System and method for image resolution characterization

Abstract

Systems, apparatus, and methods include providing an original image of a sample; observing the pixel size of the original image; converting the original image into a transformed image by applying a Fourier transform to the original image; applying a function to the transformed image based on the pixel size; and determining a key performance indicator of the resolution of the original image based on a result of the applied function.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 63 / 409,049, filed on September 22, 2022, which is incorporated herein by reference in its entirety. Technical Field

[0003] The description herein relates to the field of inspection and metrology systems, and more particularly to systems for image resolution characterization. Background Art

[0004] In the manufacturing process of integrated circuits (ICs), unfinished or completed circuit components are inspected to ensure that they are manufactured according to the design and are free of defects. Inspection systems that utilize optical microscopes typically have a resolution as low as a few hundred nanometers; and the resolution is limited by the wavelength of light. As the physical size of IC components continues to decrease to below 100 nanometers or even below 10 nanometers, there is a need for inspection systems that are capable of higher resolution than inspection systems that utilize optical microscopes.

[0005] Charged particle (e.g., electron) beam microscopes, such as scanning electron microscopes (SEMs) or transmission electron microscopes (TEMs), are capable of reducing resolution to less than 1 nanometer, serving as practical tools for inspecting IC components having feature sizes of less than 100 nanometers. Using an SEM, electrons from a single primary electron beam or electrons from multiple primary electron beams can be focused on locations of interest on an inspected wafer. The primary electrons interact with the wafer and may be backscattered, or may cause the wafer to emit secondary electrons. The intensity of the electron beam, including the backscattered electrons and the secondary electrons, may vary based on the properties of the internal and external structures of the wafer, and thus may indicate whether the wafer has defects. Summary of the invention

[0006] Embodiments of the present disclosure provide apparatus, systems and methods for characterizing image resolution. In some embodiments, the systems and methods may include: providing an original image of a sample; observing the pixel size of the original image; converting the original image into a transformed image by applying a Fourier transform to the original image; applying a function to the transformed image based on the pixel size; and determining a key performance indicator of the resolution of the original image based on the result of the applied function.

[0007] In some embodiments, systems and methods may include: providing an image of a sample; observing the pixel dimensions of the image; converting the original image into a transformed image; applying a function to the transformed image based on the pixel dimensions; and determining a key performance indicator of the resolution of the image by applying the function to the transformed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 is a schematic diagram illustrating an exemplary electron beam inspection (EBI) system consistent with embodiments of the present disclosure.

[0009] Figure 2A is a schematic diagram showing an exemplary multi-beam system consistent with an embodiment of the present disclosure, the exemplary multi-beam system is Figure 1 Portions of an exemplary charged particle beam inspection system.

[0010] Figure 2B is a schematic diagram showing an exemplary single beam system consistent with an embodiment of the present disclosure, the exemplary single beam system is Figure 1 Portions of an exemplary charged particle beam inspection system.

[0011] Figure 3 is a schematic diagram of an exemplary key performance indicator (KPI) determination system consistent with embodiments of the present disclosure.

[0012] Figure 4 Exemplary images and graphs generated by a KPI determination system consistent with embodiments of the present disclosure are shown.

[0013] Figure 5 is an exemplary graph of a resolution KPI consistent with embodiments of the present disclosure.

[0014] Figure 6 Exemplary images and charts generated by a KPI determination system consistent with embodiments of the present disclosure are shown.

[0015] Figure 7 is an exemplary graph of a resolution KPI consistent with embodiments of the present disclosure.

[0016] Figure 8 Exemplary images and charts generated by a KPI determination system consistent with embodiments of the present disclosure are shown.

[0017] Fig. 9 is an exemplary graph of a resolution KPI consistent with embodiments of the present disclosure.

[0018] Fig.10 is an exemplary graph of a resolution KPI consistent with embodiments of the present disclosure.

[0019] Fig.11 An exemplary graph of a resolution KPI consistent with some embodiments of the present disclosure is shown.

[0020] Fig.12 is a flow chart illustrating an exemplary process for image resolution characterization consistent with embodiments of the present disclosure. DETAILED DESCRIPTION

[0021] Reference will now be made in detail to exemplary embodiments, examples of which are shown in the accompanying drawings. The following description refers to the accompanying drawings, in which, unless otherwise indicated, the same reference numerals in different figures represent the same or similar elements. The implementations set forth in the following description of exemplary embodiments do not represent all implementations consistent with the present disclosure. Instead, they are merely examples of apparatus and methods consistent with aspects related to the subject matter described in the appended claims. For example, although some embodiments are described in the context of utilizing electron beams, the present disclosure is not limited thereto. Other types of charged particle beams may also be similarly applied. In addition, other imaging systems may be used, such as optical imaging, photoelectric detection, x-ray detection, extreme ultraviolet inspection, deep ultraviolet inspection, etc., where they generate images of corresponding types.

[0022] Electronic devices are made up of circuits formed on a silicon wafer called a substrate. Many circuits can be formed together on the same silicon wafer and are called an integrated circuit or IC. The size of these circuits has been greatly reduced so that more circuits can be accommodated on a substrate. For example, the IC chip in a smartphone can be as small as a thumbnail, but may include more than 2 billion transistors, each less than 1 / 1000 the size of a human hair.

[0023] Manufacturing these extremely small ICs is a complex, time-consuming and expensive process that typically involves hundreds of individual steps. An error in even one step can cause a defect in the finished IC, rendering it useless. Therefore, one goal of the manufacturing process is to avoid such defects in order to maximize the number of functional ICs manufactured in the process, i.e., to increase the overall yield of the process.

[0024] One element of improving yield is monitoring the chip manufacturing process to ensure that a sufficient number of functional ICs are produced. One way to monitor the process is to inspect the chip circuit structures at various stages of their formation. Inspection can be performed using a scanning electron microscope (SEM). The SEM can be used to image these extremely small structures, in effect taking a "photograph" of the structures of the wafer. The image can be used to determine whether the structure was formed correctly and whether the structure was formed in the correct location. If the structure is defective, the process can be adjusted so the defect is less likely to occur again. Defects can be generated during various stages of semiconductor processing. For the reasons stated above, it is very important to detect defects as early as possible, accurately and efficiently.

[0025] The working principle of SEM is similar to that of a camera. A camera takes pictures by receiving and recording the brightness and color of light reflected or emitted from a person or object. SEM takes "pictures" by receiving and recording the energy or number of electrons reflected or emitted from a structure. Before taking such a "picture", an electron beam can be provided to the structure, and when the electrons are reflected or emitted ("emitted") from the structure, the detector of the SEM can receive and record the energy or number of those electrons to generate an image. In order to take such "pictures", some SEMs use a single electron beam (referred to as "single-beam SEMs"), while some SEMs use multiple electron beams (referred to as "multi-beam SEMs") to take multiple "pictures" of the wafer. By using multiple electron beams, the SEM can provide more electron beams to the structure to obtain these multiple "pictures", thereby causing more electrons to be ejected from the structure. Therefore, the detector can receive more ejected electrons at the same time and generate images of the structure of the wafer with higher efficiency and faster speed.

[0026] The system may generate images with image resolution that needs to be adjusted (e.g., measurement of the smallest structure that can be captured in the image, size of the focused electron beam, etc.). For example, the system may use key performance indicators to determine if the resolution of the image is too low and whether the image needs to be adjusted to compensate for the resolution.

[0027] However, typical inspection and metrology systems are limited. Typical inspection and metrology systems may use key performance indicators that are sensitive to the brightness or contrast of an image, but not to the resolution of the image. Typical key performance indicators lack sensitivity to the resolution of an image, especially when the image is relatively clear (e.g., when the image has details with sharp boundaries).

[0028] Some of the disclosed embodiments provide systems and methods that address some or all of these disadvantages by determining and using key performance indicators that are sensitive to image resolution to compensate for image resolution. The disclosed embodiments may include: observing the pixel size of an original image; applying a Fourier transform to the original image to convert the original image into a transformed image; applying a function to the transformed image based on the pixel size; and determining a key performance indicator of the resolution of the original image based on the result of the applied function, thereby improving the robustness and reliability of the image resolution characterization.

[0029] For the sake of clarity, the relative sizes of components in the figures may be exaggerated.In the following description of the figures, the same or similar reference numerals refer to the same or similar components or entities, and only the differences with respect to individual embodiments are described.

[0030] As used herein, unless expressly stated otherwise, the term "or" encompasses all possible combinations unless not feasible. For example, if it is stated that a component can include A or B, then, unless expressly stated otherwise or not feasible, the component can include A, or B, or A and B. As a second example, if it is stated that a component can include A, B, or C, then, unless expressly stated otherwise or not feasible, the component can include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0031] Without limiting the scope of the present disclosure, some embodiments may be described in the context of providing detectors and detection methods in systems utilizing electron beams. However, the present disclosure is not limited thereto. Other types of charged particle beams may be similarly applied. In addition, 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.

[0032] Figure 1 An exemplary electron beam inspection (EBI) system 100 consistent with embodiments of the present disclosure is shown. The EBI system 100 can be used for imaging. Figure 1 As shown, 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 located in the main chamber 101. The EFEM 106 includes a first load port 106a and a second load port 106b. The EFEM 106 may include additional load ports. The first load port 106a and the second load port 106b receive a wafer front opening transport box (FOUP) containing a wafer (e.g., a semiconductor wafer or a wafer made of (multiple) other materials) or a sample to be inspected (wafers and samples can be used interchangeably). A "batch" is a plurality of wafers that can be loaded as a batch for processing.

[0033] One or more robots (not shown) in the EFEM 106 can transfer the wafer to the load / lock chamber 102. The load / lock chamber 102 is connected to a load / lock vacuum pump system (not shown), which removes gas molecules in the load / lock chamber 102 to reach a first pressure below atmospheric pressure. After reaching the first pressure, one or more robots (not shown) can transfer the wafer from the load / lock chamber 102 to the main chamber 101. The main chamber 101 is connected to a main chamber vacuum pump system (not shown), which removes gas molecules in the main chamber 101 to reach a second pressure below the first pressure. After reaching the second pressure, the wafer will be subjected to inspection by the electron beam tool 104. The electron beam tool 104 can be a single beam system or a multi-beam system.

[0034] The controller 109 is electrically connected to the electron beam tool 104. The controller 109 may be a computer configured to perform various controls of the EBI system 100. Figure 1 The controller 109 is shown in FIG. 1 as being external to the structure including the main chamber 101 , the load / lock chamber 102 , and the EFEM 106 , but it will be appreciated that the controller 109 may be part of the structure.

[0035] In some implementations, the controller 109 may include one or more processors (not shown). The processor may be a general or specific electronic device capable of manipulating or processing information. For example, the 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), general 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 circuit capable of data processing. The processor may also be a virtual processor comprising one or more processors distributed across multiple machines or devices coupled via a network.

[0036] In some embodiments, the controller 109 may also include one or more memories (not shown). The memory may be a general or specific electronic device capable of storing code and data accessible by a processor (e.g., via a bus). For example, the memory may include any number of random access memories (RAM), read-only memories (ROM), optical disks, magnetic disks, hard drives, solid-state drives, flash drives, secure digital (SD) cards, memory sticks, compact flash (CF) cards, or any combination of any type of storage device. The code may include an operating system (OS) and one or more applications (or "apps") for a specific task. The memory may also be a virtual memory, which includes one or more memories distributed across multiple machines or devices coupled via a network.

[0037] 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") may be designed to optimize throughput for different scanning modes. Embodiments of the present disclosure provide a multi-beam system having the ability to optimize throughput for different scanning modes by using beam arrays with different geometries and accommodating different throughput and resolution requirements.

[0038] Reference now Figure 2A, which is a schematic diagram illustrating an exemplary electron beam tool 104 consistent with an embodiment of the present disclosure, the electron beam tool 104 includes a multi-beam inspection tool, the multi-beam inspection tool is Figure 1 In some embodiments, the electron beam tool 104 may be used as a Figure 1 The single beam inspection tool of the portion of the EBI system 100 is operated. The multi-beam electron beam tool 104 (also referred to herein as the device 104) includes an electron source 201, a Coulomb aperture plate (or "gun aperture plate") 271, a converging lens 210, a source conversion unit 220, a primary projection system 230, a motorized stage 209, and a sample holder 207, the sample holder 207 being supported by the motorized stage 209 to hold a sample 208 to be inspected (e.g., a wafer or a photomask). The multi-beam electron beam tool 104 may also include a secondary projection system 250 and an electronic detection device 240. The primary projection system 230 may include an objective lens 231. The electronic detection device 240 may include a plurality of detection elements 241, 242, and 243. The beam splitter 233 and the deflection scanning unit 232 may be located within the primary projection system 230.

[0039] The electron source 201, the Coulomb aperture plate 271, the converging lens 210, the source conversion unit 220, the beam splitter 233, the deflection scanning unit 232, and the primary projection system 230 may be aligned with the primary optical axis 204 of the apparatus 104. The secondary projection system 250 and the electron detection device 240 may be aligned with the secondary optical axis 251 of the apparatus 104.

[0040] The electron source 201 may include a cathode (not shown) and an extractor or an anode (not shown), wherein during operation, the electron source 201 is configured to emit primary electrons from the cathode, and the primary electrons are extracted or accelerated by the extractor and / or the anode to form a primary electron beam 202, which forms a primary beam cross (virtual or real) 203. The primary electron beam 202 can be visualized as being emitted from the primary beam cross 203.

[0041] 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-bent micro-deflector array (not shown). In some embodiments, the pre-bent micro-deflector array deflects multiple primary sub-beams 211, 212, 213 of the primary electron beam 202 to vertically enter the beam limiting aperture array, the image forming element array, and the aberration compensator array. In some embodiments, the device 104 can be operated as a single beam system so that a single primary sub-beam is generated. In some embodiments, the converging lens 210 is designed to focus the primary electron beam 202 into a parallel beam and is vertically incident on the source conversion unit 220. The image forming element array may include a plurality of micro-deflectors or micro-lenses to affect the multiple primary sub-beams 211, 212, 213 of the primary electron beam 202 and form multiple parallel images (virtual or real) of the primary beam cross 203, each of the primary sub-beams 211, 212, and 213 having one parallel image. 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 to compensate for the field curvature aberration of the primary beamlets 211, 212, and 213. The astigmatism compensator array may include a plurality of micro stigmatizers to compensate for the astigmatism aberration of the primary beamlets 211, 212, and 213. The beam limiting aperture array may be configured to limit the diameter of the individual primary beamlets 211, 212, and 213. Figure 2A Three primary sub-beams 211, 212, and 213 are shown as an example, and it should be understood that the source conversion unit 220 can be configured to form any number of primary sub-beams. The controller 109 can be connected to Figure 1 The controller 109 may be used to control various parts of the EBI system 100, 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, as explained in further detail below, the controller 109 may perform various image and signal processing functions. The controller 109 may also generate various control signals to control the operation of the charged particle beam inspection system.

[0042] The converging lens 210 is configured to focus the primary electron beam 202. The converging lens 210 may also be configured to adjust the current of the primary sub-beams 211, 212, and 213 downstream of the source conversion unit 220 by changing the focusing power of the converging lens 210. Alternatively, the current may be changed by changing the radial size of the beam limiting aperture within the beam limiting aperture array corresponding to the individual primary sub-beams. The current may be changed by changing both the radial size of the beam limiting aperture and the focusing power of the converging lens 210. The converging lens 210 may be an adjustable converging lens that may be configured such that the position of its first principal plane is movable. The adjustable converging lens may be configured to be magnetic, which may cause the off-axis beam waves 212 and 213 to illuminate the source conversion unit 220 at a rotation angle. The rotation angle varies with the focusing power of the adjustable converging lens or the position of the first principal plane. The converging lens 210 may be an anti-rotation converging lens that may be configured to maintain a rotation angle while the focusing power of the converging lens 210 is changed. In some embodiments, the converging lens 210 may be an adjustable anti-rotation converging lens in which the rotation angle does not change when its focusing power and the position of its first principal plane are changed.

[0043] The objective lens 231 can be configured to focus the beams 211, 212, and 213 onto the sample 208 for inspection, and in the current embodiment, three detection points 221, 222, and 223 can be formed on the surface of the sample 208. The Coulomb aperture plate 271 is configured to block peripheral electrons of the primary electron beam 202 in operation to reduce the Coulomb effect. The Coulomb effect can expand the size of each of the detection points 221, 222, and 223 of the primary sub-beams 211, 212, 213, and thus reduce the inspection resolution.

[0044] The beam splitter 233 may be, for example, a Wien filter including an electrostatic deflector ( Figure 2A 213). In operation, the beam splitter 233 can be configured to exert an electrostatic force on individual electrons of the primary sub-beams 211, 212, and 213 via an electrostatic dipole field. The electrostatic force is equal in magnitude to the magnetic force exerted on the individual electrons by the magnetic dipole field of the beam splitter 233, but opposite in direction. Thus, the primary sub-beams 211, 212, and 213 can pass at least substantially straight through the beam splitter 233 at a deflection angle that is at least substantially zero.

[0045] The deflection scanning unit 232 is configured in operation to deflect the primary beamlets 211, 212 and 213 to scan the detection points 221, 222 and 223 across the individual scanning areas in the portion of the surface of the sample 208. In response to the primary beamlets 211, 212 and 213 or the detection points 221, 222 and 223 being incident on the sample 208, electrons emerge from the sample 208 and generate 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 ≤ 50 eV) and backscattered electrons (having an electron energy between 50 eV and the landing energy of the primary beamlets 211, 212 and 213). The beam splitter 233 is configured to deflect the secondary electron beams 261, 262 and 263 toward the secondary projection system 250. The secondary projection system 250 then focuses the secondary electron beams 261, 262 and 263 onto the detection elements 241, 242 and 243 of the electron detection device 240. The detection elements 241, 242 and 243 are arranged to detect the corresponding secondary electron beams 261, 262 and 263 and generate corresponding signals, which are sent to the controller 109 or a signal processing system (not shown), for example, to construct an image of the corresponding scan area of ​​the sample 208.

[0046] In some embodiments, the detection elements 241, 242, and 243 detect the 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 detection element 241, 242, and 243 may include one or more pixels. The intensity signal output of a detection element may be the sum of the signals generated by all pixels within the detection element.

[0047] In some embodiments, the controller 109 may include an image processing system, which includes an image acquisition device (not shown), a memory (not shown). The image acquisition device may include one or more processors. For example, the image acquisition device may include a computer, a server, a mainframe, a terminal, a personal computer, any type of mobile computing device, etc., or a combination thereof. The image acquisition device may be communicatively coupled to the electronic detection device 240 of the device 104 through a medium (such as an electrical conductor, an optical fiber cable, a portable storage medium, IR, Bluetooth, the Internet, a wireless network, a radio, etc., or a combination thereof). In some embodiments, the image acquisition device may receive a signal from the electronic detection device 240 and may construct an image. Thus, the image acquisition device may acquire an image of the sample 208. The image acquisition device may also perform various post-processing functions, such as generating a contour, superimposing an indicator on the acquired image, etc. The image acquisition device may be configured to perform adjustments to the brightness and contrast of the acquired image, etc. In some embodiments, the memory may be a storage medium, such as a hard disk, a flash drive, a cloud storage device, a random access memory (RAM), other types of computer-readable memory, etc. The memory may be coupled to the image acquirer and may be used to save the scanned raw image data as a raw image, and a processed image.

[0048] In some embodiments, the image acquirer can acquire one or more images of the sample based on the imaging signal received from the electronic detection device 240. The imaging signal can correspond to a scanning operation for performing charged particle imaging. The acquired image can be a single image including multiple imaging areas. The single image can be stored in a memory. The single image can be an original image that can be divided into multiple areas. Each of the areas can include an imaging area containing features of the sample 208. The acquired image can include multiple images of a single imaging area of ​​the sample 208 sampled multiple times in a time series. Multiple images can be stored in a memory. In some embodiments, the controller 109 can be configured to perform an image processing step using multiple images of the same position of the sample 208.

[0049] In some embodiments, the controller 109 may include a measurement circuit system (e.g., an analog-to-digital converter) to obtain the distribution of the detected secondary electrons. The electron distribution data collected during the detection time window is combined with the corresponding scan path data of each of the primary beamlets 211, 212, and 213 incident on the wafer surface, and can be used to reconstruct an image of the inspected wafer structure. The reconstructed image can be used to reveal various features of the internal or external structure of the sample 208, and therefore can be used to reveal any defects that may be present in the wafer.

[0050] In some embodiments, the controller 109 may control the motorized stage 209 to move the sample 208 during the inspection of the sample 208. In some embodiments, the controller 109 may enable the motorized stage 209 to continuously move the sample 208 in one direction at a constant speed. In other embodiments, the controller 109 may enable the motorized stage 209 to change the speed of movement of the sample 208 over time depending on the steps of the scanning process.

[0051] although Figure 2A The apparatus 104 is shown using three primary electron beams, but it should be understood that the apparatus 104 can use one, two, or more primary electron beams. The present disclosure does not limit the number of primary electron beams used in the apparatus 104. In some embodiments, the apparatus 104 can be a SEM used for lithography. In some embodiments, the electron beam tool 104 can be a single beam system or a multi-beam system.

[0052] For example, Figure 2B As shown, the electron beam tool 100B (also referred to herein as the apparatus 100B) can be a single beam inspection tool used in the EBI system 10 consistent with embodiments of the present disclosure. The apparatus 100B includes a wafer holder 136 supported by a motorized stage 134 to hold a wafer 150 to be inspected. The electron beam tool 100B includes an electron emitter, which may include a cathode 103, an anode 121, and a gun hole 122. The electron beam tool 100B also includes a beam limiting aperture 125, a converging lens 126, a column aperture 135, an objective lens assembly 132, and a detector 144. In some embodiments, the objective lens assembly 132 can be a modified SORIL lens, which includes a pole piece 132a, a control electrode 132b, a deflector 132c, and an excitation coil 132d. In the imaging process, the electron beam 161 emitted from the tip of the cathode 103 can be accelerated by the anode 121 voltage, pass through the gun hole 122, the beam limiting hole 125, the focusing lens 126, and focused by the improved SORIL lens into the detection point 170, and hit the surface of the wafer 150. The detection point 170 can be scanned by a deflector (such as the deflector 132c or other deflectors in the SORIL lens) across the surface of the wafer 150. Secondary or scattered primary particles (such as secondary electrons or scattered primary electrons) emitted from the wafer surface can be collected by the detector 144 to determine the intensity of the beam so that an image of the region of interest on the wafer 150 can be reconstructed.

[0053] An image processing system 199 may also be provided, which includes an image acquisition device 120, a memory 130, and a controller 109. The image acquisition device 120 may include one or more processors. For example, the image acquisition device 120 may include a computer, a server, a mainframe, a terminal, a personal computer, any type of mobile computing device, etc., or a combination thereof. The image acquisition device 120 may be connected to the detector 144 of the electron beam tool 100B through a medium (such as an electrical conductor, an optical fiber cable, a portable storage medium, IR, Bluetooth, the Internet, a wireless network, radio, or a combination thereof). The image acquisition device 120 may receive a signal from the detector 144 and may construct an image. Therefore, the image acquisition device 120 may acquire an image of the wafer 150. The image acquisition device 120 may also perform various post-processing functions, such as generating a contour, superimposing an indicator on the acquired image, etc. The image acquisition device 120 may be configured to perform adjustments to the brightness and contrast of the acquired image, etc. The memory 130 may be a storage medium, such as a hard disk, a random access memory (RAM), a cloud storage device, other types of computer-readable memory, etc. The memory 130 may be coupled to the image acquirer 120 and may be used to store scanned raw image data as raw images, as well as post-processed images. The image acquirer 120 and the memory 130 may be connected to the controller 109. In some embodiments, the image acquirer 120, the memory 130 and the controller 109 may be integrated together as an electronic control unit.

[0054] In some embodiments, the image acquirer 120 may acquire one or more images of the sample based on the imaging signal received from the detector 144. The imaging signal may correspond to a scanning operation for performing charged particle imaging. The acquired image may be a single image including a plurality of imaging regions that may contain various features of the wafer 150. The single image may be stored in the memory 130. Imaging may be performed based on imaging frames.

[0055] The condenser and illumination optics of an electron beam tool may include or be supplemented by an electromagnetic quadrupole electron lens. Figure 2B As shown, the electron beam tool 100B may 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, the first quadrupole lens 148 can be controlled to adjust the beam current, and the second quadrupole lens 158 can be controlled to adjust the beam spot size and beam shape.

[0056] Figure 2B1 shows a charged particle beam arrangement, where the inspection system may use a single primary beam that may be configured to generate secondary electrons by interacting with the wafer 150. The detector 144 may be positioned along the optical axis 105, such as Figure 2B The primary electron beam may be configured to travel along the optical axis 105. Thus, the detector 144 may include a hole at its center so that the primary electron beam may pass through to reach the wafer 150.

[0057] Reference now Figure 3 , Figure 3 Schematic diagram of a key performance indicator (KPI) determination system 300 consistent with an embodiment of the present disclosure. KPI system 300 may include an inspection system 310 and a KPI generator 320. Although inspection system 310 is shown and described for simplicity, it should be understood that a metering system may also be used.

[0058] Inspection system 310 and KPI generator 320 may be electrically coupled to each other physically (e.g., via a cable) or remotely (directly or indirectly). Inspection system 310 may be related to Figure 1 , Figure 2A and Figure 2B The system described is used to acquire images of a wafer (see, e.g., Figure 2A Sample 208, 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 (eg, the controller 109).

[0059] The KPI generator 320 may include one or more processors (e.g., processor 322, an example of which is used for simplicity) and a storage device 324. The one or more processors may include general 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), general array logic (GALs), complex programmable logic devices (CPLDs), field programmable gate arrays (FPGAs), systems on chip (SoCs), application specific integrated circuits (ASICs), and any combination of any type of circuit capable of data processing. The processor may also be a virtual processor comprising one or more processors distributed across multiple machines or devices coupled via a network.

[0060] KPI generator 320 may also include communication interface 326 to receive and send data to inspection system 310. Processor 322 may be configured to receive one or more raw images of the sample from inspection system 310. In some embodiments, inspection system 310 may provide raw images of the sample to KPI generator 320, and processor 322 of KPI generator 320 may observe the pixel dimensions of the raw images and apply a Fourier transform (e.g., discrete Fourier transform (DFT), fast Fourier transform (FFT), etc.) to the raw images (e.g., Figure 4 images 410 and 420; Figure 5 images 510, 512, 514, 516, 518; Figure 6 images 610 and 620; Figure 7 images 710, 712, 714, 716, 718; Figure 8 images 810, 812, 814, 816; Fig. 9 Images 911 and 912; Fig.10 1011 and 1012) to convert the original image into a transformed image (e.g., Figure 4 images 412 and 422; Figure 6 images 612 and 622; Figure 8 images 820, 822, 824, 826).

[0061] In some embodiments, converting the original image to the transformed image may include obtaining different spatial frequencies from the original image, where the spatial frequency may be a rate at which a feature of the original image changes. For example, one spatial frequency may be suitable for a feature of the original image, and another different spatial frequency may be suitable for other features of the original image.

[0062] In some embodiments, processor 322 may determine a plurality of coordinates in a spatial frequency space, where each coordinate corresponds to a spatial frequency of the original image. In some embodiments, each determined coordinate may 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 coordinates of the transformed image. In some embodiments, a transformed image may be generated by plotting the coordinates in the spatial frequency space.

[0063] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the original image. That is, higher z coordinate values ​​may coincide with lower spatial frequency values. In some embodiments, the z coordinate may be directly related to the resolution of the original image. That is, higher z coordinate values ​​may coincide with higher image resolutions of the original image.

[0064] In some embodiments, the processor 322 may determine a subset of the plurality of coordinates in the spatial frequency space having the highest z-coordinate values. For example, the subset may include coordinates having the top 1.5% of the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may also be used. In some embodiments, the processor 322 may generate a bright spot map image by plotting a subset of the coordinates (e.g., Figure 4 Figures 414 and 424; Figure 6 Figures 614 and 624; Figure 8 Figures 820, 822, 824, 826).

[0065] In some embodiments, processor 322 may apply the function to the transformed image by applying the function to each coordinate of the subset, based on the observed pixel size of the original image and the resolution of inspection system 310. In some embodiments, the function may be described as follows:

[0066] f(x,y,z)(1)

[0067] Where "x" is the x-coordinate describing the spatial frequency of the image in the x-direction, "y" is the y-coordinate describing the spatial frequency of the image in the y-direction, and "z" is the z-coordinate describing the grayscale value of the corresponding x and y coordinates of the transformed image. For example, processor 322 may insert the coordinates of the subset into the function and generate a weighted bright spot map (e.g., Figure 4 Figures 416 and 426; Figure 6 616 and 626). In some embodiments, different functions may be used based on the pixel size relative to the resolution of the optical system.

[0068] In some embodiments, the processor 322 may determine the KPI of the resolution of the original image based on the result of the applied function. In some embodiments, the processor 322 may determine the KPI by determining the sum of the results of the applied function, as shown in the following formula (2):

[0069] ∑ bright point f(x,y,z)(2)

[0070] For example, processor 322 may determine the KPI by determining the sum of the z-coordinate values ​​after applying the function to the coordinates.

[0071] In some embodiments, processor 322 may use the determined KPI to adjust the raw image to compensate for the resolution of the raw image. In some embodiments, processor 322 may adjust the raw image by adjusting astigmatism (e.g., in the "x" direction, in the "y" direction) in inspection system 310 based on the determined KPI. In some embodiments, processor 322 may use the determined KPI to adjust the focus value in inspection system 310.

[0072] Reference now Figure 4 , which are exemplary images and charts generated by KPI determination system 300 consistent with embodiments of the present disclosure.

[0073] In some embodiments, images 410 and 420 may be viewed in an imaging system (e.g., Figure 3 In some embodiments, image 410 may be generated in an inspection system 310 of FIG. 410 , where the imaging system pixel size is equal to or less than the optical system resolution. In some embodiments, image 410 may have a higher blurriness and lower clarity than image 420. In some embodiments, image 410 may have an image resolution that is less than the image resolution of image 420.

[0074] In some embodiments, images 410 and 420 may be raw images of the sample. In some embodiments, a processor (e.g., Figure 3 The processor 322 of the image 410 and the image 420 may apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to the images 410 and 420 to convert the images 410 and 420 into transformed images 412 and 422, respectively. For example, the processor may convert the image 410 into the image 412 by obtaining a plurality of spatial frequencies of the image 410, wherein each of the plurality of spatial frequencies characterizes the image 410. In some embodiments, each of the plurality of spatial frequencies may describe the image 410, wherein the spatial frequency may be a rate at which a feature of the image 410 changes. For example, one spatial frequency may be suitable for a feature of the image 410, and another different spatial frequency may be suitable for other features of the image 410. The processor may convert the image 420 into the image 422 in a similar manner.

[0075] In some embodiments, the processor may determine a plurality of coordinates in a spatial frequency space, wherein each coordinate corresponds to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may 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 grayscale value of the corresponding x and y coordinates of the transformed image. In some embodiments, images 412 and 422 may be generated by plotting the coordinates in the spatial frequency space.

[0076] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the original image. That is, a higher z coordinate value may be consistent with a lower spatial frequency value. In some embodiments, the z coordinate may be directly related to the resolution of the original image. That is, a higher z coordinate value may be consistent with a higher image resolution of the original image. For example, image 420 may have an image resolution higher than image 410. As seen in image 412 and image 422, image 422 has a greater number of condensed "bright" points at the center of the image than image 412, where the bright points are consistent with higher z coordinate values. In contrast, image 412 shows more scattered bright points than image 422. This may indicate that image 420 has a higher information reliability than image 410 in a lower spatial frequency.

[0077] In some embodiments, the processor may determine a subset of the plurality of coordinates in the spatial frequency space having the highest z-coordinate values. For example, the subset may include coordinates having the top 1.5% of the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may also be used. In some embodiments, the processor may generate a bright spot map chart 414 by plotting a subset of the coordinates from image 412. Similarly, the processor may generate a bright spot map chart 424 by plotting a subset of the coordinates from image 422.

[0078] In some embodiments, the processor may apply the function to the transformed images 412 and 422 based on the system pixel size and the optical system resolution by applying the function to each coordinate of the subset (e.g., by applying the function to each coordinate of the graphs 414 and 424, respectively). In some embodiments, the function may describe the relationship of the coordinate distance from the origin coordinate in the frequency space. In the function, "x" is the x-coordinate describing the spatial frequency of the image in the x-direction, "y" is the y-coordinate describing the spatial frequency of the image in the y-direction, and "z" is the z-coordinate describing the grayscale value of the corresponding x and y coordinates of the transformed image. For example, the processor may insert the coordinates of the subset into the function and generate a weighted bright spot map graph 416 by plotting the results of the function applied to the coordinates of the graph 414. Similarly, the processor may insert the coordinates of the subset into the function and generate a weighted bright spot map graph 426 by plotting the results of the function applied to the coordinates of the graph 424.

[0079] In some embodiments, the processor may determine a KPI for the resolution of images 410 and 420 based on the results of the applied function. In some embodiments, the processor may determine the KPI by determining the sum of the results of the applied function using a function that describes the relationship of the coordinate distance from the origin coordinate in frequency space, as shown in equation (2) above. For example, the processor may determine the KPI for image 410 by determining the sum of the z coordinate values ​​in chart 416. Similarly, the processor may determine the KPI for image 420 by determining the sum of the z coordinate values ​​in chart 426.

[0080] Reference now Figure 5 , which is consistent with the embodiments of the present disclosure. Figure 3 An exemplary graph 500 of resolution KPIs generated by the KPI determination system 300 for various images.

[0081] Graph 500 shows KPI values ​​for image resolution (e.g., Figure 3 Graph 500 shows a sample (e.g., Figure 2A Sample 208, Figure 2B Figure 500 may correspond to the use of the image processing method applied to generate the original image 510, 512, 514, 516 and 518 of the wafer 150). Figure 4 The KPIs of the graphs 416 and 426 may be determined by determining the KPIs of the graphs 500 based on the functions used to generate Figure 4 The z-coordinate values ​​calculated by the same function of graphs 416 and 426 are determined by the sum.

[0082] 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 shows that even if an image has a higher definition (e.g., as shown in image 518), the above description of the KPI value may be incorrect. Figure 3 and Figure 4 The described method can also determine KPIs that are sensitive to image resolution. As shown in graph 500, image 518 may have a higher image resolution than images 510, 512, 514, or 516.

[0083] Reference now Figure 6 , which are exemplary images and charts generated by KPI determination system 300 consistent with embodiments of the present disclosure.

[0084] In some embodiments, images 610 and 620 may be viewed in an imaging system (e.g., Figure 3 In some embodiments, image 610 may be generated in an inspection system 310 of FIG. 3 , where the imaging system pixel size is equal to or less than the optical system resolution. In some embodiments, image 610 may have a higher blurriness and lower clarity than image 620. In some embodiments, image 610 may have an image resolution that is less than the image resolution of image 620.

[0085] In some embodiments, images 610 and 620 may be raw images of the sample. In some embodiments, a processor (e.g., Figure 3 The processor 322 of the processor 322 can apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to the images 610 and 620 to convert the images 610 and 620 into transformed images 612 and 622, respectively. For example, the processor can convert the image 610 into the image 612 by obtaining a plurality of spatial frequencies of the image 610, wherein each of the plurality of spatial frequencies characterizes the image 610. In some embodiments, each of the plurality of spatial frequencies can describe the image 610, wherein the spatial frequency can be a rate at which a feature of the image 610 changes. For example, one spatial frequency can be suitable for a feature of the image 610, and another different spatial frequency can be suitable for other features of the image 610. The processor can convert the image 620 into the image 622 in a similar manner.

[0086] In some embodiments, the processor may determine a plurality of coordinates in a spatial frequency space, wherein each coordinate corresponds to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may 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 grayscale value of the corresponding x and y coordinates of the transformed image. In some embodiments, images 612 and 622 may be generated by plotting the coordinates in the spatial frequency space.

[0087] In some embodiments, the z coordinate can be indirectly related to the spatial frequency of the original image. That is, a higher z coordinate value can be consistent with a lower spatial frequency value. In some embodiments, the z coordinate can be directly related to the resolution of the original image. That is, a higher z coordinate value can be consistent with a higher image resolution of the original image. For example, image 620 can have an image resolution higher than image 610. As seen in images 612 and 622, image 622 has a greater number of condensed "bright" points at the center of the image than image 612, where the bright points are consistent with higher z coordinate values. In contrast, image 612 shows bright points that are more dispersed than image 622. Therefore, images 612 and 622 show that image 420 has a lower spatial frequency than image 610 and a higher image resolution and clarity.

[0088] In some embodiments, the processor may determine a subset of the plurality of coordinates in the spatial frequency space having the highest z-coordinate values. For example, the subset may include the plurality of coordinates having the top 1.5% of the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may also be used. In some embodiments, the processor may generate a bright spot map chart 614 by plotting a subset of the coordinates from image 612. Similarly, the processor may generate a bright spot map chart 624 by plotting a subset of the coordinates from image 622.

[0089] In some embodiments, the processor may apply the function to the transformed images 612 and 622 based on the system pixel size and the optical system resolution by applying the function to each coordinate of the subset (e.g., by applying the function to each coordinate of the graphs 614 and 624, respectively). In some embodiments, the function may describe a two-dimensional quadratic function. In the function, "x" is the x-coordinate describing the spatial frequency of the image in the x-direction, "y" is the y-coordinate describing the spatial frequency of the image in the y-direction, and "z" is the z-coordinate describing the grayscale value of the corresponding x and y coordinates of the transformed image. The function applied to the transformed images 612 and 622 may be the same as the function applied to the transformed images 612 and 622. Figure 4 The functions of the transformed images 412 and 422 are different. For example, the processor may insert the coordinates of the subset into the function and generate a weighted highlight graph chart 616 by plotting the result of the function applied to the coordinates of chart 614. Similarly, the processor may insert the coordinates of the subset into the function and generate a weighted highlight graph chart 626 by plotting the result of the function applied to the coordinates of chart 624. Although images 610 and 612 and chart 614 may be respectively Figure 4 410 and 412 and graph 414 are the same, but graph 616 may be different from graph 416 because a different function is applied. Similarly, although images 620 and 622 and graph 624 may be different from Figure 4 Images 420 and 422 and graph 424 in are the same, but graph 626 may be different from graph 426 because a different function is applied.

[0090] In some embodiments, the processor may determine a 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 determining the sum of the results of the applied functions using a two-dimensional quadratic function, 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 chart 616. Similarly, the processor may determine the KPI for image 620 by determining the sum of the z coordinate values ​​in chart 626.

[0091] Reference now Figure 7 , which is consistent with the embodiments of the present disclosure. Figure 3 An example graph 700 of resolution KPIs generated by the KPI determination system 300 for various images.

[0092] Graph 700 shows KPI values ​​for image resolution (e.g., Figure 3 Graph 700 shows a sample (e.g., Figure 2A Sample 208, Figure 2B 150) of the wafer 150). The graph 700 may correspond to the use of the image processing method applied to generate Figure 6 The KPIs of the graphs 616 and 626 may be determined by determining the KPIs of the graphs 700 based on the functions used to generate Figure 6 The z-coordinate values ​​calculated by the same function of graphs 616 and 626 are determined by the sum.

[0093] Graph 700 shows image resolution KPI 720 for image 710, image resolution KPI 722 for image 712, image resolution KPI 724 for image 714, image resolution KPI 726 for image 716, and image resolution KPI 728 for image 718. As shown in graph 700, higher KPI values ​​correspond to higher image resolutions. Graph 700 also shows that even if an image has a higher definition (e.g., as shown in image 718), the above description of Figure 3 and Figure 6 The described method can also determine KPIs that are sensitive to image resolution. As shown in graph 700, image 718 may have a higher image resolution than images 710, 712, 714, or 716.

[0094] Reference now Figure 8 , which are exemplary images and charts generated by KPI determination system 300 consistent with embodiments of the present disclosure.

[0095] In some embodiments, images 810, 812, 814, and 816 may be viewed in an imaging system (e.g., Figure 3 In some embodiments, images 810, 812, 814, and 816 may have increased image resolution and clarity and reduced blurriness (i.e., image 810 may have the lowest image resolution and clarity and the highest blurriness, while image 816 may have the highest image resolution and clarity and the lowest blurriness).

[0096] In some embodiments, images 810, 812, 814, and 816 may be raw images of the sample. In some embodiments, a processor (e.g., Figure 3 The processor 322 in the image 810 may apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to the images 810, 812, 814, and 816 to convert the images 810, 812, 814, and 816 into transformed images. For example, the processor may convert the image 810 by obtaining a plurality of spatial frequencies of the image 810, wherein each of the plurality of spatial frequencies characterizes the image 810. In some embodiments, each of the plurality of spatial frequencies may describe the image 810, wherein the spatial frequency may be a rate at which a feature of the image 810 changes. For example, one spatial frequency may be suitable for a feature of the image 810, and another different spatial frequency may be suitable for other features of the image 810. The processor may convert the images 812, 814, and 816 in a similar manner.

[0097] In some embodiments, the processor may determine a plurality of coordinates in a spatial frequency space, wherein each coordinate corresponds to a spatial frequency of the plurality of spatial frequencies. In some embodiments, each determined coordinate may 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 grayscale value of the corresponding x and y coordinates of the transformed image. In some embodiments, the transformed image may be generated by plotting the coordinates in the spatial frequency space.

[0098] In some embodiments, the processor may determine a subset of the plurality of coordinates having the highest z coordinate values ​​in the spatial frequency space. For example, the subset may include a plurality of coordinates having the top 1.5% of the highest z coordinate values. It should be understood that 1.5% is an example and other percentages may also be used. In some embodiments, the processor may generate a bright spot map chart 820 by plotting a subset of the coordinates of the transformed image from image 810. Similarly, the processor may generate bright spot map charts 822, 824, and 826 by plotting subsets of the coordinates of the transformed images from images 812, 814, and 816, respectively.

[0099] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the original image. That is, high z coordinate values ​​may be consistent with low spatial frequency values. In some embodiments, the z coordinate may have a periodic relationship with the resolution of the original image. That is, low z coordinate values ​​with periodic distribution may be consistent with the high image resolution of the original image. For example, image 816 may have a higher image resolution than images 810, 812, and 814. As shown in charts 820, 822, 824, and 826, as the image resolution increases, the "bright" points in the bright spot map chart may be distributed in a more periodic pattern. In contrast, as the image resolution decreases, the bright spot map chart displays more scattered bright spots. This behavior may be due to the imaging system pixel size being more than five times greater than the optical system resolution.

[0100] Reference now Fig. 9 , which is consistent with the embodiments of the present disclosure. Figure 3 An example graph 900 of resolution KPIs generated by the KPI determination system 300 for various images.

[0101] Graph 900 shows the KPI values ​​for normalized image resolution (e.g., Figure 3 The graph 900 shows an axis 901 for image brightness values ​​and an axis 902 for image brightness values. Figure 2A Sample 208, Figure 2B The graph 900 may include original images 911, 912, and 913 corresponding to the wafer 150. Figure 5 The normalized KPI curve 920 corresponds to Figure 7As shown in curves 920 and 930, point 921 of curve 920 and point 931 of curve 930 correspond to the normalized KPI of image 911. As shown in curves 920 and 930, point 922 of curve 920 and point 932 of curve 930 correspond to the normalized KPI of image 912. As shown in curves 920 and 930, point 923 of curve 920 and point 933 of curve 930 correspond to the normalized KPI of image 913. Chart 900 may include curves 940 to 942 of normalized KPIs corresponding to typical KPI determination methods.

[0102] As shown in graph 900, image 913 may have a higher brightness than image 912, and image 912 may have a higher brightness than image 911. Curves 920 and 930 indicate that the above KPI determination method is advantageously less sensitive (e.g., insensitive) to changes in brightness than the typical method shown by curves 940-942. In other words, graph 900 may indicate that, by Figures 3 to 7 The image resolution KPI determined by the method described in is independent of changes in image brightness.

[0103] Reference now Fig.10 , which is consistent with the embodiments of the present disclosure. Figure 3 An exemplary graph 1000 of resolution KPIs generated by the KPI determination system 300 for various images.

[0104] Graph 1000 shows the KPI values ​​for normalized image resolution (e.g., Figure 3 The graph 1000 shows an axis 1001 for KPI determination system 300 of the image contrast value and an axis 1002 for image contrast value. Figure 2A Sample 208, Figure 2B The graph 1000 may include original images 1011, 1012, and 1013 corresponding to the wafer 150. Figure 5 The normalized KPI curve 1020 corresponds to Figure 7 As shown by the curves 1020 and 1030, the point 1021 of the curve 1020 and the point 1031 of the curve 1030 correspond to the normalized KPI of the image 1011. As shown by the curves 1020 and 1030, the point 1022 of the curve 1020 and the point 1032 of the curve 1030 correspond to the normalized KPI of the image 1012. As shown by the curves 1020 and 1030, the point 1023 of the curve 1020 and the point 1033 of the curve 1030 correspond to the normalized KPI of the image 1013. The graph 1000 may include a curve 1040 of the normalized KPI corresponding to the typical KPI determination method.

[0105] As shown in graph 1000, image 1013 may have a higher contrast than image 1012, and image 1012 may have a higher contrast than image 1011. Curves 1020 and 1030 indicate that the above KPI determination method is advantageously less sensitive (e.g., insensitive) to changes in contrast than the typical method shown by curve 1040. In other words, graph 1000 may indicate that by Figures 3 to 7 The image resolution KPI determined by the method described in is independent of changes in image contrast.

[0106] Reference now Fig.11 , Fig.11 Exemplary graphs 1110 , 1111 , 1112 , and 1113 of resolution KPIs for various images are shown.

[0107] Graphs 1110, 1111, 1112, and 1113 each have an axis 1101 for astigmatism in the x-direction and an axis 1102 for astigmatism in the y-direction. The gradient in each of graphs 1110, 1111, 1112, and 1113 corresponds to a resolution KPI. Graph 1110 may correspond to a resolution KPI based on an actual measured resolution of an image, graph 1111 may correspond to a resolution KPI determined by a typical KPI determination method, and graph 1112 may correspond to a resolution KPI determined using Figure 4 and Figure 5 The resolution KPI determined by the function applied in , and the chart 1113 may correspond to the use of Figure 6 and Figure 7 The function applied in the KPI determines the resolution.

[0108] For the same image, chart 1110 may display actual resolution KPI 1110a, chart 1111 may display determined resolution KPI 1111a, chart 1112 may display determined resolution KPI 1112a, and chart 1113 may display determined resolution KPI 1113a. As shown in charts 1110 to 1113, Figures 3 to 7 The KPI determination method described in is 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 1111a.

[0109] The hardware that adjusts the astigmatism in the x-direction in the inspection system is orthogonal to the hardware that adjusts the astigmatism in the y-direction. Therefore, a robust and reliable KPI determination method should be orthogonal (e.g., the determined KPI should have a symmetrical circular distribution in the gradient graph). Graphs 1112 and 1113 show gradients that are more circular and more symmetrical than the gradients in graph 1111, which means that the x-direction astigmatism and the y-direction astigmatism in graphs 1112 and 1113 are more orthogonal than the x-direction astigmatism and the y-direction astigmatism in graphs 1111. Typical KPI determination methods (such as the method used to generate graph 1111) may cause crosstalk during astigmatism correction, even if the image resolution quality is higher. Figures 3 to 7 The KPI determination method described in can reduce crosstalk during astigmatism correction because it exhibits higher orthogonality than typical KPI determination methods. Advantageously, Figures 3 to 7 The KPI determination method described in can adjust the astigmatism in one direction without affecting the astigmatism in another direction.

[0110] Reference now Fig.12 , a flowchart illustrating an exemplary process 1200 for image resolution characterization consistent with embodiments of the present disclosure. The steps of method 1200 may be performed by a computing device (e.g., Figure 1 Controller 109, Figure 3 A system (e.g., Figure 3 The KPI determination system 300 of FIG. 1200 is used for the purpose of illustration. It should be understood that the illustrated method 1200 can be changed to modify the order of the steps and include additional steps that can be performed by the system.

[0111] At step 1201, the system (e.g., Figure 3 The inspection system 310) can provide a KPI generator (e.g., Figure 3 The KPI generator 320 of FIG. 3 provides an original image of the sample, and a processor (eg, Figure 3 The processor 322 may observe the pixel dimensions of the original image and apply a Fourier transform (e.g., a discrete Fourier transform (DFT), a fast Fourier transform (FFT), etc.) to the original image (e.g., Figure 4 images 410 and 420; Figure 5 images 510, 512, 514, 516, 518; Figure 6 images 610 and 620; Figure 7 images 710, 712, 714, 716, 718; Figure 8 images 810, 812, 814, 816; Fig. 9 Images 911 and 912; Fig.10 1011 and 1012) to convert the original image into a transformed image (e.g., Figure 4 images 412 and 422; Figure 6 images 612 and 622; Figure 8 images 820, 822, 824, 826).

[0112] In some embodiments, converting the original image to the transformed image may include obtaining a plurality of spatial frequencies of the original image, wherein each of the plurality of spatial frequencies characterizes the original image. In some embodiments, each of the plurality of spatial frequencies may describe the original image, wherein the spatial frequency may be a rate at which a feature of the original image changes. For example, one spatial frequency may be suitable for a feature of the original image, while another different spatial frequency may be suitable for other features of the original image.

[0113] In some embodiments, the system may determine a plurality of coordinates in a spatial frequency space, wherein each coordinate corresponds to a spatial frequency in a plurality of spatial frequencies. In some embodiments, each determined coordinate may 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 grayscale value of the corresponding x and y coordinates of the transformed image. In some embodiments, the transformed image may be generated by plotting the coordinates in the spatial frequency space.

[0114] In some embodiments, the z coordinate may be indirectly related to the spatial frequency of the original image. That is, higher z coordinate values ​​may coincide with lower spatial frequency values. In some embodiments, the z coordinate may be directly related to the resolution of the original image. That is, higher z coordinate values ​​may coincide with higher image resolutions of the original image.

[0115] In some embodiments, the system may determine a subset of the plurality of coordinates in the spatial frequency space having the highest z-coordinate values. For example, the subset may include the plurality of coordinates having the top 1.5% of the highest z-coordinate values. It should be understood that 1.5% is an example and other percentages may also be used. In some embodiments, the processor 322 may generate a bright spot map chart (e.g., Figure 4 Figures 414 and 424; Figure 6 Figures 614 and 624; Figure 8 Figures 820, 822, 824, 826).

[0116] At step 1203, the system can apply the function to the transformed image based on the pixel size by applying the function to each coordinate of the subset. For example, the processor can insert the coordinates of the subset into the function and generate a weighted highlight map (e.g., Figure 4 Figures 416 and 426; Figure 6 616 and 626).

[0117] At step 1205, the system can determine a KPI for the resolution of the original image based on the results of the applied function. In some embodiments, the system can determine the KPI by determining the sum of the results of the applied function. For example, the system can determine the KPI by determining the sum of the z-coordinate values ​​after the function is applied to the coordinates.

[0118] In some embodiments, the system may adjust the raw image using the determined KPI 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, in the "y" direction) in the inspection system based on the determined KPI. In some embodiments, the system may adjust the focus value in the inspection system using the determined KPI.

[0119] A non-transitory computer readable medium may be provided that stores a controller (eg, Figure 1 109) for controlling an electron beam tool or other system (e.g., Figure 3 KPI determination system 300), other systems and servers, or components thereof. These instructions may allow one or more processors to perform image resolution characterization, image processing, data processing, beam scanning, graphic display, operation of a charged particle beam device or another imaging device, etc. In some embodiments, the non-transitory computer readable medium may be provided, which stores instructions for the 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, tapes, or any other magnetic data storage media, compact disk read-only memories (CD-ROMs), any other optical data storage media, any physical media with hole patterns, random access memories (RAMs), programmable read-only memories (PROMs) and erasable programmable read-only memories (EPROMs), FLASH-EPROMs, or any other flash memory, non-volatile random access memories (NVRAMs), caches, registers, any other memory chips or cassettes, and networked versions thereof.

[0120] The embodiments may be further described using the following terms:

[0121] 1. A method for characterizing optical resolution, comprising:

[0122] Provide the original image of the sample;

[0123] Observe the pixel size of the original image;

[0124] converting the original image into a transformed image by applying a Fourier transform to the original image;

[0125] applying a function to the transformed image based on the pixel size; and

[0126] A key performance indicator of the resolution of the original image is determined based on the result of the applied function.

[0127] 2. The method of clause 1, wherein converting the original image into the transformed image comprises:

[0128] obtaining a plurality of spatial frequencies of the original image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the original image; and

[0129] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0130] 3. The method of clause 2, further comprising: determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

[0131] 4. The method of clause 3, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0132] 5. The method of clause 4, wherein determining the key performance indicator of the resolution of the original image comprises determining a sum of the results of the applied functions.

[0133] 6. A method according to any one of clauses 3 to 5, wherein the value of each coordinate of the subset comprises a greyscale value.

[0134] 7. A method according to any one of clauses 3 to 6, wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

[0135] 8. A method according to any one of clauses 3 to 7, wherein the value of the subset is directly related to the resolution of the original image.

[0136] 9. A method according to any one of clauses 1 to 8, wherein the key performance indicator of the resolution is independent of the brightness of the original image or the contrast of the original image.

[0137] 10. The method of any one of clauses 1 to 9, further comprising: adjusting the original image using the key performance indicator of the resolution to compensate for the resolution.

[0138] 11. The method of clause 10, wherein adjusting the original image comprises adjusting for astigmatism in an imaging system.

[0139] 12. A system for characterizing optical resolution, comprising:

[0140] One or more processors configured to execute instructions to cause the system to perform:

[0141] Provide the original image of the sample;

[0142] Observe the pixel size of the original image;

[0143] converting the original image into a transformed image by applying a Fourier transform to the original image;

[0144] applying a function to the transformed image based on the pixel size; and

[0145] A key performance indicator of the resolution of the original image is determined based on the result of the applied function.

[0146] 13. The system of claim 12, wherein converting the original image to the transformed image comprises:

[0147] obtaining a plurality of spatial frequencies of the original image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the original image; and

[0148] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0149] 14. A system according to clause 13, wherein the one or more processors are configured to execute instructions to cause the system to also perform determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

[0150] 15. The system of clause 14, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0151] 16. The system of clause 15, wherein determining the key performance indicator of the resolution of the original image comprises determining a sum of the results of the applied functions.

[0152] 17. A system according to any of clauses 14 to 16, wherein the value of each coordinate of the subset comprises a greyscale value.

[0153] 18. A system according to any of clauses 14 to 17, wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

[0154] 19. A system according to any of clauses 14 to 18, wherein the value of the subset is directly related to the resolution of the original image.

[0155] 20. A system according to any one of clauses 12 to 19, wherein the key performance indicator of the resolution is independent of the brightness of the original image or the contrast of the original image.

[0156] 21. A system according to any one of clauses 12 to 20, wherein the one or more processors are configured to execute instructions to cause the system to further perform adjusting the original image using the key performance indicator of the resolution to compensate for the resolution.

[0157] 22. The system of clause 21, wherein adjusting the original image comprises adjusting for astigmatism in an imaging system.

[0158] 23. A non-transitory computer readable medium comprising a set of instructions executable by one or more processors of a device to cause the device to perform a method comprising:

[0159] Provide the original image of the sample;

[0160] Observe the pixel size of the original image;

[0161] converting the original image into a transformed image by applying a Fourier transform to the original image;

[0162] applying a function to the transformed image based on the pixel size; and

[0163] A key performance indicator of the resolution of the original image is determined based on the result of the applied function.

[0164] 24. The non-transitory computer-readable medium of clause 23, wherein converting the original image to the transformed image comprises:

[0165] obtaining a plurality of spatial frequencies of the original image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the original image; and

[0166] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0167] 25. A non-transitory computer-readable medium according to clause 24, wherein the set of instructions capable of being executed by one or more processors of the device causes the device to also perform determining a subset of the multiple coordinates, wherein each coordinate of the subset includes a value in the highest percentile of the multiple coordinates.

[0168] 26. The non-transitory computer-readable medium of clause 25, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0169] 27. The non-transitory computer-readable medium of clause 26, wherein determining the key performance indicator of the resolution of the original image comprises determining a sum of the results of the applied functions.

[0170] 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.

[0171] 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 the plurality of spatial frequencies.

[0172] 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 original image.

[0173] 31. The non-transitory computer-readable medium of any one of clauses 23 to 30, wherein the key performance indicator of the resolution is independent of the brightness of the original image or the contrast of the original image.

[0174] 32. A non-transitory computer-readable medium according to any one of clauses 23 to 31, wherein the set of instructions capable of being executed by one or more processors of the device causes the device to also perform adjustment of the original image using the key performance indicator of the resolution to compensate for the resolution.

[0175] 33. The non-transitory computer-readable medium of clause 10, wherein adjusting the original image comprises adjusting for astigmatism in an imaging system.

[0176] 34. A method comprising:

[0177] Provide images of samples;

[0178] Observe the pixel size of the image;

[0179] converting the image into a transformed image;

[0180] applying a function to the transformed image based on the pixel size; and

[0181] A key performance indicator of the resolution of the image is determined by applying the function to the transformed image.

[0182] 35. The method of clause 34, wherein converting the image into the transformed image comprises:

[0183] obtaining a plurality of spatial frequencies of the image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the image; and

[0184] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0185] 36. The method of clause 35, further comprising: determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

[0186] 37. The method of clause 36, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0187] 38. The method of clause 37, wherein determining the key performance indicator of the resolution of the image comprises determining a sum of the results of the applied functions.

[0188] 39. A method according to any of clauses 36 to 38, wherein the value of each coordinate of the subset comprises a greyscale value.

[0189] 40. A method according to any of clauses 36 to 39, wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

[0190] 41. A method according to any of clauses 36 to 40, wherein the value of the subset is directly related to the resolution of the image.

[0191] 42. A method according to any one of clauses 34 to 41, wherein the key performance indicator of the resolution is independent of the brightness of the image or the contrast of the image.

[0192] 43. A method according to any one of clauses 34 to 42, further comprising: adjusting the image using the key performance indicator of the resolution to compensate for the resolution.

[0193] 44. The method of clause 43, wherein adjusting the image comprises adjusting for astigmatism in an imaging system.

[0194] 45. A system comprising:

[0195] One or more processors configured to execute instructions to cause the system to perform:

[0196] Provide images of samples;

[0197] Observe the pixel size of the image;

[0198] converting the image into a transformed image;

[0199] applying a function to the transformed image based on the pixel size; and

[0200] A key performance indicator of the resolution of the image is determined by applying the function to the transformed image.

[0201] 46. ​​The system of clause 45, wherein converting the image into the transformed image comprises:

[0202] obtaining a plurality of spatial frequencies of the image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the image; and

[0203] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0204] 47. A system according to clause 46, wherein the one or more processors are configured to execute instructions to cause the system to also perform determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

[0205] 48. The system of clause 47, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0206] 49. The system of clause 48, wherein determining the key performance indicator of the resolution of the image comprises determining a sum of the results of the applied functions.

[0207] 50. A system according to any of clauses 47 to 49, wherein the value of each coordinate of the subset comprises a greyscale value.

[0208] 51. A system according to any of clauses 47 to 50, wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

[0209] 52. A system according to any of clauses 47 to 51, wherein the value of the subset is directly related to the resolution of the image.

[0210] 53. A system according to any one of clauses 45 to 52, wherein the key performance indicator of the resolution is independent of the brightness of the image or the contrast of the image.

[0211] 54. A system according to any one of clauses 45 to 53, wherein the one or more processors are configured to execute instructions so that the system also performs adjusting the image using the key performance indicator of the resolution to compensate for the resolution.

[0212] 55. The system of clause 54, wherein adjusting the image comprises adjusting for astigmatism in an imaging system.

[0213] 56. A non-transitory computer readable medium comprising a set of instructions, the set of instructions being executable by one or more processors of a device to cause the device to perform a method comprising:

[0214] Provide images of samples;

[0215] Observe the pixel size of the image;

[0216] converting the image into a transformed image;

[0217] applying a function to the transformed image based on the pixel size; and

[0218] A key performance indicator of the resolution of the image is determined by applying the function to the transformed image.

[0219] 57. The non-transitory computer-readable medium of clause 56, wherein converting the image to the transformed image comprises:

[0220] obtaining a plurality of spatial frequencies of the image, wherein each spatial frequency of the plurality of spatial frequencies characterizes the image; and

[0221] A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

[0222] 58. A non-transitory computer-readable medium as described in clause 57, wherein the set of instructions capable of being executed by one or more processors of the device causes the device to also perform determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

[0223] 59. The non-transitory computer-readable medium of clause 58, wherein applying the function to the transformed image comprises applying the function to each coordinate of the subset.

[0224] 60. The non-transitory computer-readable medium of clause 59, wherein determining the key performance indicator of the resolution of the image comprises determining a sum of the results of the applied functions.

[0225] 61. The non-transitory computer-readable medium of any of clauses 58 to 60, wherein the value of each coordinate of the subset comprises a grayscale value.

[0226] 62. The non-transitory computer-readable medium of any one of clauses 58 to 61, wherein the values ​​of the subset are indirectly related to the plurality of spatial frequencies.

[0227] 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.

[0228] 64. The non-transitory computer-readable medium of any one of clauses 56 to 63, wherein the key performance indicator of the resolution is independent of the brightness of the image or the contrast of the image.

[0229] 65. A non-transitory computer-readable medium as described in any of clauses 56 to 64, wherein the set of instructions capable of being executed by one or more processors of the device causes the device to also perform adjustment of the image using the key performance indicator of the resolution to compensate for the resolution.

[0230] 66. The non-transitory computer-readable medium of clause 65, wherein adjusting the image comprises adjusting for astigmatism in an imaging system.

[0231] It should be understood that the embodiments of the present disclosure are not limited to the exact constructions that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims

1. A system for characterizing optical resolution, comprising: One or more processors configured to execute instructions to cause the system to perform: Provide the original image of the sample; Observe the pixel size of the original image; converting the original image into a transformed image by applying a Fourier transform to the original image; applying a function to the transformed image based on the pixel size; as well as A key performance indicator of the resolution of the original image is determined based on the result of the applied function.

2. The system of claim 1 , wherein converting the original image to the transformed image comprises: Obtaining a plurality of spatial frequencies of the original image, wherein each spatial frequency of the plurality of spatial frequencies represents the original image; as well as A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

3. The system of claim 2, wherein the one or more processors are configured to execute instructions to cause the system to further perform determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest percentile of the plurality of coordinates.

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

5. The system of claim 4, wherein the key performance indicator for determining the resolution of the original image comprises: A sum of the results of the applied functions is determined. 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 value of the subset is directly related to the resolution of the original image. 9 . The system according to claim 1 , wherein the key performance indicator of the resolution is independent of the brightness of the original image or the contrast of the original image.

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

11. The system of claim 10, wherein adjusting the original image comprises: Adjusts for astigmatism in imaging systems.

12. A non-transitory computer readable medium comprising a set of instructions, the set of instructions being executable by one or more processors of a device to cause the device to perform a method comprising: Provide the original image of the sample; Observe the pixel size of the original image; converting the original image into a transformed image by applying a Fourier transform to the original image; applying a function to the transformed image based on the pixel size; as well as A key performance indicator of the resolution of the original image is determined based on the result of the applied function.

13. The non-transitory computer-readable medium of claim 12, wherein converting the original image to the transformed image comprises: Obtaining a plurality of spatial frequencies of the original image, wherein each spatial frequency of the plurality of spatial frequencies represents the original image; as well as A plurality of coordinates in a spatial frequency space is determined, wherein each coordinate in the plurality of coordinates corresponds to a spatial frequency in the plurality of spatial frequencies.

14. A non-transitory computer-readable medium according to claim 13, wherein the set of instructions is executable by one or more processors of the device to cause the device to further perform determining a subset of the plurality of coordinates, wherein each coordinate of the subset includes a value in a highest 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: The function is applied to each coordinate of the subset.

Images