Method, software, and system for constant width subresolution assist feature determination

Abstract

Methods, software, and systems are disclosed for determining a mask pattern. The determination may include obtaining a mask pattern including sub-resolution assist features (SRAFs), each having a constant width. The widths are set as continuous variables, so that they can be optimized together with other variables in a mask optimization process of the mask pattern. Then, based on their population and / or statistical values, the optimized continuous widths are discretized into a limited number of global width levels. Further mask optimization processes may be performed on the SRAFs with the discretized optimized global width levels, and the widths assigned to individual SRAFs may be adjusted to different levels of the global width levels.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to International Application No. PCT / CN2021 / 137860, filed December 14, 2021, which is incorporated by reference in its entirety into this specification.

[0002]

[0002] The description herein relates generally to mask making and patterning processes. More specifically, the present disclosure includes an apparatus, method, and computer program for determining sub-resolution assist features. [Background technology]

[0003] Lithographic projection apparatus may be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device (e.g. a mask) may contain or be provided with a pattern (a "design layout") corresponding to an individual layer of the IC, and this pattern may be transferred onto a target portion (e.g. comprising one or more dies) on a substrate (e.g. a silicon wafer) that is coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the pattern on the patterning device. Generally, a single substrate will contain several adjacent target portions (one target portion at a time) onto which the pattern is successively transferred by the lithographic projection apparatus. In one type of lithographic projection apparatus, the pattern on the entire patterning device is transferred onto one target portion at a time; such an apparatus may also be referred to as a stepper. In an alternative apparatus, a step-and-scan apparatus may move the substrate parallel or anti-parallel to a given reference direction (the "scan" direction) in synchronization with the projection beam scanning the patterning device in this reference direction. Different parts of a pattern on the patterning device are transferred progressively onto one target portion. Typically, a lithographic projection apparatus has a demagnification ratio M (e.g. 4), so that the speed F at which the substrate is moved is 1 / M times the speed at which the projection beam scans the patterning device. More information on lithographic devices can be found, for example, in U.S. Pat. No. 6,046,792, which is incorporated herein by reference.

[0004]

[0004] Before 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 undergo other procedures ("post procedures") such as a post bake (PEB), development, a hard bake, and measurement / inspection of the transferred pattern. This multitude of procedures is used as a basis for making the individual layers of a device, e.g. an IC. The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all intended to finish off the individual layers of the device. If several layers are required for the device, the entire procedure, or a variant of it, is repeated for each layer. Finally, a device is present on each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, so that the individual devices can be mounted on a carrier, connected to pins, etc.

[0005]

[0005] Thus, manufacturing a device such as a semiconductor device typically involves processing a substrate (e.g., a semiconductor wafer) using several manufacturing processes to form various features and layers of the device. Such layers and features are typically manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on a substrate and then separated into individual devices. This device manufacturing process can be considered a patterning process. The patterning process includes a patterning step to transfer a pattern on a patterning device to a substrate, such as optical lithography and / or nanoimprint lithography using a patterning device in a lithography apparatus, and typically, but optionally, includes one or more associated pattern processing steps, such as developing a resist with a developer, baking the substrate using a bake tool, and etching using the pattern using an etcher.

[0006]

[0006] As mentioned above, lithography is a central step in the manufacture of devices such as ICs, where patterns formed on a substrate define the functional elements of devices such as microprocessors, memory chips, etc. Similar lithographic techniques are also used in the formation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007]

[0007] As semiconductor manufacturing processes continue to improve, the dimensions of functional elements are continually decreasing, while the amount of functional elements, such as transistors, per device has been steadily increasing for decades, following a trend known as "Moore's Law". In the current state of the art, device layers are fabricated using lithographic projection apparatus that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, producing individual functional elements with 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]

[0008] This process, in which features with dimensions below the classical resolution limit of the lithographic projection apparatus are printed, can be called low k1 lithography with the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation used (e.g., 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (typically the smallest feature size to be printed), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it is to reproduce a pattern on a substrate that closely resembles the shape and dimensions planned by the designer to achieve a 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 are 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 called "optical and process correction") in the design layout, or other methods commonly defined as "resolution enhancement techniques" (RET). As used herein, the term "projection optics" should be broadly interpreted to encompass various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and catadioptric optics. The term "projection optics" may also include components that collectively or independently operate according to any of these design types to direct, shape, or control a projection beam of radiation. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located on the optical path of the lithographic projection apparatus. The projection optics may include optical components for shaping, conditioning, and / or projecting radiation from the source before it passes through the patterning device and / or optical components for shaping, conditioning, and / or projecting radiation after it has passed through the patterning device. The projection optics generally excludes the source and the patterning device. Summary of the Invention

[0009]

[0009] According to one embodiment, a method for determining a mask pattern includes obtaining a mask pattern including sub-resolution assist features (SRAFs) each having a constant width, and adjusting the width in a mask optimization process of the mask pattern.

[0010]

[0010] In some embodiments, the method may also include accessing an initial discrete width level defined for the SRAF and assigning a width from the initial discrete width level to be the initial width. The method may include generating SRAF edges, where the SRAF edges may be generated to be approximately equidistant from a ridge point corresponding to the location of the SRAF. In some embodiments, the generated SRAF edges may be curved. Also, the ridge points may be determined such that the SRAF edges vary smoothly. In some embodiments, the ridge points may be determined from an SRAF guidance map (SGM), where the ridge points are located between the corresponding SRAF edges.

[0011]

[0011] In some embodiments, generating the SRAF edge may include performing an interpolation of at least two ridge points when a distance between the two ridge points exceeds a distance limit, the interpolation generating an interpolated ridge point. The interpolated ridge point may be generated at a midpoint of a segment between the two ridge points. The interpolated ridge point may be generated along a spline interpolation curve between the two ridge points, the spline interpolation curve being generated utilizing at least one other ridge point.

[0012]

[0012] Generating the SRAF edges may include generating control points at both ends of a segment perpendicular to a ridge point of the SRAF, the segment having a length corresponding to a constant width of the SRAF.

[0013]

[0013] In some embodiments, the method may also include adding a tip to the SRAF edge.

[0014] In some embodiments, the width of each SRAF may be set as a continuous variable that is optimized by a mask optimization process. The mask optimization process may include simulating a lithography process utilizing a lithography model, predicting imaging properties of the mask simulated by the lithography model, and adjusting the width of one or more SRAFs to optimize the imaging properties by use of a cost function related to the imaging properties.

[0015]

[0015] In some embodiments, the mask optimization process may include performing optical proximity correction optimization to generate boundaries of mask features including assist features (AF), and may also include optimizing the mask features while simultaneously simultaneously optimizing an illumination source in a source-mask optimization in a lithography system.

[0016]

[0016] In some embodiments, the cost function utilized in the mask optimization process may include parameters describing one or more of edge placement error, side lobe printing, mask rule check (MRC) compliance, or user-defined custom requirements, at least one of the parameters being a function of width.

[0017] In some embodiments, the method may include determining selected widths of the SRAF. The number of selected widths may be less than five.

[0018] In some embodiments, the method may include determining a population or population distribution of optimized widths, setting selected widths within a range of widths of the population or population distribution based on one or more rules, and setting the width of each SRAF to the closest selected width. The rules may include setting the selected widths evenly within the range of widths.

[0019] In some embodiments, the width of each SRAF may be a discrete variable that may be optimized by a further mask optimization process, where there are fewer discrete variables than there are SRAFs. Each discrete variable may correspond to a global width level. The global width level may be fixed during the mask optimization process, or the global width level may be optimized during the mask optimization process.

[0020]

[0020] In some embodiments, adjusting the width may include determining continuous widths of the SRAF as a continuous variable, discretizing the continuous widths of the SRAF into discrete widths, and continuing the mask optimization process by varying the width to be selected from the discrete widths.

[0021]

[0021] In some embodiments, there may be a non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer having at least one programmable processor, cause operations including any of the operations in the method embodiments described above.

[0022]

[0022] In some embodiments, there may be a system for determining a mask pattern, the system comprising at least one programmable processor and a non-transitory computer-readable medium having instructions recorded thereon that, when executed by a computer having at least one programmable processor, cause operations including any of the operations in the method embodiments described above.

[0023]

[0023] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain aspects of the subject matter disclosed herein and, together with the description, help to explain some of the principles associated with the disclosed implementations. [Brief description of the drawings]

[0024] [Figure 1] FIG. 1 shows a block diagram of various subsystems of a lithographic projection apparatus according to one embodiment of the present disclosure. [Diagram 2]

[0025] 1 shows an exemplary flowchart for simulating lithography in a lithographic projection apparatus, according to an embodiment of the present disclosure. [Diagram 3]

[0026] 1 illustrates an exemplary portion of a mask including main features (MF) and sub-resolution assist features (SRAF) according to one embodiment of the present disclosure. [Figure 4]

[0027] 1 illustrates an exemplary constant-width SRAF according to one embodiment of the present disclosure. [Diagram 5]

[0028] 1 illustrates an exemplary method for determining a mask pattern according to one embodiment of the present disclosure. [Figure 6]

[0029] 1 illustrates an example method for generating SRAF edges, according to one embodiment of the present disclosure. [Figure 7]

[0030] 1 illustrates an exemplary method for discretizing SRAF widths, according to one embodiment of the present disclosure. [Figure 8]

[0031] 1 illustrates a hybrid optimization method that includes optimizing width as both continuous and discrete values ​​in different parts of the optimization process, according to one embodiment of the present disclosure. [Figure 9]

[0032] FIG. 1 is a block diagram of an example computer system according to one embodiment of the present disclosure. [Figure 10]

[0033] 1 is a schematic diagram of a lithographic projection apparatus, according to one embodiment of the present disclosure; [Figure 11]

[0034] 2 is a schematic diagram of another lithographic projection apparatus, according to an embodiment; [Figure 12]

[0035] FIG. 1 depicts a detailed view of a lithographic projection apparatus, according to one embodiment of the present disclosure; [Figure 13]

[0036] FIG. 2 is a detailed diagram of a source collector module of a lithographic projection apparatus, according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025]

[0037] While specific reference may be made herein to the manufacture of ICs, it should be expressly understood that what is described herein has many other possible applications. For example, it may be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art will recognize that in the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" herein should be construed as synonymous with the more general terms "mask," "substrate," and "target portion," respectively.

[0026]

[0038] In this specification, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet, e.g., having wavelengths in the range of about 5 to 100 nm).

[0027]

[0039] A patterning device may include or form one or more design layouts. A design layout may be generated using a CAD (Computer Aided Design) program, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a predefined set of design rules to generate a functional design layout / patterning device. These rules are set by process and design limitations. For example, design rules may define the space tolerance between devices (gates, capacitors, etc.) or interconnect lines, which is done to ensure that they do not interact with each other in an undesirable manner. One or more of the design rule limitations may be referred to as a "critical dimension" (CD). A critical dimension of a device may 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 of device fabrication is to faithfully reproduce the original design intent on a substrate (via a patterning device).

[0028]

[0040] The terms "mask" or "patterning device" as used herein can be broadly interpreted to refer to any general patterning device that can be used to impart an incoming radiation beam with a patterned cross-section that corresponds to the pattern to be created in a target portion of a substrate, and the term "light valve" is also sometimes used in this context. In addition to traditional masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0029]

[0041] 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 a device is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect the incident radiation as undiffracted radiation. Using appropriate filters, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind, and in this way the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic methods.

[0030]

[0042] An example of a programmable LCD array is given in US Pat. No. 5,229,872, which is incorporated herein by reference.

[0031]

[0043] 1 shows a block diagram of various subsystems of a lithographic projection apparatus 10A, according to one embodiment. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other type of source including an extreme ultraviolet (EUV) source (as explained above, the lithographic projection apparatus itself need not have a radiation source), illumination optics, which may include, for example, optics 14A, 16Aa, and 16Ab that define the partial coherence (denoted by sigma) and shape the radiation from source 12A, a patterning device 18A, and a transmission optics 16Ac that projects an image of the patterning device pattern onto a substrate surface 22A. An adjustable filter or aperture 20A in a pupil plane of the projection optics can limit the range of beam angles impinging on the substrate surface 22A, where the maximum possible angle is determined by the numerical aperture of the projection optics, NA=nsin(Θ max ), n is the refractive index of the medium between the substrate and the last element of the projection optics, and Θ max is the maximum angle of the beam exiting the projection optics that can still impinge on the substrate surface 22A.

[0032]

[0044] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a patterning device, and a projection optics system guides and shapes the illumination through the patterning device and onto a substrate. The projection optics system may include at least some of the components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the 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 US Patent Application Publication No. 2009-0157630, the disclosure of which is incorporated herein in its entirety. The resist model is only concerned with the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-bake (PEB), and development). The optical properties of the lithographic projection apparatus (e.g., the properties of the illumination, the patterning device, and the projection optics system) dictate the aerial image, which can be defined in the optical model. Because the patterning device used in a lithographic projection apparatus may be varied, it is desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and projection optics. Details of the techniques and models used to convert the design layout into various lithographic images (e.g., aerial images, resist images, etc.), apply OPC using these techniques and models, and evaluate performance (e.g., in terms of process window) are described in U.S. Patent Application Publication Nos. 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the disclosures of each of which are incorporated herein by reference in their entirety.

[0033]

[0045] One aspect of understanding a lithographic process is to understand the interaction of radiation with a patterning device. The electromagnetic field of the radiation after it has passed through the patterning device can be determined from the electromagnetic field of the radiation before it reaches the patterning device and a function that characterizes the interaction. This function can be called the mask transmission function (the mask transmission function can be used to describe the interaction with a transmissive and / or reflective patterning device).

[0034]

[0046] The mask transmission function may have a variety of different forms. One form is binary. A binary mask transmission function has one of two values ​​(e.g., zero and a positive constant) at any location on the patterning device. A mask transmission function in binary form may be referred to as a binary mask. Another form is continuous. That is, the transmittance (or reflectance) of the patterning device is a continuous function of position on the patterning device. The phase of the transmission (or reflection) may also be a continuous function of position on the patterning device. A mask transmission function in continuous form may be referred to as a continuous tone mask or continuous transmission mask (CTM). For example, a CTM may be represented as a pixelated image, where each pixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3, etc.) rather than a binary value of either 0 or 1. In one embodiment, the CTM may be a pixelated grayscale image, where each pixel has a value (e.g., a value in the range [-255,255], a normalized value in the range [0,1] or [-1,1], or a value in another suitable range).

[0035]

[0047] To simplify the determination of the interaction of radiation with the patterning device, the thin-mask approximation, also called Kirchhoff's boundary conditions, is widely used. In the thin-mask approximation, it is assumed that the thickness of the structures on the patterning device is very small compared to the wavelength, and the width of the structures on the mask is very large compared to the wavelength. Thus, in the thin-mask approximation, it is assumed that the electromagnetic field after the patterning device is a multiplication of the incident electromagnetic field and the mask transmission function. However, as lithography processes use radiation of shorter and shorter wavelengths, and the structures on the patterning device are becoming smaller and smaller, the assumptions in the thin-mask approximation may break down. For example, the interaction of radiation with the structures (e.g., the edges between the top surface and the sidewalls) may become significant due to the finite thickness ("mask 3D effect" or "M3D"). Including this scattering in the mask transmission function may enable the mask transmission function to better capture the interaction of radiation with the patterning device. The mask transmission function under the thin-mask approximation may be referred to as the thin-mask transmission function. The mask transmission function including the M3D may be referred to as the M3D mask transmission function.

[0036]

[0048] According to an embodiment of the present disclosure, one or more images may be generated. The image includes various types of signals that may be characterized by a pixel value or intensity value of each pixel. As can be understood by one skilled in the art, depending on the relative values ​​of the pixels in the image, the signals may be referred to as, for example, weak signals or strong signals. The terms "strong" and "weak" are relative terms based on the intensity values ​​of the pixels in the image, and the specific values ​​of intensity are not intended to limit the scope of the present disclosure. In one embodiment, strong and weak signals may be identified based on a selected threshold value. In one embodiment, the threshold may be fixed (e.g., the midpoint between the highest and lowest intensity of pixels in the image. In one embodiment, a strong signal may refer to a signal having a value equal to or greater than the average signal value for the entire image, and a weak signal may refer to a signal having a value less than the average signal value. In one embodiment, the relative intensity values ​​may be based on a percentage. For example, a weak signal may be a signal having an intensity that is less than 50% of the highest intensity of the pixels in the image (e.g., a pixel corresponding to a target pattern may be considered to be the pixel having the highest intensity). Furthermore, each pixel in the image may be considered a variable. According to this embodiment, a derivative or partial derivative may be determined for each pixel in the image, and the value of each pixel may be determined or changed according to a cost function based evaluation and / or a gradient based cost function calculation. For example, a CTM image may include pixels, where each pixel is a variable that may take on any real value.

[0037]

[0049] FIG. 2 shows an exemplary flow chart for simulating lithography in a lithographic projection apparatus, according to an embodiment. The radiation source model 31 represents the optical characteristics of the radiation source (including radiation intensity distribution and / or phase distribution). The projection optics model 32 represents the optical characteristics of the projection optics (including changes to the radiation intensity distribution and / or phase distribution caused by the projection optics). The design layout model 35 represents the optical characteristics of the design layout (which is a representation of the arrangement of features on or formed by a patterning device) (including changes to the radiation intensity distribution and / or phase distribution caused by the design layout 33). An aerial image 36 can be simulated using the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using the resist model 37. For example, the lithography simulation can predict the contour and CD of the resist image.

[0038]

[0050] More specifically, it is noted that the source model 31 may represent the optical characteristics of the source, including, but not limited to, the numerical aperture setting, the illumination sigma (σ) setting, and any particular illumination shape (e.g., off-axis source, such as annular, quadrupole, dipole, etc.). The projection optics model 32 may represent the optical characteristics of the projection optics, including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc. The design layout model 35 may represent one or more physical characteristics of a physical patterning device, for example, as described in U.S. Pat. No. 7,587,704, which is incorporated by reference in its entirety. The goal of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and / or CD, which can then be compared to the intended design. The intended design is generally defined as a pre-OPC design layout, which may be provided in a standard digital file format, such as GDSII, or OASIS, or other file format.

[0039]

[0051] From this design layout, one or more portions (these are called "clips") can be identified. In one embodiment, a set of clips is extracted (typically about 50-1000 clips, although any number of clips can be used) that represent complex patterns in the design layout. These patterns or clips represent small portions of the design (i.e., circuits, cells, or patterns), and more specifically, clips typically represent small portions that require special attention and / or validation. That is, a clip may be a portion of the design layout, or may resemble, or have similar behavior of, a portion of the design layout where one or more critical features are identified by experience (including customer provided clips), by trial and error, or by running full chip simulations. A clip may include one or more test patterns or gauge patterns.

[0040]

[0052] The initial set of larger clips may be provided a priori by a customer based on one or more known critical feature areas in the design layout that require specific image optimization, or in another embodiment, the initial set of larger clips may be extracted from the entire design layout by using some type of automatic (such as machine vision) or manual algorithm that identifies one or more critical feature areas.

[0041]

[0053] In a lithographic projection apparatus, as an example, the cost function can be expressed as:

number

[0042]

[0054] The cost function may represent any one or more suitable characteristics of the lithographic projection apparatus, the lithographic process, or the substrate, such as focus, CD, image shift, image distortion, image rotation, stochastic variation, throughput, local CD variation, process window, inter-layer properties, or a combination thereof. In one embodiment, the design variables (z1, z2, ..., z N ) may include one or more selected from dose, global bias of the patterning device, and / or geometry of the illumination. Since it is often the resist image that determines the pattern on the substrate, the cost function may include a function that represents one or more characteristics of the resist image. For example, f p (z1, z2, …, z N ) is simply the distance between a point in the resist image and its intended location (i.e., the edge placement error EPE p (z1, z2, …, z N)) The design variables may include any adjustable parameters, such as adjustable parameters of the radiation source, the patterning device, the projection optics, the dose, the focus, etc.

[0043]

[0055] Lithographic apparatus may include components collectively referred to as "wavefront manipulators" that can be used to adjust the shape and intensity distribution and / or phase shift of a wavefront of a radiation beam. In an embodiment, the lithographic apparatus may adjust the wavefront and intensity distribution anywhere along the optical path of the lithographic projection apparatus, such as in front of a patterning device, near a pupil plane, near an image plane, and / or near a focal plane. The wavefront manipulator may be used to correct or compensate for certain distortions of the wavefront and intensity distribution and / or phase shift caused, for example, by temperature variations of the radiation source, the patterning device, the lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, etc. Adjusting the wavefront and intensity distribution and / or phase shift may change the value of the characteristic represented by the cost function. Such changes may be simulated from a model or may be measured in practice. The design variables may include parameters of the wavefront manipulator.

[0044]

[0056] There may be constraints on the design variables, which are (z1, z2, …, z N)∈Z, where Z is the set of possible values ​​of the design variables. One possible constraint on the design variables may be imposed by the desired throughput of the lithographic projection apparatus. Without such a constraint imposed by the desired throughput, optimization may produce an unrealistic set of values ​​for the design variables. For example, if dose is a design variable, without such a constraint, optimization may produce dose values ​​that make the throughput economically unfeasible. However, the usefulness of the constraint should not be interpreted as necessary. For example, throughput may be affected by pupil fill factor. In some illumination designs, a low pupil fill factor may waste radiation, leading to reduced throughput. Throughput may also be affected by the chemistry of the resist. A slower resist (e.g., a resist that requires a higher dose to be properly exposed) will result in reduced throughput.

[0045]

[0057] As used herein, the term "patterning process" refers to the process of creating an etched substrate by applying a specified pattern of light as part of a lithography process.

[0046]

[0058] As used herein, the term "target pattern" means the ideal pattern to be etched on a substrate.

[0047]

[0059] As used herein, the term "printed pattern" refers to a physical pattern on a substrate that is etched based on a target pattern. The printed pattern can include, for example, troughs, channels, depressions, edges, or other two- and three-dimensional features that are generated from a lithographic process.

[0048]

[0060] As used herein, the term "process model" refers to a model that includes one or more models that simulate a patterning process. For example, a process model can include any combination of an optical model (e.g., which may include modeling the lens / projection system used to deliver light in a lithography process and modeling the final optical image of the light that reaches the photoresist), a resist model (e.g., which models the physical effects of the resist, such as chemical effects caused by the light), an OPC model (e.g., which may be used to create a target pattern and may include sub-resolution resist features (SRAFs), etc.), and an imaging device model (e.g., which models what an imaging device can image from a printed pattern).

[0049]

[0061] As used herein, the term "imaging device" refers to any number or combination of devices and associated computer hardware and software that can be configured to generate an image of a target, such as a print pattern or a portion thereof. Non-limiting examples of imaging devices include scanning electron microscopes (SEMs), x-ray machines, and the like.

[0050]

[0062] As used herein, the term "calibrate" means to change (eg, improve or adjust) and / or verify something, such as a process model.

[0051]

[0063] FIG. 3 shows an example portion of a mask including a main feature (MF) and a sub-resolution assist feature (SRAF). The mask simulation / optimization process described herein may be utilized to generate a mask (or mask pattern) including MFs that generally match desired features (e.g., circuit traces) to be printed utilizing the mask. FIG. 3 depicts an example portion of a mask pattern 300 with several simplified example MFs 310. Due to manufacturing limitations, diffraction effects, or other indirect or fine-scale effects, the mask pattern may also be generated to include assist features (AFs) and / or SRAFs. AFs are not depicted in the example of FIG. 3, but should be understood to be slight deviations to the shape of the main feature. Such examples may include widening and / or narrowing the main feature in certain locations to facilitate accurate printing with the mask, placing notches at the corners of the main feature, etc. However, the present disclosure is primarily directed to determining features related to SRAFs. 3, the SRAFs 320 are mask features that are separate from the primary (and assist) features and are further utilized on the mask so that the final printed pattern better approximates the target pattern. In general, the SRAFs can vary in shape, including varying width along the SRAF. However, as described in more detail herein, the present disclosure provides a process for the determination and generation of SRAFs where each SRAF can have a constant width.

[0052]

[0064] As used herein, the term "constant width" means that the width of the SRAF is substantially constant (e.g., varies by no more than 5%) along its length. Such variations in the final physical mask containing the SRAF may result from manufacturing uncertainties. However, the calculated / simulated "constant width" SRAF described herein may have similar small variations that may result from, for example, the splines used to form the edges of the nominally "constant width" SRAF.

[0053]

[0065] FIG. 4 illustrates an exemplary constant-width SRAF. The shape of the SRAF generated by the mask optimization / generation process can vary considerably to accommodate the complex shapes required to optimize the simulated mask. Thus, it should be understood that the example of an S-shaped SRAF 410 depicted in FIG. 4 is exemplary, and that SRAFs of any shape are considered to be within the scope of this disclosure. In the embodiments used herein, the overall structure of the SRAF can be considered to have an SRAF "skeleton," and the SRAF in FIG. 4 has a skeleton 420 depicted in dashed lines at the center of the SRAF. Thus, the SRAF skeleton 420 generally represents where the SRAF should be in the mask pattern. The location of the SRAF can be determined in a mask optimization process that can include optimizing a continuous-tone (gray-tone) image (sometimes referred to as an SRAF guidance map (SGM) or CTM) that indicates where the SRAF may be placed to improve printing with the resist made with the final mask. The SGM can have detectable variations that can appear as ridges, thereby indicating candidate locations for the SRAF.

[0054]

[0066] In general, the width of an SRAF may vary and, in some implementations, may be part of an optimization process. However, this disclosure describes a process for determining / optimizing the width of an SRAF where the width of an individual SRAF is constant. The exemplary SRAF depicted in FIG. 4 should be understood to have a constant width 430 (i.e., having substantially the same distance vertically on either side of the SRAF backbone). Also depicted is an exemplary tip 440 of the SRAF that may be included to close the SRAF at an open end.

[0055]

[0067] 5 illustrates an exemplary method for determining a mask pattern. Optional initial method steps 510 and 520 are described below. In some embodiments, the method may include obtaining a mask pattern having SRAFs each having a constant width, at 530. The method may also include adjusting the widths in a mask optimization process of the mask pattern, at 540. For example, referring again to FIG. 3, while the depicted SRAFs appear to have the same width, the disclosed mask optimization process may vary / determine the constant width of the individual SRAFs needed to best fit the printing requirements.

[0056]

[0068] In some embodiments, the initial width may be selected from a group of predetermined widths. For example, the method of FIG. 5 may include, at 510, accessing an initial discrete width level defined for the SRAF. Then, at 520, the method may include assigning a width from the initial discrete width level to be the initial width.

[0057]

[0069] Throughout this disclosure, the terms "discrete" and "continuous" are used in connection with various embodiments to describe the width of an SRAF or a variable that represents the width of an SRAF. As used herein, the term "discrete" refers to a number (e.g., width) that can be varied during an optimization process, but is selected from a finite number of available discrete widths. Examples of "discrete" widths can be 5 nm, 7 nm, 10 nm, etc. In contrast, the term "continuous" refers to a number / width that can be varied in small increments during an optimization process. Examples of "continuous" widths can range, for example, from 3 to 15 nm, and examples of variations in such ranges are from 5.0 nm, to 5.01 nm, to 5.000001 nm, or any other type of small variation. The specific numerical values ​​of widths given herein are considered to be examples only, as the actual values ​​will depend heavily on the particular implementation.

[0058]

[0070] The initial widths may then be varied by the mask optimization process. Depending on the implementation, the initial widths may remain discrete or may be treated as discrete or continuous, depending on the particular implementation. For example, as described in more detail below, FIG. 8 illustrates an embodiment in which the mask optimization process may move from optimizing continuous widths to optimizing discrete widths.

[0059]

[0071] Before discussing how the width of the SRAF may be varied / optimized, embodiments related to generating the actual SRAF edge are disclosed. Although embodiments are described in detail in relation to generating the SRAF using a ridge, the disclosure is not limited thereto. Any suitable method may be used without departing from the scope of the disclosure. FIG. 6 illustrates an exemplary method for generating an SRAF edge. As previously discussed, candidate locations for the SRAF may be determined at specific locations on a mask pattern, such as points corresponding to a ridge. The upper left portion of FIG. 6 depicts several points 610, referred to herein as "ridge points," illustrating exemplary locations along the ridge. As illustrated throughout FIG. 6, the disclosed method may include generating an SRAF edge that may be generated approximately equidistant from the ridge point 610, which corresponds to the skeleton of the SRAF. The generated SRAF edge may be curved (e.g., as shown in FIG. 3), but in other embodiments may be substantially straight or have various sections that are straight or curved (e.g., as depicted in the example of FIG. 4). In some implementations, the ridge points may be determined such that the SRAF edge varies smoothly. In some implementations, the ridge points may be determined from the SGM according to the previous discussion regarding determining the SRAF positions. Thus, the ridge points may be located between corresponding SRAF edges, which will be described in more detail with reference to the remaining portions of FIG.

[0060]

[0072] The top right portion of FIG. 6 depicts an exemplary next step in the SRAF generation process. Looking at the top left portion of the SRAF skeleton, it can be seen that there are two segments 620 near the center of the SRAF skeleton whose segment lengths (the distance between the ridge points 610 corresponding to the endpoints) are significantly longer than the other segments of the SRAF skeleton. To make the distribution of ridge points more uniform, generating the SRAF edge may include performing an interpolation of at least two ridge points. This may be done, for example, when the distance between two ridge points exceeds a distance limit, whereby the interpolation generates an interpolated ridge point 630. The system may perform the interpolation when certain criteria are met, such as the absolute distance between ridge points (e.g., greater than 5 nm, 10 nm, etc.), the relative distance between ridge points (e.g., greater than 1.5 times or greater than 2.0 times the average spacing between ridge points), or other criteria. In some embodiments, such as that shown in the top right of FIG. 6, linear interpolation may be used such that an interpolated ridge point 630 may be generated at the midpoint of a segment 632 between two ridge points, while in other implementations the interpolated ridge point may be anywhere along the segment. In some implementations, the interpolated ridge point may be generated along a spline interpolated curve 640 between two ridge points. In some implementations, the spline interpolated curve may be generated using at least one other ridge point to result in a more constrained and potentially more realistic curve. The top right portion illustrates an example of what a spline interpolated curve may look like, although only exemplary linearly interpolated ridge points are shown.

[0061]

[0073] Proceeding to the lower left portion of FIG. 6, in some embodiments, generating the SRAF edge may include generating control points 650 at either end of a segment 652 that is perpendicular to the ridge points of the SRAF. As used herein, the term "control point" refers to a point along the final SRAF. As shown, the segment may have a length that corresponds to a constant width of the SRAF. It should be understood that, in this disclosure, the segments depicted in FIG. 6 are primarily for illustration purposes only, and that a computational algorithm that generates an SRAF based on ridge points need not literally calculate, generate, or display any of the depicted segments. For example, the depicted control points may simply be calculated to be in the appropriate location based on knowing the perpendicular direction at the corresponding ridge point.

[0062]

[0074] Also depicted in the bottom left portion of Figure 6 is an example where two of the segments (660, 662) intersect, and the use of such a point may result in artifacts or other irregularities in the resulting SRAF. In some embodiments, there may be a smoothing algorithm that may remove such irregularities. In this example, the two colliding segments are depicted as being merged into a single segment 664.

[0063]

[0075] The bottom right portion depicts the generation of an SRAF edge 670 based on control points. As shown, the SRAF edge can pass through the control points, e.g., it can be generated by one or more splines passing through any number of control points. As discussed above with respect to the definition of "constant width," a close inspection of the edge of the example SRAF reveals that the width of the SRAF may not be precisely constant along the length of the SRAF, depending on the particular features of the splines used to generate it (e.g., spline tension). Thus, again, it should be understood that when this disclosure refers to a constant width SRAF, it is to be construed to include such minor variations. In some embodiments, the generation of the SRAF may include adding a tip 680 to the SRAF edge, where appropriate. Such a tip may be semicircular, semi-elliptical, etc. In some embodiments, the tip may also be a direct closure (e.g., a line) between two control points at the end of the SRAF edge.

[0064]

[0076] As described with reference to the method of Figure 5, certain embodiments of the present disclosure may include certain methods for optimizing the width of the SRAF to obtain the best possible printing results. Depending on the implementation, the width may be treated as a continuous or discrete variable.

[0065]

[0077] In some embodiments, the width of each SRAF may be set as a continuous variable that is optimized by a mask optimization process. In this manner, the mask optimization process may allow the width to be varied with very high precision or with fine gradients to obtain an optimal set of SRAFs in the simulated mask. For example, such continuous variables may be treated as floating-point values ​​and may describe the optimized width with a relatively large number of decimal places (e.g., 3, 5, 7, etc.). Thus, such an implementation may have the technical advantage of providing a highly optimized mask pattern.

[0066]

[0078] Such implementations may be incorporated into a mask optimization process that may include, for example, simulating a lithography process utilizing a lithography model, predicting imaging properties of a mask simulated by the lithography model, and adjusting widths of one or more SRAFs to optimize the imaging properties by use of a cost function related to the imaging properties. The lithography model may include performing optical proximity correction optimization to generate boundaries of mask features including assist features. In other embodiments, the lithography model may further include optimizing the mask features and co-optimizing an illumination source in a source-mask optimization (SMO) in the lithography system.

[0067]

[0079] Although cost functions and their use in optimizing lithography processes have been described above (in a general sense), in some implementations consistent with those disclosed in optimizing SRAFs, a cost function associated with a constant width SRAF may be utilized in the mask optimization process. The cost function may include parameters describing one or more of edge placement error, sidelobe printing, MRC compliance, or user-defined custom requirements, where at least one of the parameters is a function of width. As an example, the cost function may be Cost(S), which is a function (e.g., a sum) of cost functions for any combination of such parameters.

number

[0068]

[0080] FIG. 7 illustrates an exemplary method for discretizing SRAF widths. The depicted method represents the ability of some disclosed embodiments to determine a selected width of an SRAF. This determination may be based on statistics of the resulting widths of the SRAFs from the optimization process presented above. In various embodiments, rather than each SRAF having its own individual width, an SRAF may have a certain number of widths, each with its own distinct value. In some embodiments, the number of selected widths may be less than 5, but may also be, for example, less than 10, less than 4, or exactly 2, 3, 5, 10, etc. One exemplary method with three widths is depicted in FIG. 7 by four graphs where a large population of different widths are adjusted to be one of the three widths.

[0069]

[0081] The top portion of Figure 7 shows that the method may include determining a population 710 or population distribution of optimized widths. The population is represented by a curve with the width of the SRAF on the horizontal axis and the number of SRAFs having that width on the vertical axis. There may be dozens or even hundreds of SRAFs, each with their own width, and the "population" of such may be represented by a histogram with any, but typically fine-scale binning. Again, the depicted graph does not require that the system be able to generate a curve representing such a histogram, but only that the population of SRAFs at a particular width be quantified.

[0070]

[0082] 7 shows three example widths within the range of widths covered by the population of SRAFs, where the method may include setting the selected widths (e.g., widths 722, 724, 726) within the range of widths of the population based on one or more rules. In some embodiments, the rules may include setting the selected widths evenly within the range of widths such that the width values ​​are evenly separated or such that there is an even number (the same number) of SRAFs in each of the widths.

[0071]

[0083] The third portion of Figure 7 shows that the system may set the width of each SRAF to the closest selected width. This is shown by dividing the population into three regions (732, 734, 736) (depicted with different cross-hatching) and selecting the border between each region to be halfway between the adjacent selected widths (e.g., the border between regions 732 and 734 is between selected widths 722 and 724). The arrows indicate that the previously varying widths may then be changed or merged to the selected width for that region.

[0072]

[0084] And the fourth (bottom) portion of FIG. 7 shows the final width distribution, where all SRAFs have a width corresponding to the selected width 722, 724, or 726. The actual population may be the same for each width, but depending on the method of region determination, the number of SRAFs with the selected width may differ. The final result depicted has several technical advantages, including providing a mask pattern that utilizes a reduced number of widths while still being a substantially optimized solution. Condensing the SRAF widths in this manner can simplify (or meet) manufacturing requirements (where a huge number of SRAF widths may not be practical) while substantially maintaining the advantages of having SRAF widths determined by high-precision optimization. Also, in some embodiments, further optimization may be performed to arrive at the final widths.

[0073]

[0085] In other embodiments, rather than the width of the SRAF being a continuous variable that can be optimized, the width of each SRAF can be a discrete variable that can be optimized by a further mask optimization process. Thus, in such implementations, there may be fewer discrete variables than SRAFs. For example, there may be three discrete values ​​for the possible widths of many SRAFs. In some embodiments, the system may define a "global width level" as a width selected from a group of widths that are acceptable for an SRAF during optimization. Thus, in certain embodiments, each discrete variable may correspond to a global width level. An example of the relationship between acceptable SRAF widths, global width levels, and representation in terms of discrete variables is shown in the table below.

[0074] [Table 1]

[0075]

[0086] Referring back to the use of cost functions to perform mask optimization, a simplified expression of such a cost function (with a cost "S" to be minimized) that utilizes widths limited to certain global width levels, but can be varied to be any combination thereof, is shown below in Equation 2: S = CF(w i (x a,b,又はc ))(Formula 2)

[0076]

[0087] In various embodiments, the global width level may be fixed or optimized in the mask optimization process. For example, in embodiments that include fixing the global width level during the mask optimization process, the global width levels may be kept at their selected values ​​(e.g., 1.0 nm, 4.0 nm, and 5.7 nm from the exemplary table above) while other parameters that affect the cost function may be varied. In other embodiments, the method may include optimizing the global width level in the mask optimization process. For example, a constraint of the system may be that there are only three discrete width levels, but the three width levels may be optimized over a continuous range. Thus, for example, the system may determine that widths of 1.2, 4.37, and 6.245 are optimized global width levels for the SRAF. In another embodiment, the optimization may include selecting a global width level from the allowable widths such that use of the global width level by the SRAF results in an optimized solution. For example, the final cost of a particular solution with global width levels of 1.0 nm, 4.0 nm, and 5.7 nm may be higher (less optimal) than the final cost of a particular solution with global width levels of 2.0 nm, 4.0 nm, and 8.2 nm, and thus the optimized solution uses the latter set of global width levels for the SRAF in the mask pattern.

[0077]

[0088] FIG. 8 illustrates a composite optimization method that includes optimizing the width as both a continuous and discrete value at different portions of the optimization process. As shown in FIG. 8, adjusting the width of the SRAF (540) may include the following additional operations (810-830). Operation 810 may include determining a continuous width of the SRAF. This operation may be similar to that depicted in the top portion of FIG. 7 where the SRAF width may be continuously optimized. Operation 820 may include discretizing the continuous width of the SRAF into discrete widths. This operation may also be similar to that depicted in the second through fourth portions of FIG. 7 where the previously determined continuous widths are converted to any of the specified discrete widths via any of the disclosed algorithms. These additional operations may continue by continuing the mask optimization process at 830 by varying the width to be selected from the discrete widths. Once such discrete widths are determined, one example where the optimization process may determine the best combination of SRAF widths from the discrete widths was described above with reference to Equation 1.

[0078]

[0089] FIG. 9 is a block diagram of an exemplary computer system CS according to one embodiment of the present disclosure.

[0079]

[0090] The computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processors) coupled to the bus BS for processing information. The computer system CS also includes a main memory MM, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus BS for storing information and instructions executed by the processor PRO. The main memory MM may also be used to store temporary variables or other intermediate information during execution of instructions executed by the processor PRO. The computer system CS further includes a read-only memory (ROM) ROM or other static storage device coupled to the bus BS for storing static information and instructions for the processor PRO. A storage device SD, such as a magnetic or optical disk for storing information and instructions, is provided and coupled to the bus BS.

[0080]

[0091] The computer system CS may be coupled via a bus BS to a display DS, such as a cathode ray tube (CRT), 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 the bus BS for communicating information and command selections to the processor PRO. Another type of user input device is a cursor control CC, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to the processor PRO and for controlling cursor movement on the display DS. This input device generally has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), allowing the device to be located in a plane. A touch panel (screen) display may also be used as an input device.

[0081]

[0092] According to an embodiment, parts of one or more methods described herein may be performed by the computer system CS in response to the processor PRO executing one or more sequences of one or more instructions contained in the main memory MM. Such instructions may be read into the main memory MM from another computer-readable medium, such as a storage device SD. Execution of the sequences of instructions contained in the main memory MM causes the processor PRO to perform the process steps described herein. One or more processors of a multi-processing arrangement may be used to execute the sequences of instructions contained in the main memory MM. In an alternative embodiment, hardwired circuitry may be used in place of or in combination with software instructions. The description herein is therefore not limited to any particular combination of hardware circuitry and software.

[0082]

[0093] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to a processor PRO for execution. Such media 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 a storage device SD. Volatile media include dynamic memories, such as a main memory MM. Transmission media include coaxial cables, copper wires, and optical fibers (including the wires that comprise the bus BS). Transmission media may 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 may be non-transitory, such as floppy disks, flexible disks, hard disks, magnetic tapes, other magnetic media, CD-ROMs, DVDs, other optical media, punch cards, paper tapes, other physical media with patterns of holes, RAM, PROMs, and EPROMs, FLASH-EPROMs, other memory chips or cartridges. Non-transitory computer-readable media may have instructions recorded on them. The instructions, when executed by a computer, may implement any of the features described herein. The transitory computer-readable medium may include a carrier wave or a propagating electromagnetic signal.

[0083]

[0094] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the processor PRO for execution. For example, the instructions may initially reside on a magnetic disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system CS may receive the data on the telephone line and convert the data to an infrared signal using an infrared transmitter. An infrared detector coupled to the bus BS may receive the data carried in the infrared signal and place the data on the bus BS. The bus BS carries the data to the main memory MM, from which the processor PRO reads and executes the instructions. The instructions received by the main memory MM may optionally be stored on a storage device SD either before or after execution by the processor PRO.

[0084]

[0095] The computer system CS may also include a communications interface CI coupled to the bus BS. The communications interface CI also provides a bidirectional data communication coupling to a network link NDL connected to a local network LAN. For example, the communications interface CI may be an Integrated Services Digital Network (ISDN) card or a modem providing a data communication connection to a corresponding type of telephone line. As another example, the communications interface CI may be a Local Area Network (LAN) card providing a data communication connection to a compatible LAN. A wireless link may also be implemented. In such an implementation, the communications interface CI transmits and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0085]

[0096] The network link NDL typically provides data communication through one or more networks to other data devices. For example, the network link NDL may provide a connection to a host computer HC through a local network LAN. This includes the data communication services provided by the World Wide Packet Data Communications Network (now commonly referred to as the "Internet" INT). Both local networks LAN (Internet) use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network data link NDL and through the communications interface CI that carry digital data to and from the computer system CS are examples of forms of carrier waves conveying information.

[0086]

[0097] The computer system CS can send messages and receive data, including program code, through one or more networks, the network data link NDL, and the communication interface CI. In the Internet example, the host computer HC may send a request code for an application program through the Internet INT, the network data link NDL, the local network LAN, and the communication interface CI. One such downloaded application may provide, for example, all or part of the method described herein. The received code may be executed by the processor PRO as received and / or stored in the storage device SD or other non-volatile storage for later execution. In this way, the computer system CS can obtain the application code in the form of a carrier wave.

[0087]

[0098] FIG. 10 depicts a schematic diagram of a lithographic projection apparatus according to one embodiment.

[0088]

[0099] The lithographic projection apparatus may comprise an illumination system IL, a first object table MT, a second object table WT, and a projection system PS.

[0089]

[0100] The illumination system IL is capable of conditioning a beam of radiation B. In this particular case, the illumination system also includes a radiation source SO.

[0090]

[0101] A first object table (e.g., patterning device table) MT may be provided with a patterning device holder for holding a patterning device MA (e.g., a reticle) and connected to a first positioner for accurately positioning the patterning device relative to the item PS.

[0091]

[0102] A second object table (substrate table) WT may be provided with a substrate holder for holding a substrate W (e.g. a resist-coated silicon wafer) and connected to a second positioner for accurately positioning the substrate relative to the item PS.

[0092]

[0103] A projection system ("lens") PS (e.g. a refractive, reflective, or catadioptric system) may image the irradiated portion of the patterning device MA onto a target portion C of the substrate W (e.g. comprising one or more dies).

[0093]

[0104] As depicted herein the apparatus may be of a transmissive type (i.e. have a transmissive patterning device). In general, however, the apparatus may be of a reflective type (with a reflective patterning device), for example. The apparatus may employ different types of patterning devices, typically a mask. Examples include a programmable mirror array or an LCD matrix.

[0094]

[0105] A 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 to an illumination system (illuminator) IL, either directly or after having traversed an adjusting device, such as a beam expander Ex. The illuminator IL may comprise adjusting devices AD for setting the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution of the beam. Furthermore 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.

[0095]

[0106] In some embodiments, the source SO may be located within the housing of the lithographic projection apparatus (as is often the case when the source SO is, for example, a mercury lamp), but it may also be remote from the lithographic projection apparatus and the radiation beam that it generates is directed into the apparatus (for example by means of suitable directing mirrors). This latter scenario may be the case when the source SO is an excimer laser (for example based on KrF, ArF or F2 lasing).

[0096]

[0107] The beam PB may subsequently intersect the patterning device MA, which is held on a patterning device table MT. After traversing the patterning device MA, the beam B may pass through a lens PL that focuses the beam B onto a target portion C of the substrate W. Using the second positioner (and the interferometric measurement device IF), the substrate table WT can be precisely moved, e.g. to position a different target portion C in the path of the beam PB. Similarly, the first positioner can be used to precisely position the patterning device MA with respect to the path of the beam B, e.g. after mechanical retrieval of the patterning device MA from a patterning device library or during a scan. In general, movement of the object table MT, WT can be realized using 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) the patterning device table MT may be connected to a short-stroke actuator only, or may be fixed.

[0097]

[0108] The depicted tool can be used in two different modes: step mode and scan mode. In step mode, the patterning device table MT remains essentially stationary and the entire patterning device image is projected onto the target portion C in one go (i.e. in a single "flash"). The substrate table WT can be shifted in the x and / or y directions so that a different target portion C can be irradiated by the beam PB.

[0098]

[0109] In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT is movable in a given direction (the so-called "scan direction", e.g. the y direction) with a speed v, such that the projection beam B is caused to scan over the patterning device image. In parallel, the substrate table WT is simultaneously moved in the same or opposite direction with a speed V = Mv, in which M is the magnification factor of the lens PL (typically, M = 1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0099]

[0110] FIG. 11 is a schematic diagram of another lithographic projection apparatus (LPA) according to an embodiment.

[0100]

[0111] The LPA may comprise a source collector module SO, an illumination system (illuminator) IL configured to condition a radiation beam B (eg EUV radiation), a support structure MT, a substrate table WT, and a projection system PS.

[0101]

[0112] A support structure (eg patterning device table) MT is constructed to support a patterning device (eg mask or reticle) MA and may be connected to a first positioner PM configured to accurately position the patterning device.

[0102]

[0113] A substrate table (eg, a wafer table) WT is constructed to hold a substrate (eg, a resist-coated wafer) W and may be connected to a second positioner PW configured to accurately position the substrate.

[0103]

[0114] The projection system (eg, a reflective projection system) PS may be configured to project a pattern imparted to the radiation beam B by a patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0104]

[0115] As depicted here, the LPA can be reflective (e.g., using a reflective patterning device). Note that since most materials are absorbing in the EUV wavelength range, the patterning device can have a multi-layer reflector including, for example, multiple stacks of molybdenum and silicon. In one example, a multi-stack reflector has 40 layer pairs of molybdenum and silicon, with each layer being a quarter wavelength thick. Even smaller wavelengths can be produced using x-ray lithography. Since most materials are absorbing at EUV and x-ray wavelengths, a thin strip of patterned absorbing material (e.g., TaN absorber on a multi-layer reflector) on the patterning device topography defines where features will or will not print (positive resist) or print (negative resist).

[0105]

[0116] The illuminator IL may receive an extreme ultraviolet radiation beam from the source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) with one or more emission lines in the EUV range. In one such method, often referred to as laser-produced plasma ("LPP"), the plasma may be generated by irradiating a fuel, such as a droplet, stream, or cluster of a material having a line-emitting element, with a laser beam. The source collector module SO may be part of an EUV radiation system that includes a laser providing a laser beam that excites 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.

[0106]

[0117] In such cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam may be passed from the laser to the source collector module using a beam delivery system including, for example, appropriate directing mirrors and / or beam expanders. 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 referred to as a DPP source.

[0107]

[0118] The illuminator IL may include 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 σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. In addition, the illuminator IL may include 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.

[0108]

[0119] The radiation beam B may be incident on a patterning device (e.g. mask) MA, which is held on a 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 a projection system PS, which focuses the beam onto a target portion C of the substrate W. Using a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example to position a different target portion C in the path of the radiation beam B. Similarly, using a first positioner PM and another position sensor PS1, the patterning device (e.g. mask) MA can be accurately positioned with respect to the path of the radiation beam B. The patterning device (e.g. mask) MA and substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0109]

[0120] The depicted apparatus LPA can be used in at least one of a step mode, a scan mode, and a stationary mode.

[0110]

[0121] In step mode, the support structure (e.g. patterning device table) MT and substrate table WT remain essentially stationary while an entire pattern imparted to the radiation beam is projected onto a target portion C in one go (i.e. a single static exposure), and the substrate table WT is then shifted in the X and / or Y directions so that a different target portion C can be exposed.

[0111]

[0122] In scan mode, the support structure (e.g. patterning device table) MT and the substrate table WT are scanned synchronously (i.e. a single dynamic exposure) while a pattern imparted to the radiation beam is projected onto a target portion C. The velocity and direction of the substrate table WT relative to the support structure (e.g. patterning device table) MT may be determined by the de-magnification and image reversal characteristics of the projection system PS.

[0112]

[0123] In a stationary mode, the support structure (e.g. patterning device table) MT holds a programmable patterning device and remains essentially stationary while the substrate table WT is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically used and the programmable patterning device is updated as required after each movement of the substrate table WT, or between successive radiation pulses during a scan. This mode of operation can be readily applied in maskless lithography employing a programmable patterning device, such as a programmable mirror array.

[0113]

[0124] FIG. 12 depicts a detailed view of a lithographic projection apparatus according to one embodiment.

[0114]

[0125] As shown, the LPA may comprise a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment may be maintained within the closed structure ES of the source collector module SO. The EUV radiation emitting high temperature plasma HP may be formed by a discharge produced plasma source. The EUV radiation may be generated by a gas or vapor (e.g. Xe gas, Li vapor, or Sn vapor from which the high temperature plasma HP is created to emit radiation in the EUV range of the electromagnetic spectrum). The high temperature plasma HP is created, for example, by a discharge that produces an at least partially ionized plasma. A partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required for efficient generation of radiation. In an embodiment, a plasma of excited tin (Sn) is provided to generate the EUV radiation.

[0115]

[0126] The radiation emitted by the high temperature plasma HP passes from the source chamber SC into the collector chamber CC via an optional gas barrier or contaminant trap CT (sometimes also called a contaminant barrier or foil trap) located in or behind the opening of the source chamber SC. The contaminant trap CT may include a channel structure. The contaminant 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 includes at least a channel structure, as known in the art.

[0116]

[0127] The collector chamber CC may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side US and a downstream radiation collector side DS. Radiation traversing the radiation collector CO may be reflected off a grating spectral filter SF to be focused to a virtual source point IF along an optical axis indicated by dashed-dotted line "O". The virtual source point IF may be referred to as an intermediate focus, and the source collector module may be positioned such that the intermediate focus IF is at or near an aperture OP of the enclosure structure ES. The virtual source point IF is an image of the radiation emitting plasma HP.

[0117]

[0128] The radiation subsequently traverses an illumination system IL, which may include a faceted field mirror device FM and a faceted pupil mirror device pm arranged to provide a desired angular distribution of the radiation beam B at the patterning device MA, and a desired uniformity of radiation amplitude at the patterning device MA. Upon reflection of the radiation beam 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 a reflective element RE, onto a substrate W, held by a substrate table WT.

[0118]

[0129] Generally, more elements than shown may be present in the illumination optics unit IL and projection system PS. A grating spectral filter SF may optionally be present depending on the type of lithographic apparatus. Further, more mirrors than shown in the drawings may be present, for example 1 to 6 additional reflective elements may be present in the projection system PS.

[0119]

[0130] The collector system CO may be a nested collector with a grazing incidence reflector GR, just as an example of a collector (or collector mirror), arranged axially symmetrically with respect to the optical axis O, and this type of collector system CO may be used in combination with a discharge produced plasma source, often referred to as a DPP source.

[0120]

[0131] FIG. 13 shows a detailed view of a source collector module SO of lithographic projection apparatus LPA according to an embodiment.

[0121]

[0132] The source collector module SO may be part of the LPA radiation system. The laser LA may be arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li) to generate a highly ionized plasma HP with an electron temperature of a few tens of eV. Energetic radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal incidence collector system CO and focused onto an aperture OP of a closed structure ES.

[0122]

[0133] The concepts disclosed herein can be used to simulate or mathematically model general imaging systems for imaging sub-wavelength features, and can be particularly useful for new imaging technologies capable of producing ever-shorter wavelengths. New technologies already in use include EUV (extreme ultraviolet), DUV lithography capable of producing wavelengths of 193 nm using ArF lasers, and even 157 nm using fluorine lasers. EUV lithography can also produce wavelengths in this range by using synchrotrons or by bombarding materials (solids or plasmas) with high energy electrons to produce photons in the 20-50 nm range.

[0123]

[0134] The concepts disclosed herein may be used for imaging on substrates such as silicon wafers, although it is understood that the disclosed concepts may be used in any type of lithographic imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0124]

[0135] The embodiments of the present disclosure may be further described by the following clauses. 1. Obtaining a mask pattern including sub-resolution assist features (SRAFs), each having a fixed width; Adjusting the width in the mask optimization process of the mask pattern; A method for determining a mask pattern, comprising: 2. Accessing an initial discrete width level defined for the SRAF; assigning a width from the initial discrete width levels to be an initial width; 2. The method of claim 1, further comprising: 3. The method of claim 1, further comprising generating SRAF edges. 4. The method of claim 3, further comprising generating SRAF edges to be approximately equidistant from a ridge point that corresponds to a location of the SRAF. 5. The method of claim 4, wherein the generated SRAF edges are curved. 6. The method of claim 4, wherein the ridge points are determined such that the SRAF edges vary smoothly. 7. The method of claim 4, further comprising determining ridge points from the SRAF guidance map (SGM), the ridge points being located between corresponding SRAF edges. 8. The method of clause 7, wherein generating an SRAF edge includes performing an interpolation of at least two ridge points when a distance between the two ridge points exceeds a distance limit, the interpolation generating an interpolated ridge point. 9. The method of claim 8, wherein an interpolated ridge point is generated at the midpoint of a segment between two ridge points. 10. The method of claim 8, wherein an interpolated ridge point is generated along a spline interpolant curve between two ridge points, the spline interpolant curve being generated utilizing at least one other ridge point. 11. The method of clause 3, wherein generating the SRAF edge includes generating control points at both ends of a segment perpendicular to a ridge point of the SRAF, the segment having a length corresponding to a constant width of the SRAF. 12. The method of claim 3, further comprising adding a tip to the SRAF edge. 13. The method of clause 1, wherein the width of each SRAF is set as a continuous variable that is optimized by a mask optimization process. 14. The mask optimization process simulating a lithography process utilizing the lithography model; predicting imaging characteristics of the simulated mask by a lithography model; adjusting the width of one or more SRAFs to optimize the imaging performance by using a cost function related to the imaging performance; 14. The method according to claim 13, comprising: 15. The method of clause 14, further comprising performing optical proximity correction optimization to generate boundaries of mask features including assist features (AF). 16. The method of claim 15, further comprising optimizing the mask features and simultaneously optimizing an illumination source in a source mask optimization (SMO) in a lithography system. 17. The method of claim 1, wherein the cost function utilized in the mask optimization process includes parameters describing one or more of edge placement error, side lobe printing, mask rule check (MRC) compliance, or user-defined custom requirements, and at least one of the parameters is a function of width. 18. The method of clause 1, further comprising determining a selected width of the SRAF based on a selected continuous variable of width. 19. The method of claim 18, wherein the number of selected widths is less than five. 20. To decide determining an optimized width population or population distribution; setting a selected range within the range of the population or population distribution based on one or more rules; Setting the width of each SRAF to the closest selected width; 19. The method of claim 18, further comprising: 21. The method of clause 20, wherein the one or more rules include setting the selected width evenly within the range of widths. 22. The method of clause 1, wherein the width of each SRAF is a discrete variable that is optimized by a further mask optimization process, and there are fewer discrete variables than SRAFs. 23. The method of clause 22, wherein each discrete variable corresponds to a global width level. 24. The method of claim 23, further comprising fixing a global width level in the mask optimization process. 25. The method of clause 23, further comprising optimizing a global width level in a mask optimization process. 26. Width adjustment, determining a continuous width of the SRAF as a continuous variable; discretizing the continuous width of the SRAF into discrete widths; continuing the mask optimization process by varying the width to be selected from the discrete widths; 2. The method according to claim 1, comprising: 27. A non-transitory computer readable medium having instructions recorded thereon which, when executed by one or more programmable processors, cause the processors to perform the method of any one of clauses 1 to 26. 28. A system for determining a mask pattern, the system comprising: at least one programmable processor; a non-transitory computer readable medium having instructions recorded thereon, the instructions, when executed by at least one programmable processor, causing the system to perform the method of any one of clauses 1 to 26; A system comprising:

[0125]

[0136] Combinations and subcombinations of the elements disclosed herein constitute separate embodiments and are provided by way of example only. Also, the above description is intended to be illustrative rather than limiting. Thus, it should be apparent to one skilled in the art that modifications can be made as described without departing from the scope of the claims set forth below.

Claims

1. Obtaining a mask pattern including sub-resolution assist features (SRAFs), each having a constant width; Adjusting the width of the SRAF in a mask optimization process of the mask pattern; A method for determining a mask pattern, comprising:

2. Accessing an initial discrete width level defined for the SRAF; assigning a width from the initial discrete width levels to be an initial width; The method of claim 1 further comprising:

3. 2. The method of claim 1, further comprising: generating SRAF edges that are approximately equidistant from ridge points that correspond to positions of the SRAFs, the generated SRAF edges being curved and the ridge points being determined such that the SRAF edges vary smoothly.

4. 4. The method of claim 3, further comprising: determining a ridge point from an SRAF guidance map (SGM); and performing an interpolation of at least two ridge points when a distance between two ridge points exceeds a distance limit, the interpolation generating an interpolated ridge point.

5. 4. The method of claim 3, wherein the generating of the SRAF edges comprises generating control points at both ends of a segment of the SRAF that is perpendicular to the ridge point, the segment having a length that corresponds to the constant width of the SRAF.

6. 2. The method of claim 1, wherein the width of each SRAF is set as a continuous variable that is optimized by the mask optimization process.

7. the mask optimization process comprising: simulating a lithography process utilizing the lithography model; predicting imaging characteristics of a mask simulated by said lithography model; adjusting the widths of one or more SRAFs to optimize the imaging performance through use of a cost function related to the imaging performance; The method of claim 6, comprising:

8. 10. The method of claim 1, further comprising performing optical proximity correction optimization to generate boundaries of mask features including assist features (AFs), or optimizing the mask features and simultaneously optimizing an illumination source in a source mask optimization (SMO) in a lithography system.

9. 2. The method of claim 1 , wherein a cost function utilized in the mask optimization process includes parameters describing one or more of edge placement error, side lobe printing, mask rule check (MRC) compliance, or predefined requirements, at least one of the parameters being a function of the width.

10. 10. The method of claim 8, further comprising determining the selected width of the SRAF based on an optimized continuous variable representing a width.

11. The determining step comprises: determining a population or population distribution of said optimized widths; setting the selected range within a range of the population or population distribution based on one or more rules; setting the width of each SRAF to a nearest selected width; The method of claim 10, comprising:

12. 2. The method of claim 1 , wherein the width of each SRAF is a discrete variable that is optimized by a further mask optimization process, wherein there are fewer discrete variables than SRAFs, and each discrete variable in the further mask optimization process corresponds to a global width level.

13. The method of claim 12 , further comprising fixing or optimizing the global width level in the mask optimization process.

14. The adjustment of the width determining a continuous width of the SRAF as a continuous variable; discretizing the continuous width of the SRAF into discrete widths; performing the mask optimization process by varying the width to be selected from the discrete widths; The method of claim 1 , comprising:

15. A non-transitory computer readable medium having instructions recorded thereon which, when executed by at least one programmable processor, perform the method of any one of claims 1 to 14.

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