Mask pattern optimization

Abstract

The present disclosure provides a computer implemented method for determining a mask pattern of a patterning device. The method comprises 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 concurrently adjusting the continuous tone mask and the binary mask.

Description

MASK PATTERN OPTIMIZATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 532,020 which was filed on August 10, 2023 and which is incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] The embodiments provided herein generally relate to lithography photomask design and patterning process, more particularly, relate to a mask pattern optimization.BACKGROUND

[0003] A lithographic apparatus can be used, for example, in the manufacturing of integrated circuits (ICs). In such a case, a mask or a reticle may contain or provide a circuit pattern corresponding to an individual layer of the IC (“design layout”), and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer). A curvilinear pattern of a patterning device can be iteratively optimized to ensure that a targeted design is transferred on a substrate.SUMMARY

[0004] Some embodiments provide a computer implemented method for determining a mask pattern of a patterning device. The method comprises 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 that is associated with the continuous tone mask and the binary mask.

[0005] Some embodiments provide a computer implemented method for determining a mask pattern of a patterning device. The method comprises 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 concurrently adjusting the continuous tone mask and the binary mask.

[0006] Some embodiments provide an apparatus for determining a mask pattern of a patterning device. The apparatus comprises a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform: 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 that is associated with the continuous tone mask and the binary mask.

[0007] Some embodiments provide an apparatus for determining a mask pattern of a patterning device. The apparatus comprises a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform: obtaining a continuoustone 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 concurrently adjusting the continuous tone mask and the binary mask.

[0008] Some embodiments provide a non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a patterning device. The method comprises 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 that is associated with the continuous tone mask and the binary mask.

[0009] Some embodiments provide a non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform a method for determining a mask pattern of a patterning device. The method comprises 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 concurrently adjusting the continuous tone mask and the binary mask.

[0010] Other advantages of the embodiments of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of the present invention.BRIEF DESCRIPTION OF FIGURES

[0011] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0012] FIG. 1A is a schematic block diagram of various subsystems of an example lithography system, consistent with embodiments of the present disclosure.

[0013] FIG. IB is a schematic block diagram of simulation models corresponding to the subsystems in FIG. 1A, consistent with embodiments of the present disclosure

[0014] FIG. 2 is a flow diagram of a first example mask optimization method, consistent with embodiments of the present disclosure.

[0015] FIG. 3A-3F illustrate graphs showing an example image initialization process, consistent with embodiments of the present disclosure.

[0016] FIG. 4A illustrates an example mapping function between an initial image to a first image, consistent with embodiments of the present disclosure.

[0017] FIG. 4B-4E are an example initial image, a first image, a second image, and a curvilinear pattern respectively, consistent with embodiments of the present disclosure.

[0018] FIG. 5 illustrates an example weight function, consistent with embodiments of the present disclosure.

[0019] FIG. 6 is a flow diagram of a second example mask optimization method, consistent with embodiments of the present disclosure.

[0020] FIG. 7 illustrates an example mapping function between an initial image and a fuzzy mask, consistent with embodiments of the present disclosure.

[0021] FIG. 8A-8E illustrate example fuzzy mask images according to a weight value, consistent with embodiments of the present disclosure.

[0022] FIG. 9 is a block diagram of an example computer system, consistent with embodiments of the present disclosure.

[0023] FIG. 10 is a schematic diagram of an example lithographic projection apparatus, consistent with embodiments of the present disclosure.

[0024] FIG. 11 is a schematic diagram of another example lithographic projection apparatus, consistent with embodiments of the present disclosure.

[0025] FIG. 12 is a more detailed view of the apparatus in FIG. 10, consistent with embodiments of the present disclosure.

[0026] FIG. 13 is a more detailed view of the source collector module SO of the apparatus of FIG. 11 and FIG. 12, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0027] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the disclosed embodiments as recited in the appended claims. Although specific reference may be made in this disclosure to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid-crystal display panels, thin- film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle”, “wafer” or “die” in this text should be considered as interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0028] A lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device (e.g., a mask) may contain or provide a pattern corresponding to an individual layer of the IC (“design layout”), and this pattern can be transferred onto a target portion (e.g. comprising one or more dies) on a substrate (e.g., silicon wafer) that has been coated with a layer of radiation-sensitive material (“resist”), by methods such as irradiating the target portion through the pattern on the patterning device. In general, a single substratecontains a plurality of adjacent target portions to which the pattern is transferred successively by the lithographic projection apparatus, one target portion at a time. In one type of lithographic projection apparatuses, the pattern on the entire patterning device is transferred onto one target portion in one go; such an apparatus is commonly referred to as a stepper. In an alternative apparatus, commonly referred to as a step-and-scan apparatus, a projection beam scans over the patterning device in a given reference direction (the “scanning” direction) while synchronously moving the substrate parallel or anti-parallel to this reference direction. Different portions of the pattern on the patterning device are transferred to one target portion progressively. Since, in general, the lithographic projection apparatus will have a reduction ratio M (e.g., 4), the speed F at which the substrate is moved will be 1 / M times that at which the projection beam scans the patterning device. More information with regard to lithographic devices as described herein can be gleaned, for example, from U.S. Pat. No. 6,046,792, incorporated herein by reference.

[0029] Prior to transferring the pattern from the patterning device to the substrate, the substrate may undergo various procedures, such as priming, resist coating and a soft bake. After exposure, the substrate may be subjected to other procedures (“post-exposure procedures”), such as a post-exposure bake (PEB), development, a hard bake and measurement / inspection of the transferred pattern. This array of procedures is used as a basis to make an individual layer of a device, e.g., an IC. The substrate may then undergo various processes such as etching, ion-implantation (doping), metallization, oxidation, chemo-mechanical polishing, etc., all intended to finish off the individual layer of the device. If several layers are required in the device, then the whole procedure, or a variant thereof, is repeated for each layer. Eventually, a device will be present in each target portion on the substrate. These devices are then separated from one another by a technique such as dicing or sawing, whence the individual devices can be mounted on a carrier, connected to pins, etc.

[0030] Thus, manufacturing devices, such as semiconductor devices, typically processes a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the devices. Such layers and features are typically manufactured and processed using, e.g., deposition, lithography, etch, chemical-mechanical polishing, and ion implantation. Multiple devices may be fabricated on a plurality of dies on a substrate and then separated into individual devices. This device manufacturing process may be considered a patterning process. A patterning process involves a patterning step, such as optical or nanoimprint lithography using a patterning device in a lithographic apparatus, to transfer a pattern on the patterning device to a substrate and typically, but optionally, involves one or more related pattern processing steps, such as resist development by a development apparatus, baking of the substrate using a bake tool, etching using the pattern using an etch apparatus, etc.

[0031] As noted, lithography is a central step in the manufacturing of device such as ICs, where patterns formed on substrates define functional elements of the devices, such as microprocessors,memory chips, etc. Similar lithographic techniques are also used in the formation of flat panel displays, micro-electro mechanical systems (MEMS) and other devices.

[0032] As semiconductor manufacturing processes continue to advance, the dimensions of functional elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as “Moore's law”. At the current state of technology, layers of devices are manufactured using lithographic projection apparatuses that project a design layout onto a substrate using illumination from a deep-ultraviolet illumination source, creating individual functional elements having dimensions well below 100 nm, i.e., less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source).

[0033] This process in which features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus are printed, is commonly known as low-kl lithography, according to the resolution formula CD=kl xz. / NA, where X is the wavelength of radiation employed (currently in most cases 248 nm or 193 nm), NA is the numerical aperture of projection optics in the lithographic projection apparatus, CD is the “critical dimension” — generally the smallest feature size printed — and kl is an empirical resolution factor. In general, the smaller kl, the more difficult it becomes to reproduce a pattern on the substrate that resembles the shape and dimensions planned by a designer in order to achieve particular electrical functionality and performance. To overcome these difficulties, sophisticated fine-tuning steps are applied to the lithographic projection apparatus, the design layout, or the patterning device. These include, for example, but not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as “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 broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting, or projecting radiation from the source before the radiation passes the patterning device, or optical components for shaping, adjusting or projecting the radiation after the radiation passes the patterning device. The projection optics generally exclude the source and the patterning device.

[0034] In the present disclosure, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193,157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[0035] The term “optimizing” and “optimization” as used herein mean adjusting a lithographic projection apparatus such that results or processes of lithography have more desirable characteristics, such as higher accuracy of projection of design layouts on a substrate, larger process windows, etc.

[0036] Further, the lithographic projection apparatus may be of a type having two or more substrate tables (or two or more patterning device tables). In such "multiple stage" devices the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposures. Twin stage lithographic projection apparatuses are described, for example, in US 5,969,441, incorporated herein by reference.

[0037] The patterning device can comprise, or can form, one or more design layouts. The design layout can be generated utilizing CAD (computer-aided design) programs, this process often being referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts / patterning devices. These rules are set by processing and design limitations. For example, design rules define the space tolerance between devices (such as gates, capacitors, etc.) or interconnect lines, so as to ensure that the devices or lines do not interact with one another in an undesirable way. One or more of the design rule limitations may be referred to as “critical dimension” (CD). A critical dimension of a device can be defined as the smallest width of a line or hole or the smallest space between two lines or two holes. Thus, the CD determines the overall size and density of the designed device. Of course, one of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0038] The term “mask” or “patterning device” as employed in this disclosure may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate; the term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include: a programmable mirror array and a programmable LCD array.

[0039] An example of a programmable mirror array is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation. Using an appropriate filter, the said undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. More information on such mirror arrays can be gleaned,for example, from U. S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0040] An example of a programmable LCD array is given in U.S. Pat. No. 5,229,872, which is incorporated herein by reference.

[0041] As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component includes A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component includes A, B, or C, then, unless specifically stated otherwise or infeasible, the component 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’ do not necessarily modify an entirety of a following list and do not necessarily modify each member of the list, such that “at least one of A, B, and C” should be understood as including 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” shall be interpreted in the broadest sense to include one of A, or one of B.

[0042] As a brief introduction, FIG. 1A illustrates an exemplary lithographic projection apparatus 10 A. Major components are a radiation source 12 A, which may be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have the radiation source); illumination optics which, e.g., define the partial coherence (denoted as sigma) and which may include optics 14 A, 16 Aa and 16 Ab that shape radiation from the source 12 A; a patterning device 18 A; and transmission optics 16 Ac that project an image of the patterning device pattern onto a substrate plane 22 A. An adjustable filter or aperture 20 A at the pupil plane of the projection optics may restrict the range of beam angles that impinge on substrate plane 22 A, where the largest possible angle defines the numerical aperture of the projection optics NA=n sin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics, and ©max is the largest angle of the beam exiting from the projection optics that can still impinge on substrate plane 22 A.

[0043] In an optimization process of a system, a figure of merit of the system can be represented as a cost function. The optimization process boils down to a process of finding a set of parameters (design variables) of the system that minimizes the cost function. The cost function can have any suitable form depending on the goal of the optimization. For example, the cost function can be weighted root mean square (RMS) of deviations of certain characteristics (evaluation points) of the system with respect to the intended values (e.g., ideal values) of these characteristics; the cost function can also be the maximum of these deviations (i.e., worst deviation). The term “evaluation points” herein should be interpreted broadly to include any characteristics of the system. The design variables of the system can be confined to finite ranges or be interdependent due to practicalities of implementations of the system. In case of a lithographic projection apparatus, the constraints are often associated withphysical properties and characteristics of the hardware such as tunable ranges, or patterning device manufacturability design rules, and the evaluation points can include physical points on a resist image on a substrate, as well as non-physical characteristics such as dose and focus.

[0044] In a lithographic projection apparatus, a source provides illumination (i.e. radiation) to a patterning device and projection optics direct and shape the illumination, via the patterning device, onto a substrate. The projection optics may include at least some of the components 14 A, 16 Aa, 16 Ab and 16 Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A resist layer on the substrate is exposed and the aerial image is transferred to the resist layer as a latent “resist image” (RI) therein. The resist image (RI) can be defined as a spatial distribution of solubility of the resist in the resist layer. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related only to properties of the resist layer (e.g., effects of chemical processes that occur during exposure, post-exposure bake (PEB) and development). Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device and the projection optics) dictate the aerial image and can be defined in an optical model. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics. Details of techniques and models used to transform a design layout into various lithographic images (e.g., an aerial image, a resist image, etc.), apply optical proximity correction (OPC) using those techniques and models and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010- 0180251, the disclosure of each which is hereby incorporated by reference in its entirety.

[0045] An exemplary flow chart for simulating lithography in a lithographic projection apparatus is illustrated in FIG. IB. As will be appreciated, the models may represent a different patterning process and need not comprise all the models described below. A source model 31 represents optical characteristics (including radiation intensity distribution or phase distribution) of the source. A projection optics model 32 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by the projection optics) of the projection optics. A patterning device / design layout model 35 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to a feature of an integrated circuit, a memory, an electronic device, etc.), which is the representation of an arrangement of features on or formed by a patterning device. An aerial image 36 can be simulated from the source model 31, the projection optics model 32 and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using a resist model 37. In some embodiments, the resist image 38 can be used asan input to a post-pattern transfer process model 39. The post-pattern transfer process model 39 defines performance of one or more post-resist development processes (e.g., etch, development, etc.). For example, the post-pattern transfer process model 39 may be an etch model 39 that may be predict an etch image using the resist image 38. The etch image may be representative of contours etched on the substrate after the etch process. Simulation of lithography can, for example, predict contours and CDs in the resist image.

[0046] More specifically, it is noted that the source model 31 can represent the optical characteristics of the source that include, but are not limited to, numerical aperture settings, NA-sigma (o) settings as well as any particular illumination source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical characteristics of the of the projection optics that include aberration, distortion, refractive indexes, physical sizes, physical dimensions, etc. The design layout model 35 can also represent physical properties of a physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. The objective of the simulation is to accurately predict, for example, edge placements, aerial image intensity slopes and CDs, which can then be compared against an intended design. The intended design is generally defined as a pre-optical proximity correction (OPC) design layout which can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0047] Thus, the model formulation describes most, if not all, of the known physics and chemistry of the overall process, and each of the model parameters desirably corresponds to a distinct physical or chemical effect. The model formulation thus sets an upper bound on how well the model can be used to simulate the overall manufacturing process.

[0048] In an example, computational analysis of the lithography or an etch process employs a prediction model (e.g., as discussed above with FIG. IB) that, when properly calibrated, can produce accurate prediction of dimensions from the lithography or the etch process. A model of lithography or etch processes is typically calibrated based on empirical measurements. This calibration may include running a test wafer with different process parameters, measuring resulting critical dimensions after lithography process, and calibrating a model to fit the measured results. In practice, fast and accurate models serve to improve device performance or yield, enhance process windows or increase design choices. It can be understood by a person skilled in the art that the methods described herein are not limited to a particular model of the lithography. For calibration of a desired model, images can be obtained after any semiconductor fabrication steps. For example, an aerial image, a resist image, an etch image, an image after a chemical mechanical polishing, or other images related to a process of the patterning process.

[0049] In computational lithography models, usually CD gauges measured by CD-SEM (Scanning Electron Microscope) are used as input data to calibrate the model. A goal of lithography modelling is to predict accurate resist contours for every location on the substrate. Similarly, a goal of etchmodelling is to predict accurate etch contours for every location on the substrate. In some embodiments, computational analysis of an etch process employs a calibrated prediction model that can predict dimensions of etched structures resulting from the etch process. For example, an etch model related to the etch process may be calibrated based on empirical measurements. The calibration process may include patterning a test wafer with different process parameters, measuring CDs of a pattern on the test wafer after the etch process, and calibrating the etch model based on the measured CDs. In practice, a fast and accurate model can be employed to improve a performance of a patterning apparatus, a patterning yield, process windows of the patterning process, or increase design choices related to e.g., determining mask patterns.

[0050] One aspect of understanding a lithographic process is understanding the interaction of the radiation and the patterning device. The electromagnetic field of the radiation after the radiation passes the patterning device may be determined from the electromagnetic field of the radiation before the radiation reaches the patterning device and a function that characterizes the interaction. This function may be referred to as the mask transmission function (which can be used to describe the interaction by a transmissive patterning device or a reflective patterning device).

[0051] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in the binary form may be referred to as a binary mask. Another form is continuous. Namely, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the location on the patterning device. A mask transmission function in the continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, the CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of binary value of either 0 or 1. In some embodiments, CTM may be a pixelated gray scale image, where each pixel having values (e.g., within a range [-255, 255], normalized values within a range [0, 1] or [-1, 1] or other appropriate ranges).

[0052] The thin-mask approximation, also called the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction of the radiation and the patterning device. The thin-mask approximation assumes that the thickness of the structures on the patterning device is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin-mask approximation assumes the electromagnetic field after the patterning device is the multiplication of the incident electromagnetic field with the mask transmission function. However, as lithographic processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device become smaller and smaller, the assumption of the thin-mask approximation can break down. For example, interaction of the radiation with the structures (e.g., edges between the top surface and a sidewall) because of their finite thicknesses(“mask 3D effect” or “M3D”) may become significant. Encompassing this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of the radiation with the patterning device. A mask transmission function under the thin-mask approximation may be referred to as a thin-mask transmission function. A mask transmission function encompassing M3D may be referred to as a M3D mask transmission function.

[0053] In the present disclosure, one or more images may be generated, including a continuous transmission mask image, a binary mask image, fuzzy mask image, curvilinear mask image, etc. The images include various types of signals that may be characterized by pixel values or intensity values of each pixel. Depending on the relative values of the pixel within the image, the signal may be referred as, for example, a weak signal or a strong signal, as may be understood by a person of ordinary skill in the art. The term “strong” and “weak” are relative terms based on intensity values of pixels within an image and specific values of intensity may not limit scope of the present disclosure. In some embodiments, the strong and weak signal may be identified based on a selected threshold value. In some embodiments, the threshold value may be fixed (e.g., a midpoint of a highest intensity and a lowest intensity of pixel) within the image. In some embodiments, a strong signal may refer to a signal with values greater than or equal to an average signal value across the image and a weak signal may refer to signal with values less than the average signal value. In some embodiments, the relative intensity value may be based on percentage. For example, the weak signal may be signal having intensity less than 50% of the highest intensity of the pixel (e.g., pixels corresponding to target pattern may be considered pixels with highest intensity) within the image. Furthermore, each pixel within an image may considered as a variable.

[0054] According to some embodiments of the present disclosure, derivatives or partial derivative may be determined with respect to each pixel within the image and the values of each pixel may be determined or modified according to a cost function-based evaluation or gradient based computation 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 a cost functionbased evaluation or gradient-based computation are described in this disclosure, it will be appreciated that any optimization approach can be applicable in evaluating a mask image or modifying or adjusting the mask image based on the evaluation. For example, the optimization approach can include genetic algorithms, reinforcement learning algorithms, etc.

[0055] In a conventional method of determining a patterning device pattern (or mask pattern, hereinafter), a CTM image corresponding to a target pattern to be printed on a substrate is generated or optimized, and then a binary mask image is generated from the CTM image or optimized to generate a final curvilinear mask (e.g., geometrical or polygonal representation shapes of a curvilinear mask or curvilinear pattern) that can further 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 desired results, a numberof iterations are performed using a continuous transmission mask and then iterations of a CTM+ process using a binary mask can be performed. SRAFs (sub-resolution assist features) are generally applied to enhance the process window of isolated and semi-isolated features by taking advantage of the optical interference between the main features and the assistant features. In a mask optimization process, SRAFs are seeded from a CTM image, but in some cases, there are missing SRAFs observed even after seeding SRAFs during a CTM process. However, missing SRAFs are hardly recovered during a CTM+ process. While CTM enhancement including a smoothing process may be an alternative avenue to resolve the missing SRAFs issue, CTM enhancement may result in seeding extra SRAFs that can cause mask rule check (MRC) violation, an edge placement error (EPE) or a sidelobe printing issue due to densely populated SRAFs. Further, these alternatives do not provide a robust solution such that can be consistently applied to various scenarios. For example, one CTM enhancement method could resolve missing SRAFs for some cases but the same CTM enhancement could result in undesirable SRAF seeds for other cases. Redundant SRAF seeding via CTM enhancement can also cause stitch boundary issues. Therefore, there is a demand for a mask transmission function optimization method that can resolve missing SRAFs. Moreover, binarization of a mask image can fail in the current CTM+ process when a peak intensity of the mask image is close to a threshold for binarization. Thus, an effective binarization technique is also demanded in the industry.

[0056] According to some embodiments of the present disclosure, a stable solution for missing SRAFs based on a superposition of a CTM process and CTM+ process in optimizing a mask pattern can be provided. According to some embodiments of the present disclosure, a stable binarization solution, e.g., using a sigmoid function when a pixel value is close to a binarization threshold can be provided. According to some embodiments of the present disclosure, a fuzzy approach in which a superposition of a continuous tone mask and a binary mask is utilized when optimizing a mask image is provided. According to some embodiments of the present disclosure, it is possible that some signals below a contour extraction threshold, which is used to generate a curvilinear pattern from a CTM image, may be captured by CTM+ contour extraction due to a CTM contribution during a mask optimization process.

[0057] Reference is now made to FIG. 2, which is a flow diagram of an exemplary first mask optimization method 200, consistent with embodiments of the present disclosure. According to some embodiments of the present disclosure, first mask optimization method 200 is for determining a mask pattern from an image corresponding to a target pattern to be printed on a substrate via a patterning process involving a lithographic process. In some embodiments, the target pattern or a design layout may be a binary design layout, a continuous tone design layout, or a design layout of another suitable form. According to some embodiments of the present disclosure, first mask optimization method 200 is an iterative process, where an initial image (e.g., a CTM image, an enhanced image of a CTM image, an initialized image from a CTM image, etc.) is progressively modified to eventually generatean information of mask patterns or an image corresponding to a final curvilinear mask that is further used to fabricate / manufacture a mask. In some embodiments, the iterative modification of the initial image may be based on a cost function, where during an iteration the initial image may be modified such that the cost function is reduced or minimized. In some embodiments, curvilinear mask patterns can be geometrical or polygonal representation shapes of a curvilinear mask or curvilinear pattern. The curvilinear mask patterns may be in the form of a vector, a table, mathematical equations, or other forms of representing geometric / polygonal shapes.

[0058] According to some embodiments of the present disclosure, first mask optimization method 200 may begin by acquiring an initial image 2001 as shown in FIG. 2. In some embodiments, 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 a CTM generation technique, an inverse lithography problem is formulated as an optimization problem. In some embodiments, initial image 2001 may include one or more mask features (e.g., SRAFs, SRIFs (sub-resolution inner features), etc.).

[0059] In some embodiments, initial image 2001 can be a CTM image, e.g., an initial CTM image. FIG. 3A-3E illustrate graphs showing an example image initialization process, consistent with embodiments of the present disclosure. FIG. 3A shows a CTM image 310 generated by a CTM generation process based on a target pattern to be printed on a substrate. For example, CTM image 310 can be generated based on an aerial image. The aerial image can be obtained by applying an optical model on a target pattern. CTM image 310 may be initialized by rendering the target pattern and by normalizing the rendered image to a [0, 1] range. As shown in FIG. 3A, CTM image 310 may include one or more features, such as one main feature corresponding to the target pattern (e.g., a peak at center of CTM image 310) and two additions features, possibly corresponding to SRAFs (e.g., two side peaks of CTM image 310). Using a certain mapping function 320, e.g., a sigmoid function as shown in FIG. 3B, an initial gray scale image 330 can be obtained, which is shown in FIG. 3C. For example, in FIG. 3B, a Y-axis represents a normalized pixel value of CTM image 310 and an X-axis represents a gray scale value of gray scale image 330 mapped to the normalized pixel value of CTM image 310. In some embodiments, initial gray scale image 330 can be a pixelated gray scale image, where each pixel having a value, e.g., within a range [-255, 255]. In some embodiments, initial gray scale image 330 can be down-sampled at pixel locations to reduce oscillations and have a smoother image, such as a down-sampled gray scale image 340, which is shown in FIG. 3D. In some embodiments, down-sampled gray scale image 340 can be interpolated to have a continuous gray scale image 350, which is shown in FIG. 3E. In some embodiments, any image among CTM image 310, initial gray scale image 330, down-sampled gray scale image 340, and continuous gray scale image 350 can be used as initial image 2001. In some embodiments, CTM image 360 as shown in FIG. 3F can be generated using a mapping function, such as mapping function 320 that is used to generate initial gray scale image 330 from CTM image 310. In some embodiments, CTM image 360 can be used as initial image 2001.

[0060] Referring back to FIG. 2, according to some embodiments of the present disclosure, two mask images can be generated based on initial image 2001 at generation processes 2110 and 2210 of first mask optimization method 200. In some embodiments, first image 2002 can be generated based on initial image 2001 at generation process 2110. In some embodiments where initial image 2001 has unbounded pixel values or pixel values greater than a certain absolute value, first image 2002 can be obtained by using a mapping function to scale down variable values cp of initial image 2001 to a certain range, e.g., [0, 1]. FIG. 4A illustrates an example mapping function 410 for transforming from initial image 2001 to first image 2002, consistent with embodiments of the present disclosure. As shown in FIG. 4A, variable value cp of initial image 2001 can be bounded to a range [0, 1] in first image 2002 by mapping function 410. In some embodiments, a sigmoid function as shown in FIG. 3B can be used as the mapping function. In some embodiments where a continuous gray scale image (e.g., continuous gray scale image 350 in FIG. 3E) is used as initial image 2001, first image 2002 can be obtained by using a mapping function to scale down variable values cp of initial image 2001 to a range, e.g., [0, 1].

[0061] According to some embodiments of the present disclosure, first image 2002 can be a continuous tone mask image. FIG. 4B and FIG. 4C illustrate examples of initial image 2001 and first image 2002, consistent embodiments of the present disclosure. As shown in FIG. 4C, first image 2002 is a bounded continuous tone mask image in a range [0, 1] while initial image 2001 is unbounded or greater scale continuous tone image in a range [0, 255]. While some embodiments are described using a certain type of a mapping function (e.g., mapping function 320 in FIG. 3B or mapping function 410 in FIG. 4A), it will be appreciated that any type of mapping function that can scale down or bound pixel values to a certain range can be utilized. In some embodiments where a CTM image (e.g., CTM image 360 in FIG. 3F) is used as initial image 2001, CTM image 360 itself can become first image 2002. It will be appreciated that other image enhancement processes (e.g., noise filtering, smoothing, etc.) can be performed when generating images in the present disclosure while they are not described here for simplicity.

[0062] Referring back to FIG. 2, second image 2003 can be generated based on initial image 2001 at generation process 2210, consistent with some embodiments of the present disclosure. In some embodiments, second image 2003 can be generated by extracting contour information from initial image 2001. As shown in FIG. 4D, second image 2003 can involve curvilinear mask pattern, e.g., having polygon shapes represented in a vector form, which generated from initial image 2001. In some embodiments, the generation of second image 2003 may involve thresholding of initial image 2001 to trace or generate curvilinear (or curved) patterns from initial image 2001. For example, thresholding may be performed using a threshold plane (e.g., an x-y plane) having a fixed value which intersects the signals of initial image 2001. The intersection of the threshold plane with the signals of initial image 2001 can generate tracings or outlines (i.e., curved polygon shapes), which form polygonal shapes that serve as the curvilinear patterns for second image 2003. For example, initialimage 2001 may be intersected with the zero-plane parallel to the (x, y) plane. Thus, second image 2003 may include any curvilinear patterns generated as above. FIG. 4E illustrates an example how the curvilinear mask pattern of second image 2003 in FIG. 4D is obtained via thresholding from initial image 2001.

[0063] FIG. 4D illustrates an example of second image 2003 obtained from initial image 2001 shown in FIG. 4B. As shown in FIG. 4D, second image 2003 includes contours of patterns in initial image 2001. In some embodiments, contours of patterns can include a target pattern, SRAFs, etc. While FIG. 4D illustrates contours corresponding to a target pattern (i.e., a plurality of contact holes), it will be appreciated that second image 2003 can also include contours of some SRAFs in initial image 2001 according to their signal level. According to some embodiments of the present disclosure, second image 2003 can be a binary mask pattern image.

[0064] Referring back to FIG. 2, first image 2002 and second image 2003 are evaluated at evaluation processes 2120 and 2220, respectively, of first mask optimization method 200, consistent with some embodiments of the present disclosure. According to some embodiments of the present disclosure, a cost function or a gradient map of each of first image 2002 and second image 2003 can be computed at evaluation processes 2120 and 2220.

[0065] According to some embodiments of the present disclosure, a cost function of first image 2002 can be computed at evaluation process 2120. In some embodiments, evaluation process 2120 can include simulating a patterning process using a process model that can generate or predict a pattern that may be printed on a substrate based on first image 2002. For example, evaluation process 2120 may involve executing or simulating a process model using first image 2002 as input and generating a process image on the substrate (e.g., an aerial image, a resist image, etch image, etc.). In some embodiments, the process model may include a mask transmission model coupled to an optical model that is further coupled to a resist model or etch model. In some embodiments, a continuous optical model can be applied on first image 2002, which is a continuous tone mask, at evaluation process 2120. In some embodiments, the continuous optical model can take a CTM image as input. In some embodiments, an output of execution or simulation of a process model may be a process image that has factored in different process variations during the simulation process. In some embodiments, a process image may be further used to determine parameters (e.g., EPE, CD, overlay, sidelobe, etc.) of the patterning process by, for example, tracing the contours of the patterns within the process image. The parameters may be further used to define a cost function, which is further used to optimize initial image 2001 such that the cost function is reduced or minimized. For example, the cost function may be an edge placement error (EPE), sidelobe, a mean squared error (MSE) or other appropriate variable defined based on the contour of the patterns in the process image. An EPE may be an edge placement error associated with one or more patterns or a summation of all the edge placement errors related to all the patterns of the process image and the corresponding target patterns. In some embodiments, the cost function may include more than one conditions that may besimultaneously reduced or minimized. For example, in addition to the MRC violation probability, the number of defects, EPE, overlay, CD or other parameter may be included, and all the conditions may be simultaneously reduced or minimized.

[0066] According to some embodiments of the present disclosure, evaluation process 2120 may involve generating a gradient map based on the cost function. The gradient map may be a derivative or a partial derivative of the cost function. In some embodiments, the partial derivative of the cost function may be determined with respect to pixels of a mask image (e.g., first image 2002) and derivative may be further chained to determine partial derivative with respect to variables of initial image 2001. Such gradient computations may involve determining inverse relationships between a mask image (e.g., first image 2002) to initial image 2001. A gradient map may provide a recommendation about increasing or decreasing the values of the mask variables (e.g., variable values of initial image 2001) in a manner such that the cost function is reduced or minimized. In some embodiments, mask variables can refer to intensities of initial image 2001.

[0067] According to some embodiments of the present disclosure, a cost function of second image 2003 can be computed in evaluation process 2220 in a similar way to the cost function computation described in evaluation process 2120. In some embodiments, a polygon-based optical model can be applied to 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 based on the cost function of second image 2003 can be generated in evaluation process 2220 in a similar way to the gradient map generation described in evaluation process 2220.

[0068] According to some embodiments of the present disclosure, a first weight (1-X) can be applied to a cost function or a gradient map (a first cost function or a first gradient map hereinafter) corresponding to first image 2002 in weight- application process 2130. Similarly, a second weight ( ) can be applied to a cost function or a gradient map (a second cost function or a second gradient map hereinafter) corresponding to second image 2003 in weight-application process 2230. According to some embodiments of the present disclosure, a total cost function can be generated by combining the weighted first cost function with the weighted second cost function. Similarly, a total gradient map 2005 can be generated by combining the weighted first gradient map with the weighted second gradient map. In some embodiments, total gradient map 2005 can be generated by a weighted summation at a pixel level of the first gradient map and the second gradient map. According to some embodiments of the present disclosure, variables of initial image 2001 may be changed based on total gradient map 2005 to gradually reduce or minimize the total cost function. Thus, the curvilinear patterns generated may gradually evolve during an iteration such that total cost function 2005 is reduced or minimized. In some embodiments, iterations can continue until the total cost function reaches a certain level or the speed of the convergence of the optimization process is below a certain level. In some embodiments, the number of iterations can be preset.

[0069] According to some embodiments of the present disclosure, first weight (1-X) and second weight ( ) can be designed to gradually change per iteration. In some embodiments, first weight (1-X) can change such that a value of the first weight at an earlier (e.g., mth) iteration is equal to or greater than a value of the first weight at a later (e.g., nth) iteration where n>m>0. Similarly, second weight ( can change such that a value of the second weight at an earlier (e.g., mth) iteration is equal to or less than a value of the second weight at a later (e.g., nth) iteration where n>m>0. In some embodiments, first weight (1-X) can gradually decrease such that contributions of a continuous tone mask (e.g., first image 2002) to the total cost function or total gradient map 2005 can decrease as the iteration progresses. Similarly, second weight ( ) can gradually increase such that contributions of a binary mask (e.g., second image 2003) to the total cost function or total gradient map 2005 can increase as the iteration progresses.

[0070] FIG. 5 illustrates an example weight function, consistent with embodiments of the present disclosure. In FIG. 5, a change of second weight ( ) is described according to a number of iterations. As shown in FIG. 5, second weight ( ) is zero till Cl number of iterations, linearly increases till C2 number of iterations, and becomes one till the end of iterations. Because the first weight is represented as (1-X), it can be noted that first weight (1-X) is one till Cl number of iterations, linearly decreases till C2 number of iterations, and becomes zero till the end of iterations. According to some embodiments of the present disclosure, instead of utilizing a sequential mask optimization mechanism such as a CTM process first and then a CTM+ process, a fuzzy mask optimization mechanism based on a superposition of a CTM process and a CTM+ process can be utilized. Therefore, according to some embodiments of the present disclosure, the signals below the contour extraction threshold in the beginning of the mask optimization process can still have a chance to be captured as curvilinear patterns later in the mask optimization process because the CTM process can still make contributions to the total cost function or total gradient map 2005 based on which initial image 2001 is modified. According to some embodiments of the present disclosure, a mask optimization mechanism that can effectively obtain curvilinear patterns for a patterning mask by reducing or minimizing loss of weak signals during optimization.

[0071] Reference is now made to FIG. 6, which is a flow diagram of a second mask optimization method 600, consistent with embodiments of the present disclosure. According to some embodiments of the present disclosure, second mask optimization method 600 is for determining a mask pattern from an image corresponding to a target pattern to be printed on a substrate via a patterning process involving a lithographic process. According to some embodiments of the present disclosure, second mask optimization method 600 is an iterative process, where an initial image (e.g., a CTM image, an enhanced image of a CTM image, an initialized image from a CTM image, etc.) is progressively modified to eventually generate an information of mask patterns or an image corresponding to a final curvilinear mask that can further used to fabricate / manufacture a mask. In some embodiments, the iterative modification of the initial image may be based on a cost function, where during an iterationthe initial image may be modified such that the cost function is reduced or minimized. In some embodiments, curvilinear mask patterns can be geometrical or polygonal representation shapes of a curvilinear mask or curvilinear pattern. According to some embodiments of the present disclosure, second mask optimization method 600 utilizes a fuzzy mask 6002 based on a weighted combination of a binary mask and a continuous tone mask during optimization process.

[0072] According to some embodiments of the present disclosure, second mask optimization method 600 may begin by acquiring an initial image 6001 as shown in FIG. 6. In some embodiments, initial image 6001 may be the same image as initial image 2001, which is described referring to FIG. 2. Accordingly, detailed descriptions to initial image 6001 will be omitted here for simplicity.

[0073] According to some embodiments of the present disclosure, a fuzzy mask 6002 can be generated based on initial image 6001 at generation process 6310 of second mask optimization method 600. According to some embodiments of the present disclosure, fuzzy mask 6002 (e.g., a combined mask image) can be generated through a weighted combination of a binary mask and a continuous tone mask. In some embodiments, fuzzy mask 6002 can be expressed as follows: m(x, y) = 2iH(<p(x, y) - <pth) + (1 - 2z)M(<p(x, y)) (Equation 1)

[0074] Here, m(x, y) represents a pixel value at a location (x, y) on fuzzy mask 6002. <p(x, y) represents a variable value at a location (x, y) on initial image 6001. Function HQ is a step function having a threshold value <pth, which can be a binarization function. For example, Function H() is a Heaviside step function. Function M() represents a continuous mapping function. In Equation 1, M(<p(x,y)) represents a function that continuously maps variable values <p of initial image 6001 to a certain line. In Equation 1, the first term including function H() represents a contribution of a binary mask into fuzzy mask 6002 (i.e., m(x, y)) and the second term including function M() represents a contribution of a continuous tone mask into fuzzy mask 6002.

[0075] As expressed in Equation 1, when combining a binary mask and a continuous tone mask, each of the masks are weighted. And the weight for the binary mask and continuous tone mask may change per iteration i. In Equation 1, a weight for the continuous tone mask is represented by a first weight (1-Xi) and a weight for a binary mask is represented by a second weight ( i) for iteration i. According to some embodiments of the present disclosure, first weight (1-X) and second weight (X) are designed to gradually change per iteration. In some embodiments, first weight (1-X) can change such that a value of the first weight at an earlier (e.g., mth) iteration is equal to or greater than a value of the first weight at a later (e.g., nth) iteration where n>m>0. Similarly, second weight (X) can change such that a value of the second weight at an earlier (e.g., mth) iteration is equal to or less than a value of the second weight at a later (e.g., nth) iteration where n>m>0. In some embodiments, first weight (1-X) can gradually decrease such that contributions of a continuous tone mask to fuzzy mask 6002 can decreaseas the iteration progresses. Similarly, second weight ( ) can gradually increase such that contributions of a binary mask to fuzzy mask 6002 can increase as the iteration progresses. In some embodiments, the weight function shown in FIG. 5 can similarly utilized in second mask optimization method 600.

[0076] One example of mask value m(x, y) of fuzzy mask 6002 can be provided as below: (Equation 2)

[0077] Here, ^,y')is utilized as an example of continuous function M(<p(x,y)). FIG. 7 illustrates an example mapping function between initial image 6001 and fuzzy mask 6002, consistent with embodiments of the present disclosure. In FIG. 7, an x-axis represents a variable value <p of initial image 6001 and a y-axis represents a mask value m(x, y) of fuzzy mask 6002. As shown in FIG. 7, contributions of the binary mask portion can be shown when variable value <p has a threshold value <pth . There is a discontinuity in the graph representing pixel value m(x, y) at threshold variable value <pth by an amount of second weight ( i) at iteration i. Except at threshold variable value <pth, the graph representing pixel value m(x, y) has a continuous mapping from variable value <p to pixel value m(x, y) with a certain slope. And the slope of the mapping graph can change according to a change of second weight (Xi). For example, when second weight (X) equals to zero, the mapping graph can be a continuous graph having a slope l / k<pthwithout discontinuity, when second weight (X) equals to one, the mapping graph can be a step function mapping variable value <p to zero till threshold value <pthand mapping variable value <p to one after threshold value <pth. When second weight (X) is greater than zero and less than one, the mapping graph can have a similar shape to the one shown in FIG. 5 with a varying slope according to a change of second weight (X).

[0078] According to some embodiments of the present disclosure, as second weight (Xi) increases, contributions of a binary mask to fuzzy mask 6002 becomes greater. To the contrary, as first weight (1-Xi) increases, contributions of a continuous tone mask to fuzzy mask 6002 becomes smaller.Images of fuzzy mask 6002 when second weight (X) equals to 0, 0.25, 0.5, 0.75, and 1.0 are illustrated in FIGs. 8A-8E. As shown in FIGs. 8A-8E, fuzzy mask 6002 with a greater second weight (X) shows clearer contours of patterns. For example, fuzzy mask 6002 with second weight (X) being zero in FIG. 8A shows a continuous tone mask and fuzzy mask 6002 with second weight (X) being one in FIG. 8E shows a binary mask. And fuzzy mask 6002 with second weight (X) being between zero and one in FIGs. 8B-8D includes continuous mask contributions and binary mask contributions in fuzzy mask 6002.

[0079] Referring back to FIG. 6, fuzzy mask 6002 can be evaluated at evaluation process 6320, consistent with some embodiments of the present disclosure. According to some embodiments of the present disclosure, evaluation at evaluation process 6320 can be based on a cost function or a gradient map 6005. The cost function computation and gradient map generation can be performed in a similarway to those described referring to first mask optimization process 200 of FIG. 2, and thus the detailed descriptions therefor will not be duplicated herein for simplicity. According to some embodiments of the present disclosure, evaluation process 6320 can also involve executing or simulating a process model using fuzzy mask 6002. In some embodiments, a new optical model for fuzzy mask 6002, which is a piecewise continuous mask as shown in FIG. 7, may be utilized for executing or simulating the process model. In some embodiments, an optical model for fuzzy mask 6002 can take into account a M3D effect on curvilinear boundaries weighted by second weight ( i). For example, when second weight (Xi) equals to zero, fuzzy mask 6002 can be fully continuous without having the M3D effect. As second weight (Xi) increases, the M3D effect can gradually increase and the M3D effect can be maximum when second weight (Xi) equals to one.

[0080] According to some embodiments of the present disclosure, variables of initial image 6001 may be changed based on gradient map 6005 to gradually reduce or minimize the cost function. Thus, the curvilinear patterns generated may gradually evolve during an iteration such that the cost function is reduced or minimized. In some embodiments, iterations can continue until the cost function reaches a certain level or the speed of the convergence of the optimization process is below a certain level. In some embodiments, the number of iterations can be preset.

[0081] FIG. 9 is a block diagram that illustrates a computer system 100 which can assist in implementing the methods, flows or the apparatus disclosed herein. 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 can include hardware accelerators) coupled with bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 104. Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0082] Computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is cursor control 116, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 104 and for controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0083] According to some embodiments, portions 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. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In an alternative embodiment, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0084] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[0085] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 either before or after execution by processor 104.

[0086] Computer system 100 may also include a communication interface 118 coupled to bus 102. Communication interface 118 provides a two-way data communication coupling to a network link 120 that is connected to a local network 122. For example, communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communicationinterface 118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 118 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0087] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. ISP 126 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet” 128. Local network 122 and Internet 128 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0088] Computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, a server 130 might transmit a requested code for an application program through Internet 128, ISP 126, local network 122 and communication interface 118. One such downloaded application may provide all or part of a method described herein, for example. The received code may be executed by processor 104 as it is received, or stored in storage device 110, or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[0089] FIG. 10 schematically depicts an exemplary lithographic projection apparatus in conjunction with the techniques described herein can be utilized. The apparatus comprises: an illumination system IL, to condition a beam B of radiation. In this particular case, the illumination system also comprises a radiation source SO; a first object table (e.g., patterning device table) MT provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS; a second object table (substrate table) WT provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS; a projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) to image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0090] As depicted herein, the apparatus is of a transmissive type (i.e., has a transmissive patterning device). However, in general, it may also be of a reflective type, for example (with a reflective patterning device). The apparatus may employ a different kind of patterning device to classic mask; examples include a programmable mirror array or LCD matrix.

[0091] The source SO (e.g., a mercury lamp or excimer laser, LPP (laser produced plasma) EUV source) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AD for setting the outer or inner radial extent (commonly referred to as o-outcr and o-inner, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0092] It should be noted with regard to FIG. 10 that the source SO may be within the housing of the lithographic projection apparatus (as is often the case when the source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam that it produces being led into the apparatus (e.g., with the aid of suitable directing mirrors); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[0093] The beam PB subsequently intercepts the patterning device MA, which is held on a patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PL, which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the beam PB. Similarly, the first positioning means can be used to accurately position the patterning device MA with respect to the path of the beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in FIG. 10. However, in the case of a stepper (as opposed to a step- and-scan tool) the patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[0094] The depicted tool can be used in two different modes: In step mode, the patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x or y directions so that a different target portion C can be irradiated by the beam PB; In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single “flash”. Instead, the patterning device table MT is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that the projection beam B is caused to scan over a patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, in which M is the magnification of the lens PL (typically, M=* or !4). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0095] FIG. 11 schematically depicts another exemplary lithographic projection apparatus LA in conjunction with the techniques described herein can be utilized. The lithographic projection apparatus LA comprises: a source collector module SO; an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation); support structure (e.g. a patterning device table) MT constructed to support a patterning device (e.g. a mask or a reticle) MA and connected to a first positioner PM configured to accurately position the patterning device; a substrate table (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist coated wafer) 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 to the radiation beam B by patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0096] As here depicted, the apparatus LA is of a reflective type (e.g., employing a reflective patterning device). It is to be noted that because most materials are absorptive within the EUV wavelength range, the patterning device may have multilayer reflectors comprising, for example, a multi-stack of Molybdenum and Silicon. In one example, the multi-stack reflector has a 40 layer pairs of Molybdenum and Silicon where the thickness of each layer is a quarter wavelength. Even smaller wavelengths may be produced with X-ray lithography. Since most material is absorptive at EUV and x-ray wavelengths, a thin piece of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multi-layer reflector) defines where features would print (positive resist) or not print (negative resist).

[0097] Referring to FIG. 11, the illuminator IL receives an extreme ultra-violet radiation beam from the source collector module SO. Methods to produce EUV radiation include, but are not necessarily limited to, converting a material into a plasma state that has at least one element, e.g., xenon, lithium or tin, with one or more emission lines in the EUV range. In one such method, often termed laser produced plasma (“LPP”) the plasma can be produced by irradiating a fuel, such as a droplet, stream or cluster of material having the line-emitting element, with a laser beam. The source collector module SO may be part of an EUV radiation system including a laser, not shown in FIG. 11, for providing the laser beam exciting the fuel. The resulting plasma emits output radiation, e.g., EUV radiation, which is collected using a radiation collector, disposed in the source collector module. The laser and the source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation.

[0098] In such cases, the laser is not considered to form part of the lithographic apparatus and the radiation beam is passed from the laser to the source collector module with the aid of a beam delivery system comprising, for example, suitable directing mirrors or a beam expander. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often termed as a DPP source.

[0099] The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer or inner radial extent (commonly referred to as o- outer and o-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[0100] The radiation beam B is incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., patterning device table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor PS2 (e.g., an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor PS 1 can be used to accurately position the patterning device (e.g. mask) MA with respect to the path of the radiation beam B. Patterning device (e.g. mask) MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[0101] The depicted apparatus LA could be used in at least one of the following modes: 1. In step mode, the support structure (e.g., patterning device table) MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X or Y direction so that a different target portion C can be exposed. 2. In scan mode, the support structure (e.g., patterning device table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (e.g., patterning device table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. 3. In another mode, the support structure (e.g., patterning device table) MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[0102] FIG. 12 shows the apparatus LA in more detail, including the source collector module SO, the illumination system IL, and the projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiation emitting plasma 210 may be formed by a discharge produced plasma source. EUV radiation may be produced by a gas or vapor, for example Xe gas, Li vapor or Sn vapor in which the very hot plasma 210 is created to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is created by, for example, an electrical discharge causing at least partially ionized plasma. Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may be required for efficient generation of the radiation. In some embodiments, a plasma of excited tin (Sn) is provided to produce EUV radiation.

[0103] The radiation emitted by the hot plasma 210 is passed from a source chamber 211 into a collector chamber 212 via an optional gas barrier or contaminant trap 230 (in some cases also referred to as contaminant barrier or foil trap) which is positioned in or behind an opening in source chamber 211. The contaminant trap 230 may include a channel structure. Contamination trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further indicated herein at least includes a channel structure, as known in the art.

[0104] The collector chamber 211 may include a radiation collector CO which may be a so-called grazing incidence collector. Radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation that traverses collector CO can be reflected off a grating spectral filter 240 to be focused in a virtual source point IF along the optical axis indicated by the dot-dashed line ‘O’. The virtual source point IF is commonly referred to as the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near an opening 221 in the enclosing structure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0105] Subsequently the radiation traverses the illumination system IL, which may include a facetted field mirror device 22 and a facetted pupil mirror device 24 arranged to provide a desired angular distribution of the radiation beam 21, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the beam of radiation 21 at the patterning device 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, 30 onto a substrate W held by the substrate table WT.

[0106] More elements than shown may generally be present in illumination optics unit IL and projection system PS. The grating spectral filter 240 may optionally be present, depending upon the type of lithographic apparatus. Further, there may be more mirrors present than those shown in the figures, for example there may be 1-6 additional reflective elements present in the projection system PS than shown in FIG. 12.

[0107] Collector optic CO, as illustrated in FIG. 12, is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, just as an example of a collector (or collector mirror). Thegrazing incidence reflectors 253, 254 and 255 are disposed axially symmetric around the optical axis O and a collector optic CO of this type may be used in combination with a discharge produced plasma source, often called a DPP source.

[0108] Alternatively, the source collector module SO may be part of an LPP radiation system as shown in FIG. 13. A laser LAS is arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), creating the highly ionized plasma 210 with electron temperatures of several 10's of eV. The energetic radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by a near normal incidence collector optic CO and focused onto the opening 221 in the enclosing structure 220.

[0109] The concepts disclosed herein may simulate or mathematically model any generic imaging system for imaging sub wavelength features, and may be especially useful with emerging imaging technologies capable of producing increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultra-violet), DUV lithography that is capable of producing a 193 nm wavelength with the use of an ArF laser, and even a 157 nm wavelength with the use of a Fluorine laser. Moreover, EUV lithography is capable of producing wavelengths within a range of 20-5 nm by using a synchrotron or by hitting a material (either solid or a plasma) with high energy electrons in order to produce photons within this range.

[0110] Embodiments of the present disclosure can be further described by the following clauses.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 that is associated with the continuous tone mask and the binary mask.2. The method of clause 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 clause 2, further comprising: simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.4. The method of clause 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 clause 3 or 4, 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 any one of clauses 3-5, wherein the gradient map is obtained by summing a multiplication result of the first gradient map with a first weight and a multiplication result of the second gradient map with a second weight.7. The method of clause 6, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.8. The method of clause 3 or 4, further comprising: calculating a combined cost function based on simulation results of the simulating the lithographic patterning process using the continuous tone mask and the binary mask, respectively.9. The method of clause 8, wherein the gradient map is based on the combined cost function.10. The method of clause 1, further comprising: obtaining a combined mask by a weighted sum of the binary mask and the continuous tone mask.11. The method of clause 10, further comprising: simulating a lithographic patterning process with an optical model using the combined mask to generate a process image on a substrate.12. The method of clause 10 or 11, wherein the gradient map is associated with the combined mask.13. The method of clause 11 or 12, wherein the gradient map is computed based on the process image.14. The method of any one of clauses 10-13, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.15. The method of clause 14, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.16. 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 by concurrently adjusting the continuous tone mask and the binary mask.17. The method of clause 16, further comprising: simulating a lithographic patterning process using the continuous tone mask and the binary mask, respectively.18. The method of clause 17, further comprising: calculating a combined cost function based on simulation results of the simulating using the continuous tone mask and the binary mask, respectively.19. The method of clause 18, wherein the iteratively optimizing the first image is performed based on the combined cost function.20. The method of clause 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.21. The method of clause 20, wherein the simulating a lithographic patterning process using the continuous tone mask and the binary mask comprises: simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.22. The method of clause 21, wherein the first cost function is computed based on the first process image and the second cost function is computed based on the second process image.23. The method of clause 21 or 22, wherein the combined cost function is obtained by summing a multiplication result of the first cost function with a first weight and a multiplication result of the second cost function with a second weight.24. The method of clause 23, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.25. The method of clause 16, further comprising: obtaining a combined mask by a weighted superposition of the binary mask and the continuous tone mask.26. The method of clause 25, further comprising: simulating a lithographic patterning process with an optical model using the combined mask.27. The method of clause 26, further comprising: calculating a cost function based on a simulation result of the simulating using the combined mask.28. The method of clause 27, wherein the iteratively optimizing the first image is performed based on the cost function.29. The method of any one of clauses 25-28, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.30. The method of clause 29, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.31. An apparatus for determining a mask pattern of a patterning device, the apparatus comprising: a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform: obtaining a continuous tone mask and a binary mask, from a first image corresponding to a target design associated with the mask pattern; anditeratively optimizing the first image based on a gradient map that is associated with the continuous tone mask and the binary mask.32. The apparatus of clause 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.33. The apparatus of clause 32, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.34. The apparatus of clause 33, wherein the first optical model takes the continuous tone mask as input and the second optical model takes the binary mask as input.35. The apparatus of clause 33 or 34, 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.36. The apparatus of any one of clauses 33-35, wherein the gradient map is obtained by summing a multiplication result of the first gradient map with a first weight and a multiplication result of the second gradient map with a second weight.37. The apparatus of clause 36, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.38. The apparatus of clause 33 or 34, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: calculating a combined cost function based on simulation results of the simulating the lithographic patterning process using the continuous tone mask and the binary mask, respectively.39. The apparatus of clause 38, wherein the gradient map is based on the combined cost function.40. The apparatus of clause 31, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: obtaining a combined mask by a weighted sum of the binary mask and the continuous tone mask.41. The apparatus of clause 40, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: simulating a lithographic patterning process with an optical model using the combined mask to generate a process image on a substrate.42. The apparatus of clause 40 or 41, wherein the gradient map is associated with the combined mask.43. The apparatus of clause 41 or 42, wherein the gradient map is computed based on the process image.44. The apparatus of any one of clauses 40-43, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.45. The apparatus of clause 44, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.46. An apparatus for determining a mask pattern of a patterning device, the apparatus comprising: a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform: 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 concurrently adjusting the continuous tone mask and the binary mask.47. The apparatus of clause 46, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: simulating a lithographic patterning process using the continuous tone mask and the binary mask, respectively.48. The apparatus of clause 47, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: calculating a combined cost function based on simulation results of the simulating using the continuous tone mask and the binary mask, respectively.49. The apparatus of clause 48, wherein in iteratively optimizing the first image, the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: iteratively optimizing the first image based on the combined cost function.50. The apparatus of clause 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.51. The apparatus of clause 50, wherein in simulating a lithographic patterning process using the continuous tone mask and the binary mask, the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.52. The apparatus of clause 51, wherein the first cost function is computed based on the first process image and the second cost function is computed based on the second process image.53. The apparatus of clause 51 or 52, wherein the combined cost function is obtained by summing a multiplication result of the first cost function with a first weight and a multiplication result of the second cost function with a second weight.54. The apparatus of clause 53, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.55. The apparatus of clause 46, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: obtaining a combined mask by a weighted superposition of the binary mask and the continuous tone mask.56. The apparatus of clause 55, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: simulating a lithographic patterning process with an optical model using the combined mask.57. The apparatus of clause 56, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: calculating a cost function based on a simulation result of the simulating using the combined mask.58. The apparatus of clause 57, wherein in iteratively optimizing the first image, the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: iteratively optimizing the first image based on the cost function.59. The apparatus of any one of clauses 55-58, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.60. The apparatus of clause 59, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.61. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform a 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 that is associated with the continuous tone mask and the binary mask.62. The computer readable medium of clause 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.63. The computer readable medium of clause 62, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform:simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.64. The computer readable medium of clause 63, wherein the first optical model takes the continuous tone mask as input and the second optical model takes the binary mask as input.65. The computer readable medium of clause 63 or 64, 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.66. The computer readable medium of any one of clauses 63-65, wherein the gradient map is obtained by summing a multiplication result of the first gradient map with a first weight and a multiplication result of the second gradient map with a second weight.67. The computer readable medium of clause 66, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.68. The computer readable medium of clause 63 or 64, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: calculating a combined cost function based on simulation results of the simulating the lithographic patterning process using the continuous tone mask and the binary mask, respectively.69. The computer readable medium of clause 68, wherein the gradient map is based on the combined cost function.70. The computer readable medium of clause 61, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: obtaining a combined mask by a weighted sum of the binary mask and the continuous tone mask.71. The computer readable medium of clause 70, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: simulating a lithographic patterning process with an optical model using the combined mask to generate a process image on a substrate.72. The computer readable medium of clause 70 or 71, wherein the gradient map is associated with the combined mask.73. The computer readable medium of clause 71 or 72, wherein the gradient map is computed based on the process image.74. The computer readable medium of any one of clauses 70-73, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.75. The computer readable medium of clause 74, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.76. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform a 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 by concurrently adjusting the continuous tone mask and the binary mask.77. The computer readable medium of clause 76, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: simulating a lithographic patterning process using the continuous tone mask and the binary mask, respectively.78. The computer readable medium of clause 77, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: calculating a combined cost function based on simulation results of the simulating using the continuous tone mask and the binary mask, respectively.79. The computer readable medium of clause 78, wherein in iteratively optimizing the first image, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: iteratively optimizing the first image based on the combined cost function.80. The computer readable medium of clause 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.81. The computer readable medium of clause 80, wherein in simulating a lithographic patterning process using the continuous tone mask and the binary mask, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: simulating a lithographic patterning process with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate a second process image on a substrate.82. The computer readable medium of clause 81, wherein the first cost function is computed based on the first process image and the second cost function is computed based on the second process image.83. The computer readable medium of clause 81 or 82, wherein the combined cost function is obtained by summing a multiplication result of the first cost function with a first weight and a multiplication result of the second cost function with a second weight.84. The computer readable medium of clause 83, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.85. The computer readable medium of clause 76, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: obtaining a combined mask by a weighted superposition of the binary mask and the continuous tone mask.86. The computer readable medium of clause 85, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: simulating a lithographic patterning process with an optical model using the combined mask.87. The computer readable medium of clause 86, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: calculating a cost function based on a simulation result of the simulating using the combined mask.88. The computer readable medium of clause 87, wherein in iteratively optimizing the first image, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: iteratively optimizing the first image based on the cost function.89. The computer readable medium of any one of clauses 85-88, wherein the combined mask is obtained by summing a multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.90. The computer readable medium of clause 89, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.

[0111] While the concepts disclosed herein may be used for imaging on a substrate such as a silicon wafer, it shall be understood that the disclosed concepts may be used with any type of lithographic imaging systems, e.g., those used for imaging on substrates other than silicon wafers.

[0112] Block diagrams in the figures may 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 a schematic diagram may represent certain arithmetical or logical operation processing that may be implemented using hardware such as an electronic circuit. Blocks may also represent a module, segment, or portion of code that comprises one or more executable instructions for implementing the specified logical functions. It should be understood that in some alternative implementations, functions indicated in a block may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed or implemented substantially concurrently, or two blocks may sometimes be executed in reverse order, depending upon the functionality involved.Some blocks may also be omitted. It should also be understood that each block of the block diagrams, and combination of the blocks, may be implemented by special purpose hardware-based systems that perform the specified functions or acts, or by combinations of special purpose hardware and computer instructions.

[0113] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof. The present disclosure has been described in connection with various embodiments, other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims

CLAIMS1. 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 that is 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 with a first optical model using the continuous tone mask to generate a first process image on a substrate; and simulating a lithographic patterning process with a second optical model using the binary mask to generate 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 multiplication result of the first gradient map with a first weight and a multiplication result of the second gradient map with a second weight.

7. The method of claim 6, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.

8. The method of claim 3, further comprising: calculating a combined cost function based on simulation results of the 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 with an optical model using the combined mask to generate 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 multiplication result of the continuous tone mask with a first weight and a multiplication result of the binary mask with a second weight.

15. The method of claim 14, wherein the first weight changes such that a value of the first weight at mthiteration is equal to or greater than a value of the first weight at nthiteration where n>m>0.

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