to aspect 96, wherein generating the OPC data comprises:

[0576] The shape and / or size of one or more main features, or one or more auxiliary features, of the mask pattern are adjusted via the OPC simulation process associated with the patterning process. The adjusted shape and / or size reduces the probability that the auxiliary features will be printed on the substrate; or

[0577] The one or more auxiliary features of the mask pattern are removed via the OPC simulation process associated with the patterning process.

[0578] 98. The method according to aspect 95, wherein the generation comprises:

[0579] Based on the printability mapping, parameters associated with the source and / or mask pattern are determined to reduce the probability that auxiliary features will be printed.

[0580] 99. The method according to aspect 98, wherein determining the source and / or the mask pattern comprises:

[0581] The source parameters and / or mask parameters are adjusted via a source mask optimization (SMO) process to reduce the probability that the auxiliary features of the mask pattern will be printed on the substrate.

[0582] 100. The method according to aspect 95, wherein the generation comprises:

[0583] Based on the printability mapping, one or more parameters associated with the patterning apparatus used to pattern the substrate are adjusted to reduce the probability that auxiliary features will be printed on the substrate.

[0584] 101. The method according to aspect 100, wherein the one or more parameters include: the dose of the scanner, the focus of the scanner, and / or the substrate stage height.

[0585] 102. The method according to any one of aspects 83 to 101, wherein one or more of the plurality of improved images is one or more binary images.

[0586] 103. The method according to any one of aspects 83 to 102, wherein the simulated improved image is a binary image.

[0587] 104. The method according to any one of aspects 83 to 102, wherein the printability mapping is a spatial distribution of probability values ​​indicating the likelihood that features of the pattern will be printed on a substrate.

[0588] 105. The method according to any one of aspects 83 to 104, wherein the plurality of images are obtained via a scanning electron microscope (SEM) on a patterned substrate.

[0589] 106. The method according to aspect 105, wherein each of the plurality of images is a SEM image.

[0590] 107. A non-transitory computer-readable medium comprising instructions for generating a printable mapping associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including:

[0591] Multiple improved images of a patterned substrate are obtained based on markers of multiple images of a patterned substrate, wherein the marker of each of the multiple images is associated with the intensity of a pixel of each image;

[0592] Sum the image intensities of the plurality of improved images; and

[0593] The summed image intensities are divided by the total number of improved images to produce the printability map associated with the mask pattern.

[0594] 108. The non-transitory computer-readable medium according to aspect 107, wherein obtaining the plurality of improved images comprises:

[0595] The labels of the plurality of images are input into an algorithm configured to generate a plurality of improved images corresponding to each of the plurality of images.

[0596] 109. A non-transitory computer-readable medium according to aspect 108, wherein the algorithm is configured to perform a watershed algorithm for image segmentation based on the identifier placed within the plurality of images.

[0597] 110. The non-transitory computer-readable medium according to aspect 109, wherein the marker for each of the plurality of images comprises:

[0598] Align the binary image of the plurality of images with the simulated improved image;

[0599] Identify features within the binary image that correspond to features within the simulated, improved image;

[0600] Align the images of the plurality of images with the aligned binary image; and

[0601] Identifiers are placed on the aligned image based on the identified features, with each identifier placed at a location associated with a local minimum of the intensity within the image surrounding the identified feature.

[0602] 111. The non-transitory computer-readable medium according to aspect 110, wherein placing the identifier comprises:

[0603] Determine the contours of the identified features within the binary image;

[0604] Align the contour with corresponding features in the plurality of images; and

[0605] Identify locations of a pair of markers around the contour, with the first marker located at a local minimum of image intensity inside the contour and the second marker located at another local minimum of image intensity outside the contour.

[0606] 112. The non-transitory computer-readable medium according to aspect 111, wherein identifying the pair of identifiers comprises:

[0607] The first identifier is located at the local minimum of the intensity of the image, in a specified direction, towards the interior of the contour; and

[0608] Oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, the second identifier is determined to be located at another local minimum value of the intensity of the image.

[0609] 113. A method for generating a printability mapping associated with a mask pattern, the method comprising:

[0610] Multiple improved images of a patterned substrate are obtained based on markers of multiple images of a patterned substrate, wherein the marker of each of the multiple images is associated with the intensity of a pixel of each image;

[0611] Sum the image intensities of the plurality of improved images; and

[0612] The summed image intensities are divided by the total number of improved images to produce the printability map associated with the mask pattern.

[0613] 114. The method according to aspect 113, wherein obtaining the plurality of improved images comprises:

[0614] The labels of the plurality of images are input into an algorithm configured to generate a plurality of improved images corresponding to each of the plurality of images.

[0615] 115. The method according to aspect 114, wherein the algorithm is configured to perform a watershed algorithm for image segmentation based on the identifiers placed within the plurality of images.

[0616] 116. The method according to aspect 115, wherein the marker for each of the plurality of images comprises:

[0617] Align the binary image of the plurality of images with the simulated improved image;

[0618] Identify features within the binary image that correspond to features within the simulated, improved image;

[0619] Align the images of the plurality of images with the aligned binary image; and

[0620] Identifiers are placed on the aligned image based on the identified features, with each identifier placed at a location associated with a local minimum of the intensity within the image surrounding the identified feature.

[0621] 117. The method according to aspect 116, wherein placing the identifier comprises:

[0622] Determine the contours of the identified features within the binary image;

[0623] Align the contour with corresponding features in the plurality of images; and

[0624] Identify locations of a pair of markers around the contour, with the first marker located at a local minimum of image intensity inside the contour and the second marker located at another local minimum of image intensity outside the contour.

[0625] 118. The method according to aspect 117, wherein identifying the pair of identifiers comprises:

[0626] The first identifier is located at the local minimum of the intensity of the image, in a specified direction, towards the interior of the contour; and

[0627] Oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, the second identifier is determined to be located at another local minimum value of the intensity of the image.

[0628] 119. A non-transitory computer-readable medium comprising instructions for generating a printable mapping associated with a mask pattern, the computer-readable medium, when executed by one or more processors, causing operations including:

[0629] Multiple binary images of the patterned substrate are obtained based on the features of the mask pattern;

[0630] Align the plurality of binary images and sum the intensities of the plurality of binary images; and

[0631] The summed image intensities are divided by the total number of binary images to generate the printability map associated with the mask pattern, wherein the intensity of each pixel in the printability map indicates the probability that a feature of the mask pattern will be printed onto the substrate.

[0632] 120. A non-transitory computer-readable medium according to aspect 119, wherein obtaining the plurality of binary images comprises:

[0633] The binary algorithm is applied to each of a plurality of images of the patterned substrate, the binary algorithm being configured to generate a binary image of the given image based on features in a given image of the plurality of images corresponding to the features of the mask pattern.

[0634] 121. The non-transitory computer-readable medium according to aspect 120, wherein the feature corresponding to the feature of the mask pattern in each of the plurality of images is identified based on a simulated image of the patterned substrate.

[0635] 122. A non-transitory computer-readable medium according to aspect 121, wherein the binary algorithm includes thresholding of each of the plurality of images of the patterned substrate, the thresholding being based on the feature corresponding to the mask pattern.

[0636] 123. The non-transitory computer-readable medium according to aspect 121, wherein the binary algorithm is a watershed algorithm configured to perform image segmentation based on identifiers placed within the plurality of images.

[0637] 124. The non-transitory computer-readable medium according to aspect 122, wherein the identifier comprises:

[0638] A first identifier, the first identifier being located in a specified direction at the local minimum of the intensity of the image, facing the interior of the contour; and

[0639] The second identifier is oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, located at another local minimum value of the intensity of the image.

[0640] 125. A method comprising instructions for generating a printability mapping associated with a mask pattern, the method comprising:

[0641] Multiple binary images of the patterned substrate are obtained based on the features of the mask pattern;

[0642] Align the plurality of binary images and sum the intensities of the plurality of binary images; and

[0643] The summed image intensities are divided by the total number of binary images to generate the printability map associated with the mask pattern, wherein the intensity of each pixel in the printability map indicates the probability that a feature of the mask pattern will be printed onto the substrate.

[0644] 126. The method according to aspect 125, wherein obtaining the plurality of binary images comprises:

[0645] The binary algorithm is applied to each of a plurality of images of the patterned substrate, the binary algorithm being configured to generate a binary image of the given image based on features in a given image of the plurality of images corresponding to the features of the mask pattern.

[0646] 127. The method according to aspect 126, wherein the feature corresponding to the feature of the mask pattern in each of the plurality of images is identified based on a simulated image of the patterned substrate.

[0647] 128. The method according to aspect 127, wherein the binary algorithm includes thresholding of each of the plurality of images of the patterned substrate, the thresholding being based on the feature corresponding to the mask pattern.

[0648] 129. The method according to aspect 127, wherein the binary algorithm is configured to perform a watershed algorithm for image segmentation based on identifiers placed within the plurality of images.

[0649] 130. The method according to aspect 129, wherein the identifier comprises:

[0650] A first identifier, the first identifier being located in a specified direction at the local minimum of the intensity of the image, facing the interior of the contour; and

[0651] The second identifier is oriented toward the outside of the contour in the specified direction and across the local maximum value of the intensity of the image, located at another local minimum value of the intensity of the image.

[0652] The above description is intended to be illustrative and not restrictive. Therefore, those skilled in the art will understand that modifications can be made as described without departing from the scope of the claims set forth below.

Claims

1. A method for determining the likelihood that auxiliary features of a mask pattern will be printed on a substrate, the method comprising: Obtain (i) multiple images of a pattern printed on a substrate, and (ii) variance data associated with the pixels of the multiple images of the pattern, the images being formed using the mask pattern; The model configured to generate variance data associated with the mask pattern is determined based on the variance data. and Based on variance data generated from a model for a given mask pattern, and a resist image or etched image associated with the given mask pattern, the likelihood that an auxiliary feature of the given mask pattern will be printed on the substrate is determined. This likelihood is applied to adjust one or more parameters associated with the patterning process or patterning apparatus to reduce the likelihood that the auxiliary feature will be printed on the substrate.

2. The method according to claim 1, wherein, Obtaining the plurality of images includes: The plurality of images of the pattern printed on the substrate are received via a measuring tool; or The plurality of images of the pattern printed on the substrate are captured via the measurement tool.

3. The method according to claim 1, wherein: The variance data is represented as another pixelated image, where each pixel is assigned the variance value of the grayscale value of each pixel in the plurality of images.

4. The method according to claim 1, wherein, Determining the model includes: Input (i) the spatial image or mask image associated with the mask pattern, and (ii) the variance data associated with the mask pattern into the model; The model is executed using the initial values ​​of the model parameters to generate initial variance data; Determine the difference between the initial variance data and the input variance data; and The initial values ​​of the model parameters are adjusted based on the difference so that the model produces variance data within a specified threshold of the input variance data.

5. The method according to claim 4, wherein, The model is determined to be an iterative process, wherein the adjustments to the values ​​of the model parameters are performed until the variance data produced by the model is within the specified threshold of the input variance data.

6. The method according to claim 5, wherein, The initial values ​​of the model parameters are adjusted based on the gradient of the difference between the output variance mapping and the input variance, the gradient being directed toward reducing or minimizing the difference to guide the values ​​of the model parameters.

7. The method according to claim 1, wherein, The model is at least one of the following: A machine learning neural network, wherein the machine learning neural network includes weights and biases as model parameters. A linear model, comprising a combination of correlation coefficients of linear terms, wherein the coefficients are model parameters, and A polynomial model, wherein the polynomial model comprises a combination of correlation coefficients of polynomial terms, and the coefficients are the model parameters.

8. The method according to claim 1, wherein, Determining the probability that the auxiliary features of the given mask pattern will be printed on the substrate includes: The resist image associated with the given mask pattern is obtained through patterning process simulation or measurement tools; Establish the correlation between the variance data generated by the model and the resist image; and Based on the correlation, identify areas of the mask pattern that have a relatively high probability of having the auxiliary features printed on the substrate, or target layouts corresponding to the mask pattern.

9. The method according to claim 8, wherein, Establishing the correlation between the variance data generated by the model and the resist image includes: Identify the intensity value along a selected line on the resist image from the resist image; Identify the variance value corresponding to the selected line from the variance data generated by the model; and The identified variance value is correlated with the identified intensity value of the resist image along the selected line.

10. The method according to claim 9, wherein, Identifying the regions with a relatively high probability of having the auxiliary features printed on the substrate includes: For one or more regions of the resist image, determine whether the intensity value exceeds a printing threshold associated with the printing of features within the resist layer on the substrate; Based on the correlation, determine whether the variance value corresponding to the one or more regions exceeds a specified variance threshold range; In response to exceeding the specified variance threshold range, a relatively higher printing probability is assigned to a portion of the one or more regions; In response to exceeding the specified variance threshold range or not exceeding the printing threshold, a relatively lower printing probability is assigned to a portion of the one or more zones; In response to not exceeding the specified variance threshold range and not exceeding the printing threshold, a zero printing probability is assigned to a portion of the one or more zones; and Identify regions with a printing probability greater than zero from the one or more regions, said regions being located around the main pattern of the mask pattern.

11. The method according to claim 10, wherein, The printing threshold includes: Upper threshold, the upper threshold indicator feature being printed within the resist layer, and A lower threshold, which indicates that the feature has not been printed on the resist layer.

12. The method according to claim 1, further comprising: Based on the model and the possibility of printing the auxiliary features, optical proximity correction (OPC) data is generated to adjust one or more main features or one or more auxiliary features of the mask pattern.

13. The method according to claim 1, further comprising: Based on the model and the probability that the auxiliary feature will be printed, a source and / or mask pattern is determined to reduce the probability that the auxiliary feature will be printed.

14. The method according to claim 1, further comprising: Based on the model and the possibility of printing using the auxiliary features, one or more parameters of the patterning process used to pattern the substrate are adjusted.

15. A non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause the processors to perform the method according to any one of claims 1 to 14.

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