Optimizing a patterning device layout and a discretized pupil profile to control facet mirrors used in a lithographic process

Abstract

A computer-implemented method for optimizing a beam of illumination used in a lithographic apparatus includes initializing a discretized illumination map including an array of adjustable elements. The lithographic apparatus includes a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus. Each adjustable element is calculated based on illumination intensity from a facet mirror of the faceted mirror device. Illumination intensities from the facet mirrors are calculated by using continuously variable elements. The computer-implemented method also includes adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.

Description

OPTIMIZING A PATTERNING DEVICE LAYOUT AND A DISCRETIZED PUPIL PROFILE TO CONTROL FACET MIRRORS USED IN A LITHOGRAPHIC PROCESSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 676,287 which was filed on July 26, 2024 and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to a lithographic apparatus or process, and more particularly to a tool to optimize an illumination from a source and a patterning device / design layout for use in the lithographic apparatus or process.BACKGROUND

[0003] Illumination from an illumination source (“source”) of a lithographic apparatus can converge (e.g., at a focal plane), as well as spread out, at a pupil plane. At the pupil plane, the profile of the illumination spread can be represented using a so-called pupil profile (e.g., a two-dimensional map of the illumination intensity distribution).

[0004] To impart a desired shape on the illumination, a programmable array of individually adjustable mirrors (e.g., field facet mirrors) can be used at a pupil plane to receive the illumination from the source. The programmable array of adjustable mirrors can create a prescribed pupil profile in a short duration, thereby eliminating the long cycle time associated with design and fabrication of complex diffractive optical elements.

[0005] Although the number of the adjustable mirrors can be as many as several hundred, the mirrors are nonetheless spatially discrete. In some lithographic projection systems, each mirror can be configured to one of several discrete states (e.g., two or more, two to six, or the like discrete states). Due to the discrete nature of the mirrors, the pupil profile that is rendered can resemble, yet substantially deviate from, a desired pupil profile that may have been provided as a spatially continuous (non-discrete) profile.

[0006] An illumination source of a lithographic apparatus can be optimized to improve overall lithographic fidelity. The optimization of the illumination source can be performed in isolation (source optimization), jointly with a mask (source-mask optimization), jointly with aberration injection (source-mask-wavefront optimization) or the like. An optimal pupil profile can result from source optimization, source-mask optimization, an empirical pupil profile, a pupil profile from another lithographic projection system, or the like. A well optimized pupil profile is conducive to accurate and efficient lithographic IC fabrication.

[0007] However, discrete optimization (e.g., branch-and-bound algorithm) can be computationally intensive, with computational run time increasing exponentially as a function of number of mirrors.SUMMARY

[0008] Embodiments of the present disclosure provides a system and method for optimizing a mask design and a discretized illumination map (e.g., a pupil profde) used for a lithographic apparatus or process.

[0009] In some embodiments, a computer-implemented method for optimizing a beam of illumination used in a lithographic apparatus is provided. The lithographic apparatus comprises a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus. The computer-implemented method can comprise initializing a discretized illumination map comprising an array of adjustable element. Each adjustable element can be calculated based on illumination intensity from a facet mirror of the facetted mirror device. Illumination intensities from the facet mirrors can be calculated by using continuously variable elements. The computer- implemented method can also comprise adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.

[0010] In some embodiments, a non-transitory computer-readable medium that stores a set of instructions for optimizing a beam of illumination used in a lithographic apparatus is provided. The set of instructions is executable by at least one processor of an apparatus to cause the apparatus to perform operations. The lithographic apparatus comprises a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus. The operations can comprise initializing a discretized illumination map comprising an array of adjustable element. Each adjustable element can be calculated based on illumination intensity from a facet mirror of the facetted mirror device. Illumination intensities from the facet mirrors can be calculated by using continuously variable elements. The operations can also comprise adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.

[0011] In some embodiments, a system for optimizing a beam of illumination used in a lithographic apparatus is provided. The lithographic apparatus can comprise a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus. The system can comprise one or more processors and a non-transitory computer-readable medium that stores a set of instructions. The set of instructions is executable by the one or more processors to cause the system to perform operations. The operations can comprise initializing a discretized illumination map comprising an array of adjustable elements. Each adjustable element can be calculated based on illumination intensity from a facet mirror of the facetted mirror device. Illumination intensities from the facet mirrors can be calculated by using continuously variable elements. The operations can also compriseadjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.BRIEF DESCRIPTION OF FIGURES

[0012] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0013] FIG. 1A is a schematic diagram illustrating exemplary subsystems of a lithographic apparatus, consistent with embodiments of the present disclosure.

[0014] FIG. IB is a schematic diagram of exemplary field facet mirrors and pupil facet mirrors of a lithographic apparatus, consistent with embodiments of the present disclosure.

[0015] FIG. 2 is a flowchart of an exemplary method for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure.

[0016] FIG. 3 is a flowchart of an exemplary method for source or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0017] FIG. 4 is a schematic of exemplary pupil plane data maps for optimizing a discrete pupil profde, consistent with embodiments of the present disclosure.

[0018] FIG. 5 is a schematic of an exemplary a multi-dimensional discretized illumination map for use in pupil profde optimizations, consistent with embodiments of the present disclosure.

[0019] FIG. 6 is an arrangement of exemplary continuously variable elements, consistent with embodiments of the present disclosure.

[0020] FIG. 7 is an arrangement of exemplary continuously variable elements, consistent with embodiments of the present disclosure.

[0021] FIG. 8 is a flowchart of an exemplary process flow for optimizing and binarizing a machine- compliant illumination map for conditioning exposure illumination of a lithographic apparatus, consistent with embodiments of the present disclosure.

[0022] FIG. 9 is a flowchart of an exemplary method for optimizing a discretized illumination map to configure PFMs for optimal lithographic performance, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0023] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations consistent with the invention. Instead, they are merely examples of apparatuses, systems, and methods consistent with aspects related to subject matter that may be recited in the appended claims.

[0024] To print nano-accurate features (such as nano-transistors) on a substrate, a lithographic apparatus can illuminate a mask. The mask acts like a stencil for the illumination and the patterned illumination is projected onto the substrate, thereby achieving a pattern transfer from mask to substrate. It is desirable for the illumination used in this process to be conditioned to a high degree of accuracy in terms of wavelength, dose, uniform intensity spread, uniform wavefront, or the like. Instability of the illumination can introduce defects and reduce yield. A goal of the manufacturing process is to avoid such defects to maximize the number / yield of functional ICs made in the process.

[0025] Along an illumination path of a lithographic apparatus (e.g., from the source, to the mask, and subsequently to the substrate), the illumination can interact with a plurality of optical hardware, such as an array of discrete adjustable mirrors. Each mirror can be toggled, thereby constructing a prescribed pupil profile. Considering that there can be hundreds of discrete mirrors at the pupil plane, each mirror activated / deactivated can improve or worsen the fidelity of the image of the mask pattern that is focused at the substrate. Hence, deciding which mirrors to activate / deactivate can be an optimization problem. Furthermore, an optimization for one mask pattern may not be optimal for another mask pattern. There can be several mask patterns to for a multiplicity of device layers and new IC architectures instigate the creation of new mask patterns. For a litho-aware optimization process, a source-mask optimization is performed each time a new mask design is created or altered.

[0026] While optimization techniques exist in the literature, it is desirable to provide even faster, less computationally intensive, and more accurate source optimization methods in order to increase yield and throughput of lithographic systems.

[0027] Embodiments of the present disclosure provide a system and method for representing and optimizing a freeform source in a machine grid of pupil facet mirrors.

[0028] Objects and advantages of the disclosure can be realized by the elements and combinations as set forth in embodiments described herein. However, embodiments of the present disclosure are not necessarily required to achieve such exemplary objects or advantages. Some embodiments can achieve a different feature or enhancement without necessarily achieving any expressly stated object or advantage.

[0029] As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component can comprise A or B, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or A and B. As a second example, if it is stated that a component can comprise A, B, or C, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0030] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings, the same or like reference numbers refer to the same or like components or entities, and only the differences with respect to the individual embodiments are described.

[0031] The term “patterning device” may be considered synonymous with similar terms of art, such as “reticle” or “mask.” The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a pattern on a cross section of a radiation beam. The radiation beam then can recreate the pattern in a target portion of a substrate.

[0032] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system.”

[0033] Illumination can be understood to be a form of radiation. The terms “radiation” and “illumination” can be used herein interchangeably. Embodiments described in the context of illumination are also applicable in the context of radiation in general. Furthermore, the terms “radiation” and “beam” can encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range 5-20 nm).

[0034] The term “optimizing” and “optimization” as used herein can indicate adjusting a lithographic apparatus such that results or processes of lithography have more desirable characteristics, such as higher accuracy of projection of design layouts on a substrate, larger process windows, etc.

[0035] FIG. 1A illustrates an exemplary lithographic apparatus 100, consistent with embodiments of the present disclosure. In some embodiments, lithographic apparatus 100 comprises a radiation source 102, which can be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (the lithographic apparatus itself need not have the radiation source), illumination optics which define the partial coherence (denoted as sigma) and which can include optic components 104, 106a, and 106b that shape radiation from source 102; a patterning device 108; and transmission optics 106c that project an image of the patterning device pattern onto a substrate plane 109. An adjustable filter or aperture 107 at disposed in among the optics can restrict the range of beam angles that impinge on the substrate plane 109. A largest possible angle ©max can define the numerical aperture NA of the projection optics as NA = n sin(Gmax), where n is the index of reflection of the medium in which the final lens element is working (e.g., a lens closest to the substrate).

[0036] In an optimization process of a lithographic projection system, a figure of merit of the system can be represented as a cost function. The optimization process can determine a set of parameters (design variables) of the system that minimizes the cost function. The cost function can have any suitable form depending on the goal of the optimization. For example, the cost function can be a weighted root mean square (RMS) of deviations of certain characteristics (evaluation points) of the system with respect to the intended values (e.g., ideal values) of these characteristics. The cost function can be the maximum of these deviations (e.g., worst deviation). The term “evaluation points”herein should be interpreted broadly to include any characteristics of the system. The design variables of the system can be confined to finite ranges or be interdependent due to practicalities of implementations of the system. In case of a lithographic apparatus, the constraints are often associated with physical properties and characteristics of the hardware such as tunable ranges or patterning device manufacturability design rules, and the evaluation points can include physical points on a resist image on a substrate, as well as non-physical characteristics such as dose and focus of the illumination used.

[0037] In a lithographic apparatus, a source can provide illumination (e.g., light). Projection optics can direct and shape the illumination via a patterning device and onto a substrate. The term “projection optics” is broadly defined to include any optical component that can alter the wavefront of the radiation beam. For example, projection optics can include at least some of components 104, 106a, 106b, and 106c. An aerial image is the radiation intensity distribution at substrate level. A resist layer on the substrate is exposed and the aerial image is transferred to the resist layer as a latent “resist image” therein. The resist image can be defined as a spatial distribution of solubility of the resist in the resist layer. A resist model can be used to calculate the resist image from the aerial image. An example of a resist model can be found in U.S. Patent No. 8,200,468, the contents of which are incorporated herein by reference in their entirety. The resist model is related to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB), and development). Optical properties of the lithographic apparatus (e.g., properties of the source, the patterning device, and the projection optics) dictate the aerial image. Since the patterning device used in the lithographic apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic apparatus including at least the source and the projection optics.

[0038] FIG. IB illustrates a schematic diagram of an exemplary facetted field mirror device 130 and facetted pupil mirror device 140 of a lithographic apparatus, consistent with embodiments of the present disclosure. In some embodiments, facetted field mirror device 130 comprises a plurality of field facet mirrors (FFMs) (e.g., FFMs 111, 112, 113 and 114). Facetted pupil mirror device 140 can comprise a plurality of pupil facet mirrors (PFMs) (e.g., PFMs 121, 122, 123, 124, 131, 132, 133, and 134). As described above in reference to FIG. 1A, illumination optics can include optic components 104, 106a, and 106b that shape radiation from source 102 (now illustrated in FIG. IB as beam of radiation 116). Beam of radiation 116 can briefly converge at a point referred to as an intermediate focus 118. Illumination optics can adjust the angular intensity distribution via FFMs and PFMs. Facetted field mirror device 130 and facetted pupil mirror device 140 can be provided in lithographic apparatus 100 as optic components 106a and 106b (FIG. IB). PFMs can be disposed at a pupil plane PP of the lithographic apparatus.

[0039] As illustrated in FIG. IB, each FFM can be associated with several PFMs by system design. A given FFM can be controlled to direct reflected radiation to a choice PFM from among a group ofPFMs that is associated with the given FFM. For example, FFM 112 is associated with PFMs 121, 122,123, and 124. FFM 112 can be flipped, toggled, or otherwise adjusted to direct the radiation reflecting from FFM 112 to one of PFMs 121, 122,123, and 124. Similarly, FFM 113 can be flipped, toggled, or otherwise adjusted to direct the radiation reflecting from FFM 113 to one of PFMs 131, 132, 123, and 134. In this specific example, the PFMs associated with an FFM are mutually exclusive in nature. For example, PFM 121 is associated with FFM 112 and no other FFM, PFM 131 is associated with FFM 113 and no other FFM, and so on. The non-overlapping arrangement can efficiently spread illumination energy across a pupil plane.

[0040] Each FFM can be flipped, toggled, or otherwise adjusted to one of a plurality of discrete predefined states (e.g., four PFMs are assigned to one FFM in FIG. IB, hence the one FFM can have four states). Each state can cause the FFM to direct the illumination to one of the PFMs associated with the FFM. For example, FFM 112 reflects illumination toward PFM 121 when FFM 112 is flipped to a first state, FFM 112 reflects illumination toward PFM 122 when FFM 112 is flipped to a second state, FFM 112 reflects illumination toward PFM 123 when FFM 112 is flipped to a third state, and so on.

[0041] From the PFMs, a beam of radiation 150 can be directed to a downstream lithographic element (e.g., a mask). The downstream intensity distribution of beam of radiation 150 is dependent on the illumination distribution defined by the PFMs (e.g., due to conjugate relationships in optics). For example, with a given PFM configuration, it is possible to provide a slit of illumination as described in FIG. 5. It is desirable to provide a source optimization method that can instruct which PFMs to activate and which PFMs to shut off so as to achieve a desired lithographic performance. The illumination intensity distribution defined at pupil plane PP by the PFMs can be referred to as a “pupil profile,” “pupil illumination profile,” “pupil illumination intensity distribution,” or the like.

[0042] FIG. 2 illustrates a flowchart of an exemplary method 200 for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure. In some embodiments, a source model 202 represents optical characteristics of the source (e.g., including radiation intensity distribution, phase distribution, or the like). A projection optics model 204 can represent optical characteristics of the projection optics (e.g., including changes to radiation intensity / phase distribution caused by the projection optics). A design layout model 206 can represent optical characteristics of a design layout (e.g., including changes to radiation intensity / phase distribution caused by a given design layout), which is the representation of an arrangement of features on, or formed by, a patterning device. An aerial image 208 can be simulated from source model 202, projection optics model 204, and design layout model 206. A resist image 212 can be simulated from aerial image 208 using a resist model 210. Simulation of lithography can, for example, predict lithographic pattern transfer results, which can include feature contours, edge placement errors (EPE), critical dimensions (CDs), or the like, in the resist image.

[0043] It is noted that the source model 202 can represent optical characteristics of the source that include, but are not limited to, NA-sigma (o) settings as well as any particular illumination source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). Projection optics model 204 can represent the optical characteristics of the projection optics that include, but are not limited to, aberration, distortion, refractive indexes, physical sizes, physical dimensions, or the like. Design layout model 206 can represent physical properties of a physical patterning device. An example of a design layout model can be found in U.S. Patent No. 7,587,704, the contents of which are incorporated herein by reference in their entirety. A goal of the simulation is to accurately predict feature contours, edge placement errors (EPE), critical dimensions (CDs), or the like, which can then be compared against an intended design for a device (e.g., a simulation to determine whether a mass fabrication of a new CPU architecture is feasible). The intended design is generally defined as a pre- optical proximity correction (OPC) design layout (OPC is sometimes also referred to as “optical and process correction”), which can be provided in a standardized digital file format. The layout file can be in a Graphic Database System (GDS) format, Graphic Database System II (GDS II) format, an Open Artwork System Interchange Standard (OASIS) format, a Caltech Intermediate Format (CIF), or the like. The intended design layout can include patterns or structures for transferring onto a wafer. The patterns or structures can be mask patterns used to transfer features from photolithography masks or reticles to a wafer. In some embodiments, a layout in GDS or OASIS format, among others, can include feature information stored in a binary file format representing planar geometric shapes, text, and other information related to the wafer design.

[0044] From the design layout, one or more portions can be identified, which are referred to as “clips.” In some embodiments, a set of clips is extracted, which represents the complicated patterns in the design layout (typically about 50 to 1000 clips, although any number of clips can be used). It is to be appreciated that these patterns or clips represent small portions (e.g., circuits, cells, or patterns) of the design and especially the clips represent small portions for which particular attention or verification is desirable. In other words, clips can be the portions of the design layout or can be similar or have a similar behavior of portions of the design layout where critical features are identified either by experience (including clips provided by a customer), by trial and error, or by running a fullchip simulation. Clips can contain one or more test patterns or gauge patterns.

[0045] An initial larger set of clips can be provided a priori by a customer based on known critical feature areas in a design layout that could benefit from image optimization. Alternatively, in some embodiments, the initial larger set of clips is extracted from the entire design layout by using some kind of automated algorithm (e.g., machine vision) or manual algorithm that identifies the critical feature areas.

[0046] In some embodiments, an optimization process (e.g., source mask optimization (SMO)) relates to one or more of a patterning process that employs process models (e.g., an optics model, a mask model, a resist model, etc. of FIG. 2). The optimization process can involve execution of the oneor more process models and computing a cost function that can be reduced by modifying one or more characteristics (e.g., source, mask pattern, etc.) of the patterning process. In some embodiments, the one or more characteristics is described by design variables. Hence, an optimized characteristic can also be referred to as an optimized design variable, where a design variable is optimized based on a cost function.

[0047] In some embodiments, modifying the one or more characteristics is based on a gradient of the cost function that guides how the characteristic should be modified to reduce the cost function. A cost function can be a function of a certain continuous metric such as an edge placement error (e.g., a difference between contours of printed pattern and a target pattern). Using a continuous metric or a cost function of a continuous nature allows use of gradient-based optimizing algorithms that have acceptable runtime performance of an optimization process.

[0048] Details of example techniques and models used to transform a patterning device pattern into various lithographic images (e.g., an aerial image, a resist image, an etch image, etc.), apply OPC (e.g., using models) and evaluate performance (e.g., in terms of process window) can be found in U.S. Patent Nos. 7,695,876; 7,707,538; 7,747,978; 7,882,480; 8,413,081; 8,438,508; and 9,360,766, the contents of which are incorporated herein by reference in their entirety.

[0049] FIG. 3 illustrates a flowchart of an exemplary method 300 of source or mask optimization of a patterning process, consistent with embodiments of the present disclosure. In a typical high-end design, almost every feature edge can benefit from some modification to achieve printed patterns that come sufficiently close to the target design. These modifications can include shifting or biasing of edge positions or line widths as well as application of “assist” features that are not intended to print themselves, but can affect the properties of an associated primary feature. Furthermore, optimization techniques applied to the source of illumination can have different effects on different edges and features. Optimization of illumination sources can include the use of pupils to restrict source illumination to a selected pattern of light. Embodiments of the present disclosure provide optimization methods that can be applied to both source and mask configurations.

[0050] A method of performing source and mask optimization (SMO) can allow full chip pattern coverage while lowering the computation cost by intelligently selecting a small set of critical design patterns from the full set of clips to be used in SMO. SMO can be performed on these selected patterns to obtain an optimized source. The optimized source can then be used to optimize the mask (e.g., using OPC and local mechanical-stress control) for the full chip, and the results can be compared. Various methods are provided for iteratively converging on an optimal result. Method 500 is an example SMO method.

[0051] A target design 301 (e.g., comprising a layout in a standard digital format such as OAIS, GDSII, etc.) for which a lithographic process is to be optimized can include memory, test patterns, and logic. From this design, a full set of clips 302 can be extracted, which represents complex patterns in design 301 (e.g., about 50 to 1000 clips). It is to be appreciated that these clips represent smallportions (i.e., circuits, cells, or patterns) of the design for which particular attention and / or verification is of interest. At operation 304, a small subset of clips 306 (e.g., 15 to 50 clips) can be selected from full set of clips 302. As will be explained in more detail below, the selection of clips can be performed such that the process window of the selected patterns matches the process window for the full set of critical patterns as close as possible. The effectiveness of the selection can be measured by the total run time (pattern selection and SMO) reduction.

[0052] At operation 308, SMO can be performed with the selected patterns (15 to 50 patterns) of subset of clips 306. In particularly, an illumination source can be optimized for the selected patterns of subset of clips 306. Source optimization can be performed as described below with respect to FIGS. 4-9. Examples of other source optimization methods can be found in, for example, U.S. Patent Application Publication No. 2004 / 0265707, the contents of which are incorporated herein by reference in their entirety.

[0053] At operation 310, manufacturability verification of the selected patterns of subset of clips 306 can be performed with the source obtained in operation 308. In particular, verification can include performing an aerial image simulation of the selected patterns of subset of clips 306 and the optimized source and verifying that the patterns will print across a sufficiently wide process window. An example verification process can be found in U.S. Patent No. 7,342,646, the contents of which are incorporated herein by reference in their entirety. If the verification at operation 310 is satisfactory, as determined in operation 312, then processing can advance to full chip optimization (e.g., advanced to operations using optimized source 314). Otherwise, processing can return to operation 308, where SMO is performed again but with a different source or set of patterns. For example, the process performance as estimated by the verification tool can be compared against thresholds for certain process window parameters such as exposure latitude and depth of focus. These thresholds can be predetermined or set by a user.

[0054] After the selected patterns meet lithography performance specification as determined in step 312, the optimized source 314 can be used for optimization of the full set of clips 316 (e.g., originating from full set of clips 302).

[0055] At operation 318, model-based sub-resolution assist feature placement (MB-SRAF) and optical proximity correction (OPC) for all the patterns in the full set of clips 316 can be performed. Examples of MB-SRAF and OPC can be found in U.S. Patent Nos. 5,663,893; 5,821,014; 6,541,167; and 6,670,081, the contents of which are incorporated herein by reference in their entirety.

[0056] At operation 320, using processes similar to step 310, full pattern simulation based manufacturability verification can be performed with the optimized source 314 and the full set of clips 316 as corrected in step 318.

[0057] At operation 322, the performance (e.g., process window parameters such as exposure latitude and depth of focus) of the full set of clips 316 can be compared against subset of clips 306. For example, the pattern selection can be considered complete and / or the source is fully qualified for thefull chip when the similar (<10%) lithography performances are obtained for both selected patterns of subset of clips 306 and critical patterns of full set of clips 316.

[0058] Otherwise, at operation 324, hotspots can be extracted. At operation 326, the hotspots can be added to subset of clips 306 and the process starts over. For example, hotspots (e.g., features among the full set of clips 316 that limit process window performance) identified during verification step 320 can be used for further source tuning or to run SMO of operation 308 again. The source can be considered fully converged when the process window of the full set of clips 316 are the same between the last run and the run before the last run of operation 322.

[0059] OPC calibration can be performed by modeling or simulation. For example, for the desired yield, the total number of features, and their respective probabilities of failure, simulation can be performed to optimize OPC for a lowest yielding feature. OPC addresses the fact that, in addition to any demagnification by the lithographic projection apparatus, the final size and placement of an image of the patterning device pattern projected on the substrate will not be identical to, or simply depend only on the size and placement of, the corresponding patterning device pattern features on the patterning device.

[0060] In some embodiments, the measurement data (e.g., stochastic variations) related to the printed pattern can be employed in optimizing the patterning process or adjusting parameters of the patterning process. For small feature sizes and high feature densities present on some design layouts, the position of a particular edge of a given feature can be influenced to a certain extent by the presence or absence of other adjacent features. These proximity effects arise from minute amounts of radiation coupled from one feature to another or non-geometrical optical effects such as diffraction and interference. Similarly, proximity effects can arise from diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching that generally follow lithography.

[0061] To ensure that the projected image of the patterning device pattern is in accordance with tolerances of a given target design, proximity effects should be predicted and compensated for using sophisticated numerical models, corrections, or pre-distortions of the patterning device pattern. The article “Full-Chip Lithography Simulation and Design Analysis — How OPC Is Changing IC Design,” C. Spence, Proc. SPIE, Vol. 5751, pp 1-14 (2005) provides an overview of “model-based” optical proximity correction processes, the contents of which are incorporated herein by reference in their entirety. In a typical high-end design, almost every feature of the patterning device pattern has some modification to achieve high fidelity of the projected image to the target design. These OPC modifications can include shifting or biasing of edge positions or line widths and / or application of “assist” features that are intended to assist projection of other features.

[0062] Application of model-based OPC to a target design can involve good process models and considerable computational resources, given the many millions of features typically present in a device design. However, applying OPC is generally an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the effect of OPC, e.g., patterningdevice paterns after application of OPC and any other resolution enhancement technique (RET), should be verified by design inspection, e.g., intensive full-chip simulation using calibrated numerical process models, to reduce or minimize the possibility of design flaws being built into the paterning device patern. This is driven by the enormous cost of making high-end paterning devices, as well as by the impact on turn-around time by reworking or repairing existing paterning devices once they have been manufactured. OPC and full-chip RET verification can be based on numerical modelling systems and methods. Examples of such methods can be found in U.S. Pat. No. 7,003,758 and an article titled “Optimized Hardware and Software For Fast, Full Chip Simulation”, by Y. Cao et al., Proc. SPIE, Vol. 5754, 405 (2005), the contents of which are incorporated herein by reference in their entirety.

[0063] The illumination source can also be optimized, either jointly with paterning device optimization or separately, to improve the overall lithography fidelity. The terms “illumination source” and “source” can be used interchangeably in this disclosure. Off-axis illumination (e.g., annular, quadrupole, dipole, or the like) can be used to resolve fine structures (e.g., target features) contained in the paterning device. However, when compared to a traditional illumination source, an off-axis illumination source usually provides less radiation intensity for the aerial image. Thus, it is can be desirable to optimize the illumination source to achieve balance between finer resolution (relevant to yield) and reduced radiation intensity (relevant to throughput).

[0064] It is evident from the descriptions of FIGS. 1A-3 above that a source is a complex optical system (e.g., complex facet mirror arrangement in FIG. IB) that can be simulated using a source model 202 (FIG. 2) and further optimized via SMO (FIG. 3) or other optimization processes. Several example documents have been referenced above that cover some aspects of source optimization. However, there is still a desire and need for faster and more accurate source optimization processes capable of generating machine instructions to control a source of a lithographic apparatus in accordance with optimal solutions found via the optimization processes of FIG. 3. Existing source optimization techniques have merits and drawbacks. For example, a freeform source optimization method can optimize a freeform source (e.g., a continuous intensity distribution) but fail to provide a discrete illumination profde that can be achieved using the discrete nature of PFMs (see FIG. 3) (that is, it is not machine compliant). Other optimization methods fail to consider lithographic performance (e.g., not litho-aware) or not provide a path to optimize a design layout of a mask. Embodiments described herein can advantageous generate machine compliant discrete pupil profdes through an SMO process. In some embodiments, lithographic performance can be taken into account, as well as accounting allowing for optimizations of a design layout of a mask.

[0065] FIG. 4 illustrates exemplary pupil plane data maps for optimizing a discrete pupil profde, consistent with embodiments of the present disclosure. In some embodiments, “intensity” maps shown in FIG. 4 are grayscale coded such that dark areas represent lower magnitude and bright areas represent high magnitude for the parameter(s) relevant to each map.

[0066] A pupil profile 404 can represent an ideal or desired distribution of illumination intensity across the pupil plane (e.g., at facetted pupil mirror device 140 of FIG. IB). Pupil profde 404 can be optimized to result in an optimal lithographic performance when implemented at pupil plane PP (FIG. 3) of the lithographic apparatus. For example, optimizing the source illumination intensity distribution at a first region 410 of pupil profde 404 can result in improved lithographic performance (e.g., it is better for optimization processes to give greater weight or priority to first region 410). In another example, optimizing the source illumination intensity at a second region 412 of pupil profile 404 can result in limited improvement to lithographic performance (e.g., it is better for an optimization process to reduce the weight or priority of second region 412). When pupil profile 404 is optimized without regard for machine constraints (e.g., discrete PFM grid), pupil profile 404 can be a freeform / continuous distribution (e.g., in a Cartesian coordinate system) that is uninformative as to how illumination intensities of the freeform / continuous distribution can be applied in the context of the machine constraints.

[0067] The freeform / continuous nature of pupil profile 404 causes it to be incompatible with a lithographic apparatus that uses discretized illumination hardware at its pupil plane (e.g., it is not machine compliant with discrete PFMs). Pupil profile 404 can also be called a freeform (FF) source, owing to its function of representing the shape of a source of illumination in a freeform domain. The FF source can be generated by a SMO process that operates in the freeform domain. The FF source can be converted to a machine domain solution in PFM grid via a separate rendering process. The machine domain solution in PFM grid is illustrated as discrete pupil profile 408. The rendering process can be followed by discrete optimization as needed. This multi-step process (e.g., FF SMO, discretizing via rendering process) can impose a significant time and computational burden. Hence, it is desirable to provide an SMO method that can generate a discrete pupil profile while avoiding intermediate conversion steps.

[0068] FIG. 5 illustrates an exemplary visual representation of a discretized illumination map 500 (or simply discretized illumination map 500) for use in pupil profile optimizations, consistent with embodiments of the present disclosure. In some embodiments, discretized illumination map 500 can be initialized in its discretized PFM grid state such that each discrete element corresponds to a facet mirror (discrete pupil profile 408 of FIG. 4 is an example of such a layout). It can be helpful to visualize discretized illumination map 500 as multiple “slices” for representing another variable of interest (e.g., slit position). According to embodiments of the present disclosure, SMO can be performed using discretized illumination map 500, thereby reducing time burden and computational burden associated with the intermediate conversion steps described above. For example, as will be described in more detail below, each discrete element (e.g., each pupil source spot intensity) can be calculated and optimized as a function of the intensity (e.g., max intensity) of a given PFM at a certain slit position and a continuously variable element. In some embodiments, the continuously variable element can be substituted via a constraint to reflect mutual exclusivity of mirror elements.

[0069] To better understand a utility of the additional dimensionality, it is instructive to first consider an example environment (as in inset 502) of a lithographic apparatus and PFMs of FIG. 3. Inset 502 shows a mask 504 irradiated using a beam of radiation 506. Mask 504 can correspond to patterning device 108 of FIG. 1 . Beam of radiation 506 can correspond to beam of radiation 150 of FIG. IB. PFMs are disposed upstream of beam of radiation 506, but out of frame (see facetted pupil mirror device 140 of FIG. IB). Mask 504 can comprise patterns 508 to be transferred via illumination projection onto a substrate. To project pattern 508 onto the substrate, beam of radiation 506 (e.g., a beam of EUV illumination) can be formed as a slit of illumination and scanned across mask 504. The slit can have an elongate shape (e.g., a length of a slit can be about 26 mm). The one or more properties of the slit (e.g., shape, intensity distribution, or the like) can be controlled by adjusting the illumination at pupil plane PP (FIG. 2) (e.g., by adjusting the PFMs). A position along the slit is a parameter of interest. The slit can have a series of positions along its length, denoted by an index sip, with slpmm and slpmax denoting the opposite boundary positions of the slit length. The different “slices” of discretized illumination map 500 can correspond to different positions sip along the slit. It follows that index sip can be represented in integer fashion as slpl through sip 100, or any number of different coordinates along the slit, or the like. It is to be appreciated that the shape of beam of radiation 506 at or near the PFMs can be different from the slit shape.

[0070] According to embodiments of the present disclosure, discretized illumination map 500 can comprise an array of adjustable elements. Adjustable elements are denoted as Pj,sip. The index j can denote a facet mirror (e.g., a PFM) of a facetted mirror device (e.g., facetted pupil mirror device 310 (FIG. 3)). In other words, the index j can be used to uniquely identify a facet mirror within the layout of discretized illumination map 500. As before, index sip can denote a position along the slit of beam of radiation 506. In FIG. 5, three example slices of discretized illumination map 500 corresponding to slit positions 1, 2, and 3 (e.g., can be the at slpmm, slpmid (center of slit), slpmax).

[0071] A j'1' PFM of a lithographic apparatus can contribute different maxima of illumination intensities throughout the different positions sip throughout the slit, e.g., based on lithography machine configuration limitations. The quantity mJ>sipcan represent maximum illumination intensity originating from a j411PFM at an sip411position along the slit. The maxima are a machine constant (noise and drift notwithstanding) that can be measured or monitored in connection with operation of the lithographic apparatus.

[0072] According to embodiments of the present disclosure, the adjustable nature of adjustable elements pj.sip can be achieved via continuously variable elements qj. Each one of continuously variable elements qj is associated with a corresponding j411PFM. Adjustable elements Pj,sipand continuously variable elements qj can have a relationship as in equation 1.Pj,p lj'p / j (Eq. 1)

[0073] According to equation 1, adjustable elements pj.sip can be calculated based on illumination intensity projected from a facet mirror of a facetted mirror device, with the illumination intensity being calculated using a continuously variable element.

[0074] Adjustable parameters described herein (e.g., adjustable elements Pj,sip, continuously variable elements qj, or the like) are allowed to have fractional values with respect to discretized wholes. For example, a fractional value can be within a range of continuum, as opposed to being limited by a finite and discrete set. A discrete set can be {0, 0.2, 0.4, 0.6, 0.8, 1.0} and a continuous element based on the discrete set can take on values in between (e.g., 0.003, 0.454, or the like). The continuous nature of continuously variable elements qj can allow for a source optimizer to simulate objects akin to virtual PFMs. Virtual PFMs (as opposed to real PFMs in a lithographic apparatus) can have a continuum of illumination intensities ranging from 0% to 100%, owing to the continuum of allowable values for continuously variable elements q. This is useful since real PFMs in the lithographic apparatus can be constrained to either be fully on or fully off (binarized as 0 (off) or 1 (on)). In turn, continuously variable elements q can loosen discretization constraints on a source optimizer by allowing for virtual PFMs with fractional illumination intensities (e.g., 1%, 5%, 10%, 13%, 57%, 89%, or the like). It is to be appreciated ranges of continuums described herein for source optimizations can have some amount of discontinuity associated with computer limitations (e.g., finite floating-point precision).

[0075] The ability to simulate virtual PFMs at less than 100% brightness can be helpful for source optimization (e.g., source-only optimization, source-mask optimization, or the like — collectively referred to as source optimization). The magnitude of continuously variable elements q can be arbitrarily adjusted by a simulation-based source optimization (e.g., an SMO process), where the values can range from 0 to 1. In some embodiments, the values act as a knob or slider parameter. Examples of simulation-based SMO processes were described above in reference to FIGS. 2 and 3. In some embodiments, one or more illumination optics of a lithographic apparatus can be limited to discrete or binarized states. Hence, the source optimization process can comprise binarizing to restore machine compliance.

[0076] FIG. 5 depicts three examples of individual adjustable elements Pj,sipfor different arbitrary indices (e.g., arbitrary PFMs jl, j2, and j3 and arbitrary slit positions sip 1, slp2, and slp3). Using grayscale intensity (e.g., white = illumination on), the different brightnesses of adjustable elements Pji.sipi, Pj2.siP2, and Pj3,siP3 can be attributed to a given selection of the corresponding continuously variable elements qi, q2, and q3 (adjustable knob in the optimization process) and the corresponding maximum illumination intensities mji,sipi, mj2,siP2, and mj3,siP3 (which can be machine constant).

[0077] In some embodiments, source optimization can comprise determining a value for each of the continuously variable elements q and calculating a value for a cost function. The cost function is at least a function that indicates a lithographic performance (higher cost indicates worse lithographicperformance). Any other terms may be included in the cost function without departing from the scope of the present disclosure. The set values for continuously variable elements q result in a corresponding value for the cost function. Afterward, a new iteration can be initiated in which the continuously variable elements q (knobs) are adjusted. The cost function can then be calculated to ascertain whether the value of the cost function has moved in the direction of better lithographic performance. The iterations of knob adjustments can be repeated until the cost is minimized (fully optimized source). In other words, source optimization can be performed by adjusting adjustable elements by iteratively adjusting the continuously variable elements associated with the PFMs based on iterative simulation of a lithographic process using the PFMs and a mask.

[0078] In some embodiments, an issue can arise in the source optimization process if one or more of the PFMs are mutually exclusive. In the earlier description of FIG. IB, it was explained that FFM 112 can be flipped, toggled, or otherwise adjusted to direct the radiation reflecting from FFM 112 to one of PFMs 121, 122, 123, or 124 (mutual exclusivity). While a source optimization method that relies on equation 1 can produce usable results on its own, there can be instances of unusable results if the final machine instructions include turning on illumination from two or more mutually exclusive PFMs.

[0079] Therefore, the source optimization method based on equation 1 can be modified to account for mutual exclusivity of PFMs. The parameters of equation 1 can be transformed according to table 1.

[0080] The index sip remains representative of a position along the length of a slit of beam of radiation 506. The index i can denote a field facet mirror (e.g., FFM 112 (FIG. IB)) of a facetted field mirror device (e.g., facetted field mirror device 130 (FIG. IB)). In other words, the index i can be used to uniquely identify the FFMs of faceted field mirror device 130 (FIG. IB). In an example, if there are a hundred FFMs, index i can be represented in integer fashion as il through ilOO, or a hundred different coordinates of the FFMs, or the like. The index st, can denote a discrete state of an FFM. For simplicity and clarity, description of some embodiments are directed to a single FFM having five discrete states. But it is to be appreciated that embodiments are not so limited (e.g., implementations of embodiments can use two, three, or more FFM states). For the five states of each FFM, the index st can be represented in integer fashion as stl, st2, st3, st4, or st5. The index j hasbeen replaced with the indices i and st. This replacement defines how a j411PFM can be flipped, toggled, or otherwise adjusted by a corresponding flip, toggle, or adjustment of an st411state of an i411FFM. The relationship of equation 1 is thus transformed to that of equation 2.Pi, st, sip ^-i,st,slpQi,st (Eq. 2)

[0081] In this manner, adjustable elements as pi,st,siPcan be calculated based on illumination intensity projected from PFMs, which in turn is dependent on a FFM of facetted field mirror device 130 (FIG. IB). Illumination intensity at each PFM can be calculated using continuously variable elements qi,stto act as a knob or slider for each of the st number of different states of the i number of FFMs. The state st can denote a direction of illumination of an FFM. Referring to FIG. IB, FFM 112 (index il) directing illumination toward PFM 121 (index stl) can be represented by indices il,stl. FFM 112 (index il) directing illumination toward PFM 122 (index st2) can be represented by indices il ,st2. FFM 113 (index i3) directing illumination toward PFM 131 (index stl) can be represented by indices i3,stl. FFM 113 (index i3) directing illumination toward PFM 132 (index st2) can be represented by indices i3,st2, and so on.

[0082] The values for each of the maximum illumination intensities m1>st,siPremains unchanged (it is a machine constant), but the element associations have been updated. Previously, maximum illumination intensities mJ>sipwere associated with a j411PFM and an sip4' position along the slit. The values of maximum illumination intensities m1>st,sipare now associated with an st411state of an i411FFM and an sip'1' position along the slit.

[0083] The continuous nature of continuously variable elements qi,stallows for defining virtual FFM states with partial activation capability for source optimization purposes. The fractionality is useful for source optimization. The continuously variable elements qi,sttemporarily circumvents this machine constraint such that partial activations of virtual FFM states can be used for source optimizations. Hence, adjustable elements p1>st,pcan represent dimmable virtual PFMs that are based on dimmable virtual FFM states for the purposes of source optimizations. The magnitude of continuously variable elements qi,stcan be arbitrarily set by the source optimizer (e.g., values ranging from 0 to 1), essentially acting as a knob or slider parameter for each dimmable virtual FFM state.

[0084] For simplicity and clarity, description of some embodiments can use a value of 0 to represent minimum illumination and a value of 1 to represent maximum illumination. Using this nomenclature, by conservation of energy, it follows that the combined illumination of five mutually exclusive PFMs associated with one FFM should add up to 1, as in equation 3.

[0085] This constraint can be provided to the source optimizer to ensure that source optimizer arrives at a result that abides by the physical constraints of the lithographic apparatus (e.g., so that the source optimizer does not attempt to simultaneously use two mutually exclusive PFMs). In some embodiments, continuously variable elements qi,stcan be substituted with substitute continuously variable elements Vi,st, according to equation 4. vi,stQi, st (Eq. 4)Ustvi,st

[0086] Substitute continuously variable elements Vi.st, can act as a knob or slider parameter for each unique dimmable virtual FFM state. The range of each of substitute continuously variable elements Vi,st can be chosen arbitrarily (e.g., from 0 to 1, from 0% to 100%, or the like). The division by the summed quantities in equation 4 creates a functional equivalent of the condition of equation 3 while also enhancing the speed at which the SMO process can converge on an optimal solution.

[0087] FIG. 6 illustrates an exemplary set of values 600 for substitute continuously variable elements Vi, st, consistent with embodiments of the present disclosure. For consistency and clarity, descriptions will continue to use the non-limiting example of five states per FFM (extrapolations to any suitable number of two or more states are within the scope of the present disclosure), as well as choosing a range from 0 to 1 for substitute continuously variable elements vl st. Of the numerous substitute continuously variable elements Vi,st, the values corresponding to the ilstFFM and the i2ndFFM have been expanded. Different ones of the states st can correspond to different PFMs. The PFMs from jl to jlO can be assigned to corresponding combinations of indices i and st as shown in FIG. 6. Though only ten different values for substitute continuously variable elements Vi,st, are shown in FIG. 6, it is to be appreciated that there can be thousands of values that correspond to thousands of PFMs disposed at a pupil plane in some embodiments.

[0088] Source optimization iterations can calculate a cost function value using equations 2 and 4. Substitute continuously variable elements vl stcan act as adjustable knobs for the optimization. As the source optimizer converges on optimal PFM configurations, certain ones of substitute continuously variable elements vl stcan be biased toward 1 while other ones can become biased toward 0. Once the optimization iterations are finished (e.g., settled at an optimal solution), binarization can commence. As it was mentioned above, the optimizer can assign partially dimmed values for sets of five virtual PFMs. It is noted that the condition of equation 3 is fulfilled. The binarization can be performed by selecting the “brightest” virtual PFM (e.g., the one with the highest qi,stamong a set of five associated with a single FFM).

[0089] In the example of FIG. 6, the brightest virtual PFMs are the j2ndPFM and the j 9d 1PFM. To generate machine-compliant instructions, the source optimizer results are analyzed and the brightestvirtual PFMs are identified for determining which real PFMs in a lithographic apparatus to turn on (and which real PFMs to turn off). The source optimizer can cope with the mutual exclusivity constraints imposed by the FFM states by implementation of equations 3 or 4.

[0090] Furthermore, the source optimization iterations based on equation 2 can also recognize optimal (or suboptimal) changes to the illumination slit profile based on the additional dimensionality of the index p, which represents the position along the length of a slit of beam of radiation. Hence, at the end of source optimization iterations, the results can reflect an optimum illumination slit profile (e.g., litho-aware optimization). The term “litho-aware” can be used to describe an optimum in the sense of lithographic performance, as opposed to a non-litho-aware optimization that converges to a pupil profile that is geometrically similar to a “target pupil” shape without regard to lithographic performance. The binarization process can be used to generate a machine-compliant optimized illumination map 602 from the multi-dimensionality of discretized illumination map 500 (FIG. 5). For example, the optimized qi,stconfigurations can be used to generate a scanner recipe file to instruct a lithographic scanner to configure the mirror positions. Adjustable elements as pi,st,siPcan be used for display and visual tracking of the pupil profile (e.g., as in FIG. 5) or further simulation purposes.

[0091] In some embodiments, certain FFMs can be turned off. The source optimizer can arrive at more optimal solutions if certain FFMs were allowed to be turned off. Furthermore, it can be desirable to include an option with a lithographic apparatus is capable of fractional use of its total FFM count. For example, a user of a lithographic apparatus can be given the option of increasing illumination and throughput performance (e.g., increasing the number of activated FFMs to reduce exposure time) or increasing lithographic and yield performance (e.g., deactivating certain FFMs associated with second region 412 (FIG. 4) while favoring activation of PFMs in first region 410 (FIG. 4)).

[0092] In some embodiments, the source optimization method based on equations 1-4 can be modified to allow for a fraction of FFMs to be turned on and the remaining fraction to be turned off. The ratio of FFMs turned on to the total number of FFMs available can be referred to as illumination efficiency IE. Instead of using the constraint of equation 3, a modified form of equation 3 can be used, which is shown as equation 5.

[0093] The sum (which used to be a sum to 1 in equation 3) has been modified such that the sum over the states st now results in an arbitrary sum value for the corresponding i'1' FFM. The arbitrary sum values are represented by FFM activation elements Ci. FFM activation elements Ci can be adjusted by the source optimizer in a range between 0 and 1 during the iterations (values other than 0 and 1 can be used to represent minimum and maximum illumination states). A value of 0 can represent an FFM that is unused (off state). A value of 1 can represent an FFM that is activated (on state). It is noted thata value of 1 collapses equation 5 into the form of equation 3. In other words, the set of possible source optimization solutions using equation 3 is a subset of the set of the possible solutions associated with equation 5. Furthermore, fractional values of Ci can represent partial activations of virtual FFMs for the purposes of source optimization. Subsequent binarization can ensure machine compliance.

[0094] Similar to the problems conveyed regarding equation 3, equation 5 can also cause issues with source optimization processes. Hence, continuously variable elements qi,stcan be substituted with substitute continuously variable elements Vi.st, according to equation 6.

[0095] In some embodiments, it is desirable to reduce illumination efficiency IE of FFMs (e.g., use a fraction of the total illumination producible by the lithographic apparatus). Such a feature can be implemented by instructing the lithographic apparatus to deactivate one or more FFMs. To allow the source optimizer to find optimal solutions according to illumination efficiency IE, a total number N of available FFMs is provided to the source optimizer along with a desired value for the illumination efficiency IE. Then, for 0 < Ci < 1, FFM activation elements Ci can be constrained according to equation 7.

[0096] For 0 < Ci < 1, the illumination efficiency IE is naturally defined within a range between 0 and 1. The value IE = 0.5 can correspond to turning on half of the FFMs while the other half are unused. A value of IE = 1 corresponds to the conditions set forth by equation 3. In other words, the set of possible source optimization solutions using equation 3 is a subset of the set of the possible solutions associated with equation 7. With equation 7 being a constraint, to avoid disrupting the source optimizer, FFM activation elements Ci can be substituted with substitute FFM activation elements m according to equation 8.

[0097] The range of each of substitute FFM activation elements Ui can be chosen arbitrarily (e.g., from 0 to 1, from 0% to 100%, or the like). The form of equation 8 is a functional equivalent equation 7 that avoids issues of constraints. To further fine tune the computational performance of the source optimizer, the source optimizer can be programmed to perform optimization iterations within theboundaries IEmni< IE < IEmax, where the minimum illumination efficiency IEmmand the maximum illumination efficiency IEmaxare provided as input to the source optimizer.

[0098] FIG. 7 illustrates an exemplary set of values 700 for substitute continuously variable elements Vi,st and substitute FFM activation elements u,. consistent with embodiments of the present disclosure. For consistency and clarity, descriptions will continue to use the non-limiting example of five states per FFM (extrapolations to any suitable number of two or more states are within the scope of the present disclosure), as well as choosing a range from 0 to 1 for substitute continuously variable elements Vi,st. as well as substitute FFM activation elements Ui. Of the numerous substitute continuously variable elements Vi,st, the values corresponding to the ilstFFM, i2ndFFM, and i3rdFFM have been expanded. Different ones of the states st can correspond to different PFMs. The PFMs from jl to j5 and jll to j 15 can be assigned to corresponding combinations of indices i and st as shown in FIG. 7.

[0099] Source optimization iterations can calculate a cost function value using equation 2 for adjustable elements Pi,st,sipand a suitable combination of equations 6-8 to achieve a fractional illumination efficiency IE. Substitute continuously variable elements Vi,stand substitute FFM activation elements Ui can act as adjustable knobs for optimization. As the source optimizer converges on optimal PFM configurations, certain ones of the substitute continuously variable elements Vi,stcan be biased toward 1 while other ones can become biased toward 0. Similarly, some substitute FFM activation elements Ui can be biased toward 1 while others can become biased toward 0.

[0100] After the optimization iterations are finished (e.g., settled at an optimal solution), binarization can commence. To meet the conditions set forth by equations 7 or 8 (with IEmm< IE < IEmax), the source optimization algorithm can select a collection of the largest optimized ones of substitute FFM activation elements u,. up to a number n of such optimized FFM elements, such that n obeys the conditions set forth in equation 9, equation 10, or both.

[0101] Equations 9 and 10 are provided as example conditions. Equations 9 and 10 reflect the condition that n is the smallest integer that can fulfill the IEmmrequirement while n - 1 does not. A similar set of equations / conditions can be associated with the upper bound IEmax(n / N < IEmaxand (n + 1) / N > IEmax). It is to be appreciated that upper and lower boundaries for the number n of optimized FFM elements can have other forms that are suitable for source optimization.

[0102] In the example of FIG. 7, the ones of substitute FFM activation elements Ui that survive the selection process based on equation 9 (or equation 10 or both) are u,i and ua. Those substitute FFM activation elements Ui that are selected to be turned off are u, . UM, and ua. The brightest virtual FFM states associated with the ‘active’ u,i and ua FFMs are those that correspond to the j2ndPFM and the j I4'1' PFM. To generate machine-compliant instructions, the source optimizer results are analyzed and the brightest virtual PFMs are identified for determining which PFMs in a lithographic apparatus to turn on. The source optimizer can cope with illumination efficiency constraints and PFM mutual exclusivity constraints because the source optimizer takes into account the conditions set forth by a suitable combination of equations 5-10.

[0103] In some embodiments, the SMO cost function comprises edge placement errors (EPEs) evaluated at different process window conditions. The SMO cost function can comprise a suitable combination of lithographic performance indicators, such as EPE, critical dimension (CD), image logslope (ILS), pattern placement error, or the like. The adjustments of the design of pattern 508 (FIG. 5) can be provided in the form of a knob parameter as described above in reference to knobs for illumination parameters. The source optimization algorithm can adjust the knobs of the mask design during the iterations. The output of the optimization process may include machine instructions for an optimized PFM activation configuration that correspond to optimized discrete illumination map 602 or 702 (FIGS. 6 and 7). SMO can be performed by adjusting adjustable elements by iteratively adjusting variable elements of a design for a mask, as well as the continuously variable elements for PFMs, based on iterative simulation of a lithographic process that uses the PFMs and the mask. As noted above, the disclosed source optimization process can be performed concurrently or sequentially with mask optimization, injected wavefront optimization, polarization optimization etc., in various embodiments.

[0104] FIG. 8 illustrates a process flow 800 for optimizing and binarizing a machine-compliant illumination map for conditioning exposure illumination of a lithographic apparatus, consistent with embodiments of the present disclosure. The process flow can be executed using devices and functions described in reference to FIGS. 1A-7.

[0105] In some embodiments, at operation 802, machine-constrained source optimization is performed. The machine-constrained source optimization can be performed using the processes described above in reference to FIGS. 2-7 and equations 1-10. At operation 802, fractional illumination values for PFMs and FFM states are allowed.

[0106] At operation 804, post-processing can be performed on the optimized fractional illumination values for PFMs and FFM states, such as binarization to generate machine-compliant instructions for controlling PFMs and FFMs, as described above.

[0107] FIG. 9 illustrates a method 900 for optimizing a discretized illumination map to configure PFMs for optimal lithographic performance, consistent with embodiments of the present disclosure. The method can be executed using devices and functions described in reference to FIGS. 1 A-8.

[0108] In some embodiments, at operation 902, a discretized illumination map is initialized (e.g., discretized illumination map 500 (FIG. 5)). The discretized illumination map can comprise an array of adjustable elements (e.g., adjustable elements Pj,sip, Pi.st.sip, or the like). Each adjustable element can be calculated based on illumination intensity from a facet mirror of the facetted mirror device. Illumination intensities from the facet mirrors can be calculated by using continuously variable elements (e.g., elements such as q, qi.st, Vi,st, or the like). The illumination intensity can be calculated by also considering the maximum illumination capabilities (e.g., maximum intensity elements mj,sip, mi.st.sip, or the like) of a lithographic apparatus (e.g., lithographic apparatus 100 (FIG. 1A)). The relationship of the quantities of the discretized illumination map can be as in equations 1 or 2.

[0109] At operation 904, the adjustable elements can be adjusted. The adjustments can be iterative according to a source optimization algorithm. The optimization conditions can be assessed based on iterative computation of outcomes of a lithographic process using a patterning device (e.g., patterning device 504 (FIG. 5)).

[0110] Further operations are envisaged to be within the scope of method 900, such as the functions described above in reference to FIGS. 1A-8.[oni] A non-transitory computer-readable medium can be provided that stores instructions for a processor of a controller for optimizing a discretized illumination map to configure PFMs for optimal lithographic performance according to the exemplary flowcharts of FIG. 9, consistent with embodiments in the present disclosure. For example, the instructions stored in the non-transitory computer-readable medium can be executed by the circuitry of the controller for performing method 900 in part or entirely. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read-Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read-Only Memory (PROM), and Erasable Programmable Read-Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0112] Embodiments of the present disclosure can be further described by the following clauses.1. A computer-implemented method for optimizing a beam of illumination used in a lithographic apparatus comprising a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus, the computer-implemented method comprising: initializing a discretized illumination map comprising an array of adjustable elements, wherein each adjustable element is calculated based on illumination intensity from a facet mirror of the facetted mirror device, and wherein illumination intensities from the facet mirrors are calculated by using continuously variable elements; and adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on a source optimization process using a design of a patterning device.2. The computer-implemented method of clause 1, further comprising binarizing the adjustable elements.3. The computer-implemented method of clause 2, wherein the binarizing comprises rounding values of the set of adjustable elements to correspond to binary illumination states of the facet mirrors.4. The computer-implemented method of clause 1, wherein: the facet mirrors at the pupil plane are configured to direct portions of the beam to form an illumination slit at the patterning device; and the each adjustable element is a function of position along the illumination slit.5. The computer-implemented method of clause 4, wherein: the each adjustable element is a functions of maximum illumination intensity associated with a corresponding position along the illumination slit and a continuously variable element that corresponds to the each adjustable element; and the maximum illumination intensity represents an upper bound of illumination intensity provided by the lithographic apparatus associated with the corresponding position along the illumination slit and the facet mirror of the facetted mirror device.6. The computer-implemented method of clause 1, further comprising, in an iteration of the source optimization process, simulating a lithography process with the design of the patterning device; and determining a value from a cost function that includes the adjustable elements and a performance metric associated with the lithographic process.7. The computer-implemented method of clause 1, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the each adjustable element is further calculated based on illumination intensity from a corresponding pupil facet mirror and a corresponding field facet mirror; and the iterative adjustments are further based on adjustments of intensity contributions from the field facet mirrors.8. The computer-implemented method of clause 7, wherein: a first field facet mirror of the facetted field mirror device is configured to be toggled to a selected state from among a first group of mutually exclusive selectable states corresponding to a first group of mutually exclusive pupil facet mirrors of the facetted pupil mirror device that are configured to receive illumination from the first field facet mirror; and the iterative adjustments are further based on mutual exclusivity of the mutually exclusive pupil facet mirrors.9. The computer-implemented method of clause 1, wherein:the adjusting is performed using substitute continuously variable elements as substitutes for the continuously variable elements; and each continuously variable element is a function of a corresponding substitute continuously variable element and a sum of a subset of the continuously variable elements.10. The computer-implemented method of clause 9, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the method further comprises adjusting fractional activation elements that represent fractional activation of the field facet mirrors; and each continuously variable element is a function of a corresponding fractional activation element.11. The computer-implemented method of clause 10, wherein: an illumination usage ratio represents a ratio of a number of field facet mirrors to be activated in the lithographic apparatus to a total number of field facet mirrors available for use in the lithographic apparatus; adjusting fractional activation elements is performed using substitute fractional activation elements; and each fractional activation element is a function of a corresponding substitute activation element, the illumination usage ratio, and a sum of a subset of the substitute fractional activation elements.12. The computer-implemented method of clause 1, further comprising adjusting variable elements based on the iterative computation of the outcomes of the lithographic process using the patterning device.13. The computer-implemented method of clause 1, further comprising generating an adjusted discretized illumination map based on adjustments to the adjustable elements of the initialized discretized illumination map.14. The computer-implemented method of clause 1, further comprising executing the lithographic process using the adjusted discretized illumination map to control the facet mirrors at the pupil plane.15. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing a beam of illumination used in a lithographic apparatus comprising a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus, the operations comprising: initializing a discretized illumination map comprising an array of adjustable elements, wherein each adjustable element is calculated based on illumination intensity from a facet mirror ofthe facetted mirror device, and wherein illumination intensities from the facet mirrors are calculated by using continuously variable elements; and adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.16. The non-transitory computer-readable medium of clause 15, wherein the operations further comprise binarizing the adjustable elements.17. The non-transitory computer-readable medium of clause 16, wherein the binarizing comprises rounding values of the set of adjustable elements to correspond to binary illumination states of the facet mirrors.18. The non-transitory computer-readable medium of clause 15, wherein: the facet mirrors at the pupil plane are configured to direct portions of the beam to form an illumination slit at the patterning device; and the each adjustable element is a function of position along the illumination slit.19. The non-transitory computer-readable medium of clause 18, wherein: the each adjustable element is a function of maximum illumination intensity associated with a corresponding position along the illumination slit and a continuously variable element that corresponds to the each adjustable element; and the maximum illumination intensity represents an upper bound of illumination intensity provided by the lithographic apparatus associated with the corresponding position along the illumination slit and the facet mirror of the facetted mirror device.20. The non-transitory computer-readable medium of clause 15, wherein the operations further comprise, at each of the iterations, determining a value from a cost function that includes the adjustable elements and a performance metric associated with the lithographic process.21. The non-transitory computer-readable medium of clause 15, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the each adjustable element is further calculated based on illumination intensity from a corresponding pupil facet mirror and a corresponding field facet mirror; and the iterative adjustments are further based on adjustments of intensity contributions from the field facet mirrors.22. The non-transitory computer-readable medium of clause 21, wherein: a first field facet mirror of the facetted field mirror device is configured to be toggled to a selected state from among a first group of mutually exclusive selectable states corresponding to a first group of mutually exclusive pupil facet mirrors of the facetted pupil mirror device that are configured to receive illumination from the first field facet mirror; andthe iterative adjustments are further based on mutual exclusivity of the mutually exclusive pupil facet mirrors.23. The non-transitory computer-readable medium of clause 15, wherein: the adjusting is performed using substitute continuously variable elements as substitutes for the continuously variable elements; and each continuously variable element is a function of a corresponding substitute continuously variable element and a sum of a subset of the continuously variable elements.24. The non-transitory computer-readable medium of clause 23, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the operations further comprise adjusting fractional activation elements that represent fractional activation of the field facet mirrors; and each continuously variable element is a function of a corresponding fractional activation element.25. The non-transitory computer-readable medium of clause 24, wherein: an illumination usage ratio represents a ratio of a number of field facet mirrors to be activated in the lithographic apparatus to a total number of field facet mirrors available for use in the lithographic apparatus; adjusting fractional activation elements is performed using substitute fractional activation elements; and each fractional activation element is a function of a corresponding substitute activation element, the illumination usage ratio, and a sum of a subset of the substitute fractional activation elements.26. The non-transitory computer-readable medium of clause 15, wherein the operations further comprise adjusting variable elements based on the iterative computation of the outcomes of the lithographic process using the patterning device.27. The non-transitory computer-readable medium of clause 15, wherein the operations further comprise generating an adjusted discretized illumination map based on adjustments to the adjustable elements of the initialized discretized illumination map.28. The non-transitory computer-readable medium of clause 15, wherein the operations further comprise executing the lithographic process using the adjusted discretized illumination map to control the facet mirrors at the pupil plane.29. A system for optimizing a beam of illumination used in a lithographic apparatus comprising a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus, the system comprising: one or more processors; anda non-transitory computer-readable medium that stores a set of instructions that is executable by the one or more processors to cause the system to perform operations comprising: initializing a discretized illumination map comprising an array of adjustable elements, wherein each adjustable element is calculated based on illumination intensity from a facet mirror of the facetted mirror device, and wherein illumination intensities from the facet mirrors are calculated by using continuously variable elements; and adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.30. The system of clause 29, wherein the operations further comprise binarizing the adjustable elements.31. The system of clause 30, wherein the binarizing comprises rounding values of the set of adjustable elements to correspond to binary illumination states of the facet mirrors.32. The system of clause 29, wherein: the facet mirrors at the pupil plane are configured to direct portions of the beam to form an illumination slit at the patterning device; and the each adjustable element is a function of position along the illumination slit.33. The system of clause 32, wherein: the each adjustable element is a function of maximum intensity associated with a corresponding position along the illumination slit and a continuously variable element that corresponds to the each adjustable element; and the maximum illumination intensity represents an upper bound of illumination intensity provided by the lithographic apparatus associated with the corresponding position along the illumination slit and the facet mirror of the facetted mirror device.34. The system of clause 29, wherein the operations further comprise, at each of the iterations, determining a value from a cost function that includes the adjustable elements and a performance metric associated with the lithographic process.35. The system of clause 29, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the each adjustable element is further calculated based on illumination intensity from a corresponding pupil facet mirror and a corresponding field facet mirror; and the iterative adjustments are further based on adjustments of intensity contributions from the field facet mirrors.36. The system of clause 35, wherein:a first field facet mirror of the facetted field mirror device is configured to be toggled to a selected state from among a first group of mutually exclusive selectable states corresponding to a first group of mutually exclusive pupil facet mirrors of the facetted pupil mirror device that are configured to receive illumination from the first field facet mirror; and the iterative adjustments are further based on mutual exclusivity of the mutually exclusive pupil facet mirrors.37. The system of clause 29, wherein: the adjusting is performed using substitute continuously variable elements as substitutes for the continuously variable elements; and each continuously variable element is a function of a corresponding substitute continuously variable element and a sum of a subset of the continuously variable elements.38. The system of clause 37, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the operations further comprise adjusting fractional activation elements Ci that represent fractional activation of the field facet mirrors; and each continuously variable element is a function of a corresponding fractional activation element.39. The system of clause 38, wherein: an illumination usage ratio represents a ratio of a number of field facet mirrors to be activated in the lithographic apparatus to a total number of field facet mirrors available for use in the lithographic apparatus; adjusting fractional activation elements is performed using substitute fractional activation elements; and each fractional activation element is a function of a corresponding substitute activation element, the illumination usage ratio, and a sum of a subset of the substitute fractional activation elements.40. The system of clause 29, wherein the operations further comprise adjusting variable elements based on the iterative computation of the outcomes of the lithographic process using the patterning device.41. The system of clause 29, wherein the operations further comprise generating an adjusted discretized illumination map based on adjustments to the adjustable elements of the initialized discretized illumination map.42. The system of clause 29, wherein the operations further comprise executing the lithographic process using the adjusted discretized illumination map to control the facet mirrors at the pupil plane.

[0113] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings and that various modifications and changes can be made without departing from the scope thereof.

Claims

CLAIMS1. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to cause the apparatus to perform operations for optimizing a beam of illumination used in a lithographic apparatus comprising a facetted mirror device comprising facet mirrors disposed at a pupil plane of the lithographic apparatus, the operations comprising: initializing a discretized illumination map comprising an array of adjustable elements, wherein each adjustable element is calculated based on illumination intensity from a facet mirror of the facetted mirror device, and wherein illumination intensities from the facet mirrors are calculated by using continuously variable elements; and adjusting the adjustable elements by iterative adjustments of the continuously variable elements based on iterative computation of outcomes of a lithographic process using a patterning device.

2. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise binarizing the adjustable elements.

3. The non-transitory computer-readable medium of claim 2, wherein the binarizing comprises rounding values of the set of adjustable elements to correspond to binary illumination states of the facet mirrors.

4. The non-transitory computer-readable medium of claim 1, wherein: the facet mirrors at the pupil plane are configured to direct portions of the beam to form an illumination slit at the patterning device; and the each adjustable element is a function of position along the illumination slit.

5. The non-transitory computer-readable medium of claim 4, wherein: the each adjustable element is a function of maximum illumination intensity associated with a corresponding position along the illumination slit and a continuously variable element that corresponds to the each adjustable element; and the maximum illumination intensity represents an upper bound of illumination intensity provided by the lithographic apparatus associated with the corresponding position along the illumination slit and the facet mirror of the facetted mirror device.

6. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise, at each of the iterations, determining a value from a cost function that includes the adjustable elements and a performance metric associated with the lithographic process.

7. The non-transitory computer-readable medium of claim 1, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the each adjustable element is further calculated based on illumination intensity from a corresponding pupil facet mirror and a corresponding field facet mirror; and the iterative adjustments are further based on adjustments of intensity contributions from the field facet mirrors.

8. The non-transitory computer-readable medium of claim 7, wherein: a first field facet mirror of the facetted field mirror device is configured to be toggled to a selected state from among a first group of mutually exclusive selectable states corresponding to a first group of mutually exclusive pupil facet mirrors of the facetted pupil mirror device that are configured to receive illumination from the first field facet mirror; and the iterative adjustments are further based on mutual exclusivity of the mutually exclusive pupil facet mirrors.

9. The non-transitory computer-readable medium of claim 1, wherein: the adjusting is performed using substitute continuously variable elements as substitutes for the continuously variable elements; and each continuously variable element is a function of a corresponding substitute continuously variable element and a sum of a subset of the continuously variable elements.

10. The non-transitory computer-readable medium of claim 9, wherein: the facet mirrors are pupil facet mirrors; the lithographic apparatus further comprises a facetted field mirror device comprising field facet mirrors disposed upstream of the pupil facet mirrors; the operations further comprise adjusting fractional activation elements that represent fractional activation of the field facet mirrors; and each continuously variable element is a function of a corresponding fractional activation element.

11. The non-transitory computer-readable medium of claim 10, wherein:an illumination usage ratio represents a ratio of a number of field facet mirrors to be activated in the lithographic apparatus to a total number of field facet mirrors available for use in the lithographic apparatus; adjusting fractional activation elements is performed using substitute fractional activation elements; and each fractional activation element is a function of a corresponding substitute activation element, the illumination usage ratio, and a sum of a subset of the substitute fractional activation elements.

12. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise adjusting variable elements based on the iterative computation of the outcomes of the lithographic process using the patterning device.

13. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise generating an adjusted discretized illumination map based on adjustments to the adjustable elements of the initialized discretized illumination map.

14. The non-transitory computer-readable medium of claim 1, wherein the operations further comprise executing the lithographic process using the adjusted discretized illumination map to control the facet mirrors at the pupil plane.

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