TW202519974A - Method and system for training a prediction model to generate a two-dimensional-element representation of a mask pattern - Google Patents

Abstract

Described herein is a method and system for predicting a 2D-element representation of a mask pattern. An input mask pattern corresponding to a target pattern is provided to a prediction model. The prediction model generates a 2D-element representation of an output mask pattern corresponding to the input mask pattern. The 2D-element representation includes multiple 2D elements representing a mask feature of the output mask pattern and each 2D element defines an enclosed area. The mask feature contours of the output mask pattern are determined based on the 2D-element representation.

Description

Method and system for training a prediction model to generate a two-dimensional element representation of a mask pattern

Embodiments provided herein relate to semiconductor manufacturing, and more particularly, to designing mask patterns.

A lithography apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, an IC chip in a smartphone can be as small as a human thumbnail and can include more than 2 billion transistors. Making ICs is a complex and time-consuming process, where circuit components are in different layers and include hundreds of individual steps. An error in even one step may cause problems in the final IC and can cause device failure. High process yields and high wafer throughput may be affected by the presence of defects.

In some embodiments, the technology described herein relates to a method for determining a mask pattern for use with a lithography process, the method comprising: providing an input mask pattern corresponding to a target pattern to a prediction model; using the prediction model to generate a two-dimensional (2D) element representation of an output mask pattern corresponding to the input mask pattern, wherein the 2D element representation includes multiple 2D elements representing a mask feature of the output mask pattern and each 2D element defines a closed region; and determining a mask feature contour of the output mask pattern based on the 2D element representation.

In some embodiments, the technology described herein relates to a method for training a prediction model to generate a 2D element representation of a mask pattern used with a lithography process, the method comprising: obtaining a 2D element representation set of an input mask pattern set and an output mask pattern set corresponding to the input mask pattern set as training data, wherein the 2D element representation in the 2D element representation set includes multiple 2D elements representing mask features of the mask pattern and each 2D element defines a closed region; and using the training data to train the prediction model to generate the 2D element representation.

In some embodiments, a non-transitory computer-readable medium having instructions is provided, which when executed by a computer causes the computer to perform the method of any one of the above embodiments.

In some embodiments, a device is provided, the device comprising: a memory storing an instruction set; and a processor configured to execute the instruction set so that the device performs the method of any one of the above embodiments.

A lithography apparatus is a machine that applies a designed pattern onto a target portion of a substrate. This process of transferring the designed pattern to the substrate is called a patterning process or a lithography process. The patterning process may include a patterning step for transferring the pattern from a patterning device (e.g., a mask) to the substrate. Various variations (e.g., variations in the patterning process or the lithography apparatus) may potentially limit the implementation of lithography for semiconductor mass manufacturing (HVM). Optimal proximity correction (OPC) may be used in reticle design to optimize the reticle pattern so that a reticle manufactured using the reticle pattern is ultimately delivered to the substrate so that the desired design layout is formed. Learned reticle optimization may include starting with target pattern polygons (e.g., representing the desired pattern to be manufactured) and extracting such polygons to serve as the basis for the reticle. However, such learned optimization of reticle features may be computationally expensive because there may be many elements that need to be adjusted in order to form optimized reticle features. Additionally, learned OPC may sometimes result in reticle features that violate reticle rule checking (MRC) rules. Some methods use a machine learning (ML) model (e.g., a neural network) to predict a reticle image (e.g., a level-set phi image of the reticle pattern), and then extract polygons from the level-set image that may be used as input to an OPC optimization procedure to adjust the reticle feature profile. Polygon extraction is extremely sensitive to the values in the phi image. Small changes in pixel values may cause large contour shifts. Learned ML models may not provide sufficient prediction accuracy, and therefore, the extracted initial polygons may have large deviations from the ground truth, MRC violations, and thus poor lithography performance.

Embodiments of two-dimensional element representations for predicting mask patterns using a prediction model (e.g., an ML model such as a neural network) are disclosed. In the two-dimensional (2D) element representation, each mask feature can be represented using multiple 2D elements (e.g., circles, ellipses, semicircles, portions of circles, etc.). Additional details regarding the 2D element representation are described in PCT application No. PCT/EP2023/055028, the disclosure of which is incorporated by reference in its entirety. A mask feature profile can be derived from the 2D elements. The derived mask feature profile can then be provided to a mask optimization process (e.g., to further adjust the mask feature profile), which can produce an optimized mask pattern that can be used to manufacture a mask to print a target pattern on a substrate.

In one embodiment, the prediction model predicts 2D element representation data from which a 2D element representation may be generated. The predicted 2D element representation data may include a set of images that define the placement of 2D elements in a grid. For example, a first image may indicate whether a 2D element exists at a particular grid position. A second image may indicate the displacement of a 2D element in the x-direction from a particular grid position, and a third image may indicate the displacement of a 2D element in the y-direction from a particular grid position. In another example, one or more images in the image set may also define associations between 2D elements that define the shape of a mask feature profile. The image set may be used to generate a 2D element representation of each mask feature in which multiple 2D elements are used to represent a mask pattern. Mask feature profiles may then be generated from the 2D elements. The resulting mask pattern may then be optimized using an OPC procedure. In some embodiments, the prediction model may be trained to predict a 2D element representation of a reticle pattern. The training data may include an input reticle pattern that may be generated from a target pattern (e.g., a GDS design layout), and a set of images indicating a 2D element representation of an optimized reticle pattern corresponding to the input reticle pattern. By having the prediction model predict a 2D element representation rather than a set of images, the reticle feature contours derived using the prediction are less sensitive to prediction errors (e.g., because any error may result in a minimal local contour shift as opposed to a large contour shift of a learned prediction technique), and thus result in a more accurate prediction of the reticle pattern. Additionally, training such prediction models is less complex than learning prediction techniques, and the prediction models are error-tolerant, converge faster, and have fewer overfitting problems.

In this disclosure, although specific reference may be made to IC manufacturing, it should be expressly understood that the description herein has many other possible applications. For example, it can be used to manufacture integrated optical systems, guide and detection patterns for magnetic memory, liquid crystal display panels, thin film heads, etc. Those skilled in the art will understand that in the context of this alternative application, any use of the terms "reduction mask", "wafer" or "die" herein should be considered interchangeable with the more general terms "mask", "substrate" and "target portion", respectively.

In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5 nm to 100 nm). In this document, the terms "radiation source" or "source" are used to cover all types of radiation sources, including laser sources, incandescent sources, etc., which may include radiation processing between the radiation source and the target portion or other portions of the optical device, including filtering, collimation, focusing, etc.

A patterned device may include or may form one or more design layouts. A CAD (computer-aided design) program may be used to generate the design layout. This program is often referred to as electronic design automation (EDA). Most CAD programs follow a set of predetermined design rules in order to generate a functional design layout/patterned device. These rules are set based on process and design constraints. For example, design rules define the spatial tolerances between devices (such as gates, capacitors, etc.) or interconnects to ensure that the devices or lines do not interact with each other in an undesirable manner. One or more of the design rule constraints may be referred to as a "critical dimension" (CD). The critical dimension of a device may be defined as the minimum width of a line or hole, or the minimum space between two lines or two holes. Thus, CD regulates the overall size and density of the designed device. One of the goals in device manufacturing is to faithfully reproduce the original design intent on the substrate (by patterning the device).

The terms "mask" or "patterning device" as used herein may be broadly interpreted as referring to a generic patterning device that can be used to impart a patterned cross-section to an incident radiation beam, which patterned cross-section corresponds to the pattern to be produced in a target portion of a substrate. In this context, the term "light valve" may also be used. In addition to classical masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays. Examples of such devices are matrix-addressable surfaces with viscoelastic control layers and reflective surfaces. The basic principle underlying such an apparatus is, for example, that addressed areas of a reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as undiffracted radiation. With the use of appropriate filters, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. Suitable electronic components can be used to perform the desired matrix addressing. Other examples of such patterned devices also include programmable LCD arrays. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

The term "projection optics" as used herein should be broadly interpreted to cover various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also include components that operate according to any of these design types for guiding, shaping, or controlling a projected radiation beam, either collectively or individually. The term "projection optics" may include any optical component in a lithography projection apparatus, regardless of where the optical component is located on the optical path of the lithography projection apparatus. Projection optics may include optical components for shaping, conditioning, and/or projecting radiation from a source before it passes through a patterning device, and/or optical components for shaping, conditioning, and/or projecting radiation after it passes through a patterning device. Projection optics typically do not include the source and patterning device.

1 shows a block diagram of various subsystems of a lithographic projection apparatus 10A according to an embodiment. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including extreme ultraviolet (EUV) sources (the lithographic projection apparatus itself need not have a radiation source); illumination optics, which, for example, define partial coherence (expressed as mean square deviation) and may include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a patterning device (or mask) 18A; and transmission optics 16Ac, which projects an image of the patterning device pattern onto substrate plane 22A.

The pupil 20A may include the transmission optics 16Ac. In some embodiments, there may be one or more pupils before and/or after the mask 18A. As described in further detail herein, the pupil 20A may provide patterning of the light that ultimately reaches the substrate plane 22A. An adjustable filter or aperture at the pupil plane of the projection optics may limit the range of angles of the light beam that impinges on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA of the projection optics = n sin(θ _max ), where n is the refractive index of the medium between the substrate and the last element of the projection optics, and θ _max is the maximum angle of the light beam emitted from the projection optics that can still impinge on the substrate plane 22A.

In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device, and projection optics direct the illumination via the patterning device onto a substrate and shapes the illumination. This does not deny that the source itself does not provide patterning, directing, or shaping to the radiation, or that the patterning, directing, or shaping does not occur between the source and the projection optics. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. An etchant model may be used to calculate the etchant image from the aerial image, an example of which may be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is concerned with the properties of the resist layer (e.g., the effects of the chemical processes that occur during exposure, post-exposure bake (PEB), and development). The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, patterning device, and projection optics) specify the aerial image and can be defined in the optical model. Since the patterning device used in the lithographic projection apparatus can be varied, 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 projection optics. Details of techniques and models for transforming design layouts into various lithographic images (e.g., aerial images, resist images, etc.), applying OPC using those techniques and models, and evaluating performance (e.g., based on process windows) are described in U.S. patent application publications US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosures of which are hereby incorporated by reference in their entirety.

One aspect of understanding lithography is understanding the interaction of radiation with the patterning device. The electromagnetic field of the radiation after it passes through the patterning device can be determined from the electromagnetic field of the radiation before it reaches the patterning device and a function that characterizes the interaction. This function can be called the mask transmission function (it can be used to describe the interaction through the transmission patterning device and/or the reflection patterning device).

The mask transmission function can 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 position on the patterned device. A mask transmission function in binary form may be referred to as a binary mask. Another form is continuous. That is, the modulus of the transmittance (or reflectance) of the patterned device is a continuous function of the position on the patterned device. The phase of the transmittance (or reflectance) may also be a continuous function of the position on the patterned device. A mask transmission function in 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.) rather than a binary value of 0 or 1. In an embodiment, the CTM may be a pixelated grayscale image, where each pixel has a number of values (e.g., a normalized value in the range [-255, 255], in the range [0, 1] or [-1, 1], or other appropriate range).

The thin mask approximation (also known as the Kirchhoff boundary condition) is widely used to simplify the determination of the interaction of radiation with the patterned device. The thin mask approximation assumes that the thickness of the structures on the patterned device is very small compared to the wavelength, and the width of the structures on the mask is very large compared to the wavelength. Therefore, the thin mask approximation assumes that the electromagnetic field behind the patterned device is the product of the incident electromagnetic field and the mask transmission function. However, as lithography processes use radiation with shorter and shorter wavelengths, and the structures on the patterned device become smaller and smaller, the assumption of the thin mask approximation breaks down. For example, due to the finite thickness of structures (e.g., the edge between the top surface and the sidewalls), the interaction of radiation with the structure ("mask 3D effect" or "M3D") can become important. Including this scattering in the mask transmission function allows the mask transmission function to better capture the interaction of radiation with the patterned device. The mask transmission function under the thin mask approximation can be called the thin mask transmission function. The mask transmission function that includes M3D can be called the M3D mask transmission function.

FIG2 schematically depicts an exemplary lithography projection device whose illumination source can be optimized using the method described herein. The device comprises: - an illumination system IL for conditioning the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO; - a first object stage (e.g., a mask stage, a patterning device stage or a doubling mask stage) MT having a patterning device holder for holding a patterning device MA (e.g., a doubling mask) and connected to a first positioner for accurately positioning the patterning device relative to the item PS; - a second object stage (substrate stage or wafer stage) WT having a substrate holder for holding a substrate W (e.g., an anti-etchant coated silicon wafer) and connected to a second positioner for accurately positioning the substrate relative to the item PS; - a projection system ("lens") PS (e.g., a refractive, reflective, or catadioptric optical system) for imaging the irradiated portion of the patterning device MA onto a target portion C of the substrate W (e.g., comprising one or more dies).

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

A source SO (e.g. a mercury lamp or an excimer laser) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed an adjustment member such as a beam expander Ex, for example. The illuminator IL may comprise an adjustment member AD for setting the outer radial extent or the inner radial extent (usually referred to as σ-external and σ-inner, respectively) of the intensity distribution in the beam. In addition, the illuminator IL will typically 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 the desired uniformity and intensity distribution in its cross section.

With respect to FIG. 2 , it should be noted that the source SO can be within the housing of the lithography projection device (this is often the case when the source SO is, for example, a mercury lamp), but it can also be remote from the lithography projection device, into which the radiation beam generated by the source SO is guided (for example, with the aid of suitable guiding mirrors); the latter situation is often the case when the source SO is an excimer laser (for example, based on KrF, ArF or _F2 lasers).

The light beam B then intercepts the patterning device MA held on the patterning device table MT. Having traversed the patterning device MA, the light beam B passes through a lens PS which focuses the light beam B onto a target portion C of the substrate W. With the aid of the second positioning element (and the interferometry element IF), the substrate table WT can be moved exactly, for example in order to position different target portions C in the path of the light beam B. Similarly, the first positioning element can be used to accurately position the patterning device MA relative to the path of the light beam B, for example after a mechanical retrieval of the patterning device MA from a patterning device library or during a scan. In general, movement of the object table 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. 11 . However, in the case of a wafer stepper (as opposed to a step-and-scan tool), the patterning table MT may only be connected to a short-stroke actuator, or may be fixed.

The depicted tool can be used in two different modes: - In step mode, the patterning device table MT remains essentially stationary and the entire patterning device image is projected onto the target portion C at once (i.e. a single "flash"). The substrate table WT is then displaced in the x or y direction so that a different target portion C can be irradiated by the light beam B; - In scan mode, essentially the same situation applies, except that a given target portion C is not exposed in a single "flash". Alternatively, the patterning device table MT can be moved in a given direction (the so-called "scanning direction", e.g. the y direction) with a speed v so as to cause the projection light beam B to scan across the patterning device image; at the same time, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, where M is the magnification of the lens PS (typically, M = 1/4 or 1/5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

FIG3 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus according to an embodiment. As will be appreciated, models may represent different patterning processes and need not include all of the models described below. Source model 300 represents the optical characteristics of the illumination of the patterning device (including the radiation intensity distribution, bandwidth, and/or phase distribution). Source model 300 may represent the optical characteristics of the illumination, including but not limited to a numerical aperture setting, an illumination mean square deviation (σ) setting, and any specific illumination shape (e.g., off-axis radiation shape, such as annular, quadrupole, dipole, etc.), where σ (or mean square deviation) is the outer radial extent of the illuminator.

The projection optics model 310 represents the optical properties of the projection optics (including changes in the radiation intensity distribution and/or phase distribution caused by the projection optics). The projection optics model 310 may represent the optical properties of the projection optics, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

The patterned device/design layout model module 320 captures how design features are placed in a pattern of a patterned device and may include a representation of detailed physical properties of a patterned device, such as described in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. In an embodiment, the patterned device/design layout model module 320 represents the optical characteristics (including changes in radiation intensity distribution and/or phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.), which is a representation of a configuration of features on or formed by a patterned device. Since the patterning device used in a lithographic projection apparatus can vary, there is a need 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 illumination and projection optics. The goal of the simulation is often to accurately predict, for example, edge placement and CD, which can then be compared to the device design. The device design is generally defined as a pre-OPC patterned device layout and will be provided in a standardized digital file format such as GDSII or OASIS.

An aerial image 330 may be simulated from source model 300, projection optics model 310, and patterning device/design layout model module 320. The aerial image (AI) is the radiation intensity distribution at the substrate level. The optical properties of the lithography projection apparatus (e.g., properties of the illumination, patterning device, and projection optics) dictate the aerial image.

The resist layer on the substrate is exposed by the aerial image, and the aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. The resist image 350 can be simulated from the aerial image 330 using a resist model 340. The resist model can be used to calculate the resist image based on the aerial image, an example of which can be found in U.S. Patent Application No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model 340 typically describes the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development in order to predict, for example, the profile of resist features formed on a substrate, and therefore it is typically only related to such properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and development). In an embodiment, the optical properties of the resist layer (e.g., refractive index, film thickness, propagation and polarization effects) may be captured as part of the projection optics model 310.

Thus, in general, the connection between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which results from the projection of the radiation onto the substrate, refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) becomes a latent "resist image" by absorbing the incident energy, which is further modified by diffusion processes and various loading effects. An efficient simulation method fast enough for full-wafer applications approximates the actual 3-dimensional intensity distribution in the resist stack by means of a 3-dimensional aerial (and resist) image.

In an embodiment, the resist image 350 may be used as an input to a post-pattern transfer process model module 360. The post-pattern transfer process model module 360 defines the performance of one or more post-resist development processes (eg, etching, developing, etc.).

The simulation of the patterning process can, for example, predict the contours, CD, edge placement (e.g., edge placement error), etc. in the resist and/or etched image. Thus, the goal of the simulation is to accurately predict, for example, edge placement of the printed pattern, and/or aerial image intensity slope, and/or CD, etc. These values can be compared to the expected design to, for example, calibrate the patterning process, identify locations where defects are predicted to occur, etc. The expected design is generally defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file formats.

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 ideally corresponds to a distinct physical or chemical effect. Thus, the model formulation sets an upper limit on how well the model can be used to simulate the overall manufacturing process.

The following paragraphs describe systems and methods for predicting 2D element representations of a mask pattern. A prediction model (e.g., an ML model such as a neural network) is trained to predict the 2D element representation based on an input mask pattern (e.g., generated from a target pattern to be printed on a substrate). The 2D element representation predicted by the prediction model is a multi-channel output (although it can be a single-channel output as described below), the 2D element representation comprising a set of images indicating position information of the 2D elements representing features of the mask. Training data (e.g., real images) comprising the input mask pattern and a set of images indicating position information of the 2D elements can be generated in a variety of ways.

4 and 5 provide a brief introduction to a 2D elemental representation of a mask feature and the generation of a mask feature outline from the 2D elemental representation, respectively.

FIG. 4 illustrates a method for placing, associating, and adjusting 2D elements that form mask features consistent with various embodiments. In some embodiments, determining a mask pattern (or portion thereof) to be used with a lithography process may include assigning locations of 2D elements 410 based on a target pattern. As shown in the first (top) portion 400A of FIG. 4 , the shape of a mask feature 401 may be represented as a collection of 2D elements 410 (shown as circles in this example). The 2D elements are located at different locations to form the shape of the mask feature, as shown by a grid of dots for reference. The dots at the grid locations may not be generated, and are shown for illustration purposes only. In some embodiments, the grid may be a collection of pixels in an image. Four of the 2D elements are labeled 410a, 410b, 410c, and 410d. Although further described herein with reference to at least FIG. 5 , it can be seen that a contour formed around a 2D element (e.g., a circle having a diameter of at least the minimum width specified by the MRC rule) can inherently and automatically satisfy the MRC rule regardless of the position of the 2D element.

The lower panel 400B in FIG. 4 depicts an example of associating 2D elements based on an association criterion to form a cluster 430 representing a mask feature. Associations 420 are depicted as line segments between 2D elements. The associated 2D elements can then be used to form a cluster 430 having a shape corresponding to mask feature 401 as further explained herein. In FIG. 4 , all 2D elements are shown as part of cluster 430. Because the elements that are associated depend on the mask feature optimization, not all 2D elements in the cluster need to be associated with each other. For example, the 2D element 410a in the upper left center is not associated with the 2D element 410d in the lower right, despite its association with other 2D elements as part of the same cluster 430. In some embodiments, the association criteria may be rule-based criteria. For example, an association criterion may be distance-based, where two 2D elements may be associated with each other if they are within a specified distance. Although the specified distance may be arbitrarily set by the user or otherwise manipulated by the system, in some embodiments, the specified distance may be based on an MRC rule for a minimum width of a reticle feature. In some embodiments, two 2D elements may be associated with each other based on predictions from a prediction model, as described at least with reference to FIGS. 7 , 8 , and 12 - 13 .

The middle portion 400C in FIG4 depicts an exemplary outline 440 surrounding the cluster 430. As described in further detail herein, such as with reference to FIG5, the outline 440 can be generated to encompass the area formed by the 2D elements and the area between the 2D elements. Thus, the outline can be an outer outline of the cluster corresponding to the outer edge of the mask feature. Similarly, for a mask feature having an inner edge, such as a donut-shaped mask feature, the outline can be an inner outline of the cluster corresponding to the inner edge of the mask feature.

The next portion 400D is similar to the middle portion, again showing 2D elements 410, associations 420, clusters 430, and outlines 440, but without showing the lines forming the regions between the 2D elements or showing mask features 401. Here, outlines 440 are more clearly visible and surround the clusters of 2D elements.

The bottom portion 400E in FIG. 4 depicts adjusting the 2D elements of cluster 430 to vary the reticle features formed by cluster 430. In some embodiments, the adjustment of the reticle features may be based on simulations associated with a lithography process (e.g., as described with reference to at least FIG. 3 ), an OPC model, etc. In other embodiments, the adjustment of the reticle features may be based on geometric properties of the reticle pattern (e.g., width, spacing, etc.) and based on rules specified for OPC (e.g., adding liner, offset, hammer, SRAF, etc. on primary features). In some embodiments where the adjustment is based on simulation, the reticle generation process in SMO or OPC, etc. may optimize the reticle features by adjusting any combination of the 2D elements of any of the clusters formed for the simulated reticle. In this example, 2D element 450a is shown as being in a slightly different position, and 2D element 450b has been added (with neighboring 2D elements also moved slightly). As used herein, "adjusting" a 2D element means moving, changing the shape of, or adding/subtracting a 2D element. For example, the center of a circular 2D element may be moved as needed to optimize the mask. In other implementations, the radius of the circular 2D element may be changed as part of the optimization process. Utilizing these methods of determining/adjusting the profile of a reticle feature, any of the disclosed methods may include manufacturing a reticle from a reticle pattern that includes a profile generated by the adjusted 2D elements.

The present disclosure contemplates the use of many types of 2D elements. Since 2D elements can be used to define at least one specific dimension (e.g., CD, minimum spacing between mask features, etc.), and in some cases to define a specific area (e.g., the minimum area allowed by the mask features), 2D elements can define non-zero areas (e.g., different from points). In some embodiments, 2D elements are two-dimensional (2D) elements. For example, 2D elements can be circular, or more generally, elliptical. 2D elements can be the same size or can vary in size within or among clusters. 2D elements are not necessarily circular/elliptical. For example, 2D elements can be polygons (e.g., squares, triangles, rectangles, hexagons, etc.) or any suitable arbitrary shape. In such embodiments, the outline can be inscribed around the vertices or inscribed against the edges. These 2D elements may define a closed area (e.g., the circular area shown), at least partially closed area, or semi-closed (e.g., a semicircle). Although shapes such as circles, polygons, etc. are examples of closed areas, in some embodiments, 2D elements may be effectively represented by arcs or other similar structures. For example, the same outline in the bottom portion of FIG. 4 may be produced by positioning arc segments having the same center as the circle and wherein the arc segments are appropriately oriented and have sufficient length to produce the depicted outline. Therefore, other 2D elements equivalent to the 2D elements depicted herein may be considered within the scope of the present disclosure.

FIG. 5 illustrates a method for obtaining an outline of a mask feature based on the 2D element consistent with various embodiments. A cluster of 2D elements may be outlined in any suitable manner without departing from the scope of the present disclosure, one implementation of which is depicted in FIG. 5 . The top portion 500A of FIG. 5 depicts two exemplary associated 2D elements 510 a and 510 b. A virtual line segment 520 may connect the centers of the 2D elements. The system need not generate the virtual line segment 520 (which is provided herein for illustrative purposes). With respect to the outline 530 a surrounding the two-dimensional element, the virtual line segment 520 may be offset on either side by a distance equal to the radius of the 2D element. This can then form what are referred to herein as "sub-regions" (areas of 2D elements based on the offset line and areas between them), one of which is shown as sub-region 522a. In implementations where the 2D elements are not of equal size, the offset can be such that the offset distance transitions from one radius to another. However, it should be understood that this discussion is merely exemplary. The offset distance or sub-regions can be defined in any other suitable manner and a mask feature can have many such sub-regions. The area enclosed by outline 530a can be the area occupied by the sub-regions and any corresponding areas within the connected set of sub-regions (e.g., the area of the sub-regions surrounding the perimeter of the mask feature and the area that such perimeters can be enclosed).

The next section 500B expands the above example to include 2D element 510c. Another virtual line segment 520a and a corresponding offset line segment that forms part of the outline 530b are shown between 510b and 510c. Thus, in various implementations, a process similar to that described above may include generating sub-regions of the outline (e.g., 522a and 522b) by applying a polygon offset operation to associated 2D element pairs (e.g., 510a/510b and 510b/510c). The process may then include operating on the union of the sub-regions, where the outline 530b is the union of the sub-regions. Since the depicted 2D elements may form a cluster, the system may thereby generate an outline of the cluster based on the 2D elements. In this example, the outline corresponds to the outer outline of all sub-areas within the cluster that form the perimeter of the cluster. This process can be extended to any number and configuration of 2D elements displayed by the bottom portion 500C, thereby displaying the outline 530c.

Although the examples of FIG. 5 in portions 500A-500C are provided to provide an exemplary step-by-step method of forming an outline, in some implementations, forming an outline may be performed using substantially fewer steps. For example, once the 2D elements that will form the basis of the mask shape are determined, these 2D elements may then be formed into a single shape (which may include any combination of polygons and line segments). This shape may then be considered a "polygon" (again, not necessarily strictly a polygon, since it may have portions that are line segments) and this "polygon" may then be formed into an outline according to any of the examples herein by performing polygon offset operations, several of which are described below.

In some embodiments, a "polygon offset" operation may be performed, wherein a polygon to be outlined may be defined by selecting the location (e.g., center) of a 2D element corresponding to a desired mask feature. An example of such a polygon 540 is shown in 500C by a thicker line, where various line segments are shown connecting certain centers of the 2D elements. Polygon 540 (including exemplary additional line segments 550) may then be offset (e.g., by the radius of the 2D element) to form the depicted outline 530c. Although not shown in the example of FIG. 5 , any interior regions (e.g., as in a "donus-shaped" mask feature) may be similarly defined, outlined, and shaped as described herein.

The defined outer contour can be further processed by any suitable technology. As seen from the examples of the circular 2D elements in Fig. 4 and Fig. 5, it is determined that some parts of the contour are naturally rounded based on the radius of the 2D element. However, in some positions such as the concave parts of the contours 530a to 530c, the disclosed method may also include performing corner rounding or any other type of smoothing operation on the outer contour. One method of corner rounding may include performing spline interpolation between two points on either side of the corner. In some embodiments, the spline interpolation can modify the contour to be smooth, but the contour can be made not to touch the 2D element. Such deviations may be acceptable because they can further enhance the compliance to the minimum width MRC rule.

In some embodiments shown in portion 500D, the system may generate "square corners" 570 (rather than rounded corners 560) around the vertices of the polygons that have formed the outline, so that the intersecting segments that would normally form a sharp vertex meet a third line segment (e.g., similar to a chamfer). Another option may allow the line segments to meet to form a "mitered corner" 580, however, in some embodiments, this may cause an undesirable extension of the outline (e.g., it may exceed a specified limit on the distance from the associated vertex). In this case, the system may square the mitered corner 580 to become another square corner 580a so that the outline does not extend beyond the specified limit. Additional details of generating 2D element representations or generating mask feature outlines from 2D element representations are described in PCT Application No. PCT/EP2023/055028, the disclosure of which is incorporated herein by reference in its entirety.

In some embodiments, the 2D element representation may be expressed using position information of the 2D elements representing the mask features. FIG. 6 illustrates a representation of the 2D element representation using position information of the 2D elements of the mask features consistent with various embodiments. For example, consider the 2D element representation 600 of the mask feature 630 shown in FIG. 6 . In some embodiments, the 2D element representation 600 is similar to the 2D element representation in portion 400E of FIG. 4 . The 2D elements may be assigned locations of a grid (e.g., a set of pixels), such as grid 625. It should be noted that the grid 625 shown as points in FIG. 6 is imaginary, for illustrative purposes only, and is not generated by the system. The grid locations may correspond to one or more pixels in the image, and the resolution or size of the grid may be user defined. For example, the grid may be a "10X10" or "25X25" grid position, where each grid position may correspond to one pixel or more than one pixel. In some embodiments, the grid 625 may be viewed as a 2D matrix.

2D elements such as the first 2D element 603 can be represented using position information. The 2D element can be assigned coordinates of a grid 625. In some embodiments, the grid coordinates assigned to the 2D element depend on the geometric properties of the 2D element. In the example of Figure 6, the grid coordinates assigned to the 2D element can be the grid coordinates closest to the center of the 2D element. For example, for the first 2D element 603, the grid coordinates (1,1) closest to the center 602 of the first 2D element 603 are assigned as the position of the first 2D element 603. Similarly, the grid coordinates (2,3) closest to the center 612 of the second 2D element 605 are assigned as the position of the second 2D element 605. Therefore, position information (e.g., grid coordinates) can be generated for all 2D elements in the 2D element representation 600. Note that although grid coordinates are used to indicate location information, other parameters may also be used. For example, (x, y) coordinates may be used instead of matrix coordinates.

In some embodiments, the location information may also include existence information, which may be a binary value indicating whether a 2D element exists at a particular grid position. For example, for a first grid coordinate (1,1), the existence information may include a value "1" indicating that a 2D element exists at the first grid coordinate (1,1). Similarly, for a second grid coordinate (1,2), the existence information may include a value "0" indicating that a 2D element does not exist at the second grid coordinate (1,2). Therefore, the location information may include existence information for all grid coordinates. Binary values may be expressed in a variety of ways (e.g., "0" or "1", "yes" or "no", "true" or "false", etc.).

In some embodiments, the position information may also include a displacement or displacement amount of a 2D element from a specific grid position. In some embodiments, the position information may provide displacement values in different directions (e.g., the x direction and the y direction). For example, the position information may include displacement information such as ((6,3), a _x ), which indicates that the 2D element (e.g., the fifth 2D element 606) is displaced in the x direction from the grid coordinate (6,3) by an amount 652, i.e., a _x . For example, the position information may include displacement information such as ((6,3), a _y ), which indicates that the 2D element (e.g., the fifth 2D element 606) is displaced in the y direction from the grid coordinate (6,3) by an amount 654, i.e., a _y .

In some embodiments, the position information may also include association information between 2D elements. For example, the association information may indicate which 2D element is associated with which other 2D element. The association information may be indicated in various ways. In the first example, associations 622, 623, and 624 may be indicated as ((1,1), (2,1), (2,2)), which indicates that a 2D element in grid coordinates (1,1) (e.g., first 2D element 603) is associated with a 2D element in grid coordinates (2,1) (e.g., third 2D element 608), and 2D elements in grid coordinates (2,2) and (2,3) (e.g., second 2D element 605). In the second example, the association information may be indicated for the x direction and the y direction, respectively. For example, the x-direction association information of the 2D element at the grid coordinate (2,1) can be expressed as ((2,1), (2,2)), indicating that the 2D element (e.g., the third 2D element 608) at the grid coordinate (2,1) is associated with another 2D element at the grid coordinate (2,2) in the x-direction. Similarly, the y-direction association information of the 2D element at the grid coordinate (2,1) can be expressed as ((2,1), (1,1), (3,2)), indicating that the 2D element (e.g., the third 2D element 608) at the grid coordinate (2,1) is associated with other 2D elements (e.g., the first 2D element 603) at the grid coordinate (1,1) and other 2D elements (e.g., the fourth 2D element 610) at the grid coordinate (3,2) in the y-direction. In a third example, the association information may be indicated as a binary value indicating whether a 2D element at a particular grid position is associated with a 2D element in a neighboring position in one or more directions. For example, the x-direction association information of a 2D element at grid coordinate (2,1) may be expressed as ((2,1), 1), indicating that a 2D element (e.g., the third 2D element 608) in grid coordinate (2,1) is associated with a 2D element in a neighboring grid (grid coordinate (2,2)) in the x-direction. Similarly, the y-direction association information of a 2D element at grid coordinate (2,1) can be expressed as ((2,1), 0), which indicates that the 2D element in grid coordinate (2,1) (e.g., the third 2D element 608) is not associated with the 2D element in the adjacent grid position (grid coordinate (3,1)) in the y direction.

In some embodiments, the above information, such as presence information, position information, displacement information, association information, etc., may be encoded into an image set that may derive a 2D element representation 600. Although the above information may be used to generate an image set, in some embodiments, the image set may be derived from a layer set image of a mask pattern. FIG. 7 shows an image set representing a 2D element representation of a mask pattern consistent with various embodiments. In the example of FIG. 7 , the first image 715a may be a binary image, wherein each pixel value may indicate whether a 2D element exists at a corresponding grid position. For example, a white pixel may indicate that a 2D element or a portion thereof exists at a corresponding grid position, and a black pixel may indicate that a 2D element does not exist at a corresponding grid position.

The second image 715b may indicate the displacement information of the 2D element in the first direction. For example, each pixel value in the second image 715b may indicate the displacement amount of the 2D element from the position of the pixel in the x direction.

The third image 715c may indicate the displacement information of the 2D element in the second direction. For example, each pixel value in the third image 715c may indicate the displacement amount of the 2D element from the position of the pixel in the y direction.

The image set may include fewer or more images than depicted in FIG. 7 . For example, the image set may not include the first image 715a, in which case the existence information is derived from the second image 715b and the third image 715c. In some embodiments, the image set may include additional images such as images indicating association information. One or more images may be generated to depict associations in different directions. For example, the first association image may be a binary image indicating associations in a first direction (e.g., the x direction). Each pixel value may indicate whether a 2D element at a particular position is associated with a 2D element in an adjacent position in the x direction. In another example, the second association image may be a binary image indicating associations in a second direction (e.g., the y direction). Each pixel value may indicate whether a 2D element at a particular position is associated with a 2D element in an adjacent position in the y direction. In yet another example, the third association image may be a binary image indicating associations in a third direction, such as the northeast (NE) direction. Each pixel value may indicate whether a 2D element at a particular location is associated with a 2D element in a neighboring location in the NE direction. For example, a pixel value corresponding to a pixel at grid coordinates (3,2) may indicate an association 635 between a 2D element at grid coordinates (3,2) and a 2D element at grid coordinates (2,3). Other images for associations in other directions, such as the northwest direction, the southeast direction, and the southwest direction, may also be generated.

In some embodiments, training a prediction model to generate an image set (e.g., one or more of the above-described image sets) that represents a 2D element representation is more efficient than training a prediction model to generate a reticle pattern itself. For example, such an ML model may be more error-tolerant, converge faster, or consume less computational resources than training an ML model to generate a reticle pattern itself. After generating the image set, a 2D element representation may be derived or constructed from the image set, and a reticle feature profile may be constructed to generate an output reticle pattern. FIGS. 8-11 describe using an ML model to generate or predict a 2D element representation of a reticle pattern.

Figure 8 is a block diagram of an exemplary system for predicting a 2D element representation of a mask pattern using a prediction model consistent with various embodiments. Figure 11 is a flow chart of a method for predicting a 2D element representation of a mask pattern using a prediction model consistent with various embodiments.

At process P1105 of FIG. 11 , the input mask pattern 805 is provided to the prediction model 850. In some embodiments, the prediction model 850 is an ML model (e.g., a neural network model) trained to predict 2D element representations of the mask pattern. Additional details of training the prediction model 850 are described with reference to at least FIG. 12 and FIG. 13 .

The input mask pattern 805 can be an image representation of an initial version of the mask pattern to be printed on the substrate. In some embodiments, the input mask pattern 805 can be generated from a target pattern (e.g., a GDS layout), as shown in FIG. 9 . FIG. 9 is a block diagram of an image representation of a mask pattern generated from a target pattern consistent with various embodiments. An imaging assembly 950 can generate the input mask pattern 805 from a target pattern 905, which is a designed layout of a pattern to be printed on the substrate. The imaging assembly 950 can generate the input mask pattern 805 using any of a number of known methods. For example, the imaging assembly 950 can generate the input mask pattern 805 from the target pattern 905 using a rasterization process. In the rasterization process, the target pattern is decomposed into trapezoids, and all the trapezoids are rasterized into a temporary buffer. The transmission and phase are then applied to the buffer to generate an image of the input mask pattern 805. In some embodiments, the corners of the features of the target pattern 905 may be rounded, the edges may be smoothed (e.g., anti-aliasing), and the pixel values may be filled (e.g., converted to a grayscale image) as part of the rasterization process. In some embodiments, the generation of the input mask pattern 805 may not include an analog lithography process (e.g., as described with reference to at least FIG. 3).

Referring back to FIG. 11 , at process P1110, the prediction model 850 generates an image set 815 representing a 2D element representation of an output mask pattern (e.g., an intermediate optimized version of an input mask pattern). The image set 815 may indicate position information of 2D elements in the 2D element representation. In some embodiments, the position information includes information about a grid position assigned to the 2D element and a displacement of the 2D element from the assigned grid position. The image set 815 may include one or more of the images described above with reference to at least FIG. 7 . For example, the image set 815 includes a binary image (e.g., a first image 715a) indicating whether a 2D element exists at a specified grid position. The image set 815 may include a second image (e.g., second image 715b) indicating the displacement of the 2D element from the specified grid position in a first direction (e.g., x direction), and a third image (e.g., third image 715c) indicating the displacement of the 2D element from the specified grid position in a second direction (e.g., y direction). In some embodiments, the image set 815 may not include the first image 715a, in which case the presence information may be derived from the second image 715b and the third image 715c.

In some embodiments, the image set 815 may also include images indicating associations between 2D elements represented by the 2D elements. For example, a first association image may be a binary image indicating whether a 2D element at a specific position is associated with a 2D element in a neighboring position in a first direction (e.g., the x direction). A second association image may be a binary image indicating whether a 2D element at a specific position is associated with a 2D element in a neighboring position in a second direction (e.g., the y direction). In some embodiments, the association information may not be predicted by a prediction model. 2D elements may be associated based on an association criterion. In some embodiments, the association criterion may be a rule-based criterion. For example, an association criterion may be distance-based, wherein if two 2D elements are within a specified distance, the two 2D elements may be associated with each other, as described with reference to at least FIG. 4. In some embodiments, prediction model 850 is referred to as a single-channel input and multiple-channel output prediction model, since multiple images (e.g., image set 815) are generated as output for a single image input (e.g., input mask pattern 805). In embodiments where prediction model 850 outputs a single image (e.g., only information such as first image 715a), prediction model 850 is referred to as a single-channel input and single-channel output prediction model.

It should be noted that the prediction model can be trained to predict any number of images based on the desired information. For example, if only the existence information of the 2D element is needed, the prediction model can be trained to predict a single image (e.g., the first image 715a). In a single-channel output embodiment, the displacement information (e.g., the displacement of the 2D element from a specific grid position) can be considered as "0". In another example, if only the displacement information of the 2D element in two directions is needed, the prediction model can be trained to predict two images (e.g., the second image 715b and the third image 715c). The existence information of the 2D elements at various positions can be derived from the displacement information included in the two images. In another example, if the presence information and the displacement information of the 2D element in two directions are required, the prediction model may be configured to generate three images (e.g., the first image 715a, the second image 715b, and the third image 715c). In yet another example, if the presence information, the displacement information of the 2D element in two directions, and the association information of the 2D element in two directions are required, the prediction model may be configured to generate five images (e.g., the first image 715a, the second image 715b, the third image 715c, and two additional images indicating the association of the 2D element in two directions (e.g., the x direction-the left side of the 2D element and the y direction-the bottom of the 2D element)). In another example, if existence information, displacement information of a 2D element in two directions, and association information of the 2D element in four directions are required, the prediction model may be configured to generate seven images, respectively (e.g., a first image 715a, a second image 715b, a third image 715c, and four additional images indicating associations of the 2D element in two directions (e.g., x direction - two images indicating associations with the left and right sides of the 2D element, respectively, and y direction - two images indicating associations with the top and bottom of the 2D element)). A variety of such outputs are possible.

A 2D element representation is generated based on image set 815. For example, the 2D element representation may be similar to 2D element representation 600 of reticle feature 630 or the 2D element representation of reticle feature 401 in bottom portion 400E of FIG. 4 , and may be generated using various information derived from image set 815. In some embodiments, a 2D element representation is generated for all reticle features of an output reticle pattern.

At process P1115, a mask feature outline is generated for the mask feature based on the 2D elements in the 2D element representation. In some embodiments, the mask feature outline can be constructed using polygonal offsets or clusters of 2D elements, as described with reference to at least FIGS. 4 and 5. For example, a 2D element can be associated with one or more other 2D elements based on association information obtained from an image set predicted by an association criterion or a free prediction model to generate one or more 2D element clusters to form the shape of the mask feature, and then the mask feature outline can be generated from the 2D elements, as described with reference to at least FIG. 5. For example, as shown in FIG. 10, a mask feature outline 1005 can be generated for a mask feature 630 based on the 2D elements in the 2D element representation 600. Generates mask feature outlines for all mask features, thus producing an output mask pattern.

In some embodiments, at process P1120, the output mask pattern may be further optimized by performing a mask optimization process such as OPC to generate an optimized mask pattern 1120. A mask or patterning device may be manufactured based on the optimized mask pattern 1120 used in a lithography process to print a target pattern on a substrate.

Figures 12-14 illustrate training a prediction model 850 to generate a 2D element representation of a mask pattern. Figure 12 is a block diagram of a system for training a prediction model to generate a 2D element representation of a mask pattern consistent with various embodiments. Figure 13 is a flow chart of a method for training a prediction model to generate a 2D element representation of a mask pattern consistent with various embodiments.

At process P1305, training data is obtained for training a prediction model. In some embodiments, the training data includes an input mask pattern image set 1205 and a plurality of image sets 1210, each of which represents a 2D element representation of an output mask pattern corresponding to the input mask pattern. For example, the training data may include an input mask pattern 1205a and image sets 1210a1 to 1210an of 2D element representations of the output mask pattern (e.g., an optimized version of the input mask pattern 1205a).

In some embodiments, the input mask pattern 1205a is an image generated from a target pattern, for example using imaging assembly 950, as described with reference to at least FIG. 9.

In some embodiments, the image sets 1210a1 to 120an may be similar to the image set 815 indicating position information, presence information, displacement information, association information, etc. of 2D elements in the 2D element representation. The image sets 1210a1 to 1210an may be generated from the 2D element representation, which may be generated in a variety of ways. In a first approach, a 2D element representation of a mask pattern may be generated in an iterative manner, as described with reference to at least FIG. 4. For example, mask features from an initial mask pattern are obtained, and a 2D element representation is generated by assigning positions, associations, and adjustments to the 2D elements to generate a 2D element representation of an output mask pattern. Adjustments to 2D elements may be based on simulations associated with a lithography process (e.g., as described with reference to at least FIG. 3 ), an OPC model, etc., or based on geometric properties of the mask pattern (e.g., width spacing, etc.) and based on rules specified for OPC (e.g., adding lining, offsets, hammers, SRAFs, etc. on key features).

In a second method, a 2D element representation of a mask pattern can be generated in a non-iterative manner, as shown in Figure 14. Figure 14 shows the generation of a 2D element representation of a mask pattern for training a prediction model consistent with various embodiments. For example, an outline 1405 of a mask feature from an initial mask pattern is obtained. The outline 1405 is reduced (e.g., shrunk) by a specified amount to produce a shrunk outline 1435. The specified amount can be related to a geometric parameter associated with the 2D element, such as the radius 1410 of a circle 1415. The 2D element is then placed at or near a grid location along the shrunk outline 1435. In some embodiments, by shrinking the outline 1405 by an amount equal to the radius of the 2D element, and placing 2D elements along the shrunken outline 1435 to generate the 2D element representation 1425, the outline 1454 reconstructed from the 2D element representation 1425 will be approximately the same size and shape as the initial outline 1405 (e.g., because the reconstructed outline 1454 will extend outward from the shrunken outline 1435 by an amount equal to the radius of the circle 1415). In some embodiments, the number of 2D elements that can be placed along the shrunken outline 1435 can depend on the resolution of the grid 1430. For example, the greater the resolution of the grid 1430, the greater the number of 2D elements that can be placed along the shrunk outline 1435, the finer the reconstructed outline 1454 will be, and the more similar the reconstructed outline 1454 will be to the initial outline 1405. In some embodiments, generating a 2D element representation using the second method may be faster and consume less computational resources than generating a 2D element representation using the first method.

After the 2D element representation is generated (using the first method or the second method), information such as existence information, position information, displacement information, association information, etc. of the 2D elements from the 2D element representation can be used to generate the image set 1210a1 to 1210an.

Referring back to FIG. 13 , at process P1310, the prediction model 850 is executed by inputting training data (e.g., input mask pattern image set 1205 and image set 1210). The prediction model 850 generates image sets 1215a1 to 1215an based on the input mask pattern 1205a. The predicted image sets 1215a1 to 1215an are compared with the input image sets 1210a1 to 1210an in the training data, and a cost function 1250 indicating the difference between the predicted image sets 1215a1 to 1215an and the input image sets 1210a1 to 1210an is calculated. It is determined whether the cost function 1250 is minimized. If the cost function 1250 is not minimized, the parameters (e.g., weights and biases) of the prediction model 850 are adjusted and the prediction model 850 is executed again to predict the image set 1215a1 to 1215an. The process of predicting the image set, determining the cost function 1250, and adjusting the prediction model parameters to reduce the cost function 1250 is repeated until the cost function 1250 is minimized. After minimizing the cost function 1250, the prediction model 850 is considered trained, and the trained prediction model can be used to generate an image set (e.g., image set 815) that represents a 2D element representation of a mask pattern of any input mask pattern (e.g., input mask pattern 805), as described with reference to at least Figures 8 and 11.

FIG. 15 is a block diagram illustrating a computer system 1500 that can assist in implementing the various methods and systems disclosed herein. The computer system 1500 can be used to implement any of the entities, components, modules, or services depicted in the examples of the various figures (and any other entities, components, modules, or services described in this specification). The computer system 1500 can be programmed to execute computer program instructions to perform the functions, methods, processes, or services described herein (e.g., any of the entities, components, or modules). The computer system 1500 can be programmed to execute computer program instructions by at least one of software, hardware, or firmware.

Computer system 1500 includes a bus 1502 or other communication mechanism for communicating information, and a processor 1504 (or multiple processors 1504 and 1505) coupled to bus 1502 for processing information. Computer system 1500 also includes a main memory 1506, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 1502 for storing information and instructions to be executed by processor 1504. Main memory 1506 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by processor 1504. Computer system 1500 further includes a read-only memory (ROM) 1508 or other static storage device coupled to bus 1502 for storing static information and instructions for processor 1504. A storage device 1510, such as a magnetic or optical disk, is provided and coupled to bus 1502 for storing information and instructions.

The computer system 1500 may be coupled to a display 1512, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display, via a bus 1502 for displaying information to a computer user. An input device 1514 including alphanumeric keys and other keys is coupled to the bus 1502 for communicating information and command selections to the processor 1504. Another type of user input device is a cursor control 1516, such as a mouse, trackball, or cursor arrow keys, for communicating directional information and command selections to the processor 1504 and for controlling the movement of a cursor on the display 1512. Such an input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

According to one embodiment, portions of one or more methods described herein may be performed by the computer system 1500 in response to the processor 1504 executing one or more sequences of one or more instructions contained in the main memory 1506. These instructions may be read into the main memory 1506 from another computer-readable medium such as the storage device 1510. Execution of the sequences of instructions contained in the main memory 1506 causes the processor 1504 to perform the program steps described herein. One or more processors in a multi-processing configuration may also be used to execute the sequences of instructions contained in the main memory 1506. In alternative embodiments, hard-wired circuitry may be used in place of or in conjunction with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

As used herein, the term "computer-readable media" refers to any media that participates in providing instructions to processor 1504 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 1510. Volatile media include dynamic memory, such as main memory 1506. Transmission media include coaxial cables, copper wire, and optical fibers, including the wires comprising bus 1502. 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, floppy disks, diskettes, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical media with a pattern of holes, RAM, PROM and EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier as described below, or any other medium that can be read by a computer.

Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to processor 1504 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem at the local end of computer system 1500 may receive data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 1502 may receive the data carried in the infrared signal and place the data on bus 1502. The bus 1502 carries the data to the main memory 1506, from which the processor 1504 retrieves and executes the instructions. The instructions received by the main memory 1506 may be stored on the storage device 1510 before or after execution by the processor 1504, as appropriate.

The computer system 1500 also preferably includes a communication interface 1518 coupled to the bus 1502. The communication interface 1518 provides two-way data communication coupled to a network link 1520, which is connected to a local area network 1522. For example, the communication interface 1518 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection with a corresponding type of telephone line. As another example, the communication interface 1518 can be a local area network (LAN) card to provide a data communication connection with a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 1518 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

Network link 1520 typically provides data communications to other data devices via one or more networks. For example, network link 1520 may provide connectivity to host computers 1524 or to data equipment operated by an Internet service provider (ISP) 1526 via a local area network 1522. ISP 1526 in turn provides data communications services via the global packet data communications network, now commonly referred to as the "Internet" 1528. Both local area network 1522 and Internet 1528 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 1520 and through the communication interface 1518 (which carry the digital data to and from the computer system 1500) are exemplary carrier forms of transporting information.

The computer system 1500 can send messages and receive data including program code via one or more networks, network links 1520, and communication interfaces 1518. In the Internet example, a server 1530 can transmit the requested program code for an application via the Internet 1528, ISP 1526, local area network 1522, and communication interface 1518. For example, one such downloaded application can provide lighting optimization of an embodiment. The received program code can be executed by the processor 1504 as it is received, or stored in the storage device 1510 or other non-volatile storage for later execution. In this way, the computer system 1500 can obtain the application code in carrier form.

Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system, for example, lithography imaging systems used for imaging on substrates other than silicon wafers.

As used herein, the terms "optimizing" and "optimization" refer to or mean adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc., so that the result and/or process has more desirable characteristics, such as higher projection accuracy of the design pattern on the substrate, a larger process window, etc. Thus, as used herein, the terms "optimizing" and "optimization" refer to or mean a process of identifying one or more values for one or more parameters that provide an improvement in at least one relevant metric, e.g., a local optimum, over an initial set of one or more values for those one or more parameters. "Optimum" and other related terms should be interpreted accordingly. In embodiments, the optimization step may be applied repeatedly to provide further improvements in one or more metrics.

Aspects of the present invention may be implemented in any convenient form. For example, embodiments may be implemented by one or more appropriate computer programs, which may be performed on an appropriate carrier medium that may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention may be implemented using suitable equipment that may specifically take the form of a programmable computer that runs a computer program configured to implement the methods described herein. Therefore, embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium that may be read and executed by one or more processors. Machine-readable media may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, machine-readable media may include: read-only memory (ROM); random access memory (RAM); disk storage media; optical storage media; flash memory devices; electrical, optical, acoustic or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.); and others. Additionally, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are for convenience only and such actions are actually caused by computing devices, processors, controllers or other devices executing firmware, software, routines, instructions, etc.

In the block diagrams, the components described are depicted as discrete functional blocks, but the embodiments are not limited to systems in which the functionality described herein is organized as described. The functionality provided by each of the components may be provided by software or hardware modules that are organized differently than presently depicted, for example, the software or hardware may be blended, combined, replicated, decomposed, assigned (e.g., within a data center or by region), or otherwise organized. The functionality described herein may be provided by one or more processors of one or more computers executing program code stored on a tangible, non-transitory, machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information communicated via the network, in which case, where information (e.g., content) is purportedly supplied or otherwise provided, the information may be provided by sending instructions to retrieve that information from the content delivery network.

Unless otherwise specifically stated, it should be understood that discussions throughout this specification using terms such as "processing," "computing," "calculating," "determining," or the like refer to actions or procedures of specific devices such as special-purpose computers or similar special-purpose electronic processing/computing devices, unless otherwise specifically stated or apparent from the description.

Embodiments of the present disclosure may be further described by the following clauses. 1. A method for determining a mask pattern for use with a lithography process, the method comprising: providing an input mask pattern corresponding to a target pattern to a prediction model; using the prediction model to generate a 2D element representation of an output mask pattern corresponding to the input mask pattern, wherein the 2D element representation includes a plurality of 2D elements representing mask features of the output mask pattern, and each 2D element defines a closed region; and determining a mask feature contour of the output mask pattern based on the 2D element representation. 2. The method of clause 1, wherein the 2D element representation includes an image set indicating position information of the 2D elements in the 2D element representation. 3. A method as in item 2, wherein the position information includes information about grid positions assigned to the 2D elements and the displacement of the 2D elements from the assigned grid positions. 4. A method as in item 2, wherein the image set includes a binary image indicating whether a 2D element exists at a specified grid position. 5. A method as in item 2, wherein the image set includes: a first image indicating the displacement of the 2D element from the specified grid position in a first direction, and a second image indicating the displacement of the 2D element from the specified grid position in a second direction. 6. A method as in item 2, wherein the image set includes: a binary image indicating whether a 2D element exists at a specified grid position; a first image indicating the displacement of the 2D element from the specified grid position in the first direction; and a second image indicating the displacement of the 2D element from the specified grid position in the second direction. 7. The method of clause 2, further comprising: Generating the 2D element representation based on an image set. 8. The method of clause 1, wherein each of the 2D elements is circular. 9. The method of clause 1, wherein each of the 2D elements is elliptical. 10. The method of clause 1, wherein each of the 2D elements is the same size. 11. The method of clause 1, wherein the 2D elements have different sizes. 12. The method of clause 1, wherein determining the mask feature outline of the output mask pattern from the 2D element representation comprises: Associating the 2D elements based on an association criterion to form a cluster representing the mask feature; and Generating an outline of the cluster based on the 2D elements. 13. The method of clause 12, wherein the association criterion comprises a rule-based criterion. 14. The method of clause 13, wherein the rule-based criterion comprises a distance-based criterion indicating the distance between two 2D elements. 15. The method of clause 12, wherein the 2D elements are associated based on association information derived from a binary image represented by the 2D elements, wherein the binary image indicates whether a 2D element at a specified position is associated with another 2D element at an adjacent position. 16. The method of clause 12, wherein the contour is an outer contour of the cluster corresponding to an outer edge of the mask feature. 17. The method of clause 12, wherein the contour is an inner contour of the cluster corresponding to an inner edge of the mask feature. 18. The method of claim 12, further comprising: generating sub-regions of the contour by applying a polygon offset operation to the associated 2D element pairs; and computing the union of the sub-regions, wherein the contour is the union of the sub-regions. 19. The method of claim 1, further comprising: optimizing the output mask pattern using an optical proximity correction procedure. 20. The method of claim 19, further comprising: producing a mask from the output mask pattern, the output mask pattern comprising the mask feature contours generated from the 2D elements. 21. The method of clause 1, wherein providing the input mask pattern comprises: obtaining a representation of the target pattern; generating an image from the target pattern, wherein the image represents the input mask pattern; and providing the image of the input mask pattern to the prediction model. 22. The method of clause 1, further comprising: training the prediction model using training data to generate a 2D element representation, wherein the training data comprises a set of input mask patterns and a set of output mask patterns corresponding to the set of input mask patterns. 23. The method of clause 22, wherein training the prediction model comprises: obtaining a first output mask pattern of an output mask pattern set corresponding to a first input mask pattern of an input mask pattern set; obtaining a first 2D element representation of the first output mask pattern; and executing the prediction model to generate a specified 2D element representation of the first output mask pattern based on the first input mask pattern and the first 2D element representation. 24. The method of clause 23, wherein obtaining the first 2D element representation comprises: assigning a position of a set of 2D elements based on the shape of the first input mask pattern; associating the set of 2D elements based on an association criterion to form a cluster representing a specified mask feature of the first input mask pattern; and adjusting the set of 2D elements of the cluster to vary the specified mask feature. 25. The method of clause 24, wherein the adjustment is based on geometric properties of the first output mask pattern and based on rules specified for a best proximity correction (OPC) procedure. 26. The method of clause 24, wherein the adjustment is based on a simulation associated with the lithography process. 27. The method of clause 24, further comprising: generating an image set indicating position information of the set of 2D elements in the first 2D element representation. 28. The method of clause 23, wherein obtaining the first 2D element representation comprises: shrinking a specified mask feature contour by a specified size associated with the 2D element to generate a shrunk contour; and assigning positions of the set of 2D elements along the shrunk contour so that the contour generated from the set of 2D elements approximates the specified mask feature contour. 29. The method of clause 23, wherein the first 2D element representation of the first mask pattern is derived from a layer set image of the first output mask pattern. 30. A method for training a prediction model to generate a 2D element representation of a mask pattern for use with a lithography process, the method comprising: Obtaining a 2D element representation set of an input mask pattern set and an output mask pattern set corresponding to the input mask pattern set as training data, wherein the 2D element representation in the 2D element representation set includes a plurality of 2D elements representing mask features of the mask pattern, and each 2D element defines at least a portion of a closed region; and Using the training data to train the prediction model to generate the 2D element representation. 31. The method of clause 30, wherein training the prediction model comprises: Obtaining a first output mask pattern of the output mask pattern set corresponding to a first input mask pattern of the input mask pattern set; Obtaining a first 2D element representation of the first output mask pattern; and Executing the prediction model to generate a specified 2D element representation of the first output mask pattern based on the first input mask pattern and the first 2D element representation. 32. The method of clause 31, wherein training the prediction model comprises: Training the prediction model until a cost function is reduced, wherein the cost function indicates a difference between (a) a specified 2D element representation generated by the prediction model and (b) the first 2D element representation. 33. The method of clause 31, wherein obtaining the first 2D element representation comprises: assigning a position of a set of 2D elements based on a shape of the first input mask pattern; associating the set of 2D elements based on an association criterion to form a cluster representing a specified mask feature of the first input mask pattern; and adjusting the set of 2D elements of the cluster to vary the specified mask feature. 34. The method of clause 33, wherein the adjustment is based on geometric properties of the first output mask pattern and based on rules specified for a best proximity correction (OPC) procedure. 35. The method of clause 33, wherein the adjustment is based on a simulation associated with the lithography process. 36. The method of clause 33, further comprising: generating an image set indicating position information of the set of 2D elements in the first 2D element representation. 37. The method of clause 33, wherein obtaining the first 2D element representation comprises: shrinking a specified mask feature contour by a specified size associated with the 2D element to generate a shrunk contour; and assigning positions of the set of 2D elements along the shrunk contour so that the contour generated from the set of 2D elements approximates the specified mask feature contour. 38. The method of clause 31, wherein the first 2D element representation of the first mask pattern is derived from a layer set image of the first output mask pattern. 39. The method of clause 30, further comprising: Providing an input mask pattern corresponding to a target pattern to a prediction model; Using the prediction model to generate a predicted 2D element representation of an output mask pattern; and Determining a mask feature profile of the output mask pattern based on the predicted 2D element representation. 40. The method of clause 39, further comprising: Optimizing the output mask pattern using an optical proximity correction procedure to generate a mask pattern. 41. The method of clause 40, further comprising: Producing a mask from the mask pattern, the mask pattern comprising the mask feature profiles generated from the 2D elements. 42. A device comprising: a memory storing an instruction set; and a processor configured to execute the instruction set so that the device performs a method as in any of the above items. 43. A non-transitory computer-readable medium having instructions recorded thereon, which when executed by a computer implement a method as in any of the above items.

The reader should understand that this application describes several inventions. These inventions have been grouped into a single document rather than separating them into multiple separate patent applications because the related subject matter of these inventions contributes to economic development in applications. However, the different advantages and aspects of these inventions should not be combined. In some cases, embodiments solve all of the shortcomings mentioned herein, but it should be understood that these inventions are independently useful and some embodiments only solve a subset of these problems or provide other benefits that are not mentioned, which will be obvious to those skilled in the art who review this disclosure. Due to cost constraints, some inventions disclosed herein may not be claimed at present, and such inventions may be claimed in subsequent applications (such as continuation applications or by amendment of the present patent scope). Similarly, due to space limitations, the invention abstract and invention content section of this document should not be considered to contain a comprehensive list of all such inventions or all aspects of such inventions.

It should be understood that the description and drawings are not intended to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

In view of this description, modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art. Therefore, this description and drawings should be interpreted as being illustrative only and for the purpose of teaching those skilled in the art the general manner of practicing the present invention. It should be understood that the forms of the present invention shown and described herein should be regarded as examples of embodiments. Elements and materials may be substituted for elements and materials illustrated and described herein, parts and procedures may be reversed or omitted, certain features may be utilized independently, and embodiments or features of embodiments may be combined, all of which will be apparent to those skilled in the art after having the benefit of this description. Changes may be made to the elements described herein without departing from the spirit and scope of the present invention as described in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the description.

As used herein, unless otherwise specifically stated, the term "or" encompasses all possible combinations except those that are not feasible. For example, if a component is stated to include A or B, then unless otherwise specifically stated or not feasible, the component may include A, or B, or A and B. As a second example, if a component is stated to include A, B, or C, then unless otherwise specifically stated or not feasible, 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 the entire list below and do not necessarily modify each member of the list, such that "at least one of A, B, and C" should be understood to include only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase "one of A and B" or "either of A and B" should be interpreted in the broadest sense to include one of A or one of B.

The description herein is intended to be illustrative rather than restrictive. Therefore, it will be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth below.

10A: Lithography projection equipment 12A: Radiation source 14A: Optical device 16Aa: Optical device 16Ab: Optical device 16Ac: Transmission optical device 18A: Mask 20A: Pupil 22A: Substrate plane 300: Source model 310: Projection optical device model 320: Patterning device/design layout model module 330: Aerial image 340: Anti-etching agent model 350: Anti-etching agent image 360: Pattern transfer post-processing model module 400A: First part 400B: Part 400C: Part 400D: Part 400E: Bottom part 401: Mask feature 410: 2D element 410a: 2D element 410b: 2D element 410c: 2D element 410d: 2D element 420: association 430: cluster 440: outline 450a: 2D element 450b: 2D element 500A: top part 500B: part 500C: part 500D: part 510a: 2D element 510b: 2D element 510c: 2D element 520: virtual line segment 520a: virtual line segment 522a: subregion 522b: subregion 530a: outline 530b: outline 530c: outline 540: polygon 550: additional line segment 560: rounded corners 570: square corners 580: mitered corners 580a: square corners 600: 2D element representation 602: center 603: first 2D element 605: second 2D element 606: fifth 2D element 608: third 2D element 610: fourth 2D element 612: center 622: association 623: association 624: association 625: grid 630: mask feature 635: association 652: quantity 654: quantity 715a: first image 715b: second image 715c: third image 805: input mask pattern 815: image 850: prediction model 905: target pattern 950: imaging assembly 1005: mask feature profile 1120: optimized mask pattern 1205: input mask pattern image 1205a: input mask pattern 1210: image 1210a1: image 1210an: image 1215a1: image 1215an: image 1250: cost function 1405: profile 1410: radius 1415: circle 1425: 2D element representation 1430: grid 1435: shrunk profile 1454: profile 1500: computer system 1502: bus 1504: processor 1505: processor 1506: Main memory 1508: Read-only memory 1510: Storage device 1512: Display 1514: Input device 1516: Cursor control 1518: Communication interface 1520: Network link 1522: Local area network 1524: Host computer 1526: ISP 1528: Internet 1530: Server AD: Adjustment component B: Radiation beam C: Target part CO: Condenser Ex: Beam expander IF: Interferometry component IL: Illumination system IN: Integrator MA: Patterning device MT: First object stage P1105: Program P1110: Program P1115: Program P1120: Program P1305: Program P1310: Program PS: Lens SO: Radiation source W: Substrate WT: Second object stage

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

FIG. 1 is a block diagram showing various subsystems of a lithographic projection apparatus according to an embodiment.

FIG2 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

FIG. 3 illustrates an exemplary flow chart for lithography in an analog lithography projection apparatus according to an embodiment.

FIG. 4 illustrates a method for placing, associating, and adjusting two-dimensional (2D) elements that form reticle features, consistent with various embodiments.

FIG. 5 illustrates a method for obtaining an outline of a mask feature based on the 2D elements, consistent with various embodiments.

FIG. 6 illustrates a representation of a 2D element representation using position information of the 2D elements of the mask feature, consistent with various embodiments.

FIG. 7 shows an image set representing a 2D element representation of a mask pattern consistent with various embodiments.

8 is a block diagram of an exemplary system for predicting a 2D element representation of a reticle pattern using a prediction model, consistent with various embodiments.

FIG. 9 is a block diagram of an image representation for generating a mask pattern from a target pattern, consistent with various embodiments.

FIG. 10 illustrates an outline of a reticle feature generated from a predicted 2D element representation of the reticle feature, consistent with various embodiments.

11 is a flow chart of a method for predicting a 2D element representation of a mask pattern using a prediction model, consistent with various embodiments.

12 is a block diagram of a system for training a prediction model to generate a 2D element representation of a mask pattern, consistent with various embodiments.

13 is a flow chart of a method for training a prediction model to generate a 2D element representation of a mask pattern, consistent with various embodiments.

FIG. 14 illustrates the generation of a 2D element representation of a mask pattern as training data for training a prediction model, consistent with various embodiments.

FIG. 15 is a block diagram illustrating a computer system that may assist in implementing the systems and methods disclosed herein.

Embodiments will now be described in detail with reference to the drawings, which are provided as illustrative examples to enable those skilled in the art to practice the embodiments. It is noteworthy that the following figures and examples are not intended to limit the scope to a single embodiment, but rather to make other embodiments possible by means of the interchange of some or all of the described or illustrated elements. Wherever convenient, the same figure symbols will be used throughout the drawings to refer to the same or similar parts. In the case where certain elements of the embodiments can be partially or completely implemented using known components, only those parts of these known components necessary for understanding the embodiments will be described, and detailed descriptions of other parts of these known components will be omitted to avoid confusing the description of the embodiments. In this specification, embodiments showing singular components should not be considered limiting; rather, unless otherwise expressly stated herein, the scope is intended to cover other embodiments including a plurality of the same components, and vice versa. In addition, unless so expressly stated, the applicant does not intend for any term in this specification or the scope of the patent application to be attributed with an uncommon or special meaning. In addition, the scope covers the current and future known equivalents of the components mentioned herein by way of description.

400A: Part 1

400B:Partial

400C: Partial

400D: Partial

400E: Bottom part

401: Mask characteristics

410:2D elements

410a:2D elements

410b: 2D elements

410c: 2D elements

410d: 2D elements

420: Association

430: Cluster

440:Outline

450a:2D elements

450b: 2D elements

Claims (15)

A non-transitory computer-readable medium having recorded thereon instructions, which when executed by a computer implement a method for determining a mask pattern for use with a lithography process, the method comprising: providing an input mask pattern corresponding to a target pattern to a prediction model; using the prediction model to generate a 2D element representation of an output mask pattern corresponding to the input mask pattern, wherein the 2D element representation includes a plurality of 2D elements representing a mask feature of the output mask pattern, and each 2D element defines a closed region; and determining a mask feature profile of the output mask pattern based on the 2D element representation. The media of claim 1, wherein the 2D element representation comprises a set of images indicating position information of the 2D elements in the 2D element representation. The medium of claim 2, wherein the position information includes information about grid positions assigned to the 2D elements and displacements of the 2D elements from the assigned grid positions. The media of claim 2, wherein the image set comprises a binary image indicating whether a 2D element exists at a specified grid location. The medium of claim 2, wherein the image set comprises: a first image indicating a displacement of a 2D element from a specified grid position in a first direction, and a second image indicating a displacement of the 2D element from the specified grid position in a second direction, wherein the method further comprises generating the 2D element representation based on the image set. The medium of claim 1, wherein each of the 2D elements is circular or elliptical, and wherein each of the 2D elements has the same size or different sizes. The medium of claim 1, wherein determining the mask feature contours of the output mask pattern from the 2D element representation comprises: associating the 2D elements based on an association criterion to form a cluster representing the mask feature; and generating a contour of the cluster based on the 2D elements, wherein the contour is an outer contour of the cluster corresponding to an outer edge of the mask feature, or an inner contour of the cluster corresponding to an inner edge of the mask feature. The medium of claim 7 , wherein the association criterion is related to a distance between two 2D elements. The method of claim 7, wherein the 2D elements are associated based on association information derived from a binary image represented by the 2D elements, wherein the binary image indicates whether a 2D element at a specified position is associated with another 2D element at a neighboring position. The medium of claim 7, wherein the method further comprises: generating sub-regions of the contour by applying a polygon offset operation to pairs of associated 2D elements; and computing the union of the sub-regions, wherein the contour is the union of the sub-regions. The medium of claim 1, wherein providing the input mask pattern comprises: obtaining a representation of the target pattern; generating an image from the target pattern, wherein the image represents the input mask pattern; and providing the image of the input mask pattern to the prediction model, and wherein the method further comprises optimizing the output mask pattern using an optical proximity correction procedure. The media of claim 1, wherein the method further comprises: Training the prediction model using training data to generate a 2D element representation, wherein the training data includes an input mask pattern set and a 2D element representation of an output mask pattern set corresponding to the input mask pattern set. The media of claim 12, wherein training the prediction model comprises: obtaining a first output mask pattern of the output mask pattern set corresponding to a first input mask pattern of the input mask pattern set; obtaining a first 2D element representation of the first output mask pattern; and executing the prediction model to generate a specified 2D element representation of the first output mask pattern based on the first input mask pattern and the first 2D element representation, and wherein obtaining the first 2D element representation comprises: assigning a position of a set of 2D elements based on a shape of the first input mask pattern; associating the set of 2D elements based on an association criterion to form a cluster representing a specified mask feature of the first input mask pattern; and adjusting the set of 2D elements of the cluster to vary the specified mask feature, Wherein the adjustment is based on geometric properties of the first output mask pattern and based on rules specified for an optimal proximity correction (OPC) process, or wherein the adjustment is based on a simulation associated with the lithography process. The medium of claim 13, wherein the method further comprises: generating an image set indicating position information of the set of 2D elements in the first 2D element representation, wherein obtaining the first 2D element representation comprises: shrinking a specified mask feature contour by a specified dimension associated with a 2D element to generate a shrunk contour; and assigning positions of a set of 2D elements along the shrunk contour such that a contour generated from the set of 2D elements approximates the specified mask feature contour. The medium of claim 13, wherein the first 2D element representation of the first mask pattern is derived from a layer set image of the first output mask pattern.