Identify mask rule check violations and mask design

Abstract

Described herein are methods and systems for determining mask rule check violations (MRC) associated with mask features using a detector having geometric properties corresponding to MRC. The detector (e.g., elliptical) is configured to include a curved portion for detecting curvature violations, an enclosed area (e.g., a fully enclosed area or a partially enclosed area with an opening), a prescribed orientation axis configured to guide relative positioning of the detector with a mask feature, and a length for detecting critical dimension violations. The orientation axis of the detector is aligned with a normal axis at a location on the mask feature. Based on the orientation axis being aligned with the normal axis of the mask feature, an MRC violation corresponding to an area of ​​the mask feature that intersects the enclosed area is determined.

Description

Technical Field

[0001] The description herein relates to a method for determining mask rule checking violations and mask designs for photolithography masks to be used in semiconductor manufacturing. Background Art

[0002] Lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (e.g., a mask) can contain or provide a circuit pattern ("design layout") corresponding to a single layer of the IC. This circuit pattern can be transferred to a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the circuit pattern on the patterning device. Typically, a single substrate contains multiple adjacent target portions, to which the circuit pattern is transferred sequentially, one at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the circuit pattern on the entire patterning device is transferred to a single target portion at a time; such apparatus is generally referred to as a stepper. In an alternative apparatus, generally referred to as a stepper-and-scan apparatus, the projection beam is scanned across the patterning device along a given reference direction (the "scanning" direction) while the substrate is synchronously moved parallel or antiparallel to this reference direction. Different portions of the circuit pattern on the patterning device are progressively transferred to a single target portion. Typically, since the lithographic projection apparatus will have a magnification factor M (typically <1), the speed F at which the substrate is moved will be a factor M times that of the projection beam scanning patterning device. Further information on the lithographic apparatus described herein can be gleaned, for example, from US 6,046,792, which is incorporated herein by reference.

[0003] Before the circuit pattern is transferred from the patterning device to the substrate, the substrate may undergo various procedures such as coating, resist coating, and soft baking. After exposure, the substrate may undergo additional procedures such as a post-exposure bake (PEB), development, a hard bake, and measurement / inspection of the transferred circuit pattern. This array of procedures serves as the basis for fabricating individual layers of a device (e.g., an IC). The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all aimed at completing a single layer of the device. If multiple layers are required in the device, the entire procedure, or a variation thereof, is repeated for each layer. Ultimately, a device will be present in each target portion of the substrate. These devices are then separated from each other by techniques such as dicing or sawing, allowing the individual devices to be mounted on a carrier and connected to pins, etc.

[0004] As mentioned, photolithography is a central step in the fabrication of integrated circuits, where patterns formed on a substrate define the functional elements of the IC, such as microprocessors, memory chips, etc. Similar photolithography techniques are also used in the formation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0005] As semiconductor manufacturing processes continue to advance, the size of functional elements has been continuously reduced, while the number of functional elements (such as transistors) per device has steadily increased for decades, following a trend generally referred to as "Moore's Law." Under current technology, the layers of a device are manufactured using a lithography projection device that projects a design layout onto a substrate using radiation from a deep ultraviolet radiation source, thereby creating individual functional elements with dimensions well below 100 nm (i.e., less than half the wavelength of the radiation from the radiation source (e.g., a 193 nm radiation source)).

[0006] The process of printing features smaller than the classical resolution limit of a lithographic projection apparatus is generally referred to as low-k1 lithography, according to the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation employed (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension," typically the minimum printed feature size, and k1 is the empirical resolution factor. Generally, the smaller k1, the more difficult it is to reproduce a pattern on the substrate with a shape and size similar to that planned by the circuit designer to achieve specific electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus and / or the design layout. These include, for example, but are not limited to, optimization of the NA and optical coherence settings, customized illumination schemes, the use of phase-shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other approaches generally defined as "resolution enhancement techniques" (RET). The term "projection optics," as used herein, should be broadly interpreted to encompass various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and catadioptric optics. The term "projection optics" may also include components that operate according to any of these design types to collectively or individually direct, shape, or control a projection beam of radiation. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located in the optical path of the lithographic projection apparatus. 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 a source and a patterning device. Summary of the Invention

[0007] Disclosed herein is a method for improving mask rule checking (MRC) associated with mask designs, for example, having curved mask features. Existing MRC techniques involve violation detection based on cut lines. Existing techniques lack tuning capabilities and cannot adapt to different curvature shapes. Moreover, these techniques rely on heuristic rules applied at the curvature regions of the mask features. As a result, existing techniques result in several false violation detections. The present disclosure provides a detector configured to determine the MRC of curved features. The detector herein provides flexibility and high tuning capabilities to adapt to the MRC of mask features of different curved shapes. Using the detector, MRC violation detection is improved, false violations are reduced, and thus MRC violation determination is accelerated. Moreover, the mask design can be improved based on information related to the MRC violations detected by the detector herein. According to the present disclosure, this in turn improves the semiconductor manufacturing process that uses masks designed based on information related to MRC violations.

[0008] According to an embodiment of the present disclosure, a method for determining mask rule checking violations associated with a mask feature is described. The method includes obtaining a detector having geometric properties corresponding to mask rule checking (MRC). The detector is configured to include a curved portion for detecting curvature violations, an enclosed area (e.g., a fully enclosed area or a partially enclosed area with an opening), a prescribed orientation axis configured to guide the relative positioning of the detector with the mask feature, and a length along the orientation axis for detecting critical dimension violations. The orientation axis of the detector is aligned with a normal axis at a location on the mask feature so that the length of the detector extends along the normal axis of the mask feature. Further, the method identifies MRC violations corresponding to an area of ​​the mask feature that intersects the enclosed area based on the alignment of the orientation axis of the detector with the normal axis of the mask feature. The alignment and geometry of the detector enable the detector to intersect an area of ​​the mask feature to identify curvature violations and / or critical dimension violations.

[0009] In an embodiment, the detector is non-circular and has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius. For example, the non-circular detector has an elliptical shape, wherein the radius of curvature is configured to detect a curvature violation, and wherein the length along the orientation axis is configured to detect a critical dimension violation.

[0010] In an embodiment, the curved portion of the detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature defined by the mask manufacturability check.

[0011] In an embodiment, the identifying step involves determining an MRC violation comprising a curvature violation and a critical dimension violation based on an intersection of a detector with a mask feature at a single location. In an embodiment, the MRC violation associated with the curvature violation and the spatial violation is determined based on an intersection between at least two mask features at a single location.

[0012] In an embodiment, the method further involves performing mask design to determine shapes and sizes of mask features of the mask design by employing a mask design process (eg, OPC, mask optimization, or SMO) to include MRC violation detection using one or more detectors herein.

[0013] According to an embodiment of the present disclosure, a method for determining a mask design for manufacturing a mask to be used in semiconductor manufacturing is described. The method involves simulating a mask optimization process (e.g., SMO, OPC, etc.) using a design layout to determine mask features of the mask design. The design layout corresponds to the features to be printed on the semiconductor chip. Using a detector, a portion of the mask feature that violates a mask rule check (MRC) is determined. The detector (e.g., elliptical) is configured to have a curved portion, a closed area (e.g., fully or partially closed), and an orientation axis at a point perpendicular to the curved portion, the orientation axis being used to guide the orientation of the detector relative to the mask feature to detect MRC violations. In response to the portion of the mask feature that violates the MRC, the corresponding portion of the mask feature is modified to satisfy the MRC.

[0014] In an embodiment, determining an MRC-violating portion of a mask feature involves obtaining a detector having geometric properties corresponding to MRC; aligning an orientation axis with a normal axis of a location on the mask feature; and identifying an MRC violation corresponding to a region of the mask feature that intersects the enclosed region based on the orientation axis of the detector and the normal axis of the mask feature.

[0015] In an embodiment, the detector is a single detector configured to determine an MRC violation comprising a curvature violation and a width violation associated with a mask feature. In an embodiment, the detector is a single detector configured to determine an MRC violation associated with a curvature violation and a spatial violation between at least two mask features.

[0016] According to an embodiment, a non-transitory computer-readable medium is provided for determining mask rule check violations associated with mask features, the medium including instructions stored therein that, when executed by one or more processors, perform operations including the method steps herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a block diagram of various subsystems of a lithography system according to an embodiment of the present disclosure.

[0018] Figure 2 According to the embodiment of the present disclosure, Figure 1 Block diagram of the simulation model of the subsystem in .

[0019] Figure 3A Illustrated is a mask rule check (MRC) performed on Manhattan features according to an embodiment of the present disclosure.

[0020] Figure 3B FIG. 4 illustrates MRC performed on a curve feature according to an embodiment of the present disclosure.

[0021] Figure 4 and 5 Mask features having rounded tips and narrower tips, respectively, are illustrated according to embodiments of the present disclosure.

[0022] Figure 6 is a flow chart of a method for determining MRC-violating mask features according to an embodiment of the present disclosure.

[0023] Figures 7A to 7F Different types of detectors are illustrated, each having a specific shape and a specific orientation axis, according to embodiments of the present disclosure.

[0024] Figure 7G The geometry of a detector according to an embodiment of the present disclosure is illustrated, including a length configured to detect dimensional violations.

[0025] Figure 7H A detector having a partially enclosed area with an opening is illustrated according to an embodiment of the present disclosure.

[0026] Figure 8A Identifying MRC violations associated with mask features by employing a circle detector according to an embodiment of the present disclosure is illustrated.

[0027] Figure 8B Identifying MRC violations associated with mask features by employing a non-circular detector according to an embodiment of the present disclosure is illustrated.

[0028] Figure 8C Illustrated is the identification of MRC violations associated with two mask features by employing a non-circular detector according to an embodiment of the present disclosure.

[0029] Figure 8D Illustrated is the identification of curvature and size violations at a single location of a mask feature using a single detector according to an embodiment of the present disclosure.

[0030] Figure 9 According to an embodiment of the present disclosure, Figures 7B to 7F Flowchart of a method for a) detector to determine a mask design.

[0031] Figure 10 is a flow chart illustrating aspects of an example method of joint optimization / co-optimization according to an embodiment of the present disclosure.

[0032] Figure 11 An embodiment of a further optimization method according to an embodiment of the present disclosure is shown.

[0033] Figure 12A 、 Figure 12B and Figure 13 An example flow chart of various optimization processes according to an embodiment of the present disclosure is shown.

[0034] Figure 14 is a block diagram of an example computer system according to an embodiment of the present disclosure.

[0035] Figure 15 is a schematic diagram of a lithographic projection apparatus according to an embodiment of the present disclosure.

[0036] Figure 16 is a schematic diagram of another lithographic projection apparatus according to an embodiment of the present disclosure.

[0037] Figure 17 According to an embodiment of the present disclosure Figure 16 A more detailed view of the devices in .

[0038] Figure 18 According to an embodiment of the present disclosure Figure 16 and Figure 17 A more detailed view of the source collector module of the device SO. DETAILED DESCRIPTION

[0039] Although specific reference may be made herein to the manufacture of ICs, it should be clearly 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 domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art will appreciate that in the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" herein should be considered interchangeable with the more general terms "mask," "substrate," and "target portion," respectively.

[0040] 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, 248, 193, 157 or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5 to 100 nm).

[0041] As used herein, the terms "optimizing" and "optimization" refer to or imply adjusting a lithographic projection apparatus, a lithographic process, or the like so that the results and / or process of the lithography have more desirable characteristics, such as greater accuracy in projecting the design layout onto the substrate, a larger process window, or the like. Accordingly, as used herein, the terms "optimizing" and "optimization" refer to or imply a process of identifying one or more values ​​of one or more parameters that provide an improvement in at least one relevant metric, such as a local optimum, compared to an initial set of one or more values ​​for those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In an embodiment, the optimization step may be applied iteratively to provide further improvements to one or more metrics.

[0042] Furthermore, the lithographic projection apparatus may be of a type having two or more tables (e.g., two or more substrate tables, a substrate table and a measurement table, two or more patterning device tables, etc.). In such a "multi-stage" apparatus, a plurality of the plurality of tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. A dual-stage lithographic projection apparatus is described, for example, in US Pat. No. 5,969,441, which is incorporated herein by reference.

[0043] The patterning device referenced above includes or can form one or more design layouts. Design layouts can be generated using a CAD (Computer-Aided Design) program, a process often referred to as EDA (Electronic Design Automation). Most CAD programs adhere to a predetermined set of design rules to create a functional design layout / patterning device. These rules are set by process and design constraints. For example, design rules define spatial tolerances between circuit devices (such as gates, capacitors, etc.) or interconnects to ensure that the circuit devices or lines do not interact with each other in undesirable ways. One or more design rule constraints may be referred to as "critical dimensions" (CDs). A critical dimension of a circuit can be defined as the minimum width of a line or hole, or the minimum space between two lines or holes. Therefore, the CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit fabrication is to faithfully reproduce the original circuit design (via the patterning device) on the substrate.

[0044] The terms "mask" or "patterning device" as used herein should be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incoming radiation beam, corresponding to the pattern to be created 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. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such a device is that, for example, addressed areas of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as undiffracted radiation. Using appropriate filters, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic components. For example, more information about such mirror arrays can be gleaned from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference. - Programmable LCD Arrays. An example of such a configuration is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0045] As a brief introduction, Figure 1 An exemplary lithographic projection apparatus 10A is illustrated. The main components are a radiation source 12A, which can be a deep ultraviolet excimer laser source or other types of sources, including: an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself does not require a radiation source); illumination optics, which define the partial coherence (denoted as σ) and can include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a patterning device 14A; and transmission optics 16Ac that projects an image of a patterning device pattern 18A onto a substrate plane 22A. An adjustable filter or aperture 20A at a pupil plane of the projection optics can limit the range of beam angles that impinge on the substrate plane 22A, with the maximum possible angle defining the numerical aperture NA of the projection optics = n sin(Θ max ), where n is the refractive index of the medium between the last element of the projection optics and the substrate, and Θ maxThe maximum angle beam that can exit the projection optics and still impinge on substrate plane 22A is the maximum angle beam. The radiation from radiation source 12A may not necessarily be of a single wavelength. Instead, the radiation may be within a range of different wavelengths. The range of different wavelengths can be characterized by a quantity referred to as "imaging bandwidth," "source bandwidth," or simply "bandwidth," which are used interchangeably herein. A small bandwidth can reduce chromatic aberration and associated focus errors in downstream components, including optics in the source (e.g., optics 14A, 16Aa, and 16Ab), the patterning device, and the projection optics. However, this does not necessarily lead to a rule that bandwidth should never be increased.

[0046] During system optimization, the system's figure of merit can be expressed as a cost function. The optimization process boils down to finding a set of system parameters (design variables) that optimizes (e.g., minimizes or maximizes) the cost function. Depending on the optimization objective, the cost function can have any suitable form. For example, the cost function can be the weighted root mean square (RMS) of the deviations of certain system characteristics (evaluation points) from their expected values ​​(e.g., ideal values); the cost function can also be the maximum of these deviations (i.e., the worst-case deviation). The term "evaluation point" herein should be interpreted broadly to include any characteristic of the system. Due to practical implementation requirements, the system's design variables may be constrained to a limited range and / or interdependent. In the case of a lithographic projection apparatus, constraints are typically associated with the physical properties and characteristics of the hardware, such as the tunable range and / or patterning device manufacturability design rules, and evaluation points can include physical points on the resist image on the substrate as well as non-physical features (such as dose and focus).

[0047] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device, and projection optics direct and shape the illumination via the patterning device onto a substrate. The term "projection optics" is broadly defined herein to include any optical component that can modify the wavefront of a radiation beam. For example, projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) is the radiation intensity distribution at the substrate level. A resist layer on the substrate is exposed, 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. A resist model can be used to calculate a resist image from an aerial image; an example of this can be found in U.S. Patent Application Publication No. US 2009-0157360, the disclosure of which is incorporated herein by reference in its entirety. The resist model is solely concerned with the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a lithographic projection apparatus (e.g., properties of the source, patterning device, and projection optics) specify an aerial image. Since the patterning device used in a 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.

[0048] An exemplary flow chart for simulating lithography in a lithographic projection apparatus is provided in Figure 2 . Source model 31 represents the optical characteristics of the source (including radiation intensity distribution, bandwidth, and / or phase distribution). Projection optics model 32 represents the optical characteristics of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). Design layout model 35 represents the optical characteristics of the design layout (including changes in the radiation intensity distribution and / or phase distribution caused by a given design layout 33), which is a representation of the arrangement of features on or formed by the patterning device. Aerial image 36 can be simulated using design layout model 35, projection optics model 32, and design layout model 35. Resist image 38 can be simulated from aerial image 36 using resist model 37. Simulation of lithography can, for example, predict the profile and CD in the resist image.

[0049] More specifically, it is noted that the source model 31 can represent the optical characteristics of the source, including but not limited to the numerical aperture setting, the illumination sigma (σ) setting, and any specific illumination shape (e.g., off-axis radiation sources such as toroidal, quadrupole, and dipole). The projection optics model 32 can represent the optical characteristics of the projection optics, including aberrations, distortion, one or more refractive indices, one or more physical dimensions, one or more physical dimensions, etc. The design layout model 35 can represent one or more physical characteristics of the physical pattern forming device, such as described in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. The goal of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and / or CD, which can then be compared to the intended design. The intended design is typically defined as a pre-OPC design layout, which can be provided in a standardized digital file format (such as GDSII or OASIS) or another file format.

[0050] From the design layout, one or more portions may be identified, which are referred to as "clips." In an embodiment, a collection of clips is extracted that represent complex patterns in the design layout (typically on the order of 50 to 1000 clips, although any number of clips may be used). These patterns or clips represent small portions of the design (e.g., circuits, cells, or patterns), and more specifically, clips typically represent small portions that require special attention and / or verification. In other words, a clip may be a portion of the design layout, or may be similar or have similar behavior to a portion of the design layout, where one or more key features are identified through experience (including clips provided by customers), through trial and error, or by running full-chip simulations. A clip may contain one or more test patterns or gauge patterns.

[0051] The initial large set of clips can be provided a priori by the customer based on known key feature areas in the design layout that require specific image optimization. Alternatively, in another embodiment, the initial large set of clips can be extracted from the entire design layout using some automatic (such as machine vision) or manual algorithm that identifies one or more key feature areas.

[0052] In an embodiment, a design layout or a portion of a design layout is used to design a mask to be used in semiconductor manufacturing. Mask design includes determining mask features based on a mask optimization simulation and checking whether mask rule checks (MRC) are satisfied. In an embodiment, the mask design includes Manhattan-shaped mask features or curved mask features. The mask features need to satisfy mask rule checks associated with the mask manufacturing process. As mask design technology (such as optical proximity correction (OPC) technology) is migrating from Manhattan to curved shapes, current MRC engines may no longer consistently flag MRC violations and drive optimization. In an embodiment, MRC includes one or more constraints related to geometric properties associated with mask features that can be manufactured. For example, geometric properties include, but are not limited to, the minimum CD of a mask feature, the minimum curvature of a mask feature that can be manufactured, or the minimum space between two features that can be manufactured.

[0053] Figure 3A illustrates a typical MRC performed on Manhattan features, and Figure 3B The figure shows a typical MRC performed on a curved feature. For example, in current MRC engines, a cutting line is drawn across the feature shape and the distance between the points where it intersects the mask feature is measured for MRC. Figure 3A As shown, horizontal cutting line 301 and vertical cutting line 302 cut across the Manhattan-shaped mask feature. The distance between the points where cutting line 301 (or cutting line 302) intersects the mask feature is used to check whether the mask feature satisfies MRC. However, when cutting lines are used to determine MRC violations for curved mask features, several false violations may be detected. Figure 3B As shown, cutting lines 311, 312 and 313 can be used to determine the MRC violation of the mask feature. It can be seen that as the cutting line gets closer and closer to the tip of the feature, the MRC violation is likely to be detected because the tip has a relatively narrow width compared to other parts of the mask feature. For example, cutting line 313 marks the position of the mask feature as violating MRC. However, such a curved tip can be easily manufactured via mask manufacturing equipment. Therefore, the violation detected by cutting line 313 is wrong. Typically, a mask may have thousands or even millions of mask features where MRC can be performed. If a large number of MRC violations are mistakenly detected, the amount of computing resources and time, manpower and time, and even manufacturing time will be very high. Therefore, curved mask features require improved detectors to minimize or even eliminate such erroneous violation detections.

[0054] Figure 4 and 5Mask features 500 and 510 are shown with rounded tips and narrower tips, respectively. A detector that can be used with both rounded and narrower tips may be desirable to avoid false violation detections. In this example, the tips are used to illustrate the limitations of existing MRC techniques. In some embodiments, sharp, curved features may be encountered anywhere along the feature length and are not limited to the tips.

[0055] The MRC detector needs to be flexible enough to accommodate different mask manufacturing technologies, especially in curved feature shapes with sharper curves, such as tips. The tip shape of a mask feature may depend on the mask manufacturing technology and may vary depending on the use case (e.g., chip design) and machine setup. The present disclosure provides a detector that can be configured to perform MRC on curved masks with different curvature shapes and sizes. In some examples, the detector can be configured to detect MRC violations that are spatially correlated between two mask features (e.g., see Figure 8C The disclosed detector provides several advantages, including but not limited to significantly reducing the number of false MRC violations compared to existing cut-line based inspection, providing a user-defined detector that a user can define based on its own manufacturing constraints, and the detector can be used to improve mask design, or improve other aspects related to the semiconductor manufacturing process.

[0056] Figure 6 1 is a flow chart of an exemplary method for determining MRC-violating mask features according to an embodiment of the present disclosure. In an embodiment, MRC violations are determined based on a detector having a specific shape and an orientation axis for guiding the relative positioning of the detector and the mask feature. The detector slides along the edge of the mask feature. The detector has a closed or substantially closed shape, and an MRC violation is detected when a portion of the mask feature is within the closed shape.

[0057] Process P602 involves obtaining a detector 601 having geometric properties and a mask feature MF configured to facilitate MRC detection. In an embodiment, the detector 601 is configured to include a curved portion for detecting curvature violations, a closed area, an orientation axis configured to guide the relative positioning of the detector 601 and the mask feature MF, and a length along the orientation axis for detecting critical dimension violations or spatial violations. In an embodiment, multiple detectors with different shapes and sizes can be used for the mask feature or multiple mask features. In an embodiment, the mask feature MF has a curved shape. In an embodiment, MRC may include one or more geometric properties associated with the mask feature MF. The geometric properties include, but are not limited to, the minimum CD of the mask feature that can be manufactured, the minimum curvature of the mask feature that can be manufactured, or the minimum space between two features that can be manufactured.

[0058] In embodiments, obtaining detector 601 involves accessing a detector from a detector library. In embodiments, obtaining involves receiving a predefined detector defined based on the shape and size of mask feature MF and mask feature manufacturing constraints associated with the mask manufacturing process. For example, a user may define the curvature, length, width, area, or geometry of the detector. Furthermore, a user may define an orientation axis for detector 601, which may indicate, for example, the direction of a vertical point along a curved portion of detector 601.

[0059] In an embodiment, the detector 601 can be, for example, non-circular and can have an elliptical, key-shaped, or irregularly curved shape with different radii of curvature. For example, the detector 601 has a first curved portion and a second curved portion that is different from the first curved portion. The first curved portion has a first radius of curvature and the second curved portion has a second radius of curvature, wherein the first radius is different from the second radius. In an embodiment, the detector 601 can be drawn using a drawing tool that is configured to allow a user to define shapes with different radii of curvature and orientation axes. In an embodiment, the detector 601 can be represented as a polynomial equation, a pixel representation, a GDSII or OASIS compatible representation, or other digital file format.

[0060] In an embodiment, obtaining the detector 601 involves receiving the detector 601 shaped based on the curvature and feature size of the mask feature MF specified by mask manufacturability or other constraints. For example, the user can define the curved portion of the detector 601 to have a shape and size corresponding to the curvature of the tip portion of the mask feature MF and the minimum size of the mask feature MF that can be manufactured.

[0061] In an embodiment, obtaining the detector 601 involves receiving (e.g., via a user interface or a database) a single detector configured to determine MRC violations including a curvature violation and a width violation associated with the mask feature MF. In an embodiment, obtaining the detector 601 involves receiving (e.g., via a user interface or a database) a single detector configured to determine MRC violations associated with a curvature violation and a spatial violation between at least two mask features.

[0062] In an embodiment, obtaining the detector 601 comprises accessing the detector 601 from a detector library to determine the MRC violation of the mask feature MF. In an embodiment, the detector library comprises a plurality of detectors, each detector having a different shape and size than the other defined detectors.

[0063] Figures 7A to 7FDetectors D1, D2, D2', D3, D4, and D4' of different shapes and sizes are illustrated according to embodiments of the present disclosure. Each detector has a specific shape and a specific orientation axis, which may be defined based on mask feature size, limitations related to the curvature of the mask features, or other geometric properties related to the mask features. Figure 7A In FIG, the detector D1 has a circular shape and an orientation channel O1. In an embodiment, the orientation axis O1 may be defined from any other point on the circumference along a desired direction defined by a user.

[0064] exist Figure 7B In FIG, the detector D2 has an elliptical shape and an orientation axis O2. In another example, in Figure 7C , detector D2' also has an elliptical shape similar to D2, but the orientation axis O21 is different from the orientation axis O2. Therefore, detector D2' is different from detector D2. In other words, the MRC violation detected by D2 may be different from the MRC violation detected by D2'. In an embodiment, the curvature of the elliptical shape can be defined based on the curvature of the tip of the mask feature that can be manufactured. Detector D2 has a first curved portion and a first orientation axis O2 that can be drawn perpendicular to the points on the first curved portion. Detector D2' has a second curved portion and a second orientation axis O21 drawn perpendicular to the points on the second curved portion. It can be seen that the first curved portion is sharper than the second curved portion. In other words, the first curved portion has a smaller radius of curvature than the second curved portion.

[0065] exist Figures 7D to 7G , detectors D3, D4, and D4' have irregular shapes (multiple curved portions with different radii of curvature) and orientation axes (such as O3) defined perpendicular to the curved portions of the irregular shapes. Detector D4 has a similar irregular shape as detector D3, however a different orientation axis O4 may be defined at a different location than in detector D3. In one embodiment, detector D4' may have different orientation axes O4 and O41 defined at different locations. Each of the orientation axes O4 and O41 may also be perpendicular to a corresponding point on the curved portion of detector D4'. Thus, detectors of similar shapes may be used differently based on the orientation axis. For example, detector D3 with orientation axis O3 may be used to detect MRC violations of wide tips, and detector D4 with orientation axis O4 may be used to detect MRC violations of narrow tips.

[0066] exist Figure 7G, detector D3 may also be characterized by a length L. In embodiments, the length L may correspond to a critical dimension of a mask feature. In embodiments, the length L may be defined as the distance between the intersection of the orientation axis and the boundary or edge of detector D3 or the length of D3 along the orientation axis. For example, the orientation axis O3 may be drawn starting from point A1 and further extended to intersect the edge at point A2. Thus, the length of detector D3 may be adjusted by moving point A2 toward A1 to decrease the length L or away from A1 to increase the length L. Thus, in embodiments, a single detector D3 may be used to determine MRC violations at the curvature of a mask feature and CD violations at different locations along the length of the mask feature. Similarly, the dimensions (e.g., length or width) of detectors D1, D2, D2', D3, D4, and D4' may be defined.

[0067] The present disclosure is not limited to the shapes and sizes discussed herein. Furthermore, although the exemplary detectors (e.g. Figures 7A to 7G ) has a completely closed shape, but the present disclosure is not limited to such closed shapes. One of ordinary skill in the art can define open shape detectors. For example, small openings can be set in the detector shape away from the orientation axis, which will not interfere with the function of detecting spatial or curvature violations. For example, even with small openings, parts of the mask features may intersect with the detector, thereby detecting curvature, dimensional violations, or both. For example, Figure 7H Detector D5 is shown with an orientation axis O5 and a small opening OC1. Opening OC1 is away from orientation axis O5 and therefore does not affect the curvature violation detection capability of detector D5. Additionally, opening OC1 is not along the length of orientation axis O5 and therefore does not interfere with the size detection capability of detector D5.

[0068] Process P604 involves aligning the orientation axis with the normal axis at a location on the mask feature MF. The normal axis is a normal line drawn perpendicular to a curve at a location of interest on the mask feature MF. In an embodiment, aligning the orientation axis of the detector 601 with the normal axis of the mask feature MF involves determining the normal axis at the location of the mask feature MF; contacting an edge of the detector 601 with an edge of the feature at that location; and aligning or orienting the orientation axis of the detector 601 with the normal axis at the feature location. This alignment of the detector 610 and the mask feature MF enables MRC violations due to curvature as well as size to be detected. Thus, during MRC detection along the mask feature MF, the detector 610 can be oriented and reoriented several times depending on the geometry of the mask feature. An advantage of such orientation and reorientation is that it provides the flexibility to check multiple MRC constraints (e.g., curvature and size) simultaneously using a single detector. Example orientations and reorientations of the detector 610 are shown in FIG. Figure 8BFigure 2. Visual understanding of detector alignment and identifying MRC violations.

[0069] Although embodiments of the present disclosure are described in detail in which the orientation axis of the detector is aligned with the normal axis at each location on the mask feature, the present disclosure is not limited thereto. In some embodiments, during detection, the detector can be slid along the edge of the mask feature with its orientation axis maintaining a certain non-zero angle with the normal axis at each location on the mask feature. In this way, the length of the detector extends along a prescribed axis at the location on the mask feature, wherein the prescribed axis forms a certain non-zero angle with the normal axis of the mask feature location.

[0070] Process P606 involves identifying MRC violations 610 corresponding to regions of the mask feature MF that intersect the closed region based on alignment of the detector 601 with the mask feature MF. In an embodiment, identifying the MRC violations 610 includes determining the MRC violations by sliding the detector 610 along an edge of the mask feature MF while maintaining alignment of the orientation axis of the detector 610 with the normal axis of each position of the mask feature MF.

[0071] In an embodiment, identifying the MRC violation 610 involves (a) aligning an orientation axis of the detector 610 with a first normal axis at a first position of the mask feature MF; (b) identifying whether an area around the first position of the mask feature MF is within a closed region based on the alignment of the detector with the mask feature MF; (c) in response to the area of ​​the mask feature MF being within the closed region, marking the first position as an MRC position; and (d) in response to the area of ​​the mask feature MF not being within the closed region, sliding the detector to a second position of the mask feature MF and identifying the MRC violation 610 by, for example, performing steps (a) to (c) at the second position using the second normal axis at the second position of the mask feature MF.

[0072] Figure 8A The diagram illustrates the identification of MRC violations associated with a mask feature using a circular detector, according to an embodiment of the present disclosure. In the illustrated example, mask feature 800 has a curved shape, with its end portion (e.g., the tip) having smaller dimensions than the remainder of feature 800. It can be seen that along the length of mask feature 800, the dimensions (e.g., CD measured vertically at different locations) vary significantly. Consequently, mask feature 800 may experience one or more MRC violations. According to some embodiments, such MRC violations are determined using detectors having different shapes and sizes, which are defined based on the geometry of the mask feature.

[0073] exist Figure 8AIn the example, a circular detector D1 having a diameter corresponding to the expected CD value (e.g., MRC rule) for a mask feature can be defined. Detector D1 also has an orientation axis O1 (e.g., a dashed line within the circle). In embodiments, an MRC violation can be determined by sliding detector D1 within the mask feature along its length. In embodiments, an MRC violation is detected when a portion of the mask feature is within detector D1. In embodiments, the absence or presence of an MRC violation at a first location L1 is determined by aligning orientation axis O1 (dashed line) with the normal axis (not shown) of the mask feature at the first location L1. At the first location L1, detector D1 includes a portion of the mask feature within the enclosed region. Therefore, the first location L1 can be marked as an MRC violation. In embodiments, geometric properties associated with the mask feature can be extracted and further used to perform mask design (e.g., OPC). For example, when an MRC violation is detected, geometric properties such as curvature, length of the feature within the detector, etc. can be determined.

[0074] Similarly, at the second position L2, the orientation axis O1 of detector D1 can be aligned with the normal axis at the second position L2. It can be seen that detector D1 does not include any portion of the mask feature within the closed area. Therefore, the second position L2 can be marked as not having an MRC violation, or can be marked as satisfying MRC. Similarly, at the third position L3, an MRC violation can be detected, and the geometric properties of the mask feature at position L3 can be extracted similarly to those at position L1.

[0075] A circular detector may be limited to either size violation detection or curvature detection, but not both. In other words, multiple circular detectors may be needed to detect different types of MRC violations. On the other hand, a detector according to the present disclosure is configured to determine different types of violations using a single detector. Thus, a single pass along a mask feature can determine different types of violations. Examples of detectors in the present disclosure are shown in FIG. Figures 7B to 7G and an example detection process using an ellipse detector is shown in Figure 8B and 8C Middle picture.

[0076] Figure 8BThe diagram illustrates the identification of MRC violations associated with mask feature 800 by a non-circular detector according to an embodiment of the present disclosure. Detector D2 has at least two curved portions, the first curved portion being narrower than the second curved portion. The curved portions can be user-defined based on the limitations of the mask features that can be manufactured. For example, the first curved portion can correspond to the minimum curvature that can be manufactured. In this example, the non-circular detector D2 has an elliptical shape. The length of detector D2 (e.g., along the major axis of the ellipse) can correspond to the CD threshold to be marked as an MRC violation. In an embodiment, an orientation axis O2 can be defined as perpendicular to the first curved portion and used to guide the orientation of detector D2 relative to mask feature 800 at any given point of the mask feature.

[0077] In an embodiment, an MRC violation can be determined by sliding detector D2 within the mask feature along an edge of the mask feature and orienting detector D2 based on orientation axis O2. In an embodiment, an MRC violation is detected when a portion of the mask feature is within detector D2. In an embodiment, the absence or presence of an MRC violation at the first location L1 is determined by aligning orientation axis O2 (dashed line) with a normal axis (not shown) of the mask feature at the first location L1.

[0078] At the first position L1, detector D2 does not include any portion of the mask feature within the enclosed area, or does not intersect the edge of the mask feature, except for one or more tangent points around L1. Therefore, the first position L1 is not marked as an MRC violation. Similarly, at the second position L2, the orientation axis O2 of detector D2 can be aligned with the second normal axis at the second position L2. It can be seen that detector D1 does not include any portion of the mask feature within the enclosed area. Therefore, the second position L2 is not marked as an MRC violation, or can be marked as satisfying MRC. At the third position L3, detector D2 is oriented by aligning the orientation axis O2 with the third normal axis at position L3 because D2 intersects the mask edge in addition to the tangent points. When oriented, an MRC violation can be detected because a portion of the mask feature 800 is within detector D2. For example, at position L3, a CD violation is detected by detector D2 because the detector length along the orientation axis (which characterizes the CD violation) causes a portion of mask feature 800 to intersect detector D2 and to be within detector D2. In embodiments, at position L3, geometric properties of the mask feature at position L3 can be extracted similarly to those at position L1. In embodiments, geometric properties associated with the mask feature can be extracted and further used to perform mask design (e.g., OPC). For example, when an MRC violation is detected, geometric properties such as curvature, length of the feature within the detector, etc. can be determined.

[0079] Figure 8C The diagram illustrates the identification of MRC violations associated with two adjacent mask features 801 and 802 by a non-circular detector according to an embodiment of the present disclosure. In this example, the detector D2' is configured so that the length along the orientation axis is equal to the minimum spacing between the two features, and the curvature portion along which the orientation axis is drawn has a radius of curvature equal to the minimum curvature that can be manufactured. In order to detect MRC violations between the two features 801 and 802, the detector slides between the edges of the two features 801 and 802 along the edge of feature 801 and / or along the edge of feature 802. As shown, the detector D2' detects at least two spatial violations, as indicated by the cross symbols. The first spatial violation is detected when the detector D2' is slid along the edge of feature 801, and the second spatial violation is detected when the detector D2' is slid along the edge of feature 802. Therefore, the orientation and size of the detector D2' allow for detection of spatial violations of different curved portions of the mask features.

[0080] Figure 8D The diagram illustrates an example of a curvature violation and a dimension (e.g., CD) violation detected by a single detector at a single location L1 on a mask feature 805. At location L1, when detector D8 is oriented based on an orientation axis (dashed line) to align with the normal to the curvature of mask feature 805 at location L1, a portion of the curvature intersects detector D8. Furthermore, along the length CD of detector D8, another portion of mask feature 805 intersects detector D8. A first portion at location L1, located within the boundaries of detector D8, indicates a detected curvature violation, and a second portion, located at the other end of location L1, within the boundaries of detector D8, indicates a violation of dimension CD of mask feature 805 at location L1. Thus, detector D8 advantageously indicates both curvature and CD violations at a single location L1.

[0081] The above examples illustrate different types of MRC violations (e.g., CD violations, curvature violations) at different locations on a mask feature. Depending on the shape of the mask feature, a detector may detect only CD violations, only curvature violations, or both CD and curvature violations at a single location. Thus, a detector configured according to the present disclosure can advantageously detect multiple types of violations at a single location on a mask feature using a single detector, thereby enhancing MRC violation detection capabilities in a single pass over the mask feature. Consequently, modifications can be made to the mask feature shape to overcome such multiple violations in a single step, which in turn will reduce the number of iterations that may be required during the mask design process and speed up the mask design process.

[0082] In an embodiment, method 600 also involves performing mask design by employing the detectors discussed herein. In an embodiment, the mask design process may use the MRC violations detected by one or more detectors discussed herein to determine the shape and size of mask features of the mask design. As an example, the execution of the mask design includes (a) simulating a mask optimization process using a design layout to determine mask features of the mask design, the design layout corresponding to the features to be printed on the semiconductor chip; (b) determining, via the detector, portions of the mask features that violate MRC (e.g., as discussed with respect to processes P602 to 606); and (c) in response to violating the MRC, modifying the corresponding portion of the mask feature to satisfy the MRC; and repeating steps (a) to (c).

[0083] In an embodiment, the mask optimization process involves a mask-only optimization process, a source-mask co-optimization process, and / or an optical proximity correction process. Example mask design process including OPC with respect to Figures 10 to 13 Discussion. In an embodiment, the OPC process may be applied to include the MRC checks discussed herein.

[0084] In an embodiment, the OPC process can be customized to include MRC violation checking using the detectors discussed herein (e.g. Figures 7A to 7G and 8A to 8D), where the detectors may be defined based on mask manufacturing constraints. In an embodiment, one or more detectors may be used to identify mask features or portions of mask features within the detectors. In an embodiment, the portion of the mask feature located within the detector may be modified to satisfy the MRC. In an embodiment, the check may be performed after a specific number of iterations, at the end of the OPC process, at a fixed number of iterations, or at other points in the simulation. After modifying the mask features that violate the MRC, the OPC may be repeated to ensure that the cost function associated with the OPC remains valid or within desired limits. In this way, the mask features obtained after the OPC simulation process will not only satisfy the MRC, but will also satisfy the design specifications associated with the cost function. Example of a mask design process relative to Figure 9 Further detailed discussion.

[0085] Figure 9 According to an embodiment of the present disclosure, Figures 7A to 7G Flowchart of method 900 for determining a mask design using a detector (e.g., a mask design method). In an embodiment, the mask design method includes determining MRC violations, such as discussed above. Based on MRC violation information associated with portions of mask features, geometric properties of the mask features may be modified. Exemplary method 900 is discussed with respect to processes P902, P904, and P906.

[0086] Process P902 involves simulating a mask optimization process using a design layout to determine mask features of a mask design. The design layout includes features corresponding to target features to be printed on a semiconductor chip. In an embodiment, the mask optimization process involves executing one or more process models of a patterning process and performing a mask design to determine the curve shape of the mask features. The process model can be a rigorous, empirical, or semi-empirical physical model or a machine learning model. In an embodiment, the mask design involves free-form mask design, a level set method, or other methods related to continuous transmission masks (CTMs), etc. However, although such curves can generate ideal target features to be printed on a semiconductor chip, MRC violations associated with the mask features need to be performed to ensure the manufacturability of the mask to be used in the patterning process.

[0087] Process P904 involves determining an MRC violation by the detector 901. In an embodiment, the determination of an MRC violation involves determining a portion of a mask feature that violates a mask rule check (MRC). As discussed herein, an example detector has a curved portion, a closed region, and an orientation axis perpendicular to a point on the curved portion (e.g., as shown relative to FIG. 1 ). Figures 7A to 7G In embodiments, the orientation axis extends inside or outside the enclosed area of ​​the detector 901.

[0088] In an embodiment, the MRC includes one or more geometric properties associated with the mask feature. For example, the geometric property includes at least one of the following: the minimum CD of the mask feature that can be manufactured, the minimum curvature of the mask feature that can be manufactured, or the minimum space between two features that can be manufactured.

[0089] In an embodiment, determining the portion of the mask feature that violates MRC involves obtaining a detector 901 having geometric properties corresponding to MRC; aligning an orientation axis with a normal axis of a location on the mask feature; and identifying, based on the aligned detector and mask feature, an MRC violation corresponding to a region of the mask feature that intersects the closed region.

[0090] In an embodiment, detector 901 is non-circular. A non-circular detector can be characterized by a shape having multiple radii of curvature. For example, the non-circular detector includes a first curved portion having a first radius of curvature and a second curved portion having a second radius of curvature. The first radius is different from the second radius. In an embodiment, detector 901 is shaped based on the curvature and feature size of a mask feature that can be manufactured. As an example, the curved portion of detector 901 has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature that can be manufactured.

[0091] In an embodiment, obtaining a detector 901 involves receiving (e.g., via a user interface or a database) a single detector configured to determine MRC violations including curvature violations and width violations associated with mask features. In an embodiment, obtaining a detector 901 involves receiving (e.g., via a user interface or a database) a single detector configured to determine MRC violations associated with curvature violations and spatial violations between at least two mask features.

[0092] In an embodiment, aligning the orientation axis of the detector 901 with the normal axis of a mask feature involves determining the normal axis at a location of the mask feature; contacting an edge of the detector 901 with an edge of the feature at that location; and orienting the orientation axis of the detector 901 along the normal axis at the feature location.

[0093] In an embodiment, identifying MRC violations involves determining the MRC violations by sliding detector 901 along the edge of the mask feature while maintaining alignment of the orientation axis of detector 910 with the normal axis of each location of the mask feature.

[0094] In an embodiment, identifying an MRC violation involves (a) aligning an orientation axis of detector 910 with a first normal axis at a first position of a mask feature; (b) identifying whether an area around the first position of the mask feature is within an enclosed region based on the aligned detector and mask feature; (c) in response to the area of ​​the mask feature being within the enclosed region, marking the first position as an MRC position; and (d) in response to the area of ​​the mask feature not being within the enclosed region, sliding detector 901 to a second position of the mask feature and identifying an MRC violation by, for example, performing steps (a) through (c) at the second position using a second normal axis at the second position of the mask feature. Examples of alignment, orientation, and identification steps for MRC violations are provided in Figures 8A to 8B Picture.

[0095] Process P906 involves, in response to a portion violating an MRC, modifying a corresponding portion of the mask feature to satisfy the MRC. In an embodiment, modifying the mask feature may involve increasing or decreasing the size and / or curvature of a portion of the mask feature using detector 901 to satisfy the MRC. In an embodiment, modifying the mask feature is an iterative process. Each iteration may involve executing one or more process models associated with a patterning process using the modified mask feature to generate a target feature to be printed on a semiconductor chip; determining whether the target feature satisfies a design specification associated with the design layout; and, in response to the design specification not being satisfied, modifying the mask feature to satisfy the design specification.

[0096] An example of a mask optimization process including an OPC process relative to Figures 10 to 13Detailed discussion further. These mask optimization processes can be modified as discussed with respect to method 900 to implement mask design. In an embodiment, the mask optimization process involves calculating a cost function as a function of parameters associated with the lithography process and the mask. For example, mask features can be represented as design variables, as discussed herein. These design variables will be affected by changes based on MRC violations detected by the detector.

[0097] According to the present disclosure, combinations and sub-combinations of the disclosed elements constitute separate embodiments. For example, a first combination includes obtaining a detector and determining MRC violations associated with mask features. A sub-combination may include a detector based on a specific closed shape and size of the mask feature, wherein an MRC violation occurs when a portion of the mask feature is inside the detector. In another sub-combination, the detector may be circular or non-circular. In another example, the combination includes determining a mask design based on MRC violations identified by the detector. A detector having a non-circular shape detects width, space, and / or curvature violations.

[0098] As an example, in the photolithography process, the cost function can be expressed as

[0099] (Equation 1)

[0100] in are N design variables or their values. Can be a design variable Functions such as the feature The difference between the actual and expected values ​​at the evaluation points for a set of values ​​of the design variable. is with An associated weight constant. An evaluation point or pattern that is more critical than other evaluation points or patterns can be assigned a higher Values. Patterns and / or evaluation points with more occurrences can also be assigned higher Examples of evaluation points may be any physical point or pattern on the substrate, any point on the virtual design layout or a resist image or an aerial image or a combination thereof. It can be a function of the radiation source, a function of the radiation source, or a function of a variable that affects the radiation source. is not limited to the form in Equation 1. It may be in any other suitable form.

[0101] The cost function may represent any one or more suitable characteristics of the lithographic projection apparatus, the lithographic process, or the substrate, such as focus, CD, image offset, image distortion, image rotation, random variation, throughput, local CD variation, process window, or a combination thereof. In one embodiment, the design variables In one embodiment, the design variables The cost function may include a function representing one or more features of the resist image. For example, the cost function may include a function representing one or more features of the resist image. can simply be the distance between a point in the resist image and the expected location of that point (i.e., the edge placement error ). Design variables may include any adjustable parameters such as the source, patterning device, adjustable parameters of the projection optics (e.g., intensity and shape), dose, focus, etc.

[0102] The lithographic apparatus may include components generally referred to as "wavefront manipulators," which may be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the radiation beam. In embodiments, the projection apparatus may adjust the wavefront and intensity distribution at any location along the optical path of the lithographic projection apparatus, such as before the patterning device, near the pupil plane, near the image plane, and / or near the focal plane. The wavefront manipulator may be used to correct or compensate for certain distortions of the wavefront and intensity distribution and / or phase shift caused by, for example, temperature changes in the source, patterning device, lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, and the like. Adjusting the wavefront and intensity distribution and / or phase shift may change the value of the evaluation point and the cost function. Such changes may be simulated from a model or actually measured.

[0103] Design variables may have constraints, which can be expressed as ,in is a set of possible values ​​for the design variables. One possible constraint on the design variables may be imposed by the desired throughput of the lithographic projection apparatus. Without such a constraint imposed by the desired throughput, the optimization may produce an unrealistic set of values ​​for the design variables. For example, if dose is the design variable, then without such a constraint, the optimization may produce dose values ​​that make the throughput economically impossible. However, the usefulness of a constraint should not be interpreted as a necessity. For example, throughput may be affected by pupil fill rate. For some illumination designs, a low pupil fill rate may discard radiation, resulting in lower throughput. Throughput may also be affected by the resist chemistry. Slower resists (e.g., resists that require higher radiation doses to be properly exposed) will result in lower production throughput. In an embodiment, the constraints on the design variables are such that the design variables cannot have values ​​that change any geometrical features of the patterning device—i.e., the pattern on the patterning device will remain unchanged during the optimization.

[0104] Therefore, the optimization process is to constrain Next, find a set of values ​​of one or more design variables that optimizes the cost function, for example to find:

[0105] (Equation 2)

[0106] According to an embodiment, the general method of optimization is Figure 10 . The method comprises a step S302 of defining a multivariate cost function for a plurality of design variables. The design variables may comprise any suitable combination of design variables selected from one or more characteristics of the illumination (300A) (e.g., pupil fill rate, i.e., the percentage of radiation of the source that passes through the pupil or aperture), one or more characteristics of the projection optics (300B), and / or one or more characteristics of the design layout (300C). For example, the design variables may comprise design variables representing one or more characteristics of the illumination (300A) (e.g., being or including bandwidth) and the design layout (300C) (e.g., a global bias), but not one or more characteristics of the projection optics (300B), which results in an illumination patterning device (e.g., mask) optimization ("source-mask optimization" or SMO). Alternatively, the design variables may comprise design variables representing one or more characteristics of the illumination (300A) (optionally polarized), the projection optics (300B), and the design layout (300C), which results in an illumination patterning device (e.g., mask)-projection system (e.g., lens) optimization ("source-mask-lens optimization" or SMLO). Alternatively, the design variables may include design variables representing one or more characteristics of the illumination (300A) (e.g., being or including bandwidth), one or more non-geometric characteristics of the patterning device, or one or more characteristics of the projection optics (300B), but not any geometric characteristics of the patterning device. In step S304, the design variables are adjusted simultaneously to move the cost function toward convergence. In embodiments, not all design variables may be adjusted simultaneously. Each design variable may also be adjusted individually. In step S306, it is determined whether a predefined termination condition is met. The predefined termination condition may include various possibilities, such as one or more selected from the following: the cost function is minimized or maximized according to the requirements of the numerical technique used, the value of the cost function is equal to or exceeds a threshold, the value of the cost function is within a preset error limit, and / or a preset number of iterations is reached. If the conditions in step S306 are met, the method ends. If one or more conditions in step S306 are not met, steps S304 and S306 are iteratively repeated until the desired result is achieved. Optimization does not necessarily result in a single set of values ​​for one or more design variables, as there may be physical limitations due to factors such as pupil fill factor, resist chemistry, throughput, etc. Optimization may provide multiple sets of values ​​for one or more design variables and associated performance characteristics (e.g., throughput), and allow a user of the lithographic apparatus to pick one or more sets.

[0107] Different subsets of design variables (e.g., one subset includes illumination characteristics, one subset includes patterning device characteristics, and one subset includes projection optics characteristics) can be optimized alternatively (referred to as alternative optimization) or simultaneously (referred to as simultaneous optimization). Thus, "simultaneously" or "jointly" optimizing two subsets of design variables means that the design variables of the two subsets are allowed to vary simultaneously. As used herein, "alternatively" optimizing two subsets of design variables means that the design variables of the first subset, but not the second subset, are allowed to vary in a first optimization, and then the design variables of the second subset, but not the first subset, are allowed to vary in a second optimization.

[0108] exist Figure 10 In the example above, the optimization of all design variables is performed simultaneously. This flow can be called a simultaneous flow or a co-optimization flow. Alternatively, the optimization of all design variables is performed as Figure 11 As shown in the figure. In this process, in each step, some design variables are fixed while other design variables are optimized to minimize the cost function; then in the next step, a different set of variables is fixed while other variables are optimized to minimize or maximize the cost function. These steps are performed alternately until convergence or some termination condition is met. Figure 11 As shown in the non-limiting example flow chart, a design layout is first obtained (step S402). Then, an illumination optimization step is performed in step S404, where one or more illumination design variables (e.g., bandwidth) are optimized (SO) to minimize or maximize a cost function, while all other design variables are fixed. Then, in the next step S406, projection optics optimization (MO) is performed, where the projection optics design variables are optimized to minimize or maximize a cost function, while all other design variables are fixed. These two steps are optionally performed until certain termination conditions are met in step S408. One or more of various termination conditions may be used, such as the cost function value becoming equal to a threshold, the cost function value exceeding a threshold, the cost function value falling within a preset error limit, a preset number of iterations being reached, etc. It is noted that the SO-LO alternative optimization is used as an example of an alternative process. As another example, a first illumination-patterning device co-optimization (SMO) or illumination-patterning device-projection optics co-optimization (SMLO) can be performed without allowing bandwidth changes, followed by a second SO or illumination-projection optics co-optimization (SLO) with bandwidth changes allowed. Finally, the output of the optimization result is obtained in step S410 and the process stops.

[0109] As previously discussed, the pattern selection algorithm can be integrated with simultaneous or alternative optimization. For example, when alternative optimization is employed, full-chip SO can be performed first, one or more 'hot spots' and / or 'warm spots' are identified, and then LO can be performed. In light of the present disclosure, numerous permutations and combinations of sub-optimizations are possible to achieve the desired optimization results.

[0110] Figure 12A An exemplary optimization method is shown, in which a cost function is minimized or maximized. In step S502, initial values ​​for one or more design variables are obtained, including one or more associated tuning ranges, if any. In step S504, a multivariate cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting point values ​​of the one or more design variables for the first iteration step (i=0). In step S508, standard multivariate optimization techniques are applied to the cost function. Note that the optimization problem can apply constraints, such as one or more tuning ranges, during the optimization process in S508 or at a later stage in the optimization process. Step S520 indicates that each iteration is performed for one or more given test patterns (also called "gauges") at identified evaluation points that have been selected to optimize the lithographic process. In step S510, the lithographic response is predicted. In step S512, the results of step S510 are compared with the expected or ideal lithographic response values ​​obtained in step S522. If the termination condition is met in step S514, that is, the optimization generates a lithographic response value that is sufficiently close to the desired value, then the final value of the design variable is output in step S518. The output step may also include outputting one or more other functions using the final value of the design variable, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized illumination map, and / or an optimized design layout. If the termination condition is not met, then in step S516, the value of one or more design variables is updated with the result of the i-th iteration, and the process returns to step S506. Figure 12A The process is explained in detail below.

[0111] In the exemplary optimization process, the design variables No relationship is assumed or approximated between and except that Smooth enough (e.g. first-order derivative , (n=1, 2, ...N) exists), which is usually effective in lithography projection equipment. Algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, gradient descent algorithm, simulated annealing algorithm, interior point algorithm and genetic algorithm can be applied to find .

[0112] Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newton algorithm is an iterative method suitable for general nonlinear multivariable optimization problems. Value In the i-th iteration of Nearby Linearize, then calculate Nearby values , which gives The minimum value of the design variable Take the value in the (i+1)th iteration The iteration continues until convergence (i.e., ) is not reduced further) or the preset number of iterations is reached.

[0113] Specifically, in the i-th iteration, nearby, (Equation 3)

[0114] Under the approximation of Equation 3, the cost function becomes:

[0115] (Equation 4)

[0116] This is the design variable A quadratic function of . Except for the design variables Except for this, every term is a constant.

[0117] If the design variable Without any constraints, It can be derived by solving N linear equations ,in .

[0118] If the design variable Be affected by The J inequality form (for example Tuning range) ; and for K equations (e.g., interdependencies between design variables) The optimization process becomes a classic quadratic programming problem, where is a constant. Additional constraints can be imposed for each iteration. For example, the "damping factor" can be introduced to limit and The difference between , so the approximation of Equation 3 holds. This constraint can be expressed as . It can be derived using, for example, the method described in Numerical Optimization (2nd edition) by Jorge Nocedal and Stephen J. Wright (Berlin New York: Vandenberg. Cambridge University Press).

[0119] Optimization is not minimization Instead of the RMS of , the magnitude of the maximum deviation (worst defect) between the evaluation points can be minimized to its expected value. In this approach, the cost function can alternatively be expressed as

[0120] (Equation 5)

[0121] in yes The maximum allowable value of . This cost function represents the worst defect among the evaluation points. Optimization using this cost function minimizes the magnitude of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0122] The cost function of Equation 5 can be approximated as:

[0123] (Equation 6)

[0124] Where q is an even positive integer, such as at least 4 or at least 10. Equation 6 mimics the behavior of Equation 5 while allowing the optimization to be performed analytically and accelerated using methods such as the deepest descent method, the conjugate gradient method, and the like.

[0125] Minimizing the worst defect size can also be done with Specifically, The same approximation as in Equation 3. The constraint on the worst defect size is then written as the inequality ,in and is specified Inserting into Equation 3, for p = 1, ... P, these constraints are transformed into,

[0126] (Equation 6')

[0127] as well as

[0128] (Equation 6'')

[0129] Since Equation 3 is usually only Nearby valid in case of desired constraints The inability to achieve this near-zero value is determined by any conflict between the inequalities, the constants and can be relaxed until the constraints are achievable. This optimization process minimizes , the worst defect size near i. Each step then gradually reduces the worst defect size, and each step is iteratively performed until some termination condition is met. This will lead to the optimal reduction of the worst defect size.

[0130] Another way to minimize the worst defect is to adjust the weights in each iteration For example, after the i-th iteration, if the r-th evaluation point is the worst defect, then can be increased in the (i+1)th iteration so that the reduction of the defect size at this evaluation point is given higher priority.

[0131] In addition, the cost functions in Equations 4 and 5 can be modified by introducing Lagrange multipliers to achieve a compromise between the optimization of the RMS defect size and the optimization of the worst defect size, i.e.,

[0132] (Equation 6')

[0133] Where λ is a preset constant that specifies the trade-off between optimizing the RMS of defect size and optimizing the worst defect size. Specifically, if λ=0, then this becomes Equation 4, and only the RMS of defect size is minimized; while if λ=1, then this becomes Equation 5, and only the worst defect size is minimized; if 0<λ<1, then both are taken into account in the optimization. This optimization can be solved using a variety of methods. For example, the weighting in each iteration can be adjusted, similar to what was previously described. Alternatively, similar to minimizing the worst defect size from inequalities, the inequalities in Equations 6' and 6'' can be viewed as constraints on the design variables during the solution of the quadratic programming problem. Then, the bounds on the worst defect size can be incrementally relaxed or the weights of the worst defect size can be incrementally increased, the cost function value for each achievable worst defect size is calculated, and the design variable value that minimizes the total cost function is selected as the starting point for the next step. By doing this iteratively, minimization of this new cost function can be achieved.

[0134] Optimizing the lithography projection equipment can expand the process window. A larger process window provides greater flexibility in process design and chip design. The process window can be defined by, for example, focus, dose, aberration, laser bandwidth (e.g., E95 or ( arrive ) and a set of intensity value-specific costs where the resist image is within specific limits of the design goals for the resist image. It is to be noted that all methods discussed here can also be extended to a generalized process window definition, which can be established by different or additional basis parameters in addition to exposure dose and defocus. These can include, but are not limited to, optical settings such as NA, σ, aberrations, polarization or optical constants of the resist layer. For example, as described earlier, if the process window (PW) also includes different patterning device pattern biases (mask biases), then the optimization includes minimization of the mask error enhancement factor (MEEF), which is defined as the ratio between the substrate edge placement error (EPE) and the induced patterning device pattern edge bias. The process windows defined on focus and dose values ​​are only used as examples in this disclosure.

[0135] A method according to an embodiment to maximize the process window using, for example, dose and focus as its parameters is described below. In a first step, from the known conditions in the process window Starting with f0 being the nominal focus and ε0 being the nominal dose, minimize One of the following cost functions nearby: (Equation 7)

[0136] or

[0137]

[0138] (Equation 7')

[0139] or

[0140]

[0141] (Equation 7")

[0142] If the nominal focus f0 and the nominal dose ε0 are allowed to shift, they can be compared with the design variables Joint optimization. In the next step, if A set of values ​​of can be found such that the cost function is within the preset limits, then Accepted as part of the process window.

[0143] If focus and dose are not allowed to shift, then the design variables The optimization is performed with the focus and dose fixed at the nominal focus f0 and nominal dose ε0. In an alternative embodiment, if the design variables A set of values ​​of can be found such that the cost function is within the preset limits, then Accepted as part of the process window.

[0144] The methods described earlier in this disclosure can be used to minimize the corresponding cost functions of Equations 7, 7', or 7". If the design variables represent one or more characteristics of the projection optics, such as Zernike coefficients, then minimizing the cost function of Equations 7, 7', or 7" results in maximizing the process window based on projection optics optimization (i.e., LO). If the design variables represent one or more characteristics of the illumination and patterning device in addition to characteristics of the projection optics, then minimizing the cost function of Equations 7, 7', or 7" results in maximizing the process window based on SMLO, such as Figure 10 If the design variables represent one or more characteristics of the source and the patterning device, then minimizing the cost function of Equation 7, 7' or 7" results in maximizing the SMO-based process window. The cost function of Equation 7, 7' or 7" may also include at least one , such as described herein, which is a function of bandwidth.

[0145] Figure 13 A specific example of how a simultaneous SMLO process can use gradient-based optimization (e.g., a quasi-Newton or Gauss-Newton algorithm) is shown. In step S702, starting values ​​for one or more design variables are identified. The tuning range for each variable can also be identified. In step S704, a cost function is defined using the one or more design variables. In step S706, the cost function is expanded around the starting values ​​for all evaluation points in the design layout. In step S708, a suitable optimization technique is applied to minimize or maximize the cost function. In optional step S710, a full-chip simulation is performed to cover all critical patterns in the full-chip design layout. The expected lithographic response metrics (such as CD, EPE, or EPE and PPE) are obtained in step S714 and compared to predicted values ​​of those quantities in step S712. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to those with respect to Figure 12A The corresponding steps S514, S516 and S518 are described. As mentioned before, the final output may be, for example, a wavefront aberration map in the pupil plane, optimized to produce the desired imaging performance. The final output may be, for example, an optimized illumination map and / or an optimized design layout.

[0146] Figure 12B An exemplary method for optimizing a cost function is shown, where the design variables Include design variables that may assume only discrete values.

[0147] The method begins by defining pixel groups for illumination and patterning device tiles for the patterning device (step S802). In general, pixel groups or patterning device tiles may also be referred to as subdivisions of a lithography process component. In one exemplary method, illumination is divided into 117 pixel groups, and 94 patterning device tiles are defined for the patterning device, substantially as described above, resulting in a total of 211 subdivisions.

[0148] In step S804, a lithography model is selected as the basis for a lithography simulation. The results generated by the lithography simulation are used to calculate one or more lithography metrics or responses. Specific lithography metrics are defined as performance indicators to be optimized (step S806). In step S808, initial (pre-optimization) conditions for the illumination and patterning device are set. The initial conditions include the initial state of the illuminated pixel group and the patterning device tiles of the patterning device, allowing for reference to an initial illumination shape and an initial patterning device pattern. The initial conditions may also include patterning device pattern bias (sometimes referred to as mask bias), NA, and / or focus ramp range. Although steps S802, S804, S806, and S808 are depicted as sequential steps, it will be appreciated that in other embodiments, these steps may be performed in other sequences.

[0149] In step S810, the pixel groups and patterning device tiles are arranged. The pixel groups and patterning device tiles can be staggered in the arrangement. Various arrangements can be used, including sequentially (e.g., from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), randomly, based on the physical location of the pixel groups and patterning device tiles (e.g., arranging pixel groups closer to the center of the shot higher), and / or based on how changing the pixel groups or patterning device tiles affects performance metrics.

[0150] Once the pixel groups and patterning device tiles are aligned, the illumination and patterning device are adjusted to improve the performance metric (step S812). In step S812, each of the pixel groups and patterning device tiles is analyzed in the order in which they were aligned to determine whether a change to the pixel group or patterning device tile will result in an improved performance metric. If it is determined that the performance metric will be improved, the pixel group or patterning device tile is modified accordingly, and the resulting improved performance metric and modified illumination shape or modified patterning device pattern form a baseline for comparison for subsequent analysis of lower-aligned pixel groups and patterning device tiles. In other words, the changes that improved the performance metric are retained. As changes to the states of the pixel groups and patterning device tiles are made and retained, the initial illumination shape and initial patterning device pattern are modified accordingly, resulting in a modified illumination shape and modified patterning device pattern resulting from the optimization process in step S812.

[0151] In other approaches, patterning device polygon shape adjustment and pairwise polling of pixel groups and / or patterning device tiles are also performed within the optimization process of S812.

[0152] In an embodiment, the staggered simultaneous optimization procedure may include changing the set of pixels being illuminated, and if an improvement in the performance metric is found, the dose or intensity is then gradually increased and / or decreased to look for further improvement. In yet another embodiment, the gradual increase and / or decrease in dose or intensity may be replaced by a bias change in the patterning device pattern to look for further improvements in the simultaneous optimization procedure.

[0153] In step S814, a determination is made as to whether the performance metric has converged. For example, if little or no improvement in the performance metric has been observed in the last few iterations of steps S810 and S812, then the performance metric may be considered to have converged. If the performance metric has not converged, then the steps of S810 and S812 are repeated in the next iteration, with the modified illumination shape and modified patterning device from the current iteration being used as the initial illumination shape and initial patterning device for the next iteration (step S816).

[0154] The above optimization method can be used to increase the throughput of a lithographic projection apparatus. For example, the cost function may include the cost as a function of the exposure time. In an embodiment, the optimization of such a cost function is constrained or influenced by a measure of bandwidth or other metrics.

[0155] Figure 14 is a block diagram illustrating a computer system 100 that can assist in implementing the preferred methods and processes disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by processor 104. Computer system 100 also includes a read-only memory (ROM) 108 or other static storage device, coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0156] The computer system 100 can be coupled to a display 112, such as a cathode ray tube (CRT) or a flat-panel or touch-pad display, via bus 102 for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating direction information and command selections to processor 104 and controlling cursor movement on display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch-pad (screen) display can also be used as an input device.

[0157] According to one embodiment, portions of the optimization process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0158] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such media can take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wire, and fiber optics, including the wires that make up bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, foldable disks, hard disks, magnetic tape, any other magnetic medium, CD-ROMs, DVDs, any other optical medium, punch cards, paper tape, any other physical medium with a pattern of holes, RAM, PROM and EPROM, flash EPROM, any other memory chip or cartridge, the carrier wave described below, or any other medium from which a computer can read.

[0159] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0160] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides two-way data communication coupled to a network link 120, which is connected to a local network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such embodiment, the communication interface 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0161] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through local network 122 to a host computer 124 or to data devices operated by an Internet Service Provider (ISP) 126. ISP 126, in turn, provides data communication services through a global packet data communication network, now commonly referred to as the "Internet" 128. Both local network 122 and Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0162] Computer system 100 can send messages and receive data, including program code, via network(s), network link 120, and communication interface 118. In the Internet example, server 130 can transmit requested code for an application via Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application might provide illumination optimization according to an embodiment. The received code can be executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage device for later execution. In this manner, computer system 100 can obtain application code in the form of a carrier wave.

[0163] Figure 15 An exemplary lithographic projection apparatus is schematically depicted, the illumination of which can be optimized using the methods described herein. The apparatus comprises:

[0164] - an illumination system IL to condition the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO;

[0165] a first stage (e.g., patterning device table) MT provided with a patterning device holder for holding a patterning device MA (e.g., a reticle) and connected to a first positioner for accurately positioning the patterning device relative to the object PS;

[0166] a second object table (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a resist-coated silicon wafer) and connected to a second positioner for accurately positioning the substrate relative to the item PS;

[0167] - A projection system ("lens") PS (eg, a refractive, reflective, or catadioptric optical system) to image the radiation portion of the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0168] As depicted herein, the device is transmissive (i.e., having a transmissive patterning device). However, in general, it can also be reflective, for example (having a reflective patterning device). The device can employ patterning devices other than classical masks; examples include programmable mirror arrays or LCD matrices.

[0169] A source SO (e.g., a mercury lamp or excimer laser, or an LPP (laser produced plasma) EUV source) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, either directly or after passing through conditioning components such as a beam expander Ex, for example. The illuminator IL may include adjustment components AD for setting the outer and / or inner radial extent of the intensity distribution in the beam (commonly referred to as σouter and σinner, respectively). In addition, it will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0170] about Figure 15 It should be noted that the source SO can be within the housing of the lithographic projection apparatus (e.g. this is typically the case when the source SO is a mercury lamp), but it can also be remote from the lithographic projection apparatus, the radiation beam it generates being introduced into the apparatus (e.g. with the aid of suitable guide mirrors); this latter scenario is typically the case when the source SO is an excimer laser (e.g. based on KrF, ArF or F2 laser irradiation).

[0171] The beam PB then intercepts the patterning device MA, which is held on the patterning device table MT. After traversing the patterning device MA, the beam PB passes through a lens PL which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and the interferometry means IF), the substrate table WT can be accurately moved, for example to position a different target portion C in the path of the beam PB. Similarly, the first positioning means can be used to accurately position the patterning device MA relative to the path of the beam B, for example after mechanically retrieving the patterning device MA from a patterning device library or during a scan. Typically, movement of the stage MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are used in the embodiment of the present invention. Figure 15 However, in the case of a stepper (as opposed to a step-and-scan tool) the patterning device table MT may be connected to a short-stroke actuator only, or may be fixed.

[0172] The depicted tool can be used in two different modes:

[0173] - in step mode, the patterning device table MT is essentially stationary and the entire patterning device image is projected at once (i.e. a single "flash") onto a target portion C. The substrate table WT is then shifted in the x and / or y direction so that a different target portion C can be irradiated by the beam PB;

[0174] In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single "flash." Instead, the patterning device table MT is movable in a given direction (the so-called "scanning direction," e.g., the y-direction) at a speed v, so that the projection beam B is scanned across the patterning device image. Concurrently, 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 PL (typically, M=1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

[0175] Figure 16 Another exemplary lithographic projection apparatus 1000 is schematically depicted, the illumination of which may be optimized using the methods described herein.

[0176] The lithographic projection apparatus 1000 comprises:

[0177] - Source Collector Module SO

[0178] - An illumination system (illuminator) IL configured to condition a radiation beam B (eg EUV radiation).

[0179] a support structure (e.g., patterning device table) MT configured to support a patterning device (e.g., mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0180] a substrate table (eg, wafer stage) WT configured to hold a substrate (eg, a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0181] - a projection system (eg, a catadioptric projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0182] As depicted here, apparatus 1000 is reflective (e.g., employing a reflective patterning device). Note that because most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector comprising, for example, multiple stacks of molybdenum and silicon. In one example, the multilayer reflector has 40 layer pairs of molybdenum and silicon, each with a thickness of a quarter wavelength. Even smaller wavelengths can be produced using X-ray lithography. Because most materials are absorptive at both EUV and X-ray wavelengths, a thin sheet of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multilayer reflector) defines where features will be printed (positive resist) or not (negative resist).

[0183] Reference Figure 16 , the illuminator IL receives a beam of extreme ultraviolet radiation from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. In one such method, often referred to as laser produced plasma ("LPP"), a plasma can be generated by irradiating a fuel (such as a droplet, stream, or cluster of material having a line-emitting element) with a laser beam. The source collector module SO can be part of an EUV radiation system that includes a device not in the EUV range. Figure 16 The laser shown in FIG. 1 is used to provide a laser beam for excitation of the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector disposed in a source collector module. The laser and source collector module can be separate entities, such as when a CO2 laser is used to provide the laser beam for fuel excitation.

[0184] In this case, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is passed from the laser to the source collector module with the aid of a beam delivery system comprising, for example, suitable guide mirrors and / or a beam expander. In other cases, the source may be an integrated part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often referred to as a DPP source.

[0185] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σouter and σinner, respectively) may be adjusted. In addition, the illuminator IL may include various other components, such as a facet field and a pupil mirror arrangement. The illuminator may be used to condition the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0186] A radiation beam B is incident on and patterned by a patterning device (e.g., mask) MA, which is held on a support structure (e.g., patterning device table) MT. After reflecting from the patterning device (e.g., mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g., an interferometer device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0187] The depicted device 1000 can be used in at least one of the following modes:

[0188] 1. In step mode, the support structure (e.g. patterning device table) MT and substrate table WT are held substantially stationary while the entire pattern imparted to the radiation beam is projected at one time onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0189] 2. In scan mode, the support structure (e.g. patterning device table) MT and substrate table WT are scanned synchronously as a pattern imparted to the radiation beam is projected onto a target portion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (e.g. patterning device table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0190] 3. In another mode, the support structure (e.g., patterning device table) MT remains essentially stationary, thereby holding the programmable patterning device, and the substrate table WT is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, typically a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can readily be applied to maskless lithography, which utilizes a programmable patterning device (such as a programmable mirror array of the type referenced above).

[0191] Figure 17The apparatus 1000 is shown in greater detail and includes a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained within the enclosed structure 220 of the source collector module SO. An EUV radiation-emitting plasma 210 can be formed by a discharge-generated plasma source. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein a very hot plasma 210 is created to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is created, for example, by an electric discharge that causes an at least partially ionized plasma. To effectively generate radiation, a partial pressure of Xe, Li, Sn vapor, or any other suitable gas or vapor, such as 10 Pa, may be required. In an embodiment, a plasma that excites tin (Sn) is provided to generate EUV radiation.

[0192] Radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or fin trap) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230, further indicated herein, includes at least a channel structure.

[0193] The collector chamber 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused along the optical axis indicated by the dotted line 'O' onto a virtual source point IF. The virtual source point IF is generally referred to as an intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near an opening 221 in the enclosure 220. The virtual source point IF is an image of the radiation-emitting plasma 210.

[0194] The radiation then traverses an illumination system IL, which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24, which are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the radiation beam 21 at the patterning device MA, held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by the substrate table WT.

[0195] More elements than shown may typically be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Further, there may be more mirrors than shown in the figures, for example with Figure 17 Compared to what is shown, there may be 1 to 6 additional reflective elements in the projection system PS.

[0196] like Figure 17 As illustrated, collector optics CO is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, merely as an example of a collector (or collector mirror). Grazing incidence reflectors 253, 254, and 255 are arranged axially symmetrically about optical axis O, and this type of collector optics CO can be used in combination with a discharge produced plasma source, commonly referred to as a DPP source.

[0197] Alternatively, the source collector module SO can be Figure 18 Part of an LPP radiation system is shown. Laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li), thereby creating a highly ionized plasma 210 with an electron temperature of tens of eV. Energetic radiation generated during the deexcitation and recombination of these ions is emitted from the plasma, collected by collector optics CO at near normal incidence, and focused onto an opening 221 in an enclosure structure 220.

[0198] The concepts disclosed herein can simulate or mathematically model any general-purpose imaging system for imaging subwavelength features and may be particularly useful for emerging imaging technologies capable of producing increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography, which can produce wavelengths of 193 nm using ArF lasers, and even 157 nm using fluorine lasers. Furthermore, EUV lithography can produce wavelengths in the 20 to 5 nm range by using synchrotrons or by bombarding materials (solid or plasma) with high-energy electrons to generate photons in this range.

[0199] Embodiments of the present disclosure may be further described in the following clauses.

[0200] 1. A non-transitory computer-readable medium configured to determine a mask rule check violation associated with a mask feature, the medium comprising instructions stored therein that, when executed by one or more processors, perform operations comprising:

[0201] obtaining a detector having geometric properties corresponding to mask rule checking (MRC), the detector configured to include a curved portion for detecting curvature violations, an enclosed region, a prescribed orientation axis configured to guide relative positioning of the detector with mask features, and a length along the orientation axis to detect critical dimension violations;

[0202] aligning an orientation axis of the detector with a normal axis at a location on the mask feature such that a length of the detector extends along a prescribed axis at the location on the mask feature; and

[0203] An MRC violation corresponding to a region of the mask feature that intersects the enclosed region is identified based on an orientation axis of the detector aligned with a prescribed axis of the mask feature, wherein the alignment and geometry of the detector causes the detector to intersect the region of the mask feature to identify curvature violations and / or critical dimension violations.

[0204] 2. The medium of clause 1, wherein the detector is non-circular and has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0205] 3. The medium of clause 2, wherein the non-circular detector is configured to have an elliptical shape having a radius of curvature configured to detect a curvature violation and a length along an orientation axis configured to detect a critical dimension violation.

[0206] 4. The medium of clause 3, wherein the curved portion of the detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature defined by the mask manufacturability check.

[0207] 5. A medium according to clause 1, wherein the identification comprises:

[0208] Based on the intersection of the detector with the mask feature at a single location, MRC violations including curvature violations and critical dimension violations are determined.

[0209] 6. A medium according to clause 1, wherein the identification comprises:

[0210] An MRC violation associated with a curvature violation and a spatial violation is determined based on an intersection between at least two mask features at a single location.

[0211] 7. The medium according to any one of clauses 1 to 6, wherein obtaining the detector comprises:

[0212] The length of the detector along the orientation axis is obtained, which is the distance between the intersection points of the orientation axis and the boundaries of the detector when the orientation axis is extended.

[0213] 8. The medium of any of clauses 1 to 7, wherein the prescribed axis corresponds to an axis normal to a location on a mask feature, wherein aligning the orientation axis of the detector with the prescribed axis of the mask feature comprises:

[0214] Identifying a normal axis at a location of a mask feature that is perpendicular to the curve at the location of the mask feature; contacting an edge of a detector with an edge of the feature at the location; and orienting an orientation axis of the detector along the normal axis at the location of the feature.

[0215] 9. A medium according to any one of clauses 1 to 7, wherein identifying the MRC violation comprises:

[0216] MRC violations are determined by sliding the detector along the edge of the mask feature while maintaining alignment of the detector's orientation axis with the normal axis of each location of the mask feature.

[0217] 10. The medium according to clause 9, wherein identifying the MRC violation includes:

[0218] (a) aligning an orientation axis of a detector with a first normal axis at a first location of a mask feature;

[0219] (b) identifying whether a region around a first position of the mask feature is within the enclosed region based on alignment of an orientation axis of the detector with a first normal axis of the mask feature;

[0220] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0221] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the detector to a second position of the mask feature and identifying an MRC violation by performing steps (a) to (c) at the second position and its second normal axis.

[0222] 11. The medium according to any one of clauses 1 to 10, wherein obtaining the detector comprises:

[0223] Detectors are accessed from a detector library, which are used to determine MRC violations for mask features.

[0224] 12. The medium of clause 11, wherein the detector bank comprises a plurality of detectors, each detector having a different shape and size than the other detectors.

[0225] 13. The medium according to any one of clauses 1 to 12, further comprising:

[0226] Based on the detector, a mask design is performed to determine the shapes and sizes of mask features of the mask design.

[0227] 14. A medium according to clause 13, wherein performing the mask design comprises:

[0228] (a) simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip;

[0229] (b) determining, via a detector, portions of the mask features that violate MRC; and

[0230] (c) in response to violating the MRC, modifying the corresponding portion of the mask feature to satisfy the MRC; and repeating steps (a) to (c).

[0231] 15. The medium of clause 14, the mask optimization process comprising: a mask optimization process only, a source mask optimization process and / or an optical proximity correction process.

[0232] 16. A medium according to any one of clauses 1 to 15, wherein the mask features are curvilinear in shape.

[0233] 17. A medium according to any of clauses 1 to 16, wherein the MRC comprises one or more geometric properties associated with the mask features, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0234] 18. A medium according to any one of clauses 1 to 17, wherein the orientation axis is perpendicular to the point of the curvature of the detector.

[0235] 19. The medium according to any one of clauses 1 to 18, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area having an opening.

[0236] 20. A non-transitory computer-readable medium configured for determining a mask rule check violation associated with a mask feature, the medium comprising instructions stored therein that, when executed by one or more processors, implement operations comprising: obtaining a non-circular detector having geometric properties corresponding to a mask rule check (MRC), the non-circular detector configured to include a curved portion for detecting a curvature violation, an enclosed area, an orientation axis at a point perpendicular to the curved portion, and a length along the orientation axis for detecting a critical dimension violation;

[0237] aligning the orientation axis with a prescribed axis of a location on the mask feature such that a length of the non-circular detector extends along the prescribed axis of the mask feature; and

[0238] MRC violations corresponding to areas of the mask feature that intersect the enclosed region are identified based on the aligned non-circular detector and mask feature, wherein the alignment and geometry of the non-circular detector causes the detector to intersect the area of ​​the mask feature to identify curvature violations and / or critical dimension violations.

[0239] 21. A medium according to clause 20, wherein the non-circular detector has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0240] 22. The medium of clause 21, wherein the non-circular detector is configured to have an elliptical shape having a radius of curvature configured to detect a curvature violation and a length along an orientation axis configured to detect a critical dimension violation.

[0241] 23. The medium of clause 20, wherein obtaining the non-circular detector comprises:

[0242] A detector is received that is shaped based on the curvature and feature size of mask features that may be fabricated.

[0243] 24. The medium of clause 23, wherein the curved portion of the non-circular detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature that can be manufactured.

[0244] 25. A medium according to clause 20, wherein the identification comprises:

[0245] Based on the intersection of a non-circular detector with a mask feature at a single location, MRC violations including curvature violations and critical dimension violations are determined.

[0246] 26. A medium according to clause 20, wherein the identification comprises:

[0247] An MRC violation associated with a curvature violation and a spatial violation is determined based on an intersection between at least two mask features at a single location.

[0248] 27. The medium according to any one of clauses 20 to 26, wherein obtaining the detector comprises:

[0249] The length of the detector along the orientation axis is obtained, which is the distance between the intersection points of the orientation axis and the boundaries of the detector when the orientation axis is extended.

[0250] 28. The medium of any one of clauses 20 to 27, wherein the prescribed axis corresponds to an axis normal to a location on a mask feature, wherein aligning the orientation axis comprises:

[0251] determining a normal axis at a location of a mask feature;

[0252] contacting an edge of the non-circular detector with an edge of the feature at the location; and

[0253] The orientation axis of the non-circular detector is oriented along the normal axis at the location of the feature.

[0254] 29. A medium according to any one of clauses 20 to 27, wherein identifying the MRC violation comprises:

[0255] MRC violations are determined by sliding a non-circular detector along the edge of a mask feature while maintaining alignment of the orientation axis of the non-circular detector with the normal axis of each location of the mask feature.

[0256] 30. A medium according to clause 29, wherein identifying an MRC violation comprises:

[0257] (a) aligning an orientation axis of a non-circular detector with a first normal axis at a first location of a mask feature;

[0258] (b) identifying whether a region around the first position of the mask feature is within the closed region based on an orientation axis of the detector aligned with a normal axis of the mask feature;

[0259] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0260] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the non-circular detector to a second position of the mask feature and identifying an MRC violation by performing steps (a) to (c) at the second position and its second normal axis.

[0261] 31. A medium according to any one of clauses 20 to 30, wherein obtaining the non-circular detector comprises:

[0262] Access a non-circular detector from the detector library to determine MRC violations for mask features.

[0263] 32. The medium of clause 10, wherein the detector bank comprises a plurality of non-circular detectors, each non-circular detector having a different shape and size than the other detectors.

[0264] 33. A medium according to any one of clauses 20 to 32, wherein the shape of the mask features is curvilinear.

[0265] 34. A medium according to any one of clauses 20 to 23, further comprising:

[0266] Based on the non-circular detector, a mask design is performed to determine the shapes and sizes of mask features of the mask design.

[0267] 35. A medium according to clause 34, wherein performing the mask design comprises:

[0268] (a) simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip;

[0269] (b) determining, via a non-circular detector, the MRC-violating portion of the mask feature; and

[0270] (c) in response to violating the MRC, modifying the corresponding portion of the mask feature to satisfy the MRC; and repeating steps (a) to (c).

[0271] 36. The medium of clause 35, wherein the mask optimization process comprises: a mask optimization process, a source mask optimization process and / or an optical proximity correction process.

[0272] 37. A medium according to any of clauses 20 to 36, wherein the MRC comprises one or more geometric properties associated with the mask features, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0273] 38. The medium according to any one of clauses 20 to 37, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area having an opening.

[0274] 39. A non-transitory computer-readable medium configured for determining a mask design to fabricate a mask to be used in semiconductor fabrication, the medium comprising instructions stored therein that, when executed by one or more processors, perform operations comprising:

[0275] simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip; and

[0276] Determining, via a detector, a portion of a mask feature that violates a mask rule check (MRC), the detector being configured to have a curved portion, a closed area, and an orientation axis at a point perpendicular to the curved portion, the orientation axis being used to guide an orientation of the detector relative to the mask feature to detect an MRC violation; and modifying, in response to the portion that violates the MRC, a corresponding portion of the mask feature to satisfy the MRC.

[0277] 40. The medium of clause 39, wherein determining the portion of the mask feature that violates the MRC comprises: obtaining a detector having geometric properties corresponding to the MRC;

[0278] aligning the orientation axis with a prescribed axis of a location on the mask feature; and identifying an MRC violation corresponding to a region of the mask feature that intersects the enclosed region based on the orientation axis of the detector and the prescribed axis of the mask feature.

[0279] 41. A medium according to clause 39, wherein the detector is non-circular and has a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0280] 42. The medium of clause 39, wherein the detector is shaped based on the curvature and feature size of mask features that can be fabricated.

[0281] 43. The medium of clause 39, wherein the curved portion of the detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature that can be manufactured.

[0282] 44. A medium according to clause 39, wherein the detector is a single detector configured to determine an MRC violation comprising a curvature violation and a width violation associated with the mask feature.

[0283] 45. A medium according to clause 39, wherein the detector is a single detector configured to determine an MRC violation associated with a curvature violation and a spatial violation between at least two mask features.

[0284] 46. ​​A medium according to any one of clauses 40 to 45, wherein the specified axis corresponds to the normal axis at the location, wherein the alignment comprises: determining the normal axis at the location of the mask feature; contacting an edge of the detector with the edge of the feature at the location; and orienting the orientation axis of the detector along the normal axis at the location of the feature.

[0285] 47. A medium according to any one of clauses 40 to 46, wherein identifying the MRC violation comprises:

[0286] The detector is slid along the edge of the mask feature while maintaining alignment of the detector's orientation axis with the normal axis of each location of the mask feature.

[0287] 48. A medium according to clause 47, wherein identifying an MRC violation comprises:

[0288] (a) aligning an orientation axis of a detector with a normal axis of a mask feature at a first location;

[0289] (b) identifying whether an area around the first position of the mask feature is within the closed region based on aligning the detector and the mask feature;

[0290] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0291] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the detector to a second position of the mask feature, and identifying an MRC violation by performing steps (a) to (c) at the second position.

[0292] 49. A medium according to any one of clauses 39 to 48, wherein the shape of the mask features is curvilinear.

[0293] 50. A medium according to any of clauses 39 to 49, wherein the MRC comprises one or more geometric properties associated with the mask features, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0294] 51. A medium according to any one of clauses 39 to 50, wherein the orientation axis extends within or outside the enclosed area of ​​the detector.

[0295] 52. A medium according to any of clauses 39 to 51, wherein modifying the mask features comprises increasing or decreasing the size and / or curvature of portions of the mask features to satisfy MRC using the detector.

[0296] 53. A medium according to any one of clauses 39 to 52, wherein modifying the mask features is an iterative process, each iteration comprising:

[0297] executing one or more process models associated with a patterning process using the modified mask features to generate target features to be printed on a semiconductor chip;

[0298] Determining whether the target feature satisfies a design specification associated with the design layout; and in response to the design specification not being satisfied, modifying the mask feature to satisfy the design specification.

[0299] 54. The medium according to any one of clauses 39 to 53, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area having an opening.

[0300] 55. A method for determining a mask rule checking violation associated with a mask feature, the method comprising:

[0301] obtaining a detector having geometric properties corresponding to mask rule checking (MRC), the detector configured to include a curved portion for detecting curvature violations, an enclosed region, a prescribed orientation axis configured to guide relative positioning of the detector with mask features, and a length along the orientation axis to detect critical dimension violations;

[0302] aligning an orientation axis of the detector with a prescribed axis at a location on the mask feature such that a length of the detector extends along the prescribed axis of the mask feature; and

[0303] An MRC violation corresponding to a region of the mask feature that intersects the enclosed region is identified based on an orientation axis of the detector aligned with a prescribed axis of the mask feature, wherein the alignment and geometry of the detector causes the detector to intersect the region of the mask feature to identify curvature violations and / or critical dimension violations.

[0304] 56. A method according to clause 55, wherein the detector is non-circular and has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0305] 57. The method of clause 56, wherein the non-circular detector is configured to have an elliptical shape having a radius of curvature configured to detect curvature violations and a length along an orientation axis configured to detect critical dimension violations.

[0306] 58. The method of clause 57, wherein the curved portion of the detector has a shape and size corresponding to a curvature of a tip portion of the mask feature and a minimum size of the mask feature defined by a mask manufacturability check.

[0307] 59. The method according to clause 55, wherein identifying comprises:

[0308] Based on the intersection of the detector with the mask feature at a single location, MRC violations including curvature violations and critical dimension violations are determined.

[0309] 60. The method according to clause 55, wherein identifying comprises:

[0310] An MRC violation associated with a curvature violation and a spatial violation is determined based on an intersection between at least two mask features at a single location.

[0311] 61. The method of any one of clauses 55 to 60, wherein obtaining the detector comprises:

[0312] The length of the detector along the orientation axis is obtained, which is the distance between the intersection points of the orientation axis and the boundaries of the detector when the orientation axis is extended.

[0313] 62. A method according to any of clauses 55 to 61, wherein the prescribed axis corresponds to the normal axis, wherein aligning comprises:

[0314] identifying a normal axis at the location of the mask feature, the normal axis being perpendicular to the curve at the location of the mask feature;

[0315] bringing an edge of the detector into contact with an edge of the feature at the location; and

[0316] Orient the detector's orientation axis along the normal axis at the location of the feature.

[0317] 63. A method according to any one of clauses 55 to 62, wherein identifying the MRC violation comprises:

[0318] MRC violations are determined by sliding the detector along the edge of the mask feature while maintaining alignment of the detector's orientation axis with the normal axis of each location of the mask feature.

[0319] 64. A method according to clause 63, wherein identifying an MRC violation comprises:

[0320] (a) aligning an orientation axis of a detector with a first normal axis at a first location of a mask feature;

[0321] (b) identifying whether a region around a first position of the mask feature is within the closed region based on an orientation axis of the detector aligned with a first normal axis of the mask feature;

[0322] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0323] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the detector to a second position of the mask feature and identifying an MRC violation by performing steps (a) to (c) at the second position and its second normal axis.

[0324] 65. The method of any one of clauses 55 to 64, wherein obtaining the detector comprises:

[0325] Access detectors from the detector library to determine MRC violations for mask features.

[0326] 66. A method according to clause 65, wherein the detector library comprises a plurality of detectors, each detector having a different shape and size from the other detectors.

[0327] 67. A method according to any one of clauses 55 to 66, further comprising:

[0328] Based on the detector, a mask design is performed to determine the shapes and sizes of mask features of the mask design.

[0329] 68. The method of clause 67, wherein performing the mask design comprises:

[0330] (a) simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip;

[0331] (b) determining, via a detector, portions of the mask features that violate MRC; and

[0332] (c) in response to violating the MRC, modifying the corresponding portion of the mask feature to satisfy the MRC; and repeating steps (a) to (c).

[0333] 69. The method of clause 68, wherein the mask optimization process comprises: a mask optimization process only, a source mask optimization process and / or an optical proximity correction process.

[0334] 70. A method according to any one of clauses 55 to 69, wherein the shape of the mask features is curvilinear.

[0335] 71. A method according to any of clauses 55 to 70, wherein the MRC comprises one or more geometric properties associated with the mask feature, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0336] 72. A method according to any one of clauses 55 to 71, wherein the orientation axis is perpendicular to a point of the curved portion of the detector.

[0337] 73. The method of any one of clauses 55 to 72, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area having an opening.

[0338] 74. A method for determining a mask rule checking violation associated with a mask feature, the method comprising:

[0339] obtaining a non-circular detector having geometric properties corresponding to a mask rule check (MRC), the non-circular detector being configured to include a curved portion for detecting a curvature violation, an enclosed area, an orientation axis perpendicular to a point of the curved portion, and a length along the orientation axis for detecting a critical dimension violation;

[0340] aligning the orientation axis with a prescribed axis of a location on the mask feature such that a length of the non-circular detector extends along the prescribed axis of the mask feature; and

[0341] MRC violations corresponding to areas of the mask feature that intersect the closed region are identified based on the aligned non-circular detector and mask feature, wherein the alignment and geometry of the non-circular detector causes the detector to intersect the area of ​​the mask feature to identify curvature violations and / or critical dimension violations.

[0342] 75. A method according to clause 74, wherein the non-circular detector has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0343] 76. The method of clause 75, wherein the non-circular detector is configured to have an elliptical shape having a radius of curvature configured to detect curvature violations and a length along an orientation axis configured to detect critical dimension violations.

[0344] 77. The method of clause 74, wherein obtaining the non-circular detector comprises:

[0345] A detector is received that is shaped based on the curvature and feature size of mask features that may be fabricated.

[0346] 78. The method of clause 77, wherein the curved portion of the non-circular detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature that can be manufactured.

[0347] 79. A method according to clause 74, wherein identifying comprises:

[0348] Based on the intersection of a non-circular detector with a mask feature at a single location, MRC violations including curvature violations and critical dimension violations are determined.

[0349] 80. A method according to clause 74, wherein identifying comprises:

[0350] An MRC violation associated with a curvature violation and a spatial violation is determined based on an intersection between at least two mask features at a single location.

[0351] 81. The method of any one of clauses 74 to 80, wherein obtaining the detector comprises:

[0352] The length of the detector along the orientation axis is obtained, which is the distance between the intersection points of the orientation axis and the boundaries of the detector when the orientation axis is extended.

[0353] 82. A method according to any one of clauses 74 to 81, wherein aligning comprises:

[0354] determining a normal axis at a location of a mask feature;

[0355] contacting an edge of the non-circular detector with an edge of the feature at the location; and

[0356] The orientation axis of the non-circular detector is oriented along the normal axis at the location of the feature.

[0357] 83. A method according to any one of clauses 74 to 82, wherein identifying the MRC violation comprises determining the MRC violation by sliding the non-circular detector along the edge of the mask feature while maintaining alignment of the orientation axis of the non-circular detector with the normal axis of each position of the mask feature.

[0358] 84. A method according to clause 83, wherein identifying an MRC violation comprises:

[0359] (a) aligning an orientation axis of a non-circular detector with a first normal axis at a first location of a mask feature;

[0360] (b) identifying whether a region around the first position of the mask feature is within the closed region based on an orientation axis of the detector aligned with a normal axis of the mask feature;

[0361] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0362] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the non-circular detector to a second position of the mask feature and identifying an MRC violation by performing steps (a) to (c) at the second position and its second normal axis.

[0363] 85. The method of any one of clauses 74 to 84, wherein obtaining the non-circular detector comprises:

[0364] Access a non-circular detector from the detector library to determine MRC violations for mask features.

[0365] 86. A method according to clause 85, wherein the detector library comprises a plurality of non-circular detectors, each non-circular detector having a different shape and size than the other detectors.

[0366] 87. A method according to any of clauses 74 to 86, wherein the mask features are curvilinear in shape.

[0367] 88. A method according to any one of clauses 74 to 87, further comprising:

[0368] Based on the non-circular detector, a mask design is performed to determine the shapes and sizes of mask features of the mask design.

[0369] 89. The method of clause 88, wherein performing the mask design comprises:

[0370] (a) simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip;

[0371] (b) determining, via a non-circular detector, the MRC-violating portion of the mask feature; and

[0372] (c) in response to violating the MRC, modifying the corresponding portion of the mask feature to satisfy the MRC; and repeating steps (a) to (c).

[0373] 90. The method of clause 89, wherein the mask optimization process comprises: a mask optimization process, a source mask optimization process and / or an optical proximity correction process.

[0374] 91. A method according to any of clauses 74 to 90, wherein the MRC comprises one or more geometric properties associated with the mask features, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0375] 92. A method according to any one of clauses 74 to 91, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area with an opening.

[0376] 93. A method for determining a mask design for manufacturing a mask to be used in semiconductor manufacturing, the method comprising:

[0377] simulating a mask optimization process to determine mask features of a mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip; and

[0378] determining, via a detector, a portion of the mask feature that violates a mask rule check (MRC), the detector being configured to have a curved portion, a closed region, and an orientation axis at a point perpendicular to the curved portion, the orientation axis for guiding an orientation of the detector relative to the mask feature to detect an MRC violation; and

[0379] In response to the portion violating the MRC, the corresponding portion of the mask feature is modified to satisfy the MRC.

[0380] 94. The method of clause 93, wherein determining the portion of the mask feature that violates the MRC comprises:

[0381] Obtaining a detector having geometric properties corresponding to MRC;

[0382] aligning the orientation axis with a normal axis of a location on the mask feature; and

[0383] Based on the orientation axis of the detector and the normal axis of the mask feature, MRC violations corresponding to regions of the mask feature that intersect the closed region are identified.

[0384] 95. A method according to clause 93, wherein the detector is non-circular and has a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius is different from the second radius.

[0385] 96. A method according to clause 93, wherein the detector is shaped based on the curvature and feature size of the mask features that can be manufactured.

[0386] 97. A method according to clause 93, wherein the curved portion of the detector has a shape and size corresponding to the curvature of the tip portion of the mask feature and the minimum size of the mask feature that can be manufactured.

[0387] 98. The method of clause 93, wherein the detector is a single detector configured to determine MRC violations comprising curvature violations and width violations associated with the mask features.

[0388] 99. The method of clause 93, wherein the detector is a single detector configured to determine an MRC violation associated with a curvature violation and a spatial violation between at least two mask features.

[0389] 100. The method of any of clauses 94 to 99, wherein aligning the orientation axis of the detector with the normal axis of the mask feature comprises:

[0390] determining a normal axis at a location of a mask feature;

[0391] contacting an edge of the detector with an edge of the feature at the location; and orienting an orientation axis of the detector along a normal axis at the location of the feature.

[0392] 101. A method according to any one of clauses 94 to 100, wherein identifying the MRC violation comprises:

[0393] The detector is slid along the edge of the mask feature while maintaining alignment of the detector's orientation axis with the normal axis of each location of the mask feature.

[0394] 102. A method according to clause 101, wherein identifying the MRC violation comprises:

[0395] (a) aligning an orientation axis of a detector with a normal axis of a mask feature at a first location;

[0396] (b) identifying whether an area around the first position of the mask feature is within the closed region based on aligning the detector and the mask feature;

[0397] (c) in response to the region of the mask feature being within the closed region, marking the first location as an MRC location; and

[0398] (d) In response to the area of ​​the mask feature not being within the enclosed region, sliding the detector to a second position of the mask feature, and identifying an MRC violation by performing steps (a) to (c) at the second position.

[0399] 103. A method according to any of clauses 93 to 102, wherein the mask features are curvilinear in shape.

[0400] 104. A method according to any of clauses 93 to 103, wherein the MRC comprises one or more geometric properties associated with the mask feature, the geometric properties comprising at least one of: a minimum CD of the mask feature that can be manufactured, a minimum curvature of the mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

[0401] 105. A method according to any of clauses 93 to 104, wherein the orientation axis extends within or outside an enclosed area of ​​the detector.

[0402] 106. A method according to any of clauses 93 to 105, wherein modifying the mask features comprises increasing or decreasing the size and / or curvature of portions of the mask features to satisfy MRC using the detector.

[0403] 107. A method according to any of clauses 93 to 106, wherein modifying the mask features is an iterative process, each iteration comprising:

[0404] executing one or more process models associated with a patterning process using the modified mask features to generate target features to be printed on a semiconductor chip;

[0405] Determining whether the target feature satisfies a design specification associated with the design layout; and in response to the design specification not being satisfied, modifying the mask feature to satisfy the design specification.

[0406] 108. A method according to any one of clauses 93 to 107, wherein the enclosed area of ​​the detector comprises: a fully enclosed area or a partially enclosed area having an opening.

[0407] 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 lithographic imaging system, such as those used for imaging on substrates other than silicon wafers.

[0408] The above description is intended to be illustrative rather than restrictive. It will therefore be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set out below.

Claims

1. A mask rule checking method, comprising: obtaining a non-circular detector having geometric properties corresponding to mask rule checking, the non-circular detector being configured to include a curved portion for detecting curvature violations, a closed area, an orientation axis perpendicular to the curved portion, and a length along the orientation axis for detecting critical dimension violations; aligning the orientation axis with a prescribed axis of a location on a mask feature such that the length of the non-circular detector extends along the prescribed axis of the mask feature; as well as identifying a mask rule checking violation corresponding to a region of the mask feature that intersects the enclosed region based on the aligned non-circular detector and the mask feature, wherein the alignment and geometry of the non-circular detector cause the detector to intersect the region of the mask feature to identify the violation; wherein the non-circular detector has at least a first curved portion and a second curved portion, wherein the first curved portion has a first radius of curvature, wherein the second curved portion has a second radius of curvature, and wherein the first radius of curvature is different from the second radius of curvature. 2 . The method of claim 1 , wherein the non-circular detector is configured to have an elliptical shape having a radius of curvature configured to detect a curvature violation and a length along an orientation axis configured to detect a critical dimension violation.

3. The method according to claim 1, wherein obtaining the non-circular detector comprises: The detector is received according to manufacturability rules, defined based on curvature and / or feature size of the mask features. 4 . The method of claim 3 , wherein the curved portion of the non-circular detector has a shape and size corresponding to a curvature of a tip portion of the mask feature and a minimum size of the mask feature according to manufacturability rules.

5. The method of claim 1 , wherein the identifying comprises: determining a mask rule check violation including a curvature violation and a critical dimension violation based on the intersection of the non-circular detector and the mask feature at a single location; or A mask rule check violation associated with a curvature violation and a spatial violation is determined based on an intersection between at least two mask features at a single location.

6. The method according to claim 1, wherein obtaining the detector comprises: The length of the detector along the orientation axis is obtained, the length being the distance between intersection points of the orientation axis and a boundary of the detector when the orientation axis is extended.

7. The method of claim 1 , wherein the prescribed axis corresponds to a normal axis of the location on the mask feature, wherein aligning the orientation axis comprises: determining the normal axis at the location of the mask feature; bringing an edge of the non-circular detector into contact with an edge of the feature at the location; as well as The orientation axis of the non-circular detector is oriented along the normal axis at the location of the feature.

8. The method of claim 1 , wherein identifying the mask rule check violation comprises: The mask rule check violation is determined by moving the non-circular detector along an edge of the mask feature while maintaining alignment of the orientation axis of the non-circular detector with a normal axis of each location of the mask feature.

9. The method of claim 1 , wherein the obtaining of the non-circular detector comprises: The non-circular detector is accessed from a detector library to determine a mask rule checking violation for the mask feature, wherein the detector library includes a plurality of different non-circular detectors.

10. The method according to claim 1, further comprising: Based on the non-circular detector, performing a mask design to determine shapes and sizes of mask features of the mask design, wherein the performing of the mask design comprises: (a) simulating a mask optimization process to determine the mask features of the mask design using a design layout, the design layout corresponding to features to be printed on a semiconductor chip; (b) determining, via the non-circular detector, portions of the mask features that violate the mask rule check; and (c) in response to violating the mask rule check, modifying the corresponding portion of the mask feature to satisfy the mask rule check; and repeating steps (a) through (c).

11. The method according to claim 10, wherein the mask optimization process comprises: A mask optimization process, a source mask optimization process, and / or an optical proximity correction process.

12. The method of claim 1 , wherein the mask rule check comprises one or more geometric properties associated with the mask features, the geometric properties comprising at least one of: a minimum critical dimension of a mask feature that can be manufactured, a minimum curvature of a mask feature that can be manufactured, or a minimum space between two features that can be manufactured.

13. The method of claim 1 , wherein the enclosed area of ​​the detector comprises: A fully enclosed area or a partially enclosed area with openings.

14. A non-transitory computer-readable medium configured for determining a mask design to manufacture a mask to be used in semiconductor manufacturing, the medium comprising instructions stored therein, which, when executed by one or more processors, implement operations comprising the method described in any one of claims 1 to 13.

Images