Detection of yield-critical defects using the medial axis of 3d-stacked charged-particle beam inspection images

Abstract

An apparatus for detecting defects in a sample includes a memory storing a set of instructions and at least one processor configured to execute the set of instructions to cause the apparatus to perform: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.

Description

DETECTION OF YIELD-CRITICAL DEFECTS USING THE MEDIAL AXIS OF 3D-STACKED CHARGED-PARTICLE BEAM INSPECTION IMAGESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23216077.0 which was filed on 12 December 2023 and which is incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] The embodiments provided herein relate to detecting defects, and more particularly to a method for detecting defects by determining a medial axis of a 3D stack of charged-particle beam inspection images.BACKGROUND

[0003] Defect inspection in semiconductor manufacturing is commonly performed using an image processing algorithm called a “difference detector.” This image processing algorithm is based on image comparison and contains a few well-defined steps: denoising the images (filtering with a kernel), aligning the images, taking the difference, and applying a threshold. In the case of repetitive patterns, each image is compared to a shifted version of itself. In the case of non-repetitive patterns, the image has to be compared to an image taken at the same location on a different die (or alternatively, to a GDS formatted layout file or to a “golden image,” i.e., an image known to be accurate).

[0004] This image processing algorithm may use rigid registration (i.e., shifting the images along the X axis, along the Y axis, or by rotation), which may be sensitive to local alignment errors. Such misalignment may generate a shift between the target image and the reference image, thereby triggering false defect indications. Using deformable registration (deforming the target image to match deformations in the reference image) is complex, since the defects can include missing features in the data, leading to artifacts in the difference image, and compromising the algorithm robustness.SUMMARY

[0005] Some embodiments provide an apparatus for performing operations for detecting defects in a sample. The apparatus can include a memory storing a set of instructions and at least one processor configured to execute the set of instructions to cause the apparatus to perform: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.

[0006] Other advantages of the embodiments of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of the present invention.BRIEF DESCRIPTION OF FIGURES

[0007] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0008] Fig. l is a schematic diagram illustrating an example method for detecting a defect using image differences.

[0009] Fig. 2 is a schematic diagram illustrating an example charged-particle beam inspection (CPBI) system, consistent with some embodiments of the present disclosure.

[0010] Fig. 3 is a schematic diagram illustrating an example charged-particle beam tool, consistent with some embodiments of the present disclosure that may be a part of the example charged-particle beam inspection system of Fig. 2.

[0011] Fig. 4 is a schematic diagram illustrating an example multi-beam tool, consistent with embodiments of the present disclosure that can be a part of the example charged-particle beam inspection system of Fig. 2.

[0012] Fig. 5 is a schematic diagram illustrating an example neural network, consistent with some embodiments of the present disclosure.

[0013] Fig. 6 is a schematic diagram illustrating examples of medial axis skeletonization for polygons, consistent with some embodiments of the present disclosure.

[0014] Fig. 7 is a schematic diagram illustrating an example process of creating a medial axis skeletonization of stacked CPBI images, consistent with some embodiments of the present disclosure.

[0015] Fig. 8 is a schematic diagram illustrating another example process of creating a medial axis skeletonization of stacked CPBI images, consistent with some embodiments of the present disclosure.

[0016] Fig. 9 is a flowchart of an example method for detecting defects in a sample, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0017] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the disclosed embodiments as recited in the appended claims. For example, although some embodiments are described in the context of utilizing electron beams, the disclosure is not so limited. Other types of charged-particle beams (e.g., including protons,ions, muons, or any other particle carrying electric charges) may be similarly applied. Furthermore, other imaging systems may be used, such as optical imaging, photon detection, x-ray detection, ion detection, etc.

[0018] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings, the same or like reference numbers refer to the same or like components or entities, and only the differences with respect to the individual embodiments are described. As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component may include A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component may include A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0019] Electronic devices are constructed of circuits formed on a piece of semiconductor material called a substrate. The semiconductor material may include, for example, silicon, gallium arsenide, indium phosphide, or silicon germanium, or the like. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. The size of these circuits has decreased dramatically so that many more of them can be fit on the substrate. For example, an IC chip in a smartphone can be as small as a thumbnail and yet may include over 2 billion transistors, the size of each transistor being less than l / 1000th the size of a human hair.

[0020] Making these ICs with extremely small structures or components is a complex, time-consuming, and expensive process, often involving hundreds of individual steps. Errors in even one step have the potential to result in defects in the finished IC, rendering it useless. Thus, one goal of the manufacturing process is to avoid such defects to maximize the number of functional ICs made in the process; that is, to improve the overall yield of the process.

[0021] One component of improving yield is monitoring the chip-making process to ensure that it is producing a sufficient number of functional integrated circuits. One way to monitor the process is to inspect the chip circuit structures at various stages of their formation. Inspection can be carried out using a scanning charged-particle microscope (SCPM). For example, an SCPM may be a scanning electron microscope (SEM). An SCPM can be used to image these extremely small structures, in effect, taking a “picture” of the structures of the wafer. The image can be used to determine if the structure was formed properly in the proper location. If the structure is defective, then the process can be adjusted, so the defect is less likely to recur.

[0022] The working principle of an SCPM (e.g., an SEM) is similar to a camera. A camera takes a picture by receiving and recording intensity of light reflected or emitted from people or objects. An SCPM takes a “picture” by receiving and recording energies or quantities of charged particles (e.g., electrons) reflected or emitted from the structures of the wafer. Typically, the structures are made on a substrate (e.g., a silicon substrate) that is placed on a platform, referred to as a stage, for imaging. Beforetaking such a “picture,” a charged-particle beam may be projected onto the structures, and when the charged particles are reflected or emitted (“exiting”) from the structures (e.g., from the wafer surface, from the structures underneath the wafer surface, or both), a detector of the SCPM may receive and record the energies or quantities of those charged particles to generate an inspection image. To take such a “picture,” the charged-particle beam may scan through the wafer (e.g., in a line-by-line or zigzag manner), and the detector may receive exiting charged particles coming from a region under charged particle -beam projection (referred to as a “beam spot”). The detector may receive and record exiting charged particles from each beam spot one at a time and join the information recorded for all the beam spots to generate the inspection image. Some SCPMs use a single charged-particle beam (referred to as a “single-beam SCPM,” such as a single-beam SEM) to take a single “picture” to generate the inspection image, while some SCPMs use multiple charged-particle beams (referred to as a “multi-beam SCPM,” such as a multi-beam SEM) to take multiple “sub-pictures” of the wafer in parallel and stitch them together to generate the inspection image. By using multiple charged-particle beams, the SCPM may provide more charged-particle beams onto the structures for obtaining these multiple “sub-pictures,” resulting in more charged particles exiting from the structures. Accordingly, the detector may receive more exiting charged particles simultaneously and generate inspection images of the structures of the wafer with higher efficiency and faster speed.

[0023] As the physical sizes of IC components continue to shrink, accuracy and yield in defect detection become more important. Metrology tools can be used to determine whether the ICs are correctly manufactured by identifying a number of defects on each wafer, including at different levels of detail, such as a pattern level, an image (field of view) level, a die level, a care area level, or a wafer level.

[0024] Fig. 1 is a schematic diagram illustrating an example method 100 for detecting a defect using image differences. A target image 102 includes a defect as shown in enlarged portion 104. A reference image 106 includes a defect as shown in enlarged portion 108. A difference detector image processing algorithm is applied to the target image 102 and the reference image 106 to determine any differences between the two images. The target image 102 and the reference image 106 are aligned (e.g., via rigid registration) and the differences between the target image 102 and the reference image 106 are determined to generate a difference image 110. If there are any differences between the target image 102 and the reference image 106, the differences would appear as detected defects 112. In some implementations, the determination of a difference between the target image 102 and the reference image 106 may be based on a number of pixels of difference or an intensity difference between pixels in the same location. For example, a threshold number of differences or a threshold difference in intensity may be required before the differences are considered to be a defect.

[0025] Embodiments of the present disclosure can provide a way to detect defects in a sample. According to some embodiments of the present disclosure, a plurality of images are acquired, each image being a location (e.g., of a zone of a die of a wafer) to be examined for potential defects. Theimages are binarized into black pixels and white pixels. Removing any gray scale from the images helps make the images easier to analyze. The binarized images are stacked into a three-dimensional (3D) volume. A medial axis of the 3D volume is calculated and a medial axis skeleton is generated of the 3D volume based on the calculated medial axis. Defects in the sample may be detected by examining the medial axis skeleton. A defect is detected in the skeleton by a discontinuity (e.g., a break) in the skeleton or a bifurcation (e.g., a branch) in the skeleton.

[0026] Fig. 2 illustrates an exemplary charged-particle beam inspection (CPBI) system 200 consistent with some embodiments of the present disclosure. CPBI system 200 may be used for imaging. For example, CPBI system 200 may use an electron beam for imaging. As shown in Fig. 2, CPBI system 200 includes a main chamber 201, a load / lock chamber 202, a beam tool 204, and an equipment front end module (EFEM) 206. Beam tool 204 is located within main chamber 201. EFEM 206 includes a first loading port 206a and a second loading port 206b. EFEM 206 may include additional loading port(s). First loading port 206a and second loading port 206b receive wafer front opening unified pods (FOUPs) that contain wafers (e.g., semiconductor wafers or wafers made of other material(s)) or samples to be inspected (the terms “wafers” and “samples” may be used interchangeably). A “lot” is a plurality of wafers that may be loaded for processing as a batch.

[0027] One or more robotic arms (not shown) in EFEM 206 may transport the wafers to load / lock chamber 202. Load / lock chamber 202 is connected to a load / lock vacuum pump system (not shown) which removes gas molecules in load / lock chamber 202 to reach a first pressure below the atmospheric pressure. After reaching the first pressure, one or more robotic arms (not shown) may transport the wafer from load / lock chamber 202 to main chamber 201. Main chamber 201 is connected to a main chamber vacuum pump system (not shown) which removes gas molecules in main chamber 201 to reach a second pressure below the first pressure. After reaching the second pressure, the wafer is subject to inspection by beam tool 204. Beam tool 204 may be a single-beam system or a multi-beam system.

[0028] A controller 209 is electronically connected to beam tool 204. Controller 209 may be a computer that may execute various controls of CPBI system 200. While controller 209 is shown in Fig. 2 as being outside of the structure that includes main chamber 201, load / lock chamber 202, and EFEM 206, it is appreciated that controller 209 may be a part of the structure.

[0029] In some embodiments, controller 209 may include one or more processors (not shown). A processor may be a generic or specific electronic device capable of manipulating or processing information. For example, the processor may include any combination of any number of a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), an optical processor, a programmable logic controller, a microcontroller, a microprocessor, a digital signal processor, an intellectual property (IP) core, a Programmable Logic Array (PLA), a Programmable Array Logic (PAL), a Generic Array Logic (GAL), a Complex Programmable Logic Device (CPLD), a Field- Programmable Gate Array (FPGA), a System On Chip (SoC), an Application-Specific Integrated Circuit (ASIC), a neural processing unit (NPU), and any other type of circuit capable of data processing.The processor may also be a virtual processor that includes one or more processors distributed across multiple machines or devices coupled via a network.

[0030] In some embodiments, controller 209 may further include one or more memories (not shown). A memory may be a generic or specific electronic device capable of storing codes and data accessible by the processor (e.g., via a bus). For example, the memory may include any combination of any number of a random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or any type of storage device. The codes may include an operating system (OS) and one or more application programs (or “apps”) for specific tasks. The memory may also be a virtual memory that includes one or more memories distributed across multiple machines or devices coupled via a network.

[0031] Fig. 3 illustrates an example imaging system 300 consistent with some embodiments of the present disclosure. Beam tool 204 of Fig. 3 may be configured for use in CPBI system 200. Beam tool 204 may be a single beam apparatus or a multi-beam apparatus. As shown in Fig. 3, beam tool 204 includes a motorized sample stage 301, and a wafer holder 302 supported by motorized sample stage 301 to hold a wafer 303 to be inspected. Beam tool 204 further includes an objective lens assembly 304, a charged-particle detector 306 (which includes charged-particle sensor surfaces 306a and 306b), an objective aperture 308, a condenser lens 310, a beam limit aperture 312, a gun aperture 314, an anode 316, and a cathode 318. Objective lens assembly 304, in some embodiments, may include a modified swing objective retarding immersion lens (SORIL), which includes a pole piece 304a, a control electrode 304b, a deflector 304c, and an exciting coil 304d. Beam tool 204 may additionally include an Energy Dispersive X-ray Spectrometer (EDS) detector (not shown) to characterize the materials on wafer 303.

[0032] A primary charged-particle beam 320 (or simply “primary beam 320”), such as an electon beam, is emitted from cathode 318 by applying an acceleration voltage between anode 316 and cathode 318. Primary beam 320 passes through gun aperture 314 and beam limit aperture 312, both of which may determine the size of charged-particle beam entering condenser lens 310, which resides below beam limit aperture 312. Condenser lens 310 focuses primary beam 320 before the beam enters objective aperture 308 to set the size of the charged-particle beam before entering objective lens assembly 304. Deflector 304c deflects primary beam 320 to facilitate beam scanning on the wafer. For example, in a scanning process, deflector 304c may be controlled to deflect primary beam 320 sequentially onto different locations of top surface of wafer 303 at different time points, to provide data for image reconstruction for different parts of wafer 303. Moreover, deflector 304c may also be controlled to deflect primary beam 320 onto different sides of wafer 303 at a particular location, at different time points, to provide data for stereo image reconstruction of the wafer structure at that location. Further, in some embodiments, anode 316 and cathode 318 may generate multiple primary beams 320, and beam tool 204 may include a plurality of deflectors 304c to project the multiple primarybeams 320 to different parts / sides of the wafer at the same time, to provide data for image reconstruction for different parts of wafer 303.

[0033] Exciting coil 304d and pole piece 304a generate a magnetic field that begins at one end of pole piece 304a and terminates at the other end of pole piece 304a. A part of wafer 303 being scanned by primary beam 320 may be immersed in the magnetic field and may be electrically charged, which, in turn, creates an electric field. The electric field reduces the energy of impinging primary beam 320 near the surface of wafer 303 before it collides with wafer 303. Control electrode 304b, being electrically isolated from pole piece 304a, controls an electric field on wafer 303 to prevent micro-arching of wafer 303 and to ensure proper beam focus.

[0034] A secondary charged-particle beam 322 (or “secondary beam 322”), such as secondary electron beams, may be emitted from the part of wafer 303 upon receiving primary beam 320. Secondary beam 322 may form a beam spot on sensor surfaces 306a and 306b of charged-particle detector 306. Charged- particle detector 306 may generate a signal (e.g., a voltage, a current, or the like) that represents an intensity of the beam spot and provide the signal to an image processing system 350. The intensity of secondary beam 322, and the resultant beam spot, may vary according to the external or internal structure of wafer 303. Moreover, as discussed above, primary beam 320 may be projected onto different locations of the top surface of the wafer or different sides of the wafer at a particular location, to generate secondary beams 322 (and the resultant beam spot) of different intensities. Therefore, by mapping the intensities of the beam spots with the locations of wafer 303, the processing system may reconstruct an image that reflects the internal or surface structures of wafer 303.

[0035] Imaging system 300 may be used for inspecting a wafer 303 on motorized sample stage 301 and includes beam tool 204, as discussed above. Imaging system 300 may also include an image processing system 350 that includes an image acquirer 360, storage 370, and controller 209. Image acquirer 360 may include one or more processors. For example, image acquirer 360 may include a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, and the like, or a combination thereof. Image acquirer 360 may connect with a detector 306 of beam tool 204 through a medium such as an electrical conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or a combination thereof. Image acquirer 360 may receive a signal from detector 306 and may construct an image. Image acquirer 360 may thus acquire images of wafer 303. Image acquirer 360 may also perform various post-processing functions, such as generating contours, superimposing indicators on an acquired image, and the like. Image acquirer 360 may perform adjustments of brightness and contrast, or the like of acquired images. Storage 370 may be a storage medium such as a hard disk, cloud storage, random access memory (RAM), other types of computer readable memory, and the like. Storage 370 may be coupled with image acquirer 360 and may be used for saving scanned raw image data as original images, post-processed images, or other images assisting of the processing. Image acquirer 360 and storage 370 may beconnected to controller 209. In some embodiments, image acquirer 360, storage 370, and controller 209 may be integrated together as one control unit.

[0036] In some embodiments, image acquirer 360 may acquire one or more images of a sample based on an imaging signal received from detector 306. An imaging signal may correspond to a scanning operation for conducting charged particle imaging. An acquired image may be a single image including a plurality of imaging areas. The single image may be stored in storage 370. The single image may be an original image that may be divided into a plurality of regions. Each of the regions may include one imaging area containing a feature of wafer 303.

[0037] Fig. 4 illustrates a schematic diagram of an example multi-beam beam tool 204 (also referred to herein as apparatus 204) and an image processing system 490 that may be configured for use in EBI system 100 (Fig. 2), consistent with embodiments of the present disclosure.

[0038] Beam tool 204 comprises a charged-particle source 402, a gun aperture 404, a condenser lens 406, a primary charged-particle beam 410 emitted from charged-particle source 402, a source conversion unit 412, a plurality of beamlets 414, 416, and 418 of primary charged-particle beam 410, a primary projection optical system 420, a motorized wafer stage 480, a wafer holder 482, multiple secondary charged-particle beams 436, 438, and 440, a secondary optical system 442, and a charged- particle detection device 444. Primary projection optical system 420 can comprise a beam separator 422, a deflection scanning unit 426, and an objective lens 428. Charged-particle detection device 444 can comprise detection sub-regions 446, 448, and 450.

[0039] Charged-particle source 402, gun aperture 404, condenser lens 406, source conversion unit 412, beam separator 422, deflection scanning unit 426, and objective lens 428 can be aligned with a primary optical axis 460 of apparatus 204. Secondary optical system 442 and charged-particle detection device 444 can be aligned with a secondary optical axis 452 of apparatus 204.

[0040] Charged-particle source 402 can emit one or more charged particles, such as electrons, protons, ions, muons, or any other particle carrying electric charges. In some embodiments, charged-particle source 402 may be an electron source. For example, charged-particle source 402 may include a cathode, an extractor, or an anode, wherein primary electrons can be emitted from the cathode and extracted or accelerated to form primary charged-particle beam 410 (in this case, a primary electron beam) with a crossover (virtual or real) 408. For ease of explanation without causing ambiguity, electrons are used as examples in some of the descriptions herein. However, it should be noted that any charged particle may be used in any embodiment of this disclosure, not limited to electrons. Primary charged-particle beam 410 can be visualized as being emitted from crossover 408. Gun aperture 404 can block off peripheral charged particles of primary charged-particle beam 410 to reduce Coulomb effect. The Coulomb effect may cause an increase in size of probe spots.

[0041] Source conversion unit 412 can comprise an array of image-forming elements and an array of beam-limit apertures. The array of image-forming elements can comprise an array of micro-deflectors or micro-lenses. The array of image-forming elements can form a plurality of parallel images (virtualor real) of crossover 408 with a plurality of beamlets 414, 416, and 418 of primary charged-particle beam 410. The array of beam-limit apertures can limit the plurality of beamlets 414, 416, and 418. While three beamlets 414, 416, and 418 are shown in Fig. 4, embodiments of the present disclosure are not so limited. For example, in some embodiments, the apparatus 204 may be configured to generate a first number of beamlets. In some embodiments, the first number of beamlets may be in a range from 1 to 1000. In some embodiments, the first number of beamlets may be in a range from 200-500. In some embodiments, an apparatus 204 may generate 400 beamlets.

[0042] Condenser lens 406 can focus primary charged-particle beam 410. The electric currents of beamlets 414, 416, and 418 downstream of source conversion unit 412 can be varied by adjusting the focusing power of condenser lens 406 or by changing the radial sizes of the corresponding beam-limit apertures within the array of beam-limit apertures. Objective lens 428 can focus beamlets 414, 416, and 418 onto a wafer 430 for imaging, and can form a plurality of probe spots 470, 472, and 474 on a surface of wafer 430.

[0043] Beam separator 422 can be a beam separator of Wien filter type generating an electrostatic dipole field and a magnetic dipole field. In some embodiments, if they are applied, the force exerted by the electrostatic dipole field on a charged particle (e.g., an electron) of beamlets 414, 416, and 418 can be substantially equal in magnitude and opposite in a direction to the force exerted on the charged particle by magnetic dipole field. Beamlets 414, 416, and 418 can, therefore, pass straight through beam separator 422 with zero deflection angle. However, the total dispersion of beamlets 414, 416, and 418 generated by beam separator 422 can also be non-zero. Beam separator 422 can separate secondary charged-particle beams 436, 438, and 440 from beamlets 414, 416, and 418 and direct secondary charged-particle beams 436, 438, and 440 towards secondary optical system 442.

[0044] Deflection scanning unit 426 can deflect beamlets 414, 416, and 418 to scan probe spots 470, 472, and 474 over a surface area of wafer 430. In response to the incidence of beamlets 414, 416, and 418 at probe spots 470, 472, and 474, secondary charged-particle beams 436, 438, and 440 may be emitted from wafer 430. Secondary charged-particle beams 436, 438, and 440 may comprise charged particles (e.g., electrons) with a distribution of energies. For example, secondary charged-particle beams 436, 438, and 440 may be secondary electron beams including secondary electrons (energies < 50 eV) and backscattered electrons (energies between 50 eV and landing energies of beamlets 414, 416, and 418). Secondary optical system 442 can focus secondary charged-particle beams 436, 438, and 440 onto detection sub-regions 446, 448, and 450 of charged-particle detection device 444. Detection sub-regions 446, 448, and 450 may be configured to detect corresponding secondary charged-particle beams 436, 438, and 440 and generate corresponding signals (e.g., voltage, current, or the like) used to reconstruct an inspection image of structures on or underneath the surface area of wafer 430.

[0045] The generated signals may represent intensities of secondary charged-particle beams 436, 438, and 440 and may be provided to image processing system 490 that is in communication with charged- particle detection device 444, primary projection optical system 420, and motorized wafer stage 480.The movement speed of motorized wafer stage 480 may be synchronized and coordinated with the beam deflections controlled by deflection scanning unit 426, such that the movement of the scan probe spots (e.g., scan probe spots 470, 472, and 474) may orderly cover regions of interest on the wafer 430. The parameters of such synchronization and coordination may be adjusted to adapt to different materials of wafer 430. For example, different materials of wafer 430 may have different resistance-capacitance characteristics that may cause different signal sensitivities to the movement of the scan probe spots.

[0046] The intensity of secondary charged-particle beams 436, 438, and 440 may vary according to the external or internal structure of wafer 430, and thus may indicate whether wafer 430 includes defects. Moreover, as discussed above, beamlets 414, 416, and 418 may be projected onto different locations of the top surface of wafer 430, or different sides of local structures of wafer 430, to generate secondary charged-particle beams 436, 438, and 440 that may have different intensities. Therefore, by mapping the intensity of secondary charged-particle beams 436, 438, and 440 with the areas of wafer 430, image processing system 490 may reconstruct an image that reflects the characteristics of internal or external structures of wafer 430.

[0047] In some embodiments, image processing system 490 may include an image acquirer 492, a storage 494, and a controller 496. Image acquirer 492 may comprise one or more processors. For example, image acquirer 492 may comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, or the like, or a combination thereof. Image acquirer 492 may be communicatively coupled to charged-particle detection device 444 of beam tool 204 through a medium such as an electric conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or a combination thereof. In some embodiments, image acquirer 492 may receive a signal from charged-particle detection device 444 and may construct an image. Image acquirer 492 may thus acquire inspection images of wafer 430. Image acquirer 492 may also perform various post-processing functions, such as generating contours, superimposing indicators on an acquired image, or the like. Image acquirer 492 may be configured to perform adjustments of brightness and contrast of acquired images. In some embodiments, storage 494 may be a storage medium such as a hard disk, flash drive, cloud storage, random access memory (RAM), other types of computer-readable memory, or the like. Storage 494 may be coupled with image acquirer 492 and may be used for saving scanned raw image data as original images, and post-processed images. Image acquirer 492 and storage 494 may be connected to controller 496. In some embodiments, image acquirer 492, storage 494, and controller 496 may be integrated together as one control unit.

[0048] In some embodiments, image acquirer 492 may acquire one or more inspection images of a wafer based on an imaging signal received from charged-particle detection device 444. An imaging signal may correspond to a scanning operation for conducting charged particle imaging. An acquired image may be a single image comprising a plurality of imaging areas. The single image may be stored in storage 494. The single image may be an original image that may be divided into a plurality of regions. Each of the regions may comprise one imaging area containing a feature of wafer 430. The acquiredimages may comprise multiple images of a single imaging area of wafer 430 sampled multiple times over a time sequence. The multiple images may be stored in storage 494. In some embodiments, image processing system 490 may be configured to perform image processing steps with the multiple images of the same location of wafer 430.

[0049] In some embodiments, image processing system 490 may include measurement circuits (e.g., analog-to-digital converters) to obtain a distribution of the detected secondary charged particles (e.g., secondary electons). The charged-particle distribution data collected during a detection time window, in combination with corresponding scan path data of beamlets 414, 416, and 418 incident on the wafer surface, can be used to reconstruct images of the wafer structures under inspection. The reconstructed images can be used to reveal various features of the internal or external structures of wafer 430, and thereby can be used to reveal any defects that may exist in the wafer.

[0050] In some embodiments, the charged particles may be electrons. When electrons of primary charged-particle beam 410 are projected onto a surface of wafer 430 (e.g., probe spots 470, 472, and 474), the electrons of primary charged-particle beam 410 may penetrate the surface of wafer 430 for a certain depth, interacting with particles of wafer 430. Some electrons of primary charged-particle beam 410 may elastically interact with (e.g., in the form of elastic scattering or collision) the materials of wafer 430 and may be reflected or recoiled out of the surface of wafer 430. An elastic interaction conserves the total kinetic energies of the bodies (e.g., electrons of primary charged-particle beam 410) of the interaction, in which the kinetic energy of the interacting bodies does not convert to other forms of energy (e.g., heat, electromagnetic energy, or the like). Such reflected electrons generated from elastic interaction may be referred to as backscattered electrons (BSEs). Some electrons of primary charged-particle beam 410 may inelastically interact with (e.g., in the form of inelastic scattering or collision) the materials of wafer 430. An inelastic interaction does not conserve the total kinetic energies of the bodies of the interaction, in which some or all of the kinetic energy of the interacting bodies convert to other forms of energy. For example, through the inelastic interaction, the kinetic energy of some electrons of primary charged-particle beam 410 may cause electron excitation and transition of atoms of the materials. Such inelastic interaction may also generate electrons exiting the surface of wafer 430, which may be referred to as secondary electrons (SEs). Yield or emission rates of BSEs and SEs depend on, e.g., the material under inspection and the landing energy of the electrons of primary charged-particle beam 410 landing on the surface of the material, among others. The energy of the electrons of primary charged-particle beam 410 may be imparted in part by its acceleration voltage (e.g., the acceleration voltage between the anode and cathode of charged-particle source 402 in Fig. 4). The quantity of BSEs and SEs may be more or fewer (or even the same) than the injected electrons of primary charged-particle beam 410.

[0051] Consistent with some embodiments of this disclosure, a computer-implemented method of training a machine learning model for defect detection may include obtaining training data that includes an inspection image of a fabricated integrated circuit (IC) and design layout data of the IC. Theobtaining operation, as used herein, may refer to accepting, taking in, admitting, gaining, acquiring, retrieving, receiving, reading, accessing, collecting, or any operation for inputting data. An inspection image, as used herein, may refer to an image generated as a result of an inspection process performed by a charged-particle inspection apparatus (e.g., system 200 of Fig. 2 or system 300 of Fig. 3). For example, an inspection image may be an SCPM image generated by image processing system 350 in Fig. 3. A fabricated IC in this disclosure may refer to an IC manufactured on a sample (e.g., a wafer) in a semiconductor manufacturing process (e.g., a photolithography process). For example, the fabricated IC may be manufactured in a die of the sample. Design layout data of an IC, as used herein, may refer to data representing a designed layout of the IC. In some embodiments, the design layout data may include a design layout file in a GDS format (e.g., a GDS layout file). The design layout file may be visualized (also referred to as “rendered”) to be a 2D image (referred to as a “rendered image” herein) that presents the layout of the IC. The rendered image may include various geometric features (e.g., vertices, edges, corners, polygons, holes, bridges, vias, or the like) of the IC.

[0052] In some embodiments, the design layout data of the IC may include an image (e.g., the rendered image) rendered based on GDS clip data of the IC. GDS clip data of an IC, as used herein, may refer to design layout data of the IC that is to be fabricated in a die, which is of the GDS format. In some embodiments, the design layout data of the IC may include only a design layout file (e.g., the GDS clip data) of the IC. In some embodiments, the design layout data of the IC may include only the rendered image of the IC. In some embodiments, the design layout data of the IC may include only a golden image of the IC. In some embodiments, the design layout data may include any combination of the design layout file, the golden image, and the rendered image of the IC.

[0053] Consistent with some embodiments of this disclosure, the computer-implemented method of detecting defects using the medial axis of 3D stacked images may also include training a machine learning model using the obtained training data. In some embodiments, the machine learning model may be trained by a computer hardware system. In some embodiments, as described elsewhere in this disclosure, the training data may include known calculated medial axis skeletons.

[0054] In some embodiments, machine learning may be employed in the generation of inspection images, reference images, or other images associated with apparatus 200, apparatus 300, or apparatus 204. For example, in some embodiments, a machine learning system may be operated in association with, e.g., controller 209, image processing system 350, image acquirer 360, storage 370, image processing system 490, image acquirer 492, or storage 494 of FIGs. 2-4. In some embodiments, machine learning may be employed in the defect detection method, e.g., method 900 of FIG. 9. In some embodiments, a machine learning system may include a discriminative model. In some embodiments, a machine learning system may include a generative model. For example, learning can feature two types of mechanisms: discriminative learning that may be used to create classification and detection algorithms, and generative learning that may be used to actually create models that, in the extreme, can render images. For example, as described further below, a generative model may be configured forgenerating an image from a design clip that resembles a corresponding location on a wafer in an SCPM image. This may be performed by 1) training the generative model with design clips and the associated actual SCPM images from those locations on the wafer; and 2) using the model in inference mode to feed the model design clips in locations for which simulated SCPM images are desired. Such simulated images can be used as reference images in, e.g., die-to-database inspection.

[0055] If the model(s) include one or more discriminative models, the discriminative model(s) may have any suitable architecture or configuration known in the art. Discriminative models, also called conditional models, are a class of models used in machine learning for modeling the dependence of an unobserved variable “y” on an observed variable “x.” Within a probabilistic framework, this may be done by modeling a conditional probability distribution P(ylx), which can be used for predicting y based on x. Discriminative models, as opposed to generative models, may not allow one to generate samples from the joint distribution of x and y. However, for tasks such as classification and regression that do not require the joint distribution, discriminative models may yield superior performance. On the other hand, generative models are typically more flexible than discriminative models in expressing dependencies in complex learning tasks. In addition, most discriminative models are inherently supervised and cannot easily be extended to unsupervised learning. Application specific details ultimately dictate the suitability of selecting a discriminative versus generative model.

[0056] A generative model can be generally defined as a model that is probabilistic in nature. In other words, a “generative” model is not one that performs forward simulation or rule-based approaches and, as such, it may not be necessary to model the physics of the processes involved in generating an actual image or output (for which a simulated image or output is being generated). Instead, the generative model can be learned (in that its parameters can be learned) based on a suitable training set of data. Such generative models may have a number of advantages for the embodiments described herein. In addition, the generative model may be configured to have a deep learning architecture in that the generative model may include multiple layers, which may perform a number of algorithms or transformations. The number of layers included in the generative model may depend on the particular use case. For practical purposes, a suitable range of layers is from two layers to a few tens of layers.

[0057] Deep learning is a type of machine learning. Machine learning can be generally defined as a type of artificial intelligence (Al) that provides computers with the ability to learn without being explicitly programmed. Machine learning focuses on the development of computer programs that can teach themselves to grow and change when exposed to new data. Machine learning explores the study and construction of algorithms that can learn from and make predictions on data — such algorithms overcome following strictly static program instructions by making data driven predictions or decisions, through building a model from sample inputs.

[0058] The machine learning described herein may be further performed as described in “Introduction to Statistical Machine Learning,” by Sugiyama, Morgan Kaufmann, 2016, 534 pages; “Discriminative, Generative, and Imitative Learning,” by Jebara, MIT Thesis, 2002, 212 pages; and “Principles of DataMining (Adaptive Computation and Machine Learning)” by Hand et al., MIT Press, 2001, 578 pages; which are incorporated by reference as if fully set forth herein. The embodiments described herein may be further configured as described in these references.

[0059] In some embodiments, a machine learning system may comprise a neural network. For example, a model may be a deep neural network with a set of weights that model the world according to the data that it has been fed to train it. Neural networks can be generally defined as a computational approach that is based on a relatively large collection of neural units loosely modeling the way a biological brain solves problems with relatively large clusters of biological neurons connected by axons. Each neural unit is connected with many others, and links can be enforcing or inhibitory in their effect on the activation state of connected neural units. These systems are self-learning and trained rather than explicitly programmed and excel in areas where the solution or feature detection is difficult to express in a traditional computer program.

[0060] Neural networks typically consist of multiple layers, and the signal path traverses from front to back. The goal of the neural network is to solve problems in the same way that the human brain would, although several neural networks are much more abstract. Modern neural network projects typically work with a few thousand to a few million neural units and millions of connections. The neural network may have any suitable architecture or configuration known in the art.

[0061] In a further embodiment, a model may comprise a convolutional and deconvolution neural network. For example, the embodiments described herein can take advantage of learning concepts such as a convolution and deconvolution neural network to solve the normally intractable representation conversion problem (e.g., rendering). The model may have any convolution and deconvolution neural network configuration or architecture known in the art.

[0062] A neural network, as used herein, may refer to a computing model for analyzing underlying relationships in a set of input data by way of mimicking human brains. Similar to a biological neural network, the neural network may include a set of connected units or nodes (referred to as “neurons”), structured as different layers, where each connection (also referred to as an “edge”) may obtain and send a signal between neurons of neighboring layers in a way similar to a synapse in a biological brain. The signal may be any type of data (e.g., a real number). Each neuron may obtain one or more signals as an input and output another signal by applying a non-linear function to the inputted signals. Neurons and edges may typically be weighted by corresponding weights to represent the knowledge the neural network has acquired. During a training process (similar to a learning process of a biological brain), the weights may be adjusted (e.g., by increasing or decreasing their values) to change the strengths of the signals between the neurons to improve the performance accuracy of the neural network. Neurons may apply a thresholding function (referred to as an “activation function”) to its output values of the nonlinear function such that a signal is outputted only when an aggregated value (e.g., a weighted sum) of the output values of the non-linear function exceeds a threshold determined by the thresholding function. Different layers of neurons may transform their input signals in different manners (e.g., by applyingdifferent non-linear functions or activation functions). The output of the last layer (referred to as an “output layer”) may output the analysis result of the neural network, such as, for example, a categorization of the set of input data (e.g., as in image recognition cases), a numerical result, or any type of output data for obtaining an analytical result from the input data.

[0063] Training of the neural network, as used herein, may refer to a process of improving the accuracy of the output of the neural network. Typically, the training may be categorized into three types: supervised training, unsupervised training, and reinforcement training. In the supervised training, a set of target output data (also referred to as “labels” or “ground truth”) may be generated based on a set of input data using a method other than the neural network. The neural network may then be fed with the set of input data to generate a set of output data that is typically different from the target output data. Based on the difference between the output data and the target output data, the weights of the neural network may be adjusted in accordance with a rule. If such adjustments are successful, the neural network may generate another set of output data more similar to the target output data in a next iteration using the same input data. If such adjustments are not successful, the weights of the neural network may be adjusted again. After a sufficient number of iterations, the training process may be terminated in accordance with one or more predetermined criteria (e.g., the difference between the final output data and the target output data is below a predetermined threshold, or the number of iterations reaches a predetermined threshold). The trained neural network may be applied to analyze other input data.

[0064] In the unsupervised training, the neural network is trained without any external gauge (e.g., labels) to identify patterns in the input data rather than generating labels for them. Typically, the neural network may analyze shared attributes (e.g., similarities and differences) and relationships among the elements of the input data in accordance with one or more predetermined rules or algorithms (e.g., principal component analysis, clustering, anomaly detection, or latent variable identification). The trained neural network may extrapolate the identified relationships to other input data.

[0065] In the reinforcement learning, the neural network is trained without any external gauge (e.g., labels) in a trial-and-error manner to maximize benefits in decision making. The input data sets of the neural network may be different in the reinforcement training. For example, a reward value or a penalty value may be determined for the output of the neural network in accordance with one or more rules during training, and the weights of the neural network may be adjusted to maximize the reward values (or to minimize the penalty values). The trained neural network may apply its learned decision-making knowledge to other input data.

[0066] During the training of a neural network, a loss function (or referred to as a “cost function”) may be used to evaluate the output data. The loss function, as used herein, may map output data of a machine learning model (e.g., the neural network) onto a real number (referred to as a “loss” or a “cost”) that intuitively represents a loss or an error (e.g., representing a difference between the output data and target output data) associated with the output data. The training of the neural network may seek to maximize or minimize the loss function (e.g., by pushing the loss towards a local maximum or a local minimumin a loss curve). For example, one or more parameters of the neural network may be adjusted or updated purporting to maximize or minimize the loss function. After adjusting or updating the one or more parameters, the neural network may obtain new input data in a next iteration of its training. When the loss function is maximized or minimized, the training of the neural network may be terminated.

[0067] By way of example, Fig. 5 is a schematic diagram illustrating an example neural network 500, consistent with some embodiments of the present disclosure. As depicted in Fig. 5, neural network 500 may include an input layer 520 that receives inputs, including input 510-1, . . ., input 510-m (m being an integer). For example, an input of neural network 500 may include any structure or unstructured data (e.g., an image). In some embodiments, neural network 500 may obtain a plurality of inputs simultaneously. For example, in Fig. 5, neural network 500 may obtain m inputs simultaneously. In some embodiments, input layer 520 may obtain m inputs in succession such that input layer 520 receives input 510-1 in a first cycle (e.g., in a first inference) and pushes data from input 510-1 to a hidden layer (e.g., hidden layer 530-1), then receives a second input in a second cycle (e.g., in a second inference) and pushes data from input the second input to the hidden layer, and so on. Input layer 520 may obtain any number of inputs in the simultaneous manner, the successive manner, or any manner of grouping the inputs.

[0068] Input layer 520 may include one or more nodes, including node 520-1, node 520-2, . . ., node 520-a (a being an integer). A node (also referred to as a “machine perceptron” or a “neuron”) may model the functioning of a biological neuron. Each node may apply an activation function to received inputs (e.g., one or more of input 510-1, . . ., input 510-m). An activation function may include a Heaviside step function, a Gaussian function, a multiquadratic function, an inverse multiquadratic function, a sigmoidal function, a rectified linear unit (ReLU) function (e.g., a ReLU6 function or a Leaky ReLU function), a hyperbolic tangent (“tanh”) function, or any non-linear function. The output of the activation function may be weighted by a weight associated with the node. A weight may include a positive value between 0 and 1 , or any numerical value that may scale outputs of some nodes in a layer more or less than outputs of other nodes in the same layer.

[0069] As further depicted in Fig. 5, neural network 500 includes multiple hidden layers, including hidden layer 530-1, . . ., hidden layer 530-n (n being an integer). When neural network 500 includes more than one hidden layer, it may be referred to as a “deep neural network” (DNN). Each hidden layer may include one or more nodes. For example, in Fig. 5, hidden layer 530-1 includes node 530-1-1, node 530-1-2, node 530-1-3, . . ., node 530-1-b (b being an integer), and hidden layer 530-n includes node 530-n-l, node 530-n-2, node 530-n-3, . . ., node 530-n-c (c being an integer). Similar to nodes of input layer 520, nodes of the hidden layers may apply the same or different activation functions to outputs from connected nodes of a previous layer, and weight the outputs from the activation functions by weights associated with the nodes.

[0070] As further depicted in Fig. 5, neural network 500 may include an output layer 540 that finalizes outputs, including output 550-1, output 550-2, . . ., output 550-d (d being an integer). Output layer 540may include one or more nodes, including node 540-1, node 540-2, . . ., node 540-d. Similar to nodes of input layer 520 and of the hidden layers, nodes of output layer 540 may apply activation functions to outputs from connected nodes of a previous layer and weight the outputs from the activation functions by weights associated with the nodes.

[0071] Although nodes of each hidden layer of neural network 500 are depicted in Fig. 5 to be connected to each node of its previous layer and next layer (referred to as “fully connected”), the layers of neural network 500 may use any connection scheme. For example, one or more layers (e.g., input layer 520, hidden layer 530-1, . . ., hidden layer 530-n, or output layer 540) of neural network 500 may be connected using a convolutional scheme, a sparsely connected scheme, or any connection scheme that uses fewer connections between one layer and a previous layer than the fully connected scheme as depicted in Fig. 5.

[0072] Moreover, although the inputs and outputs of the layers of neural network 500 are depicted as propagating in a forward direction (e.g., being fed from input layer 520 to output layer 540, referred to as a “feedforward network”) in Fig. 5, neural network 500 may additionally or alternatively use backpropagation (e.g., feeding data from output layer 540 towards input layer 520) for other purposes. For example, the backpropagation may be implemented by using long short-term memory nodes (LSTM). Accordingly, although neural network 500 is depicted similar to a convolutional neural network (CNN), neural network 500 may include a recurrent neural network (RNN) or any other neural network.

[0073] In some embodiments, defects can be detected by stacking multiple (segmented) CPBI images into a 3D volume and subsequently applying a three dimensional medial axis transform (e.g., skeletonization). The resulting skeleton can then be inspected for breaks or bifurcations to identify defects. The skeleton of the 3D volume permits relatively easy finding of defects by finding breaks (e.g., a discontinuity) or bifurcations (e.g., branches) in the skeleton.

[0074] As an overview, the method generally includes acquiring CPBI images corresponding to a same location on a reticle, segmenting the acquired images, stacking the segmented images into a 3D volume, calculating the medial axis of the 3D volume, generating a medial axis skeleton based on the calculated medial axis, and examining the medial axis skeleton to determine whether there are any defects in the CPBI images, which will manifest as breaks or bifurcations in the medial axis skeleton.

[0075] Fig. 6 is a schematic diagram illustrating examples of medial axis skeletonization for polygons, consistent with some embodiments of the present disclosure. A medial axis is defined as the collection of points within the polygon that are closest to more than one of the edges. It can also be viewed (equivalently) as the points that can be the center of a sphere that is entirely within the polygon and touches the polygon in at least two places. For example, in triangle 602, the medial axis 604 consists of the bisectors of the angles, as shown in Fig. 6. A more complicated polygon 610 results in a more complex medial axis 612, as shown in Fig. 6. From these examples, the medial axis of a polygon formsa tree-like skeleton, made of lines and points in 2D. In a 3D volume, the skeleton becomes a set of points, lines, and surfaces.

[0076] Fig. 7 is a schematic diagram illustrating an example process 700 of creating a medial axis skeletonization of stacked CPBI images, consistent with some embodiments of the present disclosure. A stack 702 of multiple CPBI images 702a-702n is created. Each CPBI image 702a-702n is taken of a same area (e.g., a zone) of different dies on a wafer. Doing so enables the process 700 to examine repetitive patterns in the stack 702 to find defects. The process 700 works in a similar manner regardless of the size of the individual images 702a-702n in the stack. For example, each image 702a-702n may be at a smaller scale (e.g., a zone of a die) or may be at a larger scale (e.g., an entire die). How the images are created (e.g., sampled) has an impact on how defects may be detected. For example, a defect should be fully visible within a single image and not cross image boundaries (e.g., where the defect cannot be determined because it is at an edge of the image such that from the image, it does not appear to be a defect).

[0077] Each of the images 702a-702n is segmented prior to creating the stack 702. As used in the present disclosure, “segmenting” the image may include binarizing the image to remove any gray scale and to represent features in the image as black pixels or white pixels. For example, if the sample being examined is made of two different materials, one material may be represented by black pixels while the other material may be represented by white pixels. Other segmentation methods may be applied, such as simple thresholding or deep learning based segmentation (which may include per-pixel classification).

[0078] The images 702a-702n may be stacked together, for example, in an order of exposure of the dies. Each image 702a-702n may also be tagged (e.g., with an identifier) such that if a defect is found, it can be determined which image contains the defect. Other ordering of the images 702a-702n in the stack are also possible.

[0079] A 3D volume 704 is then created from the stack 702. For purposes of illustration, “slices” of the 3D volume 704 are shown as image slices 704a-704n, with each image slice representing a top view of the slice in the 3D volume 704. The dashed lines across image slices 704a-704n indicate locations where the skeletonization 706 of the 3D volume 704 is taken. The skeletonization 706 is shown as a side view of the 3D volume 704.

[0080] As shown in Fig. 7, the features being analyzed include contact holes, shown as circles in image slices 704a-704n. In image slice 704a, the dashed line shows that two contact holes are shown in the skeletonization 706 as circles 708a, 708b. Because the two contact holes are separated (i.e., there is no defect connecting the two contact holes), this is reflected in the skeletonization 706 as two separate line segments 710a, 710b.

[0081] In image slice 704b, the dashed line shows that two contact holes are shown in the skeletonization 706 as circle 712, because the two contact holes are connected by a defect. In the skeletonization 706, the merger of the two contact holes is shown by point 714, where the line segments 710a, 710b indicate a merger (i.e., the defect caused by the two contact holes being connected).

[0082] In image slice 704n, the dashed line shows that one of the contact holes (bottom center of image slice 704n) is deformed, causing a bifurcation in the skeletonization 706, from point 716 into two line segments 718a, 718b.

[0083] Skeletonization is an image or volume transformation technique. It becomes simpler to calculate the defects using the skeletonization than by looking at individual images. If skeletonization is performed on a single image, the skeleton would be a group of points or blobs. When images are stacked together and if two of the points connect, the skeletonization includes a line between the two points, which is an obvious change in the skeleton. Skeletonization is an unstable transformation, such that small changes in the input lead to large changes in the output and can be advantageously used when detecting defects. For example, it becomes trivial to detect changes in the skeletal domain, but might not be trivial to detect in the image domain.

[0084] By examining the skeleton to find breaks or bifurcations, such changes indicate defects (like a missing connection). The continuity of the skeleton is disturbed when there is a defect. Continuity of the skeleton is simple to detect, for example, with a connected components algorithm. For example, in Fig. 7, the bifurcation of the skeletonization 706 at point 716 exists because the edge (as shown in image slice 704n) is not completely round. If the edge was completely round, there would be a line reaching that point in the skeletonization 706. Because there are two separate edges (i.e., vertices), the line bifurcates towards each vertex (shown as line segments 718a, 718b).

[0085] If two points connect, no matter how lightly, it will show in the skeletonization, which is helpful for detecting defects because the defect in the original image may not be obvious. For example, contact holes could be deformed, but if the contact holes do not connect in some way (no matter how small a connection, even one pixel separation), then it will not appear in the skeletonization and it will be shown in the skeletonization as two separate points. If the same structure appears in all the images of the stack, then it is assumed that the structure is correctly made. The purpose of the skeletonization is to find the images that are different from the other images in the stack (e.g., a one-time manufacturing defect). For example, if an image in the middle of the stack shows a defect, under the prior methods of examining all the images, the one image showing the defect may be difficult to find. Creating the skeletonization of the entire 3D stack of images helps identify defects by using the skeletonization to find the differences between the individual images.

[0086] Fig. 8 is a schematic diagram illustrating an example process 800 of creating a medial axis skeletonization of stacked CPBI images, consistent with some embodiments of the present disclosure. A stack 802 of multiple CPBI images 802a-802n is created in a similar manner as the stack 702 described in connection with Fig. 7. Each CPBI image 802a-802n is taken of a same area (e.g., a zone) of different dies on a wafer, is segmented, and the images are stacked in a similar manner as the CPBI images 702a-702n described in connection with Fig. 7.

[0087] A 3D volume 804 is then created from the stack 802, in a similar manner as volume 704 described in connection with Fig. 7. For purposes of illustration, “slices” of the 3D volume 804 areshown as image slices 804a-804n, with each image slice representing a top view of the slice in the 3D volume 804. The dashed lines across image slices 804a-804n indicate locations where the skeletonization 806 of the 3D volume 804 is taken. The skeletonization 806 is shown as a side view of the 3D volume 804.

[0088] As shown in Fig. 8, the features being analyzed include contact holes, shown as circles in image slices 804a-804n. In image slice 804a, the dashed line shows that the contact hole is present in skeletonization 806 by line segment 808. In image slice 804b, the contact hole in the same location (indicated by the dashed line) is missing. This appears in the skeletonization 806 as a discontinuity of the skeletonization 806 and gap 810 (e.g., a break in the skeletonization 806). In image slice 804n, the dashed line shows that the contact hole is present in skeletonization 806 by line segment 812.

[0089] Fig. 9 is a flowchart of an example method 900 for detecting defects in a sample, consistent with embodiments of the present disclosure. In some embodiments, the method 900 may be performed by image processing system 250 of Fig. 2.

[0090] At step 902, images of a same location to be examined are acquired. For example, images 702a- 702n or 802a-802n may be acquired from a CPBI tool.

[0091] At step 904, the acquired images are segmented. For example, the images may be segmented by binarizing the images to remove any gray scale and to represent features in the image as black pixels and white pixels.

[0092] At step 906, the segmented images are stacked into a 3D volume, for example, 3D volume 704 or 804.

[0093] At step 908, a medial axis of the 3D volume is calculated. The medial axis is the collection of points within the 3D volume that are closest to more than one of the edges. It can also be viewed (equivalently) as the points that can be the center of a sphere that is entirely within the 3D volume and touches the 3D volume in at least two places.

[0094] At step 910, a medial axis skeletonization based on the calculated medial axis is calculated, for example, skeletonization 706 or 806.

[0095] At step 912, defects are detected based on the medial axis skeletonization. For example, a defect may be detected based on a discontinuity (e.g., a break) or a bifurcation (e.g., a branch) in the skeleton. A change in the skeleton (such as a discontinuity or bifurcation) indicates a change in the stack of images of the 3D volume.

[0096] In some embodiments, machine learning (ML) may be used in connection with process 700, process 800, or method 900 to speed up the overall process. In some embodiments, supervised machine learning methods suitable for surrogate modeling for be used, such as neural networks, Gaussian processes, or support-vector regression. For example, the step of computing the medial axis skeletonization may be replaced with an ML prediction. In such an example, the ML model is trained with known calculated skeletons. For example, skeletons are calculated with an “expensive” algorithm, and the ML model is trained to predict the skeletons from the 3D stacks of images. It may be necessaryto train the ML model for each type of pattern it needs to detect, so different training may be required for different features to be examined, such as contact holes, line spacing, or other features.

[0097] A non-transitory computer readable medium may be provided that stores instructions for a processor of a controller (e.g., controller 209 of FIG. 2) to carry out, among other things, image inspection, image acquisition, stage positioning, beam focusing, electric field adjustment, beam bending, condenser lens adjusting, activating charged particle source, beam deflecting, and operations 700 and 800 and method 900. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read Only Memory (PROM), and Erasable Programmable Read Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0098] The embodiments may further be described using the following clauses:1. A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to cause the computing device to perform operations for detecting defects in a sample, the operations comprising: acquiring a plurality of images, each image corresponding to a location on a sample; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.2. The non-transitory computer readable medium of clause 1 , wherein each of the plurality of images is a same zone of a die on a wafer being inspected.3. The non-transitory computer readable medium of clause 2, wherein each of the plurality of images is a charged-particle beam inspection image.4. The non-transitory computer readable medium of any one of clauses 1-3, wherein the segmenting includes binarizing each image into black pixels and white pixels.5. The non-transitory computer readable medium of any one of clauses 1-4, wherein the stacking is based on an ordering of the plurality of images.6. The non-transitory computer readable medium of clause 5, wherein the ordering of the plurality of images is based on an order in which the images were acquired.7. The non-transitory computer readable medium of any one of clauses 1-6, wherein a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton.8. The non-transitory computer readable medium of clause 7, wherein evaluating the medial axis skeleton includes using a connected components algorithm to detect the discontinuity in the skeleton or the bifurcation in the skeleton.9. An apparatus for detecting defects in a sample, comprising: a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform operations comprising: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.10. The apparatus of clause 9, wherein each of the plurality of images is a same zone of a die on a wafer being inspected.11. The apparatus of clause 10, wherein each of the plurality of images is a charged-particle beam inspection image.12. The apparatus of any one of clauses 9-11, wherein the segmenting includes binarizing each image into black pixels and white pixels.13. The apparatus of any one of clauses 9-12, wherein the operations further comprise stacking the plurality of segmented images based on an ordering of the plurality of images.14. The apparatus of clause 13, wherein the ordering of the plurality of images is based on an order in which the images were acquired.15. The apparatus of any one of clauses 9-14, wherein a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton.16. The apparatus of clause 15, wherein evaluating the medial axis skeleton includes using a connected components algorithm to detect the discontinuity in the skeleton or the bifurcation in the skeleton.17. A method for detecting defects in a sample, comprising: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.18. The method of clause 17, wherein each of the plurality of images is a same zone of a die on a wafer being inspected.19. The method of clause 18, wherein each of the plurality of images is a charged-particle beam inspection image.20. The method of any one of clauses 17-19, wherein the segmenting includes binarizing each image into black pixels and white pixels.21. The method of any one of clauses 17-20, wherein the stacking is based on an ordering of the plurality of images.22. The method of clause 21, wherein the ordering of the plurality of images is based on an order in which the images were acquired.23. The method of any one of clauses 17-22, wherein a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton.24. The method of clause 23, wherein evaluating the medial axis skeleton includes using a connected components algorithm to detect the discontinuity in the skeleton or the bifurcation in the skeleton.25. A method for detecting defects in a sample, comprising: training a machine learning model on a medial axis skeleton of a pattern to be examined; acquiring a plurality of images, wherein each image is a same location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; generating the medial axis skeleton of the 3D volume by the trained machine learning model; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.26. The method of clause 25, wherein the segmenting includes binarizing each image into black pixels and white pixels.27. The method of clauses 25 or 26, wherein a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton.

[0099] 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 some embodiments, a non-transitory computer-readable medium is provided and can include instructions to perform the functions described in connection with any one or more of Figs. 7-9. In this regard, each block in a schematic diagram may represent certain arithmetical or logical operation processing that may be implemented using hardware such as an electronic circuit. Blocks may also represent a module, segment, or portion of code that comprises one or more executable instructions for implementing the specified logical functions. It should be understood that in some alternative implementations, functions indicated in a block may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed orimplemented substantially concurrently, or two blocks may sometimes be executed in reverse order, depending upon the functionality involved. Some blocks may also be omitted. It should also be understood that each block of the block diagrams, and combination of the blocks, may be implemented by special purpose hardware-based systems that perform the specified functions or acts, or by combinations of special purpose hardware and computer instructions.

[0100] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof. The present disclosure has been described in connection with various embodiments, and other embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the technology 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

CLAIMS1. A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to cause the computing device to perform operations for detecting defects in a sample, the operations comprising: acquiring a plurality of images, each image corresponding to a location on a sample; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.

2. The non-transitory computer readable medium of claim 1 , wherein each of the plurality of images is a same zone of a die on a wafer being inspected.

3. The non-transitory computer readable medium of claim 2, wherein each of the plurality of images is a charged-particle beam inspection image.

4. The non-transitory computer readable medium of claim 1 , wherein the segmenting includes binarizing each image into black pixels and white pixels.

5. The non-transitory computer readable medium of claim 1, wherein the stacking is based on an ordering of the plurality of images.

6. The non-transitory computer readable medium of claim 5, wherein the ordering of the plurality of images is based on an order in which the images were acquired.

7. The non-transitory computer readable medium of claim 1, wherein a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton.

8. The non-transitory computer readable medium of claim 7, wherein evaluating the medial axis skeleton includes using a connected components algorithm to detect the discontinuity in the skeleton or the bifurcation in the skeleton.

9. An apparatus for detecting defects in a sample, comprising: a memory storing a set of instructions; andat least one processor configured to execute the set of instructions to cause the apparatus to perform operations comprising: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; and evaluating the medial axis skeleton to determine whether there are any detected defects in the sample.

10. The apparatus of claim 9, wherein each of the plurality of images is a same zone of a die on a wafer being inspected.

11. The apparatus of claim 10, wherein each of the plurality of images is a charged- particle beam inspection image.

12. The apparatus of claim 9, wherein the segmenting includes binarizing each image into black pixels and white pixels.

13. The apparatus of claim 9, wherein the operations further comprise stacking the plurality of segmented images based on an ordering of the plurality of images and the ordering is based on an order in which the images were acquired.

14. The apparatus of claim 9, wherein: a defect appears in the skeleton as a discontinuity in the skeleton or a bifurcation in the skeleton; and evaluating the medial axis skeleton includes using a connected components algorithm to detect the discontinuity in the skeleton or the bifurcation in the skeleton.

15. A method for detecting defects in a sample, comprising: acquiring a plurality of images, wherein each image is a location to be examined; segmenting each of the plurality of images; stacking the plurality of segmented images into a three-dimensional (3D) volume; calculating a medial axis of the 3D volume; generating a medial axis skeleton of the 3D volume based on the calculated medial axis; andevaluating the medial axis skeleton to determine whether there are any detected defects in the sample.

Images