Mask pattern optimization

Abstract

The present disclosure provides a computer-implemented method for determining a mask pattern of a patterning device. The method includes: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image by simultaneously adjusting the continuous tone mask and the binary mask.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Application 63 / 532,020, filed August 10, 2023, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The embodiments provided herein generally relate to photolithographic mask design and patterning processes, and more particularly to a mask pattern optimization. Background Technology

[0004] Photolithography equipment can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a mask or template can contain or provide a circuit pattern (“design layout”) corresponding to a separate layer of the IC, and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon chip). The curve pattern of the patterning apparatus can be iteratively optimized to ensure that the target design is transferred onto the substrate. Summary of the Invention

[0005] Some embodiments provide a computer-implemented method for determining a mask pattern for a pattern forming apparatus. The method includes: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image based on gradient maps associated with the continuous tone mask and the binary mask.

[0006] Some embodiments provide a computer-implemented method for determining a mask pattern for a pattern forming apparatus. The method includes: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image by simultaneously adjusting the continuous tone mask and the binary mask.

[0007] Some embodiments provide an apparatus for determining a mask pattern using a pattern forming apparatus. The apparatus includes: a memory storing an instruction set; and at least one processor configured to execute the instruction set to cause the apparatus to perform the following operations: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image based on a gradient map associated with the continuous tone mask and the binary mask.

[0008] Some embodiments provide an apparatus for determining a mask pattern using a pattern forming apparatus. The apparatus includes: a memory storing an instruction set; and at least one processor configured to execute the instruction set to cause the apparatus to perform the following operations: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image by simultaneously adjusting the continuous tone mask and the binary mask.

[0009] Some embodiments provide a non-transitory computer-readable medium storing a set of instructions executable by at least one processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a pattern forming apparatus. The method includes: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image based on gradient maps associated with the continuous tone mask and the binary mask.

[0010] Some embodiments provide a non-transitory computer-readable medium storing a set of instructions executable by at least one processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a pattern forming apparatus. The method includes: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image by simultaneously adjusting the continuous tone mask and the binary mask.

[0011] Other advantages of embodiments of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings, in which certain embodiments of the invention are illustrated by means of illustrations and examples. Attached Figure Description

[0012] The above and other aspects of this disclosure will become clear from the description of exemplary embodiments taken in conjunction with the accompanying drawings.

[0013] Figure 1A Schematic block diagrams of various subsystems of an exemplary lithography system conforming to embodiments of this disclosure.

[0014] Figure 1B To conform to the embodiments of this disclosure Figure 1A A schematic block diagram of the simulation model of the subsystem in the diagram.

[0015] Figure 2 A flowchart of a first exemplary mask optimization method conforming to embodiments of this disclosure.

[0016] Figures 3A to 3FThe illustration is a graph showing an exemplary image initialization process conforming to an embodiment of this disclosure.

[0017] Figure 4A The illustration shows an exemplary mapping function between an initial image and a first image that conforms to an embodiment of this disclosure.

[0018] Figures 4B to 4E These are an exemplary initial image, a first image, a second image, and a curve pattern, respectively, conforming to embodiments of this disclosure.

[0019] Figure 5 The illustration shows an exemplary weighting function that conforms to an embodiment of this disclosure.

[0020] Figure 6 A flowchart of a second exemplary mask optimization method conforming to embodiments of this disclosure.

[0021] Figure 7 The illustration shows an exemplary mapping function between an initial image and a blur mask, conforming to an embodiment of this disclosure.

[0022] Figures 8A to 8E The illustration shows an exemplary blurred mask image based on weight values, conforming to an embodiment of this disclosure.

[0023] Figure 9 A block diagram of an exemplary computer system conforming to embodiments of this disclosure.

[0024] Figure 10 A schematic diagram of an exemplary photolithography projection apparatus conforming to embodiments of this disclosure.

[0025] Figure 11 A schematic diagram of another exemplary photolithography projection apparatus conforming to an embodiment of this disclosure.

[0026] Figure 12 To conform to the embodiments of this disclosure Figure 10 A more detailed view of the device.

[0027] Figure 13 To conform to the embodiments of this disclosure Figure 11 and Figure 12 A more detailed view of the device's source collector module SO. Detailed Implementation

[0028] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings, wherein, unless otherwise indicated, the same numerals in the different drawings denote the same or similar elements. The embodiments set forth in the following description of the exemplary embodiments do not represent all embodiments. Rather, they are merely examples of apparatuses and methods consistent with aspects related to the disclosed embodiments set forth in the appended claims. While specific reference may be made to IC manufacturing in this disclosure, it should be clearly understood that the description herein has many other possible applications. For example, the description herein can be used in the manufacture of integrated optical systems, for guiding and detecting patterns for magnetic domain memories, liquid crystal display panels, thin-film magnetic heads, etc. Those skilled in the art will appreciate that, in the context of these alternative applications, any use of the terms “mask,” “chip,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “die,” respectively.

[0029] Photolithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning apparatus (e.g., a mask) can include or provide a pattern (“design layout”) corresponding to a separate layer of the IC, and this pattern can be transferred onto the target portion (e.g., comprising one or more dies) of a substrate (e.g., a silicon chip) that has been coated with a radiation-sensitive material (“resist”) layer by irradiating the pattern on the patterning apparatus. Typically, a single substrate contains multiple adjacent target portions, and the pattern is continuously transferred by the photolithography projection equipment to the multiple adjacent target portions one at a time. In one type of photolithography projection equipment, the pattern on the entire patterning apparatus is transferred onto a single target portion at once; such an equipment is often referred to as a stepper. In an alternative equipment, often referred to as a step-scanning equipment, the substrate is moved synchronously, parallel or antiparallel to the reference direction, while the projection beam scans across the entire patterning apparatus in a given reference direction (“scanning” direction). Different portions of the pattern on the patterning apparatus are transferred step by step onto a single target portion. Typically, because the photolithography projection apparatus will have a reduction ratio M (e.g., 4), the speed F of moving the substrate will be 1 / M times the speed of the projection beam scanning pattern forming apparatus. Further information regarding the photolithography apparatus described herein can be obtained, for example, from U.S. Patent No. 6,046,792, which is incorporated herein by reference.

[0030] Before a pattern is transferred from a patterning apparatus to a substrate, the substrate may undergo various processes, such as applying a primer, coating with a resist, and soft baking. After exposure, the substrate may undergo other processes (“post-exposure processes”), such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred pattern. This array of processes is used as the basis for individual layers in the fabrication of devices (e.g., ICs). The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all aimed at refining the individual layers of the device. If a certain number of layers are required in the device, the entire process or variations thereof is 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 by techniques such as dicing or sawing, so that the individual devices can be mounted on a carrier, connected to pins, etc.

[0031] Therefore, the fabrication of devices such as semiconductor devices typically involves a number of fabrication processes to process a substrate (e.g., a semiconductor chip) to form various features and multiple layers of the device. These layers and features are typically fabricated and processed using techniques such as deposition, photolithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on a substrate and then separated into individual devices. This device fabrication process can be considered a patterning process. A patterning process involves patterning steps, such as optical or nanoimprint lithography, which uses a patterning apparatus in a photolithography device to transfer a pattern from the patterning apparatus to the substrate. The patterning process typically, but optionally, involves one or more associated patterning processing steps, such as resist development using a developing apparatus, baking the substrate using a baking tool, etching the pattern using an etching apparatus, etc.

[0032] As noted, photolithography is a central step in the fabrication of devices such as ICs, in which patterns formed on a substrate define the functional elements of the device, such as microprocessors and memory chips. Similar photolithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0033] As semiconductor manufacturing processes have continued to evolve, the size of functional components has been continuously reduced 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." In the current state of technology, layers of devices are fabricated using photolithography projection equipment. This equipment projects a design layout onto a substrate using irradiation from a deep ultraviolet source, resulting in individual functional components with dimensions well below 100 nm, i.e., less than half the wavelength of the radiation from the irradiation source (e.g., a 193 nm source).

[0034] This process, used to print features with dimensions smaller than the classical resolution limit of a photolithography projection apparatus, is often referred to as low-k1 lithography according to the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the photolithography projection apparatus, CD is the "critical size" (typically the smallest feature size to be printed), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it is to reproduce patterns on a substrate that resemble the shape and size planned by the designer to achieve specific electrical functionalities and performance. To overcome these difficulties, complex fine-tuning steps are applied to the photolithography projection apparatus, design layout, or patterning apparatus. These steps include, but are not limited to, optimization of NA and optical coherence settings, custom illumination schemes, use of phase-shifting patterning apparatus, optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). The term "projection optics" as used herein should be interpreted broadly to encompass various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also include elements that operate according to any of these design types to jointly or individually guide, shape, or control a projected radiation beam. The term "projection optics" can include any optical element in a photolithography projection apparatus, regardless of its location along the optical path of the apparatus. Projection optics can include optical elements for shaping, adjusting, or projecting radiation from a source before it passes through a patterning apparatus, or for shaping, adjusting, or projecting radiation after it has passed through the patterning apparatus. Projection optics typically do not include a source or patterning apparatus.

[0035] In this disclosure, 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 EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of about 5 nm to 100 nm).

[0036] The terms “optimized” and “optimized” as used in this article mean adjusting the lithography projection equipment to give the lithography results or process more desirable characteristics, such as higher accuracy of the projection of the design layout onto the substrate and a larger process window.

[0037] Furthermore, photolithography projection apparatuses can be of the type having two or more substrate stages (or two or more pattern forming apparatus stages). In these "multi-platform" apparatuses, additional stages can be used in parallel, or one or more stages can be used for exposure while preparatory steps are performed on one or more stages. Dual-platform photolithography projection apparatuses are described, for example, in US 5,969,441, which is incorporated herein by reference.

[0038] Patterning apparatuses may include or can form one or more design layouts. Design layouts can be generated using CAD (Computer-Aided Design) programs, a process often referred to as EDA (Electronic Design Automation). Most CAD processes follow a predetermined set of design rules to produce functional design layouts / patterning apparatuses. These rules are set through processing and design constraints. For example, design rules define the space tolerances between devices (such as gates, capacitors, etc.) or interconnects to ensure that devices or lines do not interact with each other in undesirable ways. One or more design rule constraints may be referred to as “critical dimensions” (CDs). The critical dimension of a device can be defined as the minimum width of a line or via, or the minimum space between two lines or two vias. Therefore, CDs determine the overall size and density of the designed device. Of course, one of the goals of device fabrication is (via the patterning apparatus) to faithfully reproduce the original design intent on the substrate.

[0039] As used in this disclosure, 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 "light valve" can also be used in this context. Examples of such patterning apparatuses, in addition to classic masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), include programmable mirror arrays and programmable LCD arrays.

[0040] An example of a programmable mirror array is a matrix-addressable surface with a viscoelastic control layer and a reflective surface. The underlying principle behind such a device is (e.g.) that addressable regions of the reflective surface cause incident radiation to be reflected as diffracted radiation, while unaddressed regions cause incident radiation to be reflected as undiffracted radiation. With the use of appropriate filters, the undiffracted radiation can be filtered out from the reflected beam, leaving only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The desired matrix addressing can be performed using suitable electronics. Further information about these 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.

[0041] An example of a programmable LCD array is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0042] As used herein, unless otherwise specifically stated or impractical, the term "or" covers all possible combinations. For example, if a statement of components includes A or B, then unless otherwise specifically stated or impractical, the components may include A, or B, or A and B. As a second example, if a statement of components includes A, B, or C, then unless otherwise specifically stated or impractical, the components may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. Expressions such as "at least one of" need not modify all of the following list and need not modify each component in the list, such that "at least one of A, B, and C" should be understood to include only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase "one of A and B" or "any one of A and B" should be interpreted in the broadest sense to include either one of A or one of B.

[0043] As a brief introduction, Figure 1A 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 necessarily have a radiation source); irradiation optics, which, for example, define partial coherence (represented as mean square deviation) and may include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a pattern forming apparatus 18A; and a transmissive optics 16Ac that projects an image of a pattern from the pattern forming apparatus onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics can limit the range of beam angles incident on the substrate plane 22A, wherein the largest possible angle defines the numerical aperture NA of the projection optics as NA = n sin(Θ). max ), where n is the refractive index of the medium between the substrate and the last element of the projection optics, and Θ max The maximum angle at which the beam emitted from the projection optics can still be incident on the substrate plane 22A.

[0044] 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 of the system (evaluation points) 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 or can 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) or the manufacturability design rules of the patterning apparatus, and the evaluation point can include physical points on the resist image located on the substrate, as well as non-physical characteristics such as dosage and focus.

[0045] In a photolithography projection apparatus, a source provides illumination (i.e., radiation) to a patterning apparatus, and projection optics guide the illumination onto a substrate and shape the illumination via the patterning apparatus. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the distribution of radiation intensity at a horizontal plane of the substrate. A resist layer on the substrate is exposed, and the spatial image is transferred to the resist layer as a potential “resist image” (RI) in the resist layer. 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 based on the spatial image; examples of calculating a resist image can be found in U.S. Patent No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model relates only to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of a lithographic projection apparatus (e.g., the properties of the illumination, patterning apparatus, and projection optics) define the spatial image and can be defined in an optical model. Since the patterning apparatus used in a lithographic projection apparatus can be modified, it is desirable to separate the optical properties of the patterning apparatus from the optical properties of the rest of the lithographic projection apparatus, which includes at least the source and projection optics. Details of the techniques and models used to transform design layouts into various lithographic images (e.g., spatial images, resist images, etc.), the application of optical proximity correction (OPC) using those techniques and models, and the evaluation of performance (e.g., in terms of process windows) are described in U.S. Patent Applications Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosure of which is hereby incorporated herein by reference in its entirety.

[0046] Figure 1BThe diagram illustrates an exemplary flowchart for simulating lithography in a lithography projection apparatus. It will be understood that the model can represent different patterning processes and does not necessarily include all the models described below. Source model 31 represents the optical characteristics of a source (including radiation intensity distribution or phase distribution). Projection optics model 32 represents the optical characteristics of a projection optics (including changes in radiation intensity distribution or phase distribution caused by the projection optics). Patterning apparatus / design layout model 35 represents the optical characteristics of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.) (including changes in radiation intensity distribution or phase distribution caused by a given design layout), which is a representation of the arrangement of features on or formed by the patterning apparatus. A spatial image 36 can be simulated from source model 31, projection optics module 32, and design layout module 35. A resist image 38 can be simulated from the spatial image 36 using resist model 37. In some embodiments, resist image 38 can be used as input to a post-pattern transfer process model 39. The post-pattern transfer process model 39 defines the performance of one or more post-resist development processes (e.g., etching, development, etc.). For example, the post-pattern transfer process model 39 could be an etching model 39 that can predict an etched image using a resist image 38. The etched image can represent the contour etched on the substrate after the etching process. Simulation of photolithography can, for example, predict the contour and CD in the resist image.

[0047] More specifically, note that source model 31 can represent the optical characteristics of a source, including but not limited to numerical aperture settings, mean square deviation (σ) settings for NA, 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 physical pattern forming apparatus, such as those described 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. The desired design is typically defined as a pre-optical proximity correction (OPC) design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

[0048] Therefore, the model formulation describes most (if not all) of the known physical and chemical processes of the overall process, and each model parameter in the model parameters is expected to correspond to a different physical or chemical effect. Thus, the model formulation sets an upper limit on how well the model can be used to simulate the overall manufacturing process.

[0049] In the example, the computational analysis of the photolithography or etching process uses a predictive model (e.g., the one mentioned above). Figure 1B As discussed herein, the predictive model, when properly calibrated, can produce accurate predictions of dimensions derived from a photolithography or etching process. Models for photolithography or etching processes are typically calibrated based on empirical measurements. Such calibration may include running test chips with different process parameters, measuring critical dimensions after the photolithography process, and calibrating the model used to fit the measurements. In practice, fast and accurate models are used to improve device performance or yield, enhance process windows, or increase design options. Those skilled in the art will understand that the methods described herein are not limited to specific photolithography models. To calibrate the desired model, images can be obtained after any semiconductor fabrication step. Examples include spatial images, resist images, etching images, images after chemical mechanical polishing, or other images associated with the patterning process.

[0050] In computational lithography modeling, CD gauges measured by CD-SEM (scanning electron microscopy) are typically used as input data to calibrate the model. The goal of lithography modeling is to predict the accurate resist profile at each location on the substrate. Similarly, the goal of etching modeling is to predict the accurate etching profile at each location on the substrate. In some embodiments, computational analysis of the etching process uses a calibrated predictive model that can predict the dimensions of the etched structure produced by the etching process. For example, the etching model associated with the etching process can be calibrated based on empirical measurements. The calibration process may include patterning a test chip using different process parameters, measuring the CD of the pattern on the test chip after the etching process, and calibrating the etching model based on the measured CD. In practice, fast and accurate models can be used to improve the performance of patterning equipment, patterning yield, process window of the patterning process, or increase design options related to, for example, determining mask patterns.

[0051] One aspect of understanding the photolithography process is understanding the interaction between radiation and the patterning apparatus. The electromagnetic field of the radiation after it has passed through the patterning apparatus can be determined based on the electromagnetic field of the radiation before it reaches the apparatus and a function characterizing this interaction. This function can be called the mask transmission function (which can be used to describe the interaction between transmissive and reflective patterning apparatuses).

[0052] Mask transmission functions can take various forms. One form is binary. A binary mask transmission function has either one of two values ​​(e.g., zero and a positive constant) at any given location on the patterning apparatus. A mask transmission function in binary form can be called a binary mask. Another form is continuous. That is, the modulus of the transmittance (or reflectance) of the patterning apparatus is a continuous function of the location on the patterning apparatus. The phase of the transmittance (or reflectance) can also be a continuous function of the location on the patterning apparatus. A mask transmission function in continuous form can be called a continuous tone mask or a continuous transmission type mask (CTM). For example, a CTM can be represented as a pixelated image where each pixel can be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of a binary value of 0 or 1. In some embodiments, the CTM may be a pixelated grayscale image, wherein each pixel has a value (e.g., a normalized value in the range [-255, 255], in the range [0, 1] or [-1, 1] or other suitable range).

[0053] The thin mask approximation, also known as the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction between radiation and patterning apparatus. The thin mask approximation assumes that the thickness of the structure on the patterning apparatus is very small compared to the wavelength, and the width of the structure on the mask is very large compared to the wavelength. Therefore, the thin mask approximation assumes that the electromagnetic field behind the patterning apparatus is the product of the incident electromagnetic field and the mask transmission function. However, as the lithography process uses radiation with increasingly shorter wavelengths and the structure on the patterning apparatus becomes smaller, the assumptions of the thin mask approximation can be decomposed. For example, due to the finite thickness of the structure (e.g., the edge between the top surface and the sidewalls), the interaction between radiation and the structure (“mask 3D effect” or “M3D”) can become significant. Including this scattering in the mask transmission function allows the mask transmission function to better capture the interaction between radiation and the patterning apparatus. The mask transmission function under the thin mask approximation can be called the thin mask transmission function. The mask transmission function that includes M3D can be called the M3D mask transmission function.

[0054] In this disclosure, one or more images may be generated, including continuous transmissive mask images, binary mask images, blurred mask images, curved mask images, etc. Images include various types of signals that can be characterized by pixel values ​​or intensity values ​​for each pixel. Depending on the relative values ​​of pixels within the image, signals may be referred to as, for example, weak signals or strong signals, as will be understood by those skilled in the art. The terms "strong" and "weak" are relative terms based on the intensity values ​​of pixels within the image, and specific values ​​of intensity may not limit the scope of this disclosure. In some embodiments, strong and weak signals may be identified based on selected thresholds. In some embodiments, the threshold may be fixed within the image (e.g., the midpoint between the highest and lowest intensities of a pixel). In some embodiments, a strong signal may refer to a signal having a value greater than or equal to the average signal value on the image, and a weak signal may refer to a signal having a value less than the average signal value. In some embodiments, relative intensity values ​​may be based on percentages. For example, a weak signal may be a signal having an intensity less than 50% of the highest intensity of a pixel within the image (e.g., a pixel corresponding to a target pattern may be considered the pixel with the highest intensity). Furthermore, each pixel within the image may be considered a variable.

[0055] According to some embodiments of this disclosure, derivatives or partial derivatives can be determined relative to each pixel within an image, and the value of each pixel can be determined or modified based on an evaluation of the cost function or a gradient-based calculation of the cost function. For example, a CTM image may include pixels, where each pixel is a variable that can take any real value, complex value, etc. While some embodiments utilizing cost function-based evaluation or gradient-based calculation are described in this disclosure, it will be understood that any optimization method can be applied to evaluate a mask image or to modify or adjust a mask image based on the evaluation. For example, optimization methods may include genetic algorithms, reinforcement learning algorithms, etc.

[0056] In conventional methods for determining a pattern for a pattern forming apparatus (or, hereinafter, a mask pattern), a CTM image corresponding to the target pattern to be printed on a substrate is generated or optimized, and then a binary mask image is generated or the binary mask image is optimized from the CTM image to produce a final curved mask (e.g., a geometric or polygonal representation of a curved mask or curved pattern) that can also be used to fabricate / manufacture a mask. In this disclosure, the optimization process using a binary mask image can be referred to as a CTM+ process, compared to a CTM optimization process using a CTM image. To achieve the desired result, multiple iterations are performed using a successive transmissive mask, and then iterations of the CTM+ process using a binary mask can be performed. SRAFs (sub-resolution auxiliary features) are typically applied to enhance process windows for isolated and semi-isolated features by utilizing optical interference between primary and auxiliary features. During mask optimization, SRAFs are seeded from the CTM image, but in some cases, missing SRAFs are observed even during the CTM process after seeding. However, missing SRAFs are difficult to recover during the CTM+ process. While CTM enhancement, including a smoothing process, can be an alternative for addressing missing SRAFs, it can lead to the seeding of additional SRAFs. This seeding can result in violations of Mask Rule Check (MRC), Edge Placement Errors (EPE), or sidelobe printing problems due to densely filled SRAFs. Furthermore, these alternatives do not provide robust solutions that can be consistently applied across various scenarios. For example, a CTM enhancement method may address missing SRAFs in some cases, but in others, the same CTM enhancement may result in undesirable SRAF seeds. Redundant SRAF seeding via CTM enhancement can also cause stitch boundary problems. Therefore, a mask transmission function optimization method that can address missing SRAFs is needed. Additionally, mask image binarization can fail in current CTM+ processes when the peak intensity of the mask image approaches the threshold used for binarization. Therefore, an efficient binarization technique is also needed in the industry.

[0057] According to some embodiments of this disclosure, a stable solution for missing SRAF can be provided based on the superposition of CTM and CTM+ processes during mask pattern optimization. According to some embodiments of this disclosure, a stable binarization solution can be provided, for example, using a sigmoid function when pixel values ​​are close to a binarization threshold. According to some embodiments of this disclosure, a blurring method is provided in which the superposition of a continuous-tone mask and a binary mask is utilized when optimizing a mask image. According to some embodiments of this disclosure, signals below a contour extraction threshold used to generate a curve pattern from a CTM image may be captured via CTM+ contour extraction, possibly attributable to CTM contributions during the mask optimization process.

[0058] Referring now to a flowchart of an exemplary first mask optimization method 200 conforming to embodiments of this disclosure Figure 2 According to some embodiments of this disclosure, a first mask optimization method 200 is used to determine a mask pattern from an image corresponding to a target pattern to be printed on a substrate via a patterning process involving photolithography. In some embodiments, the target pattern or design layout may be a binary design layout, a continuous-tone design layout, or another suitable form of design layout. According to some embodiments of this disclosure, the first mask optimization method 200 is an iterative process in which an initial image (e.g., a CTM image, an enhanced image of a CTM image, an initial image from a CTM image, etc.) is progressively modified to ultimately produce information of the mask pattern or an image corresponding to the final curved mask to be further used to make / manufacture the mask. In some embodiments, the iterative modification of the initial image may be based on a cost function in which the initial image may be modified during iterations such that the cost function is reduced or minimized. In some embodiments, the curved mask pattern may be a geometric or polygonal representation of a curved mask or a curved pattern. The curved mask pattern may be in the form of a vector, a table, a mathematical equation, or other forms representing geometric / polygonal shapes.

[0059] According to some embodiments of this disclosure, in Figure 2 As shown, the first mask optimization method 200 can begin by acquiring an initial image 2001. In some embodiments, the initial image 2001 may be a CTM image generated by a CTM generation process based on a target pattern to be printed on a substrate. For example, in CTM generation techniques, the reverse lithography problem is formulated as an optimization problem. In some embodiments, the initial image 2001 may include one or more mask features (e.g., SRAF, SRIF (sub-resolution internal features), etc.).

[0060] In some embodiments, the initial image 2001 may be a CTM image, such as an initial CTM image. Figures 3A to 3F The illustration is a graph showing an exemplary image initialization process conforming to an embodiment of this disclosure. Figure 3A A CTM image 310 is shown, generated by a CTM generation process based on a target pattern to be printed on a substrate. For example, the CTM image 310 can be generated based on a spatial image. A spatial image can be obtained by applying an optical model to the target pattern. The CTM image 310 can be initialized by providing the target pattern and normalizing the provided image to the range [0, 1]. As shown in... Figure 3AAs shown, the CTM image 310 may include one or more features, such as a primary feature corresponding to the target pattern (e.g., a peak at the center of the CTM image 310) and two additional features that may correspond to SRAF (e.g., two side peaks of the CTM image 310). Using a mapping function 320, for example... Figure 3B The sigmoid function shown can obtain Figure 3C The initial grayscale image 330 is shown in the image. For example, in... Figure 3B In this diagram, the Y-axis represents the normalized pixel values ​​of the CTM image 310, and the X-axis represents the grayscale values ​​of the grayscale image 330 mapped to the normalized pixel values ​​of the CTM image 310. In some embodiments, the initial grayscale image 330 may be a pixelated grayscale image, in which each pixel has a value, for example, within the range [-255, 255]. In some embodiments, the initial grayscale image 330 may be downsampled at pixel locations to reduce oscillations and have a smoother image, such as... Figure 3D The image shown is a downsampled grayscale image 340. In some embodiments, the downsampled grayscale image 340 may be interpolated to have... Figure 3E The continuous grayscale image 350 is shown in the figure. In some embodiments, any one of the CTM image 310, the initial grayscale image 330, the downsampled grayscale image 340, and the continuous grayscale image 350 can be used as the initial image 2001. In some embodiments, a mapping function can be used to generate Figure 3F The CTM image 360 ​​shown includes mapping functions such as mapping function 320 for generating an initial grayscale image 330 from the CTM image 310. In some embodiments, the CTM image 360 ​​can be used as an initial image 2001.

[0061] Return to reference Figure 2 According to some embodiments of this disclosure, two mask images can be generated based on an initial image 2001 at generation processes 2110 and 2210 of the first mask optimization method 200. In some embodiments, a first image 2002 can be generated based on the initial image 2001 at generation process 2110. In some embodiments where the initial image 2001 has undefined pixel values ​​or pixel values ​​greater than a certain absolute value, the first image 2002 can be obtained by using a mapping function to reduce the variable value φ of the initial image 2001 to a certain range (e.g., [0, 1]). Figure 4A The illustration shows an exemplary mapping function 410 for transforming an initial image 2001 to a first image 2002, conforming to an embodiment of this disclosure. (As shown in...) Figure 4A As shown, the variable value φ of the initial image 2001 can be defined to the range [0, 1] in the first image 2002 by the mapping function 410. In some embodiments, in Figure 3B The sigmoid function shown can be used as a mapping function. In this context, continuous grayscale images (e.g., ...) can be used. Figure 3E In some embodiments where a continuous grayscale image 350 is used as the initial image 2001, the first image 2002 can be obtained by using a mapping function to reduce the variable values ​​φ of the initial image 2001 to a range (e.g., [0, 1]).

[0062] According to some embodiments of this disclosure, the first image 2002 may be a continuous tone mask image. Figure 4B and Figure 4C The illustrations are examples of initial image 2001 and first image 2002 conforming to embodiments of this disclosure. (As shown in...) Figure 4C As shown, the first image 2002 is a bounded continuous-tone mask image in the range [0, 1], while the initial image 2001 is an unbounded or larger-scale continuous-tone image in the range [0, 255]. Although a certain type of mapping function (e.g., ...) is used... Figure 3B The mapping function 320 or Figure 4A The mapping function 410 in the image is used to describe some embodiments, but it will be understood that any type of mapping function that can reduce or limit pixel values ​​to a certain range can be used. In CTM images (e.g., Figure 3F In some embodiments where the CTM image 360 ​​is used as the initial image 2001, the CTM image 360 ​​itself can become the first image 2002. It will be understood that other image enhancement processes (e.g., noise filtering, smoothing, etc.) can be performed when images are generated in this disclosure, but these other image enhancement processes are not described herein for simplicity.

[0063] Return to reference Figure 2 A second image 2003 can be generated based on an initial image 2001 at generation process 2210, which conforms to some embodiments of this disclosure. In some embodiments, the second image 2003 can be generated by extracting contour information from the initial image 2001. (As in...) Figure 4DAs shown, the second image 2003 may involve, for example, a curve mask pattern having a polygonal shape represented in vector form, generated from the initial image 2001. In some embodiments, the generation of the second image 2003 may involve thresholding the initial image 2001 to depict or generate a curve (or curved) pattern from the initial image 2001. For example, thresholding may be performed using a threshold plane (e.g., the xy plane) that intersects the signal of the initial image 2001 with a fixed value. The intersection of the threshold plane with the signal of the initial image 2001 may generate traces or contours (i.e., curved polygonal shapes) that form the polygonal shape used as the curve pattern of the second image 2003. For example, the initial image 2001 may intersect a zero plane parallel to the (x, y) plane. Therefore, the second image 2003 may include any curve pattern generated as described above. Figure 4E The illustration shows how to obtain from the initial image 2001 via thresholding. Figure 4D Example of a curve mask pattern in the second image of 2003.

[0064] Figure 4D The diagram is from Figure 4B An example of a second image 2003 obtained from an initial image 2001 is shown. (See also...) Figure 4D As shown, the second image 2003 includes the outline of the pattern in the initial image 2001. In some embodiments, the outline of the pattern may include a target pattern, SRAF, etc. Although Figure 4D The illustration corresponds to the outline of the target pattern (i.e., multiple contact holes), but it will be understood that the second image 2003 may also include the outline of some SRAFs in the initial image 2001, depending on its signal level. According to some embodiments of this disclosure, the second image 2003 may be a binary mask pattern image.

[0065] Return to reference Figure 2 The first image 2002 and the second image 2003 are evaluated at evaluation processes 2120 and 2220 of the first mask optimization method 200 conforming to some embodiments of the present disclosure, respectively. According to some embodiments of the present disclosure, a cost function or gradient map of each of the first image 2002 and the second image 2003 can be calculated at evaluation processes 2120 and 2220.

[0066] According to some embodiments of this disclosure, a cost function of the first image 2002 can be calculated at evaluation process 2120. In some embodiments, evaluation process 2120 may include using a process model to simulate a patterning process, the process model being able to generate or predict a pattern that can be printed on a substrate based on the first image 2002. For example, evaluation process 2120 may involve performing or simulating a process model using the first image 2002 as input, and generating a process image (e.g., a spatial image, a resist image, an etched image, etc.) on the substrate. In some embodiments, the process model may include a mask transmission model coupled to an optical model, the optical model being further coupled to a resist model or an etched model. In some embodiments, a continuous optical model as a continuous tone mask may be applied to the first image 2002 at evaluation process 2120. In some embodiments, the continuous optical model may take a CTM image as input. In some embodiments, the output of the execution or simulation of the process model may be a process image that has been factored in different process variations during the simulation process. In some embodiments, the process image may be further used to determine parameters of the patterning process (e.g., EPE, CD, overlap, sidelobes, etc.) by, for example, depicting the outline of a pattern within the process image. The parameters can also be used to define a cost function, which is further used to optimize the initial image 2001 such that the cost function is reduced or minimized. For example, the cost function can be edge placement error (EPE), sidelobes, mean squared error (MSE), or other suitable variables defined based on the contours of patterns in the process image. EPE can be the edge placement error associated with one or more patterns, or the sum of all edge placement errors associated with all patterns in the process image and their corresponding target patterns. In some embodiments, the cost function can include more than one condition that can be reduced or minimized simultaneously. For example, in addition to the MRC violation probability, it can include the number of defects, EPE, overlap, CD, or other parameters, and all conditions can be reduced or minimized simultaneously.

[0067] According to some embodiments of this disclosure, the evaluation process 2120 may involve generating a gradient map based on a cost function. The gradient map may be the derivative or partial derivative of the cost function. In some embodiments, the partial derivative of the cost function may be determined relative to pixels of a mask image (e.g., first image 2002), and the derivative may also be constrained to determine the partial derivative relative to variables of an initial image 2001. These gradient calculations may involve determining an inverse relationship between the mask image (e.g., first image 2002) and the initial image 2001. The gradient map may provide suggestions on increasing or decreasing the value of a mask variable (e.g., the variable value of the initial image 2001) in a manner that reduces or minimizes the cost function. In some embodiments, the mask variable may refer to the intensity of the initial image 2001.

[0068] According to some embodiments of this disclosure, the cost function of the second image 2003 can be calculated in evaluation process 2220 in a manner similar to the cost function calculation described in evaluation process 2120. In some embodiments, a polygon-based optical model can be applied to the second image 2003 to generate a simulated process image in evaluation process 2220. In some embodiments, the polygon-based optical model can take polygon shape data as input. In some embodiments, a gradient map of the cost function based on the second image 2003 can be generated in evaluation process 2120 in a manner similar to the gradient map generation described in evaluation process 2220.

[0069] According to some embodiments of this disclosure, a first weight (1-λ) can be applied to the cost function or gradient map (hereinafter referred to as the first cost function or first gradient map) corresponding to the first image 2002 in the weighting application process 2130. Similarly, a second weight (λ) can be applied to the cost function or gradient map (hereinafter referred to as the second cost function or second gradient map) corresponding to the second image 2003 in the weighting application process 2230. According to some embodiments of this disclosure, a total cost function can be generated by combining a weighted first cost function and a weighted second cost function. Similarly, a total gradient map 2005 can be generated by combining a weighted first gradient map and a weighted second gradient map. In some embodiments, the total gradient map 2005 can be generated by a weighted sum at the pixel level of the first gradient map and the second gradient map. According to some embodiments of this disclosure, variables of the initial image 2001 can be changed based on the total gradient map 2005 to gradually reduce or minimize the total cost function. Therefore, the resulting curve pattern can gradually evolve during iteration, thereby reducing or minimizing the total cost function 2005. In some embodiments, iterations may continue until the total cost function reaches a certain level or the convergence rate of the optimization process falls below a certain level. In some embodiments, the number of iterations may be preset.

[0070] According to some embodiments of this disclosure, the first weight (1-λ) and the second weight (λ) can be designed to change gradually with each iteration. In some embodiments, the first weight (1-λ) can change such that the value of the first weight in an earlier (e.g., the m-th iteration) is greater than or equal to the value of the first weight in a later (e.g., the n-th iteration), where n > m > 0. Similarly, the second weight (λ) can change such that the value of the second weight in an earlier (e.g., the m-th iteration) is less than or equal to the value of the second weight in a later (e.g., the n-th iteration), where n > m > 0. In some embodiments, the first weight (1-λ) can be gradually decreased such that the contribution of the continuous tone mask (e.g., the first image 2002) to the total cost function or the total gradient map 2005 can decrease as the iteration progresses. Similarly, the second weight (λ) can be gradually increased such that the contribution of the binary mask (e.g., the second image 2003) to the total cost function or the total gradient map 2005 can increase as the iteration progresses.

[0071] Figure 5 The illustration shows an exemplary weighting function conforming to an embodiment of this disclosure. Figure 5 In this context, the change in the second weight (λ) is described based on the number of iterations. For example, in... Figure 5 As shown, the second weight (λ) is zero until the C1th iteration, increases linearly until the C2th iteration, and becomes zero until the end of the iteration. Since the first weight is represented as (1-λ), it can be noted that the first weight (1-λ) decreases linearly until the C1th iteration, decreases linearly until the C2th iteration, and becomes zero until the end of the iteration. According to some embodiments of this disclosure, instead of utilizing a sequential mask optimization mechanism, such as first utilizing a CTM process and then a CTM+ process, a blurred mask optimization mechanism based on the superposition of the CTM and CTM+ processes can be utilized. Therefore, according to some embodiments of this disclosure, because the CTM process can still contribute to modifying the total cost function or total gradient map 2005 on which the initial image 2001 is based, signals below the contour extraction threshold at the start of the mask optimization process still have a chance to be captured as a curve pattern later in the mask optimization process. According to some embodiments of this disclosure, the mask optimization mechanism can effectively obtain a curve pattern of the patterned mask by reducing or minimizing the loss of weak signals during optimization.

[0072] For reference Figure 6 , Figure 6A flowchart of a second mask optimization method 600 conforming to embodiments of the present disclosure is provided. According to some embodiments of the present disclosure, the second mask optimization method 600 is used to determine a mask pattern from an image corresponding to a target pattern to be printed on a substrate by a patterning process involving photolithography. According to some embodiments of the present disclosure, the second mask optimization method 600 is an iterative process in which an initial image (e.g., a CTM image, an enhanced image of a CTM image, an initialization image from a CTM image, etc.) is progressively modified to ultimately produce information about the mask pattern or information about an image corresponding to a final curved mask that can also be used to make / manufacture a mask. In some embodiments, the iterative modification of the initial image may be based on a cost function, wherein, during iteration, the initial image may be modified such that the cost function is reduced or minimized. In some embodiments, the curved mask pattern may be a geometric or polygonal representation shape of a curved mask or a curved pattern. According to some embodiments of the present disclosure, the second mask optimization method 600 utilizes a blurred mask 6002 based on a weighted combination of a binary mask and a continuous tone mask during the optimization process.

[0073] According to some embodiments of this disclosure, such as in Figure 6 As shown, the second mask optimization method 600 can begin by acquiring an initial image 6001. In some embodiments, the initial image 6001 may be a reference image. Figure 2 The initial image 2001 described is the same image. Therefore, for simplicity, a detailed description of the initial image 6001 will be omitted here.

[0074] According to some embodiments of this disclosure, a blurred mask 6002 can be generated based on an initial image 6001 at the generation process 6310 of the second mask optimization method 600. According to some embodiments of this disclosure, the blurred mask 6002 can be generated by a weighted combination of a binary mask and a continuous tone mask (e.g., a combined mask image). In some embodiments, the blurred mask 6002 can be represented as follows:

[0075] (Equation 1)

[0076] Here, m(x, y) represents the pixel value at position (x, y) on the blurred mask 6002. This represents the variable value at position (x, y) on the initial image 6001. The function H() is a threshold function. The step function can be a binary function. For example, function H() is a Heavilyhound step function. Function M() represents a continuous mapping function. In Equation 1, represents the variable values ​​of the initial image 6001. A function that continuously maps to a line. In Equation 1, the first term including the function H() represents the contribution of the binary mask to the blurred mask 6002 (i.e., m(x, y)), and the second term including the function M() represents the contribution of the continuous tone mask to the blurred mask 6002.

[0077] As shown in Equation 1, when combining a binary mask and a continuous tone mask, each of the masks is weighted. Furthermore, the weights of the binary mask and the continuous tone mask can change with each iteration i. In Equation 1, for iteration i, the weight of the continuous tone mask is determined by a first weight (1-λ). i ) represents the binary mask, and the weights of the binary mask are determined by the second weight (λ). i The first weight (1-λ) and the second weight (λ) are designed to change gradually with each iteration, according to some embodiments of this disclosure. In some embodiments, the first weight (1-λ) may change such that the value of the first weight in an earlier (e.g., the m-th iteration) is greater than or equal to the value of the first weight in a later (e.g., the n-th iteration), where n > m > 0. Similarly, the second weight (λ) may change such that the value of the second weight in an earlier (e.g., the m-th iteration) is less than or equal to the value of the second weight in a later (e.g., the n-th iteration), where n > m > 0. In some embodiments, the first weight (1-λ) may decrease gradually such that the contribution of the continuous tone mask to the blur mask 6002 decreases with iteration. Similarly, the second weight (λ) may increase gradually such that the contribution of the binary mask to the blur mask 6002 increases with iteration. In some embodiments, Figure 5 The weighting function shown can be similarly used in the second mask optimization method 600.

[0078] An example of the mask value m(x, y) for blur mask 6002 can be provided as follows:

[0079] (Equation 2)

[0080] here, An example used as a continuous function M(φ(x,y)). Figure 7 The illustration shows an exemplary mapping function between an initial image 6001 and a blurred mask 6002, conforming to an embodiment of this disclosure. Figure 7 In the diagram, the x-axis represents the variable value φ of the initial image 6001, and the y-axis represents the mask value m(x, y) of the blurred mask 6002. For example, in... Figure 7 As shown in the figure, when the variable value φ has a threshold φ th When this is done, the contribution of the binary mask portion can be shown. This is used to represent the threshold variable value φ. thThere is a discontinuity in the curve of pixel value m(x, y) at point i, and the amount of this discontinuity at iteration i is the second weight (λ). i ). Except for the threshold variable value φ th Apart from the point where φ is the variable value, the curve representing the pixel value m(x, y) has a continuous mapping from the variable value φ to the pixel value m(x, y) with a certain slope. Furthermore, the slope of the mapping curve can be determined according to the second weight (λ). i The mapping curve changes with the change of the second weight (λ). For example, when the second weight (λ) is equal to zero, the mapping curve can have a slope of 1 / kφ. th For a continuous curve without discontinuities, when the second weight (λ) equals 1, the mapping curve can map the variable value φ to zero up to the threshold φ. th And at the threshold φ th The variable value φ is then mapped to a step function of 1. When the second weight (λ) is greater than zero and less than 1, the mapping curve can have the same properties as... Figure 5 The mapping curve shown has a similar shape, where the slope varies according to the second weight (λ).

[0081] According to some embodiments of this disclosure, with the second weight (λ) i As the weight (1-λ) increases, the contribution of the binary mask to the blurred mask 6002 becomes larger. Conversely, as the first weight (1-λ) increases, the contribution of the binary mask to the blurred mask 6002 becomes larger. i As the continuous tone mask increases, its contribution to the blur mask 6002 becomes smaller. Figures 8A to 8E The image shown in the middle illustrates the blurring of mask 6002 when the second weight (λ) is equal to 0, 0.25, 0.5, 0.75, and 1.0. (As shown in...) Figures 8A to 8E As shown, the blurred mask 6002 with a larger second weight (λ) exhibits a clearer pattern outline. For example, in Figure 8A The blurred mask 6002, which has a second weight (λ) of zero, shows a continuous tone mask, and... Figure 8E A fuzzy mask 6002 with a second weight (λ) of one is shown as a binary mask. And... Figures 8B to 8D The fuzzy mask 6002 with a second weight (λ) between zero and one includes the continuous mask contribution and the binary mask contribution in the fuzzy mask 6002.

[0082] Return to reference Figure 6 The blur mask 6002 can be evaluated at evaluation process 6320, which conforms to some embodiments of this disclosure. According to some embodiments of this disclosure, the evaluation at evaluation process 6320 can be based on a cost function or gradient map 6005. This can be compared with reference to... Figure 2The cost function calculation and gradient map generation are performed in a manner similar to that described in the first mask optimization process 200, and therefore will not be repeated in its detailed description herein for simplicity. According to some embodiments of this disclosure, the evaluation process 6320 may also involve performing or simulating a process model using a blurred mask 6002. In some embodiments, it is used as... Figure 7 The novel optical model of the segmented continuous mask 6002 shown can be used to perform or simulate a process model. In some embodiments, the optical model for the fuzzy mask 6002 can be weighted by a second weight (λ). i The weighted curve boundary M3D effect is taken into account. For example, when the second weight (λ) i When the second weight (λ) is zero, the blurred mask 6002 can be completely continuous without the M3D effect. i As the second weight (λ) increases, the M3D effect can gradually increase, and when the second weight (λ) increases... i When M3D is equal to one, the M3D effect can be at its maximum.

[0083] According to some embodiments of this disclosure, variables of the initial image 6001 can be changed based on the gradient map 6005 to gradually reduce or minimize the cost function. Therefore, the resulting curve pattern can gradually evolve during iteration, causing the cost function to be reduced or minimized. In some embodiments, iteration can continue until the cost function reaches a certain level or the convergence rate of the optimization process falls below a certain level. In some embodiments, the number of iterations can be preset.

[0084] Figure 9 This is a block diagram illustrating a computer system 100 that may assist in implementing the methods, processes, or apparatus disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105, which may include hardware accelerators) coupled to the bus 102 to process information. The computer system 100 also includes main memory 106, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 102 to store information and instructions to be executed by the processor 104. Main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 to store static information and instructions of the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 to store information and instructions.

[0085] Computer system 100 can be coupled via bus 102 to a display 112 for displaying information to a computer user, such as a cathode ray tube (CRT), flat panel display, or contact panel display. An input device 114, including alphanumeric keys and other keys, is coupled to bus 102 to communicate information and command selection to processor 104. Another type of user input device is a cursor controller 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selection to processor 104 and for controlling cursor movement on display 112. Such input devices typically have two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify a position in a plane. Contact panel (screen) displays can also be used as input devices.

[0086] According to some embodiments, a portion of one or more methods described herein may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors arranged in a multiprocessor configuration may also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0087] 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 volatile memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including conductors containing 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 cartridges, the carrier waves described below, or any other media that can be read by a computer.

[0088] Various forms of computer-readable media can be used to carry one or more sequences of instructions to processor 104 for execution. For example, instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its volatile memory and transmit the instructions via a telephone line using a modem. A modem local to computer system 100 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 fetches and executes instructions. Instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0089] Computer system 100 may also include a communication interface 118 coupled to bus 102. Communication interface 118 provides bidirectional data communication coupled to network link 120 connected to local area network 122. For example, communication interface 118 may be an Integrated Services Digital Network (ISDN) card or modem to provide data communication connectivity with a corresponding type of telephone line. As another example, communication interface 118 may be a Local Area Network (LAN) card to provide data communication connectivity with 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.

[0090] Network link 120 typically provides data communication to other data devices via one or more networks. For example, network link 120 may provide a connection to host computer 124 via local network 122 or to data devices operated by Internet service provider (ISP) 126. ISP 126, in turn, provides data communication services via a global packet data communication network (now commonly referred to as "the Internet" 128). Both local network 122 and Internet 128 use electrical, electromagnetic, or optical signals to carry digital data streams. The signals through various networks and on network link 120 and through communication interface 118 are exemplary forms of carrier waves that carry digital data to and from computer system 100.

[0091] Computer system 100 can send messages and receive data including program code via one or more networks, network links 120, and communication interfaces 118. In the example of the Internet, server 130 can transmit the requested code of an application via the Internet 128, ISP 126, local area network 122, and communication interface 118. For example, such a downloaded application can provide all or part of the methods described herein. The received code can be executed by processor 104 upon receipt or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 can obtain application code in carrier form.

[0092] Figure 10 An exemplary photolithography projection apparatus that can utilize the techniques described herein is schematically depicted. The apparatus includes an irradiation system IL for adjusting a radiation beam B. In such a specific case, the irradiation system also includes: a radiation source SO; a first stage (e.g., a patterning apparatus stage) MT, the first stage being provided with a patterning apparatus holder for holding a patterning apparatus MA (e.g., a mask) and connected to a first locator for accurately positioning the patterning apparatus relative to a project PS; a second stage (substrate stage) WT, the second stage being provided with a substrate holder for holding a substrate W (e.g., a silicon chip coated with resist) and connected to a second locator for accurately positioning the substrate relative to the project PS; and a projection system (“lens”) PS (e.g., a refractive, reflective, or reflective-refractive optical system) for imaging an irradiated portion of the patterning apparatus MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0093] As described herein, the device is of the transmissive type (i.e., having a transmissive patterning apparatus). However, typically, the device can also be of the reflective type (having a reflective patterning apparatus). The device can use a different kind of patterning apparatus than a classic mask; examples include programmable mirror arrays or LCD matrices.

[0094] A source SO (e.g., a mercury lamp or excimer laser, LPP (laser-generated plasma) EUV source) generates a radiation beam. This beam is fed into the irradiation system (irradiator) IL, either directly or after passing through an adjustment device such as a beam expander Ex. The irradiator IL may include adjustment devices AD for setting the outer radial range or inner radial range of the intensity distribution in the beam (typically referred to as σ-outer and σ-inner, respectively). Additionally, the irradiator IL will typically include various other components, such as an integrator IN and a concentrator CO. In this way, the beam B incident on the pattern forming apparatus MA has the desired uniformity and intensity distribution in its cross-section.

[0095] about Figure 10 It should be noted that the source SO can be inside the housing of the photolithography projection device (for example, this is often the case where the source SO is, for example, a mercury lamp), but the source SO can also be located away from the photolithography projection device, and the radiation beam generated by the source SO can be directed to the device (for example, by means of a suitable directional mirror); this latter scenario is often the case where the source SO is an excimer laser (for example, based on KrF, ArF or F2 emitting laser light).

[0096] The beam PB then intercepts the pattern forming apparatus MA held on the pattern forming apparatus stage MT. Having already traversed the pattern forming apparatus MA, the beam B passes through the lens PL, which focuses the beam B onto the target portion C of the substrate W. With the aid of a second positioning device (and an interferometric measuring device IF), the substrate stage WT can be accurately moved, for example, to position different target portions C within the path of the beam PB. Similarly, the first positioning device can be used, for example, to accurately position the pattern forming apparatus MA relative to the path of the beam B, either after mechanical acquisition of the pattern forming apparatus MA from the pattern forming apparatus library or during scanning. Typically, this will be achieved by means of... Figure 10 The long-stroke module (coarse positioning) and short-stroke module (fine positioning) are clearly described in the diagram to realize the movement of the stage MT and WT. However, in the case of a stepper (relative to a stepping scanning tool), the pattern forming apparatus stage MT may be connected only to the short-stroke actuator, or it may be fixed.

[0097] The described tool can be used in two different modes: In step mode, the patterning apparatus stage MT is kept substantially stationary, and the entire patterning apparatus image is projected at once (i.e., a single “flash”) onto the target portion C. The substrate stage WT is then shifted in the x or y direction so that different target portions C can be irradiated by the beam PB. In scan mode, essentially the same scenario is applied, except that a given target portion C is not exposed in a single “flash.” Instead, the patterning apparatus stage MT can move at a speed v in a given direction (the so-called “scanning direction,” e.g., the y-direction), causing the projected beam B to scan across the patterning apparatus image; in parallel, the substrate stage WT is simultaneously moved in the same or opposite directions at a speed V = Mv, where M is the magnification of the lens PL (typically M = ¼ or ⅕). In this way, a relatively large target portion C can be exposed without compromising resolution.

[0098] Figure 11Another exemplary photolithography projection apparatus LA, which can utilize the techniques described herein, is schematically depicted. The photolithography projection apparatus LA includes: a source collector module SO; an illumination system (illuminator) IL configured to modulate a radiation beam B (e.g., EUV radiation); a support structure (e.g., a pattern forming apparatus stage) MT configured to support a pattern forming apparatus (e.g., a mask or stencil) MA and connected to a first positioner PM configured to accurately position the pattern forming apparatus; a substrate stage (e.g., a die stage) WT configured to hold a substrate (e.g., a die coated with resist) W and connected to a second positioner PW configured to accurately position the substrate; and a projection system (e.g., a reflective projection system) PS configured to project a pattern imparted by the pattern forming apparatus MA to the radiation beam B onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0099] As depicted here, the apparatus LA is of the reflective type (e.g., using a reflective patterning apparatus). Note that since most materials are absorptive in the EUV wavelength range, the patterning apparatus can have a multilayer reflector comprising, for example, multiple overlapping layers of molybdenum and silicon. In one example, the multilayer 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 absorptive at both EUV and X-ray wavelengths, the patterned absorbent material thins on the morphology of the patterning apparatus (e.g., a TaN absorber on top of a multilayer reflector) define the locations where features will be printed (positive resist) or not printed (negative resist).

[0100] refer to Figure 11 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 having at least one element (e.g., xenon, lithium, or tin) into a plasma state using one or more emission lines in the EUV range. In one such method (often referred to as laser-generated plasma (“LPP”), plasma can be generated by irradiating a fuel (such as a drop, stream, or cluster of material having an emission element in the spectral line) using a laser beam. The source collector module SO may include… Figure 11 The image shows a portion of the EUV radiation system of a laser, not shown, which provides a laser beam for exciting the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector disposed within a source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and the source collector module can be separate entities.

[0101] In such cases, the laser is not considered part of the lithography apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable directional mirrors or beam expanders. In other cases, such as when the source is a discharge-generated plasma EUV generator (often called a DPP source), the source can be an integral part of the source collector module.

[0102] An irradiator IL may include adjusters for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial range or the inner radial range (often referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the irradiator can be adjusted. Additionally, the irradiator IL may include various other components, such as faceted field mirror assemblies and faceted pupil mirror assemblies. The irradiator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0103] A radiation beam B is incident on a pattern forming apparatus (e.g., a mask) MA held on a support structure (e.g., a pattern forming apparatus stage) MT and patterned by the pattern forming apparatus. After being reflected from the pattern forming apparatus (e.g., the mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate stage WT can be accurately moved, for example, to position different target portions C in the path of the radiation beam B, by means of a second locator PW and a position sensor PS2 (e.g., an interferometer, a linear encoder, or a capacitive sensor). Similarly, a first locator PM and another position sensor PS1 can be used to accurately position the pattern forming apparatus (e.g., the mask) MA relative to the path of the radiation beam B. The pattern forming apparatus (e.g., the mask) MA and the substrate W can be aligned using pattern forming apparatus alignment marks M1, M2 and substrate alignment marks P1, P2.

[0104] The described apparatus LA can be used in at least one of the following modes: 1. In a stepping mode, the support structure (e.g., patterning apparatus stage) MT and the substrate stage WT are kept substantially stationary (i.e., single static exposure) while the entire pattern applied to the radiation beam is projected onto the target portion C in a single step. Then, the substrate stage WT is shifted in the X or Y direction so that different target portions C can be exposed. 2. In a scanning mode, the support structure (e.g., patterning apparatus stage) MT and the substrate stage WT are scanned synchronously while the pattern applied to the radiation beam is projected onto the target portion C (i.e., single dynamic exposure). The speed and direction of the substrate stage WT relative to the support structure (e.g., patterning apparatus stage) MT can be determined by the magnification (reduction) and image inversion characteristics of the projection system PS. 3. In another mode, the support structure (e.g., patterning apparatus stage) MT is kept substantially stationary, thereby holding the programmable patterning apparatus in place, and the pattern applied to 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 programmable patterning apparatuses, such as programmable mirror arrays of the type mentioned above.

[0105] Figure 12 The apparatus LA, comprising a source collector module SO, an irradiation system IL, and a projection system PS, is shown in more detail. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained within the enclosure 220 of the source collector module SO. An EUV radiation emission plasma 210 can be formed by generating a plasma source through discharge. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, the very hot plasma 210 is generated by a discharge that causes at least a partially ionized plasma. For efficient radiation generation, Xe, Li, Sn vapor, or any other suitable gas or vapor with a partial pressure of, for example, 10 Pa may be required. In some embodiments, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0106] Radiation emitted by thermal plasma 210 is transferred from source chamber 211 to collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or foil trap) positioned in or behind an opening in source chamber 211. Contaminant trap 230 may include a channel structure. Contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As known in the art, contaminant traps or contaminant barriers 230 further indicated herein include at least a channel structure.

[0107] Collector chamber 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from a grating spectral filter 240 to be focused into a virtual source point IF along an optical axis indicated by the dotted dashed line "O". The virtual source point IF is often referred to as the intermediate focus, and the source collector module is arranged such that the virtual source point IF is located at or near an opening 221 in the enclosure structure 220. The virtual source point IF provides an image of the radiative emission plasma 210.

[0108] Subsequently, radiation traverses an illumination system IL, which may include a faceted field mirror assembly 22 and a faceted pupil mirror assembly 24. The faceted field mirror assembly 22 and the faceted pupil mirror assembly 24 are 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. After the radiation beam 21 is reflected at the patterning apparatus MA, held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28 and 30 onto the substrate W, held by the substrate stage WT.

[0109] More components than those shown can typically be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithography equipment, the grating spectral filter 240 may optionally be present. Furthermore, more mirrors than are shown in the figures, for example, more than [number missing] mirrors may be present in the projection system PS. Figure 12 The reflective elements shown in the figure include 1 to 6 additional reflective elements.

[0110] Figure 12The collector optics CO illustrated is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, which are merely examples of collectors (or collector mirrors). The grazing incidence reflectors 253, 254, and 255 are arranged to be axially symmetrical about the optical axis O, and this type of collector optics CO can be used in combination with a discharge-generated plasma source, often referred to as a DPP source.

[0111] Alternatively, the source collector module SO can be Figure 13 The diagram shows a portion of the LPP radiation system. A laser (LAS) is arranged to deposit 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. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal incident collector optics (CO), and focused onto an opening 221 in the enclosure structure 220.

[0112] The concepts disclosed herein can be used to simulate or mathematically model any general imaging system for characterizing sub-wavelength features, and can be particularly useful for emerging imaging techniques capable of generating increasingly shorter wavelengths. Emerging techniques already in use include EUV (Extreme Ultraviolet) and DUV lithography, which can generate wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate wavelengths in the range of 20 nm to 5 nm by using synchrotrons or by utilizing high-energy electrons to bombard materials (solid-state or plasma), thereby generating photons within this range.

[0113] Embodiments of this disclosure can be further described in the following ways.

[0114] 1. A computer-implemented method for determining a mask pattern of a pattern forming apparatus, the method comprising:

[0115] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0116] The first image is iteratively optimized based on the gradient map associated with the continuous tone mask and the binary mask.

[0117] 2. The method according to aspect 1, wherein the gradient map is obtained by a weighted sum of a first gradient map associated with the continuous tone mask and a second gradient map associated with the binary mask.

[0118] 3. The method according to aspect 2 further includes:

[0119] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0120] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0121] 4. The method according to aspect 3, wherein the first optical model takes the continuous tone mask as input, and the second optical model takes the binary mask as input.

[0122] 5. The method according to aspect 3 or 4, wherein the first gradient map is calculated based on the first process image, and the second gradient map is calculated based on the second process image.

[0123] 6. The method according to any one of aspects 3 to 5, wherein the gradient map is obtained by summing the result of multiplying the first gradient map with the first weight and the result of multiplying the second gradient map with the second weight.

[0124] 7. The method according to aspect 6, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0125] 8. The method according to aspect 3 or 4 further includes:

[0126] The combination cost function is calculated based on simulation results of the photolithography patterning process using the continuous tone mask and the binary mask, respectively.

[0127] 9. The method according to aspect 8, wherein the gradient graph is based on the combined cost function.

[0128] 10. The method according to aspect 1 further includes:

[0129] A combined mask is obtained by weighting the binary mask and the continuous tone mask.

[0130] 11. The method according to aspect 10, further comprising:

[0131] The combined mask is used to simulate the photolithography patterning process using an optical model to generate process images on a substrate.

[0132] 12. The method according to aspect 10 or 11, wherein the gradient map is associated with the combined mask.

[0133] 13. The method according to aspect 11 or 12, wherein the gradient map is calculated based on the process image.

[0134] 14. The method according to any one of aspects 10 to 13, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with the first weight and the result of multiplying the binary mask with the second weight.

[0135] 15. The method according to aspect 14, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0136] 16. A computer-implemented method for determining a mask pattern of a pattern forming apparatus, the method comprising:

[0137] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0138] The first image is iteratively optimized by simultaneously adjusting the continuous tone mask and the binary mask.

[0139] 17. The method according to aspect 16 further includes:

[0140] The photolithography patterning process is simulated using the continuous tone mask and the binary mask, respectively.

[0141] 18. The method according to aspect 17 further includes:

[0142] The combined cost function is calculated based on the simulation results of the simulations using the continuous tone mask and the binary mask, respectively.

[0143] 19. The method according to aspect 18, wherein the iterative optimization of the first image is performed based on the combined cost function.

[0144] 20. The method according to aspect 18 or 19, wherein the combined cost function is obtained by a weighted sum of a first cost function associated with the continuous tone mask and a second cost function associated with the binary mask.

[0145] 21. The method according to aspect 20, wherein simulating the photolithographic patterning process using the continuous tone mask and the binary mask comprises:

[0146] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0147] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0148] 22. The method according to aspect 21, wherein the first cost function is calculated based on the first process image, and the second cost function is calculated based on the second process image.

[0149] 23. The method according to claim 21 or 22, wherein the combined cost function is obtained by summing the result of multiplying the first cost function with the first weight and the result of multiplying the second cost function with the second weight.

[0150] 24. The method according to aspect 23, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0151] 25. The method according to aspect 16 further includes:

[0152] A combined mask is obtained by weighted superposition of the binary mask and the continuous tone mask.

[0153] 26. The method according to aspect 25 further includes:

[0154] The combined mask is used to simulate the photolithographic patterning process using an optical model.

[0155] 27. The method according to aspect 26 further includes:

[0156] The cost function is calculated based on the simulation results using the combined mask.

[0157] 28. The method according to aspect 27, wherein the iterative optimization of the first image is performed based on the cost function.

[0158] 29. The method according to any one of aspects 25 to 28, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with the first weight and the result of multiplying the binary mask with the second weight.

[0159] 30. The method according to aspect 29, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0160] 31. An apparatus for determining a mask pattern of a pattern forming apparatus, the apparatus comprising:

[0161] Memory, the memory storing instruction sets; and

[0162] At least one processor, the at least one processor being configured to execute the instruction set to cause the device to perform the following operations:

[0163] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0164] The first image is iteratively optimized based on the gradient map associated with the continuous tone mask and the binary mask.

[0165] 32. The apparatus according to aspect 31, wherein the gradient map is obtained by a weighted sum of a first gradient map associated with the continuous tone mask and a second gradient map associated with the binary mask.

[0166] 33. The device according to aspect 32, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0167] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0168] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0169] 34. The device according to aspect 33, wherein the first optical model takes the continuous tone mask as input, and the second optical model takes the binary mask as input.

[0170] 35. The apparatus according to aspect 33 or 34, wherein the first gradient map is calculated based on the first process image, and the second gradient map is calculated based on the second process image.

[0171] 36. The apparatus according to any one of aspects 33 to 35, wherein the gradient map is obtained by summing the result of multiplying the first gradient map with the first weight and the result of multiplying the second gradient map with the second weight.

[0172] 37. The device according to aspect 36, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0173] 38. The device according to aspect 33 or 34, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0174] The combination cost function is calculated based on simulation results of the photolithography patterning process using the continuous tone mask and the binary mask, respectively.

[0175] 39. The device according to aspect 38, wherein the gradient graph is based on the combined cost function.

[0176] 40. The device according to aspect 31, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0177] A combined mask is obtained by weighting the binary mask and the continuous tone mask.

[0178] 41. The device according to aspect 40, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0179] The combined mask is used to simulate the photolithography patterning process using an optical model to generate process images on a substrate.

[0180] 42. The device according to aspect 40 or 41, wherein the gradient map is associated with the combined mask.

[0181] 43. The apparatus according to aspect 41 or 42, wherein the gradient map is calculated based on the process image.

[0182] 44. The apparatus according to any one of aspects 40 to 43, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with a first weight and the result of multiplying the binary mask with a second weight.

[0183] 45. The device according to aspect 44, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0184] 46. ​​An apparatus for determining a mask pattern of a pattern forming apparatus, the apparatus comprising:

[0185] Memory, the memory storing instruction sets; and

[0186] At least one processor, the at least one processor being configured to execute the instruction set to cause the device to perform the following operations:

[0187] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0188] The first image is iteratively optimized by simultaneously adjusting the continuous tone mask and the binary mask.

[0189] 47. The device according to aspect 46, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0190] The photolithography patterning process is simulated using the continuous tone mask and the binary mask, respectively.

[0191] 48. The device according to aspect 47, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0192] The combined cost function is calculated based on the simulation results of the simulations using the continuous tone mask and the binary mask, respectively.

[0193] 49. The device according to aspect 48, wherein, during iterative optimization of the first image, the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0194] The first image is iteratively optimized based on the combined cost function.

[0195] 50. The apparatus according to aspect 48 or 49, wherein the combined cost function is obtained by a weighted sum of a first cost function associated with the continuous tone mask and a second cost function associated with the binary mask.

[0196] 51. The apparatus according to aspect 50, wherein, when simulating a photolithographic patterning process using the continuous tone mask and the binary mask, the at least one processor is configured to execute the instruction set to cause the apparatus to further perform the following operations:

[0197] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0198] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0199] 52. The apparatus according to aspect 51, wherein the first cost function is calculated based on the first process image, and the second cost function is calculated based on the second process image.

[0200] 53. The apparatus according to aspect 51 or 52, wherein the combined cost function is obtained by summing the result of multiplying the first cost function with the first weight and the result of multiplying the second cost function with the second weight.

[0201] 54. The device according to aspect 53, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0202] 55. The device according to aspect 46, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0203] A combined mask is obtained by weighted superposition of the binary mask and the continuous tone mask.

[0204] 56. The device according to aspect 55, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0205] The combined mask is used to simulate the photolithographic patterning process using an optical model.

[0206] 57. The device according to aspect 56, wherein the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0207] The cost function is calculated based on the simulation results using the combined mask.

[0208] 58. The device according to aspect 57, wherein, during iterative optimization of the first image, the at least one processor is configured to execute the instruction set to cause the device to further perform the following operations:

[0209] The first image is iteratively optimized based on the cost function.

[0210] 59. The apparatus according to any one of aspects 55 to 58, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with a first weight and the result of multiplying the binary mask with a second weight.

[0211] 60. The device according to aspect 59, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0212] 61. A non-transitory computer-readable medium storing an instruction set executable by at least one processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a pattern forming apparatus, the method comprising:

[0213] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0214] The first image is iteratively optimized based on the gradient map associated with the continuous tone mask and the binary mask.

[0215] 62. The computer-readable medium according to aspect 61, wherein the gradient map is obtained by a weighted sum of a first gradient map associated with the continuous tone mask and a second gradient map associated with the binary mask.

[0216] 63. The computer-readable medium according to aspect 62, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0217] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0218] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0219] 64. The computer-readable medium according to aspect 63, wherein the first optical model takes the continuous tone mask as input, and the second optical model takes the binary mask as input.

[0220] 65. The computer-readable medium according to aspect 63 or 64, wherein the first gradient map is calculated based on the first process image, and the second gradient map is calculated based on the second process image.

[0221] 66. A computer-readable medium according to any one of aspects 63 to 65, wherein the gradient map is obtained by summing the result of multiplying the first gradient map with the first weight and the result of multiplying the second gradient map with the second weight.

[0222] 67. The computer-readable medium according to aspect 66, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, wherein n > m > 0.

[0223] 68. The computer-readable medium according to aspect 63 or 64, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0224] The combination cost function is calculated based on simulation results of the photolithography patterning process using the continuous tone mask and the binary mask, respectively.

[0225] 69. The computer-readable medium according to aspect 68, wherein the gradient graph is based on the combined cost function.

[0226] 70. The computer-readable medium according to aspect 61, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0227] A combined mask is obtained by weighting the binary mask and the continuous tone mask.

[0228] 71. The computer-readable medium according to aspect 70, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0229] The combined mask is used to simulate the photolithography patterning process using an optical model to generate process images on a substrate.

[0230] 72. The computer-readable medium according to aspect 70 or 71, wherein the gradient map is associated with the combined mask.

[0231] 73. The computer-readable medium according to aspect 71 or 72, wherein the gradient map is calculated based on the process image.

[0232] 74. A computer-readable medium according to any one of aspects 70 to 73, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with a first weight and the result of multiplying the binary mask with a second weight.

[0233] 75. The computer-readable medium according to aspect 74, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0234] 76. A non-transitory computer-readable medium storing an instruction set executable by at least one processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a pattern forming apparatus, the method comprising:

[0235] Obtain a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and

[0236] The first image is iteratively optimized by simultaneously adjusting the continuous tone mask and the binary mask.

[0237] 77. The computer-readable medium according to aspect 76, wherein the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0238] The photolithography patterning process is simulated using the continuous tone mask and the binary mask, respectively.

[0239] 78. The computer-readable medium according to aspect 77, wherein the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0240] The combined cost function is calculated based on the simulation results of the simulations using the continuous tone mask and the binary mask, respectively.

[0241] 79. The computer-readable medium according to aspect 78, wherein, during iterative optimization of the first image, the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0242] The first image is iteratively optimized based on the combined cost function.

[0243] 80. The computer-readable medium according to aspect 78 or 79, wherein the combined cost function is obtained by a weighted sum of a first cost function associated with the continuous tone mask and a second cost function associated with the binary mask.

[0244] 81. The computer-readable medium according to aspect 80, wherein, when simulating a photolithographic patterning process using the continuous tone mask and the binary mask, the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0245] Using the continuous tone mask, a first optical model is used to simulate the photolithographic patterning process to generate a first process image on the substrate; and

[0246] The binary mask is used to simulate the photolithography patterning process using a second optical model to generate a second process image on the substrate.

[0247] 82. The computer-readable medium according to aspect 81, wherein the first cost function is calculated based on the first process image, and the second cost function is calculated based on the second process image.

[0248] 83. The computer-readable medium according to aspect 81 or 82, wherein the combined cost function is obtained by summing the result of multiplying the first cost function with the first weight and the result of multiplying the second cost function with the second weight.

[0249] 84. The computer-readable medium according to aspect 83, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0250] 85. The computer-readable medium according to aspect 76, wherein the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0251] A combined mask is obtained by weighted superposition of the binary mask and the continuous tone mask.

[0252] 86. The computer-readable medium according to aspect 85, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0253] The combined mask is used to simulate the photolithographic patterning process using an optical model.

[0254] 87. The computer-readable medium according to aspect 86, wherein the instruction set executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0255] The cost function is calculated based on the simulation results using the combined mask.

[0256] 88. The computer-readable medium according to aspect 87, wherein, during iterative optimization of the first image, the set of instructions executable by at least one processor of the computing device causes the computing device to perform the following operations:

[0257] The first image is iteratively optimized based on the cost function.

[0258] 89. A computer-readable medium according to any one of aspects 85 to 88, wherein the combined mask is obtained by summing the result of multiplying the continuous tone mask with a first weight and the result of multiplying the binary mask with a second weight.

[0259] 90. The computer-readable medium according to aspect 89, wherein the first weight changes such that the value of the first weight at the m-th iteration is greater than or equal to the value of the first weight at the n-th iteration, where n > m > 0.

[0260] While the concepts disclosed herein can be used for imaging on substrates such as silicon chips, it should be understood that the disclosed concepts can be used with any type of lithography imaging system, such as a lithography imaging system for imaging on substrates other than silicon chips.

[0261] The block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer hardware or software products according to various exemplary embodiments of the present disclosure. In this regard, each block in the diagram may represent a particular arithmetic or logical computation process implemented using hardware such as electronic circuits. A block may also represent a portion of module, segment, or program code including one or more executable instructions for implementing a specified logical function. It should be understood that in some alternative embodiments, the functions indicated in the blocks may not appear in the order mentioned in the figures. For example, depending on the functionality involved, two blocks shown consecutively may be executed or implemented substantially simultaneously, or the two blocks may sometimes be executed in reverse order. Some blocks may also be omitted. It should also be understood that each block of the block diagram, and combinations of blocks, may be implemented by a system based on dedicated hardware performing the specified function or action, or by a combination of dedicated hardware and computer instructions.

[0262] It will be understood that embodiments of this disclosure are not limited to the exact constructions described above and illustrated in the accompanying drawings, and various modifications and changes can be made without departing from its scope. This disclosure has been described in conjunction with various embodiments, and other embodiments of the invention will be apparent to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This specification and examples are intended to be exemplary only, wherein the true scope and spirit of the invention are indicated by the following claims.

Claims

1. A computer-implemented method for determining a mask pattern of a patterning device, the method comprising: obtaining a continuous tone mask and a binary mask from a first image corresponding to a target design associated with the mask pattern; and iteratively optimizing the first image based on a gradient map associated with the continuous tone mask and the binary mask.

2. The method of claim 1, wherein, The gradient map is obtained by a weighted sum of a first gradient map associated with the continuous tone mask and a second gradient map associated with the binary mask.

3. The method of claim 2, further comprising: simulating a lithographic patterning process using a first optical model with the continuous tone mask to produce a first process image on a substrate; and simulating a lithographic patterning process using a second optical model with the binary mask to produce a second process image on a substrate.

4. The method of claim 3, wherein, The first optical model takes the continuous tone mask as input and the second optical model takes the binary mask as input.

5. The method of claim 3, wherein, The first gradient map is computed based on the first process image and the second gradient map is computed based on the second process image.

6. The method of claim 3, wherein, The gradient map is obtained by summing a product of the first gradient map with a first weight and a product of the second gradient map with a second weight.

7. The method of claim 6, wherein, The first weight varies such that a value of the first weight at an mth iteration is greater than or equal to a value of the first weight at an nth iteration, where n > m > 0.

8. The method of claim 3, further comprising: computing a combined cost function based on simulation results of simulating the lithographic patterning process using the continuous tone mask and the binary mask, respectively.

9. The method of claim 8, wherein, The gradient map is based on the combined cost function.

10. The method of claim 1, further comprising: obtaining a combined mask by a weighted sum of the binary mask and the continuous tone mask.

11. The method of claim 10, further comprising: simulating a lithographic patterning process using an optical model with the combined mask to produce a process image on a substrate.

12. The method of claim 10, wherein, The gradient map is associated with the combined mask.

13. The method of claim 10, wherein, The gradient map is computed based on the process image.

14. The method of claim 10, wherein, The combined mask is obtained by summing a product of the continuous tone mask with a first weight and a product of the binary mask with a second weight.

15. The method of claim 14, wherein, The first weight varies such that a value of the first weight at an mth iteration is greater than or equal to a value of the first weight at an nth iteration, where n > m > 0.

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