Area density-based misalignment index for image alignment

Abstract

Improved methods and systems for image alignment of inspection images are disclosed. The improved methods and systems include a misalignment index based on applying a density function to both the sample and reference images in a region of interest. One or more metrics, such as cross-correlation of the sample and reference images, can be used to derive a misalignment index based on regional density from the density function image. This index can yield a unique alignment solution that is robust to noise and other errors.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Patent Application No. 63 / 397,201, filed August 11, 2022, and incorporated herein by reference in its entirety.

[0002] FIELD OF THE INVENTION

[0002] Embodiments provided herein relate to image alignment techniques, and more particularly to a misalignment index for characterizing the amount of misalignment of image features. [Background technology]

[0003]

[0003] In the manufacturing process of integrated circuits (ICs), unfinished or completed circuit components are inspected to ensure they are manufactured as designed and are free of defects. Inspection systems utilizing optical microscopes such as scanning electron microscopes (SEMs) or charged particle (e.g., electron) beam microscopes may be used. As the physical size of IC components continues to shrink, accuracy and yield in defect detection become more important. Inspection images, such as SEM images, can be used to identify or classify defects in manufactured ICs. To improve defect detection performance, it is desirable to obtain accurate alignment between SEM images and corresponding design layout data. Summary of the Invention

[0004]

[0004] Embodiments of the present disclosure provide a method for image alignment, which may include obtaining a first density map of an inspection image corresponding to a region of interest using a first density function, obtaining a second density map of a reference image corresponding to the region of interest using a second density function, and aligning the inspection image and the reference image based on the obtained first and second density maps.

[0005]

[0005] Some embodiments of the present disclosure provide a non-transitory computer-readable medium storing a set of instructions executable by at least one processor of a device to cause the device to perform the above-described method.

[0006] Some embodiments of the present disclosure provide a charged particle beam device configured to perform the above-mentioned method. The charged particle beam device may include a charged particle beam source configured to generate a beam of primary charged particles, charged particle optics configured to direct the beam of primary charged particles toward a sample surface to inspect the sample surface, a charged particle detector configured to detect charged particles returned from the sample surface, the charged particle detector including a first sensing element and a second sensing element, and a controller including one or more processors and configured to cause the charged particle beam device to perform the above-mentioned method.

[0007] Some embodiments of the present disclosure provide a further method for image alignment, which may include acquiring an inspection image corresponding to a region of interest of a sample, acquiring a reference image corresponding to the region of interest of the sample, acquiring an inspection binary profile of the inspection image using a first binary function, acquiring a reference binary profile of the reference image using a second binary function, acquiring a first density map of the inspection binary profile using a first density function, acquiring a second density map of the reference binary profile using a second density function, and determining alignment parameters of the inspection image and the reference image based on the acquired first and second density maps.

[0008]

[0008] Some embodiments of the present disclosure provide a non-transitory computer-readable medium storing a set of instructions executable by at least one processor of a device to cause the device to perform the above-described further methods.

[0009] Some embodiments of the present disclosure provide a charged particle beam device configured to perform the above-mentioned method. The charged particle beam device may include a charged particle beam source configured to generate a beam of primary charged particles, charged particle optics configured to direct the beam of primary charged particles toward a sample surface to inspect the sample surface, a charged particle detector configured to detect charged particles returned from the sample surface, the charged particle detector including a first sensing element and a second sensing element, and a controller including one or more processors and configured to cause the charged particle beam device to perform the above-mentioned further method.

[0010]

[0010] The above and other aspects of the present disclosure will become more apparent from the description of illustrative embodiments taken in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic diagram illustrating an exemplary charged particle beam inspection system consistent with an embodiment of the present disclosure. [Figure 2]

[0012] 2 is a schematic diagram illustrating an example multi-beam tool that may be part of the example charged particle beam inspection system of FIG. 1, consistent with an embodiment of the present disclosure. [Figure 3A-B]

[0013] 1 illustrates an exemplary technique for generating a misalignment index. [Figure 3C-D]

[0013] An exemplary technique for generating a misalignment index is presented. [Figure 4]

[0014] 1 illustrates an exemplary technique for generating a misalignment index, consistent with an embodiment of the present disclosure. [Figure 5]

[0015] 1 illustrates an exemplary technique for generating a misalignment index, consistent with an embodiment of the present disclosure. [Figure 6A]

[0016] 1 illustrates an exemplary technique for generating a misalignment index, consistent with an embodiment of the present disclosure. [Figure 6B] 1 illustrates an exemplary technique for generating a misalignment index consistent with an embodiment of the present disclosure. [Figure 7]

[0017] 10 illustrates misalignment index performance, consistent with embodiments of the present disclosure. [Figure 8]

[0018] 1 is a process flow diagram depicting an exemplary method for generating a misalignment index, consistent with an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0012]

[0019] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings, in which like numbers in different drawings represent the same or similar elements unless otherwise noted. The implementations described in the following description of exemplary embodiments do not represent all implementations. Instead, they are merely examples of apparatus and methods consistent with aspects related to the disclosed embodiments recited in the appended claims. For example, although some embodiments are described in connection with the use of electron beams, the present disclosure is not so limited. Other types of charged particle beams may be applied as well. Furthermore, other imaging systems, such as optical imaging, photodetection, x-ray detection, etc., may be used.

[0013]

[0020] Electronic devices are composed of circuits formed on a piece of semiconductor material called a substrate. The semiconductor material can include, for example, silicon, gallium arsenide, indium phosphide, or silicon germanium. Many circuits can be formed together on the same piece of silicon and are called integrated circuits, or ICs. The dimensions of these circuits have been dramatically reduced so that many more circuits can fit on a substrate. For example, the IC chip in a smartphone can be as small as a thumbnail, yet contain over 2 billion transistors, each smaller than 1 / 1000 the size of a human hair.

[0014]

[0021] Fabricating ICs with these tiny structures or components is a complex, time-consuming, and expensive process, often involving hundreds of individual steps. An error in just one step can result in a defect in the finished IC, rendering it unusable. Therefore, one of the goals of a manufacturing process is to avoid such defects and maximize the number of functional ICs produced by the process, i.e., to improve the overall yield of the process.

[0015]

[0022] One component of improving yield is monitoring the chip fabrication process to ensure that a sufficient number of functional integrated circuits are being produced. One way to monitor the process is to inspect the chip circuit structures at various stages in their formation. Inspection can be done using a scanning charged particle microscope (SCPM). For example, an SCPM can be a scanning electron microscope (SEM). An SCPM can actually take a "picture" of the structures on the wafer and can be used to image those tiny structures. This image can be used to determine if the structures were properly formed in the correct location. If the structures are defective, the process can be adjusted to make the defect less likely to recur.

[0016]

[0023] As the physical size of IC components continues to shrink, accuracy and yield in defect detection become more important. Inspection images, such as SEM images, can be used to identify or classify defects in manufactured ICs. To improve defect detection performance, it is desirable to obtain accurate alignment between an SEM image and a corresponding reference image. For example, in die-to-database (D2DB) alignment, an SEM image can be compared to a reference image based on design layout data. In die-to-die (D2D) alignment, a defect-free SEM image can be used as a reference for aligning other SEM images with the same design layout. The difference between the SEM image and the reference image can be used to calculate a misalignment index.

[0017]

[0024] Some conventional alignment methods compare the positions of pattern edges to determine the degree of misalignment between an SEM image and a reference image. These methods may not perform well for complex misalignments, such as scaling or deformation of the SEM image relative to the reference image. Furthermore, some mathematical techniques for combining an SEM image and a reference image, such as cross-correlation, may be susceptible to measurement noise. This can lead to inaccuracies in calculating misalignment indices, such as generating a large number of possible solutions to a single alignment problem.

[0018]

[0025] Embodiments of the present disclosure can provide a misalignment index based on the area density of pattern features. The process for calculating the misalignment index can include transforming the SEM image and reference images using a density function to generate images of pattern features that are weighted more heavily at the center than at the edges. These transformed area density-based SEM image and reference image can then be evaluated, for example, using the cross-correlation described above, to achieve a misalignment measurement that is robust to measurement noise and yields a single alignment solution. The transformed area density-based SEM image and reference image can also be used to generate several other metrics, which can then be combined into an area density-based misalignment index.

[0019]

[0026] The relative dimensions of components in the drawings may be exaggerated for clarity. In the following description of the drawings, the same or similar reference numbers refer to the same or similar components or entities, and only the differences with respect to individual embodiments are described. As used herein, unless otherwise stated, the term "or" encompasses all possible combinations unless impracticable. For example, if a component is described as including A or B, the component may include A, or B, or A and B, unless otherwise stated or impracticable. As a second example, if a component is described as including A, B, or C, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A, B, and C, unless otherwise stated or impracticable.

[0020]

[0027] FIG. 1 illustrates an exemplary electron beam inspection (EBI) system 100 consistent with embodiments of the present disclosure. The EBI system 100 can be used for imaging. As shown in FIG. 1, the EBI system 100 includes a main chamber 101, a load / lock chamber 102, a beam tool 104, and an equipment front-end module (EFEM) 106. The beam tool 104 is disposed within the main chamber 101. The EFEM 106 includes a first load port 106a and a second load port 106b. The EFEM 106 may include additional load ports. The first load port 106a and the second load port 106b receive wafer front-opening unified pods (FOUPs) containing wafers (e.g., semiconductor wafers or wafers made of other materials) or samples (wafers and samples may be used interchangeably) to be inspected. A "lot" is a plurality of wafers that can be loaded for processing as a batch.

[0021]

[0028] One or more robot arms (not shown) in the EFEM 106 can transfer wafers to the load / lock chamber 102. The load / lock chamber 102 is connected to a load / lock vacuum pumping system (not shown), which removes gas molecules from the load / lock chamber 102 to reach a first pressure lower than atmospheric pressure. After the first pressure is reached, one or more robot arms (not shown) can transfer the wafers from the load / lock chamber 102 to the main chamber 101. The main chamber 101 is connected to a main chamber vacuum pumping system (not shown), which removes gas molecules from the main chamber 101 to reach a second pressure lower than the first pressure. After the second pressure is reached, the wafers are subjected to inspection by the beam tool 104. The beam tool 104 can be a single beam system or a multi-beam system.

[0022]

[0029] A controller 109 is electronically connected to the beam tool 104. The controller 109 may be a computer configured to perform various controls of the EBI system 100. While the controller 109 is illustrated in Figure 1 as being external to the structure including the main chamber 101, the load / lock chamber 102, and the EFEM 106, it will be understood that the controller 109 may be part of the structure.

[0023]

[0030] In some embodiments, the controller 109 may include one or more processors (not shown). A processor may be a general-purpose or specialized electronic device capable of manipulating or processing information. For example, a processor may include any number of central processing units (i.e., "CPUs"), graphics processing units (i.e., "GPUs"), optical processors, programmable logic controllers, microcontrollers, microprocessors, digital signal processors, intellectual property (IP) cores, programmable logic arrays (PLAs), programmable array logic (PALs), general-purpose array logic (GALs), complex programmable logic devices (CPLDs), field programmable gate arrays (FPGAs), systems-on-chips (SoCs), application-specific integrated circuits (ASICs), and any combination of any type of circuitry capable of processing data. A processor may also be a virtual processor, including one or more processors distributed across multiple machines or devices coupled via a network.

[0024]

[0031] In some embodiments, the controller 109 may further include one or more memories (not shown). Memory may be a general-purpose or specialized electronic device capable of storing code and data accessible to a processor (e.g., via a bus). For example, memory may include any number of random access memories (RAMs), read-only memories (ROMs), optical disks, magnetic disks, hard drives, solid-state drives, flash drives, security digital (SD) cards, memory sticks, compact flash (CF) cards, or any combination of any type of storage device. The code and data may include an operating system (OS) and one or more application programs (i.e., "apps") for specific tasks. Memory may also be a virtual memory, which includes one or more memories distributed across multiple machines or devices coupled via a network.

[0025]

[0032] FIG. 2 shows a schematic diagram of an exemplary multi-beam tool 104 (also referred to herein as apparatus 104) and image processing system 290 that may be configured for use in EBI system 100 (FIG. 1) consistent with an embodiment of the present disclosure.

[0026]

[0033] The beam tool 104 includes a charged particle source 202, a gun aperture 204, a condenser lens 206, a primary charged particle beam 210 emitted from the charged particle source 202, a source conversion unit 212, multiple beamlets 214, 216, and 218 of the primary charged particle beam 210, a primary projection optics 220, a motorized wafer stage 280, a wafer holder 282, multiple secondary charged particle beams 236, 238, and 240, a secondary optics 242, and a charged particle detection device 244. The primary projection optics 220 may include a beam separator 222, a deflection scanning unit 226, and an objective lens 228. The charged particle detection device 244 may include detection subregions 246, 248, and 250.

[0027]

[0034] The charged particle source 202, the gun aperture 204, the condenser lens 206, the source conversion unit 212, the beam separator 222, the deflection scanning unit 226, and the objective lens 228 may be aligned with a primary optical axis 260 of the apparatus 104. The secondary optics 242 and the charged particle detection device 244 may be aligned with a secondary optical axis 252 of the apparatus 104.

[0028]

[0035] The charged particle source 202 can emit one or more charged particles, such as electrons, protons, ions, muons, or any other particles that carry an electric charge. In some embodiments, the charged particle source 202 can be an electron emitter. For example, the charged particle source 202 can include a cathode, an extractor, or an anode, and primary electrons can be emitted from the cathode and extracted or accelerated to form a primary charged particle beam 210 (in this case, a primary electron beam) with a (virtual or real) crossover 208. For ease of explanation and to avoid ambiguity, some of the descriptions herein use electrons as an example. However, it should be noted that any charged particle, not limited to electrons, can be used in any embodiment of the present disclosure. The primary charged particle beam 210 can be visualized as it is being emitted from the crossover 208. The gun aperture 204 can block charged particles surrounding the primary charged particle beam 210 to reduce the Coulomb effect, which can cause an increase in the size of the probe spot.

[0029]

[0036] The source conversion unit 212 may include an array of image-forming elements and an array of beam-limiting apertures. The array of image-forming elements may include an array of micro-deflectors or micro-lenses. The array of image-forming elements may form multiple (virtual or real) parallel images of the crossover 208 with the multiple beamlets 214, 216, and 218 of the primary charged particle beam 210. The array of beam-limiting apertures may limit the multiple beamlets 214, 216, and 218. Although three beamlets 214, 216, and 218 are shown in FIG. 2 , embodiments of the present disclosure are not limited thereto. For example, in some embodiments, the apparatus 104 may be configured to generate a first number of beamlets. In some embodiments, the first number of beamlets may be in the range of 1 to 1000. In some embodiments, the first number of beamlets may be in the range of 200 to 500. In an exemplary embodiment, the apparatus 104 may generate 400 beamlets.

[0030]

[0037] The condenser lens 206 can focus the primary charged particle beam 210. The currents of the beamlets 214, 216, and 218 downstream of the source conversion unit 212 can be varied by adjusting the focusing power of the condenser lens 206 or by changing the radius of the corresponding beam-limiting apertures in the array of beam-limiting apertures. The objective lens 228 can focus the beamlets 214, 216, and 218 onto a wafer 230 for imaging, and can form multiple probe spots 270, 272, and 274 on the surface of the wafer 230.

[0031]

[0038] The beam separator 222 may be a Wien filter-type beam separator that generates an electrostatic dipole field and a magnetic dipole field. In some embodiments, when applied, the force that the electrostatic dipole field exerts on the charged particles (e.g., electrons) in the beamlets 214, 216, and 218 may be substantially equal in magnitude and opposite in direction to the force that the magnetic dipole field exerts on the charged particles. Thus, the beamlets 214, 216, and 218 may pass through the beam separator 222 in a straight line with a zero deflection angle. However, the total dispersion of the beamlets 214, 216, and 218 generated by the beam separator 222 may also be non-zero. The beam separator 222 may separate the secondary charged particle beams 236, 238, and 240 from the beamlets 214, 216, and 218 and direct the secondary charged particle beams 236, 238, and 240 to the secondary optics 242.

[0032]

[0039] The deflection scanning unit 226 can deflect the beamlets 214, 216, and 218 to scan probe spots 270, 272, and 274 on the surface area of ​​the wafer 230. In response to the beamlets 214, 216, and 218 impinging on the probe spots 270, 272, and 274, secondary charged particle beams 236, 238, and 240 can be emitted from the wafer 230. The secondary charged particle beams 236, 238, and 240 can include charged particles (e.g., electrons) having a distribution of energies. For example, the secondary charged particle beams 236, 238, and 240 can be secondary electron beams including secondary electrons (energy ≦50 eV) and backscattered electrons (energy between 50 eV and the landing energy of the beamlets 214, 216, and 218). The secondary optics 242 can focus the secondary charged particle beams 236, 238, and 240 onto detection subregions 246, 248, and 250 of the charged particle detection device 244. The detection subregions 246, 248, and 250 can be configured to detect the corresponding secondary charged particle beams 236, 238, and 240 and generate corresponding signals (e.g., voltages, currents, etc.) that are used to reconstruct SCPM images of structures on or below the surface area of ​​the wafer 230.

[0033]

[0040] The signals generated may represent the intensities of the secondary charged particle beams 236, 238, and 240 and may be provided to an image processing system 290 in communication with the charged particle detection device 244, the primary projection optics 220, and the motorized wafer stage 280. The speed of movement of the motorized wafer stage 280 may be synchronized and adjusted with the beam deflection controlled by the deflection scanning unit 226 so that the movement of the scanning probe spots (e.g., scanning probe spots 270, 272, and 274) systematically covers the area of ​​interest on the wafer 230. Such synchronization and adjustment parameters may be adjusted to accommodate various materials of the wafer 230. For example, different materials of the wafer 230 may have different resistance-capacitance characteristics that may cause different signal sensitivities to the movement of the scanning probe spots.

[0034]

[0041] The intensities of the secondary charged particle beams 236, 238, and 240 may vary depending on the external or internal structure of the wafer 230 and may therefore indicate whether the wafer 230 contains defects. Furthermore, as described above, the beamlets 214, 216, and 218 may be projected onto different locations on the top surface of the wafer 230 or onto different sides of a local structure of the wafer 230 to generate secondary charged particle beams 236, 238, and 240 that may have different intensities. Thus, by mapping the intensities of the secondary charged particle beams 236, 238, and 240 with areas of the wafer 230, the image processing system 290 can reconstruct an image that reflects the characteristics of the internal or external structure of the wafer 230.

[0035]

[0042] In some embodiments, the image processing system 290 may include an image acquirer 292, storage 294, and a controller 296. The image acquirer 292 may include one or more processors. For example, the image acquirer 292 may include a computer, a server, a mainframe host, a terminal, a personal computer, any type of mobile computing device, etc., or a combination thereof. The image acquirer 292 may be communicatively coupled to the charged particle detection device 244 of the beam tool 104 via a medium such as an electrical conductor, a fiber optic cable, a portable storage medium, IR, Bluetooth, the Internet, a wireless network, wireless radio, or a combination thereof. In some embodiments, the image acquirer 292 may receive signals from the charged particle detection device 244 and construct an image. In this manner, the image acquirer 292 may acquire an SCPM image of the wafer 230. The image acquirer 292 may also perform various post-processing functions, such as generating contours and overlaying designators on the acquired image. The image acquirer 292 may be configured to adjust the brightness and contrast of the acquired image, etc. In some embodiments, storage 294 may be a storage medium such as a hard disk, a flash drive, cloud storage, random access memory (RAM), or other types of computer-readable memory. Storage 294 may be coupled to image acquirer 292 and may be used to store scanned raw image data as original images and post-processed images. Image acquirer 292 and storage 294 may be connected to controller 296. In some embodiments, image acquirer 292, storage 294, and controller 296 may be integrated into one control unit.

[0036]

[0043] In some embodiments, the image acquirer 292 may acquire one or more SCPM images of the wafer based on the imaging signal received from the charged particle detection device 244. The imaging signal may correspond to a scanning motion for performing charged particle imaging. The acquired image may be a single image including multiple imaging areas. The single image may be stored in the storage 294. The single image may be an original image that may be divided into multiple regions. Each of these regions may include an imaging area that includes a feature of the wafer 230. The acquired image may include multiple images of a single imaging area of ​​the wafer 230 sampled multiple times over a temporal sequence. The multiple images may be stored in the storage 294. In some embodiments, the image processing system 290 may be configured to perform image processing steps using multiple images of the same location on the wafer 230.

[0037]

[0044] In some embodiments, image processing system 290 may include measurement circuitry (e.g., an analog-to-digital converter) to obtain a distribution of detected secondary charged particles (e.g., secondary electrons). The charged particle distribution data collected during the detection time window may be used in combination with corresponding scan path data of beamlets 214, 216, and 218 incident on the wafer surface to reconstruct an image of the wafer structure under inspection. The reconstructed image may be used to reveal various features of the internal or external structure of wafer 230, and thereby reveal any defects that may be present in the wafer.

[0038]

[0045] In some embodiments, the charged particles may be electrons. When electrons of the primary charged particle beam 210 are projected onto the surface of the wafer 230 (e.g., probe spots 270, 272, and 274), the electrons of the primary charged particle beam 210 may interact with particles of the wafer 230 and penetrate the surface of the wafer 230 to a certain depth. Some electrons of the primary charged particle beam 210 may interact with the material of the wafer 230 elastically (e.g., in the form of elastic scattering or collisions) and be reflected or bounced off the surface of the wafer 230. The elastic interaction preserves the total kinetic energy of the interacting objects (e.g., electrons of the primary charged particle beam 210), and the kinetic energy of the interacting objects is not converted into other forms of energy (e.g., heat, electromagnetic energy, etc.). The reflected electrons resulting from such elastic interactions may be referred to as backscattered electrons (BSE). Some electrons of the primary charged particle beam 210 may interact with the material of the wafer 230 inelastically (e.g., in the form of inelastic scattering or collisions). Inelastic interactions do not conserve the total kinetic energy of interacting objects, but rather convert some or all of the kinetic energy of the interacting objects into other forms of energy. For example, inelastic interactions can cause the kinetic energy of some electrons in the primary charged particle beam 210 to cause electronic excitation and transitions in atoms of a material. Such inelastic interactions can also produce electrons that leave the surface of the wafer 230, which may be called secondary electrons (SEs). The yield or emission rate of BSEs and SEs depends, among other things, on the material under inspection and the irradiation energy of the electrons of the primary charged particle beam 210 that are irradiated onto the surface of the material. The energy of the electrons of the primary charged particle beam 210 can be imparted in part by their acceleration voltage (e.g., the acceleration voltage between the anode and cathode of the charged particle source 202 in FIG. 2 ). The amount of BSEs and SEs can be greater or less than (and even the same as) the injected electrons of the primary charged particle beam 210.

[0039]

[0046] In some embodiments, images may be generated by an SEM and used, for example, for defect inspection. For example, a generated image capturing a test device area of ​​a wafer may be compared to a reference image capturing the same test device area. The reference image may be predetermined (e.g., by simulation) and may not contain known defects. If the difference between the generated image and the reference image exceeds an acceptable level, a potential defect may be identified. As another example, an SEM may scan multiple areas of a wafer, each area containing identically designed test device areas, and generate multiple images capturing those test device areas as manufactured. The multiple images may be compared to each other. If the difference between the multiple images exceeds an acceptable level, a potential defect may be identified.

[0040]

[0047] For ease of explanation and to avoid ambiguity, some of the descriptions herein use electrons as an example. However, it should be noted that any charged particle, not limited to electrons, may be used in any embodiment of the present disclosure. For example, a radiation source of a charged particle beam tool may emit one or more charged particles, such as electrons, protons, ions, muons, or any other particle carrying an electric charge. The detection systems and methods may be used in other imaging systems, such as optical imaging, photon detection, proton detection, X-ray detection, and ion detection. Photon detection may include light in infrared, visible, ultraviolet, deep UV, extreme UV, X-ray, or any other wavelength range. Thus, while the detectors of the present disclosure may be disclosed with respect to detecting electrons, some embodiments of the present disclosure may be directed to detecting other charged particles or photons using other detection systems.

[0041]

[0048] Figures 3A-D show a misalignment index 300 according to a comparative embodiment. The misalignment index in Figures 3A-B is based on subtraction of gray levels, while the index in Figures 3C-D is based on the amount of shift of pattern edge features.

[0042]

[0049] In FIG. 3A, a reference image 350 overlaps an SEM image 360 ​​at a region of interest (ROI) on the sample surface. The sample may be, for example, a semiconductor wafer. The reference image may be a template, such as a D2D reference, a pattern design layout, such as a graphic database system (GDS) or other file. The method of FIGS. 3A-D may not be suitable for D2D methods that use a defect-free SEM image as the reference image. As shown in FIG. 3A, the reference image 350 is represented by a set of empty polygons corresponding to pattern features 365 in the SEM image 360 ​​shifted by a displacement d. To measure misalignment using the method of FIG. 3A, areas of the reference image 350 are subtracted from the gray level values ​​of the SEM image 360, as shown in FIG. 3B. Patterns in the reference image that do not align with those in the SEM image leave dark areas in the gray level after subtraction. The subtraction may be used to calculate a misalignment index, which ranges from 0 to 1, with 0 representing the best alignment value and 1 representing the worst alignment value. The SEM image and the reference image can be aligned based on the misalignment index.

[0043]

[0050] In Figure 3C, a misalignment index is calculated by determining the displacement d of an edge feature in reference image 350 from a corresponding edge feature in SEM image 360. As indicated by the arrows in Figure 3D, multiple displacement measurements can be taken as an average, weighted average, or other combination. As above, the displacement can be used to calculate a misalignment index that takes a normalized range from 0 to 1, with 0 representing perfect alignment of the pattern features and 1 representing complete misalignment of the pattern features.

[0044]

[0051] The subtraction and displacement methods discussed above have several drawbacks. They rely on characteristics of the edge of pattern features rather than the central region of the pattern features to determine misalignment, which makes them difficult to use with low-quality images and less robust to noise. They are also insensitive to scaling and deformation errors. They are also relatively insensitive to small misalignments, which are becoming significant as device features continue to shrink. In addition, they may not be compatible with D2D reference images.

[0045]

[0052] FIG. 4 illustrates a system 400 for area density-based misalignment measurement consistent with an embodiment of the present disclosure. Calculations and other operations related to deriving the misalignment measurement may be performed within a controller, such as controller 109 of FIG. 1 . The left, center, and right columns illustrate cross-sectional intensity profiles under three different conditions for a reference image 450, an inspection image 460 (generated by SEM or other imaging), and a cross-correlation 470 (e.g., normalized cross-correlation) between the reference and inspection images. The cross-correlation algorithm may output an alignment result that maximizes the cross-correlation between the inspection and reference images. The three conditions may be, for example, an intensity profile, a binary transform profile, and a density transform profile.

[0046]

[0053] The reference image may be a template, such as a D2D reference image. For example, in some embodiments, the reference image may be a layout file of a wafer design corresponding to the inspection image. The layout file may be in a golden image or GDS format, Graphics Database System II (GDS II) format, Open Artwork Systems Interchange Standard (OASIS) format, Caltech Intermediate Format (CIF), or the like. The wafer design may include patterns or structures for inclusion on the wafer. The patterns or structures may be mask patterns used to transfer features from a photolithography mask or reticle to the wafer. In some embodiments, a GDS or OASIS format layout, among others, may include feature information stored in a binary file format representing planar geometry, text, and other information related to the wafer design. In some embodiments, the reference image may be an image rendered from the layout file. In some embodiments, the GDS image may be rendered to generate an image similar to the inspection image before applying an alignment algorithm, such as intensity profile reference image 450. Alternatively, intensity profile reference image 450 may be a substantially defect-free inspection image selected as a reference image for the D2D method. In the illustrated example, the intensity profile of reference image 450 may be D2D because it contains fluctuations and other irregularities that may not be present in a binary profile. Due to fluctuations in the intensity profiles of reference image 450 and test image 460, cross-correlation 470 may have several distinct peaks that may give an erroneous measure of the ideal alignment position between the reference and test images. Three such peaks are indicated by vertical dashed lines in the left column of FIG. 4.

[0047]

[0054] To overcome these fluctuations, the intensity profiles of reference image 450 and inspection image 460 can be binarized by applying a binary transform or the like, resulting in binary reference image 451 and binary inspection image 461, as shown in the center column of FIG. 4 . Here, a threshold gray level value can be selected. Points on the profile below the threshold can be labeled as not containing pattern features, while points above the threshold can be labeled as containing pattern features. It should be understood that if intensity profile reference image 450 originates from a GDS file or other design data, it may already have a binary format. Furthermore, the thresholds applied to the inspection image and reference image can be the same or different. Similarly, the binary transforms applied to the inspection image and reference image can be the same or different. For example, a binary function can be applied to inspection image 460, and a second binary function can be applied to reference image 450. In some embodiments, the first binary function and the second binary function can be the same binary function. While this binarization operation can smooth intensity fluctuations, cross-correlation 471 of the two binary images can still result in multiple alignment solutions. In fact, a continuous range of solutions is observed between the vertical dashed lines throughout the binarized cross-correlation 471 plateau.

[0048]

[0055] Therefore, further transformations can be performed on reference image 451 and inspection image 461 to yield density profiles 452 and 462 in the right column of FIG. 4 . For example, a density function can be a transformation applied to binary image profiles 451 / 461 to compress the spatial information of binary image profiles 451 / 461 toward the central portion of each pattern feature within the ROI. If the information in binary profiles 451 and 461 of reference image 450 and inspection image 460 is compressed toward the central peak of each pattern feature, as seen in density profiles 452 and 462, cross-correlation density profile 472 can yield a single unique alignment solution, as indicated by the single vertical dashed line. For example, density profiles 452 and 462 can each include a range of density values ​​that generally increase toward the center of each pattern feature. The single unique alignment solution can be based in part on the peak density value in density profile 452 of reference image 450 and the peak density value in density profile 462 of inspection image 460. In some embodiments of the present disclosure, an alignment solution may be based on multiple density values ​​in the density profile, with higher density values ​​being given greater weight. Thus, the test image and the reference image may be aligned based on a misalignment index that is based on regional density.

[0049]

[0056] Similar to the binary transforms described above, the density transforms applied to the inspection image and the reference image can be the same transform or different transforms. For example, a first density function can be applied to inspection image 460 (e.g., by applying the first density function to inspection binary profile 461), and a second density function can be applied to reference image 450 (e.g., by applying the second density function to reference binary profile 451). In some embodiments, the first density function and the second density function can be the same density function.

[0050]

[0057] The area density-based alignment of FIG. 4 may have several advantages over, for example, edge-based alignment processes. For example, flat areas of pattern features, such as dark holes or bright metal areas, may be more reliable misalignment indicators than edge patterns. The density profile of FIG. 4 may enable robust, automated center-to-center alignment using the compressed information from these flat areas. The density profile 452 / 462 may be less susceptible to noise than its intensity profile counterparts 450 / 460 and its binary counterparts 451 / 461. However, they may be more sensitive to small amounts of misalignment and scaling and deformation errors between the reference and inspection images. As discussed above, area density-based alignment can provide a single solution for each aligned feature.

[0051]

[0058] The cross-correlation density profile 472 of the reference image 452 and the test image 462 can be used to generate a misalignment index based on area density. For example, the misalignment index may be calculated as: MA index = 1-[x·y / (|x|·|y|)] (Equation 1) where x represents the test density profile 462 and y represents the reference density profile 452. The cross-correlation density profile 472 can provide a misalignment index ranging from 0 to 1, with a misalignment index of 0 being the best alignment value and a misalignment index of 1 being the worst alignment value.

[0052]

[0059] The areal density-based misalignment index can be an important performance indicator in charged particle beam inspection processes, such as inspection using the EBI tool 100 of Figure 1. The areal density-based misalignment index can be applied to various alignment processes, automatic parameter tuning, and data filtering, for example.

[0053]

[0060] In some embodiments, the area density-based misalignment index may be based on a single metric, such as Equation 1 above. However, additional metrics may be desired to evaluate the score derived using the first metric. Furthermore, in some embodiments, density profiles 452 and 462 may be used to create multiple metrics that are combined in the area density-based misalignment index. In some embodiments, classification techniques may be applied to the alignment of the test and reference images, thereby allowing a classification metric, such as maximum F1 score, to be applied to the alignment problem.

[0054]

[0061] 5 illustrates a further metric 500 for use in misalignment measurement based on area density, consistent with an embodiment of the present disclosure. In FIG. 5, a fixed binarization threshold may be applied to a reference density profile 552. The reference density profile 552 may be, for example, the reference density profile 452 of FIG. 4. A new reference binary profile 551 may be generated from the density profile 552 using the fixed threshold. A new binary profile 561 may then be generated from the test density profile 562 by selecting the binarization threshold that provides the best approximation to the reference binary profile 551.

[0055]

[0062] For example, a dilation-erosion operation can be applied to inspection image density profile 562. For example, inspection image density profile 562 can be, for example, profile 462 of FIG. 4. A range of thresholds can be determined from a maximum erosion (minimum dilation) value a, through an intermediate value b, to a maximum dilation (minimum erosion) value c. This results in a set of candidate binary inspection profiles, such as binary inspection profiles 561a-c. While only three representative values ​​are depicted in FIG. 5, it should be understood that any number of intervening thresholds can be taken.

[0056]

[0063] The values ​​may be plotted in a receiver operating characteristic (ROC) curve 572. The ROC curve 572 may be used to analyze the performance of a classification model. The ROC curve may plot the true positive rate, also known as recall (e.g., the proportion of true positives to the sum of true positives and false negatives), along the y-axis against the false positive rate (e.g., the proportion of false positives to the sum of false positives and true negatives) along the x-axis for a range of classification thresholds. A true positive may correspond to a point at which the candidate test binary profile 561 correctly predicts the presence of a pattern feature in the reference binary profile 551. In other words, a true positive occurs at any point at which both the test profile and the reference profile depict a pattern feature. A false positive may correspond to a point at which the candidate test binary profile 561 incorrectly predicts the presence of a pattern feature in the reference binary profile 551. In other words, a false positive occurs when the candidate test profile depicts a pattern feature that is not present in the reference profile. Similarly, a true negative corresponds to a point at which the candidate test binary profile 561 correctly predicts the absence of a pattern feature in the reference binary profile 551. A false negative may correspond to a point where the test binary profile candidate 561 incorrectly predicts that a pattern feature is not present in the reference binary profile 551 .

[0057]

[0064] Consider test profile 561a for illustrative purposes. In ROC curve 572 of FIG. 5, low values ​​on the x-axis correspond to high shrinkage thresholds, such as threshold 563a, which results in a narrow binary test profile 561a. Because all pattern feature points in test profile 561a align with pattern feature points in reference profile 551, all positives are true positives. However, candidate test profile 561a also fails to identify many actual positives in reference profile 551, resulting in a high number of false negatives. Therefore, the true positive rate for profile 561a is low. Furthermore, because there are few or no false positives, the numerator of the false positive rate is low.

[0058]

[0065] The optimal value may correspond to the point that optimizes the true positive rate and false positive rate. For example, the maximum F1 score can be used to determine the test binary profile 561 that best matches the reference profile 551. The F1 score can be the harmonic mean of the recall (true positive rate) and precision (i.e., the ratio of true positives to the sum of true positives and false positives). The F1 score can take values ​​in the range 0 to 1, with 0 representing the worst classification score and 1 representing the best classification score. Thus, the maximum F1 score measures the maximum similarity between the test image and its reference at all possible dilation / erosion scales.

[0059]

[0066] In FIG. 5 , three F1 scores A, B, and C are plotted along the ROC curve 572. The F1 scores A, B, and C correspond to the binarization thresholds 563a, 563b, and 563c and the binary inspection profiles 561a, 561b, and 561c, respectively. The maximum F1 score may correspond, for example, to point B and profile 561b. Thus, the F1 score B of profile 561b represents another measure of the closeness between the inspection image and the reference image and may be used as an additional metric in the misalignment index based on region density. While the maximum F1 score is discussed above as one possible classification metric, some embodiments of the present disclosure may include other classification metrics instead of or in addition to the maximum F1 score. For example, the area under the curve (AUC) of the ROC 572 in FIG. 5 may be utilized as an additional metric in deriving the misalignment index based on region density.

[0060]

[0067] 6A-B illustrate a misalignment index 600 based on area density including multiple metrics, consistent with embodiments of the present disclosure. FIG. 6A illustrates multiple inspection image maps and reference image maps for an ROI. Reference intensity map 650 and inspection intensity map 660 may be binarized into reference binary map 651 and inspection binary map 661, respectively. For example, a first binary function may be applied to inspection intensity map 660, and a second binary function may be applied to reference intensity map 650. Reference intensity map 650, inspection intensity map 660, reference binary map 651, and inspection binary map 661 may be, for example, reference intensity profile 450, inspection intensity profile 460, reference binary profile 451, and inspection binary profile 461, respectively, of FIG. 4. Similar to the process discussed with respect to FIG. 4, binary maps 651 / 661 may be converted to area density maps 652 / 662, such as by applying first and second density functions as described above. As described above with respect to Figure 4, the first binary function and the second binary function may be the same as or different from each other. Similarly, the first density function and the second density function may be the same as or different from each other.

[0061]

[0068] These area density maps can then be used to derive one or more metrics, which can be combined into a misalignment index based on area density. For example, as seen in FIG. 6A, the reference area density map 652 and the test area density map 662 can be combined using the normalized cross-correlation N c discussed with respect to FIG. 4. The normalized cross-correlation N c can take the form of the bracketed term [x·y / (|x|·|y|)] in Equation 1, where x represents the test density map 662 and y represents the reference density map 652. This normalized score ranges from 0 to 1, with 0 representing no correlation and 1 representing perfect correlation.

[0062]

[0069] In a parallel process, the same maps 652 / 662 can be used to derive a maximum F1 score as described above with respect to FIG. 5. For example, the maximum F1 score can be determined by comparing a fixed-threshold reference binary map (such as reference binary map 651) with multiple new test binary maps. The new test binary maps can be generated by applying a dilation-erosion operation to the test density map 662 to generate multiple binarization thresholds. The multiple new binary maps can be analyzed according to the classification techniques described above with respect to FIG. 5, for example, to determine the maximum F1 score for the multiple test binary maps. This maximum F1 score can also take a value between 0 and 1, with 0 representing the worst classification score and 1 representing the best classification score.

[0063]

[0070] The results of the two scores can be combined, for example, by a weighted average, to yield a misalignment index based on region density. For example, as seen in Figure 6A, the weights are equal and the combination is a simple average, giving a misalignment index as follows: MA index = 1 - [(NC + MaxF1) / 2] (Equation 2) where NC is the normalized cross-correlation value and MaxF1 is the maximum F1 score as described above. Here, the terms are averaged and subtracted from 1 so that 0 corresponds to the best alignment and 1 corresponds to the worst alignment. However, the misalignment index does not necessarily have to be represented in this form. Furthermore, the two components of the misalignment index need not be equally weighted. Generally, in some embodiments of the present disclosure, two metrics can be combined, where the first metric is assigned a coefficient C1 and the second metric is assigned a coefficient C2, such that (C1 + C2) = 1. It should be further understood that the misalignment index is not limited to the range of 0 to 1 or to combining only two metrics.

[0064]

[0071] For example, FIG. 6B shows a more generalized example of the configuration of FIG. 6A. Here, the reference region density map 652 and the inspection region density map 662 can be combined into multiple metrics M1 through Mn. As shown, the metrics can be combined and averaged into a misalignment index. Alternatively, the metrics can be combined in other ways. For example, the metrics can be combined into a misalignment index (C1+C2+C1...+C N )=1 C1~C N In general, the metrics may be combined in any suitable manner. The selection of metrics and the allocation of weights may be determined using machine learning or other data-driven approaches. In some embodiments of the present disclosure, a large training data set may be used to train a misalignment index model for use in a particular application.

[0065]

[0072] As described above with respect to FIG. 4 , a misalignment index based on area density may be used to align the inspection image and the reference image. For example, density maps 652 and 662 may each include a range of density values ​​that generally increase toward the center of each pattern feature. A unique alignment solution may be based in part on a peak density value in density map 652 of reference image map 650 and a peak density value in density map 662 of inspection image map 660. In some embodiments of the present disclosure, the alignment solution may be based on multiple density values ​​in the density profile, with higher density values ​​being given greater weight. Thus, the inspection image and the reference image may be aligned based on a misalignment index based on area density.

[0066]

[0073] FIG. 7 illustrates a comparison 700 of the misalignment index of a conventional system with a misalignment index based on area density consistent with an embodiment of the present disclosure. Three different alignment scenarios 700a-700c are shown in FIG. 7. Alignment scenario 700a represents poor alignment between reference image 750 and inspection image 760. In 700a, a precise misalignment index may result in a high index value. The middle diagram 700b represents moderate alignment between reference image 750 and inspection image 760. In 700b, a precise misalignment index may result in a medium index value. Finally, the bottom diagram 700c represents good alignment between reference image 750 and inspection image 760. In 700c, a precise misalignment index may result in a low index value.

[0067]

[0074] First, consider the comparative misalignment index based on the subtraction method described above with respect to FIGS. 3A-B. In FIG. 7, it can be seen that the subtraction method is tilted in the wrong direction for all three alignments 700a-c, resulting in low index values ​​for high misalignments, and vice versa. For example, in the worst-case alignment scenario 700a, the subtraction index results in a low misalignment value when the actual misalignment is high. Similarly, in the best-case alignment scenario 700c, the subtraction index results in a high misalignment value when the actual misalignment is low. While the subtraction index appears to provide a reasonable measurement in the intermediate scenario 700b, the subtraction index is not consistent across all scenarios 700a-c and therefore cannot be relied upon to provide accurate index values.

[0068]

[0075] Next, consider the comparative misalignment index based on the shift method described above with respect to Figures 3C-D. In Figure 7, the shift method is insensitive to changes in actual misalignment, resulting in low index values ​​in each scenario. For example, in the worst-case alignment scenario 700a, the shift misalignment index results in a low misalignment value when the actual misalignment is high. In the intermediate alignment scenario 700b, the shift misalignment index again results in a low misalignment value when the actual misalignment is moderate. While the shift misalignment index appears to provide a decent measurement in the best-case alignment scenario 700c, it consistently results in low values ​​across all scenarios 700a-c. Therefore, the shift misalignment index cannot be relied upon to provide an accurate index value in the same way as the subtractive misalignment index.

[0069]

[0076] Finally, consider an areal density-based misalignment index consistent with embodiments of the present disclosure. Here, the areal density-based misalignment index accurately tracks the actual misalignment in each of the high, medium, and low misalignment scenarios 700a-c. For example, in the worst-case alignment scenario 700a, the areal density-based misalignment index results in a high misalignment value, and the actual misalignment is also high. In the intermediate alignment scenario 700b, the areal density-based misalignment index results in a medium misalignment value, and the actual misalignment is also medium. In the best-case alignment scenario 700c, the areal density-based misalignment index results in a low misalignment value, and the actual misalignment is also low. The areal density-based misalignment index exhibits superior performance in terms of misalignment robustness and sensitivity to misalignment than the two comparable misalignment indices.

[0070]

[0077] FIG. 8 illustrates a method 800 for generating a misalignment index based on area density, consistent with an embodiment of the present disclosure. The method may be performed, for example, by one or more processors coupled to a memory. The method may be performed, for example, by a controller of an imaging or inspection device, such as the controller 109 of FIG. 1 or the image processing system 290 of FIG. 2. The inspection image used in method 800 may be generated by an inspection device, such as the EBI system 100 of FIG. 1 or the electron beam tool 104 of FIGS. 1-2. Alternatively, the inspection image may be generated by other imaging systems, such as optical imaging, photon detection, proton detection, X-ray detection, ion detection, etc. Photon detection may include light in infrared, visible, ultraviolet, deep UV, extreme UV, X-ray, or any other wavelength range.

[0071]

[0078] In step 810, an inspection image and a reference image are acquired for a region of interest (ROI). The inspection image may be generated, for example, by SEM or other imaging. The reference image may be generated, for example, from a design layout file or a representative inspection image selected as a reference. The images may represent, for example, intensity profiles or intensity maps, such as gray level maps, of the inspection image and the reference image. The ROI may be, for example, an area under inspection on a surface of a sample, such as a semiconductor wafer.

[0072]

[0079] In step 820, a binarization process is performed on the test image and the reference image. The binarization process can convert an image having multiple intensity or gray level values ​​into a binary image having two values. A first value can represent areas with pattern features, and a second value can represent areas without pattern features. For example, as seen in FIGS. 4-6B, the binary image can include a binary profile or binary map. In some embodiments, the reference image may be acquired in binary format and may not require further binarization in step 820.

[0073]

[0080] In step 830, density functions are applied to the inspection image and the reference image. The density function may be a single density function or may include a first density function applied to the inspection image (e.g., by applying the first density function to the binary inspection image derived in step 820) and a second density function applied to the reference image (e.g., by applying the second density function to the binary reference image derived in step 820). The density function may compress information in the inspection image and the reference image from peripheral or edge regions of pattern features to more central regions of the pattern features. The density function may be used to generate density images representing the inspection image and the reference image. For example, the density images may include density profiles or density maps such as those shown in FIGS. 4-6B.

[0074]

[0081] In step 840, a first metric is calculated based on the test density image and the reference density image. The first metric may include, for example, normalized cross-correlation, maximum F1 value, AUC, or other classification or alignment evaluation metric. In some embodiments, an optional further step 841 may include calculating a second such metric. In some embodiments, more than two metrics may be calculated.

[0075]

[0082] In step 850, one or more metrics generated in steps 840 or 841 are used to generate a misalignment index based on area density. The misalignment index based on area density may include a weighted average or another suitable combination of metrics to generate the misalignment index. The selection of metrics and weight distribution may be determined using machine learning or other data-driven approaches. In some embodiments of the present disclosure, a large training data set may be used to train a misalignment index model for use in a particular application.

[0076]

[0083] The method may include, for example, any of the steps discussed above with respect to Figures 1, 2, and 4-7 and with respect to Figure 8 and further below. The misalignment index generated by method 800 may be applied to a charged particle beam process performed by, for example, EBI system 100 of Figure 1 or electron beam tool 104 of Figures 1-2.

[0077]

[0084] A non-transitory computer-readable medium may be provided that stores instructions for a processor of a controller (e.g., controller 109 of FIG. 1 ) to perform, among other things, image inspection, image acquisition, stage positioning, beam focusing, field adjustment, beam bending, condenser lens adjustment, charged particle source activation, beam deflection, and other methods, including the process steps discussed with respect to method 800 or FIGS. 1 , 2, and 4-7. Common forms of non-transitory media include, for example, floppy disks, flexible disks, hard disks, solid-state drives, magnetic tape or any other magnetic data storage medium, compact disk read-only memory (CD-ROM), any other optical data storage medium, any physical medium with a pattern of holes, random access memory (RAM), programmable ROM (PROM) and erasable programmable ROM (EPROM), FLASH-EPROM or any other flash memory, non-volatile random access memory (NVRAM), cache, registers, any other memory chip or cartridge, and networked versions thereof.

[0078]

[0085] The embodiments may be further described using the following clauses: 1. A method of image alignment, comprising: obtaining a first density map of the inspection image corresponding to the region of interest using the first density function; obtaining a second density map of the reference image corresponding to the region of interest using the second density function; aligning the test image and the reference image based on the acquired first and second density maps; A method comprising: 2. The method of clause 1, wherein the first density function and the second density function are the same. 3. The method of clause 1, wherein the first density function and the second density function are different from each other. 4. Obtaining the first density map includes obtaining a first range of density values ​​that includes the first density value; obtaining the second density map includes obtaining a second range of density values ​​that includes the second density value; and aligning the test image and the reference image based on the acquired first and second density values; 2. The method of claim 1, wherein the first density value is a first peak density value within a first range of density values, and the second density value is a second peak density value within a second range of values. 5. Obtaining a first binary transform of the inspection image using a first binary function; obtaining a second binary transform of the reference image using a second binary function; 2. The method of clause 1, further comprising: 6. Obtaining a first density map using a first density function includes applying the first density function to a first binary transformation; and 6. The method of claim 5, wherein obtaining the second density map using the second density function includes applying the second density function to a second binary transform. 7. The method of clause 5, wherein the first binary function and the second binary function are the same. 8. The method of clause 5, wherein the first binary function and the second binary function are different from each other. 9. Further comprising determining a regional density-based misalignment index based on the acquired first and second density maps; The method of clause 1, wherein aligning the inspection image and the reference image based on the acquired first and second density maps includes aligning the inspection image and the reference image based on a misalignment index based on regional density. 10. Further comprising determining a first metric based on the first and second density maps obtained; 10. The method of claim 9, wherein the area density based misalignment index is determined based on a first metric. 11. Further comprising: determining a second metric based on the first on the acquired first and second density maps, the second metric being different from the first metric; 11. The method of claim 10, wherein the area density based misalignment index is determined based on a combination of the first metric and the second metric. 12. The method of clause 10, wherein the first metric is based on one of cross-correlation, normalized cross-correlation, F1 score, and area under the curve (AUC) of a receiver operating characteristic (ROC) curve. 13. The method of clause 1, further comprising determining an overlay error based on the acquired first and second density maps. 14. The method of any one of clauses 1 to 13, wherein the inspection image is a charged particle beam image. 15. The method of claim 14, wherein the charged particle beam image is an SEM image. 16. The method of any one of clauses 1 to 15, wherein the reference image is based on one of a design layout file and a reference SEM image. 17. Obtaining a first density map of the inspection image corresponding to the region of interest using the first density function; obtaining a second density map of the reference image corresponding to the region of interest using the second density function; aligning the test image and the reference image based on the acquired first and second density maps; A non-transitory computer-readable medium storing a set of instructions executable by at least one processor of the device to cause the device to perform a method including: 18. The non-transitory computer-readable medium of clause 17, wherein the first density function and the second density function are the same. 19. The non-transitory computer-readable medium of clause 17, wherein the first density function and the second density function are different from each other. 20. Obtaining the first density map includes obtaining a first range of density values ​​that includes the first density value; obtaining the second density map includes obtaining a second range of density values ​​that includes the second density value; and 18. The non-transitory computer-readable medium of clause 17, wherein the first density value is a first peak density value within a first range of values, and the second density value is a second peak density value within a second range of values. 21. A set of instructions executable by at least one processor of the device comprises: Obtaining a first binary transform of the inspection image using a first binary function; obtaining a second binary transform of the reference image using a second binary function; 18. The non-transitory computer-readable medium of clause 17, further causing the device to: 22. Obtaining a first density map using a first density function includes applying the first density function to a first binary transformation; and 22. The non-transitory computer-readable medium of clause 21, wherein obtaining the second density map using the second density function includes applying the second density function to a second binary transform. 23. The non-transitory computer-readable medium of clause 21, wherein the first binary function and the second binary function are the same. 24. The non-transitory computer-readable medium of clause 21, wherein the first binary function and the second binary function are different from each other. 25. A set of instructions executable by at least one processor of the device comprises: determining a regional density-based misalignment index based on the acquired first and second density maps; The non-transitory computer-readable medium of clause 17, wherein aligning the inspection image and the reference image based on the acquired first and second density maps includes aligning the inspection image and the reference image based on a misalignment index based on regional density. 26. A set of instructions executable by at least one processor of the device further causes the device to determine a first metric based on the first on the acquired first and second density maps; 26. The non-transitory computer-readable medium of claim 25, wherein the area density based misalignment index is determined based on a first metric. 27. A set of instructions executable by at least one processor of the apparatus further causes the apparatus to determine a second metric based on the first on the acquired first and second density maps, the second metric being different from the first metric; 27. The non-transitory computer-readable medium of claim 26, wherein the area density based misalignment index is determined based on a combination of the first metric and the second metric. 28. The non-transitory computer-readable medium of clause 26, wherein the first metric is based on one of cross-correlation, normalized cross-correlation, F1 score, and area under the curve (AUC) of a receiver operating characteristic (ROC) curve. 29. The non-transitory computer-readable medium of any one of clauses 17 to 28, wherein the inspection image is a charged particle beam image. 30. The non-transitory computer-readable medium of clause 29, wherein the charged particle beam image is an SEM image. 31. The non-transitory computer-readable medium of any one of clauses 17-30, wherein the reference image is based on one of a design layout file and a reference SEM image. 32. A charged particle beam source configured to generate a beam of primary charged particles; an optical system configured to direct the beam of primary charged particles to a sample surface for inspecting the sample surface; a charged particle detector configured to detect charged particles returned from the sample surface; a controller including one or more processors configured to cause the charged particle beam device to: acquire a first density map of the inspection image corresponding to the region of interest using a first density function; acquire a second density map of the reference image corresponding to the region of interest using a second density function; and align the inspection image and the reference image based on the acquired first and second density maps; 1. A charged particle beam device comprising: 33. A charged particle beam device according to clause 32, wherein the first density function and the second density function are the same. 34. A charged particle beam device according to clause 32, wherein the first density function and the second density function are different from each other. 35. Obtaining the first density map includes obtaining a first range of density values ​​that includes the first density value; obtaining the second density map includes obtaining a second range of density values ​​that includes the second density value; the first density value is a first peak density value within the first range of values; 33. The charged particle beam device of clause 32, wherein the second density value is a second peak density value within a second range of values. 36. The controller Obtaining a first binary transform of the inspection image using a first binary function; obtaining a second binary transform of the reference image using a second binary function; 33. The charged particle beam device of clause 32, further configured to cause the charged particle beam device to: 37. Obtaining a first density map using a first density function includes applying the first density function to a first binary transformation; 37. The charged particle beam device of clause 36, wherein obtaining the second density map using the second density function comprises applying the second density function to a second binary transformation. 38. A charged particle beam device according to clause 36, wherein the first binary function and the second binary function are the same. 39. A charged particle beam device according to clause 36, wherein the first binary function and the second binary function are different from each other. 40. The controller is further configured to cause the charged particle beam device to determine an area density-based misalignment index based on the acquired first and second density maps; A charged particle beam device as described in clause 32, wherein aligning the inspection image and the reference image based on the acquired first and second density maps includes aligning the inspection image and the reference image based on a misalignment index based on area density. 41. The controller is further configured to cause the charged particle beam device to determine a first metric based on the acquired first and second density maps; 41. The charged particle beam device of claim 40, wherein the areal density based misalignment index is determined based on a first metric. 42. The controller is further configured to cause the charged particle beam device to determine a second metric based on the first on the acquired first and second density maps, the second metric being different from the first metric; 42. The charged particle beam device of claim 41, wherein the areal density based misalignment index is determined based on a combination of the first metric and the second metric. 43. The charged particle beam device of clause 41, wherein the first metric is based on one of cross-correlation, normalized cross-correlation, F1 score, and area under the curve (AUC) of a receiver operating characteristic (ROC) curve. 44. A charged particle beam device according to any one of clauses 32 to 43, wherein the inspection image is a charged particle beam image. 45. A charged particle beam device according to clause 44, wherein the charged particle beam image is an SEM image. 46. ​​A charged particle beam device according to any one of clauses 32 to 45, wherein the reference image is based on one of a design layout file and a reference SEM image. 47. A method of image alignment comprising: acquiring an inspection image corresponding to a region of interest of the sample; acquiring a reference image corresponding to a region of interest of the sample; obtaining an inspection binary profile of the inspection image using a first binary function; obtaining a reference binary profile of the reference image using a second binary function; obtaining a first density map of the inspection binary profile using a first density function; obtaining a second density map of the reference binary profile using a second density function; determining alignment parameters for the test image and the reference image based on the acquired first and second density maps; A method comprising: 48. Acquiring an inspection image corresponding to a region of interest of the sample; acquiring a reference image corresponding to a region of interest of the sample; obtaining an inspection binary profile of the inspection image using a first binary function; obtaining a reference binary profile of the reference image using a second binary function; obtaining a first density map of the inspection binary profile using a first density function; obtaining a second density map of the reference binary profile using a second density function; determining alignment parameters for the test image and the reference image based on the acquired first and second density maps; A non-transitory computer-readable medium storing a set of instructions executable by at least one processor of the device to cause the device to perform a method including: 49. A charged particle beam source configured to generate a beam of primary charged particles; an optical system configured to direct the beam of primary charged particles to a sample surface for inspecting the sample surface; a charged particle detector configured to detect charged particles returned from the sample surface; a controller, including one or more processors, configured to cause the charged particle beam device to: acquire an inspection image corresponding to a region of interest of the sample; acquire a reference image corresponding to the region of interest of the sample; acquire an inspection binary profile of the inspection image using a first binary function; acquire a reference binary profile of the reference image using a second binary function; acquire a first density map of the inspection binary profile using the first density function; acquire a second density map of the reference binary profile using the second density function; and determine alignment parameters of the inspection image and the reference image based on the acquired first and second density maps; 1. A charged particle beam device comprising:

[0079]

[0086] The block diagrams in the figures may illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer hardware or software products according to various exemplary embodiments of the present disclosure. In this regard, each block in the schematic diagrams may represent a certain arithmetic or logical operation that may be implemented using hardware, such as electronic circuits. The blocks may also represent modules, segments, or portions of code that include one or more executable instructions for implementing the specified logical function. It should be understood that in some alternative implementations, the functions shown in the blocks may occur in an order different from that shown in the figures. For example, depending on the functionality involved, two blocks shown in succession may be executed or implemented substantially simultaneously, or the two blocks may be executed in the reverse order. Some blocks may also be omitted. It should also be understood that each block and combination of blocks in the block diagrams may be implemented by a dedicated hardware-based system that performs the specified function or act, or a combination of dedicated hardware and computer instructions.

[0080]

[0087] It is to be understood that the embodiments of the present disclosure are not limited to the exact configuration described above and illustrated in the accompanying drawings, and that various modifications and changes can be made without departing from the scope of the present invention. While the present disclosure has been described in connection with various embodiments, other embodiments of the present invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims

1. obtaining a first density map of the inspection image corresponding to the region of interest using the first density function; obtaining a second density map of the reference image corresponding to the region of interest using a second density function; aligning the inspection image and the reference image based on the acquired first and second density maps; A non-transitory computer-readable medium storing a set of instructions executable by at least one processor of a device to cause the device to perform a method including:

2. The non-transitory computer-readable medium of claim 1 , wherein the first density function and the second density function are the same.

3. The non-transitory computer-readable medium of claim 1 , wherein the first density function and the second density function are different from each other.

4. obtaining the first density map includes obtaining a first range of density values ​​that includes a first density value; obtaining the second density map includes obtaining a second range of density values ​​that includes a second density value; the first density value is a first peak density value within the first range of values; The non-transitory computer-readable medium of claim 1 , wherein the second density value is a second peak density value within the second range of values.

5. The set of instructions executable by the at least one processor of the device comprises: obtaining a first binary transform of the inspection image using a first binary function; obtaining a second binary transform of the reference image using a second binary function; The non-transitory computer-readable medium of claim 1 , further causing the device to:

6. obtaining the first density map using the first density function includes applying the first density function to the first binary transform; 6. The non-transitory computer-readable medium of claim 5, wherein obtaining the second density map using the second density function comprises applying the second density function to the second binary transform.

7. The non-transitory computer-readable medium of claim 5 , wherein the first binary function and the second binary function are the same.

8. The non-transitory computer-readable medium of claim 5 , wherein the first binary function and the second binary function are different from each other.

9. The set of instructions executable by the at least one processor of the apparatus further causes the apparatus to determine a region density based misalignment index based on the obtained first and second density maps; 2. The non-transitory computer-readable medium of claim 1, wherein aligning the inspection image and the reference image based on the acquired first and second density maps comprises aligning the inspection image and the reference image based on a misalignment index based on the regional density.

10. The set of instructions executable by the at least one processor of the device further causes the device to determine a first metric based on the first on the obtained first and second density maps; The non-transitory computer-readable medium of claim 9 , wherein the area density-based misalignment index is determined based on the first metric.

11. The set of instructions executable by the at least one processor of the device further causes the device to determine a second metric based on the first on the acquired first and second density maps, the second metric being different from the first metric; The non-transitory computer-readable medium of claim 10 , wherein the area density-based misalignment index is determined based on a combination of the first metric and the second metric.

12. 11. The non-transitory computer-readable medium of claim 10, wherein the first metric is based on one of a cross-correlation, a normalized cross-correlation, an F1 score, and an area under the curve (AUC) of a receiver operating characteristic (ROC) curve.

13. The non-transitory computer-readable medium of claim 1 , wherein the inspection image is a charged particle beam image.

14. The non-transitory computer-readable medium of claim 13 , wherein the charged particle beam image is a SEM image.

15. The non-transitory computer-readable medium of claim 1 , wherein the reference image is based on one of a design layout file and a reference SEM image.

Images