WO2024110141A1

WO2024110141A1 - Curvilinear polygon recovery for opc mask design

Info

Publication number: WO2024110141A1
Application number: PCT/EP2023/079845
Authority: WO
Inventors: Chenyang HU; Weixuan HU; Ningning JIA; Shulu WANG
Original assignee: Asml Netherlands B.V.
Priority date: 2022-11-22
Filing date: 2023-10-25
Publication date: 2024-05-30

Abstract

Disclosed are methods, systems, and computer software for generating a mask design. A method can include obtaining an initial OPC pattern contour resulting from an OPC process and determining a set of selected points on the initial OPC pattern contour. Metrics can be calculated that describe arcs between the selected points along the initial OPC pattern contour and a recovery location can be determined based on the calculation of the metrics. A recovered OPC pattern can be generated based on the recovery location.

Description

CURVILINEAR POLYGON RECOVERY FOR OPC MASK DESIGN

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority of International application PCT/CN2022/133549 which was filed on 22 November 2022 and which is incorporated herein in its entirety by reference.

TECHNICAL FIELD

[0002] The description herein relates generally to mask manufacturing and patterning processes. More particularly, the disclosure includes apparatus, methods, and computer programs for recovering OPC patterns.

BACKGROUND

[0003] A lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device (e.g., a mask) may contain or provide a pattern corresponding to an individual layer of the IC (“design layout”), and this pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer) that has been coated with a layer of radiation-sensitive material (“resist”), by methods such as irradiating the target portion through the pattern on the patterning device. In general, a single substrate contains a plurality of adjacent target portions to which the pattern is transferred successively by the lithographic projection apparatus, one target portion at a time. In one type of lithographic projection apparatuses, the pattern on the entire patterning device is transferred onto one target portion in one go; such an apparatus may also be referred to as a stepper. In an alternative apparatus, a step-and-scan apparatus can cause a projection beam to scan over the patterning device in a given reference direction (the “scanning” direction) while synchronously moving the substrate parallel or anti-parallel to this reference direction. Different portions of the pattern on the patterning device are transferred to one target portion progressively. Since, in general, the lithographic projection apparatus will have a reduction ratio M (e.g., 4), the speed F at which the substrate is moved will be 1/M times that at which the projection beam scans the patterning device. More information with regard to lithographic devices can be found in, for example, US 6,046,792, incorporated herein by reference.

[0004] Prior to transferring the pattern from the patterning device to the substrate, the substrate may undergo various procedures, such as priming, resist coating and a soft bake. After exposure, the substrate may be subjected to other procedures (“post-exposure procedures”), such as a post-exposure bake (PEB), development, a hard bake and measurement/inspection of the transferred pattern. This array of procedures is used as a basis to make an individual layer of a device, e.g., an IC. The substrate may then undergo various processes such as etching, ion-implantation (doping), metallization, oxidation, chemo-mechanical polishing, etc., all intended to finish off the individual layer of the device. If several layers are required in the device, then the whole procedure, or a variant thereof, is repeated for each layer. Eventually, a device will be present in each target portion on the substrate. These devices are then separated from one another by a technique such as dicing or sawing, whence the individual devices can be mounted on a carrier, connected to pins, etc.

[0005] Thus, manufacturing devices, such as semiconductor devices, typically involves processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the devices. Such layers and features are typically manufactured and processed using, e.g., deposition, lithography, etch, chemical-mechanical polishing, and ion implantation. Multiple devices may be fabricated on a plurality of dies on a substrate and then separated into individual devices. This device manufacturing process may be considered a patterning process. A patterning process involves a patterning step, such as optical and/or nanoimprint lithography using a patterning device in a lithographic apparatus, to transfer a pattern on the patterning device to a substrate and typically, but optionally, involves one or more related pattern processing steps, such as resist development by a development apparatus, baking of the substrate using a bake tool, etching using the pattern using an etch apparatus, etc.

[0006] As noted, lithography is a central step in the manufacturing of device such as ICs, where patterns formed on substrates define functional elements of the devices, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used in the formation of flat panel displays, micro-electro mechanical systems (MEMS) and other devices.

[0007] As semiconductor manufacturing processes continue to advance, the dimensions of functional elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend referred to as “Moore’s law.” At the current state of technology, layers of devices are manufactured using lithographic projection apparatuses that project a design layout onto a substrate using illumination from a deep-ultraviolet illumination source, creating individual functional elements having dimensions well below 100 nm, i.e. less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source).

[0008] This process in which features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus are printed, is can be referred to as low-kl lithography, according to the resolution formula CD = klx /NA, where X is the wavelength of radiation employed (e.g., 248 nm or 193 nm), NA is the numerical aperture of projection optics in the lithographic projection apparatus, CD is the “critical dimension’ -generally the smallest feature size printed-and kl is an empirical resolution factor. In general, the smaller kl the more difficult it becomes to reproduce a pattern on the substrate that resembles the shape and dimensions planned by a designer in order to achieve particular electrical functionality and performance. To overcome these difficulties, sophisticated fine- tuning steps are applied to the lithographic projection apparatus, the design layout, or the patterning device. These include, for example, but not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase shifting patterning devices, optical proximity correction (OPC, sometimes also referred to as “optical and process correction”) in the design layout, or other methods generally defined as “resolution enhancement techniques” (RET). The term “projection optics” as used herein should be broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting and/or projecting radiation from the source before the radiation passes the patterning device, and/or optical components for shaping, adjusting and/or projecting the radiation after the radiation passes the patterning device. The projection optics generally exclude the source and the patterning device.

SUMMARY

[0009] Disclosed are methods, systems, and computer software for generating a mask design. A method can include obtaining an initial OPC pattern contour resulting from an OPC process and determining a set of selected points on the initial OPC pattern contour. Metrics can be calculated that describe arcs between the selected points along the initial OPC pattern contour and a recovery location can be determined based on the calculation of the metrics. A recovered OPC pattern can be generated based on the recovery location

[0010] In some variations, the method can include modifying a portion of the initial OPC pattern contour at a recovery location based on an arc length between selected points on the initial OPC pattern contour. The method can also include joining or separating a portion of the initial OPC pattern contour at a recovery location where a distance between opposing points on the initial OPC pattern contour is a minimum.

[0011] In other variations, the method can include changing intensities of pixels at the recovery location in a mask image corresponding to the initial OPC pattern contour, where the recovered OPC pattern can be generated based on the mask image with the changed pixels. For example, the intensities of the pixels can be changed to be closer to internal intensities of pixels inside the initial OPC pattern contour and/or changed to be closer to external intensities of pixels outside the initial OPC pattern contour. The intensities of the pixels can be changed in a region surrounding the recovery location. [0012] In yet other variations, the method can include determining sample points on a Manhattan target pattern and generating the selected points along the initial OPC pattern contour by projecting the sample points on the Manhattan target pattern up to a threshold distance. This can include performing corner rounding on the Manhattan target pattern, where the sample points can be on the Manhattan target pattern after the corner rounding.

[0013] In some variations, the selected points on the initial OPC pattern contour can include a first point and a second point adjacent to the first point in a sequence of the selected points, and where the metrics include an arc length. The method can also include stepping from the first point and the second point to points along the initial OPC pattern contour, stopping the stepping when the arc length is equal to or greater than an arc length threshold, and generating the recovered OPC pattern based on the points where the stepping was stopped.

[0014] In other variations, the method can include calculating the arc length to be the sum of a) arc lengths between first point and the second point to the respective points along the initial OPC pattern contour, and b) a distance between the points at the current step.

[0015] In yet other variations, the method can include determining a chord length between the first point and the second point, where the stepping and stopping are performed unless the arc length is less than a chord length threshold. For example, the chord length threshold can be 120% of the chord length.

[0016] In some variations, the arc length threshold can be a multiple of a chord length between the first point and the second point and includes an offset length.

[0017] In other variations, the method can include calculating additional metrics as local angles indicating a converging or diverging of the initial OPC pattern contour and stopping the stepping when the local angles at the points indicate a local minimum width.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings, which are incorporated in and constitute a part of this specification, show certain aspects of the subject matter disclosed herein and, together with the description, help explain some of the principles associated with the disclosed implementations. In the drawings,

[0019] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus, according to an embodiment of the present disclosure.

[0020] Figure 2 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment of the present disclosure.

[0021] Figure 3 depicts examples of the recovery of OPC patterns, according to an embodiment of the present disclosure. [0022] Figure 4 illustrates a process flow diagram for OPC pattern recovery, according to an embodiment of the present disclosure.

[0023] Figure 5A illustrates an example of a target pattern with and without corner rounding, according to an embodiment of the present disclosure.

[0024] Figure 5B illustrates an example of projecting sample points to an initial OPC pattern contour, according to an embodiment of the present disclosure.

[0025] Figure 5C is a diagram illustrating utilizing the selected points as starting points for finding recovery locations to modify the initial OPC pattern contour, according to an embodiment of the present disclosure.

[0026] Figure 5D is a diagram illustrating selected points along the initial OPC pattern contour, according to an embodiment of the present disclosure.

[0027] Figure 5E is a diagram illustrating stepping along points on an initial OPC pattern contour to find a recovery location where the initial OPC pattern contour can be modified based on calculation of an arc length, according to an embodiment of the present disclosure.

[0028] Figure 5F is a diagram illustrating stepping along the initial OPC pattern contour to find a local minimum width, according to an embodiment of the present disclosure .

[0029] Figure 5G is a diagram illustrating calculating local angles to find a local minimum width, according to an embodiment of the present disclosure.

[0030] Figure 5H is a diagram illustrating the minimum width of an initial OPC pattern contour, according to an embodiment of the present disclosure.

[0031] Figure 51 is a diagram illustrating generating a recovered OPC pattern by changing pixel intensities, according to an embodiment of the present disclosure .

[0032] Figure 6A is a diagram illustrating selected points on a separated initial OPC pattern contour, according to an embodiment of the present disclosure.

[0033] Figure 6B is a diagram illustrating an intrinsic ordering of the selected points, according to an embodiment of the present disclosure.

[0034] Figure 6C is a diagram illustrating determining recovery locations for pixel modification, according to an embodiment of the present disclosure.

[0035] Figure 6D is a diagram illustrating generation of a recovered OPC pattern joining the separated initial OPC pattern contour, according to an embodiment of the present disclosure.

[0036] Figure 7 is a block diagram of an example computer system, according to an embodiment of the present disclosure.

[0037] Figure 8 is a schematic diagram of a lithographic projection apparatus, according to an embodiment of the present disclosure.

[0038] Figure 9 is a schematic diagram of another lithographic projection apparatus, according to an embodiment of the present disclosure. [0039] Figure 10 is a detailed view of the lithographic projection apparatus, according to an embodiment of the present disclosure.

[0040] Figure 11 is a detailed view of the source collector module of the lithographic projection apparatus, according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

[0041] Although specific reference may be made in this text to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid-crystal display panels, thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle”, “wafer” or “die” in this text should be considered as interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0042] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range of about 5-100 nm).

[0043] The patterning device can comprise, or can form, one or more design layouts. The design layout can be generated utilizing CAD (computer-aided design) programs, this process often being referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts/patterning devices. These rules are set by processing and design limitations. For example, design rules define the space tolerance between devices (such as gates, capacitors, etc.) or interconnect lines, so as to ensure that the devices or lines do not interact with one another in an undesirable way. One or more of the design rule limitations may be referred to as “critical dimension” (CD). A critical dimension of a device can be defined as the smallest width of a line or hole or the smallest space between two lines or two holes. Thus, the CD determines the overall size and density of the designed device. Of course, one of the goals in device fabrication is to faithfully reproduce the original design intent on the substrate (via the patterning device).

[0044] The term “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate; the term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array.

[0045] An example of a programmable mirror array can be a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation. Using an appropriate filter, the said undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic methods.

[0046] An example of a programmable LCD array is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0047] Figure 1 illustrates a block diagram of various subsystems of a lithographic projection apparatus 10A, according to an embodiment of the present disclosure. Major components are a radiation source 12 A, which may be a deep-ultraviolet excimer laser source or other type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have the radiation source), illumination optics which, e.g., define the partial coherence (denoted as sigma) and which may include optics 14 A, 16Aa and 16 Ab that shape radiation from the source 12A; a patterning device 18A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics may restrict the range of beam angles that impinge on the substrate plane 22A, where the largest possible angle defines the numerical aperture of the projection optics NA= n sin(0_max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics, and 0_max is the largest angle of the beam exiting from the projection optics that can still impinge on the substrate plane 22A.

[0048] In a lithographic projection apparatus, a source provides illumination (i.e. radiation) to a patterning device and projection optics direct and shape the illumination, via the patterning device, onto a substrate. The projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in U.S. Patent Application Publication No. 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related only to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB) and development). Optical properties of the lithographic projection apparatus (e.g., properties of the illumination, the patterning device and the projection optics) dictate the aerial image and can be defined in an optical model. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics. Details of techniques and models used to transform a design layout into various lithographic images (e.g., an aerial image, a resist image, etc.), apply OPC using those techniques and models and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosures of each are hereby incorporated by reference in their entirety. [0049] One aspect of understanding a lithographic process is understanding the interaction of the radiation and the patterning device. The electromagnetic field of the radiation after the radiation passes the patterning device may be determined from the electromagnetic field of the radiation before the radiation reaches the patterning device and a function that characterizes the interaction. This function may be referred to as the mask transmission function (which can be used to describe the interaction by a transmissive patterning device and/or a reflective patterning device).

[0050] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has either of two values (e.g., zero and a positive constant) at any given location on the patterning device. A mask transmission function in the binary form may be referred to as a binary mask. Another form is continuous. Namely, the modulus of the transmittance (or reflectance) of the patterning device is a continuous function of the location on the patterning device. The phase of the transmittance (or reflectance) may also be a continuous function of the location on the patterning device. A mask transmission function in the continuous form may be referred to as a continuous tone mask or a continuous transmission mask (CTM). For example, the CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) instead of a binary value of either 0 or 1. In an embodiment, CTM may be a pixelated gray scale image, where each pixel having values (e.g., within a range [-255, 255], normalized values within a range [0, 1] or [-1, 1] or other appropriate ranges).

[0051] The thin-mask approximation, also called the Kirchhoff boundary condition, is widely used to simplify the determination of the interaction of the radiation and the patterning device. The thin-mask approximation assumes that the thickness of the structures on the patterning device is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin-mask approximation assumes the electromagnetic field after the patterning device is the multiplication of the incident electromagnetic field with the mask transmission function. However, as lithographic processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device become smaller and smaller, the assumption of the thin-mask approximation can break down. For example, interaction of the radiation with the structures (e.g., edges between the top surface and a sidewall) because of their finite thicknesses (“mask 3D effect” or “M3D”) may become significant. Encompassing this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of the radiation with the patterning device. A mask transmission function under the thin-mask approximation may be referred to as a thin-mask transmission function. A mask transmission function encompassing M3D may be referred to as a M3D mask transmission function.

[0052] According to an embodiment of the present disclosure, one or more images may be generated. The images includes various types of signal that may be characterized by pixel values or intensity values of each pixel. Depending on the relative values of the pixel within the image, the signal may be referred as, for example, a weak signal or a strong signal, as may be understood by a person of ordinary skill in the art. The term “strong” and “weak” are relative terms based on intensity values of pixels within an image and specific values of intensity may not limit scope of the present disclosure. In an embodiment, the strong and weak signal may be identified based on a selected threshold value. In an embodiment, the threshold value may be fixed (e.g., a midpoint of a highest intensity and a lowest intensity of pixel within the image. In an embodiment, a strong signal may refer to a signal with values greater than or equal to an average signal value across the image and a weak signal may refer to signal with values less than the average signal value. In an embodiment, the relative intensity value may be based on percentage. For example, the weak signal may be signal having intensity less than 50% of the highest intensity of the pixel (e.g., pixels corresponding to target pattern may be considered pixels with highest intensity) within the image. Furthermore, each pixel within an image may considered as a variable. According to the present embodiment, derivatives or partial derivative may be determined with respect to each pixel within the image and the values of each pixel may be determined or modified according to a cost function based evaluation and/or gradient based computation of the cost function. For example, a CTM image may include pixels, where each pixel is a variable that can take any real value.

[0053] Figure 2 illustrates an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment of the present disclosure. Source model 31 represents optical characteristics (including radiation intensity distribution and/or phase distribution) of the source. Projection optics model 32 represents optical characteristics (including changes to the radiation intensity distribution and/or the phase distribution caused by the projection optics) of the projection optics. Design layout model 35 represents optical characteristics of a design layout (including changes to the radiation intensity distribution and/or the phase distribution caused by design layout 33), which is the representation of an arrangement of features on or formed by a patterning device. Aerial image 36 can be simulated from 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 contours and CDs in the resist image.

[0054] More specifically, it is noted that source model 31 can represent the optical characteristics of the source that include, but not limited to, numerical aperture settings, illumination sigma (o) settings as well as any particular illumination shape (e.g., off-axis radiation sources such as annular, quadrupole, dipole, etc.). Projection optics model 32 can represent the optical characteristics of the projection optics, including aberration, distortion, one or more refractive indexes, one or more physical sizes, one or more physical dimensions, etc. Design layout model 35 can represent one or more physical properties of a physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. The objective of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope and/or CD, which can then be compared against an intended design. The intended design is generally defined as a pre-OPC design layout which can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0055] From this design layout, one or more portions may be identified, which are referred to as “clips”. In an embodiment, a set of clips is extracted, which represents the complicated patterns in the design layout (typically about 50 to 1000 clips, although any number of clips may be used). These patterns or clips represent small portions (i.e. circuits, cells or patterns) of the design and more specifically, the clips typically represent small portions for which particular attention and/or verification is needed. In other words, clips may be the portions of the design layout, or may be similar or have a similar behavior of portions of the design layout, where one or more critical features are identified either by experience (including clips provided by a customer), by trial and error, or by running a full-chip simulation. Clips may contain one or more test patterns or gauge patterns.

[0056] An initial larger set of clips may be provided a priori by a customer based on one or more known critical feature areas in a design layout which require particular image optimization. Alternatively, in another embodiment, an initial larger set of clips may be extracted from the entire design layout by using some kind of automated (such as machine vision) or manual algorithm that identifies the one or more critical feature areas.

[0057] In a lithographic projection apparatus, as an example, a cost function may be expressed as

[0058] where (z_t,z₂, ••• , z_N) are N design variables or values thereof. f_p(z₁,z₂, ••• , z_N~) can be a function of the design variables (z_t, z₂, • • • , z_N~) such as a difference between an actual value and an intended value of a characteristic for a set of values of the design variables of (z_t, z₂, • • • , z_N~). w_p is a weight constant associated with f_p(z₁,z₂, ••• , z_N~). For example, the characteristic may be a position of an edge of a pattern, measured at a given point on the edge. Different f_p (z_t, z₂, • • • , z_N~) may have different weight w_p. For example, if a particular edge has a narrow range of permitted positions, the weight w_p for the f_p (z_t, z₂ , • • • , z_N~) representing the difference between the actual position and the intended position of the edge may be given a higher value. f_p (z_t, z₂, • • • , z_N~) can also be a function of an interlayer characteristic, which is in turn a function of the design variables (z_t, z₂, • • • , z_N~). Of course, CF(z_t,z₂, ••• , z_N) is not limited to the form in Eq. 1. CF(z_t,z₂, ••• , z_w) can be in any other suitable form.

[0059] The cost function may represent any one or more suitable characteristics of the lithographic projection apparatus, lithographic process or the substrate, for instance, focus, CD, image shift, image distortion, image rotation, stochastic variation, throughput, local CD variation, process window, an interlayer characteristic, or a combination thereof. In one embodiment, the design variables

(z_t, z₂ , • • • , z_N~) comprise one or more selected from dose, global bias of the patterning device, and/or shape of illumination. Since it is the resist image that often dictates the pattern on a substrate, the cost function may include a function that represents one or more characteristics of the resist image. For example, f_p (z_t, z₂ , • • • , z_N~) can be simply a distance between a point in the resist image to an intended position of that point (i.e., edge placement error EPE_p z₁, z₂, ••• , z_N~). The design variables can include any adjustable parameter such as an adjustable parameter of the source, the patterning device, the projection optics, dose, focus, etc.

[0060] The lithographic apparatus may include components collectively called a “wavefront manipulator” that can be used to adjust the shape of a wavefront and intensity distribution and/or phase shift of a radiation beam. In an embodiment, the lithographic apparatus can adjust a wavefront and intensity distribution at any location along an optical path of the lithographic projection apparatus, such as before the patterning device, near a pupil plane, near an image plane, and/or near a focal plane. The wavefront manipulator can be used to correct or compensate for certain distortions of the wavefront and intensity distribution and/or phase shift caused by, for example, the source, the patterning device, temperature variation in the lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, etc. Adjusting the wavefront and intensity distribution and/or phase shift can change values of the characteristics represented by the cost function. Such changes can be simulated from a model or actually measured. The design variables can include parameters of the wavefront manipulator.

[0061] The design variables may have constraints, which can be expressed as (z_t, z₂, • • • , z_N~) 6 Z, where Z is a set of possible values of the design variables. One possible constraint on the design variables may be imposed by a desired throughput of the lithographic projection apparatus. Without such a constraint imposed by the desired throughput, the optimization may yield a set of values of the design variables that are unrealistic. For example, if the dose is a design variable, without such a constraint, the optimization may yield a dose value that makes the throughput economically impossible. However, the usefulness of constraints should not be interpreted as a necessity. For example, the throughput may be affected by the pupil fill ratio. For some illumination designs, a low pupil fill ratio may discard radiation, leading to lower throughput. Throughput may also be affected by the resist chemistry. Slower resist (e.g., a resist that requires higher amount of radiation to be properly exposed) leads to lower throughput.

[0062] Optimization of the lithographic process (e.g., OPC or “freeform” OPC) to generate features on a mask design (or “image” of a mask design) can result in what is referred to herein as an OPC pattern. However, such optimization can sometimes result in an OPC pattern that has an unwanted joining or breaking of features that were in an initial OPC pattern contour, etc. [0063] Embodiments of the present disclosure can generate recovered OPC patterns that reduce or eliminate unwanted features, such as those described above. This recovery can be done by determining locations where a local arc length is too large (e.g., indicating a large deviation), where a minimum width exists (e.g., indicating a joining), etc. Once such recovery locations are found, the pixel intensities in the mask image can be modified to generate a recovered OPC pattern reflective of the modified mask image.

[0064] Figure 3 depicts examples of recovered OPC patterns, according to an embodiment of the present disclosure. Inset 310 shows a Manhattan target pattern 311 having two main features 314 (e.g., representing bars, lines, vias, etc.) and a sub-resolution assist feature (SRAF) 316. In this example, an initial OPC pattern contour 312 is joined rather than separated into three distinct curvilinear patterns corresponding to the target pattern 311. The initial OPC pattern contour 312 bounds the shaded region representing, for example, distinct pixel values in a mask image. In this example, the mask features can be the shaded portion(s) and the “background” of the mask image shown unshaded.

[0065] Recovery locations 320 can be identified by the disclosed processes for correction of the initial OPC pattern contour 312. Pixel values/intensity in the mask image can be modified at or around recovery locations 320 to generate a recovered OPC pattern 322 (e.g., without the joining present in the initial OPC pattern contour 312).

[0066] As used herein, “recovery locations” (e.g., for modifying pixel values) can be a point, region, or area along/around a line. In the examples of Figure 3, recovery locations 320 are depicted as points, while in the example of Figure 51, the recovery locations are depicted as lines (chords). By modifying pixels around recovery locations 320, a recovered OPC pattern 322 can be generated which, in this example, recovers the intended separation of the two main features 314 with the SRAF 316 and thus has a reduced deviation from the target pattern.

[0067] Inset 330 shows an example where an initial OPC pattern contour 332 includes two detached regions rather than being one continuous region corresponding to target pattern 331 - having a main feature and an assist feature (AF). Again, the initial OPC pattern contour 332 is indicated by the shaded regions, with an example of a recovery location 340 where the initial OPC pattern contour 332 can be corrected. A recovered OPC pattern 342 is shown that joins the two distinct regions of initial OPC pattern contour 332.

[0068] Inset 350 shows another example where an initial OPC pattern contour 352 (again indicated by the shaded regions) has examples of both types of deviations described above. Target pattern 351 is shown as including two main features that are not connected. However, one part of initial OPC pattern contour 352 has a separation (at recovery location 360) where there should not be one, while another part of the initial OPC pattern contour 352 includes a joining between the two main features. In this example, embodiments of the present disclosure can reduce the deviation from target pattern 351 and result in the shown recovered OPC pattern 362.

[0069] As used herein, the term “OPC pattern” can include initial and/or recovered OPC patterns that can be made up of one region, as shown in inset 310 or made up of multiple regions, as shown in inset 330 and inset 350. Accordingly, any “OPC pattern” described herein does not require nor imply being a single continuous pattern, nor require having any particular unconnected regions.

[0070] Figure 4 illustrates a process flow diagram for OPC pattern recovery, according to an embodiment of the present disclosure. While details of various embodiments are described further herein, in some embodiments, a method of generating a mask design can include, at 410, obtaining an initial OPC pattern contour resulting from an OPC process. At 420, a set of selected points can be determined on the initial OPC pattern contour. At 430, the method can include calculating metrics that describe arcs between the selected points along the initial OPC pattern contour. At 440, the method can include determining a recovery location based on the calculation of the metrics. At 450, the method can include generating a recovered OPC pattern based on the recovery location. Some embodiments can include separating the initial OPC pattern contour into two (or more) curvilinear patterns that form the recovered OPC pattern (such as shown by inset 310 in Figure 3). Other embodiments can include joining the initial OPC pattern contour having two curvilinear patterns into the recovered OPC pattern (such as shown by inset 330 in Figure 3).

[0071] Figures 5A-G illustrate a process for generating a recovered OPC pattern, according to an embodiment of the present disclosure. As an overview, recovery locations in the initial OPC pattern contour can be identified where, for example, the initial OPC pattern contour needs to be broken (or joined). Once the recovery locations are found, the disclosed processes for generating a recovered OPC pattern can include joining or separating portions of the initial OPC pattern contour at the identified recovery locations, modifying the shape of the OPC pattern, etc. In some embodiments, the method can include modifying a portion of the initial OPC pattern contour at a recovery location based on an arc length between selected points on the initial OPC pattern contour (see, e.g., second recovery location 546 in Figure 5C), which for example may indicate that the initial OPC pattern contour became too large in in response to the optimization process. Other embodiments can include joining or separating portions of the initial OPC pattern contour at a recovery location where a distance between opposing points on the initial OPC pattern contour is a minimum (see, e.g., second recovery location 548 in Figure 5C), which for example may indicate that the initial OPC pattern contour has joined in a place where it should not have. This can include not just analyzing differences in the sizes of the OPC patterns but also the shapes of the original Manhattan target patterns, such that separate Manhattan target patterns should correspond to separate mask patterns. Provided below are details for a specific example process. [0072] Figure 5A illustrates an example of a target pattern with and without corner rounding, according to an embodiment of the present disclosure. In some embodiments, an algorithm can perform obtaining Manhattan target pattern 510 and then determining sample points 512 on Manhattan target pattern 510 (which as explained below can refer to either a Manhattan target pattern or a target pattern with rounded corners, with both shown in Figure 5 A). Sample points 512 can be determined by, for example, at specific intervals along Manhattan target pattern 510 (e.g., some number of nanometers or other such distance measure). In other embodiments, the sample points can be determined by designating a given number of points with such points distributed evenly about the target pattern, based on a curvature of the target pattern (e.g., having more or less points where the curvature is higher or lower), etc.

[0073] To avoid situations where sample points 512 would fall on a corner of a Manhattan target pattern or other location where a normal direction (and thus a distance from the Manhattan target pattern, as discussed further with reference to Figure 5B) is poorly defined, some embodiments can include performing corner rounding on the Manhattan target pattern 510, where the sample points are the Manhattan target pattern 510 after the corner rounding. Such corner rounding can be an optional feature that may be performed on all, some, or none of the corners that may exist in a Manhattan target pattern. For example, in some embodiments the sample points 512 can be determined such that they do not fall on corners of the Manhattan target pattern, determined such that they are a maximum distance from corners of the Manhattan target pattern while still having a desired interval between them, etc. As such, it can be understood from the present disclosure that the sample points 512 can be located on target pattern 510, whether corner-rounded or purely Manhattan. Accordingly, as used herein, the term “Manhattan target pattern” is intended to cover both an original (Manhattan) target pattern or a Manhattan target pattern that has undergone some amount of corner rounding.

[0074] Figure 5B illustrates an example of projecting sample points to an initial OPC pattern contour, according to an embodiment of the present disclosure. The example process can include generating the selected points along the initial OPC pattern contour 530 by projecting the sample points 512 on the Manhattan target pattern 510 (with both Manhattan and corner-rounded versions shown) up to a threshold distance 516. Examples of selected points 520 are shown on the initial OPC pattern contour 530. However, it is also seen that not every sample point 512 may be able to be projected to the initial OPC pattern contour 530, such as where the initial OPC pattern contour 530 is outside of the threshold distance 516. In other embodiments, equivalents to selected points 520 can be directly assigned on the initial OPC pattern contour 530 (e.g., at a given interval) without using the projection methods disclosed herein. However, by certain embodiments limiting the selected points 520 to those within the threshold distance 516, this can permit a computationally efficient determination of points along the initial OPC pattern contour 530. In contrast, in embodiments where points are located along the initial OPC pattern contour 530 even outside the threshold distance 516, such points may be redundant for the process analyzing whether and where to modify the initial OPC pattern contour 530. [0075] Figure 5C is a diagram illustrating utilizing the selected points as starting points for finding locations to modify the initial OPC pattern contour, according to an embodiment of the present disclosure. Figure 5C particularly illustrates the algorithm establishing chords 540 between the selected points 520, where chords 540 can be utilized as the starting point for identifying recovery locations where the initial OPC pattern contour 530 can be modified. As described in greater detail in Figures 5E-5G, in some embodiments, the selected points 520 can be used for determining a first recovery location 546 to modify the initial OPC pattern contour 530 to have an arc length be a maximum permissible amount (Figure 5E) and/or for locating a second recovery location 548 (Figures 5F-5H) where there is a local minimum width.

[0076] Figure 5D is a diagram illustrating selected points along the initial OPC pattern contour, according to an embodiment of the present disclosure. Figure 5D shows an example sequence of selected points 520 labelled as 1, 2, 3, etc. Selected points 520 on initial OPC pattern contour 530 can include a first point (e.g., point 1), a second point (e.g., point 2) adjacent to the first point, etc., that can form the sequence of the selected points 520. The sequence can define respective chords 540 between adjacent selected points 520 that generally follow the initial OPC pattern contour 530, with some exceptions being where the initial OPC pattern contour 530 has significant deviations from the Manhattan target pattern 510 and thus the chords do not correspond to adjacent sample points 512. At any two adjacent selected points, the disclosed process can perform the operations described below, for example determining metrics that describe arcs between the selected points (for comparing to an arc length threshold) and/or determining additional metrics for identifying a minimum width location, with such determinations indicating recovery locations where the initial OPC pattern contour 530 should be modified. Also, as used herein, “adjacent” refers to selected points adjacent in the sequence, which may not be the same as adjacent geometrically on the initial OPC pattern contour (see, e.g., Figures 6A-D).

[0077] Figure 5E is a diagram illustrating stepping along points on an initial OPC pattern contour to find a recovery location where the initial OPC pattern contour can be modified based on calculation of an arc length, according to an embodiment of the present disclosure. It will be appreciated that the present disclosure is not limited to any specific metrics or characterizations in the calculation of an arc length, and not limited to any specific criteria related to arc length in determining a recovery location. In such embodiments, the calculated metrics that describes arcs between the selected points can include an arc length. In the example shown in Figure 5E, the algorithm can step from the first point (e.g., point 9) and the second point (e.g., point 10) to other points along the initial OPC pattern contour 530 in the direction indicated by the arrows. The stepping can be stopped when an arc length 560 (shown by the heavier line in Figure 5E) between selected points 520 is greater than an arc length threshold. At any given step, arc length 560 can be calculated as the sum of a) arc lengths between a first point and a second point (e.g., selected points 8 and 9) to respective points along the initial OPC pattern contour 530 (in direction of the arrows), and b) the distance along the chord between the two points where the stepping operation currently is. In various embodiments, the chord used to define the second recovery location 548 can be based on the cord that first exceeded the arc length threshold or the chord that directly preceded the arc length threshold. In some embodiments, the arc length threshold can be a preset value (e.g., 10 nm, 20 nm, etc.). In other embodiments, the arc length threshold can be determined according to Eq. 2:

Arc length threshold = A X + B. (Eq. 2)

Eq. 2 calculates the arc length threshold as the sum of a multiple (A) of a chord length (X) for chord 543 between the first projected point (point 8) and the second projected point (point 9) and an offset length (B). Once either stop condition (e.g., a minimum width or the arc length threshold) is reached, the process can then generate a recovered OPC pattern based on the points where the stepping was stopped.

[0078] In some embodiments, prior to the stepping operations described above that calculate various arc lengths, the process can include determining a chord length between the first point and the second point (e.g., selected points 8 and 9). Then, the stepping (and stopping) operations described above can be performed unless the arc length is less than a chord length threshold. In various embodiments, the chord length threshold can be 110%, 120%, 140%, etc. of the chord length. In other embodiments, the chord length threshold can be a constant addition to the chord length (e.g., lOnm + chord length), for example, additions of 5nm, lOnm, 20nm, etc. In some embodiments, the minimum width determination (described below) can similarly be skipped if the above conditions are met. Such embodiments can improve computational efficiency by avoiding calculations of arc lengths and/or finding of local minimum widths for locations on the initial OPC pattern contour that quite likely would not have excessive arc lengths or a local minimum width.

[0079] Figure 5F is a diagram illustrating stepping along the initial OPC pattern contour to find a local minimum width, according to an embodiment of the present disclosure. In some embodiments, a recovery location can be determined to be at or near a local minimum width of the initial OPC pattern contour. As described further herein, the algorithm can also check at any given step to determine whether the points indicate a local minimum at or near the points. Where points indicate a nearby local minimum, the chord representing the minimum width can be set as second recovery location 548 where the initial OPC pattern contour 530 can be modified. For cases where neither stop condition is met (e.g., permissible arc lengths, no local minimum width found), the stepping can continue until subsequent points either meet or cross. At such time, the disclosed processes can continue with the next pair of adjacent selected points 520.

[0080] Figure 5G is a diagram illustrating calculating local angles to find a local minimum width, according to an embodiment of the present disclosure. As shown in Figure 5G, points 541 along the initial OPC pattern contour 530 from selected points 520 can be determined. Also, the algorithm can calculate additional metrics that include local angles indicating a converging or diverging of the initial OPC pattern contour 530.

[0081] As one example shown by inset 550 in Figure 5G, the algorithm can determine that the local minimum width exists by calculating local angles 552 at the points connected by various chords 540, 542, 544, etc. The chords can be generated by stepping through successive points on either side of the initial OPC pattern contour, as shown by this example. The local angles 552 can represent whether the initial OPC pattern contour 530 is diverging (both greater than 90 degrees) or converging (both less than 90 degrees) during the stepping. As seen in inset 550, when local angles 552 transition from both being less than 90° to both be greater than 90° this can be identified as a minimum width location. In Figure 5G, the stepping has not yet identified a minimum width location and so would continue until arriving at the situation shown in Figure 5H.

[0082] Figure 5H is a diagram illustrating the minimum width of an initial OPC pattern contour 530, according to an embodiment of the present disclosure. The process of stepping along the initial OPC pattern contour 530 described with reference to Figure 5G can continue until existence of a minimum width is indicated. The minimum width location is illustrated in Figure 5H, with the corresponding local angles 552 depicted showing that they are both greater than 90°. Accordingly, the process can include stopping the stepping can occur when the local angles 552 at points 522 indicate a local minimum width 546.

[0083] Figure 51 is a diagram illustrating generating a recovered OPC pattern by changing pixel intensities, according to an embodiment of the present disclosure. As shown in Figure 51, mask image 570 can be used to generate initial OPC pattern contour 530, for example, with the pixel intensities describing the mask transmission. The initial OPC pattern contour 530 would then correspond to edges of mask features as determine/optimized, for example, with optical proximity correction. Continuing the previous example, the algorithm can then change intensities of pixels in mask image 570 at the recovery location(s).

[0084] Figure 51 shows that the intensities of the pixels can be changed in region(s) surrounding the recovery location(s) 546 and 548 (e.g., from white to gray). In some embodiments, as shown by the example of Figure 5, intensities of the pixels can be changed to be closer to external intensities of pixels outside the initial OPC pattern contour 530. This can have the effect of making the initial OPC pattern contour 530 smaller or introducing separations. In other embodiments, the intensities of the pixels can be changed to be closer to internal intensities of pixels inside the initial OPC pattern contour 530. This can have the effect of making the initial OPC pattern contour 530 larger or introducing joining between separated portions of the initial OPC pattern contour 530.

[0085] As seen in the modified image, changing pixel intensities in region 580 can have the effect of separating the initial OPC pattern contour 530 (e.g., into a first curvilinear pattern 590 and a second curvilinear pattern 592. Also, region 582 identified as having an impermissible arc length can be modified in a similar manner. The recovered OPC pattern 594 can be generated based on the image with the changed pixels. In this example, recovered OPC pattern 594 can include first recovered OPC pattern 590 and second recovered OPC pattern 592.

[0086] Figure 6A is a diagram illustrating selected points on a separated initial OPC pattern contour, according to an embodiment of the present disclosure. Panel 610 shows an example Manhattan target pattern 620 and a corresponding initial OPC pattern contour 630 that includes a first curvilinear pattern 632 and a second curvilinear pattern 634. It can be seen that the initial OPC pattern contour 630 should not be separated.

[0087] Panel 640 depicts determining projection lines 650 representing the threshold distance for which selected points will be determined on the initial OPC pattern contour 630. However, in this example, rather than performing corner rounding of the Manhattan target pattern 620, a similar result can be obtained by performing a spline fit or other such operation to generate a modified Manhattan target pattern 622 without corners. Projection lines 650 are shown as extending a threshold distance from the modified Manhattan target pattern 622.

[0088] Panel 660 depicts selected points 670 on first initial OPC pattern contour 632 and second initial OPC pattern contour 634 where projection lines 650 (in panel 640) were intersected. Similar to other examples herein, there are portions of first curvilinear pattern 632 and second initial OPC pattern contour 634 that do not contain selected points 670 and this region is where the disclosed processes can be utilized to join first initial OPC pattern contour 632 and second initial OPC pattern contour 634.

[0089] Figure 6B is a diagram illustrating an intrinsic ordering of the selected points, according to an embodiment of the present disclosure. Selected points 670 can form number of pairs of points where operations similar to those described herein can be performed. However, certain embodiments of the present disclosure can establish that the points have what is referred to herein as “an intrinsic ordering” that acts to specify which selected points 670 are utilized for determining recovery locations where the initial OPC pattern contour 630 will be modified. In general, the intrinsic ordering is one that follows the target pattern 620 in a single direction. In Figure 6B, the selected points 670 are shown with numbering zero, 1, 2, 3... 27, 28, and 29, as proceeding counterclockwise about target pattern 620. In various embodiments, the starting point or direction of any intrinsic ordering can vary, with Figure 6B showing just one example. [0090] Figure 6C is a diagram illustrating determining recovery locations for pixel modification, according to an embodiment of the present disclosure. Checking for various conditions (e.g., a minimum width or an impermissible arc length) can occur at any pair of adjacent selected points (e.g., 2 and 3, 3 and 4, etc.). However, as seen in panel 680, the intrinsic order can result in the chord used for analysis (as described in prior examples herein) to be between selected points 670 labelled 5 and 6 (with stepping direction shown by the arrows) rather than between selected points 5 and 27. Inset 682 shows an example of a first recovery location 684 where the minimum width is (starting from selected points 5 and 6). Inset 686 shows an example of a second recovery location 688 where the calculated arc length (again starting from selected points 5 and 6) is longer than an arc length threshold. Either or both of first recovery location 684 and second recovery location 688 can be utilized to modify pixel values to generate a recovered OPC pattern.

[0091] Figure 6D is a diagram illustrating generation of a recovered OPC pattern joining the separated initial OPC pattern contour, according to an embodiment of the present disclosure. Panel 690 depicts a first region 694 and a second region 698 (corresponding to first recovery location 684 and second recovery location 688 in Figure 6C). These regions can be utilized to modify the pixel values of a corresponding image to generate recovered OPC pattern 696. Panel 692 depicts an example of recovered OPC pattern 696, showing the joining of the first initial OPC pattern contour 632 and second initial OPC pattern contour 634 (from figure 6A).

[0092] Figure 7 is a block diagram of an example computer system CS, according to an embodiment of the present disclosure.

[0093] Computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processor) coupled with bus BS for processing information. Computer system CS also includes a main memory MM, such as a random access memory (RAM) or other dynamic storage device, coupled to bus BS for storing information and instructions to be executed by processor PRO. Main memory MM also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor PRO. Computer system CS further includes a read only memory (ROM) ROM or other static storage device coupled to bus BS for storing static information and instructions for processor PRO. A storage device SD, such as a magnetic disk or optical disk, is provided and coupled to bus BS for storing information and instructions.

[0094] Computer system CS may be coupled via bus BS to a display DS, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device ID, including alphanumeric and other keys, is coupled to bus BS for communicating information and command selections to processor PRO. Another type of user input device is cursor control CC, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor PRO and for controlling cursor movement on display DS. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0095] According to one embodiment, portions of one or more methods described herein may be performed by computer system CS in response to processor PRO executing one or more sequences of one or more instructions contained in main memory MM. Such instructions may be read into main memory MM from another computer-readable medium, such as storage device SD. Execution of the sequences of instructions contained in main memory MM causes processor PRO 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 MM. In an alternative embodiment, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0096] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor PRO for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device SD. Volatile media include dynamic memory, such as main memory MM. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus BS. 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. Computer-readable media can be non-transitory, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge. Non- transitory computer readable media can have instructions recorded thereon. The instructions, when executed by a computer, can implement any of the features described herein. Transitory computer- readable media can include a carrier wave or other propagating electromagnetic signal.

[0097] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor PRO for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system CS 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 BS can receive the data carried in the infrared signal and place the data on bus BS. Bus BS carries the data to main memory MM, from which processor PRO retrieves and executes the instructions. The instructions received by main memory MM may optionally be stored on storage device SD either before or after execution by processor PRO.

[0098] Computer system CS may also include a communication interface CI coupled to bus BS. Communication interface CI provides a two-way data communication coupling to a network link NDL that is connected to a local network LAN. For example, communication interface CI 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, communication interface CI may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface CI sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0099] Network link NDL typically provides data communication through one or more networks to other data devices. For example, network link NDL may provide a connection through local network LAN to a host computer HC. This can include data communication services provided through the worldwide packet data communication network, now commonly referred to as the “Internet” INT. Local network LAN (Internet) both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network data link NDL and through communication interface CI, which carry the digital data to and from computer system CS, are exemplary forms of carrier waves transporting the information.

[00100] Computer system CS can send messages and receive data, including program code, through the network(s), network data link NDL, and communication interface CI. In the Internet example, host computer HC might transmit a requested code for an application program through Internet INT, network data link NDL, local network LAN and communication interface CI. One such downloaded application may provide all or part of a method described herein, for example. The received code may be executed by processor PRO as it is received, and/or stored in storage device SD, or other nonvolatile storage for later execution. In this manner, computer system CS may obtain application code in the form of a carrier wave.

[00101] Figure 8 is a schematic diagram of a lithographic projection apparatus, according to an embodiment of the present disclosure.

[00102] The lithographic projection apparatus can include an illumination system IL, a first object table MT, a second object table WT, and a projection system PS.

[00103] Illumination system IL, can condition a beam B of radiation. In this particular case, the illumination system also comprises a radiation source SO.

[00104] First object table (e.g., patterning device table) MT can be provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS. [00105] Second object table (substrate table) WT can be provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS.

[00106] Projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) can image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[00107] As depicted herein, the apparatus can be of a transmissive type (i.e., has a transmissive patterning device). However, in general, it may also be of a reflective type, for example (with a reflective patterning device). The apparatus may employ a different kind of patterning device to classic mask; examples include a programmable mirror array or LCD matrix.

[00108] The source SO (e.g., a mercury lamp or excimer laser, LPP (laser produced plasma) EUV source) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning apparatuses, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting device AD for setting the outer and/or inner radial extent (commonly referred to as G-outcr and G-inncr, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[00109] In some embodiments, source SO may be within the housing of the lithographic projection apparatus (as is often the case when source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus, the radiation beam that it produces being led into the apparatus (e.g., with the aid of suitable directing mirrors); this latter scenario can be the case when source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[00110] The beam PB can subsequently intercept patterning device MA, which is held on a patterning device table MT. Having traversed patterning device MA, the beam B can pass through the lens PL, which focuses beam B onto target portion C of substrate W. With the aid of the second positioning apparatus (and interferometric measuring apparatus IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of beam PB. Similarly, the first positioning apparatus can be used to accurately position patterning device MA with respect to the path of beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT can be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning).

However, in the case of a stepper (as opposed to a step-and-scan tool) patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[00111] The depicted tool can be used in two different modes, step mode and scan mode. In step mode, patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single “flash”) onto a target portion C. Substrate table WT can be shifted in the x and/or y directions so that a different target portion C can be irradiated by beam PB.

[00112] In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single “flash.” Instead, patterning device table MT is movable in a given direction (the so-called “scan direction”, e.g., the y direction) with a speed v, so that projection beam B is caused to scan over a patterning device image; concurrently, substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, in which M is the magnification of the lens PL (typically, M = 1/4 or 1/5). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[00113] Figure 9 is a schematic diagram of another lithographic projection apparatus (LPA), according to an embodiment of the present disclosure.

[00114] LPA can include source collector module SO, illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation), support structure MT, substrate table WT, and projection system PS.

[00115] Support structure (e.g., a patterning device table) MT can be constructed to support a patterning device (e.g., a mask or a reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[00116] Substrate table (e.g., a wafer table) WT can be constructed to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate.

[00117] Projection system (e.g., a reflective projection system) PS can be configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[00118] As here depicted, LPA can be of a reflective type (e.g., employing a reflective patterning device). It is to be noted that because most materials are absorptive within the EUV wavelength range, the patterning device may have multilayer reflectors comprising, for example, a multi-stack of molybdenum and silicon. In one example, the multi-stack reflector has a 40 layer pairs of molybdenum and silicon where the thickness of each layer is a quarter wavelength. Even smaller wavelengths may be produced with X-ray lithography. Since most material is absorptive at EUV and x-ray wavelengths, a thin piece of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multi-layer reflector) defines where features would print (positive resist) or not print (negative resist).

[00119] Illuminator IL can receive an extreme ultraviolet radiation beam from source collector module SO. Methods to produce EUV radiation include, but are not necessarily limited to, converting a material into a plasma state that has at least one element, e.g., xenon, lithium or tin, with one or more emission lines in the EUV range. In one such method, often termed laser produced plasma ("LPP") the plasma can be produced by irradiating a fuel, such as a droplet, stream or cluster of material having the line-emitting element, with a laser beam. Source collector module SO may be part of an EUV radiation system including a laser for providing the laser beam exciting the fuel. The resulting plasma emits output radiation, e.g., EUV radiation, which is collected using a radiation collector, disposed in the source collector module. The laser and the source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation. [00120] In such cases, the laser may not be considered to form part of the lithographic apparatus and the radiation beam can be passed from the laser to the source collector module with the aid of a beam delivery system comprising, for example, suitable directing mirrors and/or a beam expander. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often termed as a DPP source.

[00121] Illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as o- outer and o-inncr, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[00122] The radiation beam B can be incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., patterning device table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor PS2 (e.g., an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of radiation beam B. Similarly, the first positioner PM and another position sensor PSI can be used to accurately position the patterning device (e.g., mask) MA with respect to the path of the radiation beam B. Patterning device (e.g., mask) MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[00123] The depicted apparatus LPA could be used in at least one of the following modes, step mode, scan mode, and stationary mode.

[00124] In step mode, the support structure (e.g., patterning device table) MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed.

[00125] In scan mode, the support structure (e.g., patterning device table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto target portion C (i.e. a single dynamic exposure). The velocity and direction of 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.

[00126] In stationary mode, the support structure (e.g., patterning device table) MT is kept essentially stationary holding a programmable patterning device, and substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array.

[00127] Figure 10 is a detailed view of the lithographic projection apparatus, according to an embodiment of the present disclosure.

[00128] As shown, LPA can include the source collector module SO, the illumination system IL, and the projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained in an enclosing structure ES of the source collector module SO. An EUV radiation emitting hot plasma HP may be formed by a discharge produced plasma source. EUV radiation may be produced by a gas or vapor, for example Xe gas, Li vapor or Sn vapor in which the hot plasma HP is created to emit radiation in the EUV range of the electromagnetic spectrum. The hot plasma HP is created by, for example, an electrical discharge causing at least partially ionized plasma. Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may be required for efficient generation of the radiation. In an embodiment, a plasma of excited tin (Sn) is provided to produce EUV radiation.

[00129] The radiation emitted by the hot plasma HP is passed from a source chamber SC into a collector chamber CC via an optional gas barrier or contaminant trap CT (in some cases also referred to as contaminant barrier or foil trap) which is positioned in or behind an opening in source chamber SC. The contaminant trap CT may include a channel structure. Contamination trap CT may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier CT further indicated herein at least includes a channel structure, as known in the art.

[00130] The collector chamber CC may include a radiation collector CO which may be a so-called grazing incidence collector. Radiation collector CO has an upstream radiation collector side US and a downstream radiation collector side DS. Radiation that traverses radiation collector CO can be reflected off a grating spectral filter SF to be focused in a virtual source point IF along the optical axis indicated by the dot-dashed line ‘O’. The virtual source point IF can be referred to as the intermediate focus, and the source collector module can be arranged such that the intermediate focus IF is located at or near an opening OP in the enclosing structure ES. The virtual source point IF is an image of the radiation emitting plasma HP.

[00131] Subsequently the radiation traverses the illumination system IL, which may include a facetted field mirror device FM and a facetted pupil mirror device PM arranged to provide a desired angular distribution of the radiation beam B, at the patterning device MA, as well as a desired uniformity of radiation amplitude at the patterning device MA. Upon reflection of the beam of radiation B at the patterning device MA, held by the support structure MT, a patterned beam PB is formed and the patterned beam PB is imaged by the projection system PS via reflective elements RE onto a substrate W held by the substrate table WT.

[00132] More elements than shown may generally be present in illumination optics unit IL and projection system PS. The grating spectral filter SF may optionally be present, depending upon the type of lithographic apparatus. Further, there may be more mirrors present than those shown in the figures, for example there may be 1- 6 additional reflective elements present in the projection system PS.

[00133] Collector optic CO can be a nested collector with grazing incidence reflectors GR, just as an example of a collector (or collector mirror). The grazing incidence reflectors GR are disposed axially symmetric around the optical axis O and a collector optic CO of this type may be used in combination with a discharge produced plasma source, often called a DPP source.

[00134] Figure 11 is a detailed view of source collector module SO of lithographic projection apparatus LPA, according to an embodiment of the present disclosure.

[00135] Source collector module SO may be part of an LPA radiation system. A laser LA can be arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), creating the highly ionized plasma HP with electron temperatures of several 10's of eV. The energetic radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by a near normal incidence collector optic CO and focused onto the opening OP in the enclosing structure ES.

[00136] The concepts disclosed herein may simulate or mathematically model any generic imaging system for imaging sub wavelength features and may be especially useful with emerging imaging technologies capable of producing increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography that is capable of producing a 193nm wavelength with the use of an ArF laser, and even a 157nm wavelength with the use of a Fluorine laser. Moreover, EUV lithography is capable of producing wavelengths within a range of 20-50nm by using a synchrotron or by hitting a material (either solid or a plasma) with high energy electrons in order to produce photons within this range. [00137] While the concepts disclosed herein may be used for imaging on a substrate such as a silicon wafer, it shall be understood that the disclosed concepts may be used with any type of lithographic imaging systems, e.g., those used for imaging on substrates other than silicon wafers.

[00138] The combinations and sub-combinations of the elements disclosed herein constitute separate embodiments and are provided as examples only. Also, the descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made as described without departing from the scope of the claims set out below.

[00139] In the following, further features, characteristics, and exemplary technical solutions of the present disclosure will be described in terms of clauses that may be optionally claimed in any combination:

1. A method of generating a mask design comprising: obtaining an initial OPC pattern contour resulting from an OPC process; determining a set of selected points on the initial OPC pattern contour; calculating metrics that describe arcs between the selected points along the initial OPC pattern contour; determining a recovery location based on the calculation of the metrics; and generating a recovered OPC pattern based on the recovery location.

2. The method of Clause 1, further comprising modifying a portion of the initial OPC pattern contour at a recovery location based on an arc length between selected points on the initial OPC pattern contour.

3. The method of any one of the preceding Clauses, further comprising joining or separating a portion of the initial OPC pattern contour at a recovery location where a distance between opposing points on the initial OPC pattern contour is a minimum.

4. The method of any one of the preceding Clauses, further comprising: changing intensities of pixels at the recovery location in a mask image corresponding to the initial OPC pattern contour, wherein the recovered OPC pattern is generated based on the mask image with the changed pixels.

5. The method of any one of the preceding Clauses, wherein the intensities of the pixels are changed to be closer to internal intensities of pixels inside the initial OPC pattern contour.

6. The method of any one of the preceding Clauses, wherein the intensities of the pixels are changed to be closer to external intensities of pixels outside the initial OPC pattern contour.

7. The method of any one of the preceding Clauses, wherein the intensities of the pixels are changed in a region surrounding the recovery location.

8. The method of any one of the preceding Clauses, further comprising: determining sample points on a Manhattan target pattern; and generating the selected points along the initial OPC pattern contour by projecting the sample points on the Manhattan target pattern up to a threshold distance.

9. The method of any one of the preceding Clauses, further comprising performing corner rounding on the Manhattan target pattern, wherein the sample points are on the Manhattan target pattern after the corner rounding. 10. The method of any one of the preceding Clauses, wherein the selected points on the initial OPC pattern contour include a first point and a second point adjacent to the first point in a sequence of the selected points, and wherein the metrics include an arc length, the method further comprising: stepping from the first point and the second point to points along the initial OPC pattern contour; stopping the stepping when the arc length is equal to or greater than an arc length threshold; and generating the recovered OPC pattern based on the points where the stepping was stopped.

11. The method of any one of the preceding Clauses, further comprising calculating the arc length to be the sum of a) arc lengths between first point and the second point to the respective points along the initial OPC pattern contour, and b) a distance between the points at the current step.

12. The method of any one of the preceding Clauses, further comprising determining a chord length between the first point and the second point, wherein the stepping and stopping are performed unless the arc length is less than a chord length threshold.

13. The method of any one of the preceding Clauses, wherein the chord length threshold is 120% of the chord length.

14. The method of any one of the preceding Clauses, wherein the arc length threshold is a multiple of a chord length between the first point and the second point and includes an offset length.

15. The method of any one of the preceding Clauses, the method further comprising: calculating additional metrics as local angles indicating a converging or diverging of the initial OPC pattern contour; and stopping the stepping when the local angles at the points indicate a local minimum width.

16. A non- transitory machine-readable medium storing instructions which, when executed by the at least one programmable processor, cause the at least one programmable processor to perform the method comprising those of any one of Clauses 1-15.

17. A system comprising: at least one programmable processor; and a non-transitory machine- readable medium storing instructions which, when executed by the at least one programmable processor, cause the at least one programmable processor to perform the method comprising those of any one of Clauses 1-15.

Claims

1. A non-transitory machine-readable medium storing instructions which, when executed by the at least one programmable processor, cause the at least one programmable processor to perform a method of generating a mask design, the method comprising: obtaining an initial OPC pattern contour resulting from an OPC process; determining a set of selected points on the initial OPC pattern contour; calculating metrics that describe arcs between the selected points along the initial OPC pattern contour; determining a recovery location based on the calculation of the metrics; and generating a recovered OPC pattern based on the recovery location.

2. The medium of claim 1, wherein the method further comprises modifying a portion of the initial OPC pattern contour at a recovery location based on an arc length between selected points on the initial OPC pattern contour.

3. The medium of claim 1, wherein the method further comprises joining or separating a portion of the initial OPC pattern contour at a recovery location where a distance between opposing points on the initial OPC pattern contour is a minimum.

4. The medium of claim 1, wherein the method further comprises: changing intensities of pixels at the recovery location in a mask image corresponding to the initial OPC pattern contour, wherein the recovered OPC pattern is generated based on the mask image with the changed pixels.

5. The medium of claim 4, wherein the intensities of the pixels are changed to be closer to internal intensities of pixels inside the initial OPC pattern contour.

6. The medium of claim 4, wherein the intensities of the pixels are changed to be closer to external intensities of pixels outside the initial OPC pattern contour.

7. The medium of claim 4, wherein the intensities of the pixels are changed in a region surrounding the recovery location.

8. The medium of claim 1, wherein the method further comprises: determining sample points on a Manhattan target pattern; and generating the selected points along the initial OPC pattern contour by projecting the sample points on the Manhattan target pattern up to a threshold distance.

9. The medium of claim 8, wherein the method further comprises performing corner rounding on the Manhattan target pattern, wherein the sample points are on the Manhattan target pattern after the corner rounding.

10. The medium of claim 8, wherein the selected points on the initial OPC pattern contour include a first point and a second point adjacent to the first point in a sequence of the selected points, and wherein the metrics include an arc length, the medium further comprising: stepping from the first point and the second point to points along the initial OPC pattern contour; stopping the stepping when the arc length is equal to or greater than an arc length threshold; and generating the recovered OPC pattern based on the points where the stepping was stopped.

11. The medium of claim 10, wherein the method further comprises calculating the arc length to be the sum of a) arc lengths between first point and the second point to the respective points along the initial OPC pattern contour, and b) a distance between the points at the current step.

12. The medium of claim 10, wherein the method further comprises determining a chord length between the first point and the second point, wherein the stepping and stopping are performed unless the arc length is less than a chord length threshold.

13. The medium of claim 12, wherein the chord length threshold is 120% of the chord length.

14. The medium of claim 10, wherein the arc length threshold is a multiple of a chord length between the first point and the second point and includes an offset length.

15. The medium of claim 10, wherein the method further comprises: calculating additional metrics as local angles indicating a converging or diverging of the initial OPC pattern contour; and stopping the stepping when the local angles at the points indicate a local minimum width.