Method and system for identifying center of pattern using automatic thresholding

Abstract

A method for selecting a threshold for processing an image to determine a characteristic of a pattern is described herein. The method includes accessing an image representation of the pattern and generating a plurality of two-dimensional (2D) contours of a feature of the pattern using different thresholds, wherein each of the 2D contours corresponds to a respective threshold. The 2D contour is evaluated to determine a KPI value for the 2D contour, and a specified threshold from the range of thresholds is selected based on the evaluation of the 2D contour.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. application 63 / 445,247, filed on February 13, 2023, which is incorporated herein by reference in its entirety. Technical Field

[0003] Embodiments provided herein relate to semiconductor manufacturing, and more particularly, to semiconductor metrology and inspection. Background Art

[0004] A lithography apparatus is a machine that applies a desired pattern to a target portion of a substrate. A lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, the IC chip in a smartphone can be as small as a human thumbnail and can include more than 2 billion transistors. Manufacturing ICs is a complex and time-consuming process, with circuit components in different layers and involving hundreds of individual steps. Even a mistake in a single step can cause problems in the final IC and potentially lead to device failure. High process yields and high wafer throughput can be affected by the presence of defects.

[0005] Metrology processes are used at various steps during the patterning process to monitor and / or control the patterning process. For example, metrology processes are used to measure one or more characteristics of a substrate, such as the relative positions (e.g., registration, overlay, alignment, etc.) or dimensions (e.g., line width, critical dimension (CD), thickness, etc.) of features formed on the substrate during the patterning process or random variations, so that, for example, the performance of the patterning process can be determined from the one or more characteristics. If one or more characteristics are unacceptable (e.g., outside a predetermined range for the characteristic(s),) one or more variables of the patterning process can be designed or changed, for example, based on the measurement of the one or more characteristics, so that the substrate manufactured by the patterning process has acceptable characteristic(s). Summary of the Invention

[0006] In some embodiments, a method for automatically selecting a threshold value when processing an image to determine a metrological characteristic of a pattern is provided. The method includes: accessing an image representation of the pattern; generating a plurality of two-dimensional (2D) profiles of a first feature of the pattern by processing the image representation using different thresholds, wherein each of the 2D profiles corresponds to a respective threshold value; evaluating the 2D profiles; and selecting a specified threshold value from the threshold values ​​based on the evaluation.

[0007] In some embodiments, a method for determining a center of a feature of a pattern by selecting a threshold for processing an image representing the pattern is provided. The method includes: accessing an image representation representing the pattern; iteratively thresholding the image representation using different thresholds to generate a plurality of 2D profiles of a first feature of the pattern, wherein each of the 2D profiles corresponds to a respective threshold; selecting a specified threshold among the thresholds based on a performance indicator associated with the 2D profiles; and determining the center of the first feature using the 2D profiles generated using the specified threshold.

[0008] In some embodiments, a non-transitory computer-readable medium is provided. The non-transitory computer-readable medium has instructions. When the instructions are executed by a computer, the computer performs the method of any one of the above embodiments.

[0009] In some embodiments, a device is provided. The device includes a memory storing an instruction set and a processor. The processor is configured to execute the instruction set to enable the device to perform the method of any one of the above embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0011] Figure 1 is a schematic diagram illustrating an exemplary electron beam inspection (EBI) system according to an embodiment.

[0012] Figure 2 is a schematic diagram of an exemplary electron beam tool according to an embodiment.

[0013] Figure 3 Depicted is a schematic representation of overall lithography showing the collaboration between three technologies to optimize semiconductor manufacturing, in accordance with an embodiment.

[0014] Figure 4 is a block diagram of a system for automatically selecting thresholds for processing an image of a pattern to determine attributes of features, consistent with various embodiments.

[0015] Figure 5 is a flow chart of a method for automatically selecting a threshold for processing an image of a pattern to determine attributes of a feature, consistent with various embodiments.

[0016] Figure 6 is a flow chart of a method for determining overlay error between features of a pattern using automatic thresholding, consistent with various embodiments.

[0017] 7A to 7DVarious geometric properties that may be used to determine key performance indicators (KPIs) of a two-dimensional (2D) profile of a feature are shown, consistent with various embodiments;

[0018] Figures 8A to 8N Various KPIs associated with 2D profiles are shown, consistent with various embodiments.

[0019] Figure 9 is a block diagram of an example computer system according to an embodiment.

[0020] The embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice these embodiments. It is important to note that the following figures and examples are not meant to limit the scope to a single embodiment, but rather that other embodiments are possible by interchanging some or all of the described or illustrated elements. Where convenient, the same reference numerals are used throughout the figures to represent identical or similar components. Where certain elements of these embodiments can be implemented partially or completely using known components, only those portions of such known components necessary for understanding the embodiments will be described, and detailed descriptions of the remaining portions of such known components will be omitted to avoid obscuring the description of the embodiments. In this specification, embodiments illustrating a single component should not be construed as limiting; rather, the scope is intended to encompass other embodiments including multiple identical components, and vice versa, unless expressly stated otherwise. Furthermore, applicants do not intend to attribute unusual or special meanings to any term in the specification or claims unless expressly stated otherwise. Furthermore, the scope includes currently and future known equivalents to the components mentioned herein by way of illustration. DETAILED DESCRIPTION

[0021] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. The process of transferring the desired pattern onto the substrate is called a patterning process. The patterning process may include a patterning step in which the pattern is transferred from a patterning device (e.g., a mask) to the substrate. Various variations (e.g., variations in the patterning process or the lithographic apparatus) may potentially limit the implementation of lithography for high-volume semiconductor manufacturing (HVM). High-resolution images of the substrate, such as those obtained using a scanning electron microscope (SEM), may be examined to determine any defects in the patterning process. For example, the image may be examined to determine overlay between features of the pattern. In order to determine overlay, it may be necessary to determine the position of the features. For example, in order to determine the overlay of a feature such as a via (e.g., a hole) with another feature, accurately determining the center of the via is an important step.

[0022] Conventional techniques employ various methods to determine the location of features (e.g., the center of a hole) in a pattern. For example, one method utilizes a user-input threshold to segment an SEM image and, after segmentation, counts the centers of via blob (blobs) from the binary image. However, conventional techniques have problems. For example, when there is significant overlay, the grayscale profile of the hole may be asymmetric due to interference from electronic signals from another layer in the pattern, causing the location of the midpoint of the profile (e.g., the center of the hole) to be very sensitive to the threshold selection, which affects the accuracy of overlay measurement. For example, a higher threshold may overestimate the overlay error, while a lower threshold may underestimate the overlay error. In addition, this method may require normalization of the image of the pattern, as any variation in intensity across the image may result in inaccurate determination of the center locations of various features. While other methods are available to determine the location of the center of the hole, these methods are not precise. For example, an ellipse fitting method, which finds the edge points of a hole and fits the detected edge points to an ellipse, assumes that the shape of the hole is like an ellipse, which may result in inaccurate determination of the center if the actual shape of the hole is not an ellipse. Similarly, mold matching methods that use a predefined template to locate holes and assign the template center to the hole center assume that the hole is shaped like a circle or that the hole matches a limited set of template shapes. This can lead to inaccurate determination of the center if the hole shape is not circular. These and other disadvantages exist.

[0023] Embodiments are disclosed for automatically selecting a threshold for processing an image representation of a pattern (e.g., a grayscale image) to determine properties of features of the pattern. For example, an image of the pattern is iteratively processed using thresholds within a specified search range, and for each threshold, a two-dimensional (2D) profile of a feature (e.g., a hole representing a via) is generated, and a characteristic parameter or key performance indicator (KPI) value is determined for each 2D profile. A threshold corresponding to a KPI value that matches a target KPI value can be selected as an optimal threshold for determining properties of a feature (e.g., the center of a hole). In some embodiments, the KPI is a function of a property (e.g., a geometric property) of the 2D profile. In some embodiments, the optimal threshold is where the actual 2D profile intersects an ideal 2D profile, which can result in a symmetrical 2D hole patch (e.g., height = width). By automatically determining the threshold based on the KPI, embodiments facilitate determining the location of a feature without being limited to a specific user input of the threshold or being limited to a specific shape of the 2D profile, thereby resulting in more accurate determination of (a) the location of the feature and (b) defects (e.g., overlay errors). Furthermore, because embodiments can process each feature in an image independently, the process is tolerant to image intensity variations across the image, which eliminates the need to normalize the image, thereby minimizing the time and computational resources consumed in determining defects. Thus, embodiments provide an improved defect detection process.

[0024] Now refer to Figure 1, Figure 1 An exemplary electron beam inspection (EBI) system 100 is shown in accordance with an embodiment of the present disclosure. Figure 1 As shown, the EBI system 100 includes a main chamber 110, a load lock chamber 120, an electron beam tool 140, and an equipment front end module (EFEM) 130. The electron beam tool 140 is located within the main chamber 110. The exemplary EBI system 100 can be a single beam system or a multi-beam system. Although the description and drawings are directed to electron beams, it should be understood that the embodiments are not intended to limit the present disclosure to specific charged particles.

[0025] EFEM 130 includes a first load port 130a and a second load port 130b. EFEM 130 may include additional load ports. First load port 130a and second load port 130b receive front-opening pods (FOUPs) containing wafers (e.g., semiconductor wafers or wafers made of other materials) or samples to be inspected (wafers and samples are collectively referred to as "wafers" hereinafter). One or more robotic arms (not shown) within EFEM 130 transfer the wafers to load lock chamber 120.

[0026] The load lock chamber 120 is connected to a load / lock vacuum pump system (not shown), which removes gas molecules from the load lock chamber 120 to a first pressure lower than atmospheric pressure. After reaching the first pressure, one or more robotic arms (not shown) transfer the wafer from the load lock chamber 120 to the main chamber 110. The main chamber 110 is connected to a main chamber vacuum pump system (not shown), which removes gas molecules from the main chamber 110 to a second pressure lower than the first pressure. After reaching the second pressure, the wafer is inspected by an electron beam tool 140. In some embodiments, the electron beam tool 140 may include a single beam inspection tool.

[0027] The controller 150 may be electrically connected to the electron beam tool 140 and may also be electrically connected to other components. The controller 150 may be a computer configured to perform various controls of the EBI system 100. The controller 150 may also include processing circuitry configured to perform various signal and image processing functions. Although the controller 150 is Figure 1 1. The controller 150 is shown as being external to the structure including the main cavity 110, the load lock cavity 120, and the EFEM 130, but it is understood that the controller 150 may also be part of the structure.

[0028] Figure 2 A schematic diagram of an exemplary imaging system 200 is shown, in accordance with an embodiment of the present disclosure. Figure 2The electron beam tool 140 can be configured for use in the EBI system 100. The electron beam tool 140 can be a single beam device or a multi-beam device. Figure 2 As shown, the electron beam tool 140 includes a motorized sample stage 201 and a wafer holder 202 supported by the motorized sample stage 201 to hold a wafer 203 to be inspected. The electron beam tool 140 also includes an objective lens assembly 204, an electron detector 206 (which includes electron sensor surfaces 206a and 206b), an objective lens aperture 208, a focusing lens 210, a beam limiting aperture 212, a gun aperture 214, an anode 216, and a cathode 218. In some embodiments, the objective lens assembly 204 can include a modified swinging objective retarding immersion lens (SORIL) including a pole piece 204a, a control electrode 204b, a deflector 204c, and an excitation coil 204d. The electron beam tool 140 can additionally include an energy dispersive X-ray spectrometer (EDS) detector (not shown) to characterize the material on the wafer 203.

[0029] A primary electron beam 220 is emitted from the cathode 218 by applying a voltage between the anode 216 and the cathode 218. The primary electron beam 220 passes through the gun aperture 214 and the beam limiting aperture 212, which together determine the size of the electron beam entering the converging lens 210, which is located below the beam limiting aperture 212. The converging lens 210 focuses the primary electron beam 220 before the electron beam enters the objective lens aperture 208 to set the size of the electron beam before the electron beam enters the objective lens assembly 204. The deflector 204c deflects the primary electron beam 220 to facilitate beam scanning on the wafer. For example, during a scan, the deflector 204c can be controlled to sequentially deflect the primary electron beam 220 to different locations on the top surface of the wafer 203 at different times to provide data for image reconstruction of different portions of the wafer 203. Furthermore, the deflector 204 c can also be controlled to deflect the primary electron beam 220 onto different sides of the wafer 203 at specific locations at different time points to provide data for stereoscopic image reconstruction of the wafer structure at that location. Furthermore, in some embodiments, the anode 216 and the cathode 218 can be configured to generate multiple primary electron beams 220, and the electron beam tool 140 can include multiple deflectors 204 c to simultaneously project the multiple primary electron beams 220 onto different portions / sides of the wafer, thereby providing data for image reconstruction of different portions of the wafer 203.

[0030] The excitation coil 204d and the pole piece 204a generate a magnetic field that begins at one end of the pole piece 204a and terminates at the other end of the pole piece 204a. The portion of the wafer 203 scanned by the primary electron beam 220 can be immersed in the magnetic field and can be charged, which in turn generates an electric field. The electric field reduces the energy of the primary electron beam 220 striking the wafer 203 near its surface before colliding with the wafer 203. The control electrode 204b, electrically isolated from the pole piece 204a, controls the electric field on the wafer 203 to prevent micro-arcing of the wafer 203 and ensure proper beam focusing.

[0031] Upon receiving the primary electron beam 220, a secondary electron beam 222 may be emitted from the portion of the wafer 203. The secondary electron beam 222 may form a spot on the sensor surfaces 206a and 206b of the electron detector 206. The electron detector 206 may generate a signal (e.g., voltage, current, etc.) representing the intensity of the beam spot and provide the signal to the image processing system 250. The intensity of the secondary electron beam 222 and the resulting beam spot may vary depending on the external or internal structure of the wafer 203. Furthermore, as described above, the primary electron beam 220 may be projected onto different locations on the top surface of the wafer or onto different sides of the wafer at specific locations to generate secondary electron beams 222 (and resulting beam spots) of different intensities. Thus, by mapping the intensity of the beam spot with the location of the wafer 203, the processing system may reconstruct an image reflecting the internal or surface structure of the wafer 203.

[0032] The imaging system 200 can be used to inspect a wafer 203 on a sample stage 201 and includes the electron beam tool 140, as described above. The imaging system 200 can also include an image processing system 250, which includes an image acquisition device 260, a storage device 270, and a controller 150. The image acquisition device 260 can include one or more processors. For example, the image acquisition device 260 can include a computer, a server, a mainframe, a terminal, a personal computer, any type of mobile computing device, or a combination thereof. The image acquisition device 260 can be connected to the detector 206 of the electron beam tool 140 via a medium such as an electrical conductor, a fiber optic cable, a portable storage medium, infrared (IR), Bluetooth, the internet, a wireless network, radio, or a combination thereof. The image acquisition device 260 can receive signals from the detector 206 and construct an image. The image acquisition device 260 can thereby acquire an image of the wafer 203. The image acquisition device 260 can also perform various post-processing functions, such as generating a profile and overlaying indicators on the acquired image. The image acquisition device 260 can also be configured to adjust the brightness and contrast of the acquired image. The storage device 270 may be a storage medium such as a hard disk, a cloud storage device, a random access memory (RAM), or other types of computer-readable memory. The storage device 270 may be coupled to the image acquirer 260 and may be used to save the scanned raw image data as a raw image and save a post-processed image. The image acquirer 260 and the storage device 270 may be connected to the controller 150. In some embodiments, the image acquirer 260, the storage device 270, and the controller 150 may be integrated together as a control unit.

[0033] In some embodiments, the image acquirer 260 can acquire one or more images of the sample based on the imaging signal received from the detector 206. The imaging signal can correspond to a scanning operation for performing charged particle imaging. The acquired image can be a single image including multiple imaging regions. The single image can be stored in the storage device 270. The single image can be an original image that can be divided into multiple regions. Each region can include an imaging region containing a feature of the wafer 203.

[0034] Figure 3 A schematic representation of the overall lithography is depicted, which shows the cooperation between the three technologies to optimize semiconductor manufacturing. Typically, the patterning process in the lithography apparatus LA is one of the most critical steps in the process, which requires high precision in the size and position of the structures on the substrate W ( Figure 1 To ensure this high accuracy, three systems (in this example) can be combined in a Figure 3. One of these systems is a lithography apparatus LA, which is (virtually) connected to a metrology apparatus (e.g., a metrology tool) MT (a second system) and a computer system CL (a third system). The "holistic" environment can be configured to optimize the collaboration between these three systems to enhance the overall process window and provide a tight control loop, thereby ensuring that the patterning performed by the lithography apparatus LA stays within the process window. The process window defines the range of process parameters (e.g., dose, focus, overlay) within which a particular manufacturing process produces a defined result (e.g., a functional semiconductor device)—typically, within which process parameters in a lithography process or patterning process are allowed to vary.

[0035] The computer system CL can use (portions of) the design layout to be patterned to predict which resolution enhancement techniques to use and perform computational lithography simulations and calculations to determine which mask layouts and lithography apparatus settings achieve the maximum total process window for the patterning process (in Figure 2 Typically, the resolution enhancement technique is arranged to match the patterning possibilities of the lithographic apparatus LA. The computer system CL may also be used to detect where within the process window the lithographic apparatus LA is currently operating (e.g. using input from the metrology tool MT) to predict whether resolution enhancement techniques are being employed due to, for example, suboptimal processing (e.g., in the process window). Figure 2 There is a defect (depicted by the arrow pointing to "0" in the second scale SC2).

[0036] The metrology apparatus (tool) MT may provide input to the computer system CL to enable accurate simulations and predictions, and may provide feedback to the lithographic apparatus LA to identify, for example, possible drift in the calibration state of the lithographic apparatus LA (e.g., Figure 3 ) depicted by multiple arrows in the third scale SC3.

[0037] The following paragraphs describe systems and methods for automatically selecting thresholds for processing an image of a pattern to determine attributes of features of the pattern. The following paragraphs describe processes for determining attributes of features, such as the center of a hole (e.g., a via in a pattern) as an example of an attribute and a feature. However, it must be noted that the feature is not limited to holes, nor are the attributes of the feature limited to the center of the hole. The embodiments may be applied to other features or other attributes of the feature. In some embodiments, the image representation of the pattern may include a grayscale image. Various methods and instruments may be used to measure, simulate, or otherwise generate the image. For example, a measurement tool such as a single-beam SEM, a multi-beam SEM, or an optical measurement tool may be used to generate an image by capturing a pattern printed on a substrate. In another example, an image may be generated using a simulation model (e.g., a physical model, an empirical model, an artificial intelligence (AI) model, etc.) that generates the image based on pattern data, such as a target layout of a pattern to be printed on a substrate.

[0038] Figure 4 is a block diagram of an exemplary system 400 for automatically selecting thresholds for processing an image of a pattern to determine attributes of features, consistent with various embodiments. Figure 5 is a flow chart of an exemplary method 500 for automatically selecting a threshold for processing an image of a pattern to determine attributes of features, consistent with various embodiments.

[0039] At process P505, image processing component 425 obtains an image representation of a pattern. The image representation can be an image of a pattern having multiple features, such as a hole 412 whose center is to be determined. The image representation can be image 410 including multiple holes, or image 402 including a single hole 412. In some embodiments, if image 410 having multiple holes is provided as input, image processing component 425 can segment image 410 into multiple smaller portions, where each portion (e.g., image 402) contains a single hole. In some embodiments, image 402 is an enlarged version of one of the holes in image 410.

[0040] In process P510, the 2D contour generation component 430 generates a 2D contour 404a of the hole 412 using a first threshold value. In some embodiments, the image processing component 425 generates a thresholded image 403 by thresholding the image 402 using a first threshold value from a range of threshold values. The range of threshold values ​​can be provided as a user input. The thresholded image 403 can be a binary image generated based on the pixel values ​​of the image 402 and the first threshold value. For example, all pixels with values ​​below the first threshold value can be assigned a value of "0" (which corresponds to white areas in the thresholded image 403), and pixels equal to or above the first threshold value can be assigned a value of "1" (which corresponds to black areas in the thresholded image 403). The white areas in the thresholded image 403 correspond to the hole 412. The 2D contour generation component 430 generates a 2D contour 404a from the thresholded image 403. Figure 4 An enlarged version 404b of the 2D outline 404a is shown. In some embodiments, the 2D outline 404a may represent the shape and size of the hole 412. The 2D outline 404 may be generated in any of a variety of ways.

[0041] At process P515, the KPI evaluation component 435 evaluates the 2D profile 404 to determine the value of the KPI 408 for the 2D profile 404. The KPI 408 can be defined as a function of properties associated with the 2D profile 404 or derived using the 2D profile 404. In some embodiments, the KPI 408 can be defined as a function of geometric properties (e.g., height (h) and width (w)) of the bounding box of the 2D profile 404 of the hole 412. For example, the KPI 408 can be defined as the aspect ratio of the 2D profile - KPI = h / w. Various other KPIs can be defined to measure the performance of the 2D profile 404. Figure 7A and Figures 8A to 8N Illustrate some examples of KPIs.

[0042] In determination process P520, 2D profile generation component 430 determines whether 2D profiles have been generated for all thresholds in the specified range. Based on the determination that 2D profiles have not yet been generated for all thresholds, image processing component 425 proceeds to the next iteration, in which a 2D profile is generated for the next threshold from the specified range, and a KPI value for the corresponding 2D profile is determined. As described above, the range of thresholds can be provided to method 500 as user input. In some embodiments, a step size indicating the amount by which the threshold should be increased for each iteration can also be provided to method 500 as user input. For example, if the range of thresholds is indicated as "100" to "150" with a step size of "2," then for each iteration of generating a 2D profile starting from "100," then to "102," "104," and so on, up to "150," the method increases the threshold by "2."

[0043] Referring back to determination process P520, based on the determination that 2D profiles have been generated for all thresholds within the range, at process P525, KPI evaluation component 435 determines which of the KPI values ​​matches the target KPI value. In some embodiments, the target KPI value may be a value indicating an ideal or nominal 2D profile of a feature, which helps accurately determine the location of the feature (e.g., the center of hole 412). The target KPI value may be established using any of a variety of methods. For example, the target KPI value may be calculated using a 2D profile of a hole with known center coordinates and overlay errors with other features. The target KPI value may be provided to KPI evaluation component 435 as user input. If specified criteria are met, the KPI 408 value matches the target KPI value. For example, if the KPI 408 value is the same as the target KPI value, the KPI 408 value may match the target value. In another example, if the KPI 408 value exceeds the target KPI value, the KPI 408 value may match the target value. In another example, if the difference between the KPI 408 value and the target KPI value is less than a threshold difference, then the KPI 408 value may match the target value. In another example, if the KPI 408 value is closest to the target KPI value among all KPI values, then the KPI 408 value may match the target value.

[0044] After the matching KPI value is identified, the KPI evaluation component 435 determines the threshold value corresponding to the matching KPI value as an optimal threshold value 525 that can be used to determine the center of the hole 412. In some embodiments, the optimal threshold value is where the actual 2D contour intersects the ideal 2D contour, which can result in a symmetrical 2D hole patch (e.g., height = width).

[0045] Figure 6 is a flow chart of an exemplary method 600 for determining overlay error between features of a pattern using automatic thresholding consistent with various embodiments. At process P605, an image of the pattern and a threshold value for generating a 2D profile of a feature in the pattern are obtained. In some embodiments, the image may be an image of a pattern having multiple features. For example, the image is image 402 having multiple features such as hole 412 and second feature 414. The threshold value may be a specified threshold value that is automatically selected based on a KPI for the 2D profile of the feature whose location is to be determined (e.g., the center of hole 412). For example, the specified threshold value may be a threshold value that is automatically selected using at least the method described above with reference to FIG. Figure 5 The method 500 is described while selecting the threshold 525 .

[0046] At process P610, the 2D profile generation component 430 generates a 2D profile 610 of the hole 412 (e.g., as described above with reference to at least Figure 5 In some embodiments, the 2D profile 610 may be similar to Figure 4 2D profile 404.

[0047] At process P615, 2D profile generation component 430 determines the location of center 615 of hole 412 based on 2D profile 610. In some embodiments, center 615 may include any of a centroid, a geometric center, or a center of gravity of 2D profile 610. Any of a variety of methods may be used to determine center 615 using 2D profile 610.

[0048] At process P620, 2D profile generation component 430 determines an overlay error 620 between hole 412 and another feature of the pattern, such as second feature 414. For example, 2D profile generation component 430 obtains the location of second feature 414 and uses the location of second feature 414 and the location of center 615 of hole 412 (e.g., determined in process P615) to determine overlay error 620 with hole 412.

[0049] In some embodiments, the process can be performed independently for each hole in the pattern. Figure 5 Method 500 is used to determine the optimal threshold value for each hole. For example, if the image representation input to method 500 is image 410 including a plurality of holes, method 500 is performed for each hole in image 410 to select the optimal threshold value for the corresponding hole. Similarly, method 600 is repeated for each hole to determine the center of the corresponding hole and the overlay error between the corresponding hole and another feature. One advantage of independently determining the threshold value for each hole is that the method can tolerate any variations in the image (e.g., image intensity), which eliminates the need to normalize the image, which minimizes the consumption of time and computing resources, thereby enabling faster defect detection.

[0050] KPIs for the 2D profile of a feature may be defined using various geometric properties associated with the 2D profile. 7A to 7D Various geometric properties of KPIs that can be used to define the 2D profile of a feature are shown, consistent with various embodiments. Figure 7A As shown, a maximum inclosing rectangle 702 is determined for the 2D patch associated with the feature, and the center of the maximum inclosing rectangle 702 can be used to formulate the KPI of the 2D profile. In some embodiments, the maximum inclosing rectangle is the largest rectangle that can be contained in the 2D patch.

[0051] In another example, Figure 7B As shown, a minimum bounding box or minimum enclosing rectangle 704 is determined for the 2D patch, and the center of the minimum enclosing rectangle 704 can be used to formulate the KPI of the 2D contour. In some embodiments, the minimum enclosing rectangle is the smallest rectangle that can contain the 2D patch.

[0052] In another example, Figure 7C As shown, a maximum inscribed circle 706 is determined for the 2D patch, and the center of the maximum inscribed circle 706 can be used to formulate the KPI of the 2D profile. In some embodiments, the maximum inscribed circle is the largest circle that can be contained in the 2D patch.

[0053] In another example, Figure 7D As shown, a minimum boundary or circumscribed circle 708 is determined for the 2D profile of the feature, and the center of the minimum circumscribed circle 708 can be used to formulate the KPI of the 2D profile. In some embodiments, the minimum circumscribed circle is the smallest circle that can contain the 2D patch.

[0054] One or more centers of the geometric shapes described in the above figures can be used to define various KPIs, as described below. Figures 8A to 8N exemplified.

[0055] Figures 8A to 8N Various KPIs associated with 2D profiles are shown consistent with various embodiments. In a first example, Figure 8A As shown, the KPI of a 2D profile can be defined based on the reflection symmetry of the 2D profile. A vertical axis passing through the center of the 2D profile (e.g., the center of mass, geometric center, or center of gravity of the 2D profile) is determined. A first KPI is determined based on the properties of the 2D profile image before and after flipping the image along the vertical axis. For example, the first KPI is determined as the sum of the pixel arithmetic differences between the original image and the flipped image. In some embodiments, the symmetry can describe the degree of divergence from an ideal bilaterally symmetrical shape.

[0056] Figure 8B The minimum bounding rectangle of the 2D outline of the hole is shown. A second KPI can be defined based on the width w of the minimum bounding rectangle and the distance or horizontal difference d between the center of the minimum bounding rectangle and the center of the 2D outline. For example, the second KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch.

[0057] Figure 8C The minimum circumscribed rectangle and maximum inscribed circle associated with the 2D contour of the hole are shown. A third KPI can be defined based on the width w of the minimum circumscribed rectangle and the distance or horizontal difference d between the center of the minimum circumscribed rectangle and the center of the maximum inscribed circle. For example, the third KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, the third KPI is more sensitive to changes in the concavity of the 2D contour.

[0058] Figure 8DThe minimum circumscribed rectangle and minimum circumscribed circle associated with the 2D contour of the hole are shown. A fourth KPI can be defined based on the width w of the minimum circumscribed rectangle and the distance or horizontal difference d between the center of the minimum circumscribed rectangle and the center of the circle. For example, the fourth KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, the fourth KPI is more sensitive to changes in the concavity of the 2D contour.

[0059] Figure 8E The minimum circumscribed rectangle and the maximum inscribed rectangle associated with the 2D outline of the hole are shown. A fifth KPI can be defined based on the width w of the minimum circumscribed rectangle and the distance or horizontal difference d between the center of the minimum circumscribed rectangle and the center of the maximum inscribed rectangle. For example, the fifth KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, when the threshold is changed, the fifth KPI is sensitive to horizontal clipping but not to vertical clipping.

[0060] Figure 8F The minimum circumscribed circle associated with the 2D contour of the hole is shown. A sixth KPI can be defined based on the radius r of the minimum circumscribed circle and the distance or horizontal difference d between the center of the minimum circumscribed circle and the center of the 2D contour. For example, the sixth KPI can be expressed as KPI = d / r. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, the sixth KPI is sensitive to changes in convexity when the threshold is changed.

[0061] Figure 8G The minimum circumscribed circle and the maximum inscribed circle associated with the 2D profile of the hole are shown. A seventh KPI can be defined based on the radius r of the minimum circumscribed circle and the distance or horizontal difference d between the center of the minimum circumscribed circle and the center of the maximum inscribed circle. For example, the seventh KPI can be expressed as KPI = d / r. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, when the threshold is changed, the seventh KPI is sensitive to both convex and concave changes.

[0062] Figure 8H The minimum circumscribed circle and maximum inscribed rectangle associated with the 2D outline of the hole are shown. An eighth KPI can be defined based on the radius r of the minimum circumscribed circle and the distance or horizontal difference d between the center of the minimum circumscribed circle and the center of the maximum inscribed rectangle. For example, the eighth KPI can be expressed as KPI = d / r. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, when the threshold is changed, the eighth KPI is sensitive to changes in convexity but not to vertical clipping.

[0063] Figure 8IThe largest inscribed circle associated with the 2D contour of the hole is shown. A ninth KPI can be defined based on the radius r of the largest inscribed circle and the distance or horizontal difference d between the center of the largest inscribed circle and the center of the 2D contour. For example, the ninth KPI can be expressed as KPI = d / r. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, the ninth KPI is sensitive to changes in concavity when the threshold is changed.

[0064] Figure 8J The maximum inscribed circle and maximum inscribed rectangle associated with the 2D outline of the hole are shown. A tenth KPI can be defined based on the width w of the maximum inscribed rectangle and the distance or horizontal difference d between the center of the maximum inscribed circle and the center of the rectangle. For example, the tenth KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, when the threshold is changed, the tenth KPI is more sensitive to concave changes along the horizontal direction.

[0065] Figure 8K The maximum inscribed rectangle associated with the 2D outline of the hole is shown. An eleventh KPI can be defined based on the width w of the maximum inscribed rectangle and the distance or horizontal difference d between the center of the maximum inscribed rectangle and the center of the 2D outline. For example, the eleventh KPI can be expressed as KPI = d / w. In some embodiments, the distance d describes the degree of deviation from a symmetrical patch. In some embodiments, the eleventh KPI is more sensitive to horizontal clipping when the threshold is changed.

[0066] Figure 8L A 2D patch of a hole is shown.A twelfth KPI may be determined based on the area of ​​the 2D patch.

[0067] Figure 8M A 2D patch of a hole is shown. A thirteenth KPI can be determined based on the diameter L of the 2D patch. For example, the thirteenth KPI can be defined based on the maximum Feret diameter of the 2D patch. In some embodiments, the maximum Feret diameter can be the longest distance between two points of the 2D patch. The thirteenth KPI describes the widest extension of the hole in one direction.

[0068] Figure 8N The minimum bounding rectangle associated with the 2D outline of the hole is shown. A fourteenth KPI can be defined based on the area of ​​the 2D patch and the dimensions of the minimum bounding rectangle, such as height h and width w. For example, the fourteenth KPI can be expressed as KPI = area / (w * h). In some embodiments, the fourteenth KPI describes whether the hole pixels are expanded or merged.

[0069] Another KPI can be defined based on ellipse fitting. For example, the edge of a 2D patch can be fitted with an ellipse (e.g., using the least squares method), and the eccentricity of the fitted ellipse can be used as a KPI. In some embodiments, the eccentricity describes the degree to which the 2D contour shape deviates from a circle. If the length of the major axis of the ellipse is represented as "2a" and the length of the minor axis is represented as "2b", the eccentricity e can be expressed as follows:

[0070]

[0071] In some embodiments, a KPI may be generated from one or more KPIs. For example, as an aspect ratio KPI (e.g., at least with reference to Figure 4 and Figure 5 described) and Figure 8B A first composite KPI of a combination of a second KPI can be defined as follows:

[0072]

[0073] The above KPIs can optimize the aspect ratio to 1.0 and try to keep the 2D outline as symmetrical as possible.

[0074] In another example, as an aspect ratio KPI (e.g., at least with reference to Figure 4 and Figure 5 described) and Figure 8C The second composite KPI of the combination of the third KPI can be defined as follows:

[0075]

[0076] The above KPI attempts to optimize the 2D outline into an egg shape.

[0077] Note that any of the above KPIs and / or other KPIs may be used (e.g., in method 500) to select a threshold value to determine the center of a hole. Additionally, a target value for any of these KPIs may be provided as user input.

[0078] In some embodiments, the defect detection process helps improve the patterning process by minimizing defects when patterning a target layout on a substrate. For example, based on the determined overlay error, parameters of a patterning process or a lithography apparatus used to print a pattern on the substrate can be adjusted to minimize defects when patterning the target layout on the substrate. After adjusting the parameters, a patterning process can be performed using the lithography apparatus to print a pattern corresponding to the target layout on the substrate.

[0079] Figure 9is a block diagram illustrating a computer system 900 that can help implement the various methods and systems disclosed herein. The computer system 900 can be used to implement any entity, component, module, or service depicted in the examples of the figures (as well as any other entity, component, module, or service described in this specification). The computer system 900 can be programmed to execute computer program instructions to perform the functions, methods, processes, or services described herein (e.g., the functions, methods, processes, or services of any of the entities, components, or modules). The computer system 900 can be programmed to execute computer program instructions through at least one of software, hardware, or firmware.

[0080] The computer system 900 includes a bus 902 or other communication mechanism for communicating information, and a processor 904 (or multiple processors 904 and 905) coupled to the bus 902 for processing information. The computer system 900 also includes a main memory 906, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 902 for storing information and instructions to be executed by the processor 904. The main memory 906 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 904. The computer system 900 also includes a read-only memory (ROM) 908 or other static storage device coupled to the bus 902 for storing static information and instructions for the processor 904. A storage device 910, such as a magnetic disk or optical disk, is provided and coupled to the bus 902 for storing information and instructions.

[0081] The computer system 900 can be coupled to a display 912, such as a cathode ray tube (CRT) or a flat-panel or touch panel display, via bus 902 for displaying information to a computer user. An input device 914, including alphanumeric and other keys, is coupled to bus 902 for communicating information and command selections to processor 904. Another type of user input device is a cursor controller 916, such as a mouse, trackball, or cursor direction keys, for communicating direction information and command selections to processor 904, and for controlling cursor movement on display 912. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch panel (screen) display can also be used as an input device.

[0082] According to one embodiment, portions of one or more methods described herein may be performed by the computer system 900 in response to the processor 904 executing one or more sequences of one or more instructions contained in the main memory 906. These instructions may be read into the main memory 906 from another computer-readable medium (such as a storage device 910). Execution of the sequences of instructions contained in the main memory 906 causes the processor 904 to perform the processing steps described herein. One or more processors in a multi-processing arrangement may also be deployed to execute the sequences of instructions contained in the main memory 906. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0083] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 904 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 or magnetic disks, such as storage device 910. Volatile media include dynamic memory, such as main memory 906. Transmission media include coaxial cables, copper wire, and optical fiber, including the wires that comprise bus 902. Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic medium, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical medium with a pattern of holes, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chip or cartridge, a carrier wave as described below, or any other medium from which a computer can read.

[0084] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to processor 904 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 900 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 902 can receive the data carried in the infrared signal and place the data on bus 902. Bus 902 transfers the data to main memory 906, from which processor 904 retrieves and executes the instructions. The instructions received by main memory 906 may optionally be stored on storage device 910 before or after execution by processor 904.

[0085] The computer system 900 also preferably includes a communication interface 918 coupled to the bus 902. The communication interface 918 provides a two-way data communication coupled to a network link 920 connected to a local network 922. For example, the communication interface 918 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 918 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 918 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0086] The network link 920 typically provides data communication through one or more networks to other data devices. For example, the network link 920 can provide a connection to a host computer 924 or to data equipment operated by an Internet service provider (ISP) 926 through a local network 922. The ISP 926, in turn, provides data communication services through the global packet data communication network now commonly referred to as the "Internet" 928. Both the local network 922 and the Internet 928 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 920 and the signals through the communication interface 918 (which carry the digital data to and from the computer system 900) are exemplary forms of carrier waves transporting the information.

[0087] Computer system 900 can send messages and receive data, including program code, through network(s), network link 920, and communication interface 918. In the Internet example, server 930 can send requested code for an application program through Internet 928, ISP 926, local network 922, and communication interface 918. For example, one such downloaded application can provide illumination optimization according to an embodiment. The received code can be executed by processor 904 as it is received, or stored in storage device 910 or other non-volatile storage device for later execution. In this manner, computer system 900 can obtain application code in the form of a carrier wave.

[0088] The embodiments of the present disclosure can be further described by the following clauses.

[0089] 1. A method for selecting a threshold value when processing an image to determine a characteristic of a pattern to be printed on a substrate, the method comprising:

[0090] accessing image representations of patterns;

[0091] generating a plurality of contours of a first feature of the pattern by processing the image representation using different thresholds, wherein each of the contours corresponds to a respective threshold;

[0092] evaluating the profile; and

[0093] A specified one of the thresholds is selected based on the evaluation.

[0094] 2. The method of clause 1, wherein the evaluating comprises:

[0095] A value of a characteristic parameter of the profile is determined.

[0096] 3. The method of clause 2, wherein selecting the specified threshold is based on a target value for the characteristic parameter.

[0097] 4. The method of clause 2, wherein the characteristic parameter indicates an aspect ratio of the corresponding contour.

[0098] 5. The method of clause 2, wherein the characteristic parameter is determined based on one or more attributes associated with the profile of the first feature, or is derived using the profile of the first feature.

[0099] 6. The method of clause 1, wherein generating the profile comprises:

[0100] obtaining a range of the threshold value; and

[0101] The contour is generated by iteratively selecting a threshold value within the range of the threshold value.

[0102] 7. The method of clause 6, wherein generating the contour by iteratively selecting the threshold comprises:

[0103] Get the step size for the iteration of the threshold.

[0104] 8. The method of clause 1 , wherein the image representation is a grayscale image.

[0105] 9. The method of clause 1, wherein the image representation is an image of the pattern captured using a metrology tool.

[0106] 10. The method of clause 9, wherein the metrology tool comprises a scanning electron microscope.

[0107] 11. The method of clause 1, wherein the image representation is a simulated image generated based on data of a second pattern to be printed on the substrate using one or more simulation methods.

[0108] 12. The method of clause 1, wherein the image representation represents a grayscale image, and wherein generating the 2D contour comprises:

[0109] generating a binary image based on the pixel values ​​of the grayscale image and a first threshold value among the threshold values; and

[0110] A first contour of the contours is generated using the binary image.

[0111] 13. The method of clause 1, further comprising:

[0112] A center of the first feature is determined from a contour in the contour generated using the specified threshold.

[0113] 14. The method of clause 13, wherein the center of the first feature comprises at least one of a center of gravity, a geometric center, or a center of mass of the first feature.

[0114] 15. The method according to clause 13, further comprising:

[0115] Overlay between the first feature and another feature is determined using the center of the first feature.

[0116] 16. The method according to clause 15, further comprising:

[0117] Parameters of at least one of a patterning process or a lithography apparatus are adjusted based on the overlay to minimize defects when patterning a target layout on the substrate.

[0118] 17. The method according to clause 16, further comprising:

[0119] The patterning process is performed via the photolithography apparatus to print a pattern corresponding to the target layout on the substrate.

[0120] 18. The method of clause 1, wherein the first feature is a via structure in the pattern.

[0121] 19. The method according to clause 18, further comprising:

[0122] For each via structure in the plurality of via structures in the pattern,

[0123] generating a set of contours of the via structure corresponding to a set of thresholds;

[0124] determining a set of values ​​for characteristic parameters of the set of profiles; and

[0125] A threshold value from the set of threshold values ​​is selected based on the set of values ​​of the characteristic parameter and a target value for the characteristic parameter.

[0126] 20. The method according to clause 18, further comprising:

[0127] Overlay between each of the via structures and another feature of the pattern is determined using a center of the corresponding via structure.

[0128] 21. The method of clause 20, wherein determining the overlay of each of the via structures comprises:

[0129] For each of the plurality of via structures in the pattern, a center of the corresponding via structure is determined based on a profile generated using the selected threshold.

[0130] 22. The method of clause 1, wherein each of the profiles is a two-dimensional (2D) profile.

[0131] 23. A method for determining the center of a feature of a pattern by selecting a threshold for processing an image representing the pattern, the method comprising:

[0132] accessing an image representation representing a pattern,

[0133] iteratively thresholding the image representation using different thresholds to generate a plurality of contours of a first feature of the pattern, wherein each of the contours corresponds to a respective threshold;

[0134] selecting a specified one of the thresholds based on a characteristic parameter associated with the profile; and

[0135] A center of the first feature is determined using a contour generated using the specified threshold.

[0136] 24. The method according to clause 23, further comprising:

[0137] Overlay between the first feature and another feature is determined using the center of the first feature.

[0138] 25. The method of clause 23, wherein the characteristic parameter indicates an aspect ratio of the corresponding contour.

[0139] 26. The method of clause 23, wherein the characteristic parameter is determined based on one or more attributes associated with the profile of the first feature, or is derived using the profile of the first feature.

[0140] 27. The method of clause 23, wherein iteratively thresholding the image representation comprises:

[0141] A value of the characteristic parameter is determined.

[0142] 28. The method of clause 23, wherein selecting the specified threshold is based on a target value for the characteristic parameter.

[0143] 29. The method of clause 23, wherein iteratively thresholding the image representation comprises:

[0144] obtaining a range of the threshold value; and

[0145] The contour is generated by iteratively selecting a threshold value within the range of the threshold value.

[0146] 30. The method of clause 29, wherein generating the contour by iteratively selecting the threshold comprises:

[0147] Get the step size for the iteration of the threshold.

[0148] 31. The method of clause 23, wherein the image representation is a grayscale image.

[0149] 32. The method of clause 23, wherein the image representation is an image of the pattern captured using a metrology tool.

[0150] 33. The method of clause 32, wherein the metrology tool comprises a scanning electron microscope.

[0151] 34. The method of clause 23, wherein the image representation is a simulated image generated based on data of the second pattern to be printed on the substrate using one or more simulation methods.

[0152] 35. The method of clause 23, wherein the image representation represents a grayscale image, and wherein the contour is generated by:

[0153] generating a binary image based on the pixel values ​​of the grayscale image and a first threshold value among the threshold values; and

[0154] A first contour among the contours is generated using the binary image.

[0155] 36. The method of clause 23, wherein the center of the first feature comprises at least one of a center of gravity, a geometric center, or a center of mass of the first feature.

[0156] 37. The method of clause 23, wherein the first feature is a via structure in the pattern.

[0157] 38. The method of clause 23, wherein each of the contours is a 2D contour.

[0158] 39. A non-transitory computer-readable medium having recorded thereon instructions, which, when executed by a computer, implement the method according to any one of the preceding clauses.

[0159] 40. An apparatus comprising:

[0160] a memory storing an instruction set, and

[0161] A processor is configured to execute the instruction set so as to cause the apparatus to perform the method according to any one of the above clauses.

[0162] Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system (e.g., a lithography imaging system for imaging on substrates other than silicon wafers).

[0163] As used herein, the terms "optimize..." and "optimize" refer to or mean adjusting a patterning device (e.g., a lithographic apparatus), a patterning process, or the like so that the result and / or process has more appropriate characteristics, such as higher projection accuracy of the design pattern on the substrate, a larger process window, or the like. Thus, as used herein, the terms "optimize..." and "optimize" refer to or mean identifying a process for one or more values ​​of one or more parameters that provides an improvement in at least one relevant metric compared to an initial set of one or more values ​​of those one or more parameters, such as a local optimization. "Optimal" and other related terms should be interpreted accordingly. In one embodiment, the optimization steps may be applied iteratively to provide further improvements in one or more metrics.

[0164] Aspects of the present invention may be implemented in any convenient form. For example, an embodiment may be implemented by one or more appropriate computer programs, which may be carried on an appropriate carrier medium, which may be a tangible carrier medium (e.g., a disk) or a non-tangible carrier medium (e.g., a communication signal). An embodiment of the present invention may be implemented using an appropriate device, which may specifically take the form of a programmable computer running a computer program, which is arranged to implement the method as described herein. Therefore, the embodiments of the present disclosure may be implemented in hardware, firmware, software, or any combination thereof. The embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may 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 may include a read-only memory (ROM); a random access memory (RAM); a magnetic disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), etc. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are for convenience only and that such actions actually result from a computing device, processor, controller, or other apparatus executing firmware, software, routines, instructions, or the like.

[0165] In the block diagrams, the illustrated components are depicted as discrete functional blocks, but the embodiments are not limited to systems in which the functionality described herein is organized as illustrated. The functionality provided by each component may be provided by software or hardware modules organized differently than presently described, for example, such software or hardware may be mixed, combined, replicated, decomposed, distributed (e.g., within a data center or geographically), or otherwise organized differently. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium. In some cases, a third-party content delivery network may host some or all of the information communicated on the network, in which case, to the extent that information (e.g., content) is said to be supplied or otherwise provided, the information may be provided by sending instructions to retrieve the information from the content delivery network.

[0166] Unless otherwise specifically stated, as will be apparent from the discussion, it should be understood that throughout this specification, discussions utilizing terms such as "process," "calculate," "compute," "determine," etc., refer to actions or processes of a specific apparatus such as a special purpose computer or similar special purpose electronic processing / computing device.

[0167] The reader should understand that this application describes several inventions. Instead of dividing these inventions into multiple independent patent applications, these inventions are grouped into a single file because their related subject matter helps to save the application process. However, the obvious advantages and aspects of these inventions should not be combined. In some cases, the embodiments solve all of the defects mentioned in this document, but it should be understood that the present invention is independently useful, and some embodiments only solve a subset of these problems or provide other unmentioned benefits that are obvious to those skilled in the art who read this disclosure. Due to cost constraints, some of the inventions disclosed herein may not yet be claimed for protection and may be claimed for protection in subsequent applications, such as continuing applications or by amending the present claims. Similarly, due to space limitations, neither the abstract nor the summary of the invention section of this document should be regarded as a comprehensive list containing all of these inventions or all aspects of these inventions.

[0168] It should be understood that the description and drawings are not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

[0169] In view of this specification, modifications and alternative embodiments of various aspects of the present invention will be apparent to those skilled in the art. Therefore, this specification and the accompanying drawings should be interpreted as being illustrative only and for teaching those skilled in the art to implement the general manner of the present invention. It should be understood that the forms of the present invention shown and described herein will serve as examples of embodiments. Elements and materials may be substituted for the elements and materials shown and described herein, parts and processes may be reversed or omitted, certain features may be utilized independently, and the features of the embodiments or embodiments may be combined, all of which will be apparent to those skilled in the art who have benefited from this specification. Without departing from the spirit and scope of the present invention as described in the appended claims, the elements described herein may be changed. The headings used herein are for organizational purposes only and are not meant to be used to limit the scope of this specification.

[0170] As used herein, unless specifically stated otherwise, the term "or" encompasses all possible combinations unless impractical. For example, if a component is stated to include A or B, then, unless specifically stated otherwise or impractical, the component may include A, or B, or A and B. As a second example, if a component is stated to include A, B, or C, then, unless specifically stated otherwise or impractical, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. A phrase such as "at least one of" does not necessarily modify the entirety of the following list and does not necessarily modify each member of the list, such that "at least one of A, B, and C" should be understood to include only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase "one of A and B" or "either of A and B" should be interpreted in the broadest sense to include either one of A or one of B.

[0171] The description herein is intended to be illustrative and not restrictive. It will therefore be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth.

Claims

1. A method for determining the center of a feature of a pattern by selecting a threshold for processing an image representing the pattern, the method comprising: accessing an image representation representing a pattern, iteratively thresholding the image representation using different thresholds to generate a plurality of contours of a first feature of the pattern, wherein each contour in the plurality of contours corresponds to a respective threshold; selecting a specified threshold value among the different threshold values ​​based on characteristic parameters associated with the plurality of profiles; as well as A center of the first feature is determined using a contour generated using the specified threshold.

2. The method according to claim 1, further comprising: Overlay between the first feature and another feature is determined using the center of the first feature. The method according to claim 1 , wherein the characteristic parameter indicates an aspect ratio of the corresponding contour. 4 . The method of claim 1 , wherein the characteristic parameter is determined based on one or more attributes associated with the profile of the first feature, or is derived using the profile of the first feature.

5. The method of claim 1 , wherein iteratively thresholding the image representation comprises: A value of the characteristic parameter is determined. The method of claim 1 , wherein selecting the specified threshold is based on a target value for the characteristic parameter.

7. The method of claim 1 , wherein iteratively thresholding the image representation comprises: obtaining a range of the threshold value; as well as generating the contour by iteratively selecting a threshold value within the range of the threshold value, The step of generating the contour by iteratively selecting the threshold value comprises: Get the step size for the iteration of the threshold.

8. The method of claim 1, wherein the image representation is an image of the pattern captured using a metrology tool.

9. The method of claim 8, wherein the metrology tool comprises a scanning electron microscope.

10. The method of claim 1, wherein the image representation is a simulated image generated based on data of a second pattern to be printed on a substrate using one or more simulation methods.

11. The method of claim 1 , wherein the image representation represents a grayscale image, and wherein the contour is generated by: generating a binary image based on the pixel values ​​of the grayscale image and a first threshold value among the threshold values; and A first contour among the contours is generated using the binary image. 12 . The method of claim 1 , wherein the center of the first feature comprises at least one of a center of gravity, a geometric center, or a center of mass of the first feature.

13. The method of claim 1, wherein the first feature is a via structure in the pattern. The method of claim 1 , wherein each of the contours is a 2D contour. 15 . A non-transitory computer-readable medium having instructions recorded thereon, wherein when the instructions are executed by a computer, the method according to claim 1 is implemented.

Images