Automatically initialize pupil-wavefront pair for effective pupil-wavefront-mask co-optimization

Abstract

A method for optimizing a source profile and wavefront profile to simulate a lithography process is disclosed. More particularly, a method for minimizing a phase offset between diffraction orders in a source profile to generate an optimized source profile and an optimized wavefront profile, using a cost function with a phase cost term is disclosed. The disclosed method may further include a diffraction overlap penalty term in the cost function.

Description

AUTOMATICALLY INITIALIZE PUPIL-WAVEFRONT PAIR FOR EFFECTIVE PUPIL- WAVEFRONT-MASK CO-OPTIMIZATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 736,558 which was filed on 19 December 2024, and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to a method for optimizing a source profile and wavefront profile by simulating a lithography process. More particularly, a method for minimizing a phase offset between diffraction orders caused by a Mask3D (M3D) fading effect to generate an optimized source profile and optimized wavefront profile by using a cost function with a phase cost term is disclosed.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 source profile (e.g., a two-dimensional map of the illumination intensity distribution).

[0004] 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 source profile can result from source optimization, source-mask optimization, an empirical source profile, a source profile from another lithographic projection system, or the like. A well optimized source profile is conducive to accurate and efficient lithographic IC fabrication.SUMMARY

[0005] Embodiments of the present disclosure provide a method for optimizing a source profile and wavefront profile to simulate a lithography process.

[0006] In some embodiments, the present disclosure provides a method for simulating a lithography process. The method comprises obtaining a source profile, a wavefront profile, and a mask pattern, and optimizing the source profile and the wavefront profile by simulating the lithography process that uses the mask pattern, wherein optimizing the source profile and the wavefront profile comprises using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process.

[0007] In some embodiments, the present disclosure provides a non-transitory computer readable medium comprising a set of instructions that is executable by one or more processors of a computingdevice to cause the computing device to perform operations for simulating a lithography process. The operations comprise obtaining a source profile, a wavefront profile, and a mask pattern, and optimizing the source profile and the wavefront profile by simulating the lithography process that uses the mask pattern, wherein optimizing the source profile and the wavefront profile comprises using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process.

[0008] In some embodiments, the present disclosure provides a system for simulating a lithography process, the system comprising a memory storing a set of instructions and at least one processor configured to execute the instructions to cause the system to perform operations. The operations comprise obtaining a source profile, a wavefront profile, and a mask pattern, and optimizing the source profile and the wavefront profile by simulating the lithography process that uses the mask pattern, wherein optimizing the source profile and the wavefront profile comprises using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process.

[0009] Other advantages of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of the present disclosure.BRIEF DESCRIPTION OF FIGURES

[0010] 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.

[0011] FIG. 1 is a schematic illustrating an example lithographic apparatus, consistent with embodiments of the present disclosure.

[0012] FIG. 2 is a schematic illustrating an example lithographic apparatus, consistent with embodiments of the present disclosure.

[0013] FIG. 3 is a flowchart of an example method for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure.

[0014] FIG. 4 is a flowchart of an example method for source or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0015] FIGS. 5A and, 5B illustrate a contribution of a patterning device in a lithography process, consistent with embodiments of the present disclosure.

[0016] FIG. 6 is an example flowchart of an optimization method.

[0017] FIG. 7 is an example flowchart of an optimization method.

[0018] FIG. 8 is an example flowchart of an optimization method.

[0019] FIG. 9 is an example workflow for co-optimizing a pupil profile and wavefront, consistent with embodiments of the present disclosure.

[0020] FIG. 10 is an illustration of co-optimizing a pupil profile and wavefront to minimize a phase offset between diffraction orders, consistent with embodiments of the present disclosure.

[0021] FIG. 11A and 11B are illustrations of co-optimizing a pupil profile and wavefront to minimize a phase offset between diffraction orders, consistent with embodiments of the present disclosure.

[0022] FIG. 12 is an example workflow illustrating a method, 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] Integrated circuits (ICs) may be manufactured using lithography, which is a fabrication process involving creating complex circuit patterns drawn on a mask deposited onto a substrate. The lithography process involves creating a master image on a mask or reticle (mask and reticle are used interchangeably herein), then projecting an image from the mask onto a resist-covered substrate in order to create a pattern that matches the design intent of defining functional elements, such as transistor gates, contacts, etc., on the device wafer. The mask may be a transmissive or a reflective mask. The more times a mask pattern is successfully replicated within the design specifications, the lower the cost per finished device or “chip” will be. The mask pattern is typically formed by depositing and patterning a light-absorbing material on quartz or another transparent substrate. The mask is then placed in an exposure tool known as a “stepper” or “scanner” where light of a specific exposure wavelength is directed from the mask to the wafers. The light may interact with the mask and then be diffracted into different diffraction orders. The light that passes through some regions of the mask may also be phase shifted by a desired phase angle, typically an integer multiple of 180 degrees. After being collected by the projection optics of the exposure tool, the resulting aerial image pattern is then focused onto the wafers. A light-sensitive material (photoresist or resist) deposited on the wafer surface interacts with the light to form the desired pattern on the wafer, and the pattern is then transferred into the underlying layers on the wafer to form functional electrical circuits according to well-known processes. 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.

[0025] A lithography mask may impact characteristics at the wafer level., e.g., an aerial image and lithometrics, including contrast, best focus shifts, critical dimension (CD) variations, pattern placement errors, and non-telecentricity. One impact caused by the mask in the aerial image is image fading (or M3D fading), which may be referred to as a mask 3D (“M3D”) effect. The M3D effect may cause a phase difference between diffraction orders, which then causes an aerial image shift per source point. This phase difference may cause an image shift per illumination source point, and thus introduce significant image degradation. To address this, the projection optics of a lithography apparatus may be manipulated to add a controlled aberration to compensate for the phase difference. For example, the illumination source shape may be modified, a wavefront injection may be simultaneously applied to a lens component to compensate for the phase difference. Deciding an appropriate illumination source shape and an appropriate wavefront injection profile can be an optimization problem. The mask design may be co-optimized together with the wavefront profile and the illumination source shape. Conventionally, the aberration is determined by an optimization method that adds a particular Zernike term to compensate for a phase difference between a 0thand 1stdiffraction order. However, this is not a general solution and cannot be applied to all cases for lithography processes (e.g., for compensating physical effects induced by a 2D mask pattern). Additionally, the aberration determined by the conventional method may not be achievable with a lens model, and the mask and optical hardware are not co-optimized with the aberration, thus limiting the benefits of the conventional method.

[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 method for minimizing a M3D fading effect. The present disclosure provides a method for minimizing the phase offset (in some embodiments for all pixels) in an illumination source by co-optimizing an illumination source shape and a wavefront profile. The co-optimization may be achieved by using a cost function including a phase offset term. The disclosed method uses an initial source profile and wavefront profile, thus enabling an automatic optimization method that is free of human error and sub-optimization. It is appreciated that term “source” and the term “pupil” may be used interchangeably throughout the present disclosure. For example, an “initial source profile” or a “source shape” may be understood to also mean an “initial pupil profile” or a “profile shape.”

[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). The term “source” and “illumination source” as used herein may include illumination optics.

[0034] The term “optimizing” and “optimization” as used herein can indicate adjusting a lithographic apparatus, a lithographic process, etc. 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. Thus, the term “optimizing” and “optimization” as used herein refers to or means a process that identifies one or more values for one or more parameters that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for those one or more parameters. "Optimum" and other related terms should be construed accordingly. In an embodiment, optimization steps can be applied iteratively to provide further improvements in one or more metrics.

[0035] FIG. 1 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 0maxcan define the numerical aperture NA of the projection optics as NA = n sin(0max), 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” as used herein should be broadly interpreted as encompassing various types of optical systems, including refractive optics, reflective optics, apertures and catadioptric optics, for example. The term “projection optics” may also include components operating according to any of these design types for directing, shaping or controlling the projection beam of radiation, collectively or singularly. The term “projection optics” may include any optical component in the lithographic projection apparatus, no matter where the optical component is located on an optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting or projecting radiation from the source before the radiation passes the patterning device, or optical components for shaping, adjusting or projecting the radiation after the radiation passes the patterning device. The projection optics may include components collectively called a “wavefrontmanipulator” that can be used to adjust shapes of a wavefront and intensity distribution or phase shift of the irradiation beam. The projection optics can adjust a wavefront and intensity distribution at any location along an optical path of the lithographic apparatus, such as before the patterning device, near an illumination source plane, near an image plane, near a focal plane. The projection optics can be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused by, for example, the illumination source, the patterning device, temperature variation in the lithographic apparatus, or thermal expansion of components of the lithographic apparatus. Adjusting the wavefront and intensity distribution can change values of evaluation points and a cost function. Such changes can be simulated from a model or actually measured. 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.

[0038] FIG. 2 illustrates an exemplary lithographic apparatus 200, consistent with embodiments of the present disclosure. In some embodiments, lithographic apparatus 200 may represent an EUV lithography apparatus. FIG. 2 illustrates that lithographic apparatus 200 includes an illumination source collector module 201, illumination optics 202, a patterning device 203, projection optics 204, and a sample 205. Illumination optics 202 can include optic components 104, 106a, and 106b that shape radiation from source 102 (see FIG. 1) and projection optics 204 can include optic components 104, 106b, 106b, and 106c. Illumination source collector module 201 may be constructed and arranged such that a vacuum environment can be maintained. A plasma 206 may be produced from plasma source 207, and plasma 206 may emit a radiation beam 208. Radiation beam 208 may emit radiation in the EUV range of the electromagnetic spectrum. Radiation beam 208 may be collected and reflected off a grating filter 209 to be focused to a virtual source point 210 along an optical axis. The virtual source point 210 is commonly referred to as the intermediate focus 210, and the source collector module is arranged such that intermediate focus 210 is located at or near an opening in illumination source collector module 201. Intermediate focus 210 may be an image of plasma 206 (e.g., the source). Radiation beam 208 traverses the illumination optics 202, which may include a facetted field mirror device 211 and a facetted pupil mirror device 212 arranged to provide a desired angular distribution of the radiation beam 208 as well as a desired uniformity of radiation intensitywhen reflection at patterning device 203. After reflection of radiation beam 208 at patterning device 203, a patterned beam 213 is formed, which may contain information of a pattern on patterning device 203. Patterned beam 213 is projected by projection optics 204 via reflective elements 214 and 215 onto sample 205. It is appreciated that FIG. 2 is for illustrative purposes, and it not representative in terms of, e.g., scale, orientation, or number of features in lithographic apparatus 200.

[0039] FIG. 3 illustrates a flowchart of an exemplary method 300 for simulating lithography in a lithographic apparatus, consistent with embodiments of the present disclosure. In some embodiments, a source model 302 represents optical characteristics of the source (e.g., including radiation intensity distribution, phase distribution, or the like). A projection optics model 304 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 306 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 308 can be simulated from source model 302, projection optics model 304, and design layout model 306. A resist image 312 can be simulated from aerial image 308 using a resist model 310. 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.

[0040] It is noted that the source model 302 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 304 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 306 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 (OF), 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, caninclude feature information stored in a binary file format representing planar geometric shapes, text, and other information related to the wafer design.

[0041] 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.

[0042] 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.

[0043] 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. 3). The optimization process can involve execution of the one or 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.

[0044] 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.

[0045] 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.

[0046] FIG. 4 illustrates a flowchart of an exemplary method 400 of source or mask optimization of a patterning process, consistent with embodiments of the present disclosure. In a typical high-enddesign, 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.

[0047] 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 400 is an example SMO method.

[0048] A target design 401 (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 402 can be extracted, which represents complex patterns in design 401 (e.g., about 50 to 1000 clips). It is to be appreciated that these clips represent small portions (i.e., circuits, cells, or patterns) of the design for which particular attention or verification is of interest. At operation 404, a small subset of clips 406 (e.g., 15 to 50 clips) can be selected from full set of clips 402. 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.

[0049] At operation 408, SMO can be performed with the selected patterns (15 to 50 patterns) of subset of clips 406. In particularly, an illumination source can be optimized for the selected patterns of subset of clips 406. 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.

[0050] At operation 410, manufacturability verification of the selected patterns of subset of clips 406 can be performed with the source obtained in operation 408. In particular, verification can include performing an aerial image simulation of the selected patterns of subset of clips 406 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 410 is satisfactory, as determined in operation 412, then processing can advance to full chip optimization (e.g., advanced tooperations using optimized source 414). Otherwise, processing can return to operation 408, 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.

[0051] After the selected patterns meet lithography performance specification as determined in step 412, the optimized source 414 can be used for optimization of the full set of clips 416 (e.g., originating from full set of clips 402).

[0052] At operation 418, model-based sub-resolution assist feature placement (MB-SRAF) and optical proximity correction (OPC) for all the patterns in the full set of clips 416 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.

[0053] At operation 420, using processes similar to step 410, full pattern simulation based manufacturability verification can be performed with the optimized source 414 and the full set of clips 416 as corrected in step 418.

[0054] At operation 422, the performance (e.g., process window parameters such as exposure latitude and depth of focus) of the full set of clips 416 can be compared against subset of clips 406. For example, the pattern selection can be considered complete or the source is fully qualified for the full chip when the similar (<10%) lithography performances are obtained for both selected patterns of subset of clips 406 and critical patterns of full set of clips 416.

[0055] Otherwise, at operation 424, hotspots can be extracted. At operation 426, the hotspots can be added to subset of clips 406 and the process starts over. For example, hotspots (e.g., features among the full set of clips 416 that limit process window performance) identified during verification step 420 can be used for further source tuning or to run SMO of operation 408 again. The source can be considered fully converged when the process window of the full set of clips 416 are the same between the last run and the run before the last run of operation 422.

[0056] 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.

[0057] 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 absenceof 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.

[0058] 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 or application of “assist” features that are intended to assist projection of other features.

[0059] 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., patterning device patterns 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 patterning device pattern. This is driven by the enormous cost of making high-end patterning devices, as well as by the impact on turn-around time by reworking or repairing existing patterning 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.

[0060] The illumination source can also be optimized, either jointly with patterning device optimization or separately, to improve the overall lithography fidelity. The terms “illumination source”, “pupil,” 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 patterning 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 desirable to optimize the illumination source to achieve balance between finer resolution (relevant to yield) and reduced radiation intensity (relevant to throughput).

[0061] As discussed above, the M3D effect may cause a phase difference between diffraction orders of a light beam that interacts with a mask. This may result in an aerial image shift per source point. An aerial image shift may also occur due to configuration of the lithographic apparatus, such as finite thickness of a patterning device or mask-3D (e.g., 3-D effect), pattern-dependent incident or exit angles, non-uniform intensity of zero diffraction order from different positions of the illumination source, and distortion or non-telecentricity of the projection optics. The aerial image is a result of superimposing an aerial image for each source point, so the M3D effect introduces significant degradation in overall aerial image contrast. The M3D effect with respect to image contrast loss may be referred to as “M3D fading,” which can cause up to 20% contrast loss compared to the attainable contrast expected from basic imaging considerations. Imaging theory dictates that the aerial image intensity for 2-beam imaging conditions can be expressed as:where Aois a 0thdiffraction order amplitude, A is a 1stdiffraction order amplitude, p is a pitch, and Aq>0 1is phase difference between the 0thdiffraction order and the 1stdiffraction order.

[0062] A phase difference between the 0thdiffraction order and the 1stdiffraction order results in an image shift. The image shift can be expressed as:

[0063] The image contrast of a sub-image generated from the 0thdiffraction order and the 1stdiffraction order can be expressed as:

[0064] Balancing the 0thdiffraction order and 1stdiffraction order amplitudes results in an optimal image contrast value of 1. It is appreciated that the same holds true for an image created by the 0thdiffraction order and the -1stdiffraction order, except the phase difference is opposite compared to Aq>0 1and the corresponding image shift is opposite to the image shift resulting from the 0thdiffraction order and the 1stdiffraction order. For example, the image shift resulting from the 0thdiffraction order and 1stdiffraction order may be to the right of an intended position and the image shift resulting from the 0thdiffraction order and the -1stdiffraction order may be to the left of an intended position. The final image is comprised of the superposition of the images from both lightbeams, shifted in opposite directions, leading to M3D fading with a magnitude that can be expressed as:(Eq- 4),

[0065] Equation 4 can be generalized to a partial coherent illumination source by defining the illumination source by a sufficiently dense grid of source points for which image contrast (Eq. 3) and image shift (Eq. 2) can be calculated.

[0066] Reference is now made to FIG. 5A, which is an example schematic representation of M3D fading, consistent with some embodiments of the present disclosure. FIG. 5A illustrates an aerial image shift for a vertically oriented dense line space pattern illuminated with a dipole source, in which the aerial image shift is induced by M3D fading. It is appreciated that FIG. 5A is for illustrative purposes and that embodiments of the present disclosure are not so limited. An illumination source 501 may comprise a left pole 502 that creates sub-image 503 according to a position 504 and intensity 505. Illumination source 501 may also comprise a right pole 506 that creates sub-image 507. Subimage 503 and sub-image 507 may be calculated as described above. Sub-image 503 may be shifted to the right with respect to an intended position 508, and sub-image 507 may be shifted to the light with respect to intended position 508. A final image 509, which is the superposition of left pole 502 and right pole 506, is the superposition of sub-image 503 and sub-image 507. Final image 509 is imaged (e.g., centered) at intended position 508 but has significantly degraded contrast (M3D fading) compared to sub-image 503 or sub-image 507.

[0067] Reference is now made to FIG. 5B, which illustrates a contribution of a patterning device (e.g., mask 203 in FIG. 2) in a lithography process. FIG. 5B illustrates a radiation beam 510 projected to a mask 511 and a patterned beam 512 after diffraction from mask 511. Although FIG. 5B illustrates mask 511 is horizontal, it is appreciated that mask 511 may be positioned at an angle within the lithographic apparatus. FIG. 5B also illustrates an illumination pupil 513 in radiation beam 510 and a projection pupil 514 in patterned radiation beam 512. Illumination pupil 513 and projection pupil 514 may reside in a same pupil plane in the lithographic apparatus and are optical conjugates. Because radiation beam 510 is diffracted by mask 511, patterned radiation beam 512 may have different diffraction orders. The bold lines represent a 0thdiffraction order of patterned radiation beam 512, the dashed lines 515 represent a -1stdiffraction order, and dashed lines 516 represent a +lstdiffraction order of patterned radiation beam 512. A pattern applied to a sample may primarily be based on an intensity of a 0thdiffraction order of patterned radiation beam 512. However, the 0thdiffraction order radiation beam (patterned radiation beam 512) may partially overlap with thedifferent diffraction orders, which may cause contrast degradation of a resulting image (e.g., aerial image) and thus result in wafer level imaging performance degradation.

[0068] As an illustrative example, a source for the lithographic apparatus in FIG. 5B may have a dipole pupil shape, so illumination pupil 513 may contain a first dipole 517 and a second dipole 518. First dipole 517 and second dipole 508 may be areas in illumination pupil 513 that are “activated” and thus emit radiation to mask 511. Thus, radiation emitted from first dipole 517 may be diffracted in a 0thorder 519, -1storder 520, and a +lstorder 521, and radiation emitted from second dipole 518 may be diffracted in a 0thorder 522, -1storder 523, and a +lstorder 524. FIG. 5B illustrates the diffraction orders from first dipole 517 as ellipses with vertical lines and the diffractions from second dipole 509 as ellipses with a horizontal line as an illustrative guide. As seen in FIG. 5B, 0thorder 519 (first dipole 517) overlaps with -1stdipole 523 (second dipole 518), and +lstorder 521 (first dipole 517) overlaps with 0thdipole 522 (second dipole 518) as seen by the ellipses with vertical and horizontal lines. Because different diffraction orders have different phases, this may result in a loss in contrast and cause a degradation in image quality. It is appreciated that FIG. 5B is illustrative and should not be interpreted as limiting. For example, the following description may be applicable to a radiation beam interacting with a pattern device such as patterning device 108 in FIG. 1 and diffracting into different diffraction orders. For example, the partial overlap of diffraction orders illustrated in FIG. 5B may be representative of partial overlap occurring in a lithography apparatus containing a transmissive patterning device.

[0069] Embodiments of the present disclosure provide a method to co-optimize a source profile, a mask design, or wavefront profile that can mitigate a mask effect in a lithography process. The method includes a phase cost term in a cost function that may indicate a phase offset between diffraction orders in a radiation beam diffracted by a mask. In some embodiments, the disclosed optimization method may use an initial wavefront to provide to a workflow for wavefront, pupil, and mask co-optimization, or individual optimization. In some embodiments, a phase cost term may be used for co-optimizing the source profile, mask pattern, and wavefront profile together to minimize the phase offset between diffraction orders. In some embodiments, the source profile, mask pattern, and wavefront may be co-optimized by using a cost function that includes a compensated phase term for each diffraction order for each source point in the source. A compensated phase is the predicted phase of a diffraction order for a source point after a wavefront injection. In some embodiments, the compensated phase term is a penalty term in the disclosed co-optimization method to minimize the compensated phase term and drive the compensated phase to zero. Thus, the disclosed cooptimization method can minimize a phase offset between an initial phase and the compensated phase of a diffraction order. In some embodiments, the phase offset may be minimized by minimizing a sum of the absolute phase of all diffraction orders. In some embodiments, the phase offset may be minimized by minimizing a phase offset between interference pairs of two diffraction orders for a source point. In some embodiments, the disclosed optimization method further includes a diffractionpattern overlap cost term, which may optimize the source shape by avoiding any source points that have overlapping diffraction orders. The new cost function terms disclosed herein can be used in any suitable optimization process and can be used along with any other suitable cost terms. Embodiments of the present disclosure provide an optimization method to generate an optimized wavefront by using with an initial source profile and a zero-wavefront term, thus ensuring the optimization method is optimal, automated, and free of human error.

[0070] In some embodiments, an optimization process can comprise determining a value for each of the optimization variables 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 lithographic performance). The cost function may represent any suitable characteristics of the lithographic apparatus or the substrate, for instance, focus, CD, image shift, image distortion, image rotation, defects, throughput, etc. For example, the cost function may be a function of one or more of the following lithographic metrics: phase offset (explained further below), diffraction order overlap (explained further below), edge placement error, critical dimension, resist contour distance, worst defect size, stochastic effect, three-dimensional effect of the patterning device, three-dimensional effect of the resist, best focus shift, pupil fill factor, exposure time, and throughput. Since it is the resist image that often dictates the circuit pattern on a substrate, the cost function may include a function that represents a characteristic of the resist image. For example, fp(zi, Z2, . . . , ZN) of such an evaluation point can be simply a distance between a point in the resist image to an intended position of that point (i.e., edge placement error EPEp(zi, Z2, . . . , ZN)). The design variables can be any adjustable parameters such as adjustable parameters of the source, the patterning device, the projection optics, dose, focus, etc. The design variables may have constraints, which can be expressed as (z1;z2, •" > ZN) G Z, where Z is a set of possible values of the design variables. One possible constraint on the design variables may be imposed by a desired throughput of the lithographic projection apparatus. Without such a constraint imposed by the desired throughput, the optimization may yield a set of values of the design variables that are unrealistic. For example, if the dose is a design variable, without such a constraint, the optimization may yield a dose value that makes the throughput economically impossible. However, the usefulness of constraints should not be interpreted as a necessity. For example, the throughput may be affected by the pupil fill ratio. For some illumination source designs, a low pupil fill ratio may discard radiation, leading to lower throughput. Throughput may also be affected by the resist chemistry. Slower resist (e.g., a resist that requires higher amount of radiation to be properly exposed) leads to lower throughput. In some embodiments, the constraints on the design variables are such that the design variables cannot have values that change any geometrical characteristics of the patterning device — namely, the patterns on the patterning device will remain unchanged during the optimization. Any other terms may be included in the cost function without departing from the scope of the present disclosure. The set values for optimization variables result in a corresponding value for the cost function. Afterward, a new iterationcan be initiated in which the optimization variables are adjusted. The cost function can then be calculated to ascertain whether the value of the cost function has been reduced and so that the optimization variables are moved in the direction of better lithographic performance. The iterations of variable adjustments can be repeated until the cost is minimized (fully optimized source).

[0071] The optimization process therefore is to find a set of values of the one or more design variables, under the constraints (z1;z2, •" >ZN) G Z, that optimize the cost function, e.g., to find:(z1;z2, • • • , ZJV) = arg min CF(z1, z2, --- , zw) (Eq. 5)(z1,z2,---,zN)ez

[0072] A general method of optimizing, according to an embodiment, is illustrated in FIG. 6. This method comprises a step S602 of defining a multi-variable cost function of a plurality of design variables. The design variables may comprise any suitable combination selected from design variables representing one or more characteristics of the illumination source (600A) (e.g., pupil fill ratio, namely percentage of radiation of the illumination that passes through a pupil or aperture), one or more characteristics of the projection optics (600B) and / or one or more characteristics of the design layout (600C). For example, the design variables may include design variables representing one or more characteristics of the illumination source (600A) (e.g., being or including the bandwidth) and of the design layout (600C) (e.g., global bias) but not of one or more characteristics of the projection optics (600B), which leads to an illumination-patterning device (e.g., mask) optimization (“sourcemask optimization” or SMO). Or, the design variables may include design variables representing one or more characteristics of the illumination source (600A) (optionally polarization), of the projection optics (600B) and of the design layout (600C), which leads to an illumination-patterning device (e.g., mask)-projection system (e.g., lens) optimization (“source-mask-wavefront optimization” or SMWO). Or the design variables may include design variables representing one or more characteristics of the illumination (600A) (e.g., being or including the bandwidth), one or more non-geometrical characteristics of the patterning device, or one or more characteristics of the projection optics (600B), but not any geometrical characteristics of the patterning device. In step S604, the design variables are simultaneously adjusted so that the cost function is moved towards convergence. In some embodiments, not all design variables may be simultaneously adjusted. Each design variable may also be adjusted individually. In step S606, it is determined whether a predefined termination condition is satisfied. The predetermined termination condition may include various possibilities, e.g.., one or more selected from: the cost function is minimized or maximized, as required by the numerical technique used, the value of the cost function is equal to a threshold value or crosses the threshold value, the value of the cost function reaches within a preset error limit, or a preset number of iterations is reached. If a condition in step S606 is satisfied, the method ends. If the one or more conditions in step S606 is not satisfied, the steps S604 and S606 are iteratively repeated until a desiredresult is obtained. The optimization does not necessarily lead to a single set of values for the one or more design variables because there may be a physical restraint, caused by a factor such as pupil fill factor, resist chemistry, throughput, etc. The optimization may provide multiple sets of values for the one or more design variables and associated performance characteristics (e.g., the throughput) and allows a user of the lithographic apparatus to pick one or more sets. In FIG. 6, the optimization of all the design variables is executed simultaneously. Such a flow may be called simultaneous flow or cooptimization flow.

[0073] Different subsets of the design variables (e.g., one subset including characteristics of the illumination, one subset including characteristics of patterning device and one subset including characteristics of projection optics) can be optimized alternatively (referred to as Alternative Optimization) or optimized simultaneously (referred to as Simultaneous Optimization). So, two subsets of design variables being optimized “simultaneously” or “jointly” means that the design variables of the two subsets are allowed to change at the same time. Two subsets of design variables being optimized “alternatively” as used herein means that the design variables of the first subset but not the second subset are allowed to change in the first optimization, and then the design variables of the second subset but not the first subset are allowed to change in the second optimization.

[0074] Reference is now made to FIG. 7, which illustrates an example method of optimization, where a cost function is minimized or maximized. In step S702, initial values of one or more design variables are obtained, including one or more associated tuning ranges, if any. In step S704, the multivariable cost function is set up. In step S706, the cost function is expanded within a small enough neighborhood around the starting point value of the one or more design variables for the first iterative step (i=0). In step S708, standard multi-variable optimization techniques are applied to the cost function. Note that the optimization problem can apply constraints, such as the one or more tuning ranges, during the optimization process in S708 or at a later stage in the optimization process. Step S720 indicates that each iteration is done for the one or more given test patterns (also known as “gauges”) for the identified evaluation points that have been selected to optimize the lithographic process. In step S710, a lithographic response is predicted. In step S712, the result of step S710 is compared with a desired or ideal lithographic response value obtained in step S722. If the termination condition is satisfied in step S714, i.e., the optimization generates a lithographic response value sufficiently close to the desired value, then the final value of the design variables is outputted in step S718. The output step may also include outputting one or more other functions using the final values of the design variables, such as outputting a wavefront aberration-adjusted map at the pupil plane (or other planes), an optimized illumination map, or optimized design layout etc. If the termination condition is not satisfied, then in step S716, the values of the one or more design variables is updated with the result of the i-th iteration, and the process goes back to step S706.

[0075] In an example optimization process, no relationship between the design variables (z1;z2, ••• , zN) and fp(z1;z2, ••• , zN) is assumed or approximated, except that fp(z1;z2, ••• , zN) issufficiently smooth (e.g. first order derivativesafp(~Z1'Z2' 'Zn(n= 1,2, ••• N) exist), which is generally dznvalid in a lithographic projection apparatus. An algorithm, such as the Gauss-Newton algorithm, the Levenberg-Marquardt algorithm, the Broyden-Fletcher-Goldfarb-Shanno algorithm, the gradient descent algorithm, the simulated annealing algorithm, the interior point algorithm, and the genetic algorithm, can be applied to find (z1;z2, ••• , zN).

[0076] Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newton algorithm is an iterative method applicable to a general non-linear multi-variable optimization problem. In the z'-th iteration wherein the design variables (z1;z2, •" >ZN) take values of (z , z2i, ••• , zNi), the Gauss- Newton algorithm linearizes fp z^, z2, ••• , zw) in the vicinity of (zu, z2i, ••• , zNi), and then calculates values (Zi(i+i), Z2(i+i)< ■" <zv(i+i)) inthe vicinity of (zu, z2i, ••• , zNi) that give a minimum of CF(z1, z2, ••• , zw). The design variables (z1;z2, ••• , zw) take the values of (Ziq+i), z2^+1••• , zN^i+1^)') in the (i+ 1 ) -th iteration. This iteration continues until convergence (i.e., CF z1, z2, • • • , zw) does not reduce any further) or a preset number of iterations is reached.

[0077] Reference is now made to FIG. 8, which illustrates an example of how a simultaneous SMLO process can use a gradient based optimization (e.g., quasi newton, or Gauss Newton Algorithm). In step S802, starting values of one or more design variables are identified. A tuning range for each variable may also be identified. In step S804, the cost function is defined using the one or more design variables. In step S806, the cost function is expanded around the starting values for all evaluation points in the design layout. In step S8O8, a suitable optimization technique is applied to minimize or maximize the cost function. In optional step S810, a full-chip simulation is executed to cover all critical patterns in a full-chip design layout. A desired lithographic response metric (such as phase cost, CD, EPE, or EPE and PPE) is obtained in step S814, and compared with predicted values of those quantities in step S812. In step S816, a process window is determined. Steps S818, S820, and S822 are similar to corresponding steps S714, S716 and S718, as described with respect to FIG. 7. As mentioned before, the final output may be, for example, a wavefront aberration map in the pupil plane, optimized to produce the desired imaging performance. The final output may be, for example, an optimized illumination map and / or an optimized design layout.

[0078] Reference is now made to FIG. 9, which is an example workflow for co-optimizing a source profile and wavefront by way of simulation, consistent with embodiments of the present disclosure. FIG. 9 illustrates a target pattern design 901 to pattern a substrate and mask design information 802 may be obtained. Mask design information 902 for a lithography process may include mask feature dimensions , and target pattern design 901 may include any pattern to be patterned to a wafer. FIG. 9 further illustrates an initial source profile 903 and an initial wavefront profile 904 are obtained. Initial source profile 903 may be any source profile (e.g., an off-axis illumination profile such as annular, dipole, quadrupole, etc.) and is illustrated as an annular source profile for illustrative purposes. Initial wavefront profile 904 may be arbitrary, e.g., zero aberration across the initial pupil profile 903.Target pattern design 901, mask design information 902, and initial source profile 903 may be used to simulate diffraction pattern 905, which indicates overlapping diffraction orders of a patterned radiation beam after diffracting from a mask containing the target design. Diffraction pattern 905 illustrates a 0thdiffraction order 905a, a -1stdiffraction order 905b, and a +lstdiffraction order 905c, where the overlapping diffraction orders are indicated as 905d. It is appreciated that embodiments of the present disclosure are not so limited, and may apply to 2nd, 3rd, or other diffraction orders. Initial source profile 903, initial wavefront profile 904, and diffraction pattern 905 may be provided to optimizer 906, which includes an optimization process that utilizes a cost function including a phase cost offset term. The phase cost term can be used in various optimization processes, including but not limited to, source optimization, source-mask-optimization, source-wavefront optimization, or source- mask-wavefront optimization. In some embodiments, the optimization process includes first cooptimizing initial source profile 903 and initial wavefront profile 904 and then performing a source, mask, wavefront co-optimization. According to some embodiments of the present disclosure, optimizer 906 may calculate a phase cost in the optimization process, or a phase cost and a diffraction pattern overlap cost. As a result, the optimizer 906 generates a resultant source profile 907 and a resultant wavefront profile 908. In some embodiments, applying resultant source profile 907 and resultant wavefront profile 908 can advantageously reduce imaging impact by the phase difference in diffraction orders that occur from a mask 3D effect in a lithography process. In some embodiments, resultant pupil profile 907 and resultant wavefront profile 908 may be used in a further optimization processes.

[0079] Embodiments of the present disclosure use new optimization cost functions to mitigate M3D fading, in which the cost functions include a phase cost term. The phase cost term may include components associated with a source profile (e.g., source point intensities) and components associated with a wavefront profile (e.g., Zernike coefficients or Tatian coefficients). The phase cost term may indicate a phase difference between diffraction orders, and the disclosed optimization method minimizes the phase cost term in the cost function. Minimizing the phase cost term may co-optimize a source profile and wavefront profile without external input (e.g., human input). In some embodiments, the phase cost term includes a compensated phase term, which is the predicted phase of a diffraction order for a source point after a wavefront injection. In some embodiments, the compensated phase term is driven to zero to minimize the phase cost between an initial phase and the compensated phase of a diffraction order. In some embodiments, the phase offset may be minimized by minimizing a sum of the absolute phase of all diffraction orders. In some embodiments, the phase offset may be minimized by minimizing a phase offset between interference pairs of two diffraction orders for a source point. Thus, a phase difference between diffraction orders can be achieved by co-optimization (e.g., source-wavefront co-optimization) and M3D fading can be mitigated.

[0080] In some embodiments, a cost function comprising a phase cost term, in addition to other cost terms (e.g., an EPE cost term) is provided. The phase cost term may be expressed as shown in Equation 6:where s is the phase cost term in a cost function, s( / c) is an intensity of a source point in a source profile where the source point is located at location k,is the intensity of a diffraction order of the source point, is the compensated phase for the ith diffraction order of the source point (e.g., a compensated 0th, -1st, or a +lstdiffraction order), and p is an exponential term (e.g., 2, 4, 6. . .). The compensated phase, < >;, is the predicted phase of an ith diffraction order after a round of optimization. The compensated phase, < >;, may be calculated as shown in Equation 7:where is the phase of the ith diffraction order (e.g., the phase of the -1stdiffraction order), Cj is a Zernike coefficient, Zj is a Zernike polynomial, ktis the location of an initial ith diffraction order (e.g., a position of an initial 0thdiffraction order), and k is the location of a source point to evaluate.

[0081] Reference is now made to FIG. 10, which is an illustration for defining a compensated phase and phase cost term included in a cost function to co-optimize a source profile and a wavefront profile, consistent with embodiments of the present disclosure. FIG. 10 may illustrate a process occurring in an optimizer module (e.g., optimizer 906 of FIG. 9) of a controller or a computing system. In some embodiments, the phase cost term is used to minimize a phase offset between diffraction orders. FIG. 10 illustrates a source profile 1001 with a -1st diffraction order 1002 and a -4-lst diffraction order 1003 overlapping with source profile 1001. It is appreciated that source profile 1001 corresponds to a Oth diffraction order 1001. FIG. 10 illustrates diffraction orders that may be expected as a result of a radiation beam interacting with (e.g., diffracting) a design mask pattern. Accordingly, 0thdiffraction order 1001, -1stdiffraction order 1002, and +lstdiffraction order 1003 may correspond to an initial diffraction pattern (e.g., diffraction pattern 905 in FIG. 9). The solid black circles 1001a, 1002a, and 1003a serve as illustrative centers of 0thdiffraction order 1001, -1stdiffraction order 1002, and +lstdiffraction order 1003, respectively. 0thdiffraction order 1001, -1stdiffraction order 1002, and +lstdiffraction order 1003 may each have a different initial phase,FIG. 10 further illustrates source profile 1004 with a source point 1005, where source point 1005 is in a 0thorder diffraction beam. Source point 1005 may therefore have a -1stdiffraction order 1005a and a+lstdiffraction order 1005b, as illustrated with the shaded circles. The expected diffraction orders (1001-1003) may then be shifted 1006 to account for a M3D fading effect impacting source point 1005 and the diffraction orders of source point 1005 (1005a and 1005b). Shift 1006 corresponds to ( / tj — k) in Equation 7. The second term in Equation 7 ( j CjZj(ki — )) thus corresponds to a predicted phase offset brought by a wavefront aberration at the diffraction order location (e.g., 0thdiffraction order 1005, -1stdiffraction order 1005a, or + 1stdiffraction order 1005b). The phase cost term, as expressed in Equation 6 above, can thus be obtained by summing the product of the intensity of each diffraction order and the compensated phase for each diffraction order, and then multiplying this sum by the summation of the intensity for each source point in the source profile.

[0082] As noted above, the phase cost term (Equation 6) includes components associated with a source profile (e.g., source point intensities) and components associated with a wavefront profile (e.g., Zernike coefficients). Thus, the phase cost term in the cost function can be used to co-optimize a source profile and a wavefront profile. A source profile and wavefront profile may be co-optimized by calculating equations 8 and 9 below to create a gradient and determine a minimum value for variable (e.g., each source point and Zernike coefficient).

[0083] Equations 6, 7, 8, and 9 may be calculated multiple times (e.g., multiple iterations) until an optimized (e.g., minimum) variable value is obtained. As a result, an optimizer (e.g., optimizer 906 of FIG. 9) may generate a resultant source profile 1007 and a resultant wavefront profile 1008. In some embodiments, resultant source profile 1007 or resultant wavefront profile 1008 may be further optimized according to a source-mask-wavefront co-optimization method. For example, resultant source profile 1007 and wavefront profile 1008 may be provided to a SMO framework and both may be further co-optimized with a mask pattern. Resultant source profile 1007 may contain a region 1009 in which a source point may be deactivated and a region 1010 in which a source point may be activated. Resultant source profile 1007 may be provided to projection optics of a lithography apparatus (e.g., components 104, 106a, 106b, or 106c of FIG. 1 or projection optics 204 of FIG. 2) to generate a modified source profile. Resultant wavefront profile 1008 may contain region 1011 in which a positive aberration is to be provided to a wavefront manipulator, and region 1012 in which a negative aberration is to be provided to a wavefront manipulator, and the wavefront manipulator maygenerate a wavefront that accounts for a phase offset caused by the M3D fading effect. It is appreciated that region 1009, 1010, 1011, or 1012 may be any shape or size. It is further appreciated that FIG. 10 is for illustrative purposes is not exhaustive. For example, more or different diffraction orders may be contemplated and used in equations 6-9 to determine a resultant source profile or resultant wavefront profile, and different initial conditions may be applied (e.g., a different initial source profile or diffraction pattern).

[0084] In some embodiments, a phase cost term for a phase offset between diffractions, as defined and illustrated in FIG. 10, may be determined by summing each source point intensity for all interference diffraction order pairs. In some embodiments, minimizing the sum of a phase difference between interference pairs will minimize a phase offset between two diffraction orders for each source point. Thus, in comparison to equation 6 above, the phase cost term in a cost function may thus distinguish between different diffraction orders, and is expressed in equation 10 below:where wps the intensity (magnitude) of an ith diffraction order, w,is the intensity (magnitude) of a jth diffraction order,is the compensated phase of the ith diffraction order of a first source point (e.g., a compensated 0th, -1st, or a +lstdiffraction order), and <Pj is the compensated phase of the jth diffraction order of a second source point, and where i and j represent interference pairs of diffraction orders. As described above, a source profile and wavefront profile may be co-optimized by calculating equations 11 and 12 below to create a gradient and determine a minimum value for variable (e.g., each source point and Zernike coefficient).

[0085] Equations 10, 11, and 12 may be calculated multiple times (e.g., multiple iterations) until an optimized (e.g., minimum) variable value is obtained. As a result, an optimizer (e.g., optimizer 906 of FIG. 9) may generate resultant source profile 1007 and resultant wavefront profile 1008 as described above.

[0086] In some embodiments, a source profile may be optimized to avoid any diffraction pattern overlap between two or more different source points. Reference is now made to FIGs. 11A-11B, which are illustrations for defining a diffraction pattern overlap cost term in a cost function to optimize a source profile, consistent with embodiments of the present disclosure. FIGs. 11A and 11B may illustrate a process occurring in an optimizer module (e.g., optimizer 906 of FIG. 9) of a controller or a computing system. In some embodiments, the diffraction pattern overlap cost term is used to minimize overlap between diffraction orders FIG. 11 A illustrates a source profile 1101 with a -1stdiffraction order 1102 and a +lstdiffraction order 1103 overlapping with source profile 1101. It is appreciated that source profile 1101 corresponds to a 0thdiffraction order 1001. FIG. 11A illustrates diffraction orders that may be expected as a result of a radiation beam interacting with a design mask pattern (e.g., as described above in FIG. 5B). The solid black circles 1101a, 1102a, and 1103a serve as illustrative centers of 0thdiffraction order 1101, -1stdiffraction order 1102, and +lstdiffraction order 1103, respectively. 0thdiffraction order 1101, -1stdiffraction order 1102, and +lstdiffraction order 1103 may each have a different phase. FIG. 11B illustrates pupil 1104 with a first source point1105 and second source point 1106, where first source point 1105 and second source point 1106 are in a 0thorder diffraction beam. Source point 1105 may therefore have a -1stdiffraction order 1105a and a +lstdiffraction order 1105b, as illustrated with the circles containing a horizontal line. Source point1106 may have a -1stdiffraction order 1106a and a +lstdiffraction order 1106b, as illustrated with the circles containing a vertical line. FIG. 11B illustrates that source point 1106 (e.g., 0thdiffraction order) overlaps with +lstdiffraction order 1105b of source point 1105. Additionally, source point 1105 (e.g., 0thdiffraction order) overlaps with -1stdiffraction order 1106a of source point 1106. In such a scenario as illustrated in FIG. 11B, a wavefront profile cannot account for both source point1105 and source point 1106, because the compensated phase determined for, e.g., +lstdiffraction order 1105b will not equal the compensated phase determined for source point 1106. Thus, a resultant source profile and resultant wavefront profile cannot include both source point 1105 and source point 1106. In some embodiments, an additional diffraction pattern overlap cost term is included in a cost function to prevent a scenario as illustrated in FIG. 11B. The cost term may be a vector between two source points and may identify a source point to exclude in an optimization method. The diffraction pattern cost term may be as follows, in Equation 13:(Eq. 13),where (ZC-L —2) is a distance between two source points and A0(is a vector between a diffraction order pair of krand k2, respectively. When (k^ — k2) is equal to a distance between an interference pair of diffraction orders krand k2(e.g., a distance between source point 1006 and +lstdiffractionorder 1005b, then JT j ^9^ (k^ —2) is equal to 1. Otherwise, JT j ^9^ (k — k2) is equal to 0. When equation 13 is greater than 0, the optimizer may remove one or more of the corresponding source points from the source profile during source and wavefront co-optimization (e.g., equations 6-12). In some embodiments, an optimizer may perform equation 13 in parallel with the pupil profile and wavefront optimization (e.g., equations 6-12).

[0087] In some embodiments, the cost function terms described above (e.g., equations 6-13) may be added to an optimization cost function (e.g., SMO cost function or a source-mask-wavefront cost function). In some embodiments, an optimization cost function comprises edge placement errors (EPEs) evaluated at different process window conditions. The optimization cost function can comprise a suitable combination of lithographic performance indicators, such as EPE, critical dimension (CD), image log-slope (ILS), pattern placement error, or the like. The optimization method can be performed by adjusting adjustable elements by iteratively adjusting variable elements of a design for a mask, based on iterative simulation of a lithographic process that uses the mask simultaneously with adjusting variable elements of a source profile and wavefront profile. 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.

[0088] Reference is now made to FIG. 12, illustrates a method 1200 for co-optimizing a source profile and a wavefront profile for a lithography process, consistent with embodiments of the present disclosure. The method can be executed using devices and functions described in reference to FIGS. 1-11.

[0089] In step 1201, a source profile, a wavefront profile, and a mask pattern are obtained. The source profile may be an off-axis illumination profile (e.g., an annular profile, a dipole profile, a quadrupole profile, etc.). The wavefront profile may be a zero-wavefront profile, in which the initial wavefront profile may indicate no wavefront is to be applied to a source point in the source profile. In some embodiments, the mask pattern comprises a plurality of polygon representations of a mask contour or a mask pattern, a plurality of mask images or mask patterns, or a plurality of aerial images or aerial pattern. The mask pattern may contain features with finite dimensions (e.g., finite height, width, length, or thickness).

[0090] In step 1202, the source profile and wavefront profile are optimized by simulating a lithography process. The source profile and wavefront profile are optimized by using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process. The phase offset between diffracted radiation beams may be induced by a M3D fading effect (e.g., the radiation beam interacting with the mask pattern). In some embodiments, the diffracted radiation beams correspond to a same source point in the source profile. Simulating the lithography process comprises simulating a radiation beam interacting with the maskpattern to generate a plurality of diffraction orders, and simulating a diffraction pattern based on the plurality of diffraction orders and the source profile. In some embodiments, optimizing the source profile and the wavefront profile may further comprise a penalty term for an overlap between diffraction patterns. The penalty term may indicate when a diffraction order of a first source point overlaps with a diffraction order of a second source point in the pupil profile. The penalty term may exclude the first source point or the second source point from the optimization.

[0091] Further operations are envisaged to be within the scope of method 1200, such as the functions described above in reference to FIGS. 1-11.

[0092] Embodiments of the present disclosure can be further described by the following clauses.1. A method for simulating a lithography process comprising: obtaining a source profile, a wavefront profile, and a mask pattern; and optimizing the source profile and the wavefront profile by simulating the lithography process that uses the mask pattern, wherein optimizing the source profile and the wavefront profile comprises using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process.2. The method of clause 1 , wherein the phase offset between diffracted radiation beams is caused by a Mask3D (M3D) fading effect during the lithography process.3. The method of clause 1 or 2, wherein the diffracted radiation beams correspond to a same source point in the source profile.4. The method of any one of clauses 1 to 3, wherein simulating the lithography process comprises: simulating a radiation beam interacting with the mask pattern to generate a plurality of diffraction orders; and simulating a diffraction pattern based on the plurality of diffraction orders and the source profile.5. The method of any one of clauses 1 to 4, wherein optimizing the source profile and the wavefront profile comprises minimizing the phase cost term.6. The method of any one of clauses 1 to 5, wherein the phase cost term comprises components associated with the source profile and components associated with the wavefront profile.7. The method of clause 6, wherein the components associated with the source profile comprise source point intensities.8. The method of clause 6, wherein the components associated with the wavefront profile comprise Zernike or Tatian coefficients.9. The method of any one of clauses 1 to 8, wherein the phase cost term comprises a compensated phase term, wherein the compensated phase term comprises a term representing a phase of an initial diffraction order of a radiation beam and a term representing a phase offset of a diffraction order of the radiation beam caused by the lithography process.10. The method of any one of clauses 1 to 9, wherein the phase cost term represents a summation of a compensated phase for all diffraction orders for a source point in the source profile.11. The method of clause 10, wherein optimizing the source profile and the wavefront profile comprises minimizing the summation of the compensated phase for all diffraction orders for a source point.12. The method of any one of clauses 1 to 9, wherein the phase cost term comprises a summation of source point intensity in the source profile and a summation of a product of diffraction order intensity and a compensated phase of a diffracted radiation beam.13. The method of any one of clauses 1 to 9, wherein the phase cost term comprises a summation of a compensated phase difference between pairs of diffraction orders.14. The method of clause 13, wherein optimizing the source profile and the wavefront profile comprises minimizing the summation of the compensated phase difference between pairs of diffraction orders.15. The method of clause 13 or 14, wherein the pairs of diffraction orders are interference pairs.16. The method of any one of clauses 1 to 15, wherein the source profile comprises an off-axis illumination profile.17. The method of any one of clauses 1 to 16, wherein the wavefront profile comprises a zerowavefront profile.18. The method of any one of clauses 1 to 17, wherein the mask pattern comprises a plurality of polygon representations of a mask contour or a mask pattern, a plurality of mask images or mask patterns, or a plurality of aerial images or aerial patterns.19. The method of any one of clauses 1 to 18, wherein the source profile and the wavefront profile are co-optimized without changing the mask pattern.20. The method of any one of clauses 1 to 19, wherein cost function used for optimizing the source profile and the wavefront profile further comprises a penalty term for an overlap between diffraction patterns.21. The method of clause 20, wherein the penalty term indicates when a diffraction order of a first source point overlaps with a diffraction order of a second source point in the source profile.22. The method of clause 20 or 21, wherein the penalty term excludes a first source point that has a first diffraction order that overlaps with a second diffraction order of a second source point from optimizing the source profile and the wavefront profile.23. The method of any one of clauses 20 to 22, wherein the penalty term comprises a function including a vector between two source points to calculate a phase difference between a pair of diffraction orders of the two source points.24. The method of clause 23, wherein the function provides a value of 0 when no overlap between diffraction patterns occurs.25. The method of any one of clauses 20 to 24, wherein optimizing the source profile and the wavefront profile may be performed by first applying the penalty term and then applying the phase cost term.26. The method of any one of clauses 20 to 25, wherein optimizing the source profile and the wavefront profile may be formed by applying the penalty term and the phase cost term in parallel.27. The method of any one of clauses 1 to 26, further comprising providing an optimized source profile and an optimized wavefront profile to a source-mask-optimization (SMO) process that further co-optimizes the source profile, the mask pattern, and the wavefront profile.28. The method of clause 27, wherein the co-optimized source profile, mask pattern, and wavefront profile are used to prepare a recipe for the lithography process.29. The method of clause 27, wherein the co-optimized source profile, mask pattern, and wavefront profile are used to adjust a component of a lithography apparatus.30. The method of clause 29, wherein the component of the lithography apparatus comprises a wavefront manipulator or a projection optic.31. A non-transitory computer readable medium comprising a set of instructions that is executable by one or more processors of a computing device to cause the computing device to perform operations for simulating a lithography process, the operations comprising the method of any one of clauses 1- 30.32. A system for simulating a lithography process, comprising: a memory storing a set of instructions; and at least one processor configured to execute the instructions to cause the system to perform operations comprising the method of any one of clauses 1-30.

[0093] Benefits of the present disclosure include providing a method to simulate a lithography process by reducing computational load and streamlining an optimization framework. Embodiments of the present disclosure provide an optimized pupil profile and wavefront profile by starting with an initial pupil profile and a zero-wavefront term, thus ensuring the optimization method is optimal, automated, and free of human error. In some embodiments, the present disclosure provides a method to improve imaging performance (e.g., an aerial image) compared to current technologies.

[0094] A non-transitory computer-readable medium can be provided that stores instructions for a processor of a controller for simulating a lithography process and optimizing a source profile, mask pattern, or wavefront profile using a cost function comprising a phase cost term, or a method according to the exemplary flowchart of FIG. 12, 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 1200 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 flashmemory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0095] 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 comprising a set of instructions that is executable by one or more processors of a computing device to cause the computing device to perform a method of simulating a lithography process, the method comprising: obtaining a source profile, a wavefront profile, and a mask pattern; and optimizing the source profile and the wavefront profile by simulating the lithography process that uses the mask pattern, wherein optimizing the source profile and the wavefront profile comprises using a cost function that comprises a phase cost term indicating a phase offset between diffracted radiation beams caused during the lithography process, wherein simulating the lithography process comprises: simulating a radiation beam interacting with the mask pattern to generate a plurality of diffraction orders; and simulating a diffraction pattern based on the plurality of diffraction orders and the source profile.

2. The medium of claim 1 , wherein the phase offset between diffracted radiation beams is associated with a Mask3D (M3D) fading effect during the lithography process.

3. The medium of claim 1, wherein the diffracted radiation beams correspond to a same source point in the source profile.

4. The medium of claim 1 , wherein optimizing the source profile and the wavefront profile comprises iteratively reducing the phase cost term by adjusting design variables.

5. The medium of claim 1, wherein the phase cost term comprises components associated with the source profile and components associated with the wavefront profile, and wherein the co-optimized source profile, mask pattern, and wavefront profile are used to prepare a recipe for the lithography process or adjust a component of a lithography apparatus, and wherein the component of the lithography apparatus comprises a wavefront manipulator or a projection optic.

6. The medium of claim 5, wherein the components associated with the source profile comprise source point intensities, wherein the components associated with the wavefront profile comprise Zernike or Tatian coefficients.

7. The medium of claim 1, wherein the phase cost term comprises a compensated phase term, wherein the compensated phase term comprises a term representing a phase of an initialdiffraction order of a radiation beam and a term representing a phase offset of a diffraction order of the radiation beam caused by the lithography process.

8. The medium of claim 1, wherein the phase cost term represents a summation of a compensated phase for all diffraction orders for a source point in the source profile.

9. The medium of claim 1, wherein the phase cost term comprises a summation of source point intensity in the source profile and a summation of a product of diffraction order intensity and a compensated phase of a diffracted radiation beam.

10. The medium of claim 1, wherein the phase cost term comprises a summation of a compensated phase difference between pairs of diffraction orders, and wherein optimizing the source profile and the wavefront profile comprises minimizing the summation of the compensated phase difference between pairs of diffraction orders.

11. The medium of claim 10, wherein the pairs of diffraction orders are interference pairs, wherein the source profile comprises an off-axis illumination profile, and wherein the wavefront profile comprises a zero-wavefront profile.

12. The medium of claim 1, wherein cost function used for optimizing the source profile and the wavefront profile further comprises a penalty term for an overlap between diffraction patterns, wherein the penalty term indicates when a diffraction order of a first source point overlaps with a diffraction order of a second source point in the source profile13. The medium of claim 12, wherein the penalty term excludes a first source point that has a first diffraction order that overlaps with a second diffraction order of a second source point from optimizing the source profile and the wavefront profile.

14. The medium of claim 12, wherein the penalty term comprises a function including a vector between two source points to calculate a phase difference between a pair of diffraction orders of the two source points.

15. The medium of claim 12, wherein optimizing the source profile and the wavefront profile may be performed by applying the penalty term and the phase cost term sequentially or in parallel.

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