Rule-based retargeting method for target patterns

Abstract

A method for generating a retargeting pattern for a target pattern to be printed on a substrate is described herein. The method comprises: obtaining (i) a target pattern comprising at least one feature, the at least one feature having a geometry comprising a first dimension and a second dimension; and (ii) a plurality of deviation rules defined as a function of the first dimension, the second dimension, and a property associated with the feature of the target pattern within a measurement region; determining a value of the property at a plurality of locations on the at least one feature of the target pattern, each location being encompassed by the measurement region; selecting a subset of deviations from the plurality of deviation rules based on the values ​​of the property; and generating a retargeting pattern by applying the selected subset of deviations to the at least one feature of the target pattern.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application 62 / 925,463, filed on October 24, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The description herein relates to lithographic apparatus and patterning processes, and more particularly to methods for determining corrections to a target pattern to improve the patterning process. Background Art

[0004] Lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (e.g., a mask) can contain or provide a circuit pattern (a "design layout") corresponding to a separate layer of the IC, and this circuit pattern can be transferred to a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the circuit pattern on the patterning device. Generally, a single substrate includes multiple adjacent target portions, to which the circuit pattern is transferred sequentially by the lithographic projection apparatus, one target portion at a time. In one type of lithographic projection apparatus, the circuit pattern on the entire patterning device is transferred to one target portion at a time; such an apparatus is often referred to as a wafer stepper. In an alternative apparatus, often referred to as a stepper-scan apparatus, a projection beam is scanned across the entire patterning device in a given reference direction (the "scanning" direction) while the substrate is synchronously moved parallel or antiparallel to this reference direction. Different portions of the circuit pattern on the patterning device are gradually transferred to one target portion. In general, because the lithographic projection apparatus will have a magnification factor M (typically <1), the speed F at which the substrate is moved will be a factor M times the speed at which the projection beam scans the patterning device. Further information on lithographic apparatus as described herein can be gleaned, for example, from US 6,046,792, which is incorporated herein by reference.

[0005] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate can undergo various processes, such as primer coating, resist coating and soft baking. After exposure, the substrate can undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. This series of processes is used as the basis for the individual layers of the manufacturing device (e.g., IC). The substrate can then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to complete the individual layers of the device. If several layers are needed in the device, the entire process or its variations are repeated for each layer. Ultimately, there will be a device in each target portion on the substrate. The devices are then separated from each other by techniques such as scribing or sawing, whereby the individual devices can be mounted on a carrier, connected to pins, etc.

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

[0007] As semiconductor manufacturing processes continue to advance, the size of functional elements has been continuously reduced for decades, while the number of functional elements, such as transistors, per device has been steadily increasing, following a trend commonly referred to as "Moore's Law." Under current advanced technology, the layers of a device are fabricated using a lithographic projection apparatus that projects a design layout onto a substrate using radiation from a deep ultraviolet radiation source, thereby producing individual functional elements having dimensions well below 100 nm, i.e., dimensions less than half the wavelength of the radiation from the radiation source (e.g., a 193 nm radiation source). This process for printing features having dimensions less than the classical resolution limit of the lithographic projection apparatus is commonly referred to as low-k1 lithography, based on the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation used (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (usually the smallest feature size printed), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it becomes to reproduce a pattern on the substrate that is similar to the shape and size planned by the circuit designer in order to achieve specific electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection equipment and / or design layout. These steps include (for example, but not limited to) optimization of NA and optical coherence settings, customized illumination schemes, the use of phase-shifting pattern forming devices, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement technology" (RET). The term "projection optics" as used herein should be broadly interpreted to cover various types of optical systems, including (for example,) refractive optics, reflective optics, aperture-type and catadioptric optics. The term "projection optics" may also include elements that operate according to any of these design types for collectively or individually guiding, shaping or controlling the projection radiation beam. The term "projection optics" may include any optical element in a lithographic projection apparatus, regardless of where the optical element is located in the optical path of the lithographic projection apparatus. Projection optics can include optical elements for shaping, conditioning, and / or projecting radiation from a source before it passes through a patterning device, and / or optical elements for shaping, conditioning, and / or projecting radiation after it passes through the patterning device. Projection optics typically do not include a source and a patterning device. Summary of the Invention

[0008] In an embodiment, a method for generating a retargeting pattern for a target pattern to be printed on a substrate is provided. The method comprises: obtaining (i) the target pattern including at least one feature, the at least one feature having a geometric shape including a first dimension and a second dimension; and (ii) a plurality of deviation rules defined as a function of the first dimension, the second dimension, and a property associated with the feature of the target pattern within a measurement region; determining a value of the property at a plurality of locations on the at least one feature of the target pattern, wherein each location is surrounded by the measurement region; selecting a subset of deviations for the plurality of locations on the at least one feature from the plurality of deviation rules based on the value of the property; and generating the retargeting pattern for the target pattern by applying the selected subset of deviations to the at least one feature of the target pattern.

[0009] Furthermore, in an embodiment, a method for determining a deviation rule for a target pattern to be printed on a substrate is provided. The method comprises: obtaining the target pattern including at least one feature defined by a first dimension and a second dimension; determining a plurality of deviations for the first dimension and the second dimension by executing a process correction model, and associating each of the plurality of deviations with a value of a property, wherein the process correction model biases the first dimension and the second dimension of the at least one feature and calculates the property associated with the at least one feature; and defining the deviation rule based on the plurality of deviations as a function of the first dimension, the second dimension, and the property associated with the at least one feature.

[0010] Furthermore, a computer program product is provided. The computer program product includes a non-transitory computer-readable medium on which instructions are recorded. When the instructions are executed by a computer, the method according to any one of the above claims is implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0012] Figure 1 is a block diagram of various subsystems of a lithography system according to an embodiment;

[0013] Figure 2 is according to an embodiment corresponding to Figure 1 Block diagram of the simulation model of the subsystem in;

[0014] Figure 3A is a flow chart of a method for generating a retargeting pattern for a target pattern to be imaged on a substrate according to an embodiment;

[0015] Figure 3B is a flow chart of an exemplary process for determining a value of a property at a given location, according to an embodiment;

[0016] Figure 4A An exemplary deviation table for a property is illustrated, wherein each cell in the table includes a deviation value, according to an embodiment;

[0017] Figure 4B and Figure 4C illustrates an exemplary deviation table for a plurality of properties;

[0018] Figure 5A and Figure 5B An example of determining a property of a given position for a target pattern according to an embodiment is described;

[0019] Figure 6A is an exemplary deviation range according to an existing rule-based approach, according to an embodiment;

[0020] Figure 6B and Figure 6C illustrating exemplary deviations based on properties of features within a line array according to an embodiment;

[0021] Figure 7A is an exemplary range of deviations described using the first property and the second property according to an embodiment;

[0022] Figure 7B In the application according to Figure 7A The residuals of the model after the deviation;

[0023] Figure 8A and Figure 8B illustrating exemplary deviations for ends of wires according to embodiments;

[0024] Figure 9 illustrates an exemplary pattern including contact holes and corresponding deviations for each hole according to an embodiment;

[0025] Figure 10A and Figure 10B illustrates an exemplary density calculation using a square window according to an embodiment;

[0026] Figure 11A and Figure 11B illustrating an exemplary density calculation using a circular window according to an embodiment;

[0027] Figure 12 is a flow chart of a method for determining a deviation rule for a target pattern to be printed on a substrate according to an embodiment;

[0028] Figure 13is an exemplary deviation determined using an etch correction model according to an embodiment;

[0029] Figure 14 is a flow chart illustrating aspects of an exemplary method of joint optimization according to an embodiment;

[0030] Figure 15 An embodiment of another optimization method according to an embodiment is shown;

[0031] Figure 16A 、 Figure 16B and Figure 17 An exemplary flow chart illustrating various optimization processes according to an embodiment;

[0032] Figure 18 is a block diagram of an exemplary computer system according to an embodiment;

[0033] Figure 19 is a schematic diagram of a lithographic projection apparatus according to an embodiment;

[0034] Figure 20 is a schematic diagram of another lithographic projection apparatus according to an embodiment;

[0035] Figure 21 According to the embodiment Figure 20 A more detailed view of the devices in

[0036] Figure 22 According to the embodiment Figure 20 and Figure 21 A more detailed view of the source collector module of the device SO.

[0037] The embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice the embodiments. It is important to note that the following figures and examples are not intended to limit the scope to a single embodiment, but rather that other embodiments are possible by interchange of some or all of the elements described or illustrated. Wherever convenient, the same reference numerals will be used throughout the drawings to refer to identical or similar parts. Where certain elements of these embodiments may be implemented, in part or in whole, using known components, only those portions of these known components necessary for understanding the embodiments will be described, and detailed descriptions of the remaining portions of these known components will be omitted to avoid obscuring the description of the embodiments. Throughout this specification, embodiments showing a single component should not be construed as limiting; indeed, unless expressly indicated otherwise herein, the scope is intended to encompass other embodiments including multiple identical components, and vice versa. Furthermore, applicants do not intend for any term in this specification or claims to be attributed an uncommon or special meaning unless expressly stated otherwise. Furthermore, the scope encompasses currently and future known equivalents to the components mentioned in the description. DETAILED DESCRIPTION

[0038] Although specific reference may be made to IC manufacturing in the present invention, it should be clearly understood that the description herein has many other possible applications. For example, the present application may be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. It will be understood by those skilled in the art that in the context of these alternative applications, any use of the terms "reticle," "wafer," or "die" herein should be considered interchangeable with the more general terms "mask," "substrate," and "target portion," respectively.

[0039] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of 5 nm to 20 nm).

[0040] The terms "optimize" and "improve" as used herein mean adjusting the lithography projection equipment so that the lithography results and / or process have more ideal characteristics, such as higher accuracy of projection of the design layout on the substrate, a larger process window, etc.

[0041] Furthermore, the lithographic projection apparatus may be of a type having two or more substrate tables (and / or two or more patterning device tables). In these "multi-stage" apparatuses, the additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. For example, a dual-stage lithographic projection apparatus is described in US Pat. No. 5,969,441, which is incorporated herein by reference.

[0042] The pattern forming device mentioned above includes or can form a design layout. The design layout can be generated using a CAD (computer-aided design) program, which is often referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules to generate a functional design layout / pattern forming device. These rules are set by processing and design constraints. For example, the design rules define the spacing tolerances between circuit components (such as gates, capacitors, etc.) or interconnects to ensure that the circuit components or lines do not interact with each other in an undesirable manner. The design rule constraints are generally referred to as "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or hole, or the minimum spacing between two lines or two holes. Therefore, 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 pattern forming device).

[0043] The terms "mask" or "patterning device" as used herein should be broadly interpreted as referring to a general patterning device that can be used to impart an incident radiation beam with a patterned cross-section that corresponds to the pattern to be produced in a target portion of the substrate; the term "light valve" may also be used in this context. In addition to classical masks (transmissive or reflective; binary, phase-shift, hybrid, etc.), examples of other such patterning devices include:

[0044] Programmable mirror array. An example of this device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle underlying this apparatus is that (e.g.,) addressed areas of the reflective surface cause incident radiation to be reflected as diffracted radiation, while unaddressed areas cause incident radiation to be reflected as undiffracted radiation. Using appropriate filters, this undiffracted radiation can be filtered out from the reflected beam, leaving only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. Suitable electronic components can be used to perform the required matrix addressing. More information on such mirror arrays can be gleaned, for example, from U.S. Patents Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0045] - A programmable LCD array. An example of such a configuration is given in US Patent No. 5,229,872, which is incorporated herein by reference.

[0046] As a brief introduction, Figure 1 An exemplary lithographic projection apparatus 10A is illustrated. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources including extreme ultraviolet (EUV) sources (as discussed above, the lithographic projection apparatus itself need not have a radiation source); illumination optics, which define the partial coherence (expressed as a standard deviation) and may include optics 14A, 16Aa, and 16Ab that shape the radiation from source 12A; a patterning device 14A; and transmissive optics 16Ac that project an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at a pupil plane of the projection optics may limit the range of beam angles impinging on the substrate plane 22A, where the maximum possible angle defines the numerical aperture, NA, of the projection optics = sin(Θ). max ).

[0047] In the optimization process of a system, the quality factor of the system can be expressed as a cost function. The optimization process boils down to the 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 the weighted root mean square (RMS) of the deviations of certain characteristics (evaluation points) of the system relative to the expected values ​​(e.g., ideal values) of these characteristics; the cost function can also be the maximum value of these deviations (i.e., the worst deviation). The term "evaluation point" in this article should be broadly interpreted to include any characteristic of the system. Due to the practicality of the implementation of the system, the design variables of the system can be limited to a limited range and / or be interdependent. In the case of a lithographic projection device, the constraints are often associated with the physical properties and characteristics of the hardware (such as the tunable range, and / or the manufacturability design rules of the pattern forming device), and the evaluation points can include physical points on the resist image on the substrate, as well as non-physical characteristics such as dose and focus.

[0048] 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 herein to include any optical component that can modify the wavefront of a radiation beam. For example, projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) 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 image, a "resist image" (RI). The resist image (RI) can be defined as the spatial solubility distribution of the resist in the resist layer. A resist model can be used to calculate the resist image based on the aerial image; an example of this can be found in commonly assigned U.S. patent application Ser. No. 12 / 315,849, the entire contents of which are incorporated herein by reference. The resist model is solely related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a lithographic projection apparatus (e.g., properties of the source, patterning device, and projection optics) define the aerial image. Because the patterning device used in a lithographic projection apparatus can be varied, 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 projection optics.

[0049] Figure 2 An exemplary flow chart for simulating lithography in a lithographic projection apparatus is illustrated in FIG. A source model 31 represents the optical properties of a source (including radiation intensity distribution and / or phase distribution). A projection optics model 32 represents the optical properties of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). A design layout model 35 represents the optical properties of a design layout (including changes in the radiation intensity distribution and / or phase distribution caused by a given design layout 33), which is a representation of the arrangement of features on or formed by a patterning device. An aerial image 36 can be simulated based on the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated based on the aerial image 36 using a resist model 37. Simulation of lithography can, for example, predict the profile and CD in the resist image.

[0050] More specifically, note that the source model 31 can represent the optical characteristics of the source, including but not limited to the NA standard deviation (σ) setting, and any specific illumination source shape (e.g., off-axis radiation sources such as toroidal, quadrupole, and dipole, etc.). The projection optics model 32 can represent the optical characteristics of the projection optics, including aberrations, distortions, refractive index, physical size, physical dimensions, etc. The design layout model 35 can also represent the physical properties of the physical pattern forming device, such as described in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. The goal of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and CD, which can then be compared to the expected design. The expected design is typically defined as a pre-OPC design layout that can be provided in a standardized digital file format such as GDSII or OASIS or other file format.

[0051] Based on this design layout, one or more portions referred to as "snippets" may be identified. In an embodiment, a set of snippets are extracted that represent complex patterns in the design layout (although typically on the order of 50 to 1000 snippets, any number of snippets may be used). As will be appreciated by those skilled in the art, these patterns or snippets represent smaller portions of the design (i.e., circuits, cells, or patterns), and the snippets, in particular, represent smaller portions that require special attention and / or verification. In other words, a snippet may be a portion of the design layout, or may be similar or have similar behavior to a portion of the design layout, where critical features are identified through experience (including snippets provided by the customer), through trial and error, or by performing full-chip simulations. A snippet typically comprises one or more test patterns or gauge patterns.

[0052] An initial large set of segments can be provided a priori by the customer based on known critical feature areas in the design layout that require specific image optimization. Alternatively, in another embodiment, an initial large set of segments can be extracted from the entire design layout using some automatic (such as machine vision) or manual algorithm that identifies critical feature areas.

[0053] To improve the patterning process, several types of correction models can be used to modify the desired pattern to be printed on the substrate. This modification of the desired pattern is called retargeting. Current methods related to modifying the desired pattern include rule-based retargeting and model-based retargeting.

[0054] For example, rule-based modifications to pre-OPC layouts (referred to as "retargeting") are used to improve the process window for specific features. See K. Lucas et al., "Process, Design, and OPC Requirements for the 65nm Device Generation" (Proc. SPIE, Vol. 5040, p. 408, 2003). A rule-based retargeting approach for pre-OPC layouts includes selective biasing and pattern shifting. This approach can improve the full process window performance for certain critical features by selectively changing the target edge placement that the OPC software uses as the desired end result, while still calculating OPC corrections only under nominal process conditions. Thus, instead of minimizing the error between the design dimensions and the simulated edge placement, the OPC software instead minimizes the error between the retargeted dimensions and the simulated edge placement.

[0055] Users of OPC software can retarget designs in a variety of ways to improve process window performance. In the simplest example of retargeting, rules can be applied to specific features to improve the printability and process window of that feature. For example, although isolated lines have a less favorable process window than dense lines, the process margin improves as the feature size increases. Simple rules can be applied to increase the size of smaller isolated lines, thereby improving the process window. Other rule-based retargeting methods have been developed in which metrics other than CD are used to determine the retargeted edge placement, such as normalized image log slope (NILS), sensitivity to mask CD error, or mask error enhancement factor (MEEF).

[0056] While rule-based retargeting methods can improve the printability of features across the entire process window, these methods have several drawbacks. These methods can become quite complex and are based solely on pre-OPC layouts. Once OPC corrections are added to the design, the printing performance, which is a function of process conditions, can become very different from what would have been expected based on the pre-OPC design, introducing significant error sources and preventing retargeting from achieving the desired results. Consequently, the accuracy of the printed features can become an issue. On the other hand, model-based retargeting can produce more accurate results. However, model-based retargeting methods have more problems with consistency, speed, interpretability, and precise control of retargeting.

[0057] Rule-based retargeting can be used because it has certain advantages. For example, rule-based retargeting is much faster than model-based methods. Retargeting patterns are more consistent, making it easier to explain, for example, why a circle design was modified in a certain way. However, with model-based methods, one needs to understand and explain the exact extent to which the model was observed and why the design pattern was modified in a certain way.

[0058] Another advantage of rule-based retargeting is complete control over how specific patterns are modified. Model-based approaches, on the other hand, can use a continuous function as the objective function, based on which the design pattern is modified. Therefore, if the process is not perfectly modeled by the model, the user can sometimes manually adjust the deviation so that the model results match the desired printing performance on the wafer. However, this additional deviation can be difficult to handle with an already calibrated model. On the other hand, with rule-based retargeting, one can easily determine the portions of a simulated pattern (e.g., generated by the process model) that deviate from the desired pattern on the wafer. A rule-based table can then be used to deviate from those specific portions. In other words, no changes are made to the model behavior, so other design patterns are not affected except for those that meet certain rules within the table. This is very difficult to do with model-based approaches because changes are made to the model itself. Furthermore, changing the model also changes the behavior of the corrections for other design patterns. For example, a design pattern that produces the desired printing result may be unnecessarily modified.

[0059] Although rule-based retargeting has several advantages over model-based retargeting, rule-based methods are currently limited to rules based on, for example, width and spacing for specific features. Therefore, using current rule-based methods, the deviation can be the same for the same width and spacing. However, even if the width and spacing of the features are the same, modifying the edges of a feature differently from other features may produce better printing performance. Therefore, current rule-based methods are very limited in this regard. On the other hand, model-based retargeting provides the flexibility to modify the edges of the same feature differently to produce more accurate printing results. However, as mentioned earlier, model-based methods are more computationally intensive and the patterns can be more expensive to manufacture. For example, the patterns produced using model-based retargeting are less consistent, can be curved, difficult to interpret, and it is difficult to obtain precise control over the edges selected to be modified.

[0060] One or more methods described herein extend existing rule-based aspects. The methods herein provide the advantages of both rule-based retargeting and model-based aspects. The methods herein provide a significant improvement in rule-based retargeting accuracy (e.g., in terms of EPE or CD of printed features) and widely extend their capabilities in designing pattern coverage. For example, the methods herein maintain the current benefits of rule-based retargeting, such as speed, consistency, interpretability, and precise control of retargeting.

[0061] The method herein proposes determining a property of a desired feature within a desired pattern to be retargeted. This property provides additional information based on the neighboring features surrounding the feature of interest. Thus, the descriptive power of the rule is extended beyond the width and spacing dimensions. This property provides more control and higher accuracy during retargeting. This method has many applications, including but not limited to etch calculations, OPC, resist process correction, post-OPC correction, etc. This property provides additional descriptive power beyond geometric capabilities.

[0062] Figure 3A Flowchart of method 300 for generating a retargeting pattern for a target pattern to be imaged (e.g., an optical image and a resist image), printed (e.g., after development), or formed (e.g., after etching) on ​​a substrate. In embodiments, the proposed method 300 can significantly improve the representation of rules and more accurately describe the pattern compared to current rule-based methods; ultimately, the pattern can be accurately printed on the substrate. Method 300 still provides the main advantages of rule-based retargeting, including speed, consistency, interpretability, and control, while achieving significant improvements in the accuracy domain, which is already a main advantage of model-based retargeting. In embodiments, method 300 determines a property associated with a target feature or target pattern to determine the retargeting feature or retargeting pattern. For example, the property can be a density calculation based on a geometry. The present disclosure is not limited to density. As discussed herein, the property can be calculated using a kernel function (e.g., a low-pass filter), a transform function (e.g., an FFT or a sine function), or other calculations over a given window. Method 300 includes the following steps.

[0063] Process P301 includes obtaining (i) a target pattern 301 including at least one feature having a geometry including a first dimension and a second dimension; and (ii) a plurality of deviation rules 304, wherein the plurality of deviation rules are defined as a function of the first dimension, the second dimension, and a property associated with the feature of the target pattern 301 within a measurement area.

[0064] In an embodiment, the target pattern 301 may be any desired pattern to be printed on a substrate. In an embodiment, the target pattern 301 is a design pattern, an after-development image (ADI) pattern obtained after developing a resist image on a substrate, and / or an etched pattern obtained after applying an etching process to the ADI. In an embodiment, the design pattern may be provided in a GDS file format. The target pattern may be obtained via simulation (e.g., Figure 2 ) to obtain the ADI pattern from one or more models related to the patterning process (e.g., an optical device model, a resist model, etc.). In an embodiment, the ADI can be obtained from a metrology tool configured to measure the imaged substrate. Similarly, the ADI pattern can be obtained via simulation (e.g., Figure 2 ) One or more models related to the patterning process (e.g., an optical device model, a resist model, an etching model, etc.) are used to obtain the etching pattern. In an embodiment, the ADI can be obtained from a metrology tool configured to measure the imaged substrate. In an embodiment, the target pattern can be a design pattern related to a memory (e.g., DRAM) circuit.

[0065] The target pattern 301 includes a plurality of features, such as one or more gate bars, one or more lines, one or more contact holes, etc. In an embodiment, at least one feature (also referred to as a target feature) may be characterized based on the geometry of the feature. For example, the target feature has a first dimension and a second dimension. In an example, the first dimension is the width of the target feature, and the second dimension is the height or length of the target feature, or the spacing between the target feature and an adjacent feature. For example, the spacing between two lines (e.g., Figure 5B In some embodiments, the geometry of a feature can be described as a function of a ratio of dimensions (e.g., height / width) or a geometric size (e.g., area or circumference). The dimensions width and spacing are used as examples to illustrate the concepts and do not limit the scope of the invention.

[0066] In an embodiment, a plurality of deviation rules 304 may be defined as a function of a first dimension (e.g., width), a second dimension (e.g., spacing between two features), and a property associated with a feature of the target pattern 301 within the measurement region. In an embodiment, the measurement region includes at least a portion of the target feature. In an embodiment, the measurement region may be user-defined. In an embodiment, the measurement region may have any shape. For example, the measurement region may be a rectangular box, a square box (e.g., see Figure 5A R1 and R2 in Figure 10A and Figure 10B ), circular shapes (see, for example, Figure 11A and Figure 11B) or other bounding box shapes. In an embodiment, the measurement area can be moved throughout the target pattern.

[0067] In an embodiment, one or more properties may be associated with features of the target pattern 301. For example, a first property may be determined using a first box having a first size (e.g., 100 nm x 100 nm), and a second property may be determined using a second box having a second size (e.g., 300 nm x 300 nm). In an embodiment, one property may be density, and another property may be obtained using a convolution of a kernel function (e.g., a low-pass filter kernel function) with the target pattern 301.

[0068] As an example, a property of a target feature is the density of features within a measurement area, wherein the measurement area includes at least a portion of the target feature. In an embodiment, the density may be calculated as the ratio of the area of ​​the features within the measurement area to the total area of ​​the measurement area. In other words, the density represents the fraction of the measurement area covered by the features. However, the present disclosure is not limited to density properties. In an embodiment, the property may be calculated by convolving a desired function or kernel function (e.g., a low pass filter, a sine function) with one or more target features within the measurement area. In an embodiment, the density may be calculated using a top hat function or a rectangular function convolved with an area (including the target feature). For example, in this document, reference is made to Figures 4A to 4C 、 Figures 5A to 5B 、 FIG. 10A to FIG. 10B ,and Figures 11A to 11B In this article, we will discuss examples of properties related to target features and different ways to calculate them. Based on the value of the property at the location of the target feature, multiple deviations can be applied to the target feature, even if the target features have the same width and spacing. For example, a first deviation at the center of the target feature and a second deviation at the end of the target feature.

[0069] In an embodiment, the plurality of deviations are values ​​(also referred to as retargeting values) used to modify the target pattern 301 to produce a retargeted pattern. In an embodiment, the retargeted pattern can be a mask pattern including an OPC generated using deviations according to the present disclosure. For example, a design pattern (including features of a specific width and spacing) can be modified by applying deviations based on properties (e.g., density). In an embodiment, the deviation values ​​can be determined based on a simulation of a process correction model (e.g., etching process correction) for a pattern forming process, such as with reference to FIG. Figure 12 and Figure 13 Discussed.

[0070] In the examples, reference Figures 4A to 4C , multiple deviations can be stored as a relational table. Figure 4AExemplary deviation tables 402, 404, 406, and 408 are illustrated, each cell of which includes a deviation value (not shown). The deviation table (e.g., 402) includes a set of deviation values ​​assigned based on a first dimension D1 (e.g., width) and a second dimension D2 (e.g., pitch) of a target pattern and a property PR1 (e.g., density). For specific values ​​of the first dimension D1 and the second dimension D2, multiple deviation values ​​can be used in tables 402, 404, 406, and 408, respectively, depending on the value of the property PR1. For example, for a target feature with a width of 65 nm and a pitch of 60 nm, multiple deviations are available based on the density value associated with the feature to be retargeted. For example, for D1=65 and D2=60, if the density is 0.3, a deviation of 1 nm can be used in table 404. In another example, for the same D1=65 and D2=60, if the density is 0.5, a deviation of 2 nm can be used in table 406. For example, the density value can be different depending on the location in the target pattern where the density is determined. For example, the density value at the center of a line (an exemplary target feature) may be different than the density value at the ends of the line.

[0071] In an embodiment, multiple such deviation tables may be defined for each feature type. For example, multiple deviation tables may be defined for the ends of lines, contact holes, etc. In an embodiment, properties may be used to mark specific features. For example, marking a feature as a potential hotspot or a criticality pattern. Thus, for marking purposes, properties (e.g., as discussed herein) may be determined such that a table for the ends of lines, a table for spacing, and a table for width are available. Therefore, it may not be possible to define a complete, general table that covers everything.

[0072] Reference Figure 4B and Figure 4C In an embodiment, multiple properties may be determined for a single substrate target feature. Then, depending on the range of values ​​for each property, multiple deviation tables may be determined and stored. Figure 4B is a table showing a plurality of deviation tables based on ranges of values ​​for properties PR1 and PR2. For example, a first property PR1 may be a first density calculated using a first box (e.g., 100 nm x 100 nm), and a second property PR2 may be a second density calculated using a second box (e.g., 300 nm x 300 nm). In an embodiment, the minimum and maximum ranges of densities may be from 0 to 1, where 0 indicates that a portion of the target feature is not present in the box, and 1 indicates that the entire box is filled with the target feature. Both density values ​​of 0 and 1 may be undesirable, and the optimal box size may be determined such that the density values ​​range from 0.1 to 0.9; between 0.3 and 0.8, or within other desired ranges. The present disclosure is not limited to specific properties, nor to specific ranges of values ​​for properties.

[0073] like Figure 4B As shown in , when the value of the first property PR1 is within the range of A to B and the value of the second property PR2 is within the range of a to b, Table 1 can be used. Similarly, for the table, Tables 1 to 16 can be used based on the values ​​of PR1 and PR2. Figure 4C illustrate Figure 4B Example tables - Tables 1 to 16. In an embodiment, the table can be visualized as a grid and this grid can be used to define what the deviation should be for a specific width and spacing. As mentioned earlier, these tables - such as Table 1, Table 2, Table 3, etc. - can have different deviation information for the same width and the same spacing of the target feature because the density values ​​around the target feature are different. For example, the density value at the center of the line (an exemplary target feature) can be different from the density value at the end of the line. Therefore, around a given position of the target feature (e.g., a 10 nanometer line), if there is a denser pattern in the neighborhood, Table 2 may exist instead of Table 1. The values ​​of PR1 and / or PR2 can be calculated based on the density of features in the measurement area, some kernel function, or some other complex function. In an embodiment, the density can be calculated using a top hat function or a rectangular function that is convolved with the features (including the features of interest) in the measurement area.

[0074] In an embodiment, while a table structure may be a starting point, the table structure may be a general kernel function (e.g., a low-pass filter) that can be used to generate multiple tables depending on the result of the kernel function (e.g., the range of values). For example, the result may be obtained by convolving the kernel function with features in an image of the measurement area.

[0075] In an embodiment, a plurality of deviations may be determined using a model fitted according to the first dimension, the second dimension, and the property.

[0076] Thus, one or more properties are additional variables, in addition to width and spacing, that are calculated before making a decision to retarget a portion of a target pattern. In an embodiment, the selected deviations for a given width and spacing are retargeting values, each retargeting value being for a portion of at least one feature of the target pattern.

[0077] Step P303 includes determining values ​​303 of a property at a plurality of locations on at least one feature of target pattern 301, wherein each location is surrounded by a measurement region. Figure 3B An exemplary flow chart of a process P303 for determining a value 303 of a property at a given location is shown in FIG.

[0078] exist Figure 3BIn the embodiment, step P311 includes allocating a measurement region around a given location at at least one feature. In an embodiment, the measurement region includes at least a portion of the target feature. In an embodiment, the measurement region can be user-defined. In an embodiment, the measurement region can have any shape. For example, the measurement region can be a rectangular box, a square box (e.g., see Figure 5A R1 and R2 in Figure 10A and Figure 10B ), circular shapes (see, for example, Figure 11A and Figure 11B ) or other bounding box shapes. In an embodiment, the measurement area can be moved across the entire target pattern 301.

[0079] Step P313 includes identifying one or more features within the measurement region. In an embodiment, one or more features refers to a portion of one or more features. The one or more features may be a portion of a feature of interest or features adjacent to a feature of interest. For example, the feature of interest may be a target feature that should be retargeted.

[0080] Step P315 includes calculating a value of a property associated with one or more identified features within the measurement area via a user-defined function. For example, the user-defined function is density. In one embodiment, calculating the density includes: determining the total area of ​​the one or more identified features within the defined area; determining the total area of ​​the measurement area; and calculating the density value as the ratio of the total area of ​​the features within the measurement area to the total area of ​​the measurement area.

[0081] In an embodiment, the user-defined function is a geometric function, signal processing function, or image processing function that transforms one or more features within the measurement area into a feature value. The feature value is specific to the one or more features in the defined location. In an embodiment, the geometric function is a function of the shape, size, or relative position of at least one feature of the target pattern 301. In an embodiment, the signal processing function is an image processing function, a sine function, a cosine function, or a Fourier transform. In an embodiment, the image processing function is a low-pass filter and / or an edge detection function.

[0082] In an embodiment, the calculation of the value of the property includes applying a convolution calculation between the measurement area and a user-defined function (e.g., a low-pass filter). In an embodiment, the measurement area is represented as an image including one or more features, and the value of the property is calculated by convolving the image with the user-defined function (e.g., a low-pass filter).

[0083] In an embodiment, step P317 includes selecting another location at the at least one feature and further performing steps P313 and P315 using the measurement region in P311 to determine the value of the property at a different location of the target pattern 301. In an embodiment, the location can be the center of the target feature, an end of the target feature, or any other location at or near the target feature.

[0084] Figure 5A and Figure 5B An example of determining a property at a location of a target pattern is described. Figure 5A , the target pattern includes a plurality of features F1, F2, and F3. Thus, a property is determined at a location L1 associated with a feature F2 having a given width and spacing. In an embodiment, a first property PR1 is determined based on a first region R1 defined around location L1. A second property PR2 can be determined based on a second region R2 defined around location L1, where second region R2 is larger than first region R1. Thus, depending on region R1 or R2, the target pattern will have two different property values ​​for the same location L1. In an embodiment, property PR1 or PR2 can be density.

[0085] In an embodiment, the first region R1 includes portions FP1, FP2, and FP3 of features F1, F2, and F3, respectively. The first property PR1 (e.g., density) can then be determined using the area of ​​the portions FP1, FP2, and FP3 divided by the total area of ​​the first region R1. In an embodiment, the value of the property using the first region R1 at position L1 can be 0.35. Similarly, the second property PR2 can be determined as the total area of ​​the portions of features F1, F2, and F2 within region R2 divided by the total area of ​​the second region R2. In an embodiment, the value PR2 of the second property can be 0.5. Therefore, although the target feature F2 has the same width and spacing along the length of the feature, the position L1 associated with a given target feature has two different values ​​0.35 and 0.5. Therefore, the property PR1 or PR2 provides additional information based on which target feature to be modified or retargeted.

[0086] As mentioned earlier, properties are not limited to density. In an embodiment, properties can be calculated by convolving a kernel function or a user-defined function with a target pattern (e.g., 301) or a portion of a target pattern (e.g., 301) within a measurement region. In an embodiment, the application of the kernel function may be different from using multiple regions (e.g., each region defined at a different location). For example, a kernel function may be applied to a single position (e.g., L1) covering all features (e.g., F1, F2, F3) within a single window. However, the value of the property can be obtained at each position on the target feature (e.g., F2). For example, Fourier transform (FT) or fast Fourier transform (FFT) may be applied to all features. The resulting coefficients of the FFT or the frequency terms of the FFT may be the values ​​of the property.

[0087] In another example, a sine function can be applied in the y dimension and / or the x dimension. In the example, if the target feature (e.g., F3) is a horizontal polygon with an edge along the horizontal direction (x direction), the portion surrounding the horizontal edge will have a stronger signal along the "y" axis that is a first-order sine, while other positions will produce a weaker signal. Such weaker signal areas may be potential areas where the target pattern can be modified. In an embodiment, the density can be calculated using a cap function or a rectangular function that is convolved with the area within the measurement area (e.g., R1) (including the feature of interest).

[0088] As discussed herein, the measurement region is not even limited to a completely surrounding window (or box) around a given location. The window can be selected in any complex manner and the density calculation can be directional (external vs. internal) or calculated separately for each or multiple quadrants. The window can also be concentric rings or ring sectors, etc. In embodiments, the measurement region is also referred to herein as a window or bounding box.

[0089] Figure 5B The value of a property associated with a target feature changes as the point of interest (e.g., the position at the target feature) changes. In an embodiment, as the position on the target pattern changes, the window is also moved, for example, to keep the point of interest centered in the window. Thus, the density at each position can change. Therefore, changing the position on the target pattern provides the freedom to change the deviation for each of the positions at the target feature.

[0090] exist Figure 5BIn the example of , the target pattern includes N target features F10, F20, ..., Fn. At each target feature, multiple positions can be selected and the value of the property at each position (e.g., density) can be calculated. In an embodiment, positions can be selected at regular intervals or randomly placed. For example, positions L10, L11, and L12 are selected at a certain distance along the target feature F10. In addition, measurement areas (or windows) R10, R11, and R12 are assigned to each position L10, L11, and L12, respectively, so that the position is in the center of the window. In an embodiment, each window has the same size, for example, 100nm×100nm. Then, for each position L10, L11, and L12, the density value can be calculated based on the portion of the features F10, F20, and / or F30 within the corresponding measurement area R10, R11, or R12.

[0091] Based on the calculated density value, the deviation selected for each position L10, L11 and L12 can be different. Therefore, compared with existing rule-based methods, the present method provides more flexibility in deviating differently at different locations of the target feature. For example, existing rule-based methods can recommend the same deviation value at different locations because the spacing and width of the target feature are the same at such locations (e.g., L10, L11 and L12). In addition, since the model-based deviation can recommend different deviations at different locations, the present method provides results comparable to the model-based deviation. Note that the present method selects deviations from a table based on certain rules and does not execute a process correction model. Therefore, the present method provides two advantages of rule-based retargeting and model-based retargeting.

[0092] Step P305 includes selecting a subset 305 of deviations for a plurality of locations on at least one feature from a plurality of deviation rules 304 based on the value of the property. In an embodiment, the deviation rules are represented as a table of a first dimension and a second dimension for each of the properties. In an embodiment, for example, referring to Figure 4B , selecting a deviation includes: identifying a range to which a given value of the property belongs; selecting a deviation rule from a plurality of deviation rules 304 for the identified range of the property; and selecting a deviation value associated with a given position of a plurality of positions on at least one feature from the deviation rule for a given value of the first dimension and the second dimension.

[0093] In an embodiment, each of the plurality of deviations is at least one of: etch compensation to be applied to the ADI pattern so that the etch pattern is within desired specifications; model error compensation associated with one or more process models used to simulate the pattern formation process; mask proximity effect correction to be applied to the design layout to reduce variations in the target pattern due to mask fabrication; or an initial OPC deviation to be applied to the design layout to produce an initial retargeted layout for optimal proximity effect correction.

[0094] Additionally, step P307 includes generating a retargeting pattern 307 for the target pattern 301 by applying the selected subset of deviations 305 to at least one feature of the target pattern.

[0095] In an embodiment, method 300 further includes: applying each retargeting value to a corresponding edge to generate a retargeting pattern in step P309 ; and applying optical proximity correction to the retargeting pattern to generate a post-OPC pattern 309 .

[0096] Figures 6A to 7B Exemplary results of this method are described. Figure 6A The example of the existing deviation schematic diagram 600 of the deviation value associated with dimension spacing and width is illustrated. In this schematic diagram, the X-axis is the exemplary range of the width in the target pattern, and the Y-axis is the exemplary range of the spacing in the target pattern. The color or grayscale here represents the range of the deviation slope. As shown in the figure, for the same width and spacing, if the point has a brighter color (e.g., white), this means that the target feature with almost the same width and spacing can have a deviation value at any position of the difference from 0nm to 9nm. For example, the width of 100nm and the spacing of 100nm have a difference of more than 9nm and this can not be explained based on the combination of width and spacing only. Therefore, for the same width and spacing, people can not only use width and spacing tables to define appropriate deviations. However, according to the method herein, by using additional variables (e.g., properties), people can define multiple deviations for the same width and the same.

[0097] Figure 6B and Figure 6C are exemplary results of applying bias according to the methods discussed herein. Figure 6BAn exemplary target pattern 60B is shown that includes an array of features F61, F62, F63, ... F70, etc. In target pattern 60B, each feature is associated with a width of 60nm and a spacing of 65nm. The array of features includes different deviations at different locations that can be applied to the target features to produce a retargeting pattern (a dotted line around the target feature). In the example, at the center of the array (e.g., the feature portion at 605), the deviation is approximately 14.74nm, while the deviation is smaller towards the ends of the line (e.g., the portion at 610). In an embodiment, the density decreases as one moves from the center (e.g., 605) toward the ends (e.g., 610), so some locations have deviations of 5nm, 6nm, and 5.2nm. To better understand the different deviations, an enlarged version of the end portion 610 is shown in FIG. Figure 6C Therefore, even if the target features have the same width and spacing, they can be assigned different biases because of the varying density.

[0098] Compared to existing rule-based methods, users can assign the same deviation value for the same width and spacing. For example, for a width of 60nm and a spacing of 65nm, the deviation value can be 14.75nm. However, if a deviation of 14.75nm is applied, there may be overcorrection or excessive deviation near the ends of the line (e.g., at 610). In another example, if a smaller deviation value, such as 6nm, is used, there may be insufficient deviation at the center (e.g., at 605).

[0099] On the other hand, the present method provides more descriptive capabilities about the target pattern (e.g., 60B) than using only width and spacing. For example, properties (e.g., density) are used as additional information that allows for different deviations for the same width and spacing of the target pattern. For example, the portion of the feature in 605 is different from the portion of the feature in 610. In an embodiment, Figure 6C In the example, the difference between the dotted line and the feature indicates how much distance the target feature is moved. For example, the difference may be 7 nm or 8 nm. Figure 6B It is also shown that at the center of the array 610, the deviation value is 12.875 nm, and as one moves closer to the end of the line, the deviation value is 5.75 nm. This deviation information can be expanded by considering properties such as density.

[0100] As mentioned earlier, multiple properties may be determined, such as a first property D100 and a second property D750, and the deviation may be defined as the first property (e.g., indicating 100 nm 2 D100 of the measurement area) and the second property (e.g., indicating 750nm 2The D750 of the measurement area is a function of the D100. In an embodiment, D100 is a smaller window and D750 is a relatively larger window. The smaller window size allows the capture of smaller range effects of adjacent features, and the larger window allows the capture of larger range effects of adjacent features. Figure 7A The deviations are shown as a function of the properties D100 and D750. Figure 7B Shown with Figure 7A In an embodiment, the error data shows a significant improvement in the residuals associated with the correction model associated with the patterning process.

[0101] exist Figure 7A and Figure 7B In the schematic diagram, for a pitch of 65 nm and a width of 60 nm, the x-axis shows the density value calculated using the D100 measurement area, the y-axis shows the deviation value, and the color gradient indicates the density value calculated using the D750 measurement area. For example, 0.35 indicates 100 nm 2 35% of the window (e.g., D100) or 35 nm 2 is covered by a polygon or target feature, and the rest of the D100 window is empty, a value of 0.6 indicates 100 nm 2 60% or 60nm within the window 2 Covered by target feature.

[0102] Figure 7A The diagram shows linear behavior when assigning deviation values. In other words, as the density of D100 increases, the deviation value also increases. A similar linear behavior can be seen based on the color grading indicating the density of D750. In other words, as the density increases, the deviation value increases. This diagram demonstrates that a property (e.g., density) can be described in different properties, expanding the deviation information related to the same width and spacing. Figure 7A An 8 nm deviation range is shown. In an embodiment, a linear regression may be fit based on the deviation values ​​and the values ​​of the properties. Figure 7B The second-order polynomial error of the fitted model is shown. This error is within the range of ±0.75nm or less, which is very small compared to existing rule-based methods. In an embodiment, existing rule-based methods (where the deviation can be a constant 14.75nm) can produce errors of up to 8nm. In other words, using dimensions D100 and / or D750 can have a greater descriptive power that allows for mixing from an 8nm error range or similar deviation ranges down to less than 0.75nm.

[0103] It will be understood by those skilled in the art that the methods described herein (e.g., method 300) are not limited to a particular pattern or properties associated with that pattern. Method 300 can be applied to any type of pattern. For example, Figure 8A and Figure 8B shows the deviation for the end of the line, and Figure 9 The deviation for the contact hole is shown.

[0104] Reference Figure 8A and Figure 8B , the ends of the wires are typically described in terms of width and tip-to-tip spacing. As shown, although the two target patterns 80A and 80B have the same width and spacing, the density will be different. Therefore, in target pattern 80A, the ends of the wires can be moved 8.375nm. In target pattern 80B, the ends of the wires can be moved 3.875nm. Similarly, referring to Figure 9 Contact holes H1 and H2 have the same first dimension (e.g., diameter) and pitch, and can be assigned different deviation values, such as 5.875 nm and 7.25 nm, via model-based correction. Such deviation values ​​can be explained by the density values ​​associated with the corresponding target features.

[0105] Furthermore, as discussed herein, method 300 is not limited to a particular measurement region or window. Figure 10A / Figure 10B and Figure 11A / Figure 11B Explain the use of different window shapes. FIG. 10A to FIG. 10B and Figures 11A to 11B Target pattern T100 and different window shapes are illustrated. In an embodiment, although the target pattern T100 includes four contact holes having the same size, a different offset may be applied to each hole.

[0106] Figure 10A and Figure 10B Shows that the same measurement area (e.g., 80nm 2 ) may not be suitable for capturing density values. For example, the D80 frame is used to determine a first density value at a first position of the target pattern T100. The D80' frame is used to determine a second density value at a second position of the target pattern T100. However, although the features within each of D80 and D80' have the same exact area (e.g., the area of ​​the shaded area), at least two contact holes have different deviations, such as 7.25nm and 5.875nm. Since the density is the same, the frames D80 and D80' may not be suitable for distinguishing the deviation values. In an embodiment, windows of different sizes or windows of different shapes may be more helpful. Therefore, in an embodiment, a circular window may be used.

[0107] Figure 11A and Figure 11BIt is shown that for pattern T100, circular windows appear to have density differences. For example, when a circular window C80 (e.g., having a diameter of 80 nm) is used at a first position, a first density value is determined. When a circular window C80' (e.g., having the same diameter of 80 nm) is used at a second position, a second density value is determined. These first and second density values ​​are different. Therefore, the circular window C80 may be more suitable than the square window D80. For example, the second density obtained using the circular window C80' is lower than the first density. Therefore, for example, based on C80', Figure 11B Compared to the deviation value (eg, 7.25) of the contact hole in the circular window C80, a lower deviation (eg, 5.875) may be applied to the contact hole.

[0108] Figure 12 1 is a flow chart of a method 500 for determining a deviation rule for a target pattern to be printed on a substrate. In an embodiment, a model-based correction (e.g., an etch correction) is used as ground truth for determining the deviation table. For example, deviations for each segment are collected during the model-based etch correction. For example, the width, spacing, and density of each frame size are calculated for each segment during the model-based etch correction. The method includes the steps explained below.

[0109] Step P501 includes obtaining a target pattern 502 comprising at least one feature characterized by a first dimension and a second dimension. For example, the first dimension is width and the second dimension is pitch. In an embodiment, the pitch and width associated with a plurality of features in the target pattern 502 may be obtained.

[0110] Process P503 includes determining a plurality of deviations for a first dimension (e.g., width) and a second dimension (e.g., spacing) via executing a process correction model 506. Additionally, process P503 includes associating each of the plurality of deviations with a value of a property. In an embodiment, the process correction model 506 deviates the first and second dimensions of at least one feature of the target pattern 502. Additionally, the correction process using the process correction model 506 is configured to calculate a property associated with the at least one feature. For example, the etch correction model 506 may include code that implements the calculation of one or more properties per location of the target pattern. For example, reference is made herein to Figure 5A and Figure 5B Exemplary calculations of properties (eg, density) are discussed.

[0111] In an embodiment, determining the plurality of deviations includes: generating a retargeting pattern including deviations for a first dimension and a second dimension of at least one pattern by executing a process correction model 506 using a target pattern 502; determining a difference between the retargeting pattern and the target pattern 506; and determining a plurality of deviations at a plurality of locations of the target pattern based on the difference.

[0112] In an embodiment, execution of the process correction model 506 includes determining a plurality of values ​​for a property at a plurality of locations on at least one pattern of the target pattern. Figure 5A and Figure 5B and Figure 13 Let's discuss examples of computing the value of a property.

[0113] In an embodiment, determining the value of a property includes: (a) allocating a measurement area around at least a given location on the feature; (b) identifying one or more features within the measurement area; (c) calculating the value of the property associated with the one or more identified features within the measurement area via a user-defined function; and (d) selecting another location on the at least one feature and performing steps (b) and (c) using the measurement area in step (a).

[0114] In an embodiment, a plurality of deviations are collected during execution of the process correction model for each segment (or edge) of the target pattern 502 of which the segment is a portion.

[0115] In an embodiment, during execution of the process correction model, a value of a property is calculated for each segment of the target pattern 502 and for each measurement region, which is a region (or window) around a given location of the target pattern 502 .

[0116] Step P505 includes defining a deviation rule 510 based on a plurality of deviations that is a function of a first dimension, a second dimension, and a property associated with at least one feature of the target pattern 502. In one embodiment, defining the deviation rule 510 includes defining a range of the property based on a value of the property; and assigning a set of deviations from the plurality of deviations to each range of the property. In one embodiment, each deviation in the set of deviations is associated with the first dimension and the second dimension.

[0117] The present method is not limited to a particular process model 506. As an example, the process correction model 506 is at least one of: an etch correction model that determines corrections to an etch pattern associated with a target pattern; an optical proximity correction model that determines modifications to the target pattern; or a mask proximity correction model that determines corrections associated with a mask fabrication process.

[0118] Figure 13An example of determining an etching deviation based on an etching pattern is described. In an embodiment, an etching correction model can be executed to determine a correction for the etched pattern. In an embodiment, the etching feature 702 is a target feature that is desired to be printed / etched on a substrate. In an embodiment, the etching feature 702 can be obtained via an etching process model that is configured to generate an etching profile from a design pattern, a resist image, or an after-development image (ADI). In an embodiment, the etching feature 702 can be extracted from an SEM image of the etched substrate. The etching feature 702 is used as an input to the etching correction model to generate an input pattern (e.g., a retargeted etching pattern) to the etching process, so that the desired etching pattern 702 is printed on the substrate. For example, the input pattern is a after-development image (ADI) pattern 712. The ADI pattern 712 is an example of a retargeted pattern.

[0119] In an embodiment, an ADI pattern is generated by biasing the edge of the etched feature 702. The difference between the ADI pattern 712 and the etched feature 702 is then the deviation of the etched feature 702 applied by the etch correction model. In an embodiment, the deviation applied by the etch correction model is based on a performance metric of the patterning process. For example, the deviation determined by the etch correction model minimizes the edge placement error between the etched feature 702 and the designed feature. In an embodiment, the deviation of the edge of the etched feature 702 is an amount B1. In an embodiment, the deviation B1 can be determined as the difference between the ADI pattern 712 and the etched feature 702. Thus, deviation data associated with the target pattern (e.g., the etched feature 702) is generated.

[0120] In addition, property (e.g., density) data is determined at one or more locations at the etch feature 702, as discussed herein. In an embodiment, property data refers to one or more properties determined at the etch feature 702 of the etch pattern. Thus, the deviation data and the property data can be used to establish a relationship between the property and the deviation. In addition, the etch feature 702 is characterized by width and spacing. Thus, a relationship between width, spacing, density, and deviation can be established. Similar data including multiple deviations and multiple densities can be determined at multiple locations on each of the multiple etch features, each etch feature being characterized and associated by spacing and width. Thus, the data can be used to establish a correlation between spacing and width, and between multiple densities and multiple deviations. In the present disclosure, for example, Figures 4A to 4C An exemplary deviation table is discussed in .

[0121] As mentioned earlier, although the etching correction model is used as an example, the present embodiment is not limited to etching. In an embodiment, the simulation process can use any process correction model related to the pattern formation process (e.g., resist process, etching process, OPC, etc.) and determine the first dimension (e.g., width), second dimension (e.g., spacing) and property (e.g., density) information, as discussed herein. The correction proposed by the model can then be related to the first dimension, the second dimension and one or more properties to produce a deviation table. The properties provide additional descriptive capabilities of existing rule-based retargeting methods for determining the retargeting pattern for the target pattern. For example, a deviation based on density information can indicate that a first deviation is applied at the center of the line and a second deviation is applied at the end of the line.

[0122] In one example, the application can be in mask-related corrections, such as OPC and post-OPC quality proximity effect correction. In OPC, the focus exposure window is maximized through pattern formation process simulation. For example, the OPC process can be modified to include calculation of a first dimension of the design pattern, a second dimension of the design pattern, one or more properties of the design pattern, and deviation information of the mask pattern generated by OPC.

[0123] After performing OPC, models related to the mask manufacturing process can also be used to correct for effects related to mask manufacturing. For example, deviation information can be generated to further deviate the mask pattern generated by OPC. Post-OPC correction can also be computationally intensive. Therefore, deviation tables can also accelerate the mask manufacturing process.

[0124] In an embodiment, one or more processes of method 300 and / or method 500 may be implemented as instructions (e.g., code) in a processor of a computer system (e.g., process 104 of computer system 100). In an embodiment, the processes may be distributed across multiple processors (e.g., parallel computing) to improve computing efficiency. In an embodiment, a computer program product including a non-transitory computer-readable medium has instructions recorded thereon that, when executed by a computer, implement method 300 or 500.

[0125] Combinations and subcombinations of the disclosed elements constitute separate embodiments according to the present disclosure. For example, a first combination includes using density as a property to determine a retargeting pattern. A subcombination may include using a first density and a second density as properties to determine a retargeting pattern. In another example, a combination includes determining to retarget an etch pattern to a target pattern, the retargeting being based on density data associated with the etch pattern. In another example, the combination includes determining a retargeting mask pattern for a target pattern based on a property (e.g., density).

[0126] In embodiments, the corrected and post-OPC images determined according to method 300 or 500 can be used to optimize a patterning process or adjust parameters of a patterning process. As an example, OPC addresses the fact that the final size and placement of the image of a design layout projected onto a substrate will differ from, or simply depend on, the size and placement of the design layout on a patterning device. Note that the terms "mask," "reticle," and "patterning device" are used interchangeably herein. Furthermore, those skilled in the art will recognize that the terms "mask," "patterning device," and "design layout" can be used interchangeably, particularly in the context of lithography simulation / optimization. This is because, in lithography simulation / optimization, a physical patterning device is not necessarily used; rather, a design layout may be used to represent the physical patterning device. For smaller feature sizes and higher feature densities present on a design layout, the location of a particular edge of a given feature will be affected to some 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 and / or non-geometric optical effects such as diffraction and interference. Similarly, proximity effects may arise from diffusion and other chemical effects during the post-exposure bake (PEB), resist development, and etching that typically follow photolithography.

[0127] In order to ensure that the projected image of the design layout is in accordance with the requirements of a given target circuit design, it is necessary to use complex numerical models, corrections or pre-distortions of the design layout to predict and compensate for proximity effects. The paper "Full-Chip Lithography Simulation and Design Analysis - How OPC Is Changing IC Design" (C. Spence, Proc. SPIE, Vol. 5751, pp. 1-14 (2005)) provides an overview of the current "model-based" optical proximity correction process. In a typical high-end design, almost every feature of the design layout has some modification to achieve higher fidelity of the projected image to the target design. These modifications can include shifts or deviations in edge position or line width, as well as the use of "auxiliary" features intended to assist in the projection of other features.

[0128] With millions of features typically present in chip designs, applying model-based OPC to a target design involves good process models and considerable computational resources. However, applying OPC is generally not an "exact science," but rather an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the impact of OPC (e.g., design layout after applying OPC and any other RET) needs to be verified through design inspection (i.e., intensive full-chip simulation using a calibrated numerical process model) in order to minimize the likelihood of design flaws being incorporated into the pattern of the pattern forming device. This is driven by the significant cost of manufacturing high-end pattern forming devices, which is in the millions of dollars range, and the impact on turnaround time of reworking or repairing the actual pattern forming device once it has been manufactured.

[0129] Both OPC and full-chip RET verification can be based on numerical modeling systems and methods as described, for example, in U.S. patent application Ser. No. 10 / 815,573 and in a paper by Y. Cao et al. entitled “Optimized Hardware and Software For Fast, Full Chip Simulation” (Proc. SPIE, Vol. 5754, 405 (2005)).

[0130] One type of RET is related to adjusting for the global deviation of the design layout. The global deviation is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, a 25 nm diameter ring pattern can be printed on the substrate using a 50 nm diameter pattern in the design layout, or using a 20 nm diameter pattern in the design layout but with a higher dose.

[0131] In addition to the optimization of the design layout or pattern forming device (e.g., OPC), the illumination source can also be optimized jointly or separately with the pattern forming device optimization to improve the overall lithography fidelity. The terms "irradiation source" and "source" can be used interchangeably in this document. Since the 1990s, many off-axis illumination sources such as annular, quadrupole and dipole have been introduced, and these many off-axis illumination sources have provided more degrees of freedom for OPC design, thereby improving imaging results. It is known that off-axis illumination is a proven way to distinguish fine structures (i.e., target features) included in the pattern forming device. However, compared to traditional illumination sources, off-axis illumination sources generally provide a smaller radiation intensity for aerial images (AI). Therefore, it is necessary to try to optimize the illumination source to achieve an optimal balance between finer resolution and reduced radiation intensity.

[0132] For example, a number of illumination source optimization methods can be found in the paper by Rosenbluth et al., entitled "Optimum Mask and Source Patterns to Print A Given Shape" (Journal of Microlithography, Microfabrication, Microsystems 1(1), pp. 13-20 (2002)). The source is divided into several regions, each of which corresponds to a certain region of the pupil spectrum. The source distribution is then assumed to be uniform in each source region, and the brightness of each region is optimized for the process window. However, the assumption that the source distribution is uniform in each source region is not always valid, and therefore, the effectiveness of this method is reduced. In another example, Granik, entitled "Source Optimization for Image Fidelity and Throughput" (Journal of Microlithography, Microfabrication, Microsystems 3(4), pp. 509-522 (2004), reviews several existing source optimization methods and proposes to transform the source optimization problem into a series of non-negative least squares optimization based illuminator pixel methods. Although these methods have demonstrated some success, they generally require multiple complex iterations to converge. In addition, it can be difficult to determine appropriate / optimal values ​​for some additional parameters (such as γ in Granik's method), which dictate a trade-off between optimizing the source for substrate image fidelity and the smoothness requirement of the source.

[0133] For low k1 lithography, optimization of both the source and the pattern forming device helps to ensure a feasible process window for projection of critical circuit patterns. Some algorithms (e.g., Socha et al., Proc. SPIE, Vol. 5853, 2005, p. 180) discretize the illumination into independent source points and the mask into diffraction orders in the spatial frequency domain, and separately formulate the cost function (the cost function is defined as a function of the selected design variables) based on a process window metric (such as exposure margin) that can be predicted from the source point intensity and the pattern forming device diffraction order by an optical imaging model. The term "design variables" as used herein includes a set of parameters of a lithographic projection device or a lithographic process, for example, parameters that a user of the lithographic projection device can adjust, or image characteristics that a user can adjust by adjusting those parameters. It will be understood that any characteristic of the lithographic projection process (including characteristics of the source, pattern forming device, projection optical device, and / or resist characteristics) can be among the design variables being optimized. The cost function is often a nonlinear function of the design variables. Standard optimization techniques are then used to minimize the cost function.

[0134] Relatedly, the pressure to continuously reduce design rules has driven semiconductor chip manufacturers to move deeper into the era of low-k1 lithography with the existing 193nm ArF lithography. The move towards lower k1 lithography places high demands on RET, exposure tools, and the need for lithography-friendly design. In the future, ultra-numerical aperture (NA) exposure tools of 1.35ArF may be used. To help ensure that circuit designs can be produced on substrates with a workable process window, source-patterning device optimization (referred to herein as source-mask optimization or SMO) is becoming a significant RET for the 2×nm node.

[0135] Commonly assigned International Patent Application No. PCT / US2009 / 065359, entitled “Fast Freeform Source and Mask Co-Optimization method,” filed on November 20, 2009 and published as WO2010 / 059954, the entire contents of which are incorporated herein by reference, describes a source and patterning device (design layout) optimization method and system that allows the use of a cost function to simultaneously optimize the source and patterning device without constraints and within a practicable amount of time.

[0136] Another source and mask optimization method and system involving optimizing a source by adjusting pixels of the source is described in commonly assigned U.S. patent application Ser. No. 12 / 813,456, entitled “Source-Mask Optimization in Lithographic Apparatus,” filed on Jun. 10, 2010 and published as U.S. Patent Application Publication No. 2010 / 0315614, the entire contents of which are incorporated herein by reference.

[0137] In a lithographic projection apparatus, as an example, the cost function is expressed as:

[0138]

[0139] Among them, (z1, z2, ..., z N ) are N design variables or their values. p (z1,z2,...,z N ) can be the design variables (z1, z ， ,...,z N ), such as for (z1, z2, ..., z N The difference between the actual value and the expected value of the characteristic at the evaluation point for a set of values ​​of the design variable ). p is with f p (z1,z2,...,z N ) is associated with a weight constant. A higher w may be assigned to an evaluation point or pattern that is more critical than other evaluation points or patterns. p It is also possible to assign higher w values ​​to patterns and / or evaluation points with a greater number of occurrences. p Examples of evaluation points may be any physical point or pattern on the substrate, any point on the virtual design layout, or a resist image, or an aerial image, or a combination thereof. p (z1,z2,...,z N ) can also be a function of one or more random effects such as LWR, which are the design variables (z1, z2, ..., z N). The cost function may represent any suitable characteristic of the lithographic projection apparatus or substrate, such as feature failure rate, focus, CD, image shift, image distortion, image rotation, random effects, throughput, CDU, or a combination thereof. CDU is the local CD variation (e.g., three times the standard deviation of the local CD distribution). CDU may be interchangeably referred to as LCDU. In one embodiment, the cost function represents CDU, throughput, and random effects (i.e., is a function of CDU, throughput, and random effects). In one embodiment, the cost function represents EPE, throughput, and random effects (i.e., is a function of EPE, throughput, and random effects). In one embodiment, the design variables (z1, z2, ..., z N ) includes dose, global deviation of the patterning device, shape of the shot from the source, or a combination thereof. Since the resist image often defines the circuit pattern on the substrate, the cost function often includes a function representing some characteristic of the resist image. For example, f at the evaluation point p (z1, z 2, ..., z N ) can simply be the distance between a point in the resist image and the expected position of that point (i.e., the edge placement error EPE p (z1,z2,...,z N )). The design variables may be any adjustable parameters, such as adjustable parameters of the source, the pattern forming device, the projection optics, the dose, the focus, etc. The projection optics may include components collectively referred to as "wavefront manipulators", which may be used to adjust the shape of the wavefront of the irradiation beam as well as the intensity distribution and / or phase shift. The projection optics may preferably be able to adjust the wavefront and intensity distribution at any position along the optical path of the lithographic projection apparatus, such as before the pattern forming device, near the pupil plane, near the image plane, near the focal plane. The projection optics may be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused by, for example, temperature changes in the source, the pattern forming device, the lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus. Adjusting the wavefront and intensity distribution may change the values ​​of the evaluation points and the cost function. These changes may be simulated according to a model or actually measured. Of course, CF(z1, z2, ..., z N ) is not limited to the form in equation 1. CF(z1, z2, ..., z N ) may be in any other suitable form.

[0140] It should be noted that f p (z1,z2,...,z N ) is defined as, Therefore, f p (z1,z2,...,zN ) is equivalent to minimizing the cost function defined in Equation 1. Therefore, for the sake of simplicity, f is used interchangeably here. p (z1,z2,...,z N ) and the weighted RMS of Eq. 1.

[0141] In addition, if maximizing the PW (process window) is considered, the same physical location from different PW conditions can be considered as different evaluation points of the cost function in Equation 1. For example, if N PW conditions are considered, the evaluation points can be classified according to their PW conditions and the cost function can be written as:

[0142]

[0143] in, is f under the u-th PW condition (u=1,...,U) p (z1,z2,...,z N ) value. When f p (z1,z2,...,z N ) is the EPE, then minimizing the above cost function is equivalent to minimizing the edge shift under various PW conditions, which therefore leads to maximizing the PW. Specifically, if the PW also consists of different mask deviations, then minimizing the above cost function also includes minimizing the MEEF (Mask Error Enhancement Factor), which is defined as the ratio between the substrate EPE and the induced mask edge deviation.

[0144] The design variables can have constraints, which can be expressed as (z1, z2, ..., z N)∈Z, where Z is a set of possible values ​​of the design variables. A possible constraint on the design variables can be imposed by the desired throughput of the lithographic projection equipment. The desired throughput can limit the dose and therefore have an impact on the random effects (for example, imposing a lower limit on the random effects). Higher throughput typically leads to lower doses, shorter / longer exposure times, and larger random effects. Consideration of the minimization of substrate throughput and random effects can constrain the possible values ​​of the design variables because the random effects are functions of the design variables. Without such constraints imposed by the desired throughput, optimization can result in a set of values ​​of the design variables that are unrealistic. For example, if the dose is among the design variables, then without this constraint, optimization can result in dose values ​​that make the throughput economically impossible. However, the usefulness of the constraint should not be interpreted as necessity. The throughput may be affected by adjustments to the parameters of the patterning process based on the failure rate. It is desirable to have a lower failure rate of the feature while maintaining a higher throughput. The throughput may also be affected by the chemical reaction of the resist. Slower resists (e.g., resists that require a higher amount of light to properly expose) result in lower throughput. Therefore, appropriate parameters for the patterning process can be determined based on an optimized process involving failure rates of features due to resist chemistry or fluctuations and dose requirements for higher throughput.

[0145] Therefore, the optimization process is under the constraints (z1, z2, ..., z N )∈Z to find the set of design variable values ​​that minimize the cost function, that is, to find:

[0146]

[0147] Figure 14A general method for optimizing a lithographic projection apparatus according to an embodiment is described in [ 12 ]. The method includes a step S1202 of defining a multivariate cost function for a plurality of design variables. The design variables may include any suitable combination selected from characteristics of an illumination source ( 1200A ) (e.g., pupil fill ratio, i.e., the percentage of radiation from the source that passes through the pupil or aperture), characteristics of the projection optics ( 1200B ), and characteristics of the design layout ( 1200C ). For example, while the design variables may include characteristics of the illumination source ( 1200A ) and characteristics of the design layout ( 1200C ) (e.g., global deviation), the design variables may not include characteristics of the projection optics ( 1200B ), resulting in a SMO. Alternatively, the design variables may include characteristics of the illumination source ( 1200A ), characteristics of the projection optics ( 1200B ), and characteristics of the design layout ( 1200C ), resulting in a source mask-lens optimization ( SMO ). In step S1204 , the design variables are simultaneously adjusted to move the cost function toward convergence. In step S1206 , it is determined whether a predefined termination condition is satisfied. The predetermined termination conditions may include various possibilities, namely that the cost function can be minimized or maximized (as required by the numerical technique used), the value of the cost function has equaled a threshold or has exceeded a threshold, the value of the cost function has reached a preset error limit, or a preset number of iterations has been reached. If any of the conditions in step S1206 is met, the method ends. If none of the conditions in step S1206 is met, steps S1204 and S1206 are iteratively repeated until the desired result is obtained. Optimization does not necessarily result in a single set of values ​​for the design variables, as there may be physical inhibitions caused by factors such as failure rate, pupil fill factor, resist chemistry, throughput, etc. Optimization may provide multiple sets of values ​​for design variables and associated performance characteristics (e.g., throughput), and allow a user of the lithographic apparatus to obtain one or more sets.

[0148] In a lithographic projection apparatus, the source, patterning device, and projection optics may be optimized alternately (referred to as alternating optimization), or may be optimized simultaneously (referred to as simultaneous optimization). As used herein, the terms "simultaneously," "simultaneously," "jointly," and "jointly" mean that the design variables of the characteristics of the source, patterning device, projection optics, and / or any other design variables are allowed to be varied simultaneously. As used herein, the terms "alternating" and "alternatingly" mean that not all design variables are allowed to be varied simultaneously.

[0149] exist Figure 15 In the process of performing the optimization of all design variables simultaneously, this process can be called a simultaneous process or a joint optimization process. Alternatively, the optimization of all design variables can be performed alternately, such as Figure 15In this process, in each step, while some design variables are fixed, other design variables are optimized to minimize the cost function; then, in the next step, while a different set of variables is fixed, another set of variables is optimized to minimize the cost function. These steps are performed alternately until convergence or some termination condition is met.

[0150] like Figure 15 As shown in the non-limiting exemplary flow chart of FIG, first, a design layout is obtained (step S1302). Then, in step S1304, a source optimization step is performed, wherein all design variables of the illumination source are optimized (SO) to minimize a cost function while holding all other design variables fixed. Then, in the next step S1306, mask optimization (MO) is performed, wherein all design variables of the patterning device are optimized to minimize the cost function while holding all other design variables fixed. These two steps are performed alternately until a certain termination condition is met in step S1308. Various termination conditions can be used, such as the cost function value becoming equal to a threshold, the cost function value exceeding a threshold, the cost function value falling within a preset error limit, or a preset number of iterations being reached. Note that SO-MO alternating optimization is used as an example of this alternative process. This alternative process can take many different forms, such as SO-LO-MO alternating optimization, wherein SO, LO (lens optimization), and MO are performed alternately and iteratively; or SMO can be performed once, followed by LO and MO alternating and iteratively, etc. Finally, an output of the optimization result is obtained in step S1310 and the process stops.

[0151] As previously discussed, the pattern selection algorithm can be integrated with simultaneous or alternating optimization. For example, when employing alternating optimization, full-chip SO can be performed first, "hot spots" and / or "warm spots" identified, and then MO can be performed. In light of the present disclosure, numerous permutations and combinations of sub-optimizations are possible to achieve the desired optimization results.

[0152] Figure 16AAn exemplary optimization method is shown in which a cost function is minimized. In step S502, initial values ​​of the design variables are obtained, including the tuning ranges for the design variables (if any). In step S504, a multivariate cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting values ​​of the design variables for the first iteration step (i=0). In step S508, standard multivariate optimization techniques are applied to minimize the cost function. Note that the optimization problem can impose constraints, such as tuning ranges, during the optimization process in S508 or at a later stage in the optimization process. Step S520 indicates that each iteration is performed for a given test pattern (also referred to as a "gauge") for the identified evaluation points that have been selected for optimizing the lithography process. In step S510, the lithography response is predicted. In step S512, the results of step S510 are compared with the expected or ideal lithography response value obtained in step S522. If the termination condition is met in step S514, that is, the optimization produces a lithographic response value that is sufficiently close to the expected value, the final value of the design variable is output in step S518. The output step may also include using the final value of the design variable to output other functions, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized source map, and an optimized design layout. If the termination condition is not met, in step S516, the value of the design variable is updated using the result of the i-th iteration, and the process returns to step S506. The following describes in detail Figure 16A technology.

[0153] In the exemplary optimization process, no assumptions or approximations are made about the design variables (z1, z2, ..., z N ) and f p (z1,z2,...,z N ) relationship, but f p (z1,z2,...,z N ) is sufficiently smooth (e.g., there is a first-order derivative Except for this condition, which is usually valid in lithographic projection equipment, algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, gradient descent algorithm, simulated annealing algorithm, genetic algorithm can be applied to find

[0154] Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newton algorithm is an iterative method suitable for general nonlinear multivariable optimization problems. N ) value (z 1i , z 2i ,...,z Ni ) in the i-th iteration, the Gauss-Newton algorithm will1i , z 2i ,...,z Ni ) near f p (z1,z2,...,z N ) linearized, and then calculated at (z 1i , z 2i ,...,z Ni ) gives CF(z1,z2,...,z N ) of the minimum value (z 1(i+1) , z 2(i+1) ,...,z N(i+1) ). Design variables (z1, z2, ..., z N ) takes the value (z 1(i+1) , z 2(i+1) ,...,z N(i+1) This iteration continues until convergence (i.e., CF(z1, z2, ..., z N ) no longer decreases) or reaches a preset number of iterations.

[0155] Specifically, in the i-th iteration, in (z 1i , z 2i ,...,z Ni )nearby,

[0156]

[0157] According to the approximation of Equation 3, the cost function becomes:

[0158]

[0159] It is the design variable (z1, z2, ..., z N ). All terms are constant, but the design variables (z1, z2, ..., z N )except.

[0160] If the design variables (z1, z2, ..., z N ) is not under any constraints, then it can be obtained by N linear equations (where n = 1, 2, ..., N) and derive (z 1(i+1) , z 2(i+1) ,...,z N(i+1) ).

[0161] If the design variables (z1, z2, ..., z N ) is in the form of J inequalities (e.g., (z1, z2, ..., z N ) tuning range (where j = 1, 2, ..., J); and in the form of K equations (e.g., interdependencies between design variables) in the form of constraints (where k = 1, 2, ..., K); the optimization process becomes a classic quadratic programming problem, where A nj 、B j 、C nk 、D k is a constant. Additional constraints can be imposed for each iteration. For example, a "damping factor" Δ D To limit (z 1(i+1) , z 2(i+1) ,...,z N(i+1) ) and (z1, z2, ..., z N ) so that the approximation of Equation 3 holds. Such constraints can be expressed as z ni -Δ D ≤z n ≤z ni +Δ D (z can be derived using, for example, the method described in Numerical Optimization (2nd ed.) by Jorge Nocedal and Stephen J. Wright (Berlin New York: Vandenberghe. Cambridge University Press). 1(i+1) , z 2(i+1) ,...,z N(i+1) ).

[0162] Instead of using f p (z1,z2,...,z N ), the optimization process can minimize the magnitude of the maximum deviation (worst defect) in the evaluation points to their expected values. In this method, the cost function can be alternatively expressed as

[0163]

[0164] Among them, CL p is used for f p (z1,z2,...,z N ) is the maximum allowable value. This cost function represents the worst defect among the evaluation points. Optimization using this cost function minimizes the magnitude of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0165] The cost function of Equation 5 can be approximated as:

[0166]

[0167] Wherein, q is a positive even integer, such as at least 4, preferably at least 10. Equation 6 mimics the behavior of Equation 5 while allowing the optimization to be performed analytically and accelerated using methods such as the deepest descent method, the conjugate gradient method, and the like.

[0168] Minimizing the size of the worst defect can also be related to f p (z1,z2,...,z N ). Specifically, f is approximated as in Equation 3. p (z1,z2,...,z N ). Then, the constraint on the size of the worst defect is written as inequality E Lp ≤f p (z1,z2,...,z N )≤E Up , where E Lp and E Up is specified for f p (z1,z2,...,z N ) are two constants for the minimum and maximum allowable deviations. Inserting Equation 3 transforms these constraints into the following form (where p=1, ...P):

[0169]

[0170] as well as

[0171]

[0172] Since Equation 3 is usually only valid for (z 1i , z 2i ,...,z Ni ) is valid near this point, so if the desired constraint E cannot be achieved near this point Lp ≤f p (z1,z2,...,z N )≤E Up (this can be determined by any conflicts between the inequalities), then the constant E can be relaxed Lp and E Up Until the constraints can be achieved. 1i , z 2i ,...,z Ni ). Each step then progressively reduces the worst defect size, and each step is iteratively performed until some termination condition is met. This results in an optimal reduction in the worst defect size.

[0173] Another way to minimize the worst defect is to adjust the weight w in each iteration pFor example, after the i-th iteration, if the r-th evaluation point is the worst defect, w can be increased in the (i+1)-th iteration. r , so that the reduction of the defect size toward the evaluation point is given higher priority.

[0174] In addition, the cost functions in Equations 4 and 5 can be modified by introducing Lagrange multipliers to achieve a trade-off between optimizing the RMS of the defect size and optimizing the worst defect size, i.e.:

[0175]

[0176] Here, λ is a preset constant that specifies the tradeoff between optimizing for the RMS of defect sizes and optimizing for the worst-case defect size. Specifically, if λ = 0, the equation becomes EQ 4, minimizing only the RMS of defect sizes; if λ = 1, the equation becomes EQ 5, minimizing only the worst-case defect size. If 0 < λ < 1, both cases are considered in the optimization. A variety of approaches can be used to solve this optimization. For example, similar to the previously described approach, the weighting can be adjusted in each iteration. Alternatively, similar to minimizing the worst-case defect size based on inequalities, the inequalities in EQs 6′ and 6″ can be treated as constraints on the design variables during the solution of the quadratic programming problem. The bounds on the worst-case defect size can then be incrementally relaxed, or the weights for the worst-case defect size can be incrementally increased. The cost function value for each achievable worst-case defect size is calculated, and the design variable value that minimizes the total cost function is selected as the starting point for the next step. By performing this operation iteratively, the minimization of this new cost function can be achieved.

[0177] Optimizing the lithographic projection equipment can expand the process window. A larger process window provides more flexibility in process design and chip design. The process window can be defined as a set of focus and dose values ​​that brings the resist image within certain limits of the design target of the resist image. Note that all methods discussed here can also be extended to a generalized process window definition that can be established by different or additional basis parameters in addition to exposure dose and defocus. These basis parameters may include (but are not limited to) optical settings such as NA, standard deviation, aberration, polarization, or optical constants of the resist layer. For example, as described earlier, if the PW also consists of different mask deviations, the optimization includes minimizing the MEEF (mask error enhancement factor), which is defined as the ratio between the substrate EPE and the induced mask edge deviation. The process window defined with respect to focus and dose values ​​is used as an example only in this disclosure. The following describes a method for maximizing the process window according to an embodiment.

[0178] In the first step, starting from known conditions (f0, ε0) in the process window (where f0 is the nominal focus and ε0 is the nominal dose), one of the following cost functions around (f0 ± Δf, ε0 ± Δε) is minimized:

[0179]

[0180] or

[0181]

[0182] or

[0183]

[0184] If the nominal focus f0 and the nominal dose ε0 are allowed to shift, they can be compared with the design variables (z1, z2, ..., z N ) are jointly optimized. In the next step, if (z1, z2, ..., z N , f, ε) such that the cost function is within preset limits, then accept (f0±Δf, ε0±Δε) as part of the process window.

[0185] Alternatively, if focus and dose are not allowed to shift, the design variables (z1, z2, ..., z N In an alternative embodiment, if (z1, z2, ..., z N ) such that the cost function is within preset limits, then (f0±Δf, ε0±Δε) is accepted as part of the process window.

[0186] The methods described earlier in this disclosure can be used to minimize the corresponding cost functions of Equations 7, 7', or 7". If the design variables are characteristics of the projection optics, such as Zernike coefficients, then minimizing the cost functions of Equations 7, 7', or 7" results in maximizing the process window optimized based on the projection optics (i.e., LO). If the design variables are characteristics of the source and patterning device in addition to characteristics of the projection optics, then minimizing the cost functions of Equations 7, 7', or 7" results in maximizing the process window based on SMLO, such as Figure 15 If the design variables are characteristics of the source and the patterning device, minimizing the cost function of Equation 7, 7', or 7" results in maximizing the SMO-based process window. The cost function of Equation 7, 7', or 7" may also include at least one f p (z1,z2,...,z N ), such as f in Equation 7 or Equation 8 p(z1,z2,...,z N ), which is a function of one or more random effects such as LWR or local CD variation of the 2D feature and production volume.

[0187] Figure 17 A specific example of how a simultaneous SMLO process can use the Gauss-Newton algorithm for optimization is shown. In step S702, starting values ​​for the design variables are identified. The tuning range for each variable can also be identified. In step S704, a cost function is defined using the design variables. In step S706, the cost function is expanded around the starting values ​​for all evaluation points in the design layout. In optional step S710, a full chip simulation is performed to cover all critical patterns in the full chip design layout. In step S714, the expected lithography response metrics (such as CD or EPE) are obtained, and in step S712, the expected lithography response metrics are compared with the predicted values ​​of those quantities. In step S716, the process window is determined. Steps S718, S720, and S722 are as described with reference to FIG. Figure 16A The corresponding steps S514, S516 and S518 are similar. As mentioned above, the final output can be a wavefront aberration map in the pupil plane, which is optimized to produce the desired imaging performance. The final output can also be an optimized source map and / or an optimized design layout.

[0188] Figure 16B An exemplary method for optimizing a cost function is shown, where the design variables (z1, z2, ..., z N ) includes design variables that can take only discrete values.

[0189] The method begins by defining pixel groups for the illumination source and patterning device tiles for the patterning device (step S802). Pixel groups or patterning device tiles are also commonly referred to as partitions of a lithography process component. In one exemplary method, the illumination source is partitioned into 117 pixel groups, and 94 patterning device tiles are defined for the patterning device (substantially as described above), resulting in a total of 211 partitions.

[0190] In step S804, a lithography model is selected as the basis for lithography simulation. The lithography simulation produces results for calculating lithography indicators or responses. Specific lithography indicators are defined as performance indicators to be optimized (step S806). In step S808, initial (pre-optimization) conditions for the illumination source and pattern forming device are set. The initial conditions include the initial states of the pixel groups for the illumination source and the pattern forming device tiles of the pattern forming device, so that the initial illumination shape and the pattern of the initial pattern forming device can be referenced. The initial conditions may also include mask deviation, NA, and focus slope range. Although steps S802, S804, S806, and S808 are depicted as consecutive steps, it will be understood that in other embodiments of the present invention, these steps may be performed in other orders.

[0191] In step S810, the pixel groups and patterning device tiles are sorted. The pixel groups and patterning device tiles can be interleaved in the sorting. Various sorting methods can be used, including sequentially (e.g., from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), randomly, based on the physical location of the pixel groups and patterning device tiles (e.g., sorting pixel groups closer to the center of the illumination source higher), and based on how changes to the pixel groups or patterning device tiles affect performance indicators.

[0192] Once the pixel groups and patterning device tiles are sorted, the illumination source and patterning device are adjusted to improve the performance metric (step S812). In step S812, each of the pixel groups and patterning device tiles is analyzed in the sorted order to determine whether a change to the pixel group or patterning device tile will result in an improved performance metric. If it is determined that the performance metric will be improved, the pixel group or patterning device tile is changed accordingly, and the generated improved performance metric and the modified illumination shape or modified patterning device pattern form a baseline for comparison for subsequent analysis of lower-ranked pixel groups and patterning device tiles. In other words, the changes that improve the performance metric are maintained. As changes to the states of the pixel groups and patterning device tiles are made and maintained, the initial illumination shape and the initial patterning device pattern change accordingly, so that the modified illumination shape and the modified patterning device pattern result from the optimization process in step S812.

[0193] In other approaches, patterning device polygon shape adjustments and pairwise polling of pixel groups and / or patterning device tiles are also performed within the optimization process of S812 .

[0194] In an alternative embodiment, the staggered simultaneous optimization process may include changing the pixel groups of the illumination source and, if an improvement in the performance metric is found, gradually increasing and decreasing the dose to look for further improvement. In yet another alternative embodiment, further improvements in the simultaneous optimization process may be sought by replacing the gradual increase and decrease of dose or intensity with deviation changes in the patterning device pattern.

[0195] In step S814, a determination is made as to whether the performance metric has converged. For example, if little or no improvement in the performance metric has been demonstrated in the last few iterations of steps S810 and S812, the performance metric may be considered to have converged. If the performance metric has not converged, then steps S810 and S812 are repeated in the next iteration, with the modified illumination shape and modified patterning device from the current iteration serving as the initial illumination shape and initial patterning device for the next iteration (step S816).

[0196] The optimization method described above can be used to increase the throughput of a lithographic projection apparatus. For example, the cost function may include f as a function of exposure time. p (z1,z2,...,z N ). Optimization of the cost function is preferably constrained or influenced by a measure of the random effects or other indicators. Specifically, a computer-implemented method for increasing the throughput of a lithography process may include optimizing a cost function as a function of one or more random effects of the lithography process and as a function of the exposure time of the substrate so as to minimize the exposure time.

[0197] In one embodiment, the cost function includes at least one f as a function of one or more random effects p (z1,z2,...,z N ). Random effects can include failure of features, e.g. Figure 3A In one embodiment, the random effects include random variations in the properties of the resist image, such as SEPE, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU). Including random variations in the cost function allows finding values ​​of the design variables that minimize the random variations, thereby reducing the risk of defects due to random effects.

[0198] Figure 181 is a block diagram illustrating a computer system 100 that can assist in implementing the optimization methods and processes disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to bus 102 for processing information. Computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 102 for storing information and instructions to be executed by processor 104. Main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by processor 104. Computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to bus 102 for storing static information and instructions for processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to bus 102 for storing information and instructions.

[0199] The computer system 100 can be connected to a display 112 for displaying information to a computer user via the bus 102, such as a cathode ray tube (CRT) or a flat panel display or a touch panel display. An input device 114 including alphabetic keys and other keys is connected to the bus 102 for conveying information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for conveying direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. The input device typically has two degrees of freedom on two axes - a first axis (e.g., x) and a second axis (e.g., y) - that allow the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0200] According to an embodiment, portions of the optimization process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequences of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing configuration may also be used to execute the sequences of instructions contained in main memory 106. In alternative embodiments, hardwired 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.

[0201] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. This medium can 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 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wire, and optical fiber, including the wires that comprise bus 102. Transmission media can also take the form of sound 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, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic medium, CD-ROMs, DVDs, any other optical medium, punch cards, paper tape, any other physical medium with a pattern of holes, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chip or cartridge, a carrier wave as described below, or any other medium that a computer can read.

[0202] Various forms of computer-readable media may be involved when carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into the dynamic memory of the computer and send the instructions via a telephone line using a modem. A modem local to computer system 100 may receive data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector connected to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0203] The computer system 100 also preferably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication connection to a network link 120, which is connected to a local area network 122. For example, the communication interface 118 can 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, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0204] Network link 120 typically provides data communication to other data devices via one or more networks. For example, network link 120 may provide a connection to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126 via a local area network 122. ISP 126, in turn, provides data communication services via a global packet data communication network (now commonly referred to as the "Internet") 128. Both local area network 122 and Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0205] Computer system 100 can send messages and receive data (including code) via one or more networks, network link 120, and communication interface 118. In the example of the Internet, server 130 might transmit requested code for an application via Internet 128, ISP 126, local area network 122, and communication interface 118. One such downloaded application might provide, for example, illumination optimization according to an embodiment. The received code can be executed by processor 104 as it is received and / or stored in storage device 110 or other non-volatile memory for later execution. In this way, computer system 100 can obtain application code in the form of a carrier wave.

[0206] Figure 19 An exemplary lithographic projection apparatus LA is schematically depicted, in which the method described herein may be used to optimize the illumination source. The apparatus comprises:

[0207] - an illumination system IL for conditioning the radiation beam B. In this particular case, the illumination system further comprises a radiation source SO;

[0208] a first stage (e.g., mask stage) MT having a patterning device holder for holding a patterning device MA (e.g., reticle) and connected to a first positioner for accurately positioning the patterning device relative to the object PS;

[0209] a second stage (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the object PS;

[0210] - a projection system ("lens") PS (eg a refractive, reflective or catadioptric optical system) for imaging the illuminated portion of the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0211] As depicted herein, the device is of the transmissive type (i.e., with a transmissive mask). However, in general, the device may also be of the reflective type (with a reflective mask), for example. Alternatively, the device may use another patterning device as an alternative to the use of a classical mask; examples include a programmable mirror array or an LCD matrix.

[0212] A source SO (e.g., a mercury lamp or an excimer laser) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, for example, directly or after having traversed an adjustment member such as a beam expander Ex. The illuminator IL may include adjustment members AD for setting the outer radial extent and / or inner radial extent (commonly referred to as σouter and σinner, respectively) of the intensity distribution in the beam. In addition, the illuminator IL will typically include 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.

[0213] Reference Figure 19 It should be noted that the source SO can be within the housing of the lithographic projection apparatus (this is often the case when the source SO is (for example) a mercury lamp), but the source SO can also be remote from the lithographic projection apparatus, the radiation beam generated by the source SO being guided into the apparatus (for example with the aid of suitable guiding mirrors); this latter scenario is often the case when the source SO is an excimer laser (for example based on KrF, ArF or F2 laser action).

[0214] The beam PB then intercepts the patterning device MA which is held on the patterning device table MT. Having traversed the patterning device MA, the beam B passes through a 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 the interferometry means IF), the substrate table WT can be accurately moved, for example in order to position a different target portion C in the path of the beam PB. Similarly, the first positioning means can be used to accurately position the patterning device MA relative to the path of the beam B, for example after mechanically acquiring the patterning device MA from a patterning device library or during a scan. In general, the patterning device MA will be positioned with the aid of the second positioning means (and the interferometry means IF) which are not in the path of the beam PB. Figure 19 Movement of the object tables MT, WT is achieved by a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) explicitly depicted in FIG. However, in the case of a wafer stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to the short-stroke actuator only, or may be fixed.

[0215] The depicted tools can be used in two different modes:

[0216] In step mode, the patterning device table MT is held essentially stationary and the entire patterning device image is projected at once (i.e. a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x- and / or y-direction so that a different target portion C can be illuminated by the beam PB;

[0217] 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 can be moved in a given direction (the so-called "scanning direction", e.g., the y-direction) at a speed v, such that the projection beam B is caused to scan across the patterning device image; while the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or =1 / 5). In this way, a relatively large target portion C can be exposed without having to compromise resolution.

[0218] Figure 20 Another exemplary lithographic projection apparatus LA in which the methods described herein may be utilized to optimize the illumination source is schematically depicted.

[0219] The lithographic projection apparatus LA comprises:

[0220] - Source collector module SO;

[0221] an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation);

[0222] a support structure (e.g., mask table) MT configured to support a patterning device (e.g., mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0223] a substrate table (e.g., wafer stage) WT configured 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

[0224] A projection system (eg, a reflective projection system) PS is configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0225] As depicted here, device LA is of the reflective type (e.g., using a reflective mask). Note that because most materials are absorptive in the EUV wavelength range, the mask can have a multilayer reflector comprising, for example, multiple stacks of molybdenum and silicon. In one example, the multilayer reflector has 40 layer pairs of molybdenum and silicon, where each layer is a quarter wavelength thick. Even smaller wavelengths can be produced using X-ray lithography. Because most materials are absorptive at EUV and x-ray wavelengths, thin segments of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of the multilayer reflector) define where features will be printed (positive resist) or not (negative resist).

[0226] Reference Figure 20 The illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material having at least one element (e.g., xenon, lithium, or tin) into a plasma state using one or more emission lines in the EUV range. In one such method, a plasma (often referred to as laser produced plasma "LPP") can be generated by irradiating a fuel (such as a droplet, stream, or cluster of a material having a line emitting element) with a laser beam. The source collector module SO can be a device comprising a laser ( Figure 20 The laser is used to provide a laser beam for exciting the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector disposed in a source collector module. For example, when a CO2 laser is used to provide the laser beam for fuel excitation, the laser and source collector module can be separate entities.

[0227] In such cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable steering mirrors and / or a beam expander. In other cases, for example, when the source is a discharge produced plasma EUV generator (often referred to as a DPP source), the source may be an integral part of the source collector module.

[0228] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as σouter and σinner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator can be used to condition the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0229] A radiation beam B is incident on a patterning device (e.g., mask) MA, which is held on a support structure (e.g., mask table) MT, and is patterned by the patterning device. After reflecting from the patterning device (e.g., mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g., an interferometer arrangement, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example, so that a different target portion C is positioned in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B. The patterning device (e.g., mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0230] The depicted device LA can be used in at least one of the following modes:

[0231] 1. In step mode, the support structure (e.g. mask table) MT and substrate table WT are held substantially stationary (i.e. single static exposure) while the entire pattern imparted to the radiation beam is projected at one time onto a target portion C. The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0232] 2. In scan mode, the support structure (e.g., mask table) MT and substrate table WT are scanned synchronously (i.e., single dynamic exposure) as a pattern imparted to the radiation beam is projected onto a target portion C. The velocity and direction of the substrate table WT relative to the support structure (e.g., mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0233] 3. In another mode, the support structure (e.g., mask table) MT is held substantially stationary, thereby holding the 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, a pulsed radiation source is typically used, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0234] Figure 21The apparatus LA is shown in more detail and includes a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and configured so that a vacuum environment can be maintained in an enclosure 220 of the source collector module SO. An EUV radiation emitting plasma 210 can be formed by a discharge-produced plasma source. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor), wherein an extremely hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, the extremely hot plasma 210 is generated by a discharge that causes an at least partially ionized plasma. In order to effectively generate radiation, a partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In an embodiment, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0235] Radiation emitted by the hot plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or foil trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230, further referred to herein, includes at least a channel structure.

[0236] The collector chamber 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused into a virtual source point IF along the optical axis indicated by the dotted line "O". The virtual source point IF is often referred to as an intermediate focus, and the source collector module is configured so that the intermediate focus IF is located at or near an opening 221 in the enclosure structure 220. The virtual source point IF is an image of the radiation-emitting plasma 210.

[0237] The radiation then traverses an illumination system IL, which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24, which are configured to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the radiation beam 21 at the patterning device MA, which is held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by the substrate table WT.

[0238] More elements than shown may typically be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Additionally, more mirrors may be present than shown in the figures, for example, more than 100 mirrors may be present in the projection system PS. Figure 21 The reflective elements shown have 1 to 6 additional reflective elements.

[0239] Figure 21 The illustrated collector optics CO is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are arranged axially symmetrically about the optical axis O, and this type of collector optics CO is preferably used in conjunction with a discharge produced plasma source (often referred to as a DPP source).

[0240] Alternatively, the source collector module SO may be as follows Figure 22 A portion of an LPP radiation system is shown. Laser LA is configured to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of tens of electron volts. High-energy radiation generated during the deexcitation and recombination of these ions is emitted from the plasma, collected by near-normal incidence collector optics CO, and focused onto an opening 221 in an enclosure 220.

[0241] The concepts disclosed herein can simulate or mathematically model any general imaging system that images sub-wavelength features, and can be particularly useful with emerging imaging technologies that can produce shorter and shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography, which can produce wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 5 nm to 20 nm by using a synchrotron or by using high-energy electrons to shoot at a material (solid or plasma) to produce photons in this range.

[0242] The embodiments of the present disclosure may be further described through the following aspects.

[0243] 1. A method for generating a retargeting pattern for a target pattern to be printed on a substrate, the method comprising:

[0244] obtaining (i) the target pattern including at least one feature having a geometry including a first dimension and a second dimension; and (ii) a plurality of deviation rules defined as a function of the first dimension, the second dimension, and a property associated with the feature of the target pattern within a measurement region;

[0245] determining a value of the property at a plurality of locations on the at least one feature of the target pattern, wherein each location is surrounded by the measurement region;

[0246] selecting, from the plurality of deviation rules, a subset of deviations for the plurality of locations on the at least one feature based on the value of the property; and

[0247] The retargeting pattern for the target pattern is generated by applying a selected subset of deviations to the at least one feature of the target pattern.

[0248] 2. The method of clause 1, wherein determining the value of the property at a given location comprises:

[0249] (a) allocating a measurement area around the given location at the at least one feature;

[0250] (b) identifying one or more features within the measurement area;

[0251] (c) calculating, via a user-defined function, a value of the property associated with the one or more identified features within the measurement area; and

[0252] (d) selecting another location at the at least one feature and performing steps (b) and (c) using the measurement area in step (a).

[0253] 3. The method of any one of aspects 1 to 2, wherein the property is a density or a kernel function.

[0254] 4. The method according to claim 3, wherein calculating the density comprises:

[0255] determining a total area of ​​the one or more identified features within the measurement region;

[0256] determining a total area of ​​the measurement region; and

[0257] A density value is calculated as the ratio of the total area of ​​features within the measurement region to the total area of ​​the measurement region.

[0258] 5. The method of any one of aspects 2 to 4, wherein calculating the value of the property comprises:

[0259] A convolution calculation is applied between the measurement region and the user-defined function.

[0260] 6. The method of clause 5, wherein the measurement region is represented as an image including the one or more features, and the value of the property is calculated by convolving the image with the user-defined function.

[0261] 7. The method of any one of clauses 1 to 6, wherein the measurement region is movable across the target pattern.

[0262] 8. The method of any one of clauses 1 to 7, wherein the first dimension is the width of the at least one feature and the second dimension is the spacing between the at least one feature and an adjacent feature.

[0263] 9. The method of any one of clauses 1 to 8, wherein the target pattern is a design pattern, a developed image pattern, and / or an etched pattern.

[0264] 10. The method of any of clauses 1 to 9, wherein the selected deviations for a given width and spacing are retargeting values, each retargeting value being applied to a portion of the at least one feature of the target pattern.

[0265] 11. The method according to claim 10, further comprising:

[0266] applying each retargeting value to a corresponding edge to generate the retargeting pattern; and

[0267] Optical proximity effect correction is applied to the retargeting pattern to produce a post-OPC pattern.

[0268] 12. The method of any one of aspects 1 to 11, wherein each deviation in the plurality of deviations is at least one of:

[0269] Etch compensation, which is applied to the ADI pattern so that the etch pattern is within the desired specification;

[0270] model error compensation associated with one or more process models used to simulate the patterning process;

[0271] Mask proximity effect correction, which is applied to the design layout to reduce variations in the target pattern due to mask fabrication; or

[0272] An initial OPC bias that will be applied to the design layout to produce an initial retargeted layout for optimal proximity effect correction.

[0273] 13. The method of any one of clauses 1 to 12, wherein the deviation rules are represented as a table of the first dimension and the second dimension for each of the properties.

[0274] 14. The method of clause 13, wherein the deviation rules are represented in a plurality of tables depending on the results of applying the kernel function for determining the property.

[0275] 15. The method of any one of aspects 1 to 14, wherein the selection bias comprises:

[0276] (a) identifying the range within which a given value of the property falls;

[0277] (b) selecting a deviation rule from the plurality of deviation rules for the identified range of the property; and

[0278] (c) for given values ​​of the first dimension and the second dimension, selecting, from the bias rule, a bias value associated with the given one of the plurality of positions on the at least one feature.

[0279] 16. A method as described in any one of aspects 2 to 15, wherein the user-defined function is a geometric function, a signal processing function or an image processing function that transforms the one or more features within the measurement area into feature values, and the feature values ​​are specific to the one or more features in the defined position.

[0280] 17. The method of clause 16, wherein the geometric function is a function of the shape, size, relative position of the at least one feature of the target pattern.

[0281] 18. The method of clause 16, wherein the signal processing function is an image processing function, a sine function, a cosine function, or a Fourier transform.

[0282] 19. The method of clause 16, wherein the image processing function is a low-pass filter and / or an edge detection function.

[0283] 20. A method for determining a deviation rule for a target pattern to be printed on a substrate, the method comprising:

[0284] obtaining the target pattern comprising at least one feature defined by a first dimension and a second dimension;

[0285] determining a plurality of deviations for the first dimension and the second dimension and associating each of the plurality of deviations with a value of the property via executing a process correction model, wherein the process correction model deviations the first dimension and the second dimension of the at least one feature and calculates the property associated with the at least one feature; and

[0286] Based on the plurality of deviations, the deviation rule is defined as a function of the first dimension, the second dimension, and the property associated with the at least one feature.

[0287] 21. The method of clause 20, wherein executing the process correction model comprises determining a plurality of values ​​for the property at a plurality of locations on the at least one pattern of the target pattern.

[0288] 22. The method of clause 21, wherein determining the value of the property comprises:

[0289] (a) allocating a measurement region around a given location on the at least one feature;

[0290] (b) identifying one or more features within the measurement area;

[0291] (c) calculating, via a user-defined function, a value of the property associated with the one or more identified features within the measurement area; and

[0292] (d) selecting another location on the at least one feature and performing steps (b) and (c) using the measurement area in step (a).

[0293] 23. The method of any one of aspects 20 to 22, wherein determining the plurality of deviations comprises:

[0294] generating a retargeted pattern comprising deviations for the first dimension and the second dimension of the at least one pattern by executing the process correction model using the target pattern;

[0295] determining a difference between the retargeting pattern and the target pattern; and

[0296] The plurality of deviations at the plurality of locations of the target pattern are determined based on the differences.

[0297] 24. The method of any one of aspects 20 to 23, wherein defining the deviation rule comprises:

[0298] defining a range for the property based on the value of the property; and

[0299] For each range of the property, a set of deviations from the plurality of deviations is assigned, wherein each deviation in the set of deviations is associated with the first dimension and the second dimension.

[0300] 25. The method of any one of clauses 20 to 24, wherein the process correction model is at least one of:

[0301] an etch correction model that determines a correction to an etched pattern relative to the target pattern;

[0302] an optical proximity correction model that determines modifications to the target pattern; or

[0303] A mask proximity effect correction model is provided, which determines corrections associated with a mask fabrication process.

[0304] 26. The method of any one of clauses 20 to 25, wherein during execution of the process correction model, the plurality of deviations are collected for each segment of the target pattern, a segment being a portion of the target pattern.

[0305] 27. A method as described in any of aspects 20 to 26, wherein, during the execution of the process correction model, the value of the property is calculated for each segment of the target pattern and for each defined area, the defined area being the area around a given position of the target pattern.

[0306] 28. A computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the method according to any one of the above aspects when executed by a computer.

[0307] Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0308] The above description is intended to be illustrative rather than restrictive. It will therefore be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth hereinafter.

Claims

1. A method of generating a retargeting pattern for a target pattern to be printed on a substrate, the method comprising: obtaining (i) the target pattern including at least one feature having a geometry including a first dimension and a second dimension and (ii) a plurality of deviation rules, the plurality of deviation rules being defined as a function of the first dimension, the second dimension, and a property associated with the plurality of features of the target pattern within a measurement region; determining a value of the property at a plurality of locations on the at least one feature of the target pattern, wherein each location is surrounded by the measurement region; selecting, from the plurality of deviation rules, a subset of deviations for the plurality of locations on the at least one feature based on the value of the property; and The retargeting pattern for the target pattern is generated by applying the selected subset of deviations to the at least one feature of the target pattern.

2. The method according to claim 1, wherein Determining the value of the property at a given location comprises: (a) allocating a measurement area around the given location at the at least one feature; (b) identifying one or more features within the measurement area; (c) calculating, via a user-defined function, a value of the property associated with the one or more identified features within the measurement region; and (d) selecting another location at the at least one feature and performing steps (b) and (c) using the measurement area in step (a).

3. The method according to claim 1, wherein The property is the density or kernel function of the features.

4. The method according to claim 3, wherein: Calculating the density includes: determining a total area of ​​the one or more identified features within the measurement region; determining a total area of ​​the measurement region; and A density value is calculated as the ratio of the total area of ​​features within the measurement region to the total area of ​​the measurement region.

5. The method according to claim 2, wherein: Calculating the value of the property comprises: A convolution calculation is applied between the measurement region and the user-defined function.

6. The method according to claim 5, wherein: The measurement region is represented as an image including the one or more features, and the value of the property is calculated by convolving the image with the user-defined function.

7. The method of claim 1, wherein: The measurement area is movable across the target pattern, and wherein the target pattern is a design pattern, a developed image pattern, and / or an etching pattern.

8. The method of claim 1, wherein: The first dimension is a width of the at least one feature, and the second dimension is a spacing between the at least one feature and an adjacent feature, wherein the selected deviations for a given width and spacing are retargeting values, each retargeting value being applicable to a portion of the at least one feature of the target pattern, and wherein the method further comprises: applying each retargeting value to a corresponding edge to generate the retargeting pattern; and Optical proximity effect correction is applied to the retargeting pattern to produce a post-OPC pattern.

9. The method of claim 1, wherein: Each deviation in the plurality of deviations is at least one of: Etch compensation, which is applied to the ADI pattern so that the etch pattern is within the desired specification; model error compensation associated with one or more process models used to simulate the patterning process; Mask proximity effect correction, which is applied to the design layout to reduce variations in the target pattern due to mask fabrication; or An initial OPC bias that will be applied to the design layout to produce an initial retargeted layout for optimal proximity effect correction.

10. The method of claim 3, wherein: The deviation rules are represented as a table of the first dimension and the second dimension for each of the properties, or in a plurality of tables depending on a result of applying the kernel function for determining the property.

11. The method of claim 1, wherein: Selection biases include: (a) identifying the range within which a given value of the property falls; (b) selecting a deviation rule from the plurality of deviation rules for the identified range of the property; and (c) for given values ​​of the first dimension and the second dimension, selecting, from the bias rule, a bias value associated with a given one of the plurality of positions on the at least one feature.

12. The method of claim 2, wherein: The user-defined function is a geometric function, a signal processing function, or an image processing function that transforms the one or more features within the measurement region into feature values ​​that are specific to the one or more features in a defined location.

13. The method of claim 12, wherein: The geometric function is a function of the shape, size, and relative position of the at least one feature of the target pattern.

14. The method of claim 12, wherein: The signal processing function is an image processing function, a sine function, a cosine function or a Fourier transform.

15. The method of claim 12, wherein: The image processing function is a low-pass filter and / or an edge detection function.

16. A non-transitory computer-readable medium having instructions recorded thereon, the instructions, when executed by a computer, implementing a method for generating a retargeting pattern for a target pattern to be printed on a substrate, the method as described in any one of claims 1 to 15.

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