Method for reducing stochastic failures via source-mask optimization

Abstract

Systems and methods for source or mask optimization of a patterning process. Methods may include performing a lithography simulation to predict patterning results; identifying stochastic defects from the predicted patterning results; defining a cost function and a pseudo-gradient; determining a metric of the stochastic defects and the pseudo-gradient for the cost function associated with a performance metric of the patterning process at evaluation locations; and iteratively adjusting the characteristics of the mask or the source based on the metric and the guide function. Methods may include performing a lithography simulation to generate a resist image (RI); determining stochastic errors as a function of a variable bias map (VBM) and the RI; determining a cost function comprising the stochastic errors; determining a gradient of the cost function; and iteratively adjusting the characteristics of the mask or the source based on the gradient of the cost function.

Description

METHOD FOR REDUCING STOCHASTIC FAILURES VIA SOURCE-MASK OPTIMIZATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of an International Application No. PCT / CN2023 / 117932 which was filed on September 11, 2023 and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to the field of lithographic apparatuses, methods, and systems, and more particularly to methods for source-mask optimization in patterning processes.BACKGROUND

[0003] A lithographic apparatus can be used, for example, in the manufacturing of integrated circuits (ICs). In such a case, a mask or a reticle may contain or provide a circuit pattern corresponding to an individual layer of the IC (“design layout”), and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer). Mask defects can greatly impact a process yield. Therefore, a mask status can be monitored by inspecting printed wafers to identify a mask defect and to identify when to take appropriate procedures when a mask defect is identified.SUMMARY

[0004] Embodiments of the present disclosure provide systems and methods for source or mask optimization of a patterning process. Methods may include performing a lithography simulation to predict patterning results based on characteristics of a mask or a source; identifying stochastic defects from the predicted patterning results; defining a cost function and a pseudo-gradient; determining a metric of the stochastic defects and the pseudo-gradient for the cost function associated with a performance metric of the patterning process at one or more evaluation locations within a defect ambit; and iteratively adjusting the characteristics of the mask or the source based on the metric and the guide function.

[0005] Some methods may include identifying stochastic defects from a predicted patterning; determining a measure of stochastic defects and a guide function for a cost function associated with a performance measure of the patterning process at one or more points; and iteratively modifying characteristics of the mask or the source based on the measure of stochastic defects and the guide function.

[0006] Some methods may include performing a lithography simulation to generate a resist image (RI) based on a resist model, characteristics of a mask, and characteristics of a source; determining stochastic errors as a function of a variable bias map (VBM) and the RI, wherein the VBM indicates aresist contour variation band width; determining a cost function comprising the stochastic errors; determining a gradient of the cost function with respect to the RI and the VBM using source and mask variables; and iteratively adjusting the characteristics of the mask or the source based on the gradient of the cost function with respect to the RI and the VBM.

[0007] Some methods may include generating a RI; determining stochastic errors as a function of a VBM and the RI; determining a cost function comprising the stochastic errors; calculating a gradient of the cost function with respect to the RI and the VBM and using source and mask variables; and iteratively modifying characteristics of the source or the mask based on the gradient of the cost function with respect to the RI and the VBM.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Fig. 1 is a block diagram of various subsystems of a lithography system, consistent with embodiments of the present disclosure.

[0009] Fig. 2 is a block diagram of simulation models corresponding to the subsystems in Fig. 1, consistent with embodiments of the present disclosure.

[0010] Fig. 3 is a flow chart of a method of source and / or mask optimization of a patterning process, consistent with embodiments of the present disclosure.

[0011] Fig. 4 is an example of determining measurements from a contour of an example printed pattern, consistent with embodiments of the present disclosure.

[0012] Fig. 5A illustrates a defect ambit defined around a defect in a portion of a pattern on the substrate, consistent with embodiments of the present disclosure.

[0013] Fig. 5B illustrates an example cost function associated with a bridging defect employed in the method in Fig. 3, consistent with embodiments of the present disclosure.

[0014] Figs. 6A and 6B illustrate defect ambits defined around a bridging defect and a necking defect, respectively, consistent with embodiments of the present disclosure.

[0015] Fig. 7A illustrates an example result of employing an existing OPC process to a design layout, consistent with embodiments of the present disclosure.

[0016] Fig. 7B illustrates an example result of employing an OPC process with the method of Fig. 3, consistent with embodiments of the present disclosure.

[0017] Fig. 8 shows an exemplary method for source-mask optimization in a patterning process, consistent with embodiments of the present disclosure.

[0018] Fig. 9 shows steps of an exemplary method of Fig. 8 for source-mask optimization in a patterning process, consistent with embodiments of the present disclosure.

[0019] Fig. 10 shows exemplary resist contours, consistent with embodiments of the present disclosure.

[0020] Fig. 11 shows exemplary source designs, consistent with embodiments of the present disclosure.

[0021] Fig. 12 shows an exemplary diagram related to generating a variable bias map (VBM), consistent with embodiments of the present disclosure.

[0022] Fig. 13 shows exemplary images generating during a source-mask optimization process in a patterning process, consistent with embodiments of the present disclosure.

[0023] Fig. 14 is a block diagram of an example computer system, consistent with embodiments of the present disclosure.

[0024] Fig. 15 is a schematic diagram of a lithographic projection apparatus, consistent with embodiments of the present disclosure.

[0025] Fig. 16 is a schematic diagram of another lithographic projection apparatus, consistent with embodiments of the present disclosure.

[0026] Fig. 17 is a more detailed view of the apparatus in Fig. 16, consistent with embodiments of the present disclosure.

[0027] Fig. 18 is a more detailed view of the source collector module SO of the apparatus of Figs. 16 and 17, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0028] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying 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 disclosure. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the subject matter recited in the appended claims. For example, although some embodiments are described in the context of utilizing electron beams, the disclosure is not so limited. Other types of charged particle beams may be similarly applied. Furthermore, other imaging systems may be used, such as optical imaging, photodetection, x-ray detection, extreme ultraviolet inspection, deep ultraviolet inspection, or the like, in which they generate corresponding types of images.

[0029] Electronic devices are constructed of circuits formed on a piece of silicon called a substrate. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. The size of these circuits has decreased dramatically so that many more of them can fit on the substrate. For example, an IC chip in a smart phone can be as small as a thumbnail and yet may include over 2 billion transistors, the size of each transistor being less than 1 / 1000th the size of a human hair.

[0030] Making these extremely small ICs is a complex, time-consuming, and expensive process, often involving hundreds of individual steps. Errors in even one step have the potential to result in defects in the finished IC rendering it useless. Thus, one goal of the manufacturing process is to avoidsuch defects to maximize the number of functional ICs made in the process, that is, to improve the overall yield of the process.

[0031] A lithographic apparatus can be used, for example, in the manufacturing of ICs. In such a case, a mask or a reticle may contain or provide a circuit pattern corresponding to an individual layer of the IC (“design layout”), and this circuit pattern can be transferred onto a target portion (e.g., comprising one or more dies) on a substrate (e.g., silicon wafer) that has been coated with a layer of radiation- sensitive material (“resist”), by methods such as irradiating the target portion through the circuit pattern on the mask. Mask defects can greatly impact a process yield. A mask status can be monitored by inspecting printed wafers to identify a mask defect and to take a proper follow-up procedure when a mask defect is identified. For example, procedures to remove the defect on the mask, e.g., by cleaning or reworking the mask, can be performed. As lithography moves into high volume manufacturing (HVM), locating and curing a defect(s) of a mask becomes more important.

[0032] Existing lithography systems suffer from constraints. For example, due to the increased photon energy of lithography processes (e.g., during EUV lithography), the stochastic failure rate during lithography is increased. Models, which capture, stochastic variation in lithography, may predict stochastic failures, but they do not provide methods for mitigating it or optimizing for it. Source-mask optimization (SMO) processes to reduce lithography defects exist. However, these existing SMO processes reduce traditional and deterministic defects, not stochastic defects. Therefore, improved SMO processes to mitigate and optimize for stochastic defects during lithography are desired.

[0033] The disclosed embodiments provide systems and methods that address some or all of these disadvantages by providing inventive methods for source or mask optimization of a patterning process. The disclosed embodiments may include performing a lithography simulation to predict patterning results based on characteristics of a mask or a source, identifying stochastic defects from the predicted patterning results, defining a cost function and a pseudo-gradient, and iteratively adjusting characteristics of the mask or the source based on a metric of stochastic defects and a guide function for the cost function. For example, after each iteration, the adjusted mask design or the adjusted source may result in an increased distance between stochastic edge placement error (SEPE) contours, thereby mitigating and optimizing for stochastic defects during lithography.

[0034] The disclosed embodiments may include performing a lithography simulation, determining stochastic errors as a function of a variable bias map (VBM), determining a cost function including the stochastic errors, propagating the gradient of the cost function with respect to different variables, and iteratively adjusting characteristics of the mask or the source. For example, after each iteration, the adjusted mask design or the adjusted source may result in a reduced width of a resist contour variation band, thereby mitigating and optimizing for stochastic defects during lithography.

[0035] 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 likecomponents or entities, and only the differences with respect to the individual embodiments are described.

[0036] 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 may include A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component may include A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0037] Without limiting the scope of the present disclosure, some embodiments may be described in the context of providing detectors and detection methods in systems utilizing electron beams. However, the disclosure is not so limited. Other types of charged particle beams may be similarly applied. Furthermore, systems and methods for detection may be used in other imaging systems, such as optical imaging, photon detection, x-ray detection, ion detection, etc.

[0038] Although specific reference may be made in this text to the manufacture of ICs, it should be explicitly understood that the description herein has many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid-crystal display panels, thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such applications, use of the terms “reticle”, “wafer” or “die” in this text may be interchangeable with the more general terms “mask”, “substrate” and “target portion”, respectively.

[0039] In the present document, the terms “radiation” and “beam” may be used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g., having a wavelength in the range 5-20 nm).

[0040] The term “optimizing” and “optimization” as used herein may indicate adjusting a lithographic projection apparatus such that results or processes of lithography have more desirable characteristics, such as higher accuracy of projection of design layouts on a substrate, larger process windows, etc.

[0041] Further, the lithographic projection apparatus may be of a type having two or more substrate tables (or two or more patterning device tables). In such “multiple stage” devices the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposures. Twin stage lithographic projection apparatuses are described, for example, in U.S. Patent No. 5,969,441, incorporated herein by reference in its entirety.

[0042] The patterning device referred to above comprises or can form design layouts. The design layouts can be generated utilizing CAD (computer-aided design) programs, this process often being referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules in order to create functional design layouts / patterning devices. These rules are set byprocessing and design limitations. For example, design rules define the space tolerance between circuit devices (such as gates, capacitors, etc.) or interconnect lines, so as to ensure that the circuit devices or lines do not interact with one another in an undesirable way. The design rule limitations are typically referred to as “critical dimensions” (CD). A critical dimension of a circuit can be defined as the smallest width of a line or hole or the smallest space between two lines or two holes. Thus, the CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit fabrication is to faithfully reproduce the original circuit design on the substrate (via the patterning device).

[0043] The term “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate; the term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include: a programmable mirror array. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, whereas unaddressed areas reflect incident radiation as undiffracted radiation.Using an appropriate filter, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation behind; in this manner, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. More information on such mirror arrays can be gleaned, for example, from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference in their entirety.

[0044] Another example of such patterning devices includes a programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference in its entirety.

[0045] As a brief introduction, Fig. 1 illustrates an exemplary lithographic projection apparatus 10A, consistent with embodiments of the present disclosure. Major components are a radiation source 12A, which may be a deep-ultraviolet excimer laser source or other type of source including an extreme ultra violet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have the radiation source), illumination optics which define the partial coherence (denoted as sigma) and which may include optic components 14 A, 16Aa and 16 Ab that shape radiation from the source 12A; a patterning device 14A; and transmission optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics may restrict the range of beam angles that impinge on the substrate plane 22A, where the largest possible angle defines the numerical aperture of the projection optics NA = nsin( max) where n is the index of reflection of the media between the last lens element to the substrate .

[0046] In an optimization process of a system, a figure of merit of the system can be represented as a cost function. The optimization process boils down to a process of finding 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 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 also be the maximum of these deviations (i.e., 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 projection 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.

[0047] In a lithographic projection apparatus, a source provides illumination (i.e., light); projection optics direct and shape the illumination via a patterning device and onto a substrate. The term “projection optics” is broadly defined here to include any optical component that may alter the wavefront of the radiation beam. For example, projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. An aerial image (Al) is the radiation intensity distribution at substrate level. A resist layer on the substrate is exposed and the aerial image is transferred to the resist layer as a latent “resist image” (RI) therein. The resist image (RI) 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 which can be found in commonly assigned U.S. Patent No. 8,200,468, disclosure of which is hereby incorporated by reference in its entirety. The resist model is related only to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB), and development). Optical properties of the lithographic projection apparatus (e.g., properties of the source, the patterning device, and the projection optics) dictate the aerial image. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics.

[0048] An exemplary flow chart for simulating lithography in a lithographic projection apparatus is illustrated in Fig. 2, consistent with embodiments of the present disclosure. A source model 31 represents optical characteristics (including radiation intensity distribution or phase distribution) of the source. A projection optics model 32 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by the projection optics) of theprojection optics. A design layout model 35 represents optical characteristics (including changes to the radiation intensity distribution or the phase distribution caused by a given design layout) of a design layout, which is the representation of an arrangement of features on or formed by a patterning device. An aerial image 36 can be simulated from the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using a resist model 37. Simulation of lithography can, for example, predict contours and CDs in the resist image.

[0049] More specifically, it is noted that the source model 31 can represent the optical characteristics of the source that include, but are not limited to, NA-sigma (a) settings as well as any particular illumination source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical characteristics of the projection optics that include aberration, distortion, refractive indexes, physical sizes, physical dimensions, etc. The design layout model 35 can also represent physical properties of a physical patterning device, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated by reference in its entirety. The objective of the simulation is to accurately predict, for example, edge placements, aerial image intensity slopes and CDs, which can then be compared against an intended design. The intended design is generally defined as a pre-optical proximity correction (OPC, sometimes also referred to as “optical and process correction”) design layout which can be provided in a standardized digital file format. The layout file can be in a Graphic Database System (GDS) format, Graphic Database System II (GDS II) format, an Open Artwork System Interchange Standard (OASIS) format, a Caltech Intermediate Format (CIF), etc. The wafer design may include patterns or structures for inclusion on the wafer. The patterns or structures can be mask patterns used to transfer features from the photolithography masks or reticles to a wafer. In some embodiments, a layout in GDS or OASIS format, among others, may comprise feature information stored in a binary file format representing planar geometric shapes, text, and other information related to the wafer design.

[0050] From this design layout, one or more portions may 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 may be used). As will be appreciated by those skilled in the art, 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 needed. In other words, clips may be the portions of the design layout or may be similar or have a similar behavior of portions of the design layout where critical features are identified either by experience (including clips provided by a customer), by trial and error, or by running a full-chip simulation. Clips usually contain one or more test patterns or gauge patterns.

[0051] An initial larger set of clips may be provided a priori by a customer based on known critical feature areas in a design layout which require particular image optimization. Alternatively, in someembodiments, the initial larger set of clips may be extracted from the entire design layout by using some kind of automated (such as, machine vision) or manual algorithm that identifies the critical feature areas.

[0052] In some embodiments, an optimization process (e.g., source mask optimization (SMO) discussed in Figs. 3, 8, and 9) relates to one or more of a patterning process that employs process models (e.g., an optics model, a mask model, a resist model etc. of Fig. 2). The optimization process may involve execution of the one or more process models and computation of a cost function which may 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 may be described by design variables. Hence, an optimized characteristic may also be referred to as an optimized design variable, where a design variable (e.g., z, v) is optimized based on a cost function (e.g., CF, s).

[0053] In some embodiments, the modifying of the characteristic is based on a gradient of the cost function that guides how the characteristic should be modified to reduce the cost function. In some embodiments, such a cost function is a function of certain continuous metric such as an edge placement error (e.g., a difference between contours of printed pattern and a target pattern). Using continuous metric or cost function of continuous nature allows use of gradient-based optimizing algorithms that have acceptable runtime performance of an optimization process.

[0054] In some embodiments, non-smooth or discontinuous cost functions (e.g., based on defect counts) are not employed, as such non-smooth cost function necessitates use of non-continuous optimizers which have relatively high runtime compared to the continuous cost function based optimization. In addition, such optimizers may not provide best solutions. In some embodiments, use of non-smooth cost function such as related to defects may be desired so that optimization may be performed to reduce a particular defect or several defects that may potentially be appear on a printed substrate.

[0055] The present disclosure provides methods that employ non-smooth cost function, for example, to reduce the number of defects and thereby improve yield of the patterning process. It can be understood by a person skilled in the art that concepts of a guide function (e.g., a pseudo-gradient) and discrete cost function (e.g., a first cost function discussed herein) may be applied to any aspect of the patterning process comprising an optimization process and not limited to a particular aspect of the patterning process. In some embodiments, the concepts are explained with respect to a source mask optimization process for better understandability.

[0056] Fig. 3 is a flow chart of a method 300 of source or mask optimization of a patterning process, consistent with embodiments of the present disclosure. The method involves optimizing a characteristic of a source or mask to improve a performance metric of the patterning process by identifying stochastic defects from predicted imaging results (e.g., as predicted by a stochastic edge placement error (SEPE) model) and supplementing a guide function (e.g., a gradient) of a continuous cost function (e.g., associated with EPE) with a first guide function (e.g., a pseudo-gradient)associated with a discontinuous cost function (e.g., function of a defect, hotspot, etc.). The guide function (e.g., a first guide function or pseudo gradient) can be any function that guides or provides a direction (e.g., increase or decrease by certain value) in which a characteristic being optimized should be modified so that an associated cost function is reduced or minimized (e.g., after several iterations). The method 300 improves the performance metric as well as reduce defect occurrence thereby improving e.g., yield of the patterning process.

[0057] In the following discussion, a guide function is referred to as a gradient or pseudo-gradient as an example guiding function and does not limit the scope of the present disclosure. In some embodiments, the guide function (e.g., gradient or pseudo-gradient) provides defect-related information and guides how the cost function should be modified based on the defect-related information. For example, the defect related information may be an evaluation location around a defect, a metric associated with the evaluation location, or other relevant information that can be used for optimization of an aspect of the patterning process. In some embodiments, the guide function may be a differential of a cost function used in the optimization process. In some embodiments, the guide function may not necessarily be a differential of a cost function used in the optimization process.

[0058] In some embodiments, the method 300 can be employed to optimize a source shape, or a mask pattern so that at least one of the performance metric such as a critical dimension of the pattern, or an edge placement error of a pattern that will be printed on the substrate. It can be understood by a person skilled in the art that the optimizing of the source or mask is used as an example to illustrate the use of pseudo-gradient and discontinuous function. However, the present disclosure is not limited to optimizing of the source or the mask, but can be used to optimize other aspects related to patterning process. For example, the defect based pseudo-gradient can be used to determine / optimize dose, focus, etc. of the lithographic apparatus. The steps of the method 300 are discussed further as follows.

[0059] Procedure P301 involves performing a lithography simulation to predict patterning results based on a mask design and a source. For example, procedure P301 may involve obtaining a location 302 (also referred as a hotspot location) on a substrate with the probability of having a defect equal to or greater than a threshold (e.g., greater than 0.6). For example, a hotspot location 302 is a location having a relatively high probability of defect occurrence compared to other locations on the substrate. For example, such locations are associated with a relatively high feature density compared to a feature density at other locations on the substrate. For example, with a probability value ranges between 0 and 1, a high probability may be a value between 0.5-1, or preferably greater than 0.8. In some embodiments, probability value 0 indicates no defect, and 1 indicates a defect occurrence. Typically, defects refer to a pattern that do not satisfy design specifications. In some embodiments, a characteristic (e.g., CD, distance between features, etc.) of a pattern may be associated with a defect tolerance limit. If the characteristic is within the defect tolerance limit, then the pattern may be characterized as a defect. Hence, although a printed substrate may not have a real defect, there will be location associated with patterns that may potentially occur as a defect. In some embodiments, thehotspot location 302 is associated with one or more features of the pattern having critical dimension within a defect tolerance.

[0060] In some embodiments, the defect may be a bridging defect, a necking defect, or any other defects observed in a printed pattern on the substrate. The present disclosure is not limited by the type of defect associated with a pattern on a substrate. In some embodiments, the bridging defect may be characterized by a distance between two adjacent features, where the distance is associated with a defect tolerance. Thus, if at a particular location, the distance between features is close enough to be within the tolerance, then the location is a hotspot location 302.

[0061] In some embodiments, the hotspot location 302 may refer to locations having actual defects printed on the substrate. In other words the probability of defect is 1. In some embodiments, defects may be detected using a lithographic manufacturability check (LMC) performed on a simulated pattern on a substrate or actual printed pattern captured via a metrology tool (e.g., in SEM images) of a printed substrate. The LMC may be conditions associated with a parameter of pattern that qualifies a pattern as a defective pattern or a potentially defective pattern (e.g., high probability of defect).

[0062] In some embodiments, the hotspot location 302 may refer to stochastic defects from the predicted patterning results, as predicted by a SEPE model. In some embodiments, the SEPE may be simulated by factoring in the stochastic variations in photon number fluctuation and photoacid immobility; resist profile; CD (SEPE metrology) due to focus / dose fluctuation, as well as dose sensitivity. That is, simulating stochastic errors in a lithography process may include obtaining a value of a variable indicative of stochastic variations in photon number fluctuation, photoacid immobility, resist contour, imaging characteristics sensitive to process window during the lithography process, and calculating a stochastic error based on the value of the variable. An exemplary model may be based on an aerial image slope and an Image Log Slope (ILS) used to capture dose sensitivity more accurately; a resist contour convoluted by a Gaussian filter, which is used to capture photon number fluctuation and photoacid immobility in a limited pattern area; a resist contour at different aerial image depths in the resist, which is used to address resist profile effects; and variation of CD or ILS at multiple process window conditions (PWs), which addresses the effect of the model osepe susceptibility to a design feature’s limited process window.

[0063] Procedure P303 involves defining a defect ambit 304 around the hotspot location 302 to include a portion of a pattern on the substrate and one or more evaluation locations 303 (also referred to as evaluation points 303) associated with the portion of the pattern.

[0064] In some embodiments, the defect ambit 304 is a boundary around the portion of the pattern with the hotspot location 302 at the center of the boundary. In some embodiments, the defect ambit 304 includes one or more features associated with the hotspot location 302 and the one or more evaluation locations 303 (e.g., EPl and EP2 of Fig. 5A) are locations along a contour of the one or more features. In some embodiments, the boundary is a circular boundary, square boundary, or othergeometrical shape. In some embodiments, the defect ambit 304 is based on an impact of features within a neighborhood of the hotspot location 302 on the pattern.

[0065] In some embodiments, example defect ambits (e.g., 520, 610, and 620) are illustrated in Figs. 5A, 6A and 6B, consistent with embodiments of the present disclosure. The defect ambits are defined around, for example, a detected defect such as bridging (e.g., in 520 and 620) or necking (e.g., in 610). In some embodiments, the defects are characterized by, e.g., CD or EPE measured as a distance between two contours (e.g., of a printed pattern and a desired pattern) or between evaluation locations on a contour. In some embodiments, a defect may be detected using a defect detection method or an inspection method, where one or more defect detectors are defined based on a characteristic (e.g., CD) of pattern, as discussed earlier.

[0066] Fig. 5A illustrates a target pattern (e.g., a design pattern of the design layout) comprising two target features 501 and 502 (e.g., contact holes) and a portion of a pattern 511 and 512 on the substrate, consistent with embodiments of the present disclosure. Furthermore, evaluation locations or points (e.g., EPl and EP2) are defined around the pattern on the substrate or the target pattern associated therewith. In some embodiments, a distance CH may be measured between two features 511 and 512. The distance CH is within a defect tolerance of a bridging defect, hence the pattern is said to have a bridging defect. The corresponding location (i.e., at the distance CH) on the substrate is classified as a hotspot location 302.

[0067] As mentioned in procedure P303, a defect ambit 520 is defined around the bridging defect, e.g., the bridging defect (e.g., CH) being at the center of the defect ambit 520. The evaluation points within the defect ambit are further modified via a characteristic (e.g., mask pattern, source, dose, etc.) of the patterning process. In some embodiments, the characteristic can be determined e.g., via simulation of a process model of the patterning process employing the first gradient (e.g., gradient pg in Fig. 5B) and the first cost function, as discussed herein and as illustrated in Fig. 5B, consistent with embodiments of the present disclosure. The determined characteristic is such that the first cost function (e.g., value W) is reduced (e.g., to zero) effectively reducing the second cost function (e.g., sum of EPEs at all evaluation points). The first gradient pg provides a direction in which such characteristic modification should be performed so that the first cost function is reduced.

[0068] Note that the defect ambit 520 includes two evaluation points EPl and EP2, indicating that a first guide function (e.g., a pseudo-gradient) should be assigned to a performance metric (e.g., EPEI and EPE2) associated with such evaluation points EPl and EP2. Thus, based on the defect ambit, the characteristic (e.g., a mask pattern of a mask, a source, dose, focus, of the lithographic apparatus, etc.) associated with the patterning process is determined resulting in a reduced defect occurrence.

[0069] In some embodiments, a positive value is assigned via a first cost function at EPl and EP2, in Fig. 5B. The first cost function indicates that when a defect exists (e.g., CD of a feature satisfies a defect threshold; stochastic defect is predicted by the SEPE model), the value of the first cost function increase from 0 to W. When such first cost function is used with a cost function (e.g., the second costfunction) of the optimization process, a value of the cost function is increased, thereby the optimization process recognizes a defect occurrence. Further, the first guide function pg guides the optimization process to reduce the cost function by modifying contours at EPl and EP2. In some embodiments, the first cost function may take any mathematical form defined based upon defects. For example, the first cost function can be a sum of printed defects on a substrate, a sum of potential defects (e.g., hotspots location), a probability value based function associated with a hotspot, or other appropriate mathematical form.

[0070] Similar to Fig. 5A, Figs. 6A and 6B illustrate examples of defects and associated defect ambits, consistent with embodiments of the present disclosure. Fig. 6A illustrates a necking defect and a defect ambit 610 defined around the necking defect. Fig. 6B is another example of the bridging defect and a defect ambit 620 defined around the bridging defect. In some embodiments, the first cost function(s) associated with the necking defect (and the bridging defect) may be used during the optimization process. Further, the first guide function associated with evaluation points EP within the defect ambit 610 and 620, respectively may be determined and used during the optimization process as discussed in procedures P305-P309 below.

[0071] Procedure P305 involves defining a first cost function 306 and procedure P307 involves determining and defining a first guide function 308 for the first cost function 306, where the first guide function 308 (e.g., pseudo-gradient) is associated with a performance metric of the patterning process at the one or more evaluation locations 303 within the defect ambit 304. Procedure P305 further involves determining a defect metric (e.g., number of defects, a difference between desired and measured CD value, a SEPE nominal condition (NC) contour distance, a failure probability based on SEPE NC contour distances) associated with the defect (e.g., stochastic defects) and determining a value of a first cost function 306 based on the defect metric. In some embodiments, a width of the SEPE NC contours (e.g., resist contour variations of a simulated or predicted pattern) may be referred to as band widths. For example, as shown in Fig. 10, SEPE NC contour 1210 may have a band width 1212. In some embodiments, the first cost function 306 is a sum of a number of hotspots and a number of defects printed on the substrate. In some embodiments, the first cost function 306 is defined as zero outside the defect ambit 304 and a penalty value (e.g., w) within the defect ambit 304. For example, as illustrated in Fig. 5B, the first cost function (e.g., CF1 below) is associated with a bridging defect is a non-continuous function can be expressed as follows:0, if no bridging defectCF1 = w, if bridging defect

[0072] As such, during optimization (e.g., SMO), when the hotspot (e.g., bridging defect) is identified, a cost of value w may be added to the existing cost function, which is based on a continuous function.

[0073] In some embodiments, the determining of the first guide function 308 involves determining a gradient value of the performance metric at the one or more evaluation locations 303 within the defect ambit 304; and assigning a positive value to the first cost function at the one or more evaluation locations 303 within the defect ambit 304.

[0074] The gradient value of the first guide function 308 evaluated using of the performance metric (e.g., EPE) at each of the plurality of evaluation points with respect to the characteristic of the source or the mask to be optimized, where the gradient value provides a direction in which the characteristic should be modified so that the first cost function 306 is reduced.

[0075] An example of the first guide function (e.g., pseudo-gradient) is implemented in following gradient equation, where the epej is associated with the defect.In the above equation, CF1 refers to the first cost function 306 (e.g., CF1 discussed earlier), m is a mask characteristic, i are the evaluation locations within the defect ambit 304, w is a weight constant (e.g., an evaluation location or pattern more critical than others may be assigned a higher weight constant value, an evaluation location or pattern that is predicted to result in a stochastic defect may be assigned a higher weight constant value, etc.), the epe, refers to edge placement error at i-th evaluation location within the defect ambit 304, and R(x,y) is the resist image that contains defective features (or potential defective features). In some embodiments, such value will be zero when there is no defect. However, when a defect exists, the gradientis computed as above. In some embodiments, the value of the gradient is proportional to the first cost function value. Hence, although the first cost function 306 is discontinuous or non-smooth, a guiding function (e.g., pseudo gradient) can be computed and further used in optimization processes such as SMO (e.g., discussed with respect to Figs. 8 and 9).

[0076] Procedure P309 involves adjusting a source or a mask characteristic 310 by executing a source mask optimization process for a design layout using the first cost function 306, the first guide function 308, and the defect metric. In some embodiments, such optimization process adjusts the characteristic of the source or the mask so that the performance metric and the defect metric associated with the patterning process is improved (e.g., to move nominal condition (NC) contours to resolve stochastic defects). In some embodiments, optimizing the source or mask is an iterative process that continues until all defects are resolved. For example, in some embodiments, optimizing the source or mask may continue iteratively until the distance between SEPE NC contours are increased such that stochastic defects do not occur. For example, as shown in Fig. 10, SEPE NC contour 1210 may be moved to 1214 such that the distance between contour 1210 and contour 1230 is increased and stochastic defects are less likely to occur during lithography. In some embodiments,example optimizing processes are discussed in Figs. 8 and 9, where the optimizing methods can be modified to employ the first cost function 306 and the first guide function 308.

[0077] In some embodiments, an iteration of the adjusting of the characteristic 310 involves executing the source mask optimization process using the design layout to determine a current characteristic of the source or the mask, and the performance metric of the patterning process. In some embodiments, the source mask optimization process involves a model of the source, a mask model of the design layout, a model of the projection optics, or a combination thereof, where the models are configured to simulate an aerial image produced by the source, the portion of the design layout and the projection optics. After the optimization, optimized characteristics 310 are obtained that can be used in the lithographic apparatus during the patterning process.

[0078] In some embodiments, optimizing of the source or the mask of the patterning process comprises executing at least one of the models. In some embodiments, determining the optimized source characteristics 310 involves optimizing an illumination shape or an illumination intensity.

[0079] In some embodiments, the iteration involves evaluating a second cost function and a second gradient of the second cost function, where the second cost function is a function of the performance metric. In some embodiments, evaluating of the second cost function comprises: computing values of the performance metric at a plurality of evaluation locations of the pattern on the substrate, where an evaluation location is a point on a contour of the pattern. For example, performance metric (e.g., EPE) is evaluated at EP1-EP15 of Fig. 4 discussed below.

[0080] In an example, the performance metric is EPE, then the second cost function CF2 can be as follows:CF2 (s, m) = jepW,evaiIePej Ip(Equation 2)In the above equation, s and m refers to source and mask characteristic respectively, and epej is an EPE evaluated at each evaluation point (e.g., including points outside the defect ambit 304) and satisfying a process window condition.

[0081] Furthermore, the iteration involves modifying the current characteristic of the source or the mask based on the second gradient of the second cost function and the first guide function 308 of the first cost function 306 so that a sum of the second cost function and the first cost function is reduced.

[0082] In some embodiments, modifying the current characteristic of the mask involves, (but is not limited to): modifying a shape and size of a design pattern of the design layout; modifying parameters associated with a continuous transmission mask; or placing one or more assist features into a portion of the design layout. In some embodiments, the mask may be a continuous transmission mask (CTM) and the characteristics may be related to a curvilinear pattern of the CTM. For example, a level-set method based CTM determination involves modifying of CTM variables such as a level-set threshold value or other modifiable parameters associated with the CTM. In some embodiments, the assistfeatures comprise a sub resolution assist feature, a printable resolution assist feature, or a combination thereof.

[0083] Fig. 4 illustrates example evaluation locations (or points) along a contour 401 of a simulated pattern or printed pattern on a substrate, consistent with embodiments of the present disclosure. Measurements may be made with respect to the evaluation points to determine a characteristic of the pattern (e.g., CD, EPE, etc.). In some embodiments, the measurements can be used to classify a pattern as a defect, determine a performance metric (e.g., EPE, CD), etc. In some embodiments, for measurement purposes, different cut-lines may be defined based on the geometry of the contour and locations where measurements are desired. For example, for curved portions, cut-lines CL1 and CL5 are angular cut-lines originating from respective centers of curved portions of the contour 401. For relatively straight portions, cut-lines CL2, CL3, and CL4 are horizontal cut lines separated vertically along the length of the contour 401. The cut-lines CL1 intersect with the contour 401 at EP1-EP8, which are example gauge points at which measurements may be determined. For example, a vertical distance DI may be determined between cut-lines related to gauge points EP7 and EP8 or using the uniform angle between EP7 and EP8 to place cut-lines, a distance D2 may be determined between gauge points EPl 1 and EP13, a horizontal dimension (an example of CD) may be measured between EP10 and EP11 (EP12 and EP13, or EP14 and EP15). As mentioned earlier, in some embodiments, the measurements are characteristics of a feature or the printed pattern.

[0084] In some embodiments, an edge placement error (EPE) may be determined as a difference between the contour 401 and a desired contour of a desired pattern 400 (e.g., rectangle). In some embodiments, EPEs are determined at each of the evaluation points EP1-E15, then a sum of such EPEs may be computed to determine the second cost function. During optimization, the cost function (e.g., sum of EPEs) is reduced by adjusting the contour 401 at one or more evaluation points (e.g., EP7 and EP8) so that the second cost function is reduced. In some embodiments, such an adjustment may be performed by modifying a characteristic of a patterning process e.g., mask pattern, source, dose, etc. Such modification is guided by the second gradient as discussed earlier. Also, the present disclosure provides additional guide, in form of the first gradient (e.g., based on defect ambit 304), to modify the characteristics of the patterning process so that the first cost function 306 (e.g., defect count) is reduced.

[0085] Fig. 7A illustrates an example result of employing an existing OPC process or an existing SMO process to a design layout 700 comprising contact holes (dotted), consistent with embodiments of the present disclosure. In Fig. 7A, the design pattern 700 (dotted) is overlapped with an OPC’ed mask pattern obtained via existing OPC process (e.g., Figs. 3, 8, and 9), and further overlapped with a printed pattern on a substrate. When the OPC’ed mask pattern is used via a lithographic apparatus, a bridging defect is printed on the substrate at locations 701-704, as shown.

[0086] In some embodiments, the existing optimization process (e.g., SMO) is based on reducing, for example, sum of EPE (e.g., as discussed with respect to Fig. 4) along the contour and do not includeparticularly focusing on reducing defects. As such, the characteristic associated with the patterning process are determined to reduce EPE and not necessarily defects. Hence, although the OPC’ed mask pattern (in Fig. 7A) may provide minimum EPE, as determined by the existing OPC process, it may not minimize the number of defects.

[0087] Fig. 7B illustrates an example result of employing a present method 300 (or method 1000 of Figs. 8 and 9) to a design layout 750 comprising contact holes (dotted), consistent with embodiments of the present disclosure. In Fig. 7B, the design pattern 750 (dotted) is overlapped with an OPC’ed mask pattern obtained via method 300, and further overlapped with a printed pattern on a substrate. The example result shows that upon employing the method 300 (or method 1000 of Figs. 8 and 9) (e.g., in SMO), an optimized mask pattern where features at the hotspot locations (e.g., 701-704) are modified to reduce defects. For example, the mask pattern associated with layout 750 is optimized using a first guide function 308 and a first cost function 306 of method 300. After modifying the patterns at hotspot locations (e.g., 701-704), the bridging defects are removed. For example, as seen, patterns at 751, 752, 753, and 754 do not have bridging defects.

[0088] As mentioned earlier, the use of the first guide function 308 (e.g., pseudo-gradient) is not limited to SMO process. A person skilled in art may determine a characteristic associated with a patterning process using the first guide function 308, as discussed below.

[0089] In some embodiments, the measurement data (e.g., stochastic variations) related to the printed pattern, determined according to the method of Fig. 3, may be employed in optimization of patterning process or adjusting parameters of the patterning process. It is noted that the terms “mask”, “reticle”, “patterning device” are utilized interchangeably herein. Also, person skilled in the art will recognize that, especially in the context of lithography simulation / optimization, the term “mask” / “patterning device” and “design layout” can be used interchangeably, as in lithography simulation / optimization, a physical patterning device is not necessarily used but a design layout can be used to represent a physical patterning device. For the small feature sizes and high feature densities present on some design layout, the position of a particular edge of a given feature will be influenced to a certain extent by the presence or absence of other adjacent features. These proximity effects arise from minute amounts of radiation coupled from one feature to another or non-geometrical optical effects such as diffraction and interference. Similarly, proximity effects may arise from diffusion and other chemical effects during post-exposure bake (PEB), resist development, and etching that generally follow lithography.

[0090] In a typical high-end design almost every feature of the design layout has some modification in order to achieve high fidelity of the projected image to the target design. These modifications may include shifting or biasing of edge positions or line widths (e.g., SEPE NC contour band widths) as well as application of “assist” features that are intended to assist projection of other features.

[0091] The illumination source can also be optimized, either jointly with patterning device optimization or separately, in an effort to improve the overall lithography fidelity. The terms“illumination source” and “source” are used interchangeably in this document. Since the 1990s, many off-axis illumination sources, such as annular, quadrupole, and dipole, have been introduced. As is known, off-axis illumination is a proven way to resolve fine structures (i.e., target features) contained in the patterning device.

[0092] However, when compared to a traditional illumination source, an off-axis illumination source usually provides less radiation intensity for the aerial image (Al). Thus, it becomes desirable to attempt to optimize the illumination source to achieve the optimal balance between finer resolution and reduced radiation intensity.

[0093] Numerous illumination source optimization approaches can be found, for example, in an article by Rosenbluth et aL, titled “Optimum Mask and Source Patterns to Print A Given Shape”, Journal of Microlithography, Microfabrication, Microsystems 1(1), pp.13-20, (2002). The source is partitioned into several regions, each of which corresponds to a certain region of the pupil spectrum. Then, the source distribution is assumed to be uniform in each source region and the brightness of each region is optimized for process window. However, such an assumption that the source distribution is uniform in each source region is not always valid, and as a result the effectiveness of this approach suffers. In another example set forth in an article by Granik, titled “Source Optimization for Image Fidelity and Throughput”, Journal of Microlithography, Microfabrication, Microsystems 3(4), pp.509-522, (2004), several existing source optimization approaches are overviewed and a method based on illuminator pixels is proposed that converts the source optimization problem into a series of non-negative least square optimizations. Though these methods have demonstrated some successes, they typically require multiple complicated iterations to converge. In addition, it may be difficult to determine the appropriate / optimal values for some extra parameters, such as y in Granik’ s method, which dictates the trade-off between optimizing the source for substrate image fidelity and the smoothness requirement of the source.

[0094] For low ki photolithography, optimization of both the source and patterning device is useful to ensure a viable process window for projection of critical circuit patterns. Some algorithms (e.g., Socha et. AL Proc. SPIE vol.5853, 2005, p.180) discretize illumination into independent source points and mask into diffraction orders in the spatial frequency domain, and separately formulate a cost function (which is defined as a function of selected design variables) based on process window metrics such as exposure latitude which could be predicted by optical imaging models from source point intensities and patterning device diffraction orders. The term “design variables” as used herein comprises a set of parameters of a lithographic projection apparatus or a lithographic process, for example, parameters a user of the lithographic projection apparatus can adjust, or image characteristics a user can adjust by adjusting those parameters (e.g., source or mask design variables). It should be appreciated that any characteristics of a lithographic projection process, including those of the source, the patterning device, the projection optics, or resist characteristics can be among thedesign variables in the optimization. The cost function is often a non-linear function of the design variables. Then standard optimization techniques are used to minimize the cost function.

[0095] Relatedly, the pressure of ever decreasing design rules have driven semiconductor chipmakers to move deeper into the low kj lithography era with existing 193 nm ArF lithography. Lithography towards lower ki puts heavy demands on RET, exposure tools, and the need for litho-friendly design.1.35 ArF hyper numerical aperture (NA) exposure tools may be used in the future. To help ensure that circuit design can be produced on to the substrate with workable process window, sourcepatterning device optimization (referred to herein as source-mask optimization or SMO) is becoming a significant RET for 2x nm node.

[0096] A source and patterning device (design layout) optimization method and system that allows for simultaneous optimization of the source and patterning device using a cost function without constraints and within a practicable amount of time is described in a commonly assigned International Patent Application No. PCT / US2009 / 065359, filed on November 20, 2009, and published as W02010 / 059954, titled “Fast Freeform Source and Mask Co-Optimization Method”, which is hereby incorporated by reference in its entirety.

[0097] Another source and mask optimization method and system that involves optimizing the source by adjusting pixels of the source is described in a commonly assigned U.S. Patent Application No.12 / 813456, filed on June 10, 2010, and published as U.S. Patent Application Publication No. 2010 / 0315614, titled “Source-Mask Optimization in Lithographic Apparatus”, which is hereby incorporated by reference in its entirety.

[0098] Fig. 8 shows an exemplary method 1000 for source-mask optimization in a patterning process, consistent with embodiments of the present disclosure.

[0099] Procedure Pl 002 involves performing a lithography simulation to generate a resist image RI 1002 based on a resist model, a mask design, and a source. As described above with respect to Fig. 2, an aerial image Al 1004 (e.g., aerial image 1510 of Fig. 13) is the radiation intensity distribution at substrate level. A resist layer on the substrate is exposed and the aerial image 1004 is transferred to the resist layer as a latent “resist image” (RI) 1002 (e.g., resist image 1512 of Fig. 13) therein. The resist image (RI) describes 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 which can be found in commonly assigned U.S. Patent No. 8,200,468, the disclosure of which is hereby incorporated by reference in its entirety. The resist model is related only to properties of the resist layer (e.g., effects of chemical processes which occur during exposure, post-exposure bake (PEB), and development). Optical properties of the lithographic projection apparatus (e.g., properties of the source, the patterning device, and the projection optics) dictate the aerial image. Since the patterning device used in the lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus including at least the source and the projection optics.

[0100] At procedure P1002, aerial image 1004 (e.g., aerial image 36 of Fig. 2) can be simulated from a design layout model (e.g., design layout model 35 of Fig. 2), the projection optics model (e.g., projection optics model 32 of Fig. 2), and the design layout model (e.g., design layout model 35 of Fig. 2). Resist image 1002 (e.g., resist image 38 of Fig. 2) can be simulated from the aerial image using a resist model (e.g., resist model 37 of Fig. 2). Simulation of lithography can, for example, predict contours and CDs in the resist image.

[0101] Procedure P1002 further involves generating a variable bias map (VBM) 1006 (e.g., SEPE bias map 1514 of Fig. 13), where the VBM 1006 indicates a resist bias. For example, for an evaluation point location (e.g., xo is an evaluation point location) on a resist image, a value on the VBM indicates a band width (e.g., band width 1212 of Fig. 10) of the SEPE contour at that evaluation point location (e.g., a VBM value of zero may indicate an infinitely thin band width; a VBM value of 1 nm may indicate that the band width is 1 nm; etc.). For example, a SEPE model may describe the bias between resist contour and SEPE contour and be used to generate the VBM 1006. In some embodiments, the SEPE model may be based on an aerial image slope and an Image Log Slope (ILS) used to capture dose sensitivity more accurately; a resist contour convoluted by a Gaussian filter, which is used to capture photon number fluctuation and photoacid immobility in a limited pattern area; a resist contour at different aerial image depths in the resist, which is used to address resist profile effects; and variation of CD or ILS at multiple process window conditions (PWs), which addresses the effect of the SEPE model’s susceptibility to a design feature’s limited process window.

[0102] For example, after a resist contour location (e.g., of resist contour 1410 of Fig. 12) is determined based on the resist image RI 1002 at one or more evaluation point locations (e.g., xo is an evaluation point location), the SEPE model may be used to compute a SEPE resist bias value (e.g., vector 1420 of Fig. 12) for each resist contour vertex at the one or more evaluation point locations. A corresponding SEPE contour (e.g., SEPE contour 1430 of Fig. 12) may be generated based on the SEPE resist bias value.

[0103] For unknown resist contour locations (e.g., when a resist contour is variable during SMO iterations), the SEPE model may be used to compute and generate the VBM (e.g., SEPE bias value map, points 1440 of Fig. 12) on a pre-defined grid first, then the bias value for any resist contour point of interest in an iteration may be quickly computed by interpolating bias values on the grids around that point (e.g., an approximate method).

[0104] Procedure P1004 involves determining stochastic errors as a function of a VBM and a RI. For example, stochastic errors may be determined using the following model of stochastic errors (SEPE model sepe 1008): (Equation 3),where Xo is an evaluation point location, VBM(xo) is a VBM value at an evaluation point location, WBM(XQ) is a slope of a VBM at an evaluation point location, RI(XQ) is a resist image at an evaluation point location, RI(xo) is a slope of a resist image at an evaluation point location, and n is a unit vector along a resist image slope direction.

[0105] Procedure P1004 further involves determining a cost function 1010 comprising the stochastic errors (e.g., a cost function defined based on the sepe model 1008). For example, the cost function 1010 may be defined such that the larger the stochastic errors (e.g., the larger the SEPE model), the larger the cost.

[0106] In a lithographic projection apparatus, as an example, a cost function is expressed asCF(z1, z2, ... , zw) = S^=1wpfp2(z1, z2, ... , zw) (Equation ^, wherein (zi, Z2,...,ZN) are N design variables or values thereof. fp(zi, Z2,...,ZN) can be a function of the design variables (zi, z2,.. .,ZN) such as a difference between an actual value and an intended value of a characteristic at an evaluation point for a set of values of the design variables of (zi, z2,...,ZN). WPis a weight constant associated with fP(zi, z2,.. ,,ZN). An evaluation point or pattern more critical than others can be assigned a higher wpvalue. Patterns or evaluation points with larger number of occurrences may be assigned a higher wpvalue, too. Examples of the evaluation points can be any physical point or pattern on the substrate, any point on a virtual design layout, or resist image, or aerial image, or a combination thereof. fp(zi, Z2,...,ZN) can also be a function of one or more stochastic effects such as the LWR, which are functions of the design variables (zi, z2,.. .,ZN), or stochastic errors such as sepe. The cost function may represent any suitable characteristics of the lithographic projection apparatus or the substrate, for instance, failure rate of a feature, focus, CD, image shift, image distortion, image rotation, stochastic effects, stochastic errors, throughput, CDU, or a combination thereof. CDU is local CD variation (e.g., three times of the standard deviation of the local CD distribution). CDU may be interchangeably referred to as LCDU. In some embodiments, the cost function represents (i.e., is a function of) CDU, throughput, and the stochastic effects. In some embodiments, the cost function represents (i.e., is a function of) EPE, throughput, the stochastic effects, and the stochastic errors. In some embodiments, the design variables (zi, z2,.. ,,ZN) comprise dose, global bias of the patterning device, shape of illumination from the source, or a combination thereof. Since it is the resist image that often dictates the circuit pattern on a substrate, the cost function often includes functions that represent some characteristics 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 projection optics may include componentscollectively called a “wavefront manipulator” that can be used to adjust shapes of a wavefront and intensity distribution or phase shift of the irradiation beam. The projection optics preferably can adjust a wavefront and intensity distribution at any location along an optical path of the lithographic projection apparatus, such as before the patterning device, near a pupil plane, near an image plane, 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 source, the patterning device, temperature variation in the lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus. Adjusting the wavefront and intensity distribution can change values of the evaluation points and the cost function. Such changes can be simulated from a model or actually measured. Of course, CF(zi, Z2,...,ZN) is not limited the form in Eq.l. CF(zi, zz, ... ,ZN) can be in any other suitable form.

[0107] It should be noted that the normal weighted root mean square (RMS) of fp(zi, ZZ,...,ZN) is defined as wpfp (z , z2, ... , zN}, therefore, minimizing the weighted RMS of fp(zi, Z2,...,ZN) isequivalent to minimizing the cost function CF(z}, z2, ... , zw) = 2p=iwpfp Czi>z2> ■■■ >zv)- defined in Equation 4. Thus the weighted RMS of fp(zi, ZZ,...,ZN) and Equation 4 may be utilized interchangeably for notational simplicity herein.

[0108] Further, if considering maximizing the PW (Process Window), one can consider the same physical location from different PW conditions as different evaluation points in the cost function in (Eq.l). For example, if considering N PW conditions, then one can categorize the evaluation points according to their PW conditions and write the cost functions as:(Equation s), where fpu(z ,z2, , zN) is the value of fp(zi, ZZ,...,ZN) under the u-th PW condition u =1,..., U. When fp(zi, zz,.. .,ZN is the EPE, then minimizing the above cost function is equivalent to minimizing the edge shift under various PW conditions, thus leading to maximizing the PW. In particular, if the PW also consists of different mask bias, then minimizing the above cost function also includes the minimization of MEEF (Mask Error Enhancement Factor), which is defined as the ratio between the substrate EPE and the induced mask edge bias.

[0109] The design variables may have constraints, which can be expressed as (z1;z2, ... , zw)e Z, where Z is a set of possible values of the design variables. One possible constraint on the design variables may be imposed by yield or a desired throughput of the lithographic projection apparatus. The desired yield or throughput may limit the dose and thus has implications for the stochastic effects (e.g., imposing a lower bound on the stochastic effects). Higher throughput generally leads to lower dose, shorter longer exposure time and greater stochastic effects. Higher yield generally leads to arestricted design which may be sensitive to stochastic risk. Consideration of substrate throughput, yield and minimization of the stochastic effects may constrain the possible values of the design variables because the stochastic effects are function of the design variables. 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 among the design variables, 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. The throughput may be affected by the failure rate based adjustment to parameters of the patterning process. It is desirable to have lower failure rate of the feature while maintaining a high throughput. Throughput may also be affected by the resist chemistry. Slower resist (e.g., a resist that requires higher amount of light to be properly exposed) leads to lower throughput. Thus, based on the optimization process involving failure rate of a feature due to resist chemistry or fluctuations, and dose requirements for higher throughput, appropriate parameters of the patterning process may be determined.

[0110] The optimization process therefore is to find a set of values of the design variables, under the constraints (z1,z2, ... , zw)e Z, that minimize the cost function, i.e., to find(?i ,z2, ... , zN) = arg min CF z1,z2, ... , zN) = arg min p=i ^pfp2(z1, z2, ... , zN) (z1,z2,...,zN)eZ (z1,z2,...,zN)eZ(Equation 6)

[0111] Procedure P1004 further involves calculating a gradient of the cost function s or CF with respect to sepe (calculate ds / dsepe 1012 by differentiating the cost function with respect to the sepe).

[0112] Procedure P1006 involves calculating a gradient of the cost function s or CF with respect to the RI (calculate ds / dRI 1014 by differentiating the cost function with respect to the RI) (e.g., gradient 1512d of Fig. 13) and calculating a gradient of the cost function s or CF with respect to the VBM (calculate ds / dVBM 1016, as shown in procedure 1006a of Fig. 9, by differentiating the cost function with respect to the VBM).

[0113] In some embodiments, a gradient of the cost function may provide defect data and guide modification of the cost function based on the defect data. In some embodiments, the gradient of the cost function may include a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced. For example, the cost function may be defined as zero when the lithography simulation indicates a stochastic error does not exist and the cost function is defined as a penalty value when the lithography simulation indicates a stochastic error exists.

[0114] Procedure 1006a of Fig. 9 involves calculating a gradient of the cost function s or CF with respect to the VBM (calculate ds / dVBM 1016 by differentiating the cost function with respect to the VBM) (e.g., gradient 1514d of Fig. 13), calculating a gradient of the cost function s or CF withrespect to a filter down-sampled RI (calculate ds / dFDRI 1118 by differentiating the cost function with respect to the FDRI), calculating a gradient of the cost function s or CF with respect to the resist image RI from VBM (calculate ds / dRI 1120 by differentiating the cost function with respect to the RI), and calculating a gradient of the cost function s or CF with respect to the aerial image Al (calculate ds / dAI 1018 by differentiating the cost function with respect to the Al) (e.g., gradient 1510d of Fig. 13).

[0115] That is, by differentiating the cost function with respect to the sepe model in procedure P1004, the gradient of the cost function with respect to the RI and the VBM to the gradient of the cost function with respect to the Al may be propagated in procedure P1006.

[0116] Procedure P1008 involves calculating a gradient of the cost function s or CF with respect to the design variables v (e.g., source and mask variables as described above) (calculate ds / dv 1020 by differentiating the cost function with respect to the design variables v). That is, by differentiating the cost function with respect to the Al in procedure P1006, the gradient of the cost function with respect to the design variables v may be propagated in procedure P1008.

[0117] Procedure P1008 further involves the optimizer 1022 updating the design variables v 1024 for the next iteration based on calculated gradient of the cost function with respect to the design variables. That is, the optimizer 1022 may output updated design variables v 1024 that result in a minimized cost function for the next iteration. For example, the source or mask design variables may be iteratively adjusted based on the gradient of the cost function with respect to the RI and the VBM (e.g., iteratively update source and mask design variables to reduce the cost function until convergence). In some embodiments, after each iteration, the adjusted design variables may result in a reduced SEPE NC band width (e.g., a reduced width of a resist contour) (e.g., reducing a resist contour from width 1214 to width 1216 of Fig. 10). In some embodiments, after each iteration, the adjusted design variable may result in an adjusted source (e.g., Fig. 11 shows a baseline source 1310, a source 1320 with a weight factor, a source 1330 with a weight factor greater than the weight factor of source 1320.

[0118] In some embodiments, the design variables may comprise any suitable combination selected from characteristics of the illumination source (e.g., pupil fill ratio, namely percentage of radiation of the source that passes through a pupil or aperture), characteristics of the projection optics and characteristics of the design layout. For example, the design variables may include characteristics of the illumination source and characteristics of the design layout (e.g., global bias) but not characteristics of the projection optics, which leads to an SMO. Alternatively, the design variables may include characteristics of the illumination source, characteristics of the projection optics and characteristics of the design layout, which leads to a source-mask-lens optimization (SMLO). The design variables may be simultaneously adjusted so that the cost function is moved towards convergence. In some embodiments, the optimizer determines whether a predefined termination condition is satisfied (e.g., do the determined design variables result in SEPE NC contour band widthsshort enough so that SEPE NC contour bands are unlikely to bridge or result in other stochastic defects). The predetermined termination condition may include various possibilities, i.e. the cost function may be minimized or maximized, as required by the numerical technique used, the value of the cost function has been equal to a threshold value or has crossed the threshold value, the value of the cost function has reached within a preset error limit, or a preset number of iteration is reached. If the conditions are satisfied, the method ends. If none of the conditions are satisfied, the procedures in method 1000 are iteratively repeated until a desired result is obtained. The optimization does not necessarily lead to a single set of values for the design variables because there may be physical restraints caused by factors such as the failure rates, the pupil fill factor, the resist chemistry, the throughput, etc. The optimization may provide multiple sets of values for the design variables and associated performance characteristics (e.g., the throughput) and allows a user of the lithographic apparatus to pick one or more sets.

[0119] In a lithographic projection apparatus, the source, patterning device and projection optics can be optimized alternatively (referred to as Alternative Optimization) or optimized simultaneously (referred to as Simultaneous Optimization). The terms “simultaneous”, “simultaneously”, “joint” and “jointly” as used herein mean that the design variables of the characteristics of the source, patterning device, projection optics or any other design variables, are allowed to change at the same time. The term “alternative” and “alternatively” as used herein mean that not all of the design variables are allowed to change at the same time.

[0120] Fig. 14 is a block diagram that illustrates a computer system 1600 that can assist in implementing the optimization methods and flows disclosed herein (e.g., of Figs. 2, 3, 8, and 9), consistent with embodiments of the present disclosure. Computer system 1600 includes a bus 1602 or other communication mechanism for communicating information, and a processor 1604 (or multiple processors 1604 and 1605) coupled with bus 1602 for processing information. Computer system 1600 also includes a main memory 1606, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 1602 for storing information and instructions to be executed by processor 1604. Main memory 1606 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 1604. Computer system 1600 further includes a read only memory (ROM) 1608 or other static storage device coupled to bus 1602 for storing static information and instructions for processor 1604. A storage device 1610, such as a magnetic disk or optical disk, is provided and coupled to bus 1602 for storing information and instructions.

[0121] Computer system 1600 may be coupled via bus 1602 to a display 1612, such as a cathode ray tube (CRT) or flat panel or touch panel display for displaying information to a computer user. An input device 1614, including alphanumeric and other keys, is coupled to bus 1602 for communicating information and command selections to processor 1604. Another type of user input device is cursor control 1616, such as a mouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 1604 and for controlling cursor movement on display 1612. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. A touch panel (screen) display may also be used as an input device.

[0122] According to some embodiments, portions of the optimization process may be performed by computer system 1600 in response to processor 1604 executing one or more sequences of one or more instructions contained in main memory 1606. Such instructions may be read into main memory 1606 from another computer-readable medium, such as storage device 1610. Execution of the sequences of instructions contained in main memory 1606 causes processor 1604 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 1606. In an alternative example, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0123] The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor 1604 for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non- volatile media include, for example, optical or magnetic disks, such as storage device 1610. Volatile media include dynamic memory, such as main memory 1606. Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 1602. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer -readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD- ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[0124] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 1604 for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 1600 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 1602 can receive the data carried in the infrared signal and place the data on bus 1602. Bus 1602 carries the data to main memory 1606, from which processor 1604 retrieves and executes the instructions. The instructions received by main memory 1606 may optionally be stored on storage device 1610 either before or after execution by processor 1604.

[0125] Computer system 1600 also preferably includes a communication interface 1618 coupled to bus 1602. Communication interface 1618 provides a two-way data communication coupling to anetwork link 1620 that is connected to a local network 1622. For example, communication interface 1618 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 1618 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 1618 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0126] Network link 1620 typically provides data communication through one or more networks to other data devices. For example, network link 1620 may provide a connection through local network 1622 to a host computer 1624 or to data equipment operated by an Internet Service Provider (ISP) 1626. ISP 1626 in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet” 1628. Local network 1622 and Internet 1628 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 1620 and through communication interface 1618, which carry the digital data to and from computer system 1600, are exemplary forms of carrier waves transporting the information.

[0127] Computer system 1600 can send messages and receive data, including program code, through the network(s), network link 1620, and communication interface 1618. In the Internet example, a server 1630 might transmit a requested code for an application program through Internet 1628, ISP 1626, local network 1622 and communication interface 1618. One such downloaded application may provide for the illumination optimization, for example. The received code may be executed by processor 1604 as it is received, and / or stored in storage device 1610, or other non-volatile storage for later execution. In this manner, computer system 1600 may obtain application code in the form of a carrier wave.

[0128] Fig. 15 schematically depicts an exemplary lithographic projection apparatus LA whose illumination source could be optimized utilizing the methods described herein (e.g., of Figs. 2, 3, 8, and 9), consistent with embodiments of the present disclosure. The apparatus LA comprises:- an illumination system IL, to condition a beam B of radiation. In this particular case, the illumination system also comprises a radiation source SO;- a first object table (e.g., mask table) MT provided with a patterning device holder to hold a patterning device MA (e.g., a reticle), and connected to a first positioner to accurately position the patterning device with respect to item PS;- a second object table (substrate table) WT provided with a substrate holder to hold a substrate W (e.g., a resist-coated silicon wafer), and connected to a second positioner to accurately position the substrate with respect to item PS;- a projection system (“lens”) PS (e.g., a refractive, catoptric or catadioptric optical system) to image an irradiated portion of the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0129] As depicted herein, the apparatus is of a transmissive type (i.e., has a transmissive mask). However, in general, it may also be of a reflective type, for example (with a reflective mask).

[0130] Alternatively, the apparatus may employ another kind of patterning device as an alternative to the use of a classic mask; examples include a programmable mirror array or LCD matrix.

[0131] The source SO (e.g., a mercury lamp or excimer laser) produces a beam of radiation. This beam is fed into an illumination system (illuminator) IL, either directly or after having traversed conditioning means, such as a beam expander Ex, for example. The illuminator IL may comprise adjusting means AD for setting the outer and / or inner radial extent (commonly referred to as s-outer and s-inner, respectively) of the intensity distribution in the beam. In addition, it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0132] It should be noted with regard to Fig. 15 that the source SO may be within the housing of the lithographic projection apparatus LA (as is often the case when the source SO is a mercury lamp, for example), but that it may also be remote from the lithographic projection apparatus LA, the radiation beam that it produces being led into the apparatus LA (e.g., with the aid of suitable directing mirrors); this latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF or F2 lasing).

[0133] The beam PB subsequently intercepts the patterning device MA, which is held on a patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PL, which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and interferometric measuring means IF), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the beam PB.

[0134] Similarly, the first positioning means can be used to accurately position the patterning device MA with respect to the path of the beam B, e.g., after mechanical retrieval of the patterning device MA from a patterning device library, or during a scan. In general, movement of the object tables MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in Figure 17. However, in the case of a wafer stepper (as opposed to a step-and-scan tool) the patterning device table MT may just be connected to a short stroke actuator, or may be fixed.

[0135] The depicted tool can be used in two different modes:- In step mode, the patterning device table MT is kept essentially stationary, and an entire patterning device image is projected in one go (i.e., a single“flash”) onto a target portion C.The substrate table WT is then shifted in the x- or y- directions so that a different target portion C can be irradiated by the beam PB.- In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single“flash.” Instead, the patterning device table MT is movable in a given direction (the so-called“scan direction,” e.g., the y direction) with a speed v, so that the projection beam B is caused to scan over a patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V = Mv, in which M is the magnification of the lens PL (typically, M = 1 / 4 or 1 / 5). In this manner, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0136] Fig. 16 schematically depicts another exemplary lithographic projection apparatus LA whose illumination source could be optimized utilizing the methods described herein (e.g., of Figs. 2, 3, 8, and 9), consistent with embodiments of the present disclosure.

[0137] The lithographic projection apparatus LA includes:- a source collector module SO;-an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation);-a support structure (e.g. a mask table) MT constructed to support a patterning device (e.g. a mask or a reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;-a substrate table (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and-a projection system (e.g. a reflective projection system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0138] As here depicted, the apparatus LA is of a reflective type (e.g. employing a reflective mask). It is to be noted that because most materials are absorptive within the EUV wavelength range, the mask may have multilayer reflectors comprising, for example, a multi-stack of Molybdenum and Silicon. In one example, the multi-stack reflector has a 40 layer pairs of Molybdenum and Silicon where the thickness of each layer is a quarter wavelength. Even smaller wavelengths may be produced with X-ray lithography. Since most material is absorptive at EUV and x-ray wavelengths, a thin piece of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multi-layer reflector) defines where features would print (positive resist) or not print (negative resist).

[0139] Referring to Fig. 16, the illuminator IL receives an extreme ultra violet radiation beam from the source collector module SO. Methods to produce EUV radiation include, but are not necessarilylimited to, converting a material into a plasma state that has at least one element, e.g., xenon, lithium or tin, with one or more emission lines in the EUV range. In one such method, often termed laser produced plasma ("LPP") the plasma can be produced by irradiating a fuel, such as a droplet, stream or cluster of material having the line-emitting element, with a laser beam. The source collector module SO may be part of an EUV radiation system including a laser, not shown in Fig. 16, for providing the laser beam exciting the fuel. The resulting plasma emits output radiation, e.g., EUV radiation, which is collected using a radiation collector, disposed in the source collector module. The laser and the source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation.

[0140] In such cases, the laser is not considered to form part of the lithographic apparatus and the radiation beam is passed from the laser to the source collector module with the aid of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often termed as a DPP source.

[0141] The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and / or inner radial extent (commonly referred to as s- outer and s-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[0142] The radiation beam B is incident on the patterning device (e.g., mask) MA, which is held on the support structure (e.g., mask table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor PS2 (e.g., an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor PS 1 can be used to accurately position the patterning device (e.g., mask) MA with respect to the path of the radiation beam B. Patterning device (e.g., mask) MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[0143] The depicted apparatus LA could be used in at least one of the following modes:

[0144] 1. In step mode, the support structure (e.g., mask table) MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e., a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0145] 2. In scan mode, the support structure (e.g., mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a targetportion C (i.e., a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (e.g., mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0146] 3. In another mode, the support structure (e.g., mask table) MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[0147] Fig. 17 shows the apparatus LA in more detail, including the source collector module SO, the illumination system IL, and the projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained in an enclosing structure 1920 of the source collector module SO. An EUV radiation emitting plasma 1910 may be formed by a discharge produced plasma source. EUV radiation may be produced by a gas or vapor, for example Xe gas, Li vapor or Sn vapor in which the very hot plasma 1910 is created to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 1910 is created by, for example, an electrical discharge causing an at least partially ionized plasma. Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may be required for efficient generation of the radiation. In some embodiments, a plasma of excited tin (Sn) is provided to produce EUV radiation.

[0148] The radiation emitted by the hot plasma 1910 is passed from a source chamber 1911 into a collector chamber 1912 via an optional gas barrier or contaminant trap 2030 (in some cases also referred to as contaminant barrier or foil trap) which is positioned in or behind an opening in source chamber 1911. The contaminant trap 2030 may include a channel structure. Contamination trap 2030 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 2030 further indicated herein at least includes a channel structure, as known in the art.

[0149] The collector chamber 1911 may include a radiation collector CO which may be a so-called grazing incidence collector. Radiation collector CO has an upstream radiation collector side 1951 and a downstream radiation collector side 1952. Radiation that traverses collector CO can be reflected off a grating spectral filter 1940 to be focused in a virtual source point IF along the optical axis indicated by the dot-dashed line ‘O’ . The virtual source point IF is commonly referred to as the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near an opening 2021 in the enclosing structure 1920. The virtual source point IF is an image of the radiation emitting plasma 1910.

[0150] Subsequently the radiation traverses the illumination system IL, which may include a facetted field mirror device 1922 and a facetted pupil mirror device 1924 arranged to provide a desired angulardistribution of the radiation beam 1921, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the beam of radiation 1921 at the patterning device MA, held by the support structure MT, a patterned beam 1926 is formed and the patterned beam 1926 is imaged by the projection system PS via reflective elements 1928, 1930 onto a substrate W held by the substrate table WT.

[0151] More elements than shown may generally be present in illumination optics unit IL and projection system PS. The grating spectral filter 1940 may optionally be present, depending upon the type of lithographic apparatus. Further, there may be more mirrors present than those shown in the figures, for example there may be 1-6 additional reflective elements present in the projection system PS than shown in Fig. 17.

[0152] Collector optic CO, as illustrated in Fig. 17, is depicted as a nested collector with grazing incidence reflectors 1953, 1954 and 1955, just as an example of a collector (or collector mirror). The grazing incidence reflectors 1953, 1954 and 1955 are disposed axially symmetric around the optical axis O and a collector optic CO of this type is preferably used in combination with a discharge produced plasma source, often called a DPP source.

[0153] Alternatively, the source collector module SO may be part of an LPP radiation system as shown in Fig. 18. A laser LA is arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), creating the highly ionized plasma 1910 with electron temperatures of several 10's of eV. The energetic radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by a near normal incidence collector optic CO and focused onto the opening 2021 in the enclosing structure 1920.

[0154] The concepts disclosed herein may simulate or mathematically model any generic imaging system for imaging sub wavelength features, and may be especially useful with emerging imaging technologies capable of producing increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultra violet), DUV lithography that is capable of producing a 193nm wavelength with the use of an ArF laser, and even a 157nm wavelength with the use of a Fluorine laser. Moreover, EUV lithography is capable of producing wavelengths within a range of 20-5nm by using a synchrotron or by hitting a material (either solid or a plasma) with high energy electrons in order to produce photons within this range.

[0155] A non- transitory computer readable medium may be provided that stores instructions for a processor of a controller (e.g., controller 109 of Fig. 8, computer system 1600 of Fig. 14, etc.) for controlling the electron beam tool, the lithographic system or apparatus, or other systems of other systems and servers, or components thereof, consistent with embodiments in the present disclosure. These instructions may allow the one or more processors to carry out image processing, data processing, beamlet scanning, graphical display, operations of a charged particle beam apparatus, or another imaging device, or the like for providing operations consistent with those described above for Figs. 2, 3, 8, and 9. In some embodiments, the non-transitory computer readable medium may beprovided that stores instructions for a processor to perform the steps of the methods of the disclosed embodiments. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read Only Memory (PROM), and Erasable Programmable Read Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0156] The embodiments may further be described using the following clauses:1. A method for source or mask optimization of a patterning process, comprising: performing a lithography simulation to predict patterning results based on characteristics of a mask or a source; identifying stochastic defects from the predicted patterning results; defining a cost function and a pseudo-gradient; determining a metric of the stochastic defects and the pseudo-gradient for the cost function associated with a performance metric of the patterning process at one or more evaluation locations within a defect ambit; and iteratively adjusting the characteristics of the mask or the source based on the metric and the guide function.2. The method of clause 1, wherein the predicted patterning results are based on a stochastic edge placement error (SEPE) model.3. The method of clause 2, wherein the SEPE model is based on an aerial image slope, an image log slope (ILS), a resist contour, and variation of critical dimensions or ILS at process window conditions.4. The method of clause 3, wherein the resist contour comprises a resist contour convoluted by a Gaussian filter and a resist contour at different aerial image depths in a resist.5. The method of any one of clauses 1-4, wherein the pseudo-gradient provides defect data and guides modification of the cost function based on the defect data.6. The method of clause 5, wherein the pseudo-gradient includes a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced.7. The method of any one of clauses 1-6, wherein the cost function and the pseudo-gradient are based on a SEPE contour distance.8. The method of clause 7, wherein the cost function and the pseudo-gradient are based on a direct measurement of the SEPE contour distance or a failure probability based on the SEPE contour distance.9. The method of any one of clauses 1-8, wherein the cost function and the pseudo-gradient are based on a resist image and the characteristics of the mask or the source.10. The method of any one of clauses 1-9, wherein the metric of stochastic defects comprises a SEPE contour distance.11. The method of any one of clauses 1-10, wherein the performance metric of the patterning process comprises a stochastic edge placement error of a simulated pattern to be printed on a substrate.12. The method of any one of clauses 1-11, wherein determining the pseudo-gradient comprises computing values of the performance metric at the one or more evaluation locations within the defect gambit.13. The method of any one of clauses 1-12, wherein the cost function is defined as zero when the predicted patterning results indicate a stochastic defect does not exist and the cost function is defined as a penalty value when the predicted patterning results indicate a stochastic defect exists.14. The method of any one of clauses 1-13, wherein the source characteristics comprise at least one of an illumination shape or an illumination intensity.15. The method of any one of clauses 1-14, wherein the mask characteristics comprise at least one of a shape of a design pattern of a mask or a size of the design pattern of the mask.16. The method of any one of clauses 1-15, wherein the stochastic defects comprise a bridging defect.17. The method of any one of clauses 1-16, wherein with each iteration, the adjusted characteristics of the mask or the source result in an increased distance between SEPE contours.18. A method for source or mask optimization of a patterning process, comprising: identifying stochastic defects from a predicted patterning; determining a measure of stochastic defects and a guide function for a cost function associated with a performance measure of the patterning process at one or more points; and iteratively modifying characteristics of the mask or the source based on the measure of stochastic defects and the guide function.19. The method of clause 18, wherein the predicted patterning are based on a stochastic edge placement error (SEPE) model.20. The method of clause 19, wherein the SEPE model is based on an aerial image slope, an image log slope (ILS), a resist contour, and variation of critical dimensions or ILS at process window conditions.21. The method of clause 20, wherein the resist contour comprises a resist contour convoluted by a Gaussian filter and a resist contour at different aerial image depths in a resist.22. The method of any one of clauses 18-21, wherein the guide function provides defect data and guides modification of the cost function based on the defect data.23. The method of clause 22, wherein the guide function includes a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced.24. The method of any one of clauses 18-23, wherein the cost function and the guide function are based on a SEPE contour distance.25. The method of clause 24, wherein the cost function and the guide function are based on a direct measurement of the SEPE contour distance or a failure probability based on the SEPE contour distance.26. The method of any one of clauses 18-25, wherein the cost function and the guide function are based on a resist image and the characteristics of the mask or the source.27. The method of any one of clauses 18-26, wherein the metric of stochastic defects comprises a SEPE contour distance.28. The method of any one of clauses 18-27, wherein the performance measure of the patterning process comprises a stochastic edge placement error of a simulated pattern to be printed on a substrate.29. The method of any one of clauses 18-28, wherein determining the guide function comprises computing values of the performance measure at the one or more points.30. The method of any one of clauses 18-29, wherein the cost function is defined as zero when the predicted patterning indicate a stochastic defect does not exist and the cost function is defined as a penalty value when the predicted patterning indicate a stochastic defect exists.31. The method of any one of clauses 18-30, wherein the source characteristics comprise at least one of an illumination shape or an illumination intensity.32. The method of any one of clauses 18-31, wherein the mask characteristics comprise at least one of a shape of a design pattern of a mask or a size of the design pattern of the mask.33. The method of any one of clauses 18-32, wherein the stochastic defects comprise a bridging defect.34. The method of any one of clauses 18-33, wherein with each iteration, the modified characteristics of the mask or the source result in an increased distance between SEPE contours.35. A method for source and mask optimization of a patterning process, comprising: performing a lithography simulation to generate a resist image (RI) based on a resist model, characteristics of a mask, and characteristics of a source; determining stochastic errors as a function of a variable bias map (VBM) and the RI, wherein the VBM indicates a resist contour variation band width; determining a cost function comprising the stochastic errors; determining a gradient of the cost function with respect to the RI and the VBM using source and mask variables; and iteratively adjusting the characteristics of the mask or the source based on the gradient of the cost function with respect to the RI and the VBM.36. The method of clause 35, wherein generating the RI comprises generating an aerial image (Al) and transferring the Al to a resist layer.37. The method of clause 36, wherein generating the RI comprises calculating the RI from the Al using the resist model.38. The method of any one of clauses 35-37, wherein determining the VBM comprises determining a resist contour location at one or more evaluation locations on the RI and computing a resist bias value based on the resist contour location at the one or more evaluation locations.39. The method of any one of clauses 35-38, wherein the stochastic errors are a function of an evaluation location of the RI.40. The method of clause 39, wherein determining the stochastic errors further comprises calculating a slope of the RI at the evaluation location and calculating a slope of the VBM at the evaluation point.41. The method of any one of clauses 35-40, wherein the gradient of the cost function provides defect data and guides modification of the cost function based on the defect data.42. The method of clause 41, wherein the gradient of the cost function includes a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced.43. The method of any one of clauses 35-42, wherein the cost function is defined based on a model of the stochastic errors.44. The method of clause 43, further comprising calculating a gradient of the cost function with respect to the model of the stochastic errors after determining the cost function.45. The method of any one of clauses 35-44, wherein calculating the gradient of the cost function with respect to the VBM further comprises: calculating a gradient of the cost function with respect to a filter down-sampled RI (FDRI); calculating a gradient of the cost function with respect to the RI from the VBM; and calculating a gradient of the cost function with respect to an aerial image (Al).46. The method of any one of clauses 35-45, wherein iteratively adjusting the characteristics of the mask or the source comprises iteratively updating source and mask variables to reduce the cost function until convergence.47. The method of any one of clauses 35-46, wherein after each iteration, the adjusted characteristics of the mask or the source results in a reduced band width of a resist contour variation.48. The method of any one of clauses 35-47, wherein the cost function is defined as zero when the lithography simulation indicates a stochastic error does not exist and the cost function is defined as a penalty value when the lithography simulation indicates a stochastic error exists.49. The method of any one of clauses 35-48, wherein the characteristics of the source comprise at least one of an illumination shape or an illumination intensity.50. The method of any one of clauses 35-49, wherein the characteristics of the mask comprise at least one of a shape of a design pattern of a mask or a size of the design pattern of the mask.51. The method of any one of clauses 35-50, wherein the stochastic errors indicate a bridging defect.52. A method for source and mask optimization of a patterning process, comprising: generating a resist image (RI); determining stochastic errors as a function of a variable bias map (VBM) and the RI;determining a cost function comprising the stochastic errors; calculating a gradient of the cost function with respect to the RI and the VBM and using source and mask variables; and iteratively modifying characteristics of the source or the mask based on the gradient of the cost function with respect to the RI and the VBM.53. The method of clause 52, wherein generating the RI comprises generating an aerial image (Al) and transferring the Al to a resist layer.54. The method of clause 53, wherein generating the RI comprises calculating the RI from the Al using a resist model.55. The method of any one of clauses 52-54, wherein determining the VBM comprises determining a resist contour location at one or more evaluation locations on the RI and computing a resist bias value based on the resist contour location at the one or more evaluation locations.56. The method of any one of clauses 52-55, wherein the stochastic errors are a function of an evaluation location of the RI.57. The method of clause 56, wherein determining the stochastic errors further comprises calculating a slope of the RI at the evaluation location and calculating a slope of the VBM at the evaluation point.58. The method of any one of clauses 52-57, wherein the gradient of the cost function provides defect data and guides modification of the cost function based on the defect data.59. The method of clause 58, wherein the gradient of the cost function includes a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced.60. The method of any one of clauses 52-59, wherein the cost function is defined based on a model of the stochastic errors.61. The method of clause 60, further comprising calculating a gradient of the cost function with respect to the model of the stochastic errors after determining the cost function.62. The method of any one of clauses 52-61, wherein calculating the gradient of the cost function with respect to the VBM further comprises: calculating a gradient of the cost function with respect to a filter down-sampled RI (FDRI); calculating a gradient of the cost function with respect to the RI from the VBM; and calculating a gradient of the cost function with respect to an aerial image (Al).63. The method of any one of clauses 52-62, wherein iteratively modifying the characteristics of the mask or the source comprises iteratively updating source and mask variables to reduce the cost function until convergence.64. The method of any one of clauses 52-63, wherein after each iteration, the modified characteristics of the mask or the source results in a reduced band width of a resist contour variation.65. The method of any one of clauses 52-64, wherein the cost function is defined as zero when a lithography simulation indicates a stochastic error does not exist and the cost function is defined as a penalty value when the lithography simulation indicates a stochastic error exists.66. The method of any one of clauses 52-65, wherein the characteristics of the source comprise at least one of an illumination shape or an illumination intensity.67. The method of any one of clauses 52-66, wherein the characteristics of the mask comprise at least one of a shape of a design pattern of a mask or a size of the design pattern of the mask.68. The method of any one of clauses 52-67, wherein the stochastic errors indicate a bridging defect.69. A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to cause the computing device to perform operations for source and mask optimization of a patterning process according to any one of clauses 1-68.

[0157] 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 may be made without departing from the scope thereof.

Claims

CLAIMS1. A method for source or mask optimization of a patterning process, comprising: identifying stochastic defects from a predicted patterning; determining a measure of stochastic defects and a guide function for a cost function associated with a performance measure of the patterning process at one or more points; and iteratively modifying characteristics of the mask or the source based on the measure of stochastic defects and the guide function.

2. The method of claim 1, wherein the predicted patterning are based on a stochastic edge placement error (SEPE) model.

3. The method of claim 2, wherein the SEPE model is based on an aerial image slope, an image log slope (ILS), a resist contour, and variation of critical dimensions or ILS at process window conditions.

4. The method of claim 3, wherein the resist contour comprises a resist contour convoluted by a Gaussian filter and a resist contour at different aerial image depths in a resist.

5. The method of claim 1, wherein the guide function provides defect data and guides modification of the cost function based on the defect data.

6. The method of claim 5, wherein the guide function includes a function that provides a direction in which the characteristics of the mask or the source should be modified such that the cost function is reduced.

7. The method of claim 1, wherein the cost function and the guide function are based on a SEPE contour distance.

8. The method of claim 7, wherein the cost function and the guide function are based on a direct measurement of the SEPE contour distance or a failure probability based on the SEPE contour distance.

9. The method of claim 1, wherein the cost function and the guide function are based on a resist image and the characteristics of the mask or the source.

10. The method of claim 1, wherein the metric of stochastic defects comprises a SEPE contour distance.

11. The method of claim 1, wherein the performance measure of the patterning process comprises a stochastic edge placement error of a simulated pattern to be printed on a substrate.

12. The method of claim 1, wherein determining the guide function comprises computing values of the performance measure at the one or more points.

13. The method of claim 1, wherein the cost function is defined as zero when the predicted patterning indicate a stochastic defect does not exist and the cost function is defined as a penalty value when the predicted patterning indicate a stochastic defect exists.

14. The method of claim 1, wherein the source characteristics comprise at least one of an illumination shape or an illumination intensity.

15. The method of claim 1, wherein the mask characteristics comprise at least one of a shape of a design pattern of a mask or a size of the design pattern of the mask.

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