Systems and methods for characterizing image resolution

Abstract

The system, apparatus, and method includes providing a raw image of a sample, observing a pixel size of the raw image, converting the raw image to a transformed image by applying a Fourier transform to the raw image, applying a function to the transformed image based on the pixel size, and determining a key performance indicator of the resolution of the raw image based on the result of the applied function.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63 / 409,049, filed September 22, 2022, which is incorporated herein by reference in its entirety. [Background technology]

[0002] FIELD OF THE INVENTION

[0002] The description herein relates to the field of inspection and metrology systems, and more particularly to systems for characterizing image resolution.

[0003]

[0003] In the integrated circuit (IC) manufacturing process, unfinished and finished circuit components are inspected to ensure they are manufactured as designed and are free of defects. Inspection systems based on optical microscopes typically have resolutions down to several hundred nanometers, which is limited by the wavelength of light. As the physical size of IC components continues to shrink to less than 100 nanometers and even less than 10 nanometers, inspection systems that provide higher resolution than those based on optical microscopes are needed.

[0004]

[0004] Charged particle (e.g., electron) beam microscopes, such as scanning electron microscopes (SEMs) or transmission electron microscopes (TEMs), which enable resolution down to less than 1 nanometer, serve as practical tools for inspecting IC components with feature sizes less than 100 nanometers. Using an SEM, electrons from a single primary electron beam, or from multiple primary electron beams, can be focused onto a location of interest on a wafer under inspection. The primary electrons interact with the wafer and may be backscattered or cause the wafer to emit secondary electrons. The intensity of the electron beam, including the backscattered and secondary electrons, can vary based on the characteristics of the wafer's internal and external structure, which can indicate whether the wafer has defects. Summary of the Invention

[0005]

[0005] Embodiments of the present disclosure provide apparatus, systems, and methods for characterizing image resolution. In some embodiments, the systems and methods may include providing a raw image of a sample, observing a pixel size of the raw image, converting the raw image to a transformed image by applying a Fourier transform to the raw image, applying a function to the transformed image based on the pixel size, and determining a key performance indicator of the resolution of the raw image based on a result of the applied function.

[0006]

[0006] In some embodiments, the system and method may include providing a sample image, observing the pixel size of the image, converting the raw image to a transformed image, applying a function to the transformed image based on the pixel size, and determining a key performance indicator of the image resolution by applying the function to the transformed image. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a schematic diagram illustrating an exemplary electron beam inspection (EBI) system consistent with an embodiment of the present disclosure. [Figure 2A]

[0008] 2 is a schematic diagram illustrating an example multi-beam system that is part of the example charged particle beam inspection system of FIG. 1, consistent with an embodiment of the present disclosure. [Figure 2B]

[0009] 2 is a schematic diagram illustrating an example single beam system that is part of the example charged particle beam inspection system of FIG. 1, consistent with an embodiment of the present disclosure. [Figure 3]

[0010] 1 is a schematic diagram of an exemplary key performance indicator (KPI) determination system consistent with an embodiment of the present disclosure. [Figure 4]

[0011] 10A-10C illustrate example images and graphs generated by a KPI determination system consistent with embodiments of the present disclosure. [Figure 5]

[0012] 10 is an exemplary graph of a resolution KPI, consistent with an embodiment of the present disclosure. [Figure 6]

[0013] 10A-10C illustrate example images and graphs generated by a KPI determination system consistent with embodiments of the present disclosure. [Figure 7]

[0014] 10 is an exemplary graph of a resolution KPI, consistent with an embodiment of the present disclosure. [Figure 8]

[0015] 10A-10C illustrate example images and graphs generated by a KPI determination system consistent with embodiments of the present disclosure. [Figure 9]

[0016] 10 is an exemplary graph of a resolution KPI, consistent with an embodiment of the present disclosure. [Figure 10]

[0017] 10 is an exemplary graph of a resolution KPI, consistent with an embodiment of the present disclosure. [Figure 11]

[0018] 10 is an exemplary graph of a resolution KPI, consistent with certain embodiments of the present disclosure. [Figure 12]

[0019] 1 is a flowchart illustrating an exemplary process for characterizing image resolution, consistent with an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0008]

[0020] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description will refer 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 consistent with the present invention. Instead, they are merely examples of apparatus and methods consistent with aspects related to the subject matter as recited in the appended claims. For example, while some embodiments are described in the context of utilizing electron beams, the disclosure is not so limited. Other charged particle beams can be similarly applied. Furthermore, other imaging systems, such as optical imaging, photodetection, x-ray detection, extreme ultraviolet inspection, deep ultraviolet inspection, etc., can be used, which generate corresponding types of images.

[0009]

[0021] Electronic devices are built from circuits formed on a piece of silicon called a substrate. Many circuits can be formed together on the same piece of silicon, and they are called integrated circuits, or ICs. The size of these circuits is shrinking dramatically, resulting in more circuits being able to 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 less than 1 / 1000 the size of a human hair.

[0010]

[0022] Manufacturing these tiny ICs is a complex, time-consuming, and expensive process, often involving hundreds of individual steps. An error in even one step can result in a defect that renders the finished IC unusable. Therefore, one of the goals of the manufacturing process is to prevent such defects and maximize the number of functional ICs produced during the process—in other words, to increase the overall process yield.

[0011]

[0023] One factor in improving yield is monitoring the chip manufacturing process to ensure that a sufficient number of functional ICs are being produced. One way to monitor the process is to inspect the chip circuit structures at various stages of their formation. Inspection can be done using a scanning electron microscope (SEM). The SEM can be used to image these extremely small structures, essentially taking a "picture" of the structures on the wafer. The images can be used to determine whether the structures were formed properly and in the right location. If the structures are defective, the process can be adjusted to make the defect less likely to recur. Defects can occur during various stages of semiconductor processing. For the reasons stated above, it is important to find defects as early, accurately, and efficiently as possible.

[0012]

[0024] The operating principle of an SEM is similar to that of a camera. A camera takes a picture by receiving and recording the brightness and color of light reflected or emitted from a person or object. An SEM takes a "picture" by receiving and recording the energy or quantity of electrons reflected or emitted from a structure. Before taking such a "picture," an electron beam can be directed onto the structure. As electrons reflect or emit ("emit") from the structure, the SEM's detector can receive and record the energy or quantity of those electrons to generate an image. Some SEMs use a single electron beam to take such a "picture" (called a "single-beam SEM"), while other SEMs use multiple electron beams to take multiple "photographs" of the wafer (called a "multi-beam SEM"). By using multiple electron beams, the SEM can direct more electron beams onto the structure to obtain these multiple "photographs," resulting in more electrons being emitted from the structure. Thus, the detector can simultaneously receive more emitted electrons, allowing for more efficient and faster generation of images of the wafer's structures.

[0013]

[0025] The system may generate images with image resolution that requires adjustment (e.g., a measurement of the smallest structure that can be captured in the image, the size of the focused e-beam, etc.) For example, the system may use key performance indicators to determine whether the image resolution is too low and whether the image needs to be adjusted to compensate for the resolution.

[0014]

[0026] However, typical inspection and metrology systems suffer from limitations. Typical inspection and metrology systems may use key performance indicators that are sensitive to image brightness or contrast, but not to image resolution. Typical key performance indicators lack sensitivity to image resolution, especially when the image is relatively sharp (e.g., when the image has details with well-defined boundaries).

[0015]

[0027] Some of the disclosed embodiments provide systems and methods that address some or all of these disadvantages by determining and using a key performance indicator that is sensitive to image resolution to compensate for image resolution. The disclosed embodiments may include observing the pixel size of a raw image, applying a Fourier transform to the raw image to convert the raw image into a transformed image, applying a function to the transformed image based on the pixel size, and determining a key performance indicator for the resolution of the raw image based on the result of the applied function, thereby improving the robustness and reliability of the characterization of the image resolution.

[0016]

[0028] The relative dimensions of components in the figures 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 elements, and only the differences with respect to individual embodiments are described.

[0017]

[0029] As used herein, unless otherwise indicated, the term "or" includes 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 indicated 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 indicated or impracticable.

[0018]

[0030] Some embodiments may be described in the context of providing detectors and methods of detection in systems utilizing electron beams without limiting the scope of the disclosure. However, the disclosure is not so limited. Other types of charged particle beams may be similarly applicable. Furthermore, the systems and methods for detection may be used in other imaging systems, such as optical imaging, photon detection, x-ray detection, ion detection, etc.

[0019]

[0031] 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, an electron beam tool 104, and an equipment front-end module (EFEM) 106. The electron beam tool 104 is disposed within the main chamber 101. The EFEM 106 includes a first loading port 106a and a second loading port 106b. The EFEM 106 may include additional loading ports. The first loading port 106a and the second loading port 106b receive wafer front-opening integrated pods (FOUPs) containing wafers (e.g., semiconductor wafers or wafers made of other materials) or samples to be inspected (the terms wafer and sample may be used interchangeably). A "lot" is a plurality of wafers that can be loaded for processing as a batch.

[0020]

[0032] 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 that is less 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 that is less than the first pressure. After the second pressure is reached, the wafers are inspected by the electron beam tool 104. The electron beam tool 104 can be a single beam system or a multi-beam system.

[0021]

[0033] The controller 109 is electronically connected to the electron beam tool 104. The controller 109 may be a computer configured to perform various controls of the EBI system 100. Although the controller 109 is shown in FIG. 1 outside the structure that includes 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 this structure.

[0022]

[0034] In some embodiments, the controller 109 may include one or more processors (not shown). A processor may be a general-purpose or specific electronic device capable of manipulating or processing information. For example, a processor may include any number of central processing units (or "CPUs"), graphics processing units (or "GPUs"), optical processors, programmable logic controllers, microcontrollers, microprocessors, digital signal processors, intellectual property (IP) cores, programmable logic arrays (PLAs), programmable array logic (PALs), generic 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.

[0023]

[0035] In some embodiments, the controller 109 may further include one or more memories (not shown). Memory may be a general-purpose or specific electronic device capable of storing code and data accessible by 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. Code may include an operating system (OS) and one or more application programs (or "apps") for specific tasks. Memory may also be virtual memory, including one or more memories distributed across multiple machines or devices coupled via a network.

[0024]

[0036] Embodiments of the present disclosure may provide a single charged particle beam imaging system ("single beam system"). Compared to a single beam system, a multiple charged particle beam imaging system ("multi-beam system") can be designed to optimize throughput for different scanning modes. Embodiments of the present disclosure provide a multi-beam system that has the ability to optimize throughput for different scanning modes by using beam arrays with different geometries to accommodate different throughput and resolution requirements.

[0025]

[0037] Reference is now made to FIG. 2 , which is a schematic diagram illustrating an exemplary electron beam tool 104, including a multi-beam inspection tool that is part of the EBI system 100 of FIG. 1 , consistent with embodiments of the present disclosure. In some embodiments, the electron beam tool 104 can be operated as a single-beam inspection tool that is part of the EBI system 100 of FIG. 1 . The multi-beam electron beam tool 104 (also referred to herein as apparatus 104) includes an electron source 201, a Coulomb aperture plate (or “gun aperture plate”) 271, a condenser lens 210, a source transformation unit 220, a primary projection system 230, a motorized stage 209, and a sample holder 207 supported by the motorized stage 209 for holding a sample 208 (e.g., a wafer or photomask) to be inspected. The multi-beam electron beam tool 104 may further include a secondary projection system 250 and an electron detection device 240. The primary projection system 230 may include an objective lens 231. The electronic detection device 240 may include a number of detection elements 241, 242 and 243. The beam separator 233 and the deflection scanning unit 232 may be arranged inside the primary projection system 230.

[0026]

[0038] The electron source 201, the Coulomb aperture plate 271, the condenser lens 210, the source conversion unit 220, the beam separator 233, the deflection scanning unit 232 and the primary projection system 230 may be aligned with a primary optical axis 204 of the apparatus 104. The secondary projection system 250 and the electron detection device 240 may be aligned with a secondary optical axis 251 of the apparatus 104.

[0027]

[0039] The electron source 201 may include a cathode (not shown) and an extractor or anode (not shown), and during operation, the electron source 201 is configured to emit primary electrons from the cathode, which are extracted or accelerated by the extractor and / or anode to form a primary electron beam 202 that forms a primary beam crossover (virtual or real) 203. The primary electron beam 202 may be visualized as emerging from the primary beam crossover 203.

[0028]

[0040] The source conversion unit 220 may include an image forming element array (not shown), an aberration compensator array (not shown), a beam-limiting aperture array (not shown), and a pre-bending micro-deflector array (not shown). In some embodiments, the pre-bending micro-deflector array deflects multiple primary beamlets 211, 212, 213 of the primary electron beam 202 so that they perpendicularly enter the beam-limiting aperture array, the image forming element array, and the aberration compensator array. In some embodiments, the apparatus 104 can be operated as a single beam system such that a single primary beamlet is generated. In some embodiments, the condenser lens 210 is designed to focus the primary electron beam 202 into a parallel beam that is perpendicularly incident on the source conversion unit 220. The image forming element array may include a plurality of micro-deflectors or micro-lenses, one for each of the primary beamlets 211, 212, 213, for influencing the plurality of primary beamlets 211, 212, 213 of the primary electron beam 202 and for forming a plurality of parallel images (virtual or real images) of the primary beam crossover 203. In some embodiments, the aberration compensator array may include a field curvature compensator array (not shown) and an astigmatism compensator array (not shown). The field curvature compensator array may include a plurality of micro-lenses for compensating for field curvature aberration of the primary beamlets 211, 212, and 213. The astigmatism compensator array may include a plurality of micro-astigmatism correctors for compensating for astigmatism of the primary beamlets 211, 212, and 213. The beam-limiting aperture array may be configured to limit the diameter of each of the primary beamlets 211, 212, and 213. 2A shows three primary beamlets 211, 212, and 213 by way of example, it will be understood that the source conversion unit 220 can be configured to form any number of primary beamlets. The controller 109 can be connected to various parts of the EBI system 100 of FIG. 1, such as the source conversion unit 220, the electronic detection device 240, the primary projection system 230, or the motorized stage 209. In some embodiments, the controller 109 can perform various image and signal processing functions, as described in more detail below.The controller 109 may also generate various control signals to govern the operation of the charged particle beam inspection system.

[0029]

[0041] The condenser lens 210 is configured to focus the primary electron beam 202. The condenser lens 210 may be further configured to adjust the current of the primary beamlets 211, 212, and 213 downstream of the source conversion unit 220 by varying the focusing power of the condenser lens 210. Alternatively, the current may be varied by changing the radial size of a beam-limiting aperture in a beam-limiting aperture array corresponding to each primary beamlet. The current may be varied by changing both the radial size of the beam-limiting aperture and the focusing power of the condenser lens 210. The condenser lens 210 may be an adjustable condenser lens configured such that the position of its first main surface is movable. The adjustable condenser lens may be configured to be magnetic, such that the off-axis beamlets 212 and 213 may illuminate the source conversion unit 220 with a rotation angle. The rotation angle varies depending on the focusing power or the position of the first main surface of the adjustable condenser lens. The collecting lens 210 may be an anti-rotation collecting lens that may be configured to maintain a constant rotation angle while changing the focusing power of the collecting lens 210. In some embodiments, the collecting lens 210 may be an adjustable anti-rotation collecting lens whose rotation angle does not change when its focusing power and the position of its first major surface change.

[0030]

[0042] The objective lens 231 may be configured to focus the beamlets 211, 212, and 213 onto the sample 208 for inspection, which in this embodiment may form three probe spots 221, 222, and 223 on the surface of the sample 208. The Coulomb aperture plate 271 is configured, in operation, to block peripheral electrons of the primary electron beam 202 to reduce the Coulomb effect, which may increase the size of each of the probe spots 221, 222, and 223 of the primary beamlets 211, 212, 213, and therefore degrade the inspection resolution.

[0031]

[0043] The beam separator 233 may be, for example, a Wien filter including electrostatic deflectors that generate electrostatic and magnetic dipole fields (not shown in FIG. 2A ). In operation, the beam separator 233 may be configured to exert an electrostatic force due to the electrostatic dipole field on individual electrons of the primary beamlets 211, 212, and 213. The electrostatic force is equal in magnitude but opposite in direction to the magnetic force that the magnetic dipole field of the beam separator 233 exerts on the individual electrons. Thus, the primary beamlets 211, 212, and 213 may pass at least substantially straight through the beam separator 233 with at least substantially zero deflection angle.

[0032]

[0044] The deflection scanning unit 232 is configured, in operation, to deflect the primary beamlets 211, 212, and 213 to scan the probe spots 221, 222, and 223 over respective scan areas on a section of the surface of the sample 208. In response to the primary beamlets 211, 212, and 213, or the probe spots 221, 222, and 223, impinging on the sample 208, electrons are generated from the sample 208, generating three secondary electron beams 261, 262, and 263. Each of the secondary electron beams 261, 262, and 263 typically includes secondary electrons (having an electron energy of 50 eV or less) and backscattered electrons (having an electron energy of 50 eV to the landing energy of the primary beamlets 211, 212, and 213). The beam separator 233 is configured to deflect the secondary electron beams 261, 262, and 263 towards the secondary projection system 250. Secondary projection system 250 then focuses secondary electron beams 261, 262, and 263 onto detector elements 241, 242, and 243 of electron detection device 240. Detector elements 241, 242, and 243 are arranged to detect corresponding secondary electron beams 261, 262, and 263 and generate corresponding signals that are sent to controller 109 or a signal processing system (not shown), for example, to construct an image of a corresponding scanned area of ​​sample 208.

[0033]

[0045] In some embodiments, detector elements 241, 242, and 243 detect corresponding secondary electron beams 261, 262, and 263, respectively, and generate corresponding intensity signal outputs (not shown) to an image processing system (e.g., controller 109). In some embodiments, each detector element 241, 242, and 243 may include one or more pixels. The intensity signal output of a detector element may be the sum of signals generated by all of the pixels in the detector element.

[0034]

[0046] In some embodiments, the controller 109 may include an image processing system including an image acquirer (not shown) and storage (not shown). The image acquirer may include one or more processors. For example, the image acquirer 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 may be communicatively coupled to the electronic detection device 240 of the apparatus 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, among others. In some embodiments, the image acquirer may receive signals from the electronic detection device 240 and construct an image. In this manner, the image acquirer may acquire an image of the sample 208. The image acquirer may also perform various post-processing functions such as generating contours and overlaying indicators on the acquired image. The image acquirer may be configured to adjust the brightness and contrast of the acquired image, etc. In some embodiments, the storage may be a storage medium such as a hard disk, a flash drive, cloud storage, random access memory (RAM), or other type of computer-readable memory. The storage may be coupled to the image acquirer and may be used to store the scanned raw image data as the original image and the post-processed image.

[0035]

[0047] In some embodiments, the image acquirer may acquire one or more images of the sample based on an imaging signal received from the electronic detection device 240. The imaging signal may correspond to a scanning operation for performing charged particle imaging. The acquired image may be a single image including multiple imaging areas. The single image may be stored in storage. The single image may be an original image that may be divided into multiple regions. Each region may include one imaging area that includes a feature of the sample 208. The acquired image may include multiple images of a single imaging area of ​​the sample 208 sampled multiple times over a time sequence. The multiple images may be stored in storage. In some embodiments, the controller 109 may be configured to perform image processing steps using multiple images of the same location of the sample 208.

[0036]

[0048] In some embodiments, the controller 109 may include measurement circuitry (e.g., an analog-to-digital converter) to obtain a distribution of detected secondary electrons. The electron distribution data collected during the detection time window, in combination with the corresponding scan path data of each of the primary beamlets 211, 212, and 213 incident on the wafer surface, may be used 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 the sample 208, and thereby reveal defects that may be present in the wafer.

[0037]

[0049] In some embodiments, the controller 109 can control the motorized stage 209 to move the sample 208 during inspection of the sample 208. In some embodiments, the controller 109 can enable the motorized stage 209 to move the sample 208 in a direction continuously at a constant speed. In other embodiments, the controller 109 can enable the motorized stage 209 to vary the speed of movement of the sample 208 over time depending on the step in the scanning process.

[0038]

[0050] 2A shows that the apparatus 104 uses three primary electron beams, it will be understood that the apparatus 104 may use one, two, or more primary electron beams. This disclosure does not limit the number of primary electron beams used in the apparatus 104. In some embodiments, the apparatus 104 may be an SEM used for lithography. In some embodiments, the electron beam tool 104 may be a single beam system or a multi-beam system.

[0039]

[0051] For example, as shown in FIG. 2B , electron beam tool 100B (also referred to herein as apparatus 100B) can be a single-beam inspection tool used in EBI system 10 consistent with embodiments of the present disclosure. Apparatus 100B includes a wafer holder 136 supported by a motorized stage 134 to hold a wafer 150 to be inspected. Electron beam tool 100B includes an electron emitter, which may include a cathode 103, an anode 121, and a gun aperture 122. Electron beam tool 100B further includes a beam-limiting aperture 125, a condenser lens 126, a column aperture 135, an objective lens assembly 132, and a detector 144. Objective lens assembly 132 can be a modified SORIL lens in some embodiments, which includes a pole piece 132a, a control electrode 132b, a deflector 132c, and an excitation coil 132d. In the imaging process, electron beam 161 emitted from the tip of cathode 103 is accelerated by the voltage on anode 121, passes through gun aperture 122, beam limiting aperture 125, condenser lens 126, and is focused by a modified SORIL lens to a probe spot 170, which can impinge on the surface of wafer 150. A deflector, such as deflector 132c or another deflector in a SORIL lens, can scan probe spot 170 across the surface of wafer 150. Secondary particles or scattered primary particles, such as secondary electrons or scattered primary electrons emitted from the wafer surface, can be collected by detector 144 to determine the beam intensity and allow an image of the area of ​​interest on wafer 150 to be reconstructed.

[0040]

[0052] An image processing system 199 may also be provided, including an image acquirer 120, storage 130, and controller 109. The image acquirer 120 may include one or more processors. For example, the image acquirer 120 may include a computer, a server, a mainframe host, a terminal, a personal computer, any type of mobile computing device, or the like, or a combination thereof. The image acquirer 120 may be connected to the detector 144 of the electron beam tool 100B 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. The image acquirer 120 may receive signals from the detector 144 and construct an image. Thus, the image acquirer 120 may acquire an image of the wafer 150. The image acquirer 120 may also perform various post-processing functions, such as generating contours and overlaying indicators on the acquired image. The image acquirer 120 may also be configured to adjust the brightness and contrast of the acquired image, etc. The storage 130 may be a storage medium such as a hard disk, random access memory (RAM), cloud storage, or other type of computer-readable memory. The storage 130 may be coupled to the image acquirer 120 and may be used to store scanned raw image data as original images and post-processed images. The image acquirer 120 and the storage 130 may be connected to the controller 109. In some embodiments, the image acquirer 120, the storage 130, and the controller 109 may be integrated together as one electronic control unit.

[0041]

[0053] In some embodiments, the image acquirer 120 can acquire one or more images of the sample based on an imaging signal received from the detector 144. The imaging signal can correspond to a scanning motion for performing charged particle imaging. The acquired image can be a single image that includes multiple imaging areas that can include various features of the wafer 150. The single image can be stored in the storage 130. The imaging can be based on imaging frames.

[0042]

[0054] The condenser and illumination optics of an electron beam tool can include or be supplemented by electromagnetic quadrupole electron lenses. For example, as shown in FIG. 2B , electron beam tool 100B can include a first quadrupole lens 148 and a second quadrupole lens 158. In some embodiments, the quadrupole lenses are used to control the electron beam. For example, first quadrupole lens 148 can be controlled to adjust the beam current, and second quadrupole lens 158 can be controlled to adjust the beam spot size and beam shape.

[0043]

[0055] 2B shows a charged particle beam device in which the inspection system can use a single primary beam that can be configured to generate secondary electrons by interacting with the wafer 150. As in the embodiment shown in FIG. 2B, the detector 144 can be positioned along the optical axis 105. The primary electron beam can be configured to travel along the optical axis 105. Thus, the detector 144 can include a hole in the center to allow the primary electron beam to pass through and reach the wafer 150.

[0044]

[0056] Reference is now made to Figure 3, which is a schematic diagram of a key performance indicator (KPI) determination system 300 consistent with an embodiment of the present disclosure. The KPI system 300 may include an inspection system 310 and a KPI generator 320. While the inspection system 310 is shown and described for simplicity, it will be appreciated that a metrology system may also be used.

[0045]

[0057] The inspection system 310 and the KPI generator 320 may be electrically coupled to each other (directly or indirectly) either physically (e.g., by a cable) or remotely. The inspection system 310 may be the system described with respect to Figures 1, 2A, and 2B and is used to acquire images of a wafer (see, e.g., sample 208 in Figure 2A and wafer 150 in Figure 2B). In some embodiments, the KPI determination system 300 may be part of the inspection system 310. In some embodiments, the KPI determination system may be part of a controller (e.g., controller 109).

[0046]

[0058] The KPI generator 320 may include one or more processors (e.g., processor 320; for simplicity, this example of processor 320 will be used) and storage 324. The one or more processors may be general-purpose or specific electronic devices capable of manipulating or processing information. For example, the one or more processors may include any number of central processing units (or “CPUs”), graphics processing units (or “GPUs”), optical processors, programmable logic controllers, microcontrollers, microprocessors, digital signal processors, intellectual property (IP) cores, programmable logic arrays (PLAs), programmable array logic (PALs), generic 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. The processor may also be a virtual processor, including one or more processors distributed across multiple machines or devices coupled via a network.

[0047]

[0059] The KPI generator 320 may also include a communication interface 326 for receiving data and transmitting data to the inspection system 310. The processor 322 may be configured to receive one or more raw images of the sample from the inspection system 310. In some embodiments, the inspection system 310 can provide a raw image of the sample to the KPI generator 320, and a processor in the KPI generator 320 can observe the pixel size of the raw image and apply a Fourier transform (e.g., discrete Fourier transform (DFT), fast Fourier transform (FFT), etc.) to the raw image (e.g., images 410 and 420 in Figure 4; images 510, 512, 514, 516, 518 in Figure 5; images 610 and 620 in Figure 6; images 710, 712, 714, 716, 718 in Figure 7; images 810, 812, 814, 816 in Figure 8; images 911 and 912 in Figure 9; images 1011 and 1012 in Figure 10) to convert the raw image into a transformed image (e.g., images 412 and 422 in Figure 4; images 612 and 622 in Figure 6; images 820, 822, 824, 826 in Figure 8).

[0048]

[0060] In some embodiments, converting the raw image to the transformed image can include obtaining different spatial frequencies from the raw image, where the spatial frequencies can be the rates at which features of the raw image change. For example, one spatial frequency can match a feature of the raw image, and another, different spatial frequency can match another feature of the raw image.

[0049]

[0061] In some embodiments, the processor 322 can determine a plurality of coordinates in spatial frequency, each coordinate corresponding to a spatial frequency of the raw image. In some embodiments, each determined coordinate can have three variables: an "x" coordinate that describes the spatial frequency of the image in the "x" direction, a "y" coordinate that describes the spatial frequency of the image in the "y" direction, and a "z" coordinate that describes the gray level value of the corresponding x and y coordinate in the transformed image. In some embodiments, the transformed image can be generated by plotting the coordinates in spatial frequency space.

[0050]

[0062] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the raw image, i.e., a high z coordinate value may correspond to a low spatial frequency value. In some embodiments, the z coordinate may be directly related to the resolution of the raw image, i.e., a high z coordinate value may correspond to a high image resolution of the raw image.

[0051]

[0063] In some embodiments, the processor 322 can determine a subset of coordinates in the spatial frequency space that have the highest z-coordinate values. For example, the subset can include the top 1.5% of coordinates with the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may be used. In some embodiments, the processor 322 can generate a bright spot map image (e.g., graphs 414 and 424 in FIG. 4; graphs 614 and 624 in FIG. 6; graphs 820, 822, 824, 826 in FIG. 8) by plotting the subset of coordinates.

[0052]

[0064] In some embodiments, the processor 322 may apply this function to the transformed image by applying the function to each coordinate of the subset based on the observed pixel size of the raw image and the resolution of the inspection system 310. In some embodiments, the function may be described as shown in Function (1) below.

number

[0053]

[0065] In some embodiments, the processor 322 may determine a KPI for the resolution of the raw image based on the results of the applied functions. In some embodiments, the processor 322 may determine the KPI by determining the sum of the results of the applied functions, as shown in equation (2) below.

number

[0054]

[0066] For example, the processor 322 may determine the KPI by determining the sum of the z coordinate values ​​after a function is applied to the coordinates.

[0055]

[0067] In some embodiments, the processor 332 may use the determined KPIs to adjust the raw image to compensate for the resolution of the raw image. In some embodiments, the processor 322 may adjust the raw image by adjusting astigmatism (e.g., in the "x" direction, the "y" direction) in the inspection system 310 based on the determined KPIs. In some embodiments, the processor 322 may adjust the focus value in the inspection system 310 using the determined KPIs.

[0056]

[0068] Reference is now made to FIG. 4, which is an exemplary image and graph generated by the KPI determination system 300, consistent with an embodiment of the present disclosure.

[0057]

[0069] In some embodiments, images 410 and 420 may be generated in an imaging system (e.g., inspection system 310 of FIG. 3 ), where the pixel size of the imaging system is equal to or less than the resolution of the optical system. In some embodiments, image 410 may have more blur and less sharpness than image 420. In some embodiments, image 410 may have less image resolution than that of image 420.

[0058]

[0070] In some embodiments, images 410 and 420 may be raw images of the sample. In some embodiments, a processor (e.g., processor 322 of FIG. 3 ) may apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to images 410 and 420 to convert images 410 and 420 into transformed images 412 and 422, respectively. For example, the processor may convert image 410 to image 412 by obtaining multiple spatial frequencies of image 410, each spatial frequency characterizing image 410. In some embodiments, each spatial frequency of the multiple spatial frequencies may describe image 410, and the spatial frequency may be the rate at which a feature of image 410 changes. For example, one spatial frequency may match a feature of image 410, and another, different spatial frequency may match another feature of image 410. The processor may convert image 420 to image 422 in a similar manner.

[0059]

[0071] In some embodiments, the processor may determine a plurality of coordinates in spatial frequency space, each coordinate corresponding to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may have three variables: an "x" coordinate describing the spatial frequency of the image in the "x" direction, a "y" coordinate describing the spatial frequency of the image in the "y" direction, and a "z" coordinate describing the gray level value of the corresponding x and y coordinate in the transformed image. In some embodiments, images 412 and 422 may be generated by plotting the coordinates in spatial frequency space.

[0060]

[0072] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the raw image. That is, a higher z coordinate value may correspond to a lower spatial frequency value. In some embodiments, the z coordinate may be directly related to the resolution of the raw image. That is, a higher z coordinate value may correspond to a higher image resolution of the raw image. For example, image 420 may have a higher image resolution than image 410. As can be seen in images 412 and 422, image 422 has a greater number of densely packed "bright" points in the center of the image than image 412, with the bright points corresponding to a higher z coordinate value. In contrast, image 412 shows bright points that are more dispersed than image 422. This may indicate that image 420 has higher information reliability at low spatial frequencies than image 410.

[0061]

[0073] In some embodiments, the processor may determine a subset of coordinates in spatial frequency space that have the highest z-coordinate values. For example, the subset may include the top 1.5% of coordinates with the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may be used. In some embodiments, the processor may generate the bright spot map graph 414 by plotting the subset of coordinates from the image 412. Similarly, the processor may generate the bright spot map graph 424 by plotting the subset of coordinates from the image 422.

[0062]

[0074] In some embodiments, the processor can apply a function to the transformed images 412 and 422 based on the pixel size of the system and the resolution of the optical system by applying the function to each coordinate of the subset (e.g., by applying the function to each coordinate of graphs 414 and 424, respectively). In some embodiments, the function can describe the relationship of the distance of the coordinates in frequency space from the origin coordinate. In this function, "x" is an x-coordinate that describes the spatial frequency of the image in the "x" direction, "y" is a y-coordinate that describes the spatial frequency of the image in the "y" direction, and "z" is a z-coordinate that describes the gray-level value of the corresponding x- and y-coordinate in the transformed image. For example, the processor can generate the weighted bright spot map graph 416 by substituting the coordinates of the subset into the function and plotting the results of the function applied to the coordinates of graph 414. Similarly, the processor can generate the weighted bright spot map graph 426 by substituting the coordinates of the subset into the function and plotting the results of the function applied to the coordinates of graph 424.

[0063]

[0075] In some embodiments, the processor may determine the KPI for the resolution of images 410 and 420 based on the results of the applied functions. In some embodiments, the processor may determine the KPI by determining the sum of the results of the applied functions, as shown in equation (2) above, using a function that describes the relationship of the distance of coordinates in frequency space from the origin coordinate. For example, the processor may determine the KPI for image 410 by determining the sum of the z-coordinate values ​​in graph 416. Similarly, the processor may determine the KPI for image 420 by determining the sum of the z-coordinate values ​​in graph 426.

[0064]

[0076] Reference is now made to FIG. 5, which is an exemplary graph 500 of resolution KPIs generated for various images by the KPI determination system 300 of FIG. 3, consistent with an embodiment of the present disclosure.

[0065]

[0077] Graph 500 shows an axis 501 of image resolution KPI values ​​(e.g., as determined by KPI determination system 300 of FIG. 3 ) and an axis 502 of optical lens focus values. Graph 500 shows raw images 510, 512, 514, 516, and 518 of a sample (e.g., sample 208 of FIG. 2A , wafer 150 of FIG. 2B ). Graph 500 may correspond to KPIs determined using the functions applied to generate graphs 416 and 426 of FIG. 4 . For example, the KPIs of graph 500 may be determined by determining the sum of z-coordinate values ​​calculated from the same functions used to generate graphs 416 and 426 of FIG. 4 .

[0066]

[0078] Graph 500 shows image resolution KPI 520 for image 510, image resolution KPI 522 for image 512, image resolution KPI 524 for image 514, image resolution KPI 526 for image 516, and image resolution KPI 528 for image 518. As shown in graph 500, lower KPI values ​​correspond to higher image resolutions. Graph 500 also illustrates that the method described above with respect to Figures 3 and 4 determines KPIs that are sensitive to image resolution even when the images have higher definition (e.g., as shown in image 518). As shown in graph 500, image 518 may have a higher image resolution than images 510, 512, 514, or 516.

[0067]

[0079] Reference is now made to FIG. 6, which is an exemplary image and graph generated by the KPI determination system 300, consistent with an embodiment of the present disclosure.

[0068]

[0080] In some embodiments, images 610 and 620 may be generated in an imaging system (e.g., inspection system 310 of FIG. 3 ), where the pixel size of the imaging system is equal to or less than the resolution of the optical system. In some embodiments, image 610 may have more blur and less sharpness than image 620. In some embodiments, image 610 may have less image resolution than that of image 620.

[0069]

[0081] In some embodiments, images 610 and 620 may be raw images of the sample. In some embodiments, a processor (e.g., processor 322 of FIG. 3 ) may apply a Fourier transform (such as a discrete Fourier transform (DFT) or a fast Fourier transform (FFT)) to images 610 and 620 to convert images 610 and 620 into transformed images 612 and 622, respectively. For example, the processor may convert image 610 to image 612 by obtaining multiple spatial frequencies of image 610, each spatial frequency characterizing image 610. In some embodiments, each spatial frequency of the multiple spatial frequencies may describe image 610, where the spatial frequency may be the rate at which a feature of image 610 changes. For example, one spatial frequency may match a feature of image 610, and another, different spatial frequency may match another feature of image 610. The processor may convert image 620 to image 622 in a similar manner.

[0070]

[0082] In some embodiments, the processor may determine a plurality of coordinates in spatial frequency space, each coordinate corresponding to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may have three variables: an "x" coordinate describing the spatial frequency of the image in the "x" direction, a "y" coordinate describing the spatial frequency of the image in the "y" direction, and a "z" coordinate describing the gray level value of the corresponding x and y coordinate in the transformed image. In some embodiments, images 612 and 622 may be generated by plotting the coordinates in spatial frequency space.

[0071]

[0083] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the raw image. That is, a higher z coordinate value may correspond to a lower spatial frequency value. In some embodiments, the z coordinate may be directly related to the resolution of the raw image. That is, a higher z coordinate value may correspond to a higher image resolution of the raw image. For example, image 620 may have a higher image resolution than image 610. As can be seen in images 612 and 622, image 622 has a greater number of densely packed "bright" points in the center of the image than image 612, which correspond to a higher z coordinate value. In contrast, image 612 exhibits more dispersed bright points than image 622. Thus, images 612 and 622 demonstrate that image 620 has a lower spatial frequency than image 610 and also has higher image resolution and sharpness than image 610.

[0072]

[0084] In some embodiments, the processor may determine a subset of coordinates having the highest z-coordinate values ​​in the spatial frequency space. For example, the subset may include the top 1.5% of coordinates having the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may be used. In some embodiments, the processor may generate the bright spot map graph 614 by plotting a subset of coordinates from the image 612. Similarly, the processor may generate the bright spot map graph 624 by plotting a subset of coordinates from the image 622.

[0073]

[0085] In some embodiments, the processor can apply a function to the transformed images 612 and 622 based on the pixel size of the system and the resolution of the optical system by applying a function to each coordinate of the subset (e.g., by applying a function to each coordinate of graphs 614 and 624, respectively). In some embodiments, the function represents a two-dimensional quadratic function, where "x" is the x-coordinate that describes the spatial frequency of the image in the "x" direction, "y" is the y-coordinate that describes the spatial frequency of the image in the "y" direction, and "z" is the z-coordinate that describes the gray-level value of the corresponding x- and y-coordinate in the transformed image. The function applied to the transformed images 612 and 622 can be different from the function applied to the transformed images 412 and 422 of FIG. 4. For example, the processor can generate the weighted bright spot map graph 616 by substituting the coordinates of the subset into the function and plotting the results of the function applied to the coordinates of graph 614. Similarly, the processor may generate weighted brightness map graph 626 by substituting the coordinates of the subset into a function and plotting the result of the function applied to the coordinates in graph 624. Images 610 and 612 and graph 614 may be the same as images 410 and 412 and graph 414 of Figure 4, respectively, but graph 616 may differ from graph 416 because a different function is applied. Similarly, images 620 and 622 and graph 624 may be the same as images 420 and 422 and graph 424 of Figure 4, respectively, but graph 626 may differ from graph 426 because a different function is applied.

[0074]

[0086] In some embodiments, the processor may determine the KPI for the resolution of images 610 and 620 based on the results of the applied functions. In some embodiments, the processor may determine the KPI by using a two-dimensional quadratic function to determine the sum of the results of the applied functions, such as shown in equation (2) above. For example, the processor may determine the KPI for image 610 by determining the sum of the z-coordinate values ​​in graph 616. Similarly, the processor may determine the KPI for image 620 by determining the sum of the z-coordinate values ​​in graph 626.

[0075]

[0087] Reference is now made to FIG. 7, which is an exemplary graph 700 of resolution KPIs generated for various images by the KPI determination system 300 of FIG. 3, consistent with an embodiment of the present disclosure.

[0076]

[0088] Graph 700 shows an axis 701 of image resolution KPI values ​​(e.g., as determined by KPI determination system 300 of FIG. 3 ) and an axis 702 of optical lens focus values. Graph 700 shows images 710, 712, 714, 716, and 718 of a sample (e.g., sample 208 of FIG. 2A , wafer 150 of FIG. 2B ). Graph 700 may correspond to KPIs determined using the functions applied to generate graphs 616 and 626 of FIG. 6 . For example, the KPIs of graph 700 may be determined by determining the sum of z-coordinate values ​​calculated from the same functions used to generate graphs 616 and 626 of FIG. 6 .

[0077]

[0089] Graph 700 shows an image resolution KPI 720 for image 710, an image resolution KPI 722 for image 712, an image resolution KPI 724 for image 714, an image resolution KPI 726 for image 716, and an image resolution KPI 728 for image 718. As shown in graph 700, higher KPI values ​​correspond to higher image resolutions. Graph 700 also illustrates that the method described above with respect to Figures 3 and 6 determines KPIs that are sensitive to image resolution even when an image has higher sharpness (e.g., as shown in image 718). As shown in graph 700, image 718 may have a higher image resolution than images 710, 712, 714, or 716.

[0078]

[0090] Reference is now made to FIG. 8, which is an exemplary image and graph generated by the KPI determination system 300, consistent with an embodiment of the present disclosure.

[0079]

[0091] In some embodiments, images 810, 812, 814, and 816 may be generated in an imaging system (e.g., inspection system 310 in FIG. 3), where the pixel size of the imaging system is more than five times larger than the resolution of the optical system. In some embodiments, images 810, 812, 814, and 816 may have increasing image resolution and sharpness and decreasing blur (i.e., image 810 may have the lowest image resolution and sharpness and the most blur, while image 816 may have the highest image resolution and sharpness and the least blur).

[0080]

[0092] In some embodiments, images 810, 812, 814, and 816 may be raw images of the sample. A processor (e.g., processor 322 of FIG. 3 ) may apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to images 810, 812, 814, and 816 to convert images 810, 812, 814, and 816 into transformed images. For example, the processor may transform image 810 by obtaining multiple spatial frequencies of image 810, each of which characterizes image 810. In some embodiments, each of the multiple spatial frequencies may describe image 810, where a spatial frequency may be the rate at which a feature of image 810 changes. For example, one spatial frequency may match a feature of image 810, and another, different spatial frequency may match another feature of image 810. The processor may transform images 812, 814, and 816 in a similar manner.

[0081]

[0093] In some embodiments, the processor may determine a plurality of coordinates in spatial frequency space, each coordinate corresponding to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may have three variables: an "x" coordinate describing the spatial frequency of the image in the "x" direction, a "y" coordinate describing the spatial frequency of the image in the "y" direction, and a "z" coordinate describing the gray level value of the corresponding x and y coordinate in the transformed image. In some embodiments, the transformed image may be generated by plotting the coordinates in the spatial frequency space.

[0082]

[0094] In some embodiments, the processor may determine a subset of coordinates having the highest z-coordinate values ​​in spatial frequency space. For example, the subset may include the top 1.5% of coordinates having the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may be used. In some embodiments, the processor may generate a bright spot map graph 820 by plotting a subset of coordinates from the transformed image of image 810. Similarly, the processor may generate bright spot map graphs 822, 824, and 826 by plotting subsets of coordinates from the transformed images of images 812, 814, and 816, respectively.

[0083]

[0095] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the raw image. That is, a high z coordinate value may correspond to a low spatial frequency value. In some embodiments, the z coordinate may have a periodic relationship with the resolution of the raw image. That is, a low z coordinate value with a periodic distribution may correspond to a high image resolution of the raw image. For example, image 816 may have a higher image resolution than images 810, 812, and 814. As seen in graphs 820, 822, 824, and 826, the "bright" spots in the bright spot map graph may be distributed in a more periodic pattern as the image resolution increases. In contrast, as the image resolution decreases, the bright spot map graph shows more dispersed bright spots. This behavior is a consequence of the pixel size of the imaging system being more than five times larger than the resolution of the optical system.

[0084]

[0096] Reference is now made to FIG. 9, which is an exemplary graph 900 of resolution KPIs generated for various images by the KPI determination system 300 of FIG. 3, consistent with an embodiment of the present disclosure.

[0085]

[0097] Graph 900 shows an axis 901 of normalized image resolution KPI values ​​(e.g., determined by KPI determination system 300 of FIG. 3 ) and an axis 902 of image brightness values. Graph 900 shows raw images 911, 912, and 913 of a sample (e.g., sample 208 of FIG. 2A or wafer 150 of FIG. 2B ). Graph 900 may include a curve 920 corresponding to the normalized KPI of FIG. 5 and a curve 930 corresponding to the normalized KPI of FIG. 7 . As shown by curves 920 and 930, point 921 on curve 920 and point 931 on curve 930 correspond to the normalized KPI of image 911. As shown by curves 920 and 930, point 922 on curve 920 and point 932 on curve 930 correspond to the normalized KPI of image 912. As shown by curves 920 and 930, point 923 on curve 920 and point 933 on curve 930 correspond to normalized KPIs for image 913. Graph 900 may include curves 940-942 that correspond to normalized KPIs for exemplary KPI determination methods.

[0086]

[0098] As shown in graph 900, image 913 may have a higher brightness than image 912, which may have a higher brightness than image 911. Curves 920 and 930 indicate that the KPI determination method described above is advantageously less sensitive (e.g., insensitive) to changes in brightness when compared to the exemplary method illustrated by curves 940-942. In other words, graph 900 may indicate that the image resolution KPI determined by the method described in FIGS. 3-7 is independent of changes in image brightness.

[0087]

[0099] Reference is now made to FIG. 10, which is an exemplary graph 1000 of resolution KPIs generated for various images by the KPI determination system 300 of FIG. 3, consistent with an embodiment of the present disclosure.

[0088]

[0100] Graph 1000 shows axis 1001 of normalized image resolution KPI value (e.g., determined by KPI determination system 300 of FIG. 3 ) and axis 1002 of image contrast. Graph 1000 shows raw images 1011, 1012, and 1013 of a sample (e.g., sample 208 of FIG. 2A or wafer 150 of FIG. 2B ). Graph 1000 may include curve 1020 corresponding to the normalized KPI of FIG. 5 and curve 1030 corresponding to the normalized KPI of FIG. 7 . As shown by curves 1020 and 1030, point 1021 on curve 1020 and point 1031 on curve 1030 correspond to the normalized KPI of image 1011. As shown by curves 1020 and 1030, point 1022 on curve 1020 and point 1032 on curve 1030 correspond to the normalized KPI of image 1012. As shown by curves 1020 and 1030, point 1023 of curve 1020 and point 1033 of curve 1030 correspond to normalized KPIs for image 1013. Graph 1000 may include curve 1040 corresponding to normalized KPIs for an exemplary KPI determination method.

[0089]

[0101] As shown in graph 1000, image 1013 may have higher contrast than image 1012, which may have higher contrast than image 1011. Curves 1020 and 1030 indicate that the KPI determination method described above is advantageously less sensitive (e.g., insensitive) to changes in contrast when compared to the exemplary method illustrated by curve 1040. In other words, graph 1000 may indicate that the image resolution KPI determined by the method described in FIGS. 3-7 is independent of changes in image contrast.

[0090]

[0102] Reference is now made to FIG. 11, which shows exemplary graphs 1110, 1111, 1112 and 1113 of resolution KPIs for various images.

[0091]

[0103] Graphs 1110, 1111, 1112, and 1113 each have an axis 1101 relating to astigmatism in the x-direction and an axis 1102 relating to astigmatism in the y-direction. The slope in each of graphs 1110, 1111, 1112, and 1113 corresponds to a resolution KPI. Graph 1110 may correspond to a resolution KPI based on the actual measured resolution of the image, graph 1111 may correspond to a resolution KPI determined by a typical KPI determination method, graph 1112 may correspond to a resolution KPI determined using the functions applied in FIGS. 4-5, and graph 1113 may correspond to a resolution KPI determined using the functions applied in FIGS. 6-7.

[0092]

[0104] For the same image, graph 1110 can show actual resolution KPI 1110a, graph 1111 can show determined resolution KPI 1111a, graph 1112 can show determined resolution KPI 1112a, and graph 1113 can show determined resolution KPI 1113a. As shown in graphs 1110-1113, the KPI determination methods described in Figures 3-7 are advantageously more accurate than typical KPI determination methods. That is, resolution KPIs 1112a and 1113a are closer to the value of resolution KPI 1110a than resolution KPI 111a.

[0093]

[0105] The hardware for adjusting the astigmatism in the X direction and the hardware for adjusting the astigmatism in the Y direction of the inspection system are orthogonal to each other. Therefore, a robust and reliable KPI determination method should be orthogonal (e.g., the determined KPIs should have a symmetric and circular distribution in the gradient graph). Graphs 1112 and 1113 exhibit a more circular and symmetric gradient than that of graph 1111, which means that the astigmatism in the x and y directions in graphs 1112 and 1113 is more orthogonal than that of graph 1111. Typical KPI determination methods, such as the method used to generate graph 1111, can result in crosstalk during astigmatism correction, even when the image resolution is high. The KPI determination method described in FIGS. 3-7 exhibits higher orthogonality than typical KPI determination methods, and therefore may reduce crosstalk during astigmatism correction. Advantageously, the KPI determination method described in FIGS. 3-7 can adjust astigmatism in one direction without affecting astigmatism in another direction.

[0094]

[0106] Reference is now made to Figure 12, a flowchart illustrating an exemplary process 1200 for characterizing image resolution consistent with embodiments of the present disclosure. The steps of method 1200, for illustrative purposes, may be performed by a system running on a computing device (e.g., controller 109 of Figure 1, KPI determination system 300 of Figure 3, or any component thereof) or using functionality of a computing device (e.g., KPI determination system 300 of Figure 3). It will be understood that the illustrated method 1200 can be modified to modify the order of steps and to include additional steps that may be performed by a system.

[0095]

[0107] In step 1201, an inspection system (e.g., inspection system 310 in FIG. 3) can provide a raw image of a sample to a KPI generator (e.g., KPI generator 320 in FIG. 3), and a processor (e.g., processor 322 in FIG. 3) can observe the pixel size of the raw image and generate a KPI for the raw image (e.g., images 410 and 420 in FIG. 4; images 510, 512, 514, 516, 518 in FIG. 5; images 610 and 620 in FIG. 6; image 710 in FIG. 7). 10, 712, 714, 716, 718; images 810, 812, 814, 816 of FIG. 8; images 911 and 912 of FIG. 9; images 1011 and 1012 of FIG. 10) can be subjected to a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to convert the raw images into transformed images (e.g., images 412 and 422 of FIG. 4; images 612 and 622 of FIG. 6; images 820, 822, 824, 826 of FIG. 8).

[0096]

[0108] In some embodiments, converting the raw image to the transformed image may include obtaining multiple spatial frequencies of the raw image, where each spatial frequency of the multiple spatial frequencies characterizes the raw image. In some embodiments, each spatial frequency of the multiple spatial frequencies may describe the image, where the spatial frequencies may be a rate at which features of the image change. For example, one spatial frequency may match a feature of the image, and another, different spatial frequency may match a different feature of the image.

[0097]

[0109] In some embodiments, the system can determine a plurality of coordinates in spatial frequency space, each coordinate corresponding to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate can have three variables: an "x" coordinate describing the spatial frequency of the image in the "x" direction, a "y" coordinate describing the spatial frequency of the image in the "y" direction, and a "z" coordinate describing the gray level value of the corresponding x and y coordinate in the transformed image. In some embodiments, the transformed image can be generated by plotting the coordinates in the spatial frequency space.

[0098]

[0110] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the raw image, i.e., a high z coordinate value may correspond to a low spatial frequency value. In some embodiments, the z coordinate may be directly related to the resolution of the raw image, i.e., a high z coordinate value may correspond to a high image resolution of the raw image.

[0099]

[0111] In some embodiments, the system can determine a subset of coordinates in spatial frequency space that have the highest z-coordinate values. For example, the subset can include the top 1.5% of coordinates with the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may be used. In some embodiments, the processor 322 can generate a bright spot map graph (e.g., graphs 414 and 424 in FIG. 4; graphs 614 and 624 in FIG. 6; graphs 820, 822, 824, 826 in FIG. 8) by plotting the subset of coordinates.

[0100]

[0112] In step 1203, the system can apply a function to the transformed image based on pixel size by applying the function to each coordinate of the subset. For example, the processor can generate a weighted bright spot map (e.g., graphs 416 and 426 in FIG. 4; graphs 616 and 626 in FIG. 6) by substituting the coordinates of the subset into the function and plotting the results of the applied function.

[0101]

[0113] In step 1205, the system may determine a KPI for the resolution of the raw image based on the results of the applied function. In some embodiments, the system may determine the KPI by determining the sum of the results of the applied function. For example, the system may determine the KPI by determining the sum of the z coordinate values ​​after the function is applied to the coordinates.

[0102]

[0114] In some embodiments, the system may use the determined KPIs to adjust the raw image to compensate for the resolution of the raw image. In some embodiments, the processor 322 may adjust the raw image by adjusting the astigmatism (e.g., in the "x" direction, "y" direction) in the inspection system based on the determined KPIs. In some embodiments, the system may use the determined KPIs to adjust the focus value in the inspection system.

[0103]

[0115] Consistent with embodiments of the present disclosure, 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 ) for controlling other systems (e.g., KPI determination system 300 of FIG. 3 ) or components thereof of an electron beam tool or other system and a server. These instructions may cause one or more processors to perform image resolution characterization, image processing, data processing, beamlet scanning, graphical display, operation of a charged particle beam instrument or another imaging device, etc. In some embodiments, a non-transitory computer-readable medium may be provided that stores instructions that cause a processor to perform the steps of process 1200. 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 media, compact disk read-only memory (CD-ROM), any other optical data storage media, any physical media with a pattern of holes, random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), flash EPROM or any other flash memory, non-volatile random access memory (NVRAM), cache, registers, any other memory chip or cartridge, and network-connected versions thereof.

[0104]

[0116] The embodiments can be further described using the following clauses. 1. A method for characterizing optical resolution, comprising: Providing a raw image of the sample; Observing the pixel size of the raw image; Transforming the raw image into a transformed image by applying a Fourier transform to the raw image; applying a function to the transformed image based on pixel size; determining a key performance indicator of raw image resolution based on the results of the applied function; A method comprising: 2. Converting raw images to transformed images is acquiring a plurality of spatial frequencies of a raw image, each spatial frequency of the plurality of spatial frequencies characterizing the raw image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 2. The method according to clause 1, comprising: 3. The method of clause 2, further comprising determining a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates. 4. The method of clause 3, wherein applying a function to the transformed image includes applying a function to each coordinate of the subset. 5. The method of clause 4, wherein determining the key performance indicator of resolution of the raw image includes determining a sum of results of the applied functions. 6. The method of any one of clauses 3 to 5, wherein the value of each coordinate of the subset comprises a grayscale value. 7. The method of any one of clauses 3 to 6, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 8. The method of any one of clauses 3 to 7, wherein the value of the subset is directly related to the resolution of the raw image. 9. The method of any one of clauses 1 to 8, wherein the key performance indicator of resolution does not depend on raw image brightness or raw image contrast. 10. The method of any one of clauses 1 to 9, further comprising adjusting the raw image using a key performance indicator of resolution to compensate for resolution. 11. The method of clause 10, wherein adjusting the raw image includes adjusting for astigmatism in the imaging system. 12. A system for characterizing optical resolution, comprising: Executing instructions to cause the system to: Providing a raw image of the sample; Observing the pixel size of the raw image; Transforming the raw image into a transformed image by applying a Fourier transform to the raw image; applying a function to the transformed image based on pixel size; determining a key performance indicator of raw image resolution based on the results of the applied function; 1. A system comprising one or more processors configured to: 13. Converting a raw image to a transformed image is acquiring a plurality of spatial frequencies of a raw image, each spatial frequency of the plurality of spatial frequencies characterizing the raw image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 13. The system of claim 12, comprising: 14. The system of clause 13, wherein the one or more processors are configured to execute instructions to further cause the system to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates. 15. The system of clause 14, wherein applying a function to the transformed image includes applying a function to each coordinate of the subset. 16. The system of clause 15, wherein determining the key performance indicator of resolution of the raw image includes determining a sum of results of the applied functions. 17. A system described in any one of clauses 14 to 16, wherein the value of each coordinate of the subset comprises a grayscale value. 18. A system according to any one of clauses 14 to 17, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 19. A system according to any one of clauses 14 to 18, wherein the value of the subset is directly related to the resolution of the raw image. 20. A system according to any one of clauses 12 to 19, wherein the key performance indicator of resolution does not depend on raw image brightness or raw image contrast. 21. The system of any one of clauses 12 to 20, wherein the one or more processors are configured to execute instructions to cause the system to further adjust the original image using the resolution key performance indicator to compensate for the resolution. 22. The system of clause 21, wherein adjusting the original image includes adjusting for astigmatism in the imaging system. 23. A non-transitory computer-readable medium containing a set of instructions executable by one or more processors of a device, the instructions causing the device to: Providing a raw image of the sample; Observing the pixel size of the raw image; Transforming the raw image into a transformed image by applying a Fourier transform to the raw image; applying a function to the transformed image based on pixel size; determining a key performance indicator of raw image resolution based on the results of the applied function; A non-transitory computer-readable medium for causing a method to be performed, the method comprising: 24. Converting a raw image into a transformed image is acquiring a plurality of spatial frequencies of a raw image, each spatial frequency of the plurality of spatial frequencies characterizing the raw image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 23. A non-transitory computer-readable medium as set forth in clause 23, comprising: 25. The non-transitory computer-readable medium of clause 24, wherein the set of instructions executable by one or more processors of the device further causes the device to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates. 26. The non-transitory computer-readable medium of clause 25, wherein applying a function to the transformed image includes applying the function to each coordinate of the subset. 27. The non-transitory computer-readable medium of clause 26, wherein determining a key performance indicator of resolution of the raw image includes determining a sum of results of the applied functions. 28. The non-transitory computer-readable medium of any one of clauses 25 to 27, wherein the value of each coordinate of the subset comprises a grayscale value. 29. The non-transitory computer-readable medium of any one of clauses 25 to 28, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 30. The non-transitory computer-readable medium of any one of clauses 25 to 29, wherein the value of the subset is directly related to the resolution of the raw image. 31. The non-transitory computer-readable medium of any one of clauses 23 to 30, wherein the key performance indicator of resolution does not depend on raw image brightness or raw image contrast. 32. A non-transitory computer-readable medium described in any one of clauses 23 to 31, wherein a set of instructions executable by one or more processors of the device further causes the device to adjust the raw image using a key performance indicator of resolution to compensate for the resolution. 33. The non-transitory computer-readable medium of clause 10, wherein adjusting the raw image includes adjusting for astigmatism in the imaging system. 34. Provide sample images; Observing the pixel size of the image; Transforming the image into a transformed image; applying a function to the transformed image based on pixel size; determining a key performance indicator of image resolution by applying a function to the transformed image; A method comprising: 35. Converting an image to an image acquiring a plurality of spatial frequencies of an image, each spatial frequency of the plurality of spatial frequencies characterizing the image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 35. The method of claim 34, comprising: 36. The method of clause 35, further comprising determining a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in the highest percentile of the plurality of coordinates. 37. The method of clause 36, wherein applying a function to the transformed image includes applying the function to each coordinate of the subset. 38. The method of clause 37, wherein determining the key performance indicator of image resolution includes determining a sum of results of the applied functions. 39. The method of any one of clauses 36 to 38, wherein the value of each coordinate of the subset comprises a grayscale value. 40. The method of any one of clauses 36 to 39, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 41. The method of any one of clauses 36 to 40, wherein the value of the subset is directly related to the resolution of the image. 42. The method of any one of clauses 34 to 41, wherein the key performance indicator of resolution does not depend on image brightness or image contrast. 43. The method of any one of clauses 34 to 42, further comprising adjusting the image to compensate for resolution using a key performance indicator of resolution. 44. The method of clause 43, wherein adjusting the image includes adjusting for astigmatism in the imaging system. 45. Execute the command to the system. Providing sample images, Observing the pixel size of the image; Transforming the image into a transformed image; applying a function to the transformed image based on pixel size; determining a key performance indicator of image resolution by applying a function to the transformed image; 1. A system comprising one or more processors configured to: 46. ​​Converting an image to an image acquiring a plurality of spatial frequencies of an image, each spatial frequency of the plurality of spatial frequencies characterizing the image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 46. ​​The system of claim 45, comprising: 47. The system of clause 46, wherein the one or more processors are configured to execute instructions to further cause the system to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates. 48. The system of clause 47, wherein applying a function to the transformed image includes applying the function to each coordinate of the subset. 49. The system of clause 48, wherein determining the key performance indicator of image resolution includes determining a sum of results of the applied functions. 50. A system described in any one of clauses 47 to 49, wherein the value of each coordinate of the subset comprises a grayscale value. 51. A system according to any one of clauses 47 to 50, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 52. A system according to any one of clauses 47 to 51, wherein the value of the subset is directly related to the resolution of the image. 53. A system according to any one of clauses 45 to 52, wherein the key performance indicator of resolution is independent of image brightness or image contrast. 54. The system of any one of clauses 45 to 53, wherein the one or more processors are configured to execute instructions to cause the system to further adjust the image using the resolution key performance indicator to compensate for the resolution. 55. The system of clause 54, wherein adjusting the image includes adjusting for astigmatism in the imaging system. 56. A non-transitory computer-readable medium containing a set of instructions executable by one or more processors of a device, the instructions causing the device to: Providing sample images, Observing the pixel size of the image; Transforming the image into a transformed image; applying a function to the transformed image based on pixel size; determining a key performance indicator of image resolution by applying a function to the transformed image; A non-transitory computer-readable medium for causing a method to be performed, the method comprising: 57. Converting an image into a converted image acquiring a plurality of spatial frequencies of an image, each spatial frequency of the plurality of spatial frequencies characterizing the image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 56. A non-transitory computer-readable medium according to claim 56, comprising: 58. The non-transitory computer-readable medium of clause 57, wherein the set of instructions executable by one or more processors of the device further causes the device to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates. 59. The non-transitory computer-readable medium of clause 58, wherein applying a function to the transformed image includes applying the function to each coordinate of the subset. 60. The non-transitory computer-readable medium of clause 59, wherein determining a key performance indicator of image resolution includes determining a sum of results of the applied functions. 61. The non-transitory computer-readable medium of any one of clauses 58 to 60, wherein the value of each coordinate of the subset comprises a grayscale value. 62. The non-transitory computer-readable medium of any one of clauses 58-61, wherein the values ​​of the subset are indirectly related to a plurality of spatial frequencies. 63. The non-transitory computer-readable medium of any one of clauses 58 to 62, wherein the value of the subset is directly related to the resolution of the image. 64. The non-transitory computer-readable medium of any one of clauses 56 to 63, wherein the key performance indicator of resolution is independent of image brightness or image contrast. 65. A non-transitory computer-readable medium according to any one of clauses 56 to 64, wherein a set of instructions executable by one or more processors of the device further causes the device to adjust the image using a key performance indicator of resolution to compensate for resolution. 66. The non-transitory computer-readable medium of clause 65, wherein adjusting the image includes adjusting for astigmatism in the imaging system.

[0105]

[0117] It will be understood that the embodiments of the present disclosure are not limited to the precise structures described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims

1. 1. A system for characterizing optical resolution, comprising: Executing instructions to cause the system to: Providing a raw image of the sample; Observing the pixel size of the raw image; Transforming the raw image into a transformed image by applying a Fourier transform to the raw image; applying a function to the transformed image based on the pixel size; determining a key performance indicator of resolution of the raw image based on the results of the applied function; and 1. A system comprising one or more processors configured to:

2. Transforming the raw image into the transformed image includes: acquiring a plurality of spatial frequencies of the raw image, each spatial frequency of the plurality of spatial frequencies characterizing the raw image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; The system of claim 1 , comprising:

3. 3. The system of claim 2, wherein the one or more processors are configured to execute instructions that further cause the system to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates.

4. The system of claim 3 , wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

5. The system of claim 4 , wherein determining the key performance indicator of the resolution of the raw image comprises determining a sum of the results of the applied functions.

6. The system of claim 3 , wherein the value of each coordinate of the subset comprises a grayscale value.

7. The system of claim 3 , wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

8. The system of claim 3 , wherein the values ​​of the subset are directly related to the resolution of the raw image.

9. The system of claim 1 , wherein the key performance indicator of the resolution is independent of the brightness of the raw image or the contrast of the raw image.

10. 2. The system of claim 1, wherein the one or more processors are configured to execute instructions that further cause the system to adjust the raw image using the key performance indicator of the resolution to compensate for the resolution.

11. The system of claim 10 , wherein adjusting the raw image comprises adjusting for astigmatism in an imaging system.

12. 1. A non-transitory computer-readable medium comprising a set of instructions executable by one or more processors of a device, the instructions causing the device to: Providing a raw image of the sample; Observing the pixel size of the raw image; Transforming the raw image into a transformed image by applying a Fourier transform to the raw image; applying a function to the transformed image based on the pixel size; determining a key performance indicator of resolution of the raw image based on the results of the applied function; and A non-transitory computer-readable medium for causing a method to be performed, the method comprising:

13. Transforming the raw image into the transformed image includes: acquiring a plurality of spatial frequencies of the raw image, each spatial frequency of the plurality of spatial frequencies characterizing the raw image; determining a plurality of coordinates in a spatial frequency space, each coordinate of the plurality of coordinates corresponding to a spatial frequency of the plurality of spatial frequencies; 13. The non-transitory computer-readable medium of claim 12, comprising:

14. 14. The non-transitory computer-readable medium of claim 13, wherein the set of instructions executable by one or more processors of the device further causes the device to determine a subset of the plurality of coordinates, each coordinate of the subset comprising a value that is in a top percentile of the plurality of coordinates.

15. The non-transitory computer-readable medium of claim 14 , wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

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