Process window based on failure rate

Abstract

A method for determining a process window for a patterning process based on a failure rate is described herein. The method includes: (a) obtaining a plurality of features printed on a substrate; (b) grouping the features into a plurality of groups based on an indicator; and (c) generating a base failure rate model for a group of features based on measurement data associated with the group of features, wherein the base failure rate model identifies the process window related to the failure rate of the group of features. The method further includes generating a feature-specific failure rate model for a particular feature using the base failure rate model, wherein the feature-specific failure rate model identifies a feature-specific process window such that an estimated failure rate of the particular feature is below a specified threshold.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to PCT application PCT / CN2020 / 100137, filed on July 3, 2020, and PCT application PCT / CN2021 / 081068, filed on March 16, 2021, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to techniques for improving the performance of device manufacturing processes. These techniques can be used in conjunction with photolithography equipment or metrology equipment. Background Technology

[0004] A photolithography apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Photolithography apparatuses can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a pattern forming apparatus, alternatively referred to as a mask or photomask, can be used to generate a circuit pattern corresponding to a separate layer of the IC, and this pattern can be imaged onto a target portion (e.g., a portion including a die, a die, or several dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will contain a network of adjacent target portions that are exposed sequentially. Known photolithography apparatuses include: a so-called stepper, in which the target portion is irradiated by exposing the entire pattern onto each target portion at once; and a so-called scanner, in which each target portion is irradiated by scanning the pattern via a beam in a given direction (“scanning” direction) while simultaneously scanning the substrate parallel to or antiparallel to that direction.

[0005] Before the circuit pattern is transferred from the patterning apparatus to the substrate, the substrate may undergo various processes, such as primer coating, resist coating, and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. This array of processes is used as the basis for fabricating individual layers of devices, such as ICs. The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are expected to ultimately complete individual layers of the device. If several layers are required in the device, the entire process or a variation thereof is repeated for each layer. Ultimately, a device will be present in each target portion of the substrate. These devices are then separated from each other by techniques such as dicing or sawing, thereby allowing individual devices to be mounted on carriers, connected to pins, etc.

[0006] Therefore, fabricating devices such as semiconductor devices typically involves processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the device. These layers and features are typically fabricated and processed using processes such as deposition, photolithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on the substrate and subsequently separated into individual devices. This device fabrication process can be viewed as a patterning process. A patterning process involves using patterning apparatus in a photolithography apparatus, such as optical lithography and / or nanoimprint lithography, to transfer a pattern from the patterning apparatus to the substrate, and the patterning process typically, but optionally, involves one or more associated patterning processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching using an etching apparatus, etching with the pattern, and so on. Summary of the Invention

[0007] According to embodiments of the present invention, a non-transitory computer-readable medium is provided comprising instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process based on the failure rate of a feature. The method includes: obtaining a plurality of features printed on a substrate; grouping the features into a plurality of groups based on indicators; and generating a base failure rate model for the feature groups based on measurement data associated with the feature groups, wherein the base failure rate model identifies the process window associated with the failure rate of the feature groups.

[0008] In some embodiments, the metric includes: (a) a process window for each of the features, wherein the process window is a function of a process variable associated with the corresponding feature; and (b) a parameter associated with the corresponding feature.

[0009] In some embodiments, the process variables include focal length and dose values ​​associated with the device used for the patterning process, and wherein the parameters include critical size (CD) values ​​of the corresponding features.

[0010] In some embodiments, grouping the features includes: (a) for each of the features, obtaining an average CD value for the corresponding feature and a plurality of dose and focal length values ​​associated with the average CD at the edge of the process window of the corresponding feature as an index value, and clustering the features into the feature group based on the index values ​​of the features, wherein features within a particular group have index values ​​that vary within a first threshold.

[0011] In some embodiments, the clustering of the features includes clustering the features using the k-means algorithm.

[0012] In some embodiments, obtaining the features includes: obtaining a plurality of images having the features printed on the substrate, and analyzing the images to select those features that satisfy specified criteria as the plurality of features.

[0013] In some embodiments, the designation criteria include the number of times a feature appears on the entire substrate is less than a first threshold, or the number of times a feature appears in one image of the image is less than a second threshold.

[0014] In some embodiments, generating the baseline failure rate model for the feature group includes: (a) obtaining the average CD of the feature group; (b) determining local CD uniformity (LCDU) data of the feature group as the measurement data associated with the feature group; (c) obtaining, based on the LCDU data: (i) a probability density function of the CD of the feature group, the probability density function being defined as a function of the average CD, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) a CD limit of the failure rate measurement results of the patterning process based on the features in the feature group; (d) determining the estimated failure rate of the feature group based on the CD limit and the probability density function of the CD; and (e) generating the baseline failure rate model, the baseline failure rate model identifying the process window associated with the dose value such that the estimated failure rate of the feature group is less than a predetermined threshold.

[0015] In some embodiments, determining the LCDU data of the feature group includes: determining the LCDU data of the group by: (a) obtaining the LCDU data of each feature in the group across the plurality of images; (b) obtaining the CD mean of each feature in each of the plurality of images; and (c) removing the CD mean from the LCDU data.

[0016] In some embodiments, obtaining the probability density function of the CD of the feature group includes: determining the probability density function of the dose for the dose value based on the variance of the dose value; and converting the probability density function of the dose into the probability density function of the CD based on a transformation function, wherein the transformation function is determined based on the function of the dose.

[0017] In some embodiments, the failure rate involves one or more failures of the feature, including physical failures, transfer failures, and / or delay failures of the feature.

[0018] In some embodiments, the method further includes: storing the basic failure rate model in a database, wherein the database includes multiple basic failure rate models, wherein each basic failure rate model corresponds to a feature group having a specified index value.

[0019] In some embodiments, the method further includes using the base failure rate model to generate a feature-specific failure rate model for a particular feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the particular feature is below a specified threshold.

[0020] In some embodiments, the method further includes generating a feature-specific failure rate model for a specified feature group using the base failure rate model, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specified feature group is below a specified threshold.

[0021] In some embodiments, generating the feature-specific failure rate model includes: (a) receiving measurement data associated with the specified feature, wherein the measurement data includes CD values ​​for the specified feature for a plurality of dose values ​​and focal length values; (b) determining a specified index value from the measurement data, wherein the specified index value is determined as a function of a specified average CD value and a plurality of dose values ​​and focal length values ​​associated with the specified average CD value located at the edge of a process window associated with the specified feature; and (c) selecting a specified baseline failure rate model from a database, wherein the index value of the specified baseline failure rate model matches the specified index value.

[0022] In some embodiments, generating the feature-specific failure model further includes: obtaining a base probability density function of CD from the specified base failure rate model; and adjusting the average CD of the base probability density function based on the specified average CD value to generate an adjusted probability density function.

[0023] In some embodiments, the method further includes determining at least one of a first CD limit or a second CD limit of the patterning process using the adjusted probability density function, wherein if the CD of the specified feature is higher than the first CD limit or lower than the second CD limit, the estimated failure rate of the specified feature is within the specified threshold.

[0024] In some embodiments, the method further includes: obtaining at least one of inter-field CD variation, intra-field CD variation, and probability density function of the CD of the specified feature as CD contour data; and convolving the adjusted probability density function with the CD contour data to generate a convolved probability density function.

[0025] In some embodiments, the method further includes: determining the estimated failure rate of the specific feature based on the first CD limit, the second CD limit, and the convolved probability density function; and generating the feature-specific failure rate model, the feature-specific failure rate model identifying the feature-specific process window such that the estimated failure rate of the specified feature is less than the specified threshold.

[0026] In some embodiments, the method further includes adjusting one or more devices of the patterning process based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

[0027] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process based on a failure rate. The method includes: (a) selecting a plurality of features printed on a substrate; (b) grouping the features into a plurality of groups based on an index, wherein each of the plurality of groups comprises a subset of the features; (c) generating a base failure rate model for the groups based on measurement data associated with features in the groups of the plurality of groups, wherein the base failure rate model identifies a process window associated with an estimated failure rate of the feature group; and (d) generating a feature-specific failure rate model for the specified feature using the base failure rate model and measurement data associated with a specified feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specified feature is below a specified threshold.

[0028] In some embodiments, grouping the features includes: (a) for each of the features, obtaining an average CD value for the corresponding feature and a plurality of dose values ​​and focal length values ​​associated with the average CD located at the edge of the process window of the corresponding feature, and clustering the features into the group based on the index values ​​of the features, wherein the features within a particular group have index values ​​that vary within a first threshold.

[0029] In some embodiments, the method further includes: storing the basic failure rate model in a database, wherein the database includes multiple basic failure rate models, wherein each basic failure rate model corresponds to a feature group having a specified index value.

[0030] In some embodiments, generating the feature-specific failure rate model includes: (a) receiving measurement data associated with the specified feature, wherein the measurement data includes an average CD value of the specified feature for a plurality of dose values ​​and focal length values; (b) determining a specified index value from the measurement data associated with the specified feature, wherein the specified index value is determined as a function of the specified average CD value and a dose value associated with the specified average CD value located at the edge of a process window associated with the specified feature at a specified focal length value; and (c) selecting a specified baseline failure rate model from a database, wherein the index value of the specified baseline failure rate model matches the specified index value.

[0031] In some embodiments, the method further includes: obtaining a base probability density function of CD from the specified base failure rate model; and adjusting the average CD of the base probability density function based on the specified average CD value to produce an adjusted probability density function.

[0032] In some embodiments, the method further includes: determining a first CD limit or a second CD limit of the patterning process using the adjusted probability density function, wherein the estimated failure rate of the specified feature is within the specified threshold when the CD of the specified feature is higher than the first CD limit or lower than the second CD limit.

[0033] In some embodiments, the method further includes: obtaining at least one of inter-field CD variation, intra-field CD variation, and probability density function of the CD of the specified feature as CD contour data; and convolving the adjusted probability density function with the CD contour data to generate a convolved probability density function.

[0034] In some embodiments, the method further includes: determining the estimated failure rate of the specific feature based on the first CD limit, the second CD limit, and the convolved probability density function; and generating the feature-specific failure rate model, the feature-specific failure rate model identifying the feature-specific process window such that the estimated failure rate of the specified feature is less than the specified threshold.

[0035] In some embodiments, the method further includes adjusting one or more devices of the patterning process based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

[0036] In some embodiments, the one or more devices include a photolithography apparatus configured to perform patterning on the substrate based on the feature-specific process window.

[0037] Furthermore, in some embodiments, a method is provided for determining a process window for a patterning process based on a failure rate. The method includes: obtaining a plurality of features printed on a substrate; grouping the features into a plurality of groups based on indicators; and generating a base failure rate model for the feature groups based on measurement data associated with the feature groups, wherein the base failure rate model identifies the process window associated with the failure rate of the feature groups.

[0038] Furthermore, in some embodiments, a method is provided for determining a process window for a patterning process based on a failure rate. The method includes: obtaining a plurality of features printed on a substrate; grouping the feature group into a plurality of groups based on an index, wherein each of the plurality of groups includes a subset of the features; generating a base failure rate model for the group based on measurement data associated with features in the group of the plurality of groups, wherein the base failure rate model identifies a process window associated with an estimated failure rate of the feature group; and generating a feature-specific failure rate model for the specified feature using the base failure rate model and measurement data associated with a specified feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specified feature is below a specified threshold.

[0039] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided, comprising instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process. The method includes: obtaining measurement data of a plurality of features printed on a substrate; deriving characteristic parameters of the plurality of features from the measurement data, wherein the measurement data includes data indicating placement errors of the plurality of features; and generating a failure rate model of the features based on the characteristic parameters associated with the features, wherein the failure rate model is configured to determine a process window corresponding to the failure rate of the features.

[0040] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided, the instructions of which, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process. The method includes: obtaining measurement data of a plurality of features printed on a substrate, wherein the measurement data includes one or more CD values, edge placement error (EPE) values, or placement error (PE) values ​​associated with the features; deriving characteristic parameters of the plurality of features, wherein the characteristic parameters include CDe parameters derived from the CD values ​​and the PE values; and generating a failure rate model of the features based on the characteristic parameters associated with the features, wherein the failure rate model is configured to identify a process window associated with the failure rate of the features.

[0041] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided, the instructions of which, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process. The method includes: obtaining measurement data of a plurality of features printed on a substrate, wherein the measurement data includes one or more CD values, edge placement error (EPE) values, or placement error (PE) values ​​associated with the features; deriving characteristic parameters of the features, wherein the characteristic parameters include PEe parameters derived from target CD values ​​and the PE values; and generating a failure rate model of the features based on the characteristic parameters associated with the features, wherein the failure rate model is configured to identify a process window associated with the failure rate of the features.

[0042] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided having instructions that, when executed by a computer, cause the computer to perform a method for determining critical features printed on a substrate. The method includes: obtaining measurement data of a plurality of features printed on the substrate; obtaining a first set of process windows for the features based on the measurement data, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, wherein the first set of process windows includes a first process window for a first feature among the features; obtaining a plurality of process window indices for each of the features based on the first set of process windows; and identifying those features having one or more of the process window indices that satisfy a specified threshold as critical features.

[0043] Furthermore, in some embodiments, a non-transitory computer-readable medium is provided having instructions that, when executed by a computer, cause the computer to perform a method for determining critical features printed on a substrate. The method includes: obtaining measurement data of a plurality of features printed on a substrate; obtaining a first set of process windows for the features based on the measurement data, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, wherein the first set of process windows includes a first process window of a first feature among the features; obtaining a second set of process windows for the features based on the measurement data, wherein the second set of process windows represents a second characteristic parameter of the feature for a second set of dose values ​​and focal length values, wherein the second characteristic parameter is different from the first characteristic parameter, wherein the second set of process windows includes a second process window of the first feature; performing an overlay operation using the first process window and the second process window to generate a first overlaid process window, wherein the first overlaid process window is the intersection area of ​​the shapes of the first process window and the second process window on a graph; obtaining a plurality of process window indices for each of the features based on the overlaid process windows of the corresponding features; and identifying those features of the features that have one or more of the process window indices that satisfy a specified threshold as critical features.

[0044] In addition, a non-transitory computer-readable medium having instructions recorded thereon, which, when executed by a computer, perform the method as described in any of the above methods. Attached Figure Description

[0045] Figure 1 A lithography apparatus according to an embodiment is schematically depicted.

[0046] Figure 2 An embodiment of a lithography unit or lithography cluster is schematically depicted.

[0047] Figure 3 Exemplary detection devices and measurement techniques are schematically depicted.

[0048] Figure 4 An exemplary detection device is schematically depicted.

[0049] Figure 5 The diagram illustrates the relationship between the irradiation spot of the detection device and the measurement target.

[0050] Figure 6 This schematically depicts the process of deriving multiple variables of interest based on measurement data.

[0051] Figure 7 Examples of categories for processing variables are shown.

[0052] Figure 8 The flow of a patterned simulation method according to an embodiment is illustrated schematically.

[0053] Figure 9 The flowchart of a measurement simulation method according to an embodiment is illustrated schematically.

[0054] Figure 10 The flowchart of a method for determining a defect-based process window according to an embodiment is illustrated schematically.

[0055] Figure 11A The illustration shows an exemplary relationship between measured CD and dose according to an embodiment.

[0056] Figure 11B The illustration shows exemplary dosage PDFs under different dosage settings according to the embodiments.

[0057] Figure 11C The illustration shows exemplary CDPDFs under different dosage settings according to an embodiment.

[0058] Figure 11D The illustration shows exemplary failure modes according to an embodiment.

[0059] Figure 11E The illustration shows another exemplary failure mode according to an embodiment.

[0060] Figure 11F The illustration shows exemplary parameter limits at a dosage setting according to an embodiment.

[0061] Figure 11G The illustration shows exemplary parameter limits and associated failure probabilities under different dosage settings according to the embodiments.

[0062] Figure 11H The figure illustrates an exemplary process window according to an embodiment.

[0063] Figure 12A The figure illustrates an exemplary process window for a first feature according to an embodiment.

[0064] Figure 12B The figure illustrates an exemplary process window for the second feature according to an embodiment.

[0065] Figure 12C The illustration is based on an embodiment. Figure 12A and Figure 12B Overlapping process windows.

[0066] Figure 13 The diagram illustrates a multi-dimensional process window according to an embodiment.

[0067] Figure 14A block diagram of an exemplary method for generating a basic failure rate model and ultimately a feature-specific failure rate model, conforming to various embodiments.

[0068] Figure 15 A flowchart of an exemplary method for generating a basic failure rate model, conforming to various embodiments.

[0069] Figure 16A PDFs illustrating features based on three different index groupings conforming to various embodiments CD Line graph.

[0070] Figure 16B PDFs showing features within groups of three different metrics conforming to various embodiments CD change.

[0071] Figure 16C The illustrations are exemplary graphs depicting the relationship between the number of clusters and indicators, consistent with various embodiments.

[0072] Figure 16D The illustration shows exemplary graphs of the failure rate prediction accuracy of various feature grouping methods conforming to various embodiments.

[0073] Figure 16E A defect-based process window is shown that conforms to the feature groups of various embodiments.

[0074] Figure 17 A flowchart illustrating an exemplary method for generating a basic failure rate model of a feature set, conforming to various embodiments.

[0075] Figure 18 The illustration shows a flowchart of an exemplary method for generating a feature-specific FR model, consistent with various embodiments.

[0076] Figure 19A The illustrations depict defect-based process windows for a given feature, consistent with various embodiments.

[0077] Figure 19B The illustrations depict defect-based process windows for a given set of features, consistent with various embodiments.

[0078] Figure 20 The illustration shows the edge placement error of the target features in various embodiments.

[0079] Figure 21 A flowchart illustrating an exemplary method for generating a basic failure rate model of feature groups based on CDE data, in accordance with various embodiments.

[0080] Figure 22 A flowchart illustrating an exemplary method for generating a basic failure rate model of feature groups based on PEE data, conforming to various embodiments.

[0081] Figure 23 The illustrations show various failure rate process windows corresponding to different embodiments.

[0082] Figure 24 This is a block diagram of an exemplary computer system according to an embodiment.

[0083] Figure 25 This is a flowchart of a process for classifying features according to one or more embodiments.

[0084] Figure 26A An exemplary CD process window is shown, illustrating features according to one or more embodiments.

[0085] Figure 26B An exemplary failure rate (FR) process window is shown, illustrating features according to one or more embodiments.

[0086] Figure 27 The illustrations are based on one or more embodiments. Figure 26B Ellipse fitting of the FR process window.

[0087] Figure 28A The illustration shows a stacking operation that overlays two process windows according to one or more embodiments.

[0088] Figure 28B The illustrations are based on one or more embodiments. Figure 28A Ellipse fitting of the overlaid process window. Detailed Implementation

[0089] A photolithography apparatus is a machine that applies a desired pattern onto a target portion of a substrate. This process of transferring a desired pattern onto a substrate is called a patterning process. During or after a device fabrication process (e.g., a patterning process or a photolithography process), the substrate may undergo various types of measurements. These measurements can determine if the substrate has defects and can establish adjustments to the process and the equipment used in the process.

[0090] Failure rate modeling determines a process window (“defect-based process window”) based on defect criteria for one or more features. For example, a defect-based process window could be a set of dose and / or focal length values ​​where the feature’s defect / failure rate (e.g., the feature’s critical size (CD) varies beyond a desired range) lies within a desired threshold. Failure rate modeling may require a large amount of measurement data (e.g., CD data) for the feature to ensure accurate estimation / prediction of the failure rate. These sampling volumes can be achieved by utilizing measurements with high-volume inspection tools (e.g., scanning electron microscopy (SEM)) for dense features (e.g., repetitive features that occur more than a threshold number of times on the substrate, such as features on static random access memory (SRAM) and dynamic RAM (DRAM). However, such sampling can be challenging for features in random logical structures because: (a) features may not be sufficiently present in every pattern or section of the substrate; (b) features may repeat little from one section of the substrate to another; (c) too many different features are presented on the substrate (e.g., millions or more); or (d) the features are presented too sparsely on the substrate, which can lead to significant time and other resource expenditure for the detection tool. In cases where very few instances of features are presented within a SEM image, accurate local CD uniformity may be difficult to achieve, making it challenging to capture the full CD variation for each focal length / dose value. Therefore, new methods may be needed to determine the defect-based process window developed for features in random logical structures.

[0091] This invention describes a method for obtaining a defect-based process window for features in a random logical structure. For example, the process groups features (e.g., features that are less repetitive and randomly appear on a substrate) into feature groups based on metrics (e.g., process windows associated with the features and CD mean), and determines a base failure rate (FR) model for each feature group as a function of measurement data associated with the features in said feature group. The base FR model indicates a defect-based process window for the features in a particular feature group, which is determined based on the local CD uniformity of the features within that feature group. The base FR model can then be used to generate a feature-specific FR model, specific to the given feature, by convolving the base model with measurement data associated with the given feature. Alternatively, the base FR model can be used to generate a feature group-specific FR model, specific to the given feature group.

[0092] During patterning, some features may be more critical than others. For example, features with smaller process windows are more critical than others. Identifying these critical features and ensuring that a basic FR model is generated for these critical features can help minimize defects in the patterning process and thus help improve the yield of the patterning process. In some embodiments, the random logic structure may have a large number of features (e.g., millions), and identifying critical features in these logic structures may have a significant impact on improving yield.

[0093] This invention describes a method for classifying features based on one or more metrics (e.g., process window metrics). After feature classification, features with metrics that meet a threshold (e.g., below the threshold) can be identified as critical features. Feature groups can be analyzed (e.g., generated as described above) to identify those feature groups with critical features, and a basic FR model can be generated for the identified feature groups.

[0094] Before describing the embodiments in detail, presenting an exemplary environment in which the embodiments may be implemented is instructive.

[0095] Figure 1 An embodiment of a photolithography apparatus (LA) is schematically depicted. The apparatus includes:

[0096] - Irradiation system (irradiator) IL, the irradiation system being configured to modulate the radiation beam B (e.g., UV radiation or DUV radiation);

[0097] - A support structure (e.g., a mask stage) MT, which is configured to support a pattern forming apparatus (e.g., a mask) MA and is connected to a first positioner PM configured to accurately position the pattern forming apparatus according to certain parameters;

[0098] - A substrate stage (e.g., a wafer stage) WT (e.g., WTa, WTb, or both), said substrate stage being configured to hold a substrate (e.g., a wafer coated with resist) W and being connected to a second positioner PW configured to accurately position the substrate according to certain parameters; and

[0099] - A projection system (e.g., a refractive projection lens system) PS, which is configured to project a pattern imparted to a radiation beam B by a patterning device MA onto a target portion C (e.g., comprising one or more dies and often referred to as a field) of a substrate W, the projection system being supported on a reference frame (RF).

[0100] As depicted here, the device is of the transmissive type (e.g., using a transmissive mask). Alternatively, the device may be of the reflective type (e.g., using a programmable mirror array of the type mentioned above, or using a reflective mask).

[0101] The irradiator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithography apparatus can be separate entities. In such cases, the source is not considered part of the lithography apparatus, and the radiation beam is delivered from the source SO to the irradiator IL by means of a beam delivery system BD, which includes, for example, suitable directional mirrors and / or beam expanders. In other cases, such as when the source is a mercury lamp, the source can be part of the apparatus. The source SO and the irradiator IL, together with the beam delivery system BD (if necessary), can be referred to as the radiation system.

[0102] The illuminator IL can alter the intensity distribution of the beam. The illuminator can be arranged to limit the radial range of the radiation beam such that the intensity distribution within an annular region in the pupil plane of the illuminator IL is non-zero. Alternatively, the illuminator IL can be operable to limit the beam distribution in the pupil plane such that the intensity distribution in multiple equidistant segments within the pupil plane is non-zero. The intensity distribution of the radiation beam in the pupil plane of the illuminator IL can be referred to as the illumination mode.

[0103] Therefore, the illuminator IL may include an adjuster AM configured to adjust the (angular / spatial) intensity distribution of the beam. Typically, at least the outer radial range and / or inner radial range (often referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. The illuminator IL may be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular range of segments in the pupil plane where the intensity distribution is non-zero. Different illumination modes can be achieved by adjusting the intensity distribution of the beam in the pupil plane of the illuminator. For example, by limiting the radial and angular ranges of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution can have a multi-pole distribution, such as, for example, a bipolar, quadrupole, or hexapolar distribution. The illumination mode can be obtained, for example, by inserting an optics providing the desired illumination mode into the illuminator IL or by using a spatial light modulator.

[0104] The illuminator IL can be operable to change the polarization of the beam and can be operable to adjust the polarization using an adjuster AM. The polarization state of the radiation beam across the entire pupil plane of the illuminator IL can be referred to as the polarization mode. Using different polarization modes can allow for greater contrast in the image formed on the substrate W. The radiation beam can be unpolarized. Alternatively, the illuminator can be arranged to linearly polarize the radiation beam. The polarization direction of the radiation beam can vary across the entire pupil plane of the illuminator IL. The polarization direction of the radiation can be different in different regions of the pupil plane of the illuminator IL. The polarization state of the radiation can be selected depending on the illuminator mode. For multi-polar illuminator modes, the polarization of each pole of the radiation beam can typically be perpendicular to the position vector of said pole in the pupil plane of the illuminator IL. For example, for bipolar illuminator modes, the radiation can be linearly polarized in a direction substantially perpendicular to the line bisecting the two opposite segments of the bipolar. The radiation beam can be polarized in one of two different orthogonal directions, which can be referred to as the X-polarization state and the Y-polarization state. For a quadrupole illumination mode, the radiation in each pole segment can be linearly polarized in a direction generally perpendicular to the line bisecting the segment. This polarization mode can be called XY polarization. Similarly, for a hexapole illumination mode, the radiation in each pole segment can be linearly polarized in a direction generally perpendicular to the line bisecting the segment. This polarization mode can be called TE polarization.

[0105] In addition, the irradiator IL typically includes various other components, such as the integrator IN and the concentrator CO. The irradiation system may include various types of optical components for guiding, shaping, or controlling radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof.

[0106] Therefore, the irradiator provides a modulated radiation beam B with the desired uniformity and intensity distribution in its cross-section.

[0107] The support structure MT supports the patterning apparatus in a manner dependent on the orientation of the patterning apparatus, the design of the lithography equipment, and other conditions such as whether the patterning apparatus is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic, or other clamping techniques to hold the patterning apparatus. The support structure can be, for example, a frame or stage, which may be fixed or movable as needed. The support structure can ensure that the patterning apparatus is, for example, in a desired position relative to a projection system. Any use of the terms "mask" or "mask" in this invention may be considered synonymous with the more general term "patterning apparatus".

[0108] The term "patterning apparatus" as used herein should be broadly interpreted to refer to any apparatus that can be used to impart a pattern to a target portion of a substrate. In embodiments, a patterning apparatus is any apparatus that can be used to impart a pattern to a radiation beam in the cross-section of the radiation beam to generate a pattern in a target portion of the substrate. It should be noted that, for example, if the pattern imparted to the radiation beam includes phase-shifting features or so-called auxiliary features, the pattern may not correspond precisely to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) generated in the target portion.

[0109] Pattern forming apparatuses can be transmissive or reflective. Examples of pattern forming apparatuses include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in photolithography and include mask types such as binary, alternating phase-shift, and attenuation phase-shift masks, as well as various hybrid mask types. Examples of programmable mirror arrays use a matrix arrangement of small mirrors, each of which can be individually tilted to reflect the incident radiation beam in different directions. The tilted mirrors impart a pattern to the radiation beam reflected by the mirror matrix.

[0110] The term "projection system" as used herein should be broadly interpreted to encompass any type of projection system suitable for the exposure radiation used or for other factors such as immersion in liquids or vacuum, including refractive, reflective, reflective-refractive, magnetic, electromagnetic, and electrostatic optical systems, or any combination thereof. Any use of the term "projection lens" in this invention may be considered synonymous with the more general term "projection system."

[0111] The projection system PS has an optical transfer function that can be non-uniform and may affect the pattern imaged onto the substrate W. For unpolarized radiation, such effects can be described fairly well by two scalar mappings that describe the transmission (apodization) and relative phase (aberration) of the radiation as a function of its position in the pupil plane of the radiation exiting the projection system PS. These scalar mappings, which can be called transmittance mappings and relative phase mappings, can be expressed as a linear combination of the entire set of basis functions. A particularly suitable set is a set of Zernike polynomials that form an orthogonal set of polynomials defined on the unit circle. Determining each scalar mapping may involve determining the coefficients in this expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients can be determined by successively calculating the inner product of the measured scalar mapping with each Zernike polynomial and dividing this inner product by the square of the norm of the Zernike polynomial.

[0112] Transmittance mapping and relative phase mapping are field- and system-dependent. That is, typically, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial location in the image plane of the projection system). The relative phase of the projection system PS in its pupil plane can be determined by projecting radiation from a point-like source, for example, from the object plane of the projection system PS (i.e., the plane of the pattern forming device MA), via the projection system PS and measuring the wavefront (i.e., the trajectory of points with the same phase) using a shearing interferometer. The shearing interferometer is a common-path interferometer and therefore advantageously eliminates the need for a secondary reference beam to measure the wavefront. The shearing interferometer may include a diffraction grating (e.g., a two-dimensional grating) in the image plane of the projection system (i.e., the substrate stage WT) and a detector arranged to detect the interference pattern in a plane conjugate to the pupil plane of the projection system PS. The phase of the interference pattern with respect to the radiation is related to the derivative of the coordinates in the pupil plane in the shear direction. The detector may include an array of sensing elements such as, for example, a charge-coupled device (CCD).

[0113] The projection system (PS) of a photolithography apparatus may not produce visible fringes, and therefore phase-stepping techniques (such as, for example, moving a diffraction grating) can be used to enhance the accuracy of wavefront determination. Stepping can be performed in the plane of the diffraction grating and in a direction perpendicular to the scanning direction of the measurement. The stepping range can be one grating period, and at least three (uniformly distributed) phase steps can be used. Thus, for example, three scan measurements can be performed in the y-direction, with each scan measurement performed in the x-direction for different positions. This stepping of the diffraction grating effectively converts phase changes into intensity changes, thereby allowing phase information to be determined. The grating can be stepped in a direction perpendicular to the diffraction grating (z-direction) to calibrate the detector.

[0114] The diffraction grating can be scanned sequentially in two vertical directions, which may coincide with or be angled (e.g., 45 degrees) to the coordinate system of the projection system PS. The scan can be performed over an integer number of grating periods (e.g., one grating period). The scan averages the phase change in one direction, allowing reconstruction of the phase change in the other direction. This allows the wavefront to be determined as a function of both directions.

[0115] The transmission (apoptosis) of the projection system PS in its pupil plane can be determined by projecting radiation from a point-like source, for example, from the object plane of the projection system PS (i.e., the plane of the pattern forming device MA), via the projection system PS, and by measuring the radiation intensity in a plane conjugate to the pupil plane of the projection system PS using a detector. The same detector used to measure the wavefront to determine aberrations can be employed.

[0116] A projection system PS may include multiple optical (e.g., lens) elements and may also include an adjustment mechanism AM configured to adjust one or more of the optical elements to correct for aberrations (phase changes in the pupil plane across the entire field). To achieve this adjustment, the adjustment mechanism may be operable to manipulate one or more optical (e.g., lens) elements within the projection system PS in one or more different ways. The projection system may have a coordinate system in which the optical axis of the projection system extends in the z-direction. The adjustment mechanism may be operable to perform any combination of: shifting one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. Shifting of optical elements can be performed in any direction (x, y, z, or a combination thereof). Tilting of optical elements is typically performed outside a plane perpendicular to the optical axis by rotation about axes in the x and / or y directions, but for non-rotationally symmetric aspherical optical elements, rotation about the z-axis may be used. Deformation of an optical element can include low-frequency shapes (e.g., astigmatism) and / or high-frequency shapes (e.g., free-form aspherical surfaces). Deformation of an optical element can be performed, for example, by using one or more actuators to apply force to one or more sides of the optical element and / or by using one or more heating elements to heat one or more selected areas of the optical element. Typically, it is not possible to adjust the projection system PS to correct apodization (transmittance variation across the entire pupil plane). Transmittance mapping of the projection system PS can be used when designing a patterning apparatus (e.g., a mask) MA for a lithography apparatus LA. Using computational lithography techniques, the patterning apparatus MA can be designed to at least partially correct apodization.

[0117] Photolithography equipment can belong to the type having two (dual-platform) or more stages (e.g., two or more substrate stages WTa, WTb, two or more patterning apparatus stages, or substrate stages WTa and WTb below the projection system in the absence of a substrate specifically for facilitating, for example, measurement and / or cleaning). In these "multi-platform" machines, additional stages can be used in parallel, or one or more other stages can be used for exposure while preparatory steps are performed on one or more stages. For example, alignment measurements can be performed using an alignment sensor AS and / or level (or horizontal) measurements can be performed using a level sensor (or horizontal sensor) LS.

[0118] Photolithography apparatuses can also fall into the category where at least a portion of the substrate can be covered by a liquid (e.g., water) with a relatively high refractive index to fill the space between the projection system and the substrate. Immersion liquids can also be applied to other spaces within the photolithography apparatus, such as the space between the patterning apparatus and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of a projection system. The term "immersion" as used herein does not imply that structures such as the substrate must be submerged in the liquid, but simply that the liquid is located between the projection system and the substrate during exposure.

[0119] Therefore, in the operation of the photolithography equipment, the radiation beam is regulated and provided by the irradiation system IL. The radiation beam B is incident on a patterning apparatus (e.g., a mask) MA held on a support structure (e.g., a mask stage) MT and is patterned by the patterning apparatus. Having traversed the patterning apparatus MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. By means of a second positioner PW and a position sensor IF (e.g., an interferometer, a linear encoder, a 2-D encoder, or a capacitive sensor), the substrate stage WT can be accurately moved, for example, to position different target portions C in the path of the radiation beam B. Similarly, for example, after mechanical retrieval from the mask library or during scanning, a first positioner PM and another position sensor (the other position sensor is in...) Figure 1 (Not explicitly depicted) can be used to accurately position the pattern forming apparatus MA relative to the path of the radiation beam B. Typically, the movement of the support structure MT can be achieved by means of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) of the components forming the first positioner PM. Similarly, the movement of the substrate stage WT can be achieved using a long-stroke module and a short-stroke module of the components forming the second positioner PW. In the case of a stepper (relative to a scanner), the support structure MT may be connected only to the short-stroke actuator, or it may be fixed. The pattern forming apparatus MA and the substrate W can be aligned using pattern forming apparatus alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks, as illustrated, occupy dedicated target portions, they can be located in the space between the target portions (these marks are called scribing alignment marks). Similarly, in cases where more than one die is provided on the pattern forming apparatus MA, the pattern forming apparatus alignment marks can be located between the dies.

[0120] The depicted device can be used in at least one of the following modes:

[0121] 1. In stepping mode, the entire pattern applied to the radiation beam is projected onto the target portion C in a single exposure while the support structure MT and substrate stage WT remain substantially stationary (i.e., a single static exposure). Subsequently, the substrate stage WT is shifted in the X and / or Y directions, allowing different target portions C to be exposed. In stepping mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

[0122] 2. In scanning mode, the support structure MT and the substrate stage WT are scanned synchronously, while the pattern applied to the radiation beam is projected onto the target portion C (i.e., single dynamic exposure). The speed and direction of the substrate stage WT relative to the support structure MT can be determined by the (reduced) magnification and image inversion characteristics of the projection system PS. In scanning mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning motion determines the height of the target portion (in the scanning direction).

[0123] 3. In another mode, the support structure MT is kept substantially stationary, thereby holding the programmable patterning apparatus in place, and the substrate stage WT is moved or scanned while the pattern imparted to the radiation beam is projected onto the target portion C. In this mode, a pulsed radiation source is typically used, and the programmable patterning apparatus is updated as needed after each movement of the substrate stage WT or between successive radiation pulses during scanning. This mode of operation can be readily applied to maskless lithography utilizing programmable patterning apparatuses, such as programmable mirror arrays of the type mentioned above.

[0124] You can also use combinations and / or variations or completely different usage patterns described above.

[0125] While specific reference may be made to the use of photolithography equipment in IC manufacturing within this invention, it should be understood that the photolithography equipment described herein can have other applications, such as manufacturing integrated optical systems, guiding and detecting patterns for magnetic domain memories, liquid crystal displays (LCDs), thin-film magnetic heads, etc. Those skilled in the art will understand that, in the context of these alternative applications, any use of the terms "wafer" or "die" in this invention can be considered synonymous with the more general terms "substrate" or "target portion," respectively. The substrates mentioned herein can be processed before or after exposure, for example, in a coating and developing system or track (typically a tool for applying a resist layer to the substrate and developing the exposed resist), or in a measurement or inspection tool. Where applicable, the disclosures of this invention can be applied to these and other substrate processing tools. Furthermore, the substrate can be processed more than once, for example, to produce a multilayer IC, such that the term "substrate" as used herein can also refer to a substrate that already comprises multiple processed layers.

[0126] The terms “radiation” and “beam” as used in this invention cover all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having wavelengths of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5 nm to 20 nm) as well as particle beams, such as ion beams or electron beams.

[0127] Various patterns on or provided by a pattern forming apparatus can have different process windows, i.e., the space of processing variables in which the pattern within the generated specification is located. Examples of pattern specifications related to potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlay, resist top loss, resist undercut, and / or bridging. Process windows for all patterns on or in a region of the pattern forming apparatus can be obtained by merging the process windows of each individual pattern (e.g., by overlaying the process windows). The boundaries of the process windows for all patterns contain the boundaries of the process windows of some of the individual patterns. In other words, these individual patterns limit the process windows for all patterns. These patterns may be referred to as “hot spots” or “process window limited patterns (PWLP)”, which are used interchangeably in this invention. Focusing on hot spots is possible and economical when controlling a portion of the patterning process. When hot spots are defect-free, it is most likely that all patterns are defect-free.

[0128] like Figure 2 As shown, the lithography apparatus LA can form part of a lithography unit LC (sometimes also called a lithography cell or lithography cluster), which also includes equipment for performing pre- and post-exposure processes on the substrate. Typically, these devices include one or more spin coaters SC for depositing one or more resist layers, one or more developers DE for developing the post-exposure resist, one or more chillers CH, and / or one or more bake plates BK. A substrate handling device or robot RO picks up one or more substrates from input / output ports I / O1, I / O2, moves these substrates between different process units, and transfers them to the lithography apparatus's feed stage LB. These devices, often collectively referred to as the coating and developing system or track, are controlled by a coating and developing system control unit or track control unit TCU, which in turn is controlled by a management control system SCS, which in turn controls the lithography apparatus via the lithography control unit LACU. Thus, different devices can be operated to maximize throughput and processing efficiency.

[0129] To ensure correct and consistent exposure of a substrate exposed by a lithography apparatus and / or to monitor a patterning process (e.g., a device fabrication process) that includes at least one pattern transfer step (e.g., an optical lithography step), it is desirable to examine the substrate or other objects to measure or determine one or more properties, such as alignment, overlap (which can be, for example, overlap between structures in an overlapping layer or overlap between structures in the same layer that have been provided separately from the layer by, for example, a double patterning process), line thickness, critical dimension (CD), focus offset, material properties, etc. Therefore, a manufacturing facility with a lithography unit LC typically also includes a metrology system (MET) that measures some or all of the substrate W processed in the lithography unit, or other objects in the lithography unit. The metrology system MET can be a component of the lithography unit LC; for example, the metrology system MET can be a component of the lithography apparatus LA (e.g., an alignment sensor AS).

[0130] For example, one or more measured parameters may include: overlap between successive layers formed in or on a patterned substrate; critical dimensions (CD) (e.g., critical linewidth) of features formed in or on a patterned substrate; focusing or focusing error of an optical lithography step; dose or dose error of an optical lithography step; optical aberration of an optical lithography step; etc. Such measurements can be performed on targets inherent to the product substrate itself and / or on dedicated measurement targets provided on the substrate. The measurements can be performed after resist development but before etching, or after etching.

[0131] Various techniques exist for measuring structures formed during patterning, including the use of scanning electron microscopy, image-based metrology tools, and / or various specialized tools. As discussed above, a rapid and non-invasive form of specialized metrology tool is a measuring instrument in which a radiation beam is directed onto a target on the surface of a substrate and the properties of the scattered (diffracted / reflected) beam are measured. By evaluating one or more properties of the radiation scattered by the substrate, one or more properties of the substrate can be determined. This can be referred to as diffraction-based metrology. One such application of diffraction-based metrology is measuring the characteristics of asymmetry within a target. This can be used as a measure of, for example, overlap, but other applications are also known. For example, asymmetry can be measured by comparing relative portions of the diffraction spectrum (e.g., comparing the -1st order with the +1st order in the diffraction spectrum of a periodic grating). This can be done as described above and, for example, as described in U.S. Patent Application Publication No. US2006-066855, which is incorporated herein by reference in its entirety. Another application of diffraction-based metrology is the measurement of the feature width (CD) within a target. Such technology can be achieved using the devices and methods described below.

[0132] Therefore, during device fabrication processes (e.g., patterning or photolithography), substrates or other objects can undergo various types of measurements during or after the process. Measurements can determine if a particular substrate has defects, can adjust the process and equipment used in the process (e.g., aligning two layers on a substrate or aligning a patterning apparatus with a substrate), can measure the performance of the process and equipment, or can be used for other purposes. Examples of measurements include optical imaging (e.g., optical microscopy), non-imaging optical measurements (e.g., diffraction-based measurements, such as the ASML YieldStar metrology tool and the ASMLSMASH metrology system), mechanical measurements (e.g., profilometry using a stylus, atomic force microscopy (AFM)), and / or non-optical imaging (e.g., scanning electron microscopy (SEM)). The SMASH (Smart Alignment Sensor Hybrid) system, as described in U.S. Patent No. 6,961,116, which is incorporated herein by reference in its entirety, uses a self-reference interferometer that generates two superimposed and relatively rotated images of an alignment marker, detects the intensity in a pupil plane that causes interference when the Fourier transform of the images is applied, and extracts position information from the phase difference between the diffraction orders of the two images, the phase difference being represented as an intensity change in the interference order.

[0133] Measurement results can be provided directly or indirectly to the management and control system (SCS). If an error is detected, adjustments can be made to the subsequent exposure of substrates (especially where inspection of one or more other substrates in the batch that will still be exposed can be completed quickly and efficiently) and / or to the subsequent exposure of already exposed substrates. Furthermore, exposed substrates can be stripped and reworked to improve yield, or discarded, thereby avoiding further processing of substrates known to be defective. In cases where only some target portions of the substrate are defective, further exposure can be performed only on those good target portions.

[0134] Within a metrology system (MET), metrology equipment is used to determine one or more properties of a substrate, and specifically, how one or more properties vary between different substrates or between different layers of the same substrate. As mentioned above, metrology equipment can be integrated into a lithography apparatus (LA) or a lithography unit (LC), or it can be a separate device.

[0135] To enable measurement, one or more targets can be provided on the substrate. In embodiments, the targets are specifically designed and may include periodic structures. In embodiments, the targets are part of a device pattern, such as a periodic structure of the device pattern. In embodiments, the device pattern is a periodic structure of a memory device (e.g., a bipolar transistor (BPT), bit line contact (BLC), or similar structure).

[0136] In one embodiment, the target on the substrate may include one or more one-dimensional periodic structures (e.g., gratings) printed such that, after development, the periodic structure features are formed by solid resist lines. In another embodiment, the target may include one or more two-dimensional periodic structures (e.g., gratings) printed such that, after development, the one or more periodic structures are formed by solid resist pillars or vias in the resist. The gratings, pillars, or vias may alternatively be etched into the substrate (e.g., etched into one or more layers on the substrate).

[0137] In an embodiment, one of the parameters of interest in the patterning process is overlap. Overlap can be measured using dark-field scattering metrology, where zero-order diffraction (corresponding to specular reflection) is blocked, and only higher orders are processed. Examples of dark-field metrology can be found in PCT patent applications WO 2009 / 078708 and WO 2009 / 106279, which are hereby incorporated by reference in their entirety. Further developments of the technique have been described in U.S. patent applications US2011-0027704, US2011-0043791, and US2012-0242970, which are hereby incorporated by reference in their entirety. Overlap measurement of small targets is achieved using dark-field detection of diffraction orders. These targets can be smaller than the illumination spot and can be surrounded by a device product structure on a substrate. In an embodiment, multiple targets can be measured in a single radiation trap.

[0138] Figure 3 An exemplary inspection apparatus (e.g., a scatterer) is depicted. The scatterer includes a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The redirected radiation is passed to a spectrometer detector 4, which measures the spectrum 10 of the radiation reflected by the specular surface (intensity as a function of wavelength), as shown, for example, in the graph shown in the lower left corner. Based on this data, the processor PU can perform analysis, for example, through rigorous coupled-wave analysis and nonlinear regression, or through... Figure 3 The structure or profile of the detected spectrum is reconstructed by comparing it with a library of simulated spectra shown in the lower right corner. Typically, for reconstruction, the general form of the structure is known, and several variables are assumed based on knowledge of the process of manufacturing the structure, leaving only a few variables to determine the structure based on the measured data. Such an inspection device can be configured as a normal incidence inspection device or an oblique incidence inspection device.

[0139] Figure 4Another inspection apparatus that can be used is shown. In this apparatus, radiation emitted by radiation source 2 is collimated by using lens system 12 and transmitted through interference filter 13 and polarizer 17, and reflected by partially reflective surface 16 and focused by objective lens 15 onto spot S on substrate W, said objective lens having a high numerical aperture (NA), preferably at least 0.9 or at least 0.95. Immersion inspection apparatus (using a fluid with a relatively high refractive index, such as water) can even have a numerical aperture greater than 1.

[0140] As in a photolithography apparatus (LA), one or more substrate stages can be provided during measurement operations to hold the substrate W. The form of the substrate stages can be similar to... Figure 1 The substrate stage WT is similar to or the same as the substrate stage. In examples where the inspection equipment is integrated with the lithography equipment, the substrate stage can even be the same substrate stage. Coarse positioning and fine positioning devices can be provided to a second positioner PW, which is configured to accurately position the substrate relative to the measurement optics system. Various sensors and actuators are provided, for example, to acquire the position of the target of interest and to bring the target of interest into a position below the objective lens 15. Typically, many measurements will be performed on the target at different locations across the entire substrate W. The substrate support can move in the X and Y directions to obtain different targets and in the Z direction to obtain the desired location of the target relative to the focal length of the optical system. For example, when in practice the optical system can remain substantially stationary (typically in the X and Y directions, but possibly also in the Z direction) and only the substrate moves, it is convenient to consider and describe the operation as if the objective lens is brought into different positions relative to the substrate. Assuming the relative positions of the substrate and the optical system are correct, it is in principle irrelevant which of the substrate and the optical system moves in the real world, or both move, or a combination of a portion of the optical system (e.g., in the Z direction and / or tilt direction) moves while the rest of the optical system remains stationary and the substrate (e.g., in the X and Y directions, and optionally also in the Z direction and / or tilt direction) moves.

[0141] The radiation redirected by the substrate W is then transmitted through the partially reflective surface 16 into the detector 18 for spectrum detection. The detector 18 may be located at the back-projection focal plane 11 (i.e., at the focal length of the lens system 15), or the plane 11 may be re-imaged onto the detector 18 using auxiliary optics (not shown). The detector may be a two-dimensional detector, enabling the measurement of the two-dimensional angular scattering spectrum of the substrate target 30. The detector 18 may be, for example, a CCD or CMOS sensor array, and may use, for example, an integration time of 40 milliseconds per frame.

[0142] A reference beam can be used, for example, to measure the intensity of incident radiation. To perform such a measurement, when the radiation beam is incident on the partially reflective surface 16, a portion of the beam is transmitted through the partially reflective surface 16 as a reference beam toward the reference mirror 14. The reference beam is then projected onto different portions of the same detector 18 or, alternatively, onto different detectors (not shown).

[0143] One or more interference filters 13 can be used to select wavelengths of interest in, for example, the range of 405 nm to 790 nm or even lower (e.g., 200 nm to 300 nm). The interference filters can be adjustable and do not consist of a collection of different filters. Gratings can be used instead of interference filters. Aperture stops or spatial light modulators (not shown) can be positioned in the illumination path to control the range of the angle of incidence of radiation on the target.

[0144] Detector 18 can measure the intensity of redirected radiation at a single wavelength (or a narrow wavelength range), the intensity of redirected radiation separately at multiple wavelengths, or the intensity of redirected radiation integrated over a certain wavelength range. Furthermore, the detector can separately measure the intensity of transversely magnetically polarized radiation and transversely electrically polarized radiation, and / or the phase difference between transversely magnetically polarized radiation and transversely electrically polarized radiation.

[0145] The target 30 on the substrate W can be a one-dimensional grating, which is printed such that, after development, the grating strips are formed by solid resist lines. The target 30 can also be a two-dimensional grating, which is printed such that, after development, the grating is formed by solid resist pillars or vias in the resist. The grating strips, pillars, or vias can be etched into or on the substrate (e.g., etched into one or more layers on the substrate). The pattern (e.g., the pattern of the grating strips, pillars, or vias) is sensitive to changes in the processing during the patterning process (e.g., optical aberrations, focal length changes, dose changes, etc. in the photolithographic projection apparatus (specifically, the projection system PS)) and will show changes in the printed grating. Therefore, the measured data of the printed grating is used to reconstruct the grating. Based on knowledge of the printing steps and / or other inspection processes, one or more parameters of a one-dimensional grating (such as line width and / or shape) or one or more parameters of a two-dimensional grating (such as guide post or via width or length or shape) can be input into a reconstruction process executed by the processor PU.

[0146] In addition to parameter measurement via reconstruction, angle-resolved scattering measurements are also used to measure the asymmetry of features in product and / or resist patterns. A specific application of asymmetry measurement is for overlapping measurements, where target 30 comprises a set of periodic features superimposed on another set of periodic features. Figure 3 or Figure 4 The concept of measuring asymmetry in instruments is described, for example, in U.S. Patent Application Publication US2006-066855, the entire contents of which are incorporated herein by reference. Simply put, while the positions of diffraction orders in the diffraction spectrum of a target are determined solely by the periodicity of the target, asymmetry in the diffraction spectrum indicates asymmetry in individual features constituting said target. Figure 4 In the instrument (where detector 18 can be an image sensor), this asymmetry in the diffraction order is directly presented as an asymmetry in the pupil image recorded by detector 18. This asymmetry can be measured by digital image processing in unit PU and can be calibrated relative to a known overlap value.

[0147] Figure 5 The diagram illustrates a plan view of a typical target 30, and Figure 4 The range of the illumination spot S in the device. To obtain a diffraction spectrum without interference from surrounding structures, in an embodiment, the target 30 is a periodic structure (e.g., a grating) larger than the width (e.g., diameter) of the illumination spot S. The width of the spot S may be smaller than the width and length of the target. In other words, the target is illuminated "underfilled," and the diffraction signal essentially lacks any signal from product features and the like located outside the target itself. Illumination arrangements 2, 12, 13, 17 can be configured to provide illumination of uniform intensity across the entire back focal plane of the objective lens 15. Alternatively, illumination can be restricted to an axial or off-axial direction, for example, by including an aperture stop in the illumination path.

[0148] Figure 6 An exemplary process is schematically depicted for determining the values ​​of one or more variables of interest for a target pattern 30′ based on measurement data obtained using measurements. Radiation detected by detector 18 provides the measured radiation distribution 108 for the target 30′.

[0149] For a given target 30′, the radiation distribution 208 can be calculated / simulated using, for example, a numerical Maxwell solver 210 based on a parametric model 206. The parametric model 206 illustrates exemplary layers of various materials constituting and associated with the target. The parametric model 206 may include one or more variables representing characteristics and layers of the target under consideration, which can vary and be derived. Figure 6As shown, one or more of the variables may include the thickness t of one or more layers, the width w (e.g., CD) of one or more features, the height h of one or more features, and / or the sidewall angle α of one or more features. Although not shown, one or more variables may also include, but are not limited to: the refractive index of one or more layers (e.g., real or complex refractive index, refractive index tensor, etc.), the extinction coefficient of one or more layers, the absorptivity of one or more layers, resist loss during development, the base of one or more features, and / or the line edge roughness of one or more features. The initial values ​​of the variables may be initial values ​​expected for the target being measured. The measured radiation distribution 108 is then compared with the calculated radiation distribution 208 at 212 to determine the difference between the two. If a difference exists, the values ​​of one or more variables in the parameterized model 206 can be changed to calculate a new calculated radiation distribution 208. This new calculated radiation distribution 208 is then compared with the measured radiation distribution 108 until a sufficient match exists between the measured radiation distribution 108 and the calculated radiation distribution 208. At this point, the values ​​of the variables in the parameterized model 206 provide a good or optimal match for the geometry of the actual target 30′. In this embodiment, a sufficient match exists when the difference between the measured radiation distribution 108 and the calculated radiation distribution 208 is within a tolerance threshold.

[0150] The variables in the patterning process are called "process variables". The patterning process can include the upstream and downstream processes of the actual transfer of the pattern in the photolithography equipment. Figure 7Exemplary categories of processing variables 370 are shown. The first category can be variables 310 of the lithography apparatus or any other apparatus used in the lithography process. Examples of this category include variables of the lithography apparatus's illumination, projection system, substrate platform, etc. The second category can be variables 320 of one or more processes performed during the patterning process. Examples of this category include focus control or focus measurement, dose control or dose measurement, bandwidth, exposure duration, development temperature, chemical composition used in development, etc. The third category can be variables 330 of the design layout and its implementation in the patterning apparatus or its implementation using the patterning apparatus. Examples of this category can include the shape and / or position of auxiliary features, adjustments applied by resolution enhancement techniques (RET), the CD of mask features, etc. The fourth category can be variables 340 of the substrate. Examples include characteristics of the structure beneath the resist layer, the chemical composition and / or physical dimensions of the resist layer, etc. The fifth category can be characteristics 350 of the time-varying nature of one or more variables in the patterning process. Examples of this category include characteristics of high-frequency platform movement (e.g., frequency, amplitude, etc.), high-frequency laser bandwidth changes (e.g., frequency, amplitude, etc.), and / or high-frequency laser wavelength changes. These high-frequency changes or movements are high-frequency changes or movements that exceed the response time of the mechanism used to adjust the fundamental variables (e.g., platform position, laser intensity). A sixth category can be characteristics 360 of upstream or downstream processes in pattern transfer within a photolithography apparatus, such as spin coating, post-exposure baking (PEB), development, etching, deposition, doping, and / or encapsulation.

[0151] As will be understood, many, if not all, of these variables will affect the parameters of the patterning process, and often the parameters of interest. Non-limiting examples of parameters for the patterning process may include critical dimension (CD), critical dimension uniformity (CDU), focal length, overlap, edge position or placement, sidewall angles, pattern shift or offset, etc. Often, these parameters express errors relative to nominal values ​​(e.g., design values, averages, etc.). The parameter values ​​may be values ​​of individual pattern characteristics or statistics of a set of pattern characteristics (e.g., mean, variance, etc.).

[0152] The values ​​of some or all of the processing variables, or parameters related to the processing variables, can be determined by suitable methods. For example, the values ​​can be determined based on data obtained using various measurement tools (e.g., substrate measurement tools). The values ​​can be obtained from various sensors or systems in the patterning process equipment (e.g., sensors such as leveling or alignment sensors in lithography equipment, control systems of lithography equipment (e.g., substrate or patterning stage control systems), sensors in coating and developing system tools or track tools, etc.). The values ​​can also originate from the operator of the patterning process.

[0153] Figure 8 The diagram illustrates an exemplary flowchart for modeling and / or simulating portions of the patterning process. As will be understood, the model may represent different patterning processes and need not include all the models described below. Source model 1200 represents the optical characteristics of the illumination of the patterning apparatus (including radiation intensity distribution, bandwidth, and / or phase distribution). Source model 1200 may represent the optical characteristics of the illumination, including but not limited to: numerical aperture setting, illumination sigma (σ) setting, and any particular illumination shape (e.g., off-axis radiation shape, such as toroidal, quadrupole, bipolar, etc.), where σ (or sigma) is the outer radial extent of the illuminator.

[0154] The projection optics model 1210 represents the optical characteristics of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). The projection optics model 1210 can represent the optical characteristics of the projection optics, including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0155] The patterning apparatus / design layout model module 1220 captures how the design features are arranged in a pattern within the patterning apparatus and may include a detailed representation of the physical properties of the patterning apparatus, as described, for example, in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. In an embodiment, the patterning apparatus / design layout model module 1220 represents the optical characteristics (including changes in radiation intensity distribution and / or phase distribution caused by a given design layout) of a design layout (e.g., a device design layout corresponding to features of an integrated circuit, memory, electronic device, etc.), which is a representation of the arrangement of features on or formed by the patterning apparatus. Since the patterning apparatus used in a photolithography projection apparatus can be modified, it is desirable to separate the optical properties of the patterning apparatus from the optical properties of the rest of the photolithography projection apparatus, which includes at least irradiation devices and projection optics. The goal of the simulation is often to accurately predict, for example, edge placement and CD, which can then be compared with the device design. The device design is typically defined as a pre-OPC patterning apparatus layout and is provided in a standardized digital file format such as GDSII or OASIS.

[0156] The spatial image 1230 can be simulated based on the source model 1200, the projection optics model 1210, and the pattern forming apparatus / design layout model 1220. The spatial image (AI) is the radiation intensity distribution at the horizontal plane of the substrate. The optical properties of the photolithography projection apparatus (e.g., the properties of the irradiator, the pattern forming apparatus, and the projection optics) define the spatial image.

[0157] A resist layer on a substrate is exposed using a spatial image, and the spatial image is transferred to the resist layer as a potential "resist image" (RI). The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. A resist image 1250 can be simulated using a resist model 1240 based on the spatial image 1230. An example of using a resist model to calculate a resist image based on a spatial image can be found in U.S. Patent Application Publication No. 2009-0157360, the disclosure of which is hereby incorporated by reference in its entirety. Resist models typically describe the effects of chemical processes occurring during resist exposure, post-exposure baking (PEB), and development in order to predict, for example, the profile of resist features formed on the substrate, and therefore are generally only related to these properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). In an embodiment, the optical properties of the resist layer can be captured as part of the projection optics model 1210. These optical properties include, for example, refractive index, film thickness, propagation, and polarization effects.

[0158] Therefore, typically, the connection between the optical model and the resist model is the simulated spatial image intensity within the resist layer, which originates from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections within the resist film stack. The radiation intensity distribution (spatial image intensity) is transformed into a latent image, the "resist image," by absorbing incident energy, which is further modified by diffusion processes and various loading effects. A sufficiently fast and efficient simulation method for full-chip applications approximates the actual three-dimensional intensity distribution within the resist stack using a two-dimensional spatial (and resist) image.

[0159] In an embodiment, a resist image can be used as input to a pattern transfer post-process model module 1260. The pattern transfer post-process model 1260 defines the performance of one or more resist development post-processes (e.g., etching, development, etc.).

[0160] Simulation of the patterning process can, for example, predict contours, CD (cutoff point), edge placement (e.g., edge placement error), etc., in the resist and / or etched image. Therefore, the goal of the simulation is to accurately predict, for example, the edge placement of the printed pattern, and / or the spatial image intensity slope, and / or CD, etc. These values ​​can be compared with the intended design to, for example, correct the patterning process, identify locations where defects are predicted to occur, etc. The intended design is typically defined as a pre-OPC design layout that can be provided using a standardized digital file format such as GDSII or OASIS or other file formats.

[0161] Therefore, the model formula describes most (if not all) of the known physical and chemical effects of the entire process, and each model parameter in the model parameters is expected to correspond to a different physical or chemical effect. Thus, the model formula sets an upper limit on how well the model can be used to simulate the entire manufacturing process.

[0162] Figure 9 The diagram illustrates an exemplary flowchart for modeling and / or simulating a measurement process. As will be understood, the following models may represent different measurement processes and need not include all the models described below (e.g., some models may be combined). Source model 1300 represents the optical characteristics of the illumination of the measurement target (including radiation intensity distribution, radiation wavelength, polarization, etc.). Source model 1300 may represent the optical characteristics of the illumination, including but not limited to wavelength, polarization, illumination sigma (σ) setting (where σ (or sigma) is the radial range of illumination in the illuminator), any particular illumination shape (e.g., off-axis radiation shapes, such as toroidal, quadrupole, bipolar, etc.), etc.

[0163] The measurement optics model 1310 represents the optical characteristics of the measurement optics (including changes in the radiation intensity distribution and / or phase distribution caused by the measurement optics). The measurement optics model 1310 can represent the optical characteristics of the illumination of the measurement target by the measurement optics, and the optical characteristics of the redirected radiation from the measurement target towards the detector of the measurement device. The measurement optics model can represent various characteristics involving the illumination of the target and the transfer of the redirected radiation from the measurement target towards the detector, including aberrations, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc.

[0164] The measurement target model 1320 can represent the optical characteristics of illumination redirected by the measurement target (including changes in the intensity and / or phase distribution of the illumination radiation caused by the measurement target). Therefore, the measurement target model 1320 can model the conversion from illumination radiation to redirected radiation from the measurement target. Thus, the measurement target model can simulate the resulting illumination distribution of the redirected radiation from the measurement target. The measurement target model can represent various characteristics (related to the illumination of the target and the radiation redirected according to the measurement), including one or more refractive indices, one or more physical dimensions of the measurement, the physical layout of the measurement target, etc. Since the measurement target used can be varied, it is necessary to separate the optical properties of the measurement target from the optical properties of the rest of the measurement equipment, including at least the irradiator, projection optics, and detector. The simulated target is often used to accurately predict, for example, intensity, phase, etc., which can then be used to derive parameters of interest in the patterning process, such as overlap, CD, focal length, etc.

[0165] A pupil or spatial image 1330 can be simulated based on the source model 1300, the measurement optics model 1310, and the measurement target model 1320. The pupil or spatial image is the radiation intensity distribution at the detector level. The optical properties of the measurement optics and the measurement target (e.g., illumination, properties of the measurement target and the measurement optics) define the pupil or spatial image.

[0166] The detector of the measurement device is exposed to a pupil or spatial image and detects one or more optical properties of the pupil or spatial image (e.g., intensity, phase, etc.). The detection model module 1340 represents how radiation from the measurement optics is detected by the detector of the measurement device. The detection model can describe how the detector detects the pupil or spatial image and can include signal-to-noise ratio, sensitivity to incident radiation on the detector, etc. Therefore, typically, the connection between the measurement optics model and the detector model is a simulated pupil or spatial image derived from the illumination of the measurement target by the optics, the redirection of radiation by the target, and the transfer of the redirected radiation to the detector. The radiation distribution (pupil or spatial image) is converted into a detection signal by absorbing incident energy on the detector.

[0167] The simulation of the measurement process can, for example, be based on the detection of the pupil or spatial image by the detector to predict the spatial intensity signal, spatial phase signal, etc. at the detector, or to predict other calculated values ​​from the detection system, such as overlap, CD, etc. Therefore, the goal of the simulation is to accurately predict, for example, the detector signal corresponding to the measurement target or derived values ​​such as overlap, CD, etc. These values ​​can be compared with expected design values ​​to, for example, correct the patterning process, identify the locations where defects are predicted to occur, etc.

[0168] Therefore, the model formula describes most (if not all) of the known physical and chemical effects of the entire measurement process, and each model parameter in the model parameters is expected to correspond to a different physical and / or chemical effect in the measurement process.

[0169] Various patterns set on or provided by the patterning apparatus can have different process windows, i.e., the space of processing variables in which the pattern within the specification will be generated. Examples of pattern specifications associated with potential systematic defects include checking for necking, line pullback, line thinning, CD, edge placement, overlay, resist top loss, resist undercut, and / or bridging. For example, a process window is defined on two processing variables (i.e., dose and focal length) such that the CD obtained after patterning is within ±10% of the desired CD of the characteristics of the pattern. Process windows for all patterns on the patterning apparatus or its area can be obtained by merging the process windows of individual patterns (e.g., overlaying the process windows).

[0170] Typically, a pattern may include several instances of one or more features arranged in a certain way to form the pattern (e.g., 10 features of feature A). 6 10 instances, feature B 4 (Examples, etc.) During the patterning process, one or more features may fail under certain conditions, such as dose / focal length settings, resulting in defects in the substrate and thus affecting the yield of the patterning process. Therefore, it is important to select an appropriate range of dose / focal length values ​​or processing windows to achieve the desired or selected yield. For example, a high yield (e.g., 99.9%) or a yield range (e.g., 98% to 99.99%) can be selected by, for example, the designer or manufacturer.

[0171] This disclosure describes a method for obtaining a process window based on desired yield and / or defect criteria for one or more features. For example, the process window may be a set of dose and / or focal length values ​​(also referred to as dose / focus settings) that are sensitive to the failure of individual features and / or the desired yield of the patterning process.

[0172] Figure 10 This is a flowchart of process 1600 used to determine the process window based on the desired die yield and / or failure rate of the patterning process. Process 1600 begins when measurements of parameters 602 (e.g., CD, overlap, etc.) and process variables 1604 (e.g., dose, focus, etc.) of the patterning process are obtained. For example, the measurements of the process variables may include approximately 20 dose settings (i.e., a range of dose values), and features (which appear in the pattern, for example, 10) 6The measurement results of the parameters (times) can include CD values ​​for approximately 1000 instances with characteristics set for each dose. Therefore, approximately 1000 × 20 CD values ​​can be measured. This disclosure is not limited to the total number of measurements. The number of instances can be chosen to achieve the desired accuracy of the variance. For example, for a large number of instances and a normal distribution, the standard deviation is approximately 1 / √(2 × number of instances), such that the standard deviation of 1000 instances results in an error of approximately 2% of the estimated standard deviation at a 99.7% confidence interval (i.e., 3σ).

[0173] Based on measurements of parameters (e.g., CD) and process variables (dose), a functional relationship 610 between the parameters (e.g., CD) and process variables (e.g., dose) can be determined and / or obtained in process P10. For example, the functional relationship 610 can be based on a mathematical model of statistical analysis such as linear regression analysis. In embodiments, the functional relationship can be linear or non-linear, such as a polynomial function, trigonometric function, etc. An exemplary functional relationship between CD and dose is described below.

[0174]

[0175] In the exemplary functional relation (1), (i)f CD (ii)n refers to the parameter CD, which is defined as a function of dose (d), and (iii)a n This refers to the polynomial d of the nth dose of CD. n Sensitivity. In an embodiment, the functional relationship (1) may be based on, for example, a curve fitting algorithm that minimizes the mean square error between the measured value and the fitted value. In an embodiment, the functional relationship may be a linear, polynomial, or other nonlinear function of the process variable. In an embodiment, the measurement result 602 may also be used, for example, to determine the variance of the parameter values ​​using different functional relationships, with the intention of suppressing noise in the variance of the parameter values.

[0176] In another example, Figure 11A The diagram illustrates a Bossung curve 702 (which is an example of a functional relationship 610) defining the relationship between the measured CD and the dose value. This can be applied to values ​​between 40 mJ / cm². 2 Up to 60mJ / cm 2 The Poisson curve 702 is obtained by applying various dose settings (e.g., 20 dose settings). For each dose setting, approximately 1000 CD values ​​can be obtained, which may be between 12 nm and 24 nm. In an embodiment, the Poisson curve can be obtained using modeling and / or simulation of a patterning process.

[0177] Return to reference Figure 10In process P20, a probability density function (PDF) 620 for each setting of the process variable can be calculated. Hereinafter, for the purpose of understanding the concept and simplifying the discussion, the probability density function (PDF) 1620 for each setting of the process variable is referred to as the process variable PDF 620. The process variable PDF 620 is defined as a function of the process variable and its variations. The process variable PDF 620 enables the capture of the effects of any variations in the dose setting that may ultimately affect the parameters. Variations in the process variable for each setting may occur, for example, at a specific moment during the patterning process or may be inherent to the process variable (e.g., dose). These variations may affect the parameters of the patterning process, leading to, for example, feature failure in some cases. In embodiments, the process variable PDF 1620 may be a normal distribution, a Poisson distribution, or other standard distribution.

[0178] In an embodiment, the process variable PDF 620 may be based on the functional relationship between the parameter and the process variable (e.g., f). CD (d) The distribution is calculated. This calculation can be performed by modifying / replacing, for example, the variance of a standard distribution (e.g., a normal distribution) using the calculated variance. The variance can be determined based on the parameter variance (e.g., σ). CD 2 (d) and functional relationships (e.g., f) CD (d) is used to calculate the variance. For example, in the case of parameters CD and dose d, the variance of the dose can be limited by the following variance equation (2):

[0179]

[0180] In the above difference equation (2), (i)σ d It is the standard deviation of the dose (which can also be used interchangeably to refer to the variance); (ii) σ CD It is the standard deviation of CD (which can also be used interchangeably to refer to variance); and (iii) the partial derivative term. Provides a conversion from the variance of CD to the variance of the dose under a specific dose setting.

[0181] For example, refer to Figure 11B It is possible to obtain 45 mJ / cm at the first dose setting. 2 The first dose of PDF 721 was administered under these conditions, and the second dose was set at 50 mJ / cm². 2 The second dose of PDF 722 in the case, and at a dose setting of 55 mJ / cm 2 The third dose of PDF 723, etc., under these circumstances. Dose changes can be observed based on the change in CD set for each dose. For example, at lower doses (e.g., at 45 mJ / cm²),2 In the case of ) change (e.g., 3σ) d It is approximately 3.2 mJ / cm 2 At higher doses (e.g., 55), the variation (e.g., 3σ) d It is approximately 2.5 mJ / cm 2 Therefore, the inverse determination of dose change can be obtained based on the CD value under a specific dose setting.

[0182] The variance of the PDF used to calculate process variables (e.g., dosage) (e.g., in equation (2)) allows for the consideration of random variations in the patterning process that cause deviations in parameters (i.e., variations that cannot be explained by, for example, physical effects of the device). The process variable PDF allows for the determination of improved dosage settings for the patterning process and can ultimately reduce defects and improve the yield of the patterning process.

[0183] Return to reference Figure 10 In process P30, the probability density function (PDF) 630 of the patterned process parameters for each setting of the process variables can be determined and / or obtained based on the process variable PDF 620 for each setting of the process variables (e.g., from process P20) and based on the functional relationship (e.g., from process P10). In the following text, for the purpose of understanding the concept and simplifying the discussion, the probability density function (PDF) 630 for each setting of the process variables is referred to as the parameter PDF 630.

[0184] According to an embodiment, parameter PDF 630 can be non-standardly distributed when calculated from process variable PDF 620. Using such a non-standard distribution also allows for the consideration of any random variations in the patterning process that may cause deviations in the parameter, thus providing an improved estimate of the probability that the parameter (e.g., CD) value will fall within the expected range of each process variable setting (e.g., dosage) in the patterning process. This probability can be further used to identify the probability of defects and processing windows to reduce defects and effectively improve yield.

[0185] In an embodiment, the parameter PDF 630, such as CD PDF, can be calculated using the dose PDF and a conversion function (or conversion factor) based on the following equation (3), which converts the dose PDF into CD PDF:

[0186]

[0187] In equation (3) above, (i)PDF CD (CD, d) refers to CD PDF (which is an example of parameter PDF 630) and is a function of dose (d), (ii)g d(CD) is the inverse function of the functional relationship between dose and CD 610 (e.g., in equation (1)), (iii) PDF d (g d (CD), σ d (g d (CD))) is the process variable PDF 620, where σ d (g d (CD) is based on g d The variance of (CD) can be calculated, for example, using an equation similar to equation (2), where the transformation function (or transformation factor) can be g. d (CD) partial derivatives, and (iv) the absolute values ​​of the partial derivative terms (i.e., ) is a transformation function (or transformation factor) that converts the process variable PDF into the parameter PDF under a specific dose setting.

[0188] Therefore, the dose PDF is converted into a CD PDF, which can be further used to calculate the probability that the CD will be within the desired range for each dose setting, the failure probability of the patterning process, or other statistically significant values. According to this disclosure, the calculation of the failure probability (or failure rate) is further discussed with respect to process P60.

[0189] In an embodiment, when the original functional relationship 610 can be non-monotonic (i.e., a multi-process value can produce the same parameters), the right-hand side of Equation 3 will be replaced by the sum of the multi-process values ​​(e.g., dosage).

[0190] Figure 11C Examples of CD PDF 630 obtained using, for example, equation (3) above under different dose settings are illustrated. For example, a first dose setting of 45 mJ / cm² can be obtained. 2 In the case of the first CD PDF 731, the second dose was set at 50 mJ / cm. 2 The second CD PDF 732 under the condition, and at a dose setting of 55 mJ / cm 2 In cases such as the third CD PDF 733, etc. Figure 11C The standard normal CD PDF for each dose setting is also illustrated to show the deviation of the calculated CD PDF from the standard or normal distribution of the assumed normal operating conditions, which may differ from normal conditions. Therefore, such CD PDFs (e.g., 731, 732, 733) provide a more realistic estimate (e.g., an estimate of the probability of failure) compared to the assumed normal operating conditions.

[0191] Return to reference Figure 10In process P40, the failure rate of a feature with respect to the parameter (e.g., CD) can be obtained / measured for each setting of the process variable (e.g., dosage). In this disclosure, the term "feature failure rate versus failure probability" can be used interchangeably. In embodiments, the failure rate of an individual feature can be expressed, for example, as parts per million (ppm) or parts per billion (ppb) of the features of the pattern. In other words, 1 ppm can mean that one feature is expected to fail in one million occurrences. In embodiments, the failure rate can correspond to different failure modes associated with an individual feature, such as physical failure, transfer failure, and delayed failure. Feature failure can be determined based on, for example, failure analysis of SEM images of the substrate or by electrical measurements.

[0192] In embodiments, physical failure can refer to failure that can be quantified based on the physical aspects of a feature, such as the resist physically failing at a certain CD and / or a feature having a certain CD failing to transfer to the substrate. Examples include the aspect ratio of the post (i.e., the ratio of vertical thickness to horizontal width), the thickness of the resist, the size of the contact hole, and other measurable parameters. Based on measurement, physical failure can indicate that the CD of a feature has an aspect ratio greater than a threshold (e.g., >3), which causes the feature to fail. For example, in Figure 11D In the process of pattern transfer or resist development, the guide post 771 is bent at a certain angle relative to the substrate because the aspect ratio is greater than 3. Therefore, although the guide post is transferred to the substrate, physical deformation occurs.

[0193] In some cases, the desired pattern may be transferred only partially or not at all to the substrate. This failure can be termed a transfer failure. For example, out of 20 contact holes, only 15 may be transferred, and 5 contact holes may be missing, both of which were originally present in the resist. Such missing holes can be termed a transfer failure. In embodiments, transfer failure may occur due to parameters exceeding the threshold limits of the patterning process. For example, in Figure 11E In some cases, the contact holes may be too small (e.g., less than 5 nm) and the resist layer may be relatively thick, which does not allow for the transfer of such small contact holes. Therefore, incomplete pattern transfer can be observed; for example, at foot 772, the contact holes may be blocked at the substrate. In another embodiment, necking 173 can be observed, where the top layer of resist may not be removed, resulting in incomplete holes at the substrate. In either case, holes cannot be formed through the resist to the substrate. This transfer failure may be due to, for example, contact holes that are too small to transfer to the next layer, or there may be excessive etch load due to resist thickness or type.

[0194] Delayed feature failure can occur in the next step of the patterning process because a parameter (e.g., CD) exceeds its specified limits in the current processing step. For example, feature failure may occur during the development stage after the patterning process.

[0195] It is understood that this disclosure is not limited to one type of failure. Furthermore, in some cases, multiple types of failure can be used interchangeably to refer to a general failure. In embodiments, transfer failure may also be referred to as physical failure, or delay failure may also be referred to as physical failure. This disclosure is not limited to one type of failure, and generally any deviation from the design intent exceeding a certain threshold can be considered a failure.

[0196] In an embodiment, the failure rate can be measured for failures occurring at the ends of the curve fitted between the parameters and the process variables. For example, as Figure 11F and Figure 11G As shown, failure rates can be measured with process parameters R1, R2, R3, R4, and R5. The failure measurement location can be defined as a point on curve 702 that exceeds a certain dose value for failure, for example, based on experience or previously observed. In this example, failure rate measurements are defined at both ends of the curve, i.e., at doses higher than approximately 55 mJ / cm². 2 The dose value is below or approximately 43 mJ / cm 2 The dose value. In an embodiment, one or more failures of a feature can be weighted based on the frequency of a specific failure to produce a weighted failure rate of the feature. For example, if at approximately 43 mJ / cm 2 Contact hole failures occur more frequently under certain dosage settings, so higher weights can be assigned to such failures under those dosage settings. In another embodiment, a weighted function of the process variables can be obtained / generated based on the correlation between one or more failures and process variables. For example, a weighted function can be assigned to lower doses (e.g., below 40 mJ / cm² in the example herein). 2 A higher weight is assigned because higher failure rates can be observed at this dose compared to other doses. Therefore, the weighted parameter limit of the parameters can be calculated based on the weighting function of the process variables, and the process window can then be calculated.

[0197] In embodiments, failure rate measurements can be performed selectively based on process variables and parameter values. Additionally, the failure of one or more features can be correlated with parameters and / or process variables (e.g., through linear regression or other statistical techniques). For example, one or more features may be sensitive to higher doses, and one or more features may be sensitive to lower doses. In other words, for example, feature A at 50 mJ / cm²... 2At a dose compared to 45 mJ / cm 2 Higher doses can result in a higher failure probability. During the patterning process, the dose may vary between different dies, so the same feature (e.g., feature A) can be exposed under different dose conditions, which ultimately affects the failure probability of the feature and therefore the failure probability of different dies. Thus, depending on the number of feature instances in the die and the dose, the failure probability may vary between different dies. In other words, for example, if a particular feature is more likely to fail under high dose conditions and the substrate dies include 10... 6 Given this characteristic, the failure rate of the die may be high relative to that of a die exposed at relatively low doses (e.g., 1 / 10). 4 ).

[0198] Alternatively, the failure may be related to parameters such as CD (Displacement Capacity). For example, the CD of a contact hole may be too small (e.g., less than a threshold, such as less than 10 nm), resulting in foot formation (i.e., the hole is not transferred to the substrate); the CD of a post may be too large, causing the post to bend; the CD (i.e., thickness) of the resist layer may be too large, resulting in necking; or an excessively large CD may lead to the observation of random via contacts; and so on. This correlation also makes it possible to determine the failure rate of each individual feature based on parameters and / or process variables. Therefore, based on the failure rate of a feature, a sampling scheme for optimizing measurements can be defined.

[0199] In an embodiment, a failure rate map can be generated / obtained by modeling and / or simulating the relationship between failure rate and process variables (e.g., dose) based on the failure rate of a feature (e.g., feature A) and scanner data (e.g., dose values) across the entire die and / or substrate. Similarly, a failure rate map for the entire substrate can be determined based on the failure rate of the pattern and / or die. Based on this failure rate map, a sampling scheme for measurements on the substrate can be defined. For example, the sampling scheme can be modified to perform more measurements at certain dose values ​​at locations on the substrate with a relatively high failure probability, thus reducing the measurement burden and improving the efficiency of the patterning process. Furthermore, process variables such as dose values ​​can be modified based on the failure rate of one or more features to maximize yield.

[0200] According to the embodiments, failure rate, process variables, and parameters may be related. For example, failure rate, dose value, and CD are related, so a CD limit can also be determined for each dose value to limit failure and increase the yield of the patterning process. The process for generally determining such CD limits or parameter limits is then discussed.

[0201] In process P50, parameter limits can be calculated based on the measured failure rate and parameter PDF (such as 630) for each setting of the process variable. Parameter limits can be about... Figure 11F and Figure 11G A further discussion of the common theoretical limit is that, in the case of the common theoretical limit, the characteristic failure is less than a predetermined number or percentage (e.g., 50%) for each setting of the process variable. The parameter limit can be determined iteratively based on the cumulative distribution of the parameter PDF. An example equation for determining the CD limit is provided in the following equation (4):

[0202]

[0203] In equation (4) above, (i)R fail It is the failure rate for each set of process variables (i.e., dose); (ii) PDF CD (CD, d) refers to parameter PDF, such as parameter PDF 630 obtained in process P30; and (iii) CDF CD (CD lim d) is in CD lim Location and beyond CD lim Provide a PDF showing the total probability of failure under certain circumstances. CD The cumulative distribution function of (CD, d). In the embodiment, PDF CD (CD, d) can be a normal distribution as previously discussed. The parameter limits can be determined using corresponding failure rates under one or more settings of the process variable (e.g., dosage), where failure features do not affect each other's failure rates (i.e., each failure can be considered an "isolated failure" or "isolated failure"), and there are still a sufficient number of failure features to limit the variance of the measured or determined failure rate. A typical failure rate can be approximately 1%. In embodiments, the parameter limits can be common parameter limits determined based on multiple probability density functions of the parameters, each probability density function of the parameters being determined under a specific setting of the process variable, for example, as... Figure 11G As shown in the diagram.

[0204] Further information Figure 11F and Figure 11G The parameter CD is used to graphically interpret the determination of the parameter limit using equation (4). In the example, the measured failure rate for each set value above a predetermined threshold (e.g., greater than or equal to 50%) can be compared with the failure rate using CDF. CD (CD lim The calculated total failure rate (d) is compared to determine the CD characteristic for each dose. lim This CD characteristic limThis indicates that, under specific dosage conditions, the characteristic CD value may not exceed CD. lim Otherwise, a high failure rate can be observed. For example, CD lim It can be 23.5 nm. The parameter limit set at a 50% failure rate represents the theoretical process limit in the absence of random or inferential statistics. CD is determined by considering multiple process variables. lim This confirms that process variables are correlated with relevant defect patterns in the expected manner.

[0205] Figure 11F This is shown at the end of curve 702, specifically at CD for 23.5. lim The relatively high dose value was 58 mJ / cm. 2 Near the vicinity, the failure rate (shaded area) can be 6.3% when calculated using parameter PDF630 (or 8.1% assuming the nominal distribution of CD). Similarly, Figure 11G This shows that for a CD of 23.5nm... lim The failure rate per dose setting is within the expected limits. For example, the failure rate is 0.2% at dose 57; 1.4% at dose 57.5; 6.3% at dose 58; 19% at dose 58.5; and 43% at dose 59. Therefore, for several doses, the 23.5 nm CD... lim It meets or satisfies the failure rate specification.

[0206] In another example, it could also be aimed at situations that could lead to a second CD. lim2 The relatively low dose value (e.g., approximately 44 mJ / cm) 2 See Figure 11H The failure rate is calculated based on the characteristics of the exposure under the condition of ), therefore, based on two different CDs. lim1 and CD lim2 The failure rate equation can be expressed as the sum of the characteristic resist thickness at the lower end of curve 702 and the failure rate at the upper end of curve 1702, as follows:

[0207]

[0208] Return to reference Figure 10 In process P60, after determining the parameter limits, failure rate equations such as (4) and (5) can also be used to estimate the failure rate for any dose value. In other words, the parameter limits can be substituted into the failure rate equation (e.g., equation 4 or 5), and the failure rate can be treated as unknown. Such an equation with an unknown failure rate is called an estimated failure rate. The failure rate can be estimated / determined (or solved) for different values ​​of the process variable (e.g., dose).

[0209] The estimated failure rate can be further used to determine a process window over a process variable (e.g., dose). For example, the process window can be a range of dose values ​​for which the estimated failure rate can be less than 10%. -9 In an embodiment, the yield can be determined, for example, by using the following equation (6) based on the desired yield (e.g., for 10). 6 The expected failure rate is determined by using 99.9% of the features:

[0210] R fail (d)=(1-Y(d))...(6)

[0211] In an embodiment, the process window can be graphically determined by plotting the estimated failure rate equation, such as... Figure 11H As shown in the diagram. For example, an estimated failure rate curve can be plotted relative to a process variable (e.g., dose). Subsequently, a curve can be plotted at the desired failure rate (e.g., 10). -9 Draw a horizontal line at the point (), which may intersect with the estimated failure rate; the intersection point provides the range of dose values, i.e., the process window PW.

[0212] In an embodiment, the yield can be calculated using the estimated failure rate (e.g., in Equation 4 or 5) as follows:

[0213] Y(d)=(1-R fail (d)) N ...(7)

[0214] In equation (7) above, Y(d) is the yield for N individual features at a specific dose (d), and R fail (d) is the estimated failure rate (e.g., in Equation 4 or 5). Based on this calculated yield, a process window can be selected in which the calculated yield is greater than or equal to the expected yield (e.g., 99.9%).

[0215] In this embodiment, the process window based on yield can also be determined graphically, see [link to example]. Figure 11H For example, a yield curve (or estimated failure rate) can be plotted relative to a process variable (e.g., dose). A line can then be plotted at the desired yield (e.g., 99.9%), intersecting the yield curve (or estimated failure rate). The intersection point then provides a range of dose values, i.e., the process window PW. Thus, the process window not only defines the limits of the parameters of the feature obtainable from the patterned process but also ensures that within these limits, the feature has the desired yield or failure rate.

[0216] Furthermore, the above method can be extended to calculate the process window for each individual feature, and overlapping process windows for different features can be determined to identify the effective process window for the patterning process. Additionally, the process window can be defined on multiple process variables; for example, the above method can be performed with different alternative process settings such as focusing (or overlap, aberration, coating development system temperature, or track temperature). Here, the functional forms 610, 620, 630 (e.g., f) CD (d) PDF d (d) PDF CD (d) and the parameter limit CD lim These additional parameters can be included as additional dimensions (e.g., CD). lim Also includes focusing on CDs lim (focus)). Subsequently, the two-dimensional dose-focusing process window can be determined. Figure 12A and Figure 12B The diagram illustrates this two-dimensional dose-focus window for different features, and Figure 12C The image further illustrates the overlap processing window.

[0217] Figure 12A The illustration shows a process window for a first feature (e.g., an isoelectric contact hole feature with a diameter of approximately 8 nm). Process window 1901 can be for the first feature, and process window 1903 can be for N features. Furthermore, process window 1903 can be further improved by defining an elliptical process window 1905 within the boundaries of process window 1903, such that the elliptical process window 1905 has relatively higher accuracy (or lower CD variation) particularly at the elliptical boundaries compared to the accuracy at the boundaries of process window 1903. It is understood that this disclosure is not limited to elliptical fitting, and other suitable fittings such as rectangular fitting can be applied depending on other process variables or constraints (e.g., rectangular fitting can be used for strong correlations between process parameters, while elliptical fitting can be used for uncorrelated process parameters).

[0218] Similarly, in Figure 12B In this process, a process window can be determined for the second feature (e.g., a densely packed contact hole with a diameter of approximately 13 nm). Process window 1911 can be for a single such feature, and process window 1913 can be for N (10^ ... 4 Such features are used, and the elliptical window 1915 is fitted within the process window 1913 to improve the accuracy of the patterning process.

[0219] Subsequently, as Figure 12CAs shown, an overlapping process window 1920 can be determined based on a process window 1903 of the first feature and a process window 1913 of the second feature. The overlapping process window 1920 is the common area within process windows 1903 and 1913. For example, the overlapping process window 1920 can be determined by calculating the product of multiple individual yields (based on which the first process window 1903 and the second process window 1913 are determined), where each process window can vary with focus and dose. In another example, an intersection operation can be performed, where process windows 1903 and 1913 are expressed according to a set of values, such as dose and / or focus.

[0220] Those skilled in the art will understand that the operation is not limited to calculating yield products or intersections, and that any other suitable mathematical calculations / graphical methods / simulations can be performed to determine the overlap process window 1920. This overlap process window 1920 between multiple features can be used as a process window for the entire substrate used in the patterning process to obtain the desired yield with minimal defects.

[0221] Furthermore, this disclosure is not limited to a two-dimensional process window (e.g., a dose-focus process window). The method can be extended to provide a multi-dimensional process window. For example, a third variable: overlap can be considered. Subsequently, yield and / or failure rate can be considered as functions of dose, focus, overlap, or a combination thereof. Therefore, a process window can be determined such that it conforms to constraints or specifications based on all three process variables. As an example, Figure 13 The diagram illustrates a multi-dimensional process window based on yield. Figure 13 In this process, the first yield curve Y1 can be defined between overlap and dose, and the second yield curve Y2 can be defined between focus and dose. Subsequently, an ellipse fitting can be performed based on three variables (i.e., dose, focus or focal length, and overlap), such that the ellipse is defined by the first yield curve Y1 and the second yield curve Y2. The elliptical process window can then be viewed as a multi-dimensional process window. It is understood that the term "curve" is used only for visual clarity and understanding purposes and is not limiting. A curve can generally be any function. Furthermore, the ellipse fitting is exemplary, and other appropriate fittings (e.g., rectangular fittings) can be performed depending on the process conditions affecting the process window.

[0222] In another embodiment, it can be further extended. Figure 10 The method provides a process window for an entire layer of a die with several features, each appearing multiple times on each die of the substrate. For example,

[0223]

[0224] In equation (8) above, the yield Y i (CDlim i ) refers to CDs with CD limits lim i The expected yield of a single feature i, and N is the total number of features on a particular layer. Subsequently, the yield of the layer is the product of the yields of the individual features. The yields of the layers can be further used to calculate the process window in a manner similar to that discussed regarding step P60, for example using equations (6) and (7). For practical reasons in application, when the parameter limits of the feature and PDF... CD Similarly, to simplify evaluation (e.g., contact holes and wires), the features can be grouped into “types” or “categories”.

[0225] In this embodiment, the above method for determining the process window based on defects (or yield) can be further improved to provide more accurate results. For example, by improving the variation of the parameters used to calculate the process variable PDF. The improved process variable PDF can be further used to calculate an improved parameter PDF, which can produce a more accurate processing window. In other words, a better estimate of the variance of the parameters can be obtained by adjusting for known and / or random variances caused by different factors within the patterning process, to further produce more accurate results (i.e., process windows) compared to the methods described above.

[0226] This invention describes a defect-based process window for obtaining features in a random logical structure.

[0227] Figure 14 A block diagram illustrating exemplary methods for generating a base failure rate model and ultimately a feature-specific failure rate model, conforming to various embodiments. As relative to... Figure 2As discussed, various images (“SEM images”) of a substrate can be obtained using inspection tools such as SEM, and these images can be used to obtain measurement data associated with various features on the substrate. A number of SEM images 1405 of the substrate are input to a feature selection module 1410. The SEM images 1405 may have different portions of the substrate, and each SEM image may include one or more features printed on the substrate. The feature selection module 1410 analyzes the SEM images 1405 to select those features that meet specified criteria as features 1415. In some embodiments, the specified criteria may be related to the occurrence rate of features. For example, the feature selection module 1410 may be configured to select: (a) features that are less repeated within or throughout the SEM image; (b) features that appear randomly on the substrate; (c) features that appear less than a first threshold number of times throughout the SEM image; (d) features that appear less than a second threshold number of times in the SEM image; or (e) features that are different from other more repeated features. Typically, feature 1415 is a feature that appears in a random logical structure.

[0228] Feature grouping module 1420 groups features 1415 into a number of feature groups 1422 based on specified metrics. Various methods can be used to perform the grouping, such as k-means clustering. Each feature group includes one or more features with similar metric values ​​(e.g., metric values ​​within a predefined range). For example, feature group 1425 includes features with metric values ​​within a first predefined range, and another feature group includes features with metric values ​​within a second predefined range.

[0229] The feature grouping module 1420 can group feature 1415 based on any one of a number of metrics, such as the mean CD of feature 1415, the process window of feature 1415, the mean CD of the process window plus the feature, the tail CD of feature 1415, the Burson-Stokes fit coefficient of the Focus Exposure Matrix (FEM), the original failure rate of feature 1415, the CD distribution probability, etc. Various performance indicators can be used to determine which metric produces better grouping. One such performance indicator is a probability density function (referred to as CD PDF or PDF) associated with the parameter (e.g., CD) value of the feature. cD The probability density function provides the probability that parameter values ​​will fall within the desired range for each process variable setting (e.g., dosage) during the patterning process. This probability density function can also be used to identify the probability of defects and processing windows to reduce defects and effectively improve yield. PDF can be calculated using Equation 3. CD , such as at least refer to Figure 10 As described. In some embodiments, the PDF of features within the group CDThe variation appears to be minimal for the CD mean of the indicator process window + feature. Therefore, in some embodiments, the CD mean of the indicator process window + feature can be used to group features. Additional details regarding the grouping of reference features are provided below. Figure 15 To describe.

[0230] The basic FR model generator 1430 processes each of the feature groups to generate a basic FR model for the corresponding feature group and stores the basic FR models in a storage system, such as database 1440. For example, the basic FR model generator 1430 processes feature group 1425 to generate a basic FR model 1435 corresponding to feature group 1425, and processes another feature group to generate another basic FR model corresponding to the other feature groups. The basic FR model 1435 provides an estimated failure rate (or more precisely, for features with index values, i.e., the index values ​​of features within feature group 1425) for the features in feature group 1425, the estimated failure rate being determined based on the local CD uniformity of the features within feature group 1425. The basic FR model generator 1430 may also generate a defect-based process window for feature group 1425, which is a graph plotted based on a set of dose values ​​and focal length values, wherein the estimated failure rate of the features within feature group 1425 is within a selected or predefined threshold. Additional details on generating the basic FR model 1435 refer at least to Figure 17 To describe.

[0231] A base FR model can be used to generate feature-specific FR models that provide an estimated failure rate for any given feature. A feature-specific FR model generator 1445 determines an index value (e.g., process window + CD average) associated with a given feature 1450, obtains a base FR model matching the index value of the given feature 1450 from a database 1440, and processes the obtained base model, for example, by convolving it with measurement data associated with the given feature 1450, to generate a feature-specific FR model 1460. The feature-specific FR model 1460 provides an estimated failure rate for a given feature for various focal length and dose values. The feature-specific FR model generator 1445 can also generate a defect-based process window for the given feature 1450, which is a graph plotted based on a set of dose and focal length values, wherein the estimated failure rate of the given feature 1450 lies within a selected or predefined threshold. In some embodiments, the base FR model 1435 and the feature-specific FR model 1460 are stored as data structures. Additional details for generating the feature-specific FR model 1460 are referenced at least to... Figure 18 To describe.

[0232] Figure 15The flowchart illustrates an exemplary method 1500 for generating a basic failure rate model, conforming to various embodiments. At process P1505, a certain number of features are obtained and printed on a substrate. In some embodiments, features such as feature 1415 that satisfy a specified criterion related to the occurrence rate of the features are obtained (e.g., as at least referenced). Figure 14 (As described). Feature 1415 is obtained by analyzing the SEM image 1405 of the substrate. In some embodiments, the SEM image is an image of the substrate captured using a tool such as a SEM. Various measurement data associated with feature 1415 can be obtained using the SEM image 1405 (e.g., using at least a reference). Figure 1 (The measurement method described). Measurement data associated with a feature may include, among other data, the average CD of each of the features 1415 and a process window for each of the features 1415, the process window indicating a set of focal length and dose values, wherein the CD of the corresponding feature is within specifications (e.g., ±10% CD variation limit).

[0233] In process P1510, feature 1415 is grouped into one or more feature groups 1422 based on indicators. In some embodiments, indicators such as process window + CD mean are selected from a number of indicators (e.g., as at least referenced). Figure 14 (As described). In some embodiments, based on, such as PDF CD Performance indicators like the Process Window + CD Mean are used to determine whether a metric performs better than other metrics such as the CD Mean and Process Window. Figure 16A and Figure 16B As shown in the diagram.

[0234] Figure 16A PDFs illustrating features based on three different index groupings conforming to various embodiments CD Line graphs. For example, line graph 1605 illustrates PDFs of feature groups grouped based on the CD mean index. CD The curve chart 1610 illustrates the PDF of feature groups grouped based on the process window + CD mean index. CD Furthermore, graph 1615 illustrates the PDF of feature groups grouped based on process window indicators. CD In some embodiments, Equation 3 can be used to calculate the PDF. CD , such as at least refer to Figure 10 As described. For example, calculating PDF for the DCD value of each feature in the group. CD PDF CD CD data for various focal length and dose values, where the average CD of the features is removed based on the SEM image.

[0235] Figure 16B PDFs showing features within groups of three different metrics conforming to various embodiments CD Changes. In some embodiments, the PDF will be... CD The change is calculated as the average change of dCD (e.g., 3σ) values ​​above and below the mean CD. For example, a PDF with features grouped based on the CD mean index. CD The change to "0.24" indicates a PDF with features grouped based on process window indicators. cD The PDF changes to "0.13" and features a group of characteristics based on the process window + CD mean index. CD The change is "0.11". Therefore, in some embodiments, the PDF... CD The changes are minimal in the process window + CD mean index; therefore, the features are grouped using the process window + CD mean index.

[0236] Feature 1415 can be grouped into one or more groups. In some embodiments, the number of groups formed can affect the measurement time (e.g., computational resources) and accuracy of failure rate prediction. In some embodiments, a smaller number of groups may lead to lower accuracy in FR prediction, while a larger number of groups may consume more measurement time. Therefore, it may be necessary to determine the optimal number of clusters. In some embodiments, the within-cluster sum of squares (WCSS) is such an indicator that can be used to determine the optimal number of clusters. Figure 16C The illustrations are exemplary graphs depicting the relationship between the number of clusters and an indicator, consistent with various embodiments. In graph 1635, the optimal cluster count is determined to be "3" based on WCSS.

[0237] Figure 16D The illustrations are exemplary graphs showing the failure rate prediction accuracy of various feature grouping methods conforming to various embodiments. Graph 1640 indicates FR error prediction without grouping, and the other graphs indicate FR error prediction for other groupings such as FEM grouping, process window + CD mean grouping, LCDU grouping, and average CD grouping, respectively. From these exemplary graphs, it can be seen that the prediction accuracy is improved by 23%, 35%, 28%, and 25% for the other groupings without grouping, with the process window + CD mean grouping 1645 showing the best improvement in accuracy (e.g., 35%) among the groupings.

[0238] Returning to reference process P1510, in some embodiments, grouping features 1415 may include determining an index value 1511 for each of features 1415, and clustering features 1415 based on the index values ​​1511 (e.g., using one of many clustering algorithms such as k-means clustering) to produce feature groups 1422. For an index such as process window + mean CD, the index value 1511 of a feature is determined as the average CD value of the feature and multiple dose and focal length values ​​associated with the average CD located at the edges or boundaries of the feature's process window. As discussed above, the process window of a feature indicates a set of focal length and dose values, wherein the CD of the corresponding feature is within specification, and the process window can be plotted as a curve of focal length and dose values ​​as x-axis and y-axis, respectively, resulting in the formation of a shape. The shape of the process window includes boundaries or edges, and different portions of the edges may correspond to different focal length and dose values. Any of many methods can be used to generate the process window of a feature.

[0239] For each of the features 1415, an index value 1511 is calculated, and the features 1415 are grouped (e.g., clustered) into feature groups 1422 based on the index values ​​1511. In some embodiments, each feature group has features with similar index values ​​(e.g., features with index values ​​within a specified range). In some embodiments, the PDF of the features within the group... CD It has minimal changes.

[0240] In process P1515, a basic FR model is generated for each of feature groups 1422. For example, a basic FR model 1435 is generated for feature group 1425. As described above, the basic FR model 1435 provides an estimated failure rate (or more precisely, for features with index values, i.e., the index values ​​of features within feature group 1425) for the features in feature group 1425, the estimated failure rate being determined based on the local CD uniformity of the features within feature group 1425. The basic FR model 1435 can be stored as a data structure in database 1440. In some embodiments, the data structure includes ranges of focal length and dose values, and failure rates for features in feature group 1425 for those focal length and dose values. A defect-based process window, such as defect-based process window 1650, can be generated from the basic FR model 1435 of feature group 1425. The defect-based process window 1650 is a graph plotted based on a set of dose and focal length values, wherein the estimated failure rate of features within feature group 1425 is within a selected or predefined threshold. Figure 16EA defect-based process window conforming to various embodiments is shown. The defect-based process window 1650 shows a process window (e.g., a range of focal length and dose values) within which the failure rate of features of feature group 1425 is maintained at a predefined threshold (e.g., 1E-9 or 1*10). -9 (Within) Additional details for generating the basic FR model should at least refer to [reference needed]. Figure 17 To describe.

[0241] Figure 17 This is a flowchart of an exemplary method 1700 for generating a base failure rate model for a feature group, conforming to various embodiments. In some embodiments, method 1700 is performed as part of process P1515 of method 1500. At process P1705, the base failure rate model generator 1430 obtains measurement data 1701 of the features within the feature group. Measurement data 1701 may include measurements of features' parameters (e.g., CD) and process variables (e.g., dose, focal length, etc.). For example, measurement data 1701 may include the average CD of all features within feature group 1425, and dose and focal length values ​​associated with the average CD. Measurement data 1701 can then be used for CD uniformity (CDU) modeling, such as using, for example, a... Figure 10 Process P10 and Figure 11A The equation (1) discussed determines the functional relationship between parameters (e.g., mean CD) and process variables (e.g., dose value and focal length value) 1706.

[0242] At process P1710, the base FR model generator 1430 performs local CD uniformity (LCDU) modeling, which yields LCDU data 1713 for feature group 1425. In some embodiments, LCDU data 1711 for each feature in feature group 1425 is obtained across all SEM images 1405, and the average CD 1712 of the determined features for each SEM image is removed from the LCDU data to determine LCDU data 1713. For example, LCDU modeling can use methods such as... Figure 10 The process described in equation (1) on page 20 yields LCDU data 1713.

[0243] At process P1715, the basic FR model generator 1430 determines the PDF of feature group 1425. CD 1716. PDF can be determined and / or obtained based on LCDU data 1713 and functional relationship 1706. CD 1716 (PDF) CD 1716 is a function of the average CD of all features, the dose value of the patterning process, and the variance of the dose value (e.g., as at least referenced). Figure 10The process P30 is described using equation (3) in process P30.

[0244] In some embodiments, as referenced Figure 10 As described, such as PDF CD A parameter PDF like 1716 provides an estimate of the probability that a parameter (e.g., CD) value will fall within a desired range for each process variable setting (e.g., dosage) in the patterning process. This probability estimate can also be used to identify the probability of defects and the processing window to reduce defects. In some embodiments, the process variable PDF (e.g., such as...) Figure 10 The dosage of PDF 620 is used to determine the PDF. CD The PDF is a function of the process variable and its variation. The process variable PDF allows for capturing the effect of any changes in the dose setting, which may ultimately affect the parameters. A transformation function can be used to determine the PDF from the dose PDF. CD 1716, as referenced Figure 10 Process P30 and Figure 11C As described.

[0245] At process P1720, the basic FR model generator 1430 performs CD limit modeling, which determines the CD limit 1722 of feature group 1425. In some embodiments, the CD limit may be a common theoretical limit of the CD values ​​of features, at which less than a predetermined number or percentage of features fail at each setting of process variables (e.g., per-focal length and dose values). In some embodiments, the failure rate 1721 and PDF measured at each setting of process variables may be used as a basis. CD 1716, for example, using reference Figure 10 Equation (4) described on page 50 is used to calculate the CD limit 1722. In some embodiments, a pair of CD limits may be determined, wherein a first CD limit is located at the lower end of the PDF distribution curve and a second CD limit is located at the upper end of the PDF distribution curve, such that the CD values ​​between these CD limits (e.g., CD values ​​greater than the first CD limit and less than the second CD limit) keep the failure rate of each setting of the process variable (e.g., each focal length value and dose value) within a predetermined failure rate. Additional details regarding the CD limits refer at least to Figure 10 The process P50 and Figure 11F and Figure 11G To describe.

[0246] The failure rate 1721 for determining the CD limit 1722 can be obtained from measurement data 1701. In some embodiments, feature failure can be determined based on failure analysis, such as SEM images. The failure rate of a feature can be obtained / measured with reference to parameters (e.g., CD) at each setting of process variables (e.g., dose). In some embodiments, the failure rate of an individual feature can be expressed as, for example, parts per million (ppm) or parts per billion (ppb) of a feature of a pattern. In other words, 1 ppm can mean that one feature is expected to fail in one million occurrences of the feature. In some embodiments, the failure rate can correspond to different failure modes associated with an individual feature, such as physical failure, transfer failure, and delayed failure. Additional details regarding failure and measurement failure rates can be found at least in reference to Figure 10 The process P40, Figure 11D and Figure 11E To describe.

[0247] At process P1725, the basic FR model generator 1430, for various focal lengths or dose values, is based on the CD limit 1722 and PDF. CD 1716 determines the estimated failure rate 1726 of the features in feature group 1425. After determining the CD limit 1722, methods such as... Figure 10 The failure rate equations, such as equations (4) and (5) in processes P40 and P50, are used to estimate the failure rate for any focal length and dose value 1726. Additional details regarding the estimation of failure rate should be found at least in the reference [reference needed]. Figure 10 The process P60, Figure 11D and Figure 11E To describe.

[0248] At process P1730, the basic FR model generator 1430 uses the estimated failure rate 1726 to generate a defect-based process window 1650 for feature set 1425. For example, the process window can be a series of focal length and dose values ​​(or a range of focal length and dose values) within which the estimated failure rate can be less than 10%. -9 .

[0249] The basic FR model generator 1430 stores the basic FR model 1435 in the database 1440. In some embodiments, the basic FR model 1435 is a PDF that includes features from feature group 1425, among other data. CD Data structures for 1716, CD limit 1722, estimated failure rate 1726, and defect-based process window 1650.

[0250] Figure 18The illustration shows a flowchart of an exemplary method 1800 for generating a feature-specific FR model according to various embodiments. At process P1805, a feature-specific FR model generator 1445 obtains measurement data 1801 associated with a given feature 1450. In some embodiments, the measurement data 1801 may include FEM data of the given feature 1450, which contains a CD value of the given feature 1450 comprising a series of focal length values ​​and dose values.

[0251] At process P1810, the feature-specific FR model generator 1445 determines an index value 1811 for a given feature 1450 based on measurement data 1801. For an index such as process window + mean CD (e.g., an index used to generate the underlying FR model), the index value 1811 for the given feature 1450 is determined as the mean CD value of the given feature 1450 and multiple dose and focal length values ​​associated with the mean CD located at the edges or boundaries of the process window of the given feature 1450. The process window can be generated using measurement data 1801 using any of a number of methods.

[0252] At process P1815, the feature-specific FR model generator 1445 selects a base FR model from database 1440 that has an index value that matches the index value 1811. For example, the feature-specific FR model generator 1445 selects a base FR model 1435 whose process window + CD mean matches the process window + CD mean of a given feature 1450. In some embodiments, the index value is considered to match the index value 1811 if the difference between the index value of the base FR model and the index value 1811 does not exceed a specified matching threshold.

[0253] At process P1820, the feature-specific FR model generator 1445 obtains the PDF from the base FR model 1435. CD 1716.

[0254] At process P1825, the feature-specific FR model generator 1445 adjusts the PDF based on the average CD value of the given feature 1450. CD 1716 average CD. In some embodiments, adjust the PDF. CD The average CD of 1716 includes PDFs. CD The difference between the average CD of 1716 and the average CD value of a given feature of 1450 and the PDF CD The average CD values ​​of 1716 are added together to produce the adjusted PDF. CD 1826. In some embodiments, an adjusted PDF is generated. CD Equivalent to PDF CD1716 Shift left or right equals PDF CD The amount of difference between the average CD of 1716 and the average CD value of a given feature of 1450 (plotted as PDF vs CD in a graph). For example, if PDF CD If the average CD of 1716 (e.g., "5nm") is less than the average CD value of a given feature 1450 (e.g., "7nm"), then the PDF will be... CD 1716 to PDF CD The average CD of 1716 shifts to the right of the difference (e.g., shifts by "2nm"). If PDF CD If the average CD of 1716 (e.g., "8nm") is greater than the average CD value of a given feature 1450 (e.g., "7nm"), then the PDF will be... CD 1716 to PDF CD The average CD of 1716 shifts to the left of the difference (e.g., shifts by "1nm").

[0255] At process P1830, the feature-specific FR model generator 1445, for example, uses a reference... Figure 10 Equation (4) described by P50, based on the adjusted PDF CD 1826 and determine the CD limit 1831 for a given feature 1450. In some embodiments, a pair of CD limits may be determined, wherein a first CD limit is located at the lower end of the PDF distribution curve and a second CD limit is located at the upper end of the PDF distribution curve, such that the CD values ​​between these CD limits (e.g., CD values ​​greater than the first CD limit and less than the second CD limit) keep the failure rate of each setting of the process variable (e.g., each focal length value and dose value) within a predetermined failure rate. Additional details regarding the CD limits refer at least to Figure 10 The process P50, Figure 11F and Figure 11G To describe.

[0256] At process P1835, the feature-specific FR model generator 1445 obtains at least one of the inter-field CD variation or intra-field CD variation of a given feature 1450 as CD profile data 1837. In some embodiments, the average CD deviation (or variation) of a given feature 1450 across different SEM images in the die / field is referred to as intra-field CD variation, and any die-to-die or field-to-field average CD deviation (or variation) is referred to as inter-field CD variation. In some embodiments, if the given feature 1450 is a feature group (e.g., a set of features), a PDF of the given feature 1450 is obtained. CD As CD outline data 1837.

[0257] At process P1840, the feature-specific FR model generator 1445 modifies the adjusted PDF based on the CD contour data 1837. CD 1826 Perform convolution to produce a convolved PDF CD 1841.

[0258] At process P1845, the feature-specific FR model generator 1445 uses, for example, a generator such as... Figure 10 The failure rate equations, such as equations (4) and (5) in processes P40 and P50, are based on convolutional PDFs. CD 1841 Determine the failure rate 1846 for a given feature 1450.

[0259] At process P1850, the feature-specific FR model generator 1445 uses the estimated failure rate 1846 to generate a defect-based process window 1851 for a given feature 1450. For example, the process window could be a series of focal length and dose values ​​within which the estimated failure rate could be less than 10. -9 . Figure 19A The illustration shows a defect-based process window 1851 corresponding to a given feature 1450 in various embodiments. A feature-specific FR model generator 1445 generates a feature-specific FR model 1460 for the given feature 1450 and stores the feature-specific FR model 1460 in a database 1440. In some embodiments, the feature-specific FR model 1460 is a convolutional PDF that includes the given feature 1450 among other data. CD Data structures for 1841, CD limit 1831, estimated failure rate 1846, and defect-based process window 1851.

[0260] In some embodiments, the feature-specific FR model generator 1445 can determine the failure rate and generate a defect-based process window for a given set of features (e.g., a set of features) in a manner similar to that described above for a given feature 1450. Figure 19B The illustration shows a defect-based process window 1910 for a given set of features, consistent with various embodiments.

[0261] Although it can be based on such Figure 17While CD data is described in the text for predicting failure rate, in some embodiments, failure rate can also be predicted based on other characteristic parameters of the feature, such as the CDe parameter or the PEe parameter. In some embodiments, characteristic parameters of the feature, such as CD data, edge placement error (EPE) data, or placement error (PE) data, can be derived from one or more measurement data. For example, a first characteristic parameter such as CDe can be derived from CD data and PE data. In another example, a second characteristic parameter such as PEe can be derived from target CD data and PE data. Figure 21 The diagram illustrates a flowchart used to estimate failure rates based on CDE data and to generate a process window based on EPE defects. In another example, Figure 22 The diagram illustrates a flowchart for estimating failure rates based on PEe data and generating a process window based on PE defects.

[0262] Figure 20 The illustrations depict edge placement errors of target features according to various embodiments. In some embodiments, EPE is the deviation of the printed edge of the target feature from the target edge of the target feature. EPE can be along one or more directions, such as along the x-axis or along the y-axis. For example, Figure 20 EPE diagram left 2010 and EPE left 2015, EPE left 2010 can be the offset of the printed edge 2025 of a feature (e.g., a contact hole) along the x-axis from the target edge 2020 on the left side of the target feature, EPE. left 2015 can be the deviation of the printed edge 2025 along the x-axis from the target edge 2020 on the right side of the target feature. EPE can be obtained using the following equation:

[0263] EPE Left =(CD) X -tgt X ) / 2-PE X (9)

[0264] EPE Right =(CD) X -tgt X ) / 2+PE X (10)

[0265] Among them, CD X For the printed feature along the x-direction CD, tgt X Let CD be the target feature along the x-direction, and PE XThe placement error 2005 is the centering error of the contact hole. This placement error 2005 can be the deviation of the center of the printed contact hole from the center of the target contact hole. The EPE can be similarly defined for other feature types and in other directions (e.g., the EPE in the y-axis). up and EPE down PE data can also be determined similarly in other directions (e.g., PE in the y-axis). y ).

[0266] Figure 21 The flowchart illustrates an exemplary method 2100 for generating a failure rate model of a feature group based on CDe data, in accordance with various embodiments. In some embodiments, method 2100 is similar to method 1700, but method 2100 is based on CDe data, rather than on the CD data of method 1700, or also on the CD data of method 1700.

[0267] At process P2105, the basic FR model generator 1430 obtains measurement data 2101 for the features within the feature group. In some embodiments, similar to measurement data 1701, measurement data 2101 may include average CD, EPE, and PE data for all features within feature group 1425, and dose and focal length values ​​associated with the average CD. Measurement data 2101 can then be used for CDU modeling (or modeling), for example using... Figure 10 Process P10 and Figure 11A The equation (1) discussed determines the functional relationship between parameters (e.g., mean CD) and process variables (e.g., dose value and focal length value) 2106.

[0268] Characteristic parameters can be defined as functions of placement error data, such as functions of EPE or PE combined with CD values. Characteristic parameters can be used to construct failure rate models based on their probability distribution functions. Given a specified failure rate, the model is configured to calculate the limits of the characteristic parameters and thus derive the corresponding process window. Without departing from the scope of the invention, characteristic parameters can be related to CD, EPE, and / or PE in any form or mathematical way. Furthermore, characteristic parameters can be derived from any suitable type of measurement data indicating placement error characteristics.

[0269] In some embodiments, the derived parameter CDe of the feature can be obtained using measurement data 2101. The CDe parameter can be derived from the feature's CD and PE values. For example, CDe can be determined using the following equation:

[0270] CDe Left =CD X -2*PE X ...(11)

[0271] CDe Right =CD X +2*PE X ...(12)

[0272] For EPE, derive parameters CDe from the equation Left and CDE Right (For example, equations 9 and 10):

[0273] CD X -2*PE X = tgt + 2 * EPE Left

[0274] CD X +2*PE X = tgt + 2 * EPE Right

[0275] The measurement data 2101 can then be used for CDeU modeling, for example, using... Figure 10 Process P10 and Figure 11A The equation (1) discussed determines the functional relationship between the derived parameters (e.g., CDe or EPE) and process variables (e.g., dose and focal length) 2106.

[0276] At process P2110, the basic FR model generator 1430 performs LCDU modeling to obtain LCDU data 2113 of feature group 1425 (e.g., by using a process similar to obtaining LCDU data 1713 in process P1710), as at least referring to Figure 17 The process is described on page 1710.

[0277] In some embodiments, process P2110 performs LCDeU modeling based on CDe data to obtain LCDeU data 2113 for feature group 1425. LCDeU modeling can be performed in addition to LCDU modeling, or LCDeU modeling can be performed instead of LCDU modeling.

[0278] At process P2115, the basic FR model generator 1430 determines the PDF of feature group 1425. CD e2116 (e.g., as in the PDF in at least reference process P1715) CD (As described in 1716). PDFs can be determined and / or obtained based on LCDeU data 2113 and functional relationships 2106. CD e2116, PDF CD e2116 is a function of the CDe of all features, the dose value of the patterning process, and the variance of the dose value (e.g., as at least referenced). Figure 10The process P30 is described using equation (3) in process P30.

[0279] At process P2120, the basic FR model generator 1430 performs CDe limit modeling, which determines the CDe limit 2122 of feature group 1425 (e.g., as described with reference at least to CDe limit 1722 in process P1720). In some embodiments, the CDe limit may be a common theoretical limit of the CDe values ​​of the features, at which less than a predetermined number or percentage of features fail at each setting of the process variable (e.g., per-focal length value and dose value). In some embodiments, the failure rate and PDF measured at each setting of the process variable may be used as a basis. CD e2116, for example, using reference Figure 10 Equation (4) described on page 50 calculates the CDe limit 2122. In some embodiments, a pair of CDe limits may be determined, wherein a first CDe limit is located at the lower end of the PDF distribution curve and a second CDe limit is located at the upper end of the PDF distribution curve, such that the CDe values ​​between these CDe limits (e.g., CDe values ​​greater than the first CDe limit and less than the second CDe limit) keep the failure rate of each setting of the process variable (e.g., each focal length value and dose value) within a predetermined failure rate.

[0280] At process P2125, the basic FR model generator 1430, for various focal lengths or dose values, is based on CDe limits 2122 and PDF. CD e2116 determines the estimated failure rate 2126 of the features in feature group 1425 (e.g., as described in at least reference process P1725, where the estimated failure rate 2126 is used). After determining the CDe limit 2122, methods such as Figure 10 The failure rate equations, such as equations (4) and (5) in processes P40 and P50, are used to estimate the failure rate for any focal length and dose value. 2126. For additional details on estimating the failure rate, refer at least to [reference needed]. Figure 10 The process P60, Figure 11D and Figure 11E To describe.

[0281] In process P2130, the basic FR model generator 1430 uses the estimated failure rate 2126 to generate a process window 2150 for EPE-based defects in feature set 1425. For example, the process window can be a series of focal length and dose values ​​within which the estimated failure rate can be less than 10%. -4 In some embodiments, more than one process window based on EPE defects (e.g., EPE) can be generated. left Process window, EPE right Process window, EPEup Process window and EPE down (Process window).

[0282] Figure 22 The flowchart illustrates an exemplary method 2200 for generating a failure rate model of a feature group based on PEE data, conforming to various embodiments. In some embodiments, method 2200 is similar to method 1700, but method 2200 is based on PEE data, rather than on the CD data of method 1700, or also on the CD data.

[0283] At process P2205, the basic FR model generator 1430 obtains measurement data 2201 for the features within the feature group. In some embodiments, similar to measurement data 1701, measurement data 2201 may include average CD, EPE, and PE data for all features within feature group 1425, as well as dose and focal length values ​​associated with the average CD. Measurement data 2201 can then be used for CDU modeling, for example using... Figure 10 Process P10 and Figure 11A The equation (1) discussed determines the functional relationship between parameters (e.g., mean CD) and process variables (e.g., dose value and focal length value) 2206.

[0284] In some embodiments, the derived parameter PEE of the feature can be obtained using measurement data 2201. The PEE parameter can be derived from the target CD value and PE value of the feature. For example, the PEE parameter can be determined using the following equation:

[0285] PEe Left =tgt X -2*PE X ...(13)

[0286] PEe Right =tgt X +2*PE X ...(14)

[0287] The measurement data 2201 can then be used for CDU modeling, for example, by using... Figure 10 Process P10 and Figure 11A The equation (1) discussed determines the functional relationship between the computational parameters (e.g., CD) and the process variables (e.g., dose value and focal length value) 2206.

[0288] At process P2210, the basic FR model generator 1430 performs LCDU modeling to obtain LCDU data 2213 for feature group 1425 (e.g., LCDU data 1713 similar to that in process P1710), as at least referenced Figure 17 The process is described on page 1710.

[0289] At process P2215, the basic FR model generator 1430 determines the PDF of feature group 1425. PEe 2216 (e.g., as in the PDF in at least process P1715) CD (As described in 1716). PDFs can be determined and / or obtained based on LCDU data 2213 and functional relationships 2206. PEe 2216, PDF PEe 2216 is a function of PEE, dose value, and variance of dose value for all features of the patterning process (e.g., as at least referenced). Figure 10 The process P30 is described using equation (3) in process P30.

[0290] At process P2220, the basic FR model generator 1430 performs PEE limit modeling, which determines the PEE limit 2222 of feature group 1425 (e.g., as described with reference at least to the CD limit 1722 in process P1720). In some embodiments, the PEE limit may be a common theoretical limit of the PEE values ​​of features, at which less than a predetermined number or percentage of features fail at each setting of the process variable (e.g., per-focal length value and dose value). In some embodiments, the failure rate and PDF measured at each setting of the process variable may be used as a basis. PEe 2216, for example, using reference Figure 10 Equation (4) described on page 50 calculates the PEE limit 2222. In some embodiments, a pair of PEE limits may be determined, wherein a first PEE limit is located at the lower end of the PDF distribution curve and a second PEE limit is located at the upper end of the PDF distribution curve, such that the PEE values ​​between these PEE limits (e.g., a PEE value greater than the first PEE limit and less than the second PEE limit) keep the failure rate of each setting of the process variable (e.g., each focal length value and dose value) within a predetermined failure rate.

[0291] At process P2225, the basic FR model generator 1430, for various focal length or dose values, is based on the PEE limit 2222 and PDF. PEe 2216 determines the estimated failure rate 2226 of the features in feature set 1425 (e.g., as described in the estimated failure rate 2226 in at least reference process P1725). After determining the PEE limit 2222, methods such as Figure 10 The failure rate equations, such as equations (4) and (5) in processes P40 and P50, are used to estimate the failure rate for any focal length and dose value. 2226. For additional details on estimating the failure rate, refer at least to [reference needed]. Figure 10 The process P60, Figure 11Dand Figure 11E To describe.

[0292] At process P2230, the basic FR model generator 1430 uses the estimated failure rate 2226 to generate a process window 2250 based on PEE defects for feature set 1425. For example, the process window can be a series of focal length and dose values ​​within which the estimated failure rate can be less than 10. -4 .

[0293] Although methods 2100 and 2200 are described as generating process windows for features within a feature group, in some embodiments, these methods can also be used to generate process windows for multiple features without any grouping (e.g., no feature clusters).

[0294] Figure 23 The illustrations depict various failure rate process windows corresponding to different embodiments. For example, the first FR process window 2315 is a defect-based process window generated based on CD data, such as the defect-based process window 1650. The second FR process window 2305 is an EPE-based process window generated based on CDe data. left Defect-based process windows, such as defect-based process window 2150. The third FR process window 2310 is generated based on CDE data and EPE. Right A defect-based process window, such as defect-based process window 2150. A fourth FR process window 2320 is a PEE defect-based process window generated based on PEE data, such as defect-based process window 2250. In some embodiments, multiple FR process windows may be combined (e.g., using any of several process window combination methods) to produce a combined FR process window 2325.

[0295] In some embodiments, the methods described above can be used to optimize (e.g., determine or adjust) "design variables," which include a set of user-adjustable parameters of the lithography projection equipment used in the patterning process (e.g., lithography process, lithography projection equipment, etc.), or other adjustable parameters such as adjustable parameters of the illumination mode, pattern of the pattern forming apparatus, projection optics, dose, focal length, etc. The design variables can be optimized using the methods described above to minimize the failure rate of the features to be printed on the substrate or to keep it within a desired failure rate threshold. Some exemplary applications of the methods described above are given below.

[0296] Exemplary applications of the above methods (such as resist slag removal, or other post-patterning processes or resist optimization, source mask optimization (SMO), optical proximity correction (OPC) calibration) can be found in PCT patent application publication number WO / 2019 / 121486, which is hereby incorporated by reference in its entirety.

[0297] Figure 24 This is a block diagram illustrating a computer system 100 that can assist in implementing the methods and processes disclosed herein. The 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 the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0298] Computer system 100 can be coupled via bus 102 to a display 112 for displaying information to a computer user, such as a cathode ray tube (CRT), flat panel display, or touch panel display. Input device 114, including alphanumeric keys and other keys, is coupled to bus 102 for communicating information and command selections to processor 104. Another type of user input device is a cursor controller 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to processor 104 and for controlling cursor movement on display 112. Such input devices typically have two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

[0299] According to one embodiment, a portion of a process may be executed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors arranged in a multiprocessor configuration may also be used to execute the sequence of instructions contained in main memory 106. In alternative embodiments, hard-wired circuitry may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0300] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage device 110. Volatile media include volatile memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing bus 102. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, floppy disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tapes, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carrier waves as described below, or any other media that can be read by a computer.

[0301] Various forms of computer-readable media are used to carry one or more sequences of instructions to processor 104 for execution. For example, the instructions may initially be carried on the disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit them over a telephone line using a modem. A modem local to computer system 100 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled 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 fetches and executes instructions. Instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0302] Computer system 100 also desirably includes a communication interface 118 coupled to bus 102. Communication interface 118 provides bidirectional data communication coupling with network link 120 connected to local area network 122. For example, communication interface 118 may be an Integrated Services Digital Network (ISDN) card or modem to provide data communication connectivity to a corresponding type of telephone line. As another example, communication interface 118 may be a local area network (LAN) card to provide data communication connectivity to a compatible LAN. A wireless link may also be implemented. In any such implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0303] Network link 120 typically provides data communication to other data devices via one or more networks. For example, network link 120 may provide connectivity to host computer 124 or to data equipment operated by Internet Service Provider (ISP) 126 via 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. Signals via various networks and signals on network link 120 and via communication interface 118 (which carry digital data to and from computer system 100) are exemplary forms of carriers for transmitting information.

[0304] Computer system 100 can send messages and receive data including process code via one or more networks, network links 120, and communication interfaces 118. In the example of the Internet, server 130 can transmit requested code for an application via the Internet 128, ISP 126, local area network 122, and communication interface 118. For example, such a downloaded application can provide illumination optimizations for an embodiment. The received code can be executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, computer system 100 can obtain application code in carrier form.

[0305] This invention describes a method for classifying features (e.g., features in a random logic structure) printed on a substrate. Features can be classified based on one or more metrics (e.g., process window metrics). After feature classification, features with metrics that meet a threshold (e.g., below a threshold) can be identified as critical features. Analysis (e.g., as at least referred to above) can be performed... Figure 14 and Figure 15 The feature sets generated as described above are used to identify those feature sets with critical features, and a basic FR model is generated for the identified feature sets (e.g., as at least referred to above). Figure 14 , Figure 15 and Figure 17 (As described) or can generate feature-specific FR models for critical features (e.g., as at least referred to above). Figure 14 and Figure 18 (As described).

[0306] Figure 25This is a flowchart of a process 2500 for feature grading according to one or more embodiments. In operation P2505, measurement data 2501 can be obtained for a certain number of features printed on a substrate. In some embodiments, features are obtained by analyzing an SEM image of the substrate, such as SEM image 1405. In some embodiments, the SEM image is an image of the substrate captured using a tool such as a SEM. Various measurement data associated with the features can be obtained using SEM image 1405 (e.g., using at least a reference). Figure 1 The measurement method described herein. Measurement data 2501 may include measurement results of one or more characteristic parameters for various process variables (e.g., dose, focal length, etc.). For example, measurement data 1701 may include CD data, defect counts, failure rates, edge placement error (EPE), placement error (PE), etc., for various dose and focal length values. In some embodiments, measurement data 2501 may also include modeled data obtained using simulation models (e.g., CDU modeling, LCDU modeling, CD limit modeling, CDeU modeling, failure rate modeling, etc., where at least some are described above), such as modeled CD data and modeled failure rate data. In some embodiments, measurement data 2501 may include Figure 17 Measurement data 1701, which is used to determine the basic FR model of the feature group.

[0307] In operation P2510, process window data 2513 of the feature is obtained using measurement data 2501. Process window data 2513 may include one or more process windows for each feature. As discussed above, a feature's process window indicates a set of focal length and dose values ​​where the characteristic parameters of the corresponding feature are within specifications. For example, a feature's CD process window may be a set of dose values ​​or focal length values ​​where the deviation of the feature's CD from the target CD value is within a desired threshold. In another example, a defect-free (DF) process window may be a set of dose values ​​or focal length values ​​where the measured defect count of the feature is zero. In another example, a failure rate (FR) process window (e.g., as at least referenced) Figure 14 , Figure 15 , Figure 17 or Figure 18 The (as described) generated can be a set of dose values ​​or focal length values ​​in which the failure rate of the characteristic lies within a desired threshold. In yet another example, the EPE process window (e.g., as at least referenced) Figure 21 The (as described) generated can be a set of dose or focal length values ​​where the failure rate, determined based on the characteristic EPE, lies within a desired threshold. In yet another example, the PE process window (e.g., as at least referenced) Figure 22The failure rate (as described) can be a set of dose or focal length values ​​where the failure rate, determined based on the characteristic PE, is within a desired threshold.

[0308] A process window can be plotted as a curve with focal length and dose values ​​as the x-axis and y-axis, respectively, resulting in a shape. The shape of the process window includes boundaries or edges, and different portions of the edges can correspond to different focal length and dose values. A variety of methods can be used to generate a characteristic process window. Figure 26A Example CD process window 2605 shows features according to one or more embodiments. Figure 26B An exemplary FR process window 2610 is shown, illustrating features according to one or more embodiments. While the figures illustrate the CD process window and the FR process window, various other process windows (e.g., EPE process window, PE process window, etc.) can be generated.

[0309] In operation P2515, process window metrics 2516 for each of the features are obtained using process window data 2513. In some embodiments, process window metrics 2516 represent characteristics of the process window (e.g., size). In some embodiments, the process window may be characterized by performing a shape fitting operation that fits a shape (e.g., an ellipse, rectangle, or other shape) within the process window to determine (e.g., quantize) the characteristics of the process window. Process window metrics 2516 may be determined based on the properties of the shape. Process window metrics 2516 may include exposure latitude, depth of focus, or the area of ​​the shape. For example, a process window may be characterized using an ellipse, such as... Figure 27 As shown in the diagram. Figure 27 The illustrations are based on one or more embodiments. Figure 26B Ellipse fitting to the FR process window. Several ellipse fitting algorithms can be used to fit ellipse 2720 to the FR process window 2610. Ellipse 2720 can be fitted based on constraints. For example, ellipse 2720 can be fitted to obtain an ellipse with maximum area. In another example, ellipse 2720 can be fitted such that its center 2725 is located at a specified position in the graph (e.g., at a specified dose or focal length value). In yet another example, ellipse 2720 can be fitted to obtain a specified exposure latitude.

[0310] After fitting an ellipse in the FR process window 2610, the process window index 2516 can be determined as follows. Exposure latitude can be defined as a function of the height of ellipse 2720 and the dose value corresponding to the center 2725 of ellipse 2720. For example, the equation used to obtain exposure latitude (EL) using ellipse fitting can be expressed as follows:

[0311]

[0312] The height of the ellipse is the range of dose values ​​reached by the extension of ellipse 2720. The depth of focus parameter corresponds to the width of ellipse 2720, which is the range of focal length values ​​reached by the extension of ellipse 2720. The area parameter is the area of ​​ellipse 2720, which is determined as a function of the height and width of ellipse 2720.

[0313] While the process window index 2516 can be obtained by fitting the shape in a separate process window, such as FR process window 2610, it can also be obtained from, for example, Figure 28A and Figure 28B The process window obtained by overlaying the process window shown in the figure is 2516. Figure 28A The illustration depicts a stacking operation that overlays two process windows according to one or more embodiments. The stacking operation overlaps one process window with another to obtain a stacked process window, which is the intersection area of ​​the two process windows. For example, as... Figure 28A As shown in the figure, the CD process window 2605 and the FR process window 2610 are overlaid to produce the overlaid process window 2830. Figure 28B The illustrations are based on one or more embodiments. Figure 28A Ellipse fitting of the overlaid process window. Ellipse 2845 can be fitted into the overlaid process window 2830, and process window indices 2516 can be determined using ellipse 2845 (e.g., as referenced). Figure 27 (as described by ellipse 2720 in the image).

[0314] It should be noted that, although Figure 28A and Figure 28B The illustration shows an ellipse fitted in an overlaid process window obtained by overlaying two separate process windows of the feature, but an overlaid process window can be obtained by overlaying more than two process windows of the feature.

[0315] Furthermore, it should be noted that while the preceding paragraphs describe fitting shapes such as ellipses to characterize process windows, shape fitting algorithms can also be used to fit other shapes (e.g., rectangles) to process windows to characterize them. Other process window characterization methods, along with shape fitting algorithms or alternatives to the shape fitting algorithms, can also be used to obtain process window indices 2516. Operation P2515 is performed to obtain the process window indices 2516 for each of the features.

[0316] In operation P2520, features are graded based on process window metric 2516 to generate a graded list 2522 of features. The features can be graded based on exposure latitude, depth of focus, area of ​​shape, or other such process window metrics. In some embodiments, the smaller the value of process window metric 2516, the more critical the feature.

[0317] In operation P2525, critical features 2526 are identified based on gradation. Features that have a process window metric 2516 that satisfies (e.g., user-defined) a specified threshold are identified as critical features 2526. For example, a feature may be identified as a critical feature based on the fact that its exposure latitude is less than a threshold exposure latitude. In another example, a feature may be identified as a critical feature based on the fact that its exposure latitude and depth of focus are less than the threshold exposure latitude and threshold depth of focus, respectively.

[0318] Information about critical feature 2526 can be used in the process of generating a base FR model containing a feature set of critical features. For example, in operation P2530, information about critical feature 2526 can be input to... Figure 14 The basic FR model generator 1430 identifies feature groups containing critical features and generates a basic FR model 2531 for the identified feature groups. In some embodiments, the basic FR model generator 1430 can use information about the critical feature 2526 for other analyses (e.g., analyzing the grouping coverage of the critical feature 2526).

[0319] In some embodiments, after the base FR model generator 1430 generates base FR models for various feature groups, the feature groups can also be classified based on process window indices 2516 obtained using FR process windows, which are generated by the base FR model generator 1430 for feature groups.

[0320] The concepts disclosed in this paper can be simulated or mathematically modeled for any general imaging system used to image subwavelength features, and may be particularly useful in emerging imaging techniques capable of producing wavelengths with increasingly smaller dimensions. Emerging techniques already in use include EUV (Extreme Ultraviolet) lithography, which can produce wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. Furthermore, EUV lithography can produce wavelengths in the range of 5 nm to 20 nm by using synchrotrons or by using high-energy electrons to strike materials (solids or plasmas) to generate photons within this range.

[0321] While the concepts disclosed herein can be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of lithography imaging system, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0322] While reference may be specifically made herein to embodiments used in IC manufacturing, it should be understood that the embodiments described herein can have many other possible applications. For example, the embodiments described herein can be used in the manufacture of integrated optical systems, for guiding and detecting patterns for magnetic domain memories, liquid crystal displays (LCDs), thin-film magnetic heads, micromechanical systems (MEMS), and the like. Those skilled in the art will appreciate that, in the context of such alternative applications, any use of the terms “mask,” “wafer,” or “die” herein can be considered synonymous with or interchangeable with the more general terms “patterning apparatus,” “substrate,” or “target portion,” respectively. The substrates mentioned herein can be processed before or after exposure in, for example, in a coating and developing system (typically a tool that applies a resist layer to the substrate and develops the exposed resist) or in a measurement or inspection tool. Where applicable, the disclosure herein can be applied to these and other substrate processing tools. Furthermore, the substrate can be processed more than once, for example to produce a multilayer IC, such that the term “substrate” as used herein can also refer to a substrate that already contains multiple processed layers.

[0323] In this invention document, the terms “radiation” and “beam” as used herein cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of about 365 nm, about 248 nm, about 193 nm, about 157 nm, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5 nm to 20 nm) and particle beams, such as ion beams or electron beams.

[0324] As used herein, the term "optimizing / optimization" refers to or implies adjusting patterning equipment (e.g., photolithography equipment), patterning processes, etc., to give the results and / or processes more desirable characteristics, such as higher accuracy of the projection of the designed pattern onto the substrate, a larger process window, etc. Therefore, as used herein, the terms "optimizing" and "optimized" refer to or imply the process of identifying one or more values ​​of one or more parameters that provide an improvement in at least one relevant metric, such as a local optimum, compared to an initial set of values ​​for those parameters. The terms "optimal" and other related terms should be interpreted accordingly. In embodiments, optimization steps may be applied iteratively to provide a further improvement in one or more metrics.

[0325] The aspects of the invention can be implemented in any convenient form. For example, embodiments can be implemented by one or more suitable computer programs that can be carried on a suitable carrier medium, which can be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the invention can be implemented using suitable devices capable of specifically taking the form of a programmable computer running a computer program arranged to implement the methods described herein. Therefore, embodiments of the present disclosure can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure can also be implemented as instructions stored on a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium can include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium can include: read-only memory (ROM); random access memory (RAM); disk storage media; optical storage media; flash memory devices; electrical, optical, acoustic, or other forms of propagation signals (e.g., carrier waves, infrared signals, digital signals, etc.); and so on. Additionally, firmware, software, routines, and instructions can be described herein as performing certain actions. However, it should be understood that these descriptions are for convenience only, and these actions are actually caused by computing devices, processors, controllers, or other devices that execute firmware, software, routines, instructions, etc.

[0326] In the block diagram, the illustrated components are depicted as discrete functional blocks, but the embodiments are not limited to systems organized as illustrated in terms of functionality described herein. The functionality provided by each component may be provided by software or hardware modules organized in a manner different from that currently depicted, such as mixing, combining, copying, disassembling, distributing (e.g., within a data center or by region), or otherwise organizing such software or hardware. The functionality described herein may be provided by one or more processors of one or more computers executing process code stored on a tangible, non-transitory machine-readable medium. In some cases, a third-party content delivery network may have control over some or all of the information transmitted via the network, in which case, in cases where information (e.g., content) is allegedly supplied or otherwise provided, the information may be provided by sending instructions to retrieve it from the content delivery network.

[0327] Unless otherwise specifically stated, it should be understood from the discussion that throughout this specification, the use of terms such as “processing,” “computing / calculating,” “determining,” etc., refers to the operation or process of a particular device such as a dedicated computer or similar dedicated electronic processing / computing apparatus.

[0328] Embodiments of the present invention can be further described in the following aspects.

[0329] 1. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process, the method comprising:

[0330] Obtain measurement data for multiple features printed on a substrate;

[0331] Based on the indicators, the multiple features are grouped into multiple groups; and

[0332] A baseline failure rate model for the feature group is generated based on the measurement data associated with the feature group, wherein the baseline failure rate model is configured to identify process windows related to the failure rate of the feature group.

[0333] 2. The computer-readable medium according to aspect 1, wherein the index comprises: (a) a process window for each of the features, wherein the process window is a function of a process variable associated with the corresponding feature; and (b) a characteristic parameter associated with the corresponding feature.

[0334] 3. The computer-readable medium according to aspect 2, wherein the process variables include focal length and dose values ​​associated with the apparatus for the patterning process, and wherein the characteristic parameters include critical size (CD) values ​​of the corresponding features.

[0335] 4. The computer-readable medium according to aspect 3, wherein grouping the features comprises:

[0336] For each of the features, the average CD value of the corresponding feature and multiple dose and focal length values ​​associated with the average CD located at the edge of the process window of the corresponding feature are obtained as index values, and

[0337] The features are clustered into feature groups based on the index values ​​of the features, wherein features within a specific group have index values ​​that are within a first threshold.

[0338] 5. The computer-readable medium according to any one of aspects 1 to 4, wherein the clustering feature includes:

[0339] The features were clustered using the k-means algorithm.

[0340] 6. The computer-readable medium according to aspect 5, wherein obtaining the measurement data of the plurality of features includes:

[0341] Obtain an image having the features printed on the substrate, and

[0342] The image is analyzed to select those features that satisfy specified criteria as the plurality of features.

[0343] 7. The computer-readable medium according to aspect 6, wherein the designation criteria include the number of times a feature appears on the substrate is less than a first threshold, or the number of times the feature appears in one image of the image is less than a second threshold.

[0344] 8. The computer-readable medium according to aspect 6, wherein generating the basic failure rate model for the set of features comprises:

[0345] Obtain the average CD of the feature group;

[0346] The local CD uniformity (LCDU) data of the feature group are determined as the measurement data associated with the feature group;

[0347] Based on the LCDU data, obtain: (i) the probability density function of the CD of the feature group, which is defined as a function of the average CD, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the CD limit of the patterning process based on the failure rate measurement results of the features in the feature group.

[0348] The estimation failure rate of the feature set is determined based on the CD limit and the probability density function of the CD; and

[0349] A baseline failure rate model is generated, which identifies the process window associated with the dose value such that the estimated failure rate of the feature group is less than a predetermined threshold. 9. The computer-readable medium according to aspect 8, wherein the LCDU data for determining the feature group includes:

[0350] The LCDU data of the group is determined by the following operations:

[0351] The LCDU data for each feature in the group is obtained across the multiple images;

[0352] Obtain the CD mean for each feature of each of the plurality of images; and

[0353] Remove the CD mean from the LCDU data.

[0354] 10. The computer-readable medium according to aspect 8, wherein obtaining the probability density function of the CD of the feature set comprises:

[0355] Based on the variance of the dose value, the probability density function of the dose is determined for the dose value; and

[0356] The probability density function of the dose is converted into the probability density function of the CD based on a transformation function, wherein the transformation function is determined based on the function of the dose.

[0357] 11. The computer-readable medium according to aspect 1, wherein the failure rate relates to one or more failures of the feature, the one or more failures including physical failures, transfer failures, and / or delay failures of the feature.

[0358] 12. The computer-readable medium according to aspect 8 further includes:

[0359] The basic failure rate model is stored in a database, wherein the database includes multiple basic failure rate models, and each basic failure rate model corresponds to a feature group with a specified index value.

[0360] 13. The computer-readable medium according to aspect 12 further includes:

[0361] The base failure rate model and the characteristic data of the specific feature are used to generate a feature-specific failure rate model for the specific feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specific feature is below a specified threshold.

[0362] 14. The computer-readable medium according to aspect 12 further includes:

[0363] The base failure rate model is used to generate a feature-specific failure rate model for a specified feature group, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specified feature group is lower than a specified threshold.

[0364] 15. The computer-readable medium according to aspect 13, wherein generating the feature-specific failure rate model comprises:

[0365] Receive measurement data associated with the specific feature, wherein the measurement data includes CD values ​​of the specific feature for multiple dose values ​​and focal length values;

[0366] A specified index value is determined from the measurement data, wherein the specified index value is determined as a function of a specified average CD value and a plurality of dose values ​​and focal length values ​​associated with the specified average CD value located at the edge of a process window associated with the specific feature; and

[0367] Select a specified baseline failure rate model from the database, wherein the index value of the specified baseline failure rate model matches the specified index value.

[0368] 16. The computer-readable medium according to aspect 15 further includes:

[0369] The fundamental probability density function of CD is obtained from the specified fundamental failure rate model; and

[0370] The average CD of the base probability density function is adjusted based on the specified average CD value to produce an adjusted probability density function.

[0371] 17. The computer-readable medium according to aspect 16 further includes:

[0372] The adjusted probability density function is used to determine at least one of a first CD limit or a second CD limit for the patterning process, wherein if the CD of the specified feature is higher than the first CD limit or lower than the second CD limit, the estimated failure rate of the specified feature is within the specified threshold.

[0373] 18. The computer-readable medium according to aspect 17 further includes:

[0374] Obtain at least one of the inter-field CD variation, intra-field CD variation, and probability density function of the CD with the specific feature to serve as CD contour data; and

[0375] The adjusted probability density function is convolved with the CD contour data to produce a convolved probability density function associated with the specific feature.

[0376] 19. The computer-readable medium according to aspect 18 further includes:

[0377] The estimation failure rate of the specific feature is determined based on the first CD limit, the second CD limit, and the convolved probability density function; and

[0378] A failure rate model of the feature-specific process window is generated, which is configured to identify the feature-specific process window.

[0379] 20. The computer-readable medium according to aspect 19 further includes:

[0380] One or more devices of the patterning process are adjusted based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

[0381] 21. The computer-readable medium according to aspect 6, wherein generating the basic failure rate model for the set of features comprises:

[0382] Obtain the CDe parameters of the feature group.

[0383] The local CDe uniformity (LCDeU) data of the feature group is determined as the measurement data associated with the feature group.

[0384] Based on the LCDeU data, obtain: (i) the probability density function of CDe for the feature group, the probability density function being defined as a function of the CDe parameters, the dose values ​​of the patterning process, and the variance of the dose values ​​of the patterning process; and (ii) the CDe limit of the patterning process based on the failure rate measurement results of the features in the feature group.

[0385] The estimation failure rate of the feature set is determined based on the CDE limit and the probability density function of the CDE; and

[0386] The baseline failure rate model is generated, which identifies the process window associated with the dose value, such that the estimated failure rate of the feature set is less than a predetermined threshold.

[0387] 22. The computer-readable medium according to aspect 21, wherein the LCDeU data for determining the feature group comprises:

[0388] The LCDeU data of the group is determined by the following operations:

[0389] The LCDeU data for each feature in the group is obtained across the multiple images.

[0390] Obtain the mean CDE value for each feature of each of the plurality of images, and

[0391] Remove the mean CDe value from the LCDeU data.

[0392] 23. The computer-readable medium according to aspect 21, wherein obtaining the CDE parameters includes:

[0393] The CDe parameter is determined based on the edge placement error associated with the features of the feature group.

[0394] 24. The computer-readable medium according to aspect 23, wherein the edge placement error is determined based on the CD of the feature, the CD of the target feature corresponding to the feature, and the placement error of the feature.

[0395] 25. The computer-readable medium according to aspect 24, wherein the feature is a contact hole, and wherein the placement error is the deviation of the center of the contact hole printed on the substrate from the center of the target contact hole.

[0396] 26. The computer-readable medium according to aspect 6, wherein generating the basic failure rate model for the set of features comprises:

[0397] Obtain the average CD and PEe parameters of the feature group.

[0398] The LCDU data of the feature group are determined as the measurement data associated with the feature group, wherein the LCDU is determined based on the average CD.

[0399] Based on the LCDU data, obtain: (i) the probability density function of PEE for the feature group, the probability density function being defined as a function of the PEE parameters, the dose values ​​of the patterning process, and the variance of the dose values ​​of the patterning process; and (ii) the PEE limit of the patterning process based on the failure rate measurement results of the features in the feature group.

[0400] The estimated failure rate of the feature set is determined based on the PEe limit and the probability density function of PEe.

[0401] The baseline failure rate model is generated, which identifies the process window associated with the dose value, such that the estimated failure rate of the feature set is less than a predetermined threshold.

[0402] 27. The computer-readable medium according to aspect 26, wherein obtaining the PEE parameter comprises:

[0403] The PEe parameter is determined based on the CD of the target feature corresponding to the feature group and the placement error of the feature.

[0404] 28. The computer-readable medium according to aspect 1, wherein obtaining the measurement data includes:

[0405] Obtain a first set of process windows for the feature, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, wherein the first set of process windows includes a first process window of a first feature in the feature;

[0406] Based on the first set of process windows, multiple process window indicators for the feature are obtained; and

[0407] The features are classified based on one or more of the process window indicators.

[0408] 29. The computer-readable medium according to aspect 28 further includes:

[0409] Critical features are determined based on the grading, wherein the critical features include those features that have one or more process window indicators that satisfy a specified threshold.

[0410] 30. The computer-readable medium according to aspect 29, wherein generating the basic failure rate model for the set of features comprises:

[0411] Determine a first feature group within the group that has one or more of the critical features; and

[0412] Generate the basic failure rate model of the first feature group.

[0413] 31. The computer-readable medium according to aspect 28, wherein obtaining the first set of process windows includes:

[0414] Plot the relationship between the first characteristic parameter of the first feature and the dose value and focal length value on a graph to generate the shape of the first process window.

[0415] 32. The computer-readable medium according to aspect 28, wherein the first characteristic parameter includes one of the CD of the first feature, defect count, failure rate, random edge placement error failure rate, or random placement error.

[0416] 33. The computer-readable medium according to aspect 28, wherein obtaining the process window index includes:

[0417] Perform a shape fitting operation to insert the shape into the first process window to obtain one or more of the exposure latitude, depth of focus, or area of ​​the shape as the process window metric.

[0418] 34. The computer-readable medium according to aspect 33, wherein performing the shape fitting operation comprises:

[0419] The shape fitting operation is performed based on specified conditions to fit the ellipse into the first process window.

[0420] 35. The computer-readable medium according to aspect 34, wherein the specified conditions include an ellipse having (i) a specified area, (ii) a specified exposure latitude, or (iii) a position representing a specified dose value and focal length value on a graph.

[0421] 36. The computer-readable medium according to aspect 34, wherein performing the shape fitting operation comprises:

[0422] The exposure tolerance is defined as a function of the height of the ellipse and the dose value corresponding to the center of the ellipse.

[0423] 37. The computer-readable medium according to aspect 36, wherein the height is determined by the range of dose values ​​occupied by the ellipse on a graph of the first process window.

[0424] 38. The computer-readable medium according to aspect 34, wherein performing the shape fitting operation comprises:

[0425] The depth of focus is determined based on the width of the ellipse, wherein the width is determined by the range of focal length values ​​occupied by the ellipse on the graph of the first process window.

[0426] 39. The computer-readable medium according to aspect 28, wherein obtaining the process window index for the first feature comprises:

[0427] Obtain a second set of process windows for the feature, wherein the second set of process windows includes a second process window for the first feature, wherein the second set of process windows is a function of (i) a second characteristic parameter associated with the feature and (ii) a second set of dose values ​​and focal length values ​​associated with the second characteristic parameter;

[0428] An overlay operation is performed using the first process window and the second process window to generate an overlay process window, wherein the overlay process window is the intersection area of ​​the shapes of the first process window and the second process window on the graph; and

[0429] The process window index for the first feature is obtained based on the overlaid process window.

[0430] 40. The computer-readable medium according to aspect 28 further includes:

[0431] A set of process window indices for each group in the feature group is obtained based on the process window associated with the failure rate of the corresponding group; and

[0432] The feature groups are hierarchically classified based on one or more of the group process window indicators.

[0433] 41. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process, the method comprising:

[0434] Obtain measurement data for multiple features printed on a substrate;

[0435] Characteristic parameters of the plurality of features are derived from the measurement data, wherein the measurement data includes data indicating the placement error of the plurality of features; and

[0436] A failure rate model for the feature is generated based on the characteristic parameters associated with the feature, wherein the failure rate model is configured to determine a process window corresponding to the failure rate of the feature.

[0437] 42. The computer-readable medium according to aspect 41, wherein the measurement data includes one or more edge placement error (EPE) values ​​or placement error (PE) values ​​associated with a feature of the feature.

[0438] 43. The computer-readable medium according to aspect 42, wherein the PE value is determined based on the deviation of a portion of the feature from a corresponding portion of a corresponding target feature.

[0439] 44. The computer-readable medium according to aspect 42, wherein the EPE value is determined based on the CD value of the feature, the PE value of the feature, and the target CD value of the corresponding target feature.

[0440] 45. The computer-readable medium according to aspect 42, wherein the characteristic parameter is a parameter derived from at least one of the PE value or the EPE value in combination with the CD value.

[0441] 46. ​​The computer-readable medium according to aspect 42, wherein the characteristic parameter includes a CDe parameter derived from the CD value and the PE value associated with the characteristic.

[0442] 47. The computer-readable medium according to aspect 42, wherein the characteristic parameter includes a PEe parameter derived from a target CD value of a target feature corresponding to the feature and a PE value associated with the feature.

[0443] 48. The computer-readable medium according to aspect 41, wherein the failure rate model that generates the feature comprises:

[0444] The LCDU data of the feature is determined based on the aforementioned characteristic parameters;

[0445] Based on the LCDU data, obtain (i) the probability density function of the characteristic parameter of the feature, the probability density function being defined as a function of the characteristic parameter, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the characteristic parameter limit of the failure rate measurement result of the patterning process based on the feature.

[0446] The estimation failure rate of the feature is determined based on the limit of the characteristic parameter and the probability density function of the characteristic parameter; and

[0447] The failure rate model is generated, which is operable to determine a process window related to the dose value such that the estimated failure rate of the feature is less than a predetermined threshold.

[0448] 49. The computer-readable medium according to aspect 48, wherein the LCDU data for determining the feature includes:

[0449] The LCDU data for the feature is determined by the following operations:

[0450] Obtain the LCDU data for each of the features.

[0451] Obtain the average value of the characteristic parameters for each feature, and

[0452] Remove the average value from the LCDU data.

[0453] 50. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window of a patterning process, the method comprising:

[0454] Measurement data of multiple features printed on a substrate are obtained, wherein the measurement data includes one or more of a CD value, an edge placement error (EPE) value, or a placement error (PE) value associated with the feature.

[0455] Derive characteristic parameters of the plurality of features, wherein the characteristic parameters include CDe parameters derived from the CD value and the PE value; and

[0456] A failure rate model for the feature is generated based on the characteristic parameters associated with the feature, wherein the failure rate model is configured to identify process windows related to the failure rate of the feature.

[0457] 51. The computer-readable medium according to aspect 50, wherein generating the failure rate model comprises:

[0458] The local CDeU (LCDeU) data of the feature is determined based on the CDe parameters.

[0459] Based on the LCDeU data, obtain: (i) the probability density function of CDe for the feature, which is defined as a function of the CDe parameters, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the CDe limit of the failure rate measurement results of the patterning process based on the feature.

[0460] The estimation failure rate of the feature is determined based on the CDE limit and the probability density function of the CDE; and

[0461] The failure rate model is generated, and the failure rate model identifies the process window associated with the dose value, such that the estimated failure rate of the feature is less than a predetermined threshold.

[0462] 52. The computer-readable medium according to aspect 51, wherein the LCDeU data for determining the feature includes:

[0463] The LCDeU data of the feature is determined by the following operations:

[0464] Obtain the LCDeU data for each of the features;

[0465] Obtain the CDE mean for each feature; and

[0466] Remove the mean CDe value from the LCDeU data.

[0467] 53. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process, the method comprising:

[0468] Measurement data of multiple features printed on a substrate are obtained, wherein the measurement data includes one or more of a CD value, an edge placement error (EPE) value, or a placement error (PE) value associated with the feature.

[0469] Derive the characteristic parameters of the feature, wherein the characteristic parameters include the PEE parameter derived from the target CD value and the PE value; and

[0470] A failure rate model for the feature is generated based on the characteristic parameters associated with the feature, wherein the failure rate model is configured to identify process windows related to the failure rate of the feature.

[0471] 54. The computer-readable medium according to aspect 53, wherein generating the failure rate model comprises:

[0472] Obtain the average CD of the aforementioned features;

[0473] The LCDU data for the feature is determined based on the average CD;

[0474] Based on the LCDU data, obtain: (i) the probability density function of PEE for the feature, which is defined as a function of the PEE parameter, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the PEE limit of the patterning process based on the failure rate measurement results of the feature in the feature.

[0475] The estimation failure rate of the feature is determined based on the PEe limit and the probability density function of the PEe; and

[0476] The failure rate model is generated, which identifies the process window associated with the dose value, such that the estimated failure rate of the feature is less than a predetermined threshold.

[0477] 55. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window of a patterning process based on a failure rate, the method comprising:

[0478] Multiple features are grouped into multiple groups based on indicators, wherein each of the multiple groups includes a subset of the features;

[0479] A baseline failure rate model for the groups is generated based on measurement data associated with features within the groups, wherein the baseline failure rate model identifies a process window associated with the estimated failure rate of the feature groups; and

[0480] The base failure rate model and measurement data associated with the specified feature are used to generate a feature-specific failure rate model for the specified feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specified feature is below a specified threshold.

[0481] 56. The computer-readable medium according to any one of aspects 55, wherein grouping the features comprises:

[0482] For each of the features, obtain the average CD value for the corresponding feature and multiple dose and focal length values ​​associated with the average CD located at the edge of the process window for the corresponding feature.

[0483] The features are clustered into groups based on the index values ​​of the features, wherein the features in a particular group have index values ​​that vary within a first threshold.

[0484] 57. The computer-readable medium according to aspect 55 further includes:

[0485] The basic failure rate model is stored in a database, wherein the database includes multiple basic failure rate models, and each basic failure rate model corresponds to a feature group with a specified index value.

[0486] 58. The computer-readable medium according to aspect 57, wherein generating the feature-specific failure rate model comprises:

[0487] Receive measurement data associated with the specified feature, wherein the measurement data includes an average CD value of the specified feature for multiple dose values ​​and focal length values;

[0488] A specified index value is determined from the measurement data associated with the specified feature, wherein the specified index value is determined as a function of a specified average CD value and a dose value associated with the specified average CD value located at the edge of the process window associated with the specified feature at a specified focal length value; and

[0489] Select a specified baseline failure rate model from the database, wherein the index value of the specified baseline failure rate model matches the specified index value.

[0490] 59. The computer-readable medium according to aspect 58 further includes:

[0491] The fundamental probability density function of CD is obtained from the specified fundamental failure rate model; and

[0492] The average CD of the base probability density function is adjusted based on the specified average CD value to produce an adjusted probability density function.

[0493] 60. The computer-readable medium according to aspect 59 further includes:

[0494] The adjusted probability density function is used to determine a first CD limit or a second CD limit for the patterning process, wherein the estimated failure rate of the specified feature is within the specified threshold when the CD of the specified feature is higher than the first CD limit or lower than the second CD limit.

[0495] 61. The computer-readable medium according to aspect 60 further includes:

[0496] Obtain at least one of the inter-field CD variation, intra-field CD variation, and probability density function of the specified CD feature as CD contour data; and

[0497] The adjusted probability density function is convolved with the CD contour data to produce a convolved probability density function.

[0498] 62. The computer-readable medium according to aspect 61 further includes:

[0499] The estimation failure rate of the specific feature is determined based on the first CD limit, the second CD limit, and the convolved probability density function; and

[0500] Generate the feature-specific failure rate model, which identifies the feature-specific process window such that the estimated failure rate of the specified feature is less than the specified threshold.

[0501] 63. The computer-readable medium according to aspect 62 further includes:

[0502] One or more devices of the patterning process are adjusted based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

[0503] 64. The computer-readable medium according to aspect 63, wherein the one or more devices include a photolithography apparatus configured to perform patterning on the substrate based on the feature-specific process window.

[0504] 65. A method for determining a process window in a patterning process, the method comprising:

[0505] Obtain measurement data for multiple features printed on a substrate;

[0506] The features are grouped into multiple groups based on indicators; and

[0507] A baseline failure rate model for the feature group is generated based on the measurement data associated with the feature group, wherein the baseline failure rate model is configured to identify process windows related to the failure rate of the feature group.

[0508] 66. A method for determining a process window in a patterning process, the method comprising:

[0509] Obtain measurement data for multiple features printed on a substrate;

[0510] The multiple features are grouped into multiple groups based on indicators, wherein each of the multiple groups includes a subset of the features;

[0511] A base failure rate model for the plurality of groups is generated based on the measurement data associated with the feature groups, wherein the base failure rate model is configured to identify process windows related to the failure rate of the feature groups; and

[0512] The feature-specific failure rate model is generated using the base failure rate model and measurement data associated with the feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the feature is below a specified threshold.

[0513] 67. A non-transitory computer-readable medium having instructions recorded thereon, which, when executed by a computer, perform the method as described in any of the preceding aspects.

[0514] 68. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining critical features printed on a substrate, the method comprising:

[0515] Obtain measurement data for multiple features printed on a substrate;

[0516] The first set of process windows for the feature is obtained based on the measurement data, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, and wherein the first set of process windows includes a first process window of a first feature in the feature;

[0517] Based on the first set of process windows, obtain multiple process window indices for each of the features; and

[0518] Those features that have one or more process window indicators that satisfy a specified threshold are identified as critical features.

[0519] 69. The computer-readable medium according to aspect 68 further includes:

[0520] The multiple features are grouped into multiple groups based on the indicators;

[0521] Determine a feature group within the group that has one or more of the critical features; and

[0522] A baseline failure rate model for the feature group is generated based on the measurement data associated with the feature group, wherein the baseline failure rate model is configured to identify process windows related to the failure rate of the feature group.

[0523] 70. The computer-readable medium according to aspect 68, wherein obtaining the process window index comprises:

[0524] Perform a shape fitting operation to insert the shape into the first process window to obtain one or more of the exposure latitude, depth of focus, or area of ​​the shape as the process window index of the first feature.

[0525] 71. The computer-readable medium according to aspect 70, wherein performing the shape fitting operation comprises:

[0526] The shape fitting operation is performed based on specified conditions to fit the ellipse into the first process window.

[0527] 72. The computer-readable medium according to aspect 71, wherein the specified conditions include an ellipse having (i) a specified area, (ii) a specified exposure latitude, or (iii) a position representing a specified dose value and focal length value on a graph.

[0528] 73. The computer-readable medium according to aspect 71, wherein performing the shape fitting operation comprises:

[0529] The exposure tolerance is defined as a function of the height of the ellipse and the dose value corresponding to the center of the ellipse.

[0530] 74. The computer-readable medium according to aspect 73, wherein the height is determined by the range of dose values ​​occupied by the ellipse on a graph of the first process window.

[0531] 75. The computer-readable medium according to aspect 71, wherein performing the shape fitting operation comprises:

[0532] The depth of focus is determined based on the width of the ellipse, wherein the width is determined by the range of focal length values ​​occupied by the ellipse on the graph of the first process window.

[0533] 76. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining critical features printed on a substrate, the method comprising:

[0534] Obtain measurement data for multiple features printed on a substrate;

[0535] The first set of process windows for the feature is obtained based on the measurement data, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, and wherein the first set of process windows includes a first process window of a first feature in the feature;

[0536] A second set of process windows is obtained based on the measurement data to obtain the feature, wherein the second set of process windows represents a second characteristic parameter of the feature for a second set of dose values ​​and focal length values, wherein the second characteristic parameter is different from the first characteristic parameter, and wherein the second set of process windows includes the second process window of the first feature;

[0537] An overlay operation is performed using the first process window and the second process window to generate a first overlay process window, wherein the first overlay process window is the intersection area of ​​the shapes of the first process window and the second process window on the graph;

[0538] Based on the overlay process windows of the corresponding features, multiple process window indices for each of the features are obtained; and

[0539] Those features that have one or more process window indicators that satisfy a specified threshold are identified as critical features.

[0540] 77. The computer-readable medium according to aspect 76 further includes:

[0541] The multiple features are grouped into multiple groups based on the indicators;

[0542] Determine a feature group within the group that has one or more of the critical features; and

[0543] A baseline failure rate model for the feature group is generated based on the measurement data associated with the feature group, wherein the baseline failure rate model is configured to identify process windows related to the failure rate of the feature group.

[0544] 78. The computer-readable medium according to aspect 76, wherein obtaining the process window index comprises:

[0545] Perform a shape fitting operation to insert the shape into the first process window to obtain one or more of the process window indices of the first feature, such as exposure latitude, depth of focus, or area of ​​the shape.

[0546] 79. The computer-readable medium according to aspect 78, wherein performing the shape fitting operation comprises:

[0547] The shape fitting operation is performed based on specified conditions to fit the ellipse into the first process window.

[0548] 80. The computer-readable medium according to aspect 79, wherein the specified conditions include an ellipse having (i) a specified area, (ii) a specified exposure latitude, or (iii) a position centered on a specified dose value and focal length value on a graph.

[0549] 81. The computer-readable medium according to aspect 79, wherein performing the shape fitting operation comprises:

[0550] The exposure tolerance is defined as a function of the height of the ellipse and the dose value corresponding to the center of the ellipse.

[0551] 82. The computer-readable medium according to aspect 81, wherein the height is determined by the range of dose values ​​occupied by the ellipse on a graph of the first process window.

[0552] 83. The computer-readable medium according to aspect 79, wherein performing the shape fitting operation comprises:

[0553] The depth of focus is determined based on the width of the ellipse, wherein the width is determined by the range of focal length values ​​occupied by the ellipse on the graph of the first process window.

[0554] 84. A method comprising

[0555] Obtain measurement data for multiple features printed on a substrate; and

[0556] A basic failure rate model for a feature set is generated based on the measurement data associated with that feature set, wherein the features in the feature set are distinct, and the basic failure rate model is configured to identify a process window based on the failure rate of the feature set.

[0557] 85. The method according to aspect 84 further includes grouping the plurality of features into a plurality of groups including the groups based on an index.

[0558] 86. The computer-readable medium according to aspect 84, wherein the index comprises: (a) a process window for each of the features, wherein the process window is a function of a process variable associated with the corresponding feature; and (b) a characteristic parameter associated with the corresponding feature.

[0559] 87. The method according to aspect 85, wherein the process variables include focal length and dose values ​​associated with the device used for the patterning process, and wherein the characteristic parameter includes the critical size (CD) value of the corresponding feature.

[0560] 88. The method according to aspect 85, wherein grouping the features comprises:

[0561] For each of the features, the average CD value of the corresponding feature and multiple dose and focal length values ​​associated with the average CD located at the edge of the process window of the corresponding feature are obtained as index values, and

[0562] The features are clustered into feature groups based on the index values ​​of the features, wherein features within a specific group have index values ​​that are within a first threshold.

[0563] 89. The method according to aspect 84, wherein obtaining the measurement data of the plurality of features comprises:

[0564] Obtain an image having the features printed on the substrate, and

[0565] The image is analyzed to select features that meet specified criteria as the plurality of features.

[0566] 90. The method according to aspect 89, wherein the designation criteria include the number of times a feature appears on the substrate is less than a first threshold, or the number of times the feature appears in one image of the image is less than a second threshold.

[0567] 91. The method according to aspect 84, wherein generating the basic failure rate model for the feature set comprises:

[0568] Obtain the average CD of the feature group;

[0569] The local CD uniformity (LCDU) data of the feature group are determined as the measurement data associated with the feature group;

[0570] Based on the LCDU data, obtain: (i) the probability density function of the CD of the feature group, which is defined as a function of the average CD, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the CD limit of the patterning process based on the failure rate measurement results of the features in the feature group.

[0571] The estimation failure rate of the feature set is determined based on the CD limit and the probability density function of the CD; and

[0572] The baseline failure rate model is generated, which identifies the process window associated with the dose value, such that the estimated failure rate of the feature set is less than a predetermined threshold.

[0573] 92. The method according to aspect 84 further includes:

[0574] The base failure rate model and the characteristic data of the specific feature are used to generate a feature-specific failure rate model for the specific feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specific feature is below a specified threshold.

[0575] 93. The method according to aspect 92, wherein generating the feature-specific failure rate model comprises:

[0576] Receive measurement data associated with the specific feature, wherein the measurement data includes CD values ​​of the specific feature for multiple dose values ​​and focal length values;

[0577] A specified index value is determined from the measurement data, wherein the specified index value is determined as a function of a specified average CD value and a plurality of dose values ​​and focal length values ​​associated with the specified average CD value located at the edge of a process window associated with the specific feature; and

[0578] Select a specified baseline failure rate model from the database, wherein the index value of the specified baseline failure rate model matches the specified index value.

[0579] 94. The method according to aspect 92 further includes:

[0580] The fundamental probability density function of CD is obtained from the specified fundamental failure rate model; and

[0581] The average CD of the base probability density function is adjusted based on the specified average CD value to produce an adjusted probability density function.

[0582] 95. The computer-readable medium according to aspect 94 further includes:

[0583] Obtain at least one of the inter-field CD variation, intra-field CD variation, and probability density function of the CD with the specific feature to serve as CD contour data; and

[0584] The adjusted probability density function is convolved with the CD contour data to produce a convolved probability density function associated with the specific feature.

[0585] 96. The computer-readable medium according to aspect 12 further includes:

[0586] The estimation failure rate of the specific feature is determined based on the first CD limit, the second CD limit, and the convolved probability density function; and

[0587] A failure rate model of the feature-specific process window is generated, which is configured to identify the feature-specific process window.

[0588] 97. The method according to aspect 92 further includes:

[0589] One or more devices of the patterning process are adjusted based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

[0590] 98. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform the methods described in aspects 84 to 97.

[0591] Readers should understand that this application describes several inventions. These inventions have been combined into a single document rather than separated into multiple individual patent applications because the related subject matter of the inventions makes them conducive to economic development in application. However, the different advantages and items of these inventions should not be combined. In some cases, embodiments resolve all the deficiencies mentioned herein, but it should be understood that the inventions are independently useful and some embodiments solve only a subset of these problems or provide other unmentioned benefits that will be apparent to those skilled in the art upon review of this disclosure. Due to cost constraints, some inventions disclosed herein may not be claimed at present, and such inventions may be claimed in later applications (such as continuation-in-process or by amending the claims of the invention). Similarly, due to space limitations, the abstract and the section on the content of the invention in this document should not be considered as containing a comprehensive list of all such inventions or all items of such inventions.

[0592] It should be understood that the description and drawings are not intended to limit this disclosure to the specific forms disclosed, but rather, the invention is intended to cover all modifications, equivalents and alternatives that fall within the spirit and scope of the invention as defined by the appended claims.

[0593] Based on this specification, those skilled in the art will understand modifications and alternative embodiments of various items of the invention. Therefore, this specification and drawings should be understood as illustrative only and for the purpose of teaching those skilled in the art the general manner of the invention. It should be understood that the forms of the invention shown and described herein should be considered as examples of embodiments. Elements and materials may be substituted for the parts and materials illustrated and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and features of embodiments or embodiments may be combined, as will be understood by those skilled in the art upon obtaining the benefits of this specification. Changes may be made to the elements described herein without departing from the spirit and scope of the invention as described in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of this specification.

[0594] As used throughout this application, the word “may” is used in a permissive sense (i.e., meaning possible) rather than a mandatory sense (i.e., meaning must). The words “include / including / includes” and so on mean, but are not limited to. As used throughout this application, the singular form “a / an / the” includes multiple references unless explicitly indicated otherwise. Thus, for example, a reference to an element “a / an or a” includes a combination of two or more elements, but other terms and phrases such as “one or more” may be used for one or more elements. Unless otherwise indicated, the term “or” is non-exclusive, i.e., encompasses both “and” and “or”. Terms describing conditional relationships, such as “in response to X, and Y,” “after X, Y,” “if X, then Y,” “when X, Y,” etc., encompass causal relationships, where the premise is a necessary causal condition, the premise is a sufficient causal condition, or the premise is a contributing causal condition to the outcome. For example, “after condition Y is obtained, state X occurs” is general for “only after Y, X occurs” and “after Y and Z, X occurs.” These conditional relationships are not limited to results obtained immediately by following the premises, because some results may be delayed, and in conditional statements, the premise is connected to its outcome, for example, the premise is related to the probability of the outcome occurring. Unless otherwise indicated, a statement that multiple properties or functions are mapped to multiple objects (e.g., one or more processors performing steps A, B, C, and D) covers both cases where all these properties or functions are mapped to all these objects and cases where a subset of said properties or functions is mapped to a subset of properties or functions (e.g., all processors perform steps A through D respectively, and processor 1 performs step A, processor 2 performs a portion of steps B and C, and processor 3 performs a portion of step C and step D). Furthermore, unless otherwise indicated, a statement that a value or action is “based on” another condition or value covers both the case where the condition or value is the only factor and the case where the condition or value is a factor among multiple factors. Unless otherwise indicated, a statement that “each” instance in a set has a certain property should not be construed as excluding the case where some other identical or similar components of a larger set do not have the stated property (i.e., each does not necessarily mean every). References to selections from a range include the endpoints of the range.

[0595] In the above description, any process, description, or block in the flowchart should be understood as representing a module, fragment, or portion of code, which includes one or more executable instructions for implementing a specific logical function or step in the process, and alternative implementations are included within the scope of exemplary embodiments of the present invention, wherein functionality may depend on the functionality involved and may not be performed in the order shown or discussed, including substantially simultaneously or in reverse order, as will be understood by those skilled in the art.

[0596] Where certain U.S. patents, U.S. patent applications, or other materials (e.g., papers) are incorporated by reference, the text of those U.S. patents, U.S. patent applications, and other materials is incorporated by reference only if there is no conflict between such materials and the statements and figures set forth herein. In the event of such a conflict, any such conflicting text in those U.S. patents, U.S. patent applications, and other materials is not specifically incorporated by reference herein.

[0597] While certain embodiments have been described, these embodiments are presented by way of example only and are not intended to limit the scope of this disclosure. In fact, the novel methods, apparatuses, and systems described herein may be embodied in many other forms; furthermore, various omissions, substitutions, and changes may be made to the forms of the methods, apparatuses, and systems described herein without departing from the spirit of the invention. The appended claims and their equivalents are intended to cover such forms or modifications that fall within the scope and spirit of this disclosure.

Claims

1. A non-transitory computer-readable medium having instructions that, when executed by a computer, cause the computer to perform a method for determining a process window for a patterning process, the method comprising: Obtain measurement data for multiple features printed on a substrate; A baseline failure rate model for a set of features is generated based on measurement data associated with that set of features, wherein the features in the set are distinct, and the baseline failure rate model is configured to identify a process window based on the failure rate of the set of features; and The base failure rate model and characteristic data of the specific feature are used to generate a feature-specific failure rate model for the specific feature, wherein the feature-specific failure rate model identifies a feature-specific process window such that the estimated failure rate of the specific feature is below a specified threshold.

2. The computer-readable medium of claim 1 further comprises grouping the plurality of features into a plurality of groups including the groups based on an index.

3. The computer-readable medium according to claim 2, wherein, The metrics include: (a) a process window for each of the features, wherein the process window is a function of a process variable associated with the corresponding feature; and (b) a characteristic parameter associated with the corresponding feature.

4. The computer-readable medium according to claim 3, wherein, The process variables include focal length and dose values ​​associated with the device used for the patterning process, and the characteristic parameters include the critical size (CD) value of the corresponding feature.

5. The computer-readable medium according to claim 3, wherein, The feature grouping includes: For each of the features, the average CD value of the corresponding feature and multiple dose and focal length values ​​associated with the average CD located at the edge of the process window of the corresponding feature are obtained as index values, and The features are clustered into feature groups based on the index values ​​of the features, wherein features within a specific group have index values ​​that are within a first threshold.

6. The computer-readable medium according to claim 1, wherein, Obtaining the measurement data for the multiple features includes: Obtain an image having the features printed on the substrate, and The image is analyzed to select features that meet specified criteria as the plurality of features.

7. The computer-readable medium according to claim 6, wherein, The specified criteria include the number of times a feature appears on the substrate is less than a first threshold, or the number of times a feature appears in one of the images is less than a second threshold.

8. The computer-readable medium according to claim 1, wherein, Generating the base failure rate model for the feature set includes: Obtain the average CD of the feature group; The local CD uniformity (LCDU) data of the feature group are determined as the measurement data associated with the feature group; Based on the LCDU data, obtain: (i) the probability density function of the CD of the feature group, which is defined as a function of the average CD, the dose value of the patterning process, and the variance of the dose value of the patterning process; and (ii) the CD limit of the patterning process based on the failure rate measurement results of the features in the feature group. The estimation failure rate of the feature set is determined based on the CD limit and the probability density function of the CD; and The baseline failure rate model is generated, which identifies the process window associated with the dose value, such that the estimated failure rate of the feature set is less than a predetermined threshold.

9. The computer-readable medium according to claim 1, wherein, Generating the feature-specific failure rate model includes: Receive measurement data associated with the specific feature, wherein the measurement data includes CD values ​​of the specific feature for multiple dose values ​​and focal length values; A specified index value is determined from the measurement data, wherein the specified index value is determined as a function of a specified average CD value and a plurality of dose values ​​and focal length values ​​associated with the specified average CD value located at the edge of a process window associated with the specific feature; and Select a specified baseline failure rate model from the database, wherein the index value of the specified baseline failure rate model matches the specified index value.

10. The computer-readable medium of claim 1, further comprising: The fundamental probability density function of CD is obtained from the specified fundamental failure rate model; as well as The average CD of the base probability density function is adjusted based on the specified average CD value to produce an adjusted probability density function.

11. The computer-readable medium of claim 10, further comprising: At least one of the inter-field CD change, intra-field CD change, and probability density function of the CD with the specific feature is obtained as CD contour data; as well as The adjusted probability density function is convolved with the CD contour data to produce a convolved probability density function associated with the specific feature.

12. The computer-readable medium of claim 11, further comprising: The estimation failure rate of the specific feature is determined based on the first CD limit, the second CD limit, and the convolved probability density function. as well as A failure rate model of the feature-specific process window is generated, which is configured to identify the feature-specific process window.

13. The computer-readable medium of claim 1, further comprising: One or more devices of the patterning process are adjusted based on the process window associated with the specified feature to minimize the failure rate associated with the specified feature.

14. The computer-readable medium according to claim 1, wherein, Obtaining the measurement data includes: Obtain a first set of process windows for the feature, wherein the first set of process windows represents a first characteristic parameter of the feature for a first set of dose values ​​and focal length values, wherein the first set of process windows includes a first process window of a first feature in the feature; Based on the first set of process windows, obtain multiple process window indicators for the feature; and The features are graded based on one or more of the process window indicators. Furthermore, obtaining the process window index for the first feature includes: Obtain a second set of process windows for the feature, wherein the second set of process windows includes a second process window for the first feature, wherein the second set of process windows is a function of (i) a second characteristic parameter associated with the feature and (ii) a second set of dose values ​​and focal length values ​​associated with the second characteristic parameter; An overlay operation is performed using the first process window and the second process window to generate an overlay process window, wherein the overlay process window is the intersection area of ​​the shapes of the first process window and the second process window on the graph; and The process window index for the first feature is obtained based on the overlaid process window.

Images