A system and method for determining a noise characteristic from images of an inspection apparatus

Abstract

A non-transitory computer-readable medium stores a set of instructions that is executable by at least one processor of an apparatus to perform operations for determining a noise characteristic from images acquired using an inspection apparatus. The operations include analyzing the images. The images represent a same region of a substrate having a device pattern. The images include lines of pixels. The images are associated with different line sampling frequencies of the inspection apparatus. The analyzing includes extracting position information of edges of the device pattern from grayscale values of each pixel line of the images. The analyzing also includes transforming the position information into frequency domain information having aliased noise information. The analyzing also includes determining a noise frequency higher than Nyquist frequencies based on the aliased noise information.

Description

A SYSTEM AND METHOD FOR DETERMINING A NOISE CHARACTERISTIC FROM IMAGES OF AN INSPECTION APPARATUSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of WO application PCT / CN2024 / 132039 which was filed on 14 November 2024 and which is incorporated herein in its entirety by reference.FIELD

[0002] The description herein relates to systems and methods directed to image analysis in microscopybased metrology, for example inspection metrology used in connection with photolithography processes.BACKGROUND

[0003] In manufacturing processes of integrated circuits (ICs), unfinished or finished circuit components are inspected to ensure that they are manufactured according to design and are free of defects. Inspection can be performed using systems such as optical microscopes or charged particle beam microscopes (e.g., a scanning electron microscope (SEM)). As the sizes of IC components continue to shrink, accuracy and speed of defect detection become more and more important for yield and throughput. However, imaging resolution and throughput of inspection tools struggle to keep pace with the ever-decreasing feature size of IC components.SUMMARY

[0004] Embodiments of the present disclosure provide a system and method for determining a noise characteristic from images acquired using an inspection apparatus.

[0005] In some embodiments, a non-transitory computer-readable medium that stores a set of instructions for determining a noise characteristic from images acquired using an inspection apparatus is provided. The instructions are executable by at least one processor of an apparatus to cause the apparatus to perform operations. The operations can comprise analyzing the images that represent a same region of a substrate comprising a device pattern. The images can comprise lines of pixels. The images can be associated with different line sampling frequencies of the inspection apparatus. The analyzing can comprise extracting position information of edges of the device pattern from grayscale values of each pixel line of the images. The analyzing can also comprise transforming the position information into frequency domain information comprising aliased noise information. The analyzing can also comprise determining a noise frequency higher than Nyquist frequencies based on the aliased noise information.

[0006] In some embodiments, a non-transitory computer-readable medium that stores a set of instructions for determining a noise characteristic of a scanning electron microscopy (SEM) apparatus is provided. The instructions are executable by at least one processor of an apparatus to perform operations. The operations can comprise analyzing SEM images captured by the SEM apparatus to extract grayscalevalues of pattern edges from each pixel line of the SEM images. The SEM images can be associated with different line sampling frequencies of the SEM apparatus. The operations can also comprise recovering a noise frequency higher than Nyquist frequencies based on the aliased noise information using a recovery algorithm.

[0007] In some embodiments, a method for determining a noise characteristic from images acquired using an inspection apparatus is provided. The method can comprise analyzing the images that represent a same region of a substrate comprising a device pattern. The images can comprise lines of pixels. The images can be associated with different line sampling frequencies of the inspection apparatus. The analyzing can comprise extracting position information of edges of the device pattern from grayscale values of each pixel line of the images. The analyzing can also comprise transforming the position information into frequency domain information comprising aliased noise information. The analyzing can also comprise determining a noise frequency higher than Nyquist frequencies based on the aliased noise information.

[0008] In some embodiments, a system for determining a noise characteristic from images acquired using an inspection apparatus is provided. The system can comprise one or more processors and one or more memory devices. The memory devices can store instructions for determining a noise frequency from images acquired using an inspection apparatus. The instructions are executable by the one or more processors to perform operations. The operations can comprise analyzing the images that represent a same region of a substrate comprising a device pattern. The images can comprise lines of pixels. The images can be associated with different line sampling frequencies of the inspection apparatus. The analyzing can comprise extracting position information of edges of the device pattern from grayscale values of each pixel line of the images. The analyzing can also comprise transforming the position information into frequency domain information comprising aliased noise information. The analyzing can also comprise determining the noise frequency in a frequency range higher than Nyquist frequencies based on the aliased noise information.BRIEF DESCRIPTION OF FIGURES

[0009] The above and other aspects of the present disclosure will become more apparent from the description of example embodiments, taken in conjunction with the accompanying drawings.

[0010] FIG. 1 is a schematic diagram illustrating an example charged-particle beam inspection system, consistent with embodiments of the present disclosure.

[0011] FIG. 2A is a schematic diagram illustrating an example single beam inspection apparatus, consistent with embodiments of the present disclosure that can be a part of the example charged-particle beam inspection system of FIG. 1.

[0012] FIG. 2B is a schematic diagram illustrating an example multi-beam inspection apparatus, consistent with embodiments of the present disclosure that can be a part of the example charged-particle beam inspection system of FIG. 1.

[0013] FIG. 3 illustrates an example of a set of SEM images, consistent with embodiments of the present disclosure.

[0014] FIG. 4 illustrates an example of graphical data analysis, consistent with embodiments of the present disclosure.

[0015] FIG. 5 illustrates an example of a set of SEM images, consistent with embodiments of the present disclosure.

[0016] FIG. 6 illustrates an example graph of noise spectra, consistent with embodiments of the present disclosure.

[0017] FIG. 7 illustrates an example method for determining a noise characteristic from images acquired using an inspection apparatus, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0018] Reference will now be made in detail to example embodiments, examples of which are illustrated in the drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of example embodiments do not represent all implementations consistent with the invention. Instead, they are merely examples of apparatuses, systems, and methods consistent with aspects related to subject matter that may be recited in the appended claims. For example, although some embodiments are described in the context of utilizing charged-particle beams (e.g., electron beams), the disclosure is not so limited. Unless infeasible, embodiments described herein can be implemented in any other type of charged particle device (e.g., proton beams). Furthermore, other imaging systems may be used, such as optical imaging, photodetection, x-ray detection, or the like.

[0019] Electronic devices are constructed of circuits formed on a piece of silicon called a substrate. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. With advancements in technology, the size of these circuits has decreased dramatically so that many more of them can fit on the substrate. For example, an IC chip in a smart phone can be as small as a fingernail and yet may include over 2 billion transistors, the size of each transistor being less than 1 / 1, 000th the width of a human hair.

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

[0021] Yield is a metric that characterizes failure rate in device fabrication, which relates to cost and efficiency. Yield can be defined as a ratio of all the wafers that are produced by a fab to the number of wafers that were introduced to the fab. Or yield can be the number of working chips that survive the device fabrication process performed on a wafer to the number of potential chips that can be fabricatedfrom that wafer in the ideal case of zero failure. As some wafers or chips fail during fabrication, the overall yield is less than 100%. For example, to obtain a 75% yield for a 50-step process (where a step can be indicative of the number of layers formed on a wafer), each individual step should have a yield greater than 99.4%. In contrast, if individual steps have a yield of 95%, the compounding errors at each step result in an overall process yield as low as 7-8%. Every wafer or chip lost during fabrication is a sunk cost and lost time for the fab.

[0022] Integral to the making of these ICs with extremely small structures are highly accurate inspection processes, performed in between one or more fabrication steps, to ascertain whether fabrication steps are performing at expected tolerances. Errors in even one step have the potential to result in defects in the finished IC, rendering it useless. A goal of the manufacturing process is to avoid such defects to maximize the number / yield of functional ICs made in the process.

[0023] Inspection can be carried out using a scanning charged-particle microscope (e.g., a scanning electron microscope (SEM)). A scanning charged-particle microscope can be used to image extremely small structures of ICs, by capturing an image of the structures on the wafer. The image can be used to determine if the structure was formed properly (e.g., having the expected dimensions and being properly located on the wafer). If the structure is defective, then the process can be adjusted, so the defect is less likely to recur.

[0024] The working principle of a SEM is analogous to that of a camera. A camera takes a picture by receiving and recording intensity of light reflected or emitted from people or objects. SEMs capture images by receiving and recording energies or quantities of electrons reflected or emitted from the structures of the wafer. Similar to how a camera uses a light source (e.g., ambient, sunlight, or a flash), SEMs use an electron source to send a beam(s) of electron to a surface of a wafer that has structures of interest for imaging. The electron beam(s) can be deflected and the wafer can be moved (on a movement stage) so that a plurality of regions of the wafer can be irradiated by the electrons. When the electrons are reflected or emitted (“exiting”) from the structures (e.g., from the wafer surface, from the structures underneath the wafer surface, or both), a detector of the SEM can receive and record the energies or quantities of those electrons to generate an inspection image of the regions of the wafer that were irradiated by electrons.

[0025] Speed, or throughput, has been a traditionally important metric alongside yield. Throughput is a measurable quantity that characterizes the manufacture speed of a fab (e.g., number of IC units produced per unit time). Generating and processing these images to determine whether any defects exist (sometimes as small as the nanometer scale) are computationally intensive and affect throughput. And as the physical sizes of IC components continue to shrink, accuracy and efficiency in defect detection become more important. To inspect a single wafer, it is not uncommon for an inspection system to generate and process a substantial number of images. For example, if each image taken corresponds to 6 pm x 6 pm portion of a wafer, for a 200mm wafer, it would take over 872 million images to image the entire wafer. If theseimages are not processed and evaluated efficiently, not surprisingly, speed will be dramatically impacted, thereby affecting the wafer throughput.

[0026] Throughput has become even more important in view of recent global chip shortages. As there are multiple steps in the fabrication of a chip device (e.g., multiple steps for multiple layers), each step can have a characteristic throughput. For an inspection operation among the fabrication steps, throughput can characterize how quickly an inspection process can clear a wafer before moving on to the next wafer. Innovations in the design or functions of inspection tools can increase throughput, or at least resolve problems in another aspect while mitigating adverse impact to throughput.

[0027] [Noise elimination is a continuous effort in the field of photolithographic fabrication. For ultrasmall structures (e.g., nano-transistors on a chip), an inspection tool having sub-nanometer resolution (high resolution or high sensitivity) can be essential in ascertaining whether a photolithographic fabrication step is non-compliant. Identifying and fixing non-compliant processes increases yield. High resolution and sensitivity goes hand in hand with higher sensitivity to noise. A small vibration in an SEM system can cause blurring of an acquired image, thereby inviting large error margins and uncertainty in the inspection processes. SEMs are a class of complex tools that are assembled using numerous precision parts and modules, many of which are ‘active’ in some form (e.g., communicating an electrical signal, moving or actuating a stage or lock, circulating a fluid or gas, or the like). Hence, when an SEM image is captured using an SEM tool (the image comprising some noise), it can be difficult to identify, or even narrow down, the source of the noise due to the complexity of the SEM assembly] .

[0028] Depending on system complexity, noise analysis techniques can have limited usefulness in identifying a source of noise (e.g., due to physics-based limitations). In one example, for a given sampling rate (e.g., SEM line scan rate), the Nyquist frequency is the frequency whose period is twice the interval between samples of a sampled signal (or half the sampling frequency). When the frequency of a signal is higher than the Nyquist frequency of the sampler, the resulting discrete-time sequence can include false lower frequency components known as aliasing.

[0029] Embodiments of the present disclosure provide devices and operations to determine real noise signals and avoid false signals and artifacts. For example, devices and operations described herein provide capabilities for efficiently and accurately identify true noise frequencies from the noise content of an SEM image. Embodiments of the present disclosure can overcome the difficulties of conventional noise analysis techniques in dealing with false signals (aliased signals).

[0030] Objects and advantages of the disclosure can be realized by the elements and combinations as set forth in embodiments described herein. However, embodiments of the present disclosure are not necessarily required to achieve such example objects or advantages. Some embodiments can achieve a different feature or enhancement without necessarily achieving any expressly stated object or advantage.

[0031] As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component can comprise A or B, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or A and B.As a second example, if it is stated that a component can comprise A, B, or C, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0032] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings, the same or like reference numbers refer to the same or like components or entities, and only the differences with respect to the individual embodiments are described.

[0033] FIG. 1 illustrates a schematic diagram of an example electron beam inspection (EBI) system 100, consistent with embodiments of the present disclosure. EBI system 100 can be used for imaging. EBI system 100 can comprise a main chamber 101, a load / lock chamber 102, a beam tool 104, and an equipment front end module (EFEM) 106. Beam tool 104 can be located within main chamber 101. EFEM 106 can comprise a first loading port 106a and a second loading port 106b. EFEM 106 can comprise additional loading port(s). First loading port 106a and second loading port 106b can receive wafer front opening unified pods (FOUPs) that contain wafers (e.g., semiconductor wafers or wafers made of other material(s)) or samples to be inspected (wafers and samples may be used interchangeably). The term “lot” can refer to a plurality of wafers that can be loaded for processing as a batch.

[0034] One or more robotic arms (not shown) in EFEM 106 can transport the wafers to load / lock chamber 102. Load / lock chamber 102 can be connected to a load / lock vacuum pump system (not shown) that can evacuate gas molecules in load / lock chamber 102 to reach a first pressure below atmospheric pressure. After reaching the first pressure, one or more robotic arms (not shown) can transport the wafer from load / lock chamber 102 to main chamber 101. Main chamber 101 can be connected to a main chamber vacuum pump system (not shown) that can evacuate gas molecules in main chamber 101 to reach a second pressure below the first pressure. After reaching the second pressure, the wafer can be subject to inspection by beam tool 104. Beam tool 104 can be a single-beam system or a multibeam system.

[0035] A controller 109 can be electronically connected to beam tool 104. Controller 109 can be a computer configured to execute various controls of EBI system 100. While controller 109 is shown in FIG. 1 as being outside of the structure that includes main chamber 101, load / lock chamber 102, and EFEM 106, in some embodiments, controller 109 can be part of the structure.

[0036] In some embodiments, controller 109 comprises one or more processors (not shown). A processor may be a generic or specific electronic device capable of manipulating or processing information. For example, the processor can comprise a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), an optical processor, a programmable logic controllers, a microcontroller, a microprocessor, a digital signal processor, an intellectual property (IP) core, a Programmable Logic Array (PLA), a Programmable Array Logic (PAL), a Generic Array Logic (GAL), a Complex Programmable Logic Device (CPLD), a Field-Programmable Gate Array (FPGA), a System On Chip (SoC), an Application-Specific Integrated Circuit (ASIC), any type circuitry capable of data processing, or any combination ofany number thereof. The processor can be a virtual processor. The virtual processor can include one or more processors distributed across multiple machines or devices coupled via a network.

[0037] In some embodiments, controller 109 further comprises one or more memories (not shown). A memory can be a generic or specific electronic device capable of storing instructions, code, or data accessible by the processor (e.g., via a bus). For example, the memory can comprise a random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, any type of storage device, or any combination of any number thereof. The instructions, code, or data can include an operating system (OS) and one or more application programs (or “apps”) for specific tasks. The memory can be a virtual memory. The virtual memory can include one or more memories distributed across multiple machines or devices coupled via a network.

[0038] FIG. 2A illustrates a schematic diagram of an example beam tool 104A and an image processing system 199 that can be configured for use with EBI system 100 (FIG. 1), consistent with embodiments of the present disclosure. Beam tool 104A can be provided as beam tool 104 of FIG. 1. In some embodiments, beam tool 104 A is a single-beam tool that uses one primary electron beam to scan locations on a wafer in series (one location after the other).

[0039] Beam tool 104 A can comprise a wafer holder 136 supported by motorized stage 134 to hold a wafer 150 to be inspected. Beam tool 104A can also comprise an electron emitter comprising several elements, such as a cathode 103, an anode 121, and a gun aperture 122. Beam tool 104A can also comprise a beam limit aperture 125, a condenser lens 126, a column aperture 135, an objective lens assembly 132, and a detector 144. Objective lens assembly 132 can be a swing objective retarding immersion lens (SORIL) or a modified version thereof. Objective lens assembly 132 can comprise a pole piece 132a, a control electrode 132b, a deflector unit 132c, and an exciting coil 132d. In a detection or imaging process, an electron beam 161 emanating from the tip of cathode 103 can be accelerated by anode 121 voltage, can pass through gun aperture 122, beam limit aperture 125, condenser lens 126, and can be focused into a probe spot 170 by objective assembly 132. Electron beam 161 can impinge onto the surface of wafer 150. A deflector can be used to scan probe spot 170 across the surface of wafer 150 (e.g., deflector unit 132c or other deflector(s) in the SORIL lens). Secondary or scattered particles, such as secondary electrons or scattered primary electrons emanated from the wafer surface can be collected by detector 144 to determine intensity of the beam and so that an image of an area of interest on wafer 150 can be reconstructed.

[0040] In some embodiments, image processing system 199 comprises an image acquirer 120, a storage 130, and controller 109. Image acquirer 120 can comprise one or more processors. For example, image acquirer 120 can comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, or the like. Image acquirer 120 can be connected with detector 144 of beam tool 104A through a communication medium, such as an electrical conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or the like. Image acquirer 120can receive a signal from detector 144. Image acquirer 120 can construct an image based on the signal from detector 144. Image acquirer 120 can thus acquire images of wafer 150. Image acquirer 120 can also perform various post-processing functions, such as image averaging, generating contours, superimposing indicators on an acquired image, or the like. Image acquirer 120 can perform adjustments of brightness and contrast, etc. of acquired images. Storage 130 can be a storage medium, such as a hard disk, random access memory (RAM), cloud storage, other types of computer readable memory, or the like. Storage 130 can be coupled with image acquirer 120 and can be used for saving scanned raw image data as original images, as well as post-processed images. Image acquirer 120 and storage 130 can be connected to controller 109. In some embodiments, image acquirer 120, storage 130, and controller 109 can be integrated together as one electronic control unit (e.g., on the same chip).

[0041] In some embodiments, image acquirer 120 acquires one or more images of a sample based on an imaging signal received from detector 144. An imaging signal can correspond to a scanning operation that is executed for the purposes of charged particle imaging. An acquired image can be a single image comprising a plurality of imaging areas that can contain various features of wafer 150. The single image can be stored in storage 130. Imaging can be performed on the basis of imaging frames.

[0042] The condenser and illumination optics of the electron beam tool can comprise, or be supplemented by, electromagnetic quadrupole electron lenses. In the example of FIG.2A, electron beam tool 104A comprises a first quadrupole lens 148 and a second quadrupole lens 158. The quadrupole lenses can be used for controlling the electron beam. First quadrupole lens 148 can be controlled to adjust the beam current and second quadrupole lens 158 can be controlled to adjust the beam spot size and beam shape.

[0043] The single primary beam of beam tool 104A can be used to generate secondary electrons by interacting with wafer 150. Detector 144 can be placed proximal to or aligned with optical axis 105. The primary electron beam can be configured to travel along optical axis 105. Accordingly, detector 144 can comprise a hole at its center so that the primary electron beam can pass through to reach wafer 150. In some embodiments, a detector can be placed off-axis relative to the optical axis along which the primary electron beam travels. In such instances a beam separator can be provided to divert secondary electron beams toward a detector placed off-axis.

[0044] The images generated by scanning charged-particle microscope (e.g., an SEM) can be used for defect inspection. A generated image capturing a test device region of a wafer can be compared with a reference image of the same test device region. The reference image can be predetermined (e.g., by simulation) and include no known defect. If a difference between the generated image and the reference image exceeds a tolerance level, a potential defect can be identified. For another example, an SEM is used to scan multiple regions of a wafer, each region including a test device region designed to be constant from region to region. The SEM can generate multiple images capturing those test device regions as fabricated. The multiple images can be compared with each other. If a difference between the multiple images exceeds a tolerance level, a potential defect can be identified.

[0045] Another example of a charged particle beam apparatus will now be described with reference to FIG. 2B, which illustrates a schematic diagram of an example beam tool 104B and an image processing system 290 that can be configured for use in EBI system 100 (FIG. 1), consistent with embodiments of the present disclosure. Beam tool 104B can be provided as beam tool 104 of FIG. 1. In some embodiments, beam tool 104B is a multibeam tool that uses multiple beams of primary electrons to scan multiple locations on a wafer. It is appreciated that hardware and functions described in reference to an element in one of FIGS.2A and 2B can be applicable to a corresponding element in the other of FIGS.2A and 2B (e.g., structure and function of a condenser lens, defect analysis of a sample, or the like), unless infeasible.

[0046] Beam tool 104B can comprise a charged-particle source 202 configured to emit a primary charged-particle beam 210, a gun aperture 204, a condenser lens 206, a source conversion unit 212, a primary projection optical system 220, a motorized wafer stage 280, a wafer holder 282, a secondary optical system 242, and a charged-particle detection device 244. Primary charged-particle beam 210 can comprise a plurality of beamlets 214, 216, and 218 of primary charged-particle beam 210. Primary projection optical system 220 can comprise a beam separator 222, a deflection scanning unit 226, and an objective lens 228. Charged-particle detection device 244 can comprise detection sub-regions 246, 248, and 250.

[0047] Charged-particle source 202, gun aperture 204, condenser lens 206, source conversion unit 212, beam separator 222, deflection scanning unit 226, and objective lens 228 can be aligned with a primary optical axis 260 of beam tool 104B. Secondary optical system 242 and charged-particle detection device 244 can be aligned with a secondary optical axis 252 of beam tool 104B.

[0048] Charged-particle source 202 can emit one or more charged particles, such as electrons, protons, ions, muons, or other particle carrying electric charges. In some embodiments, charged-particle source 202 can be an electron source. For example, charged-particle source 202 can comprise a cathode, an extractor, or an anode. Primary electrons can be emitted from the cathode and extracted or accelerated to form primary charged-particle beam 210 (in this case, a primary electron beam) with a crossover 208 (virtual or real crossover). For simplicity, some embodiments will be described in the context of electrons as the charged particles. However, it is appreciated that any charged particle can be used in any embodiment of this disclosure, not limited to electrons. Primary charged-particle beam 210 can be visualized as being emitted from crossover 208. Gun aperture 204 can block off peripheral charged particles of primary charged-particle beam 210 to reduce Coulomb interactions (or Coulomb effect). The Coulomb effect can cause the size of a probe spot (or beam spot) of an electron beam to increase and blur, thereby reducing resolution.

[0049] Source conversion unit 212 can comprise an array of image-forming elements and an array of beam-limit apertures. The array of image-forming elements can comprise an array of micro-deflectors or micro-lenses. The array of image-forming elements can form a plurality of parallel images (virtual or real) of crossover 208 with a plurality of beamlets 214, 216, and 218 of primary charged-particle beam210. The array of beam-limit apertures can limit the plurality of beamlets 214, 216, and 218. While three beamlets 214, 216, and 218 are shown in FIG. 2B, embodiments of the present disclosure are not so limited. In some embodiments, beam tool 104B can be configured to generate a first number of beamlets. For example, the first number of beamlets can be in a range from 1 to 1000 or from 200-500. The first number of beamlets can be, for example, 400 beamlets.

[0050] Condenser lens 206 can focus primary charged-particle beam 210. The electric currents of beamlets 214, 216, and 218 downstream of source conversion unit 212 can be varied by adjusting the focusing power of condenser lens 206 or by changing the radial sizes of the corresponding beam-limit apertures within the array of beam -limit apertures. Condenser lens 206 may be an adjustable condenser lens that may be configured so that the position of its first principal plane is movable. The adjustable condenser lens may be configured to be magnetic, which may result in off-axis beamlets 216 and 218 landing on the beamlet-limit apertures with rotation angles. The rotation angles change with the focusing power and the position of the first principal plane of the adjustable condenser lens. In some embodiments, the adjustable condenser lens may be an adjustable anti-rotation condenser lens, which involves an antirotation lens with a movable first principal plane. An example of an adjustable condenser lens is further described in U.S. Publication No. 2017 / 0025241, which is incorporated by reference herein in its entirety.

[0051] Objective lens 228 can focus beamlets 214, 216, and 218 onto a wafer 230 for imaging, and can form a plurality of probe spots 270, 272, and 274 on a surface of wafer 230.

[0052] Beam separator 222 can be a beam separator of Wien filter type, generating an electrostatic dipole field and a magnetic dipole field. The force exerted by the electrostatic dipole field on a charged particle (e.g., an electron) of beamlets 214, 216, and 218 can be substantially equal in magnitude and opposite in a direction to the force exerted on the charged particle by magnetic dipole field. Beamlets 214, 216, and 218 can, therefore, pass straight through beam separator 222 with zero or minimal deflection angle. However, the total dispersion of beamlets 214, 216, and 218 generated by beam separator 222 can also be non-zero. Beam separator 222 can separate secondary charged-particle beams 236, 238, and 240 from beamlets 214, 216, and 218 and direct secondary charged-particle beams 236, 238, and 240 towards secondary optical system 242.

[0053] Deflection scanning unit 226 can deflect beamlets 214, 216, and 218 to scan probe spots 270, 272, and 274 over a surface area of wafer 230. In response to the incidence of beamlets 214, 216, and 218 at probe spots 270, 272, and 274, secondary charged-particle beams 236, 238, and 240 can be emitted from wafer 230. Secondary charged-particle beams 236, 238, and 240 can comprise charged particles (e.g., electrons) with a distribution of energies. For example, secondary charged-particle beams 236, 238, and 240 can be secondary electron beams including secondary electrons (energies < 50 eV) and backscattered electrons (energies between 50 eV and landing energies of beamlets 214, 216, and 218). Secondary optical system 242 can focus secondary charged-particle beams 236, 238, and 240 onto detection sub-regions 246, 248, and 250 of charged-particle detection device 244. Detection sub-regions 246, 248, and 250 can be configured to detect corresponding secondary charged-particle beams 236, 238,and 240 and generate corresponding signals (e.g., voltage, current, or the like) used to reconstruct a scanning charged-particle microscope image (e.g., SEM image) of structures on or underneath the probed surface of wafer 230.

[0054] The generated signals can represent intensities of secondary charged-particle beams 236, 238, and 240 and can be provided to image processing system 290 that is in communication with charged-particle detection device 244, primary projection optical system 220, and motorized wafer stage 280. The movement speed of motorized wafer stage 280 can be synchronized and coordinated with the beam deflections controlled by deflection scanning unit 226, such that the movement of the scanning of probe spots (e.g., probe spots 270, 272, and 274) can orderly cover regions of interests on the wafer 230. The movement of the scanning can be, for example, a raster movement. The parameters of such synchronization and coordination can be adjusted to adapt to different materials of wafer 230. For example, different materials of wafer 230 can have different resistance-capacitance characteristics that can cause different signal sensitivities to the movement of the scanning of the probe spots.

[0055] The intensity of secondary charged-particle beams 236, 238, and 240 can vary according to the external or internal structure of wafer 230, and thus can indicate whether wafer 230 includes defects. Moreover, as discussed above, beamlets 214, 216, and 218 can be projected onto different locations of the top surface of wafer 230, or different sides of local structures of wafer 230, to generate secondary charged-particle beams 236, 238, and 240 that can have different intensities. Therefore, by mapping the intensity of secondary charged-particle beams 236, 238, and 240 with the areas of wafer 230, image processing system 290 can reconstruct an image that reflects the characteristics of internal or external structures of wafer 230.

[0056] In some embodiments, image processing system 290 can include an image acquirer 292, a storage 294, and a controller 296. Image acquirer 292 can comprise one or more processors. For example, image acquirer 292 can comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, or the like, or a combination thereof. Image acquirer 292 can be communicatively coupled to charged-particle detection device 244 of beam tool 104B through a medium such as an electric conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or a combination thereof. Image acquirer 292 can receive a signal from charged-particle detection device 244. Image acquirer 292 can construct an image (e.g., as a digital representation, an image data file) based on one or more signals from charged-particle detection device 244. Image acquirer 292 can thus acquire scanning charged-particle microscope images of probed regions of wafer 230. Image acquirer 292 can perform various post-processing functions, such as generating contours that are representative of structures in the image, superimposing indicators on an acquired image, or the like. Image acquirer 292 can perform adjustments of brightness and contrast of acquired images.

[0057] In some embodiments, storage 294 is a storage medium such as a hard disk, flash drive, cloud storage, random access memory (RAM), other types of computer-readable memory, or the like. Storage 294 can be coupled with image acquirer 292. Storage 294 can be used for saving scanned raw image dataas original images, as well as post-processed images. Image acquirer 292 and storage 294 can be connected to controller 296. Image acquirer 292, storage 294, and controller 296 can be integrated together as one control unit.

[0058] In some embodiments, image acquirer 292 acquires one or more scanning charged-particle microscope images of a wafer based on one or more imaging signals received from charged-particle detection device 244. An imaging signal can correspond to a scanning operation for conducting charged-particle imaging. An acquired image can be a single image comprising a plurality of imaging areas or an image of an imaging area. The single image can be stored in storage 294. The single image can be an original image that is divided into a plurality of regions. Each of the regions can comprise one imaging area containing a feature of wafer 230. The acquired images can comprise multiple images of a single imaging area of wafer 230 sampled multiple times over a time sequence. The multiple images can be stored in storage 294. In some embodiments, image processing system 290 performs image processing steps with the multiple images of the same location of wafer 230.

[0059] In some embodiments, image processing system 290 comprises measurement circuits (e.g., analog-to-digital converters) to obtain a distribution of the detected secondary charged particles (e.g., secondary electrons). The charged-particle distribution data collected during a detection time window, in combination with corresponding scan path data of beamlets 214, 216, and 218 incident on the wafer surface, can be used to reconstruct images of the wafer structures under inspection. The reconstructed images can be used to reveal various features of the internal or external structures of wafer 230, and thereby can be used to reveal defects in the wafer.

[0060] In some embodiments, when electrons of primary charged-particle beam 210 are projected onto a surface of wafer 230 (e.g., probe spots 270, 272, and 274), the electrons of primary charged-particle beam 210 can penetrate the surface of wafer 230 for a certain depth to interact with deeper matter in wafer 230. Some electrons of primary charged-particle beam 210 can elastically interact with (e.g., in the form of elastic scattering or collision) the materials of wafer 230. Electrons can be reflected or recoiled out of the surface of wafer 230. An elastic interaction conserves the total kinetic energies of the bodies (e.g., electrons of primary charged-particle beam 210) of the interaction, in which the kinetic energy of the interacting bodies does not convert to other forms of energy (e.g., heat, electromagnetic energy, or the like). Such reflected electrons generated from elastic interaction may be referred to as backscattered electrons (BSEs).

[0061] In some embodiments, some electrons of primary charged-particle beam 210 inelastically interact with (e.g., in the form of inelastic scattering or collision) the materials of wafer 230. An inelastic interaction does not conserve the total kinetic energies of the bodies of the interaction, in which some or all of the kinetic energy of the interacting bodies convert to other forms of energy. For example, through the inelastic interaction, the kinetic energy of some electrons of primary charged-particle beam 210 can cause electron excitation and transition of atoms of the materials. Such inelastic interaction can also generate electrons that exit the surface of wafer 230, which may be referred to as secondary electrons(SEs). Yield or emission rates of BSEs and SEs can depend on, e.g., the material under inspection and the landing energy of the electrons of primary charged-particle beam 210 landing on the surface of the material, among others. The energy of the electrons of primary charged-particle beam 210 can be imparted in part by its acceleration voltage (e.g., the acceleration voltage between the anode and cathode of charged-particle source 202 in FIG. 2B). The quantity of BSEs and SEs can be more or fewer (or even the same) than the injected electrons of primary charged-particle beam 210.

[0062] An image can be in the form of an analog signal (e.g., detector signals from an SEM).Alternatively, or additionally, an image can have a digital form, which can be stored as a digital file, reside in volatile memory, be transmitted as a digital signal, or the like. When describing image analysis, image manipulation, and other image processes, it is to be appreciated that such processes can be executed on any form or representation of the image. For example, cropping an image can correspond to truncating the corresponding pixels in a digital image file.

[0063] The images generated by SEM can be used for defect inspection. For example, a generated image of a test device region of a wafer can be compared with a reference image that corresponds to the same test device region. The reference image can be predetermined (e.g., by simulation) and include no known defect. If a difference between the generated image and the reference image exceeds a tolerance level, a potential defect can be identified. For another example, the SEM can scan multiple regions of the wafer, each region including a test device region designed as the same, and generate multiple images capturing those test device regions as manufactured. The multiple images can be compared with each other. If a difference between the multiple images exceeds a tolerance level, a potential defect can be identified.

[0064] FIG. 3 illustrates an example of a set of SEM images 300, consistent with embodiments of the present disclosure. In some embodiments, SEM images 300 are acquired via beam tool 104A or 104B (FIGS.2A and 2B). The visual representation of SEM images in FIG.3 can be one example representation of image information. Image information can be represented in several forms. For example, SEM images 300 can be represented as digital data (e.g., saved in memory as ones and zeros). The graphical representation shown in FIG.3 can be what is shown at a computer display based on an inspection measurement using the systems described in FIGS. 1-2B or based on opening a digital file with image information. An analog representation or partially analog representation can be in the form of electrical signals from a detector (e.g., charged-particle detection device 244 (FIG. 2B)) along with positional information of the scanned electron beam.

[0065] In some embodiments, analyses and processing of image information will be described in the context of the graphical representation of FIG. 3. However, it is appreciated that such analyses and image processing operations are applicable to any form of representation of an image. For example, the generating of SEM images 300 from an inspection measurement can refer to one or more digital functions for determining pixel intensities of SEM images 300 as part of post-processing of detection signals from an SEM detector.

[0066] In some embodiments, each of SEM images 300 is acquired at a same region of a wafer. The wafer, at the inspected region, can comprise a bare portion 302 of the wafer, as well as patterns 304 disposed on the wafer. The set of SEM images 300 can comprise an SEM image 306, an SEM image 308, an SEM image 310, and an SEM image 312.

[0067] For the purposes of clarifying the broader context of noise analyses embodiments in the present disclosure, SEM images 306, 308, 310, and 312 will be described according to a specific example involving a horizontal raster scan and specific sampling rates. It is to be appreciated that the specific scan method and sampling rates in the example are not limiting. And implementations of embodiments described herein include any suitable scan method and sampling rates.

[0068] In the example, a horizontal raster can scan an electron beam over the wafer one horizontal line at a time (e.g., left to right) (the electron beam can be a beam in an SEM tool (e.g., beam tool 104A / B in FIGS. 2A and 2B)). For example, an upper-left comer 314 of an upper-most line 316 (e.g., row) of SEM image 306 can represent the starting point of an SEM raster scan. As one line scan ends, the electron beam can fly back to the left and start a new line scan, iterating the process until the entirety of SEM image 306 is captured (the same can be performed when capturing SEM images 308, 310, and 312). Scanning a line takes a finite amount of time. The time is knowable based on scan speed of the electron beam. The per-line scan time can be adjusted by adjusting the scan speed. If one sample is defined as one line (e.g., one row), then the process of scanning from line to line can have an associated line sampling frequency. Since the scanning time per line is known (e.g., the line scan speed is known), the line sampling frequency (the line-to-line frequency, labeled as fsin FIG.3) can be calculated as the inverse of the per-line scan time.

[0069] In the example of FIG. 3, the scan speed is different from one SEM image to the next. Hence, SEM image 306 can correspond tofy = 2.88 kHz, SEM image 308 can correspond to fy = 5.76 kHz, SEM image 310 can correspond tofy = 11.36 kHz, and SEM image 312 can correspond tofy = 21.48 kHz (these are non-limiting examples of sampling frequencies). By varying the sampling frequencies, the presence of noise can be revealed. While the stripe of pattern 304 are much straighter in reality than shown in the SEM images, the effects of noise can cause the image of the stripes to bend. For example, the stripe in SEM image 312 (fastest line sampling rate) has a slight wave or ripples of the edges (the actual stripe on the wafer is much straighter). In SEM image 310 (slower line sampling rate), the ripples have a shorter wavelength and larger amplitude. In SEM image 308 (even slower line sampling rate), the ripples have an even shorter wavelength and an even larger amplitude. And in SEM image 306 (slowest line sampling rate), the ripples are the most pronounced.

[0070] In some embodiments, the (false) ripples can affect the accuracy in determining a position of the edge of the stripes. Accuracy of edge placement is an important metric in the overlay of different device layers. Large edge placement errors (EPE) can result in reduced yield. The position of an edge can be calculated by, for example, determining a contour 317 of the stripe edge. The determination of contour 317 can be performed in post-processing of the image (e.g., by at least one of the processors described inreference to FIGS. 1-2B). A contour that follows an edge with noise effects can produce inaccurate positioning data.

[0071] Contour 317 can be determined via an image vibrational analysis technique. Image vibrational analysis can be used to perform spectral analysis on the grayscale signal of each row in the image. By analyzing the phase delay of the main frequency components in the spectrum, the technique determines the time differences for each row and converts the time differences into row noise information. Since image vibration analysis treats each line as a whole without considering individual edges, only one noise curve can be extracted regardless of the number of edges (e.g., there are four edges in each image). Alternatively, a visual approximation can be used to determine of the number of “spikes” at the stripe edge. However, a visual determination can be too imprecise and inconsistent to yield reliable noise data.

[0072] Furthermore, the ripples reveal a presence of noise. Knowing that noise is present is not enough information to solve the noise problem. Identifying the source of the noise can be difficult because electron beam tools can be very complex. It is desirable to identify the source of the noise, for then steps can be taken to mitigate the noise (e.g., redesigning an actuator, implementing strategically placed dampers, shielding noisy electronics, or the like).

[0073] Embodiments of the present disclosure provide devices and operations for correct edge extraction from a noisy image, as well as determination of the correct noise frequency in frequency regimes where aliasing is a concern.

[0074] FIG. 4 illustrates an example of graphical data analysis 400, consistent with embodiments of the present disclosure. In some embodiments, graphical data analysis 400 is performed on an SEM image 406 by analyzing one or more lines of pixels. SEM image 406 can correspond to an image in set of SEM images 300 (e.g., SEM image 306) (FIG. 3). A region of a wafer can be scanned using an SEM to capture SEM image 406. The wafer, at the inspected region, can comprise a bare portion 402 of the wafer, as well as patterns 404 (e.g., stripe patterns) disposed on the wafer.

[0075] A line 416 of SEM image 406 can be analyzed. Graph 418 is a plot representation of the gray level data present in line 416. The vertical axis (grayscale) represents a pixel brightness in arbitrary units, with a gray level of zero corresponding to black pixels (dark) and a gray level of 256 corresponding to white pixels (bright) (any arbitrary grayscale can be used, e.g., 0 to 1, 1 to 10, or the like). The horizontal axis of graph 418 can correspond to horizontal pixel position. For example, if SEM image 406 is 512 pixels wide (also referred to as scanwidth), the left-most pixel of line 416 can be the zeroth pixel and the right-most pixel can be the 5111,1pixel of line 416. Plot line 420 corresponds to the gray level data of line 416. An SEM image is not limited to 512 pixels along a given direction and can have any suitable width / length based on the scan settings of the SEM tool.

[0076] A histogram can be used as part of graphical data analysis 400. Histogram data can be generated from the gray level data of graph 418. The histogram data is shown in FIG. 4 via histogram 422. The vertical axis of histogram 422 is scaled to match the vertical axis of grayscale axis of graph 418. Thehorizontal axis of histogram 422 indicates the number of occurrences or counts of a given gray level value.

[0077] In some embodiments, one or more processors of a computing device (e.g., a controller 109 (FIG. 1), image processing system 199 (FIG. 2A), image processing system 290 (FIG.2B), or the like) is used to generate the data of graph 418 and histogram 422, as well as analyze the data. The computing device, analyzing histogram 422, can determine that the highest counts of gray level are centered around gray levels 57 and 129. It is to be appreciated that these are example gray level values specific to the illustrated histogram 422. In general, the values can be different from one image to another depending on SEM settings, structure of patterns 404, or other variables. An important feature is that the computing device can be configured to determine the two gray level peaks of the histogram data and determine the edges of patterns 404 by determining locations of plot 420 at which the plot goes from low histogram peak (e.g., 57) to high histogram peak (e.g., 129) or vice versa. The computing device can be configured to search for the edges of the stripe patterns between the low and high histogram peaks.

[0078] For determining the edges of patterns 404, the computing device can be programmed to include a trigger and noise suppression band 424 about a central value 426. Central value 426 can be a center value between the low histogram peak and the high histogram peak (e.g., central gray level value of 93). Central value 426 can serve as an approximation (e.g., a first guess, starting point, or trigger) in the search for the edges of patterns 404. As plot 420 crosses central value 426, an approximate edge position range 428 can be defined (e.g., search boundaries). To determine a location for an edge of patterns 404, hysteresis can be used to prevent false triggering.

[0079] Within approximate edge position range 428, the computing device can determine a more exact position of the edge based on a weight-based threshold (adjustable). An example of adjustable weighting is shown in FIG.4. In the example, the computing device can assign a weight of 0.2 to the low peak value and a weight of 0.8 to the high peak value, thereby setting a threshold of 0.2 * 57 + 0.8 x 129 = 115. The computing device can then determine the pixel position of an edge 430 having a gray level that matches the threshold value of 115. For different SEM images, the optimal weight coefficients can be different and can be suitably adjusted.

[0080] In some embodiments, the visual representation of graph 418 and histogram 422 of FIG. 4 can be one example representation of image information. Image information can be represented in several forms. For example, graph 418 and histogram 422 can be represented as digital data (e.g., saved in memory as ones and zeros). The graphical representation shown in FIG. 4 can be what is shown at a computer display. Analyses and processing of graph information will be described in the context of the graphical representation of FIG. 4. However, it is appreciated that such analyses and processing of graphable data are applicable to any form of representation of the graphable data. For example, the analysis and extraction of information from graph 418 and histogram 422 can refer to one or more digital functions that receive, as input, the digital data containing the information of graph 418 and histogram 422.

[0081] FIG. 5 illustrates an example of a set of SEM images 500, consistent with embodiments of the present disclosure. In some embodiments, SEM images 500 comprises an SEM image 506, an SEM image 508, an SEM image 510, and an SEM image 512. Unless otherwise stated, some elements shown in FIG. 5 can have substantially similar structures as corresponding elements of FIG. 3. For brevity, description of elements in FIG.5 that are substantially similar to structures in FIG. 3 can be inferred from the above description of FIG.3. For corresponding elements, the leading (left-most) digit(s) can denote the figure in which the elements first appear while the trailing (right-most) digit(s) can identify the element. Examples of corresponding elements can include a bare portion 502 of a wafer, patterns 504 disposed on the wafer, and SEM images 506, 508, 510, and 512.

[0082] Edge-extracted contour 517 can be different from contour 317 (FIG.3). Edge-extracted contour 517 can be comprised of edge positions extracted via the process described above in reference to FIG. 4.The edge positions can be extracted line by line so as to generate the dot pattern for edge-extracted contour 517. For visual comparison, contour 317 is reproduced in FIG. 5. Edge-extracted contour 517 is more accurate to the actual edge of patterns 504 on the wafer as compared to contour 317. A desirable feature of the edge extraction process of FIG. 4 is that each determined edge (and noise information contained therein) is analyzable edge by edge (e.g., four edges in an image) and line by line, whereas the image vibrational analysis for edge 317 yielded only one noise data point for an entire line of pixels. Spectral analysis can be performed on edge-extracted contour 517 to analyze noise information.

[0083] FIG. 6 illustrates an example graph 600 of noise spectra, consistent with embodiments of the present disclosure. In some embodiments, the noise spectra includes data that correspond to the edge extractions described above in reference to FIGS. 4 and 5. Edge-extracted contour 517 (FIG. 5) was extracted based on the technique referencing of FIG.4 and is specifically associated with line sampling frequency f = 11.36 kHz (SEM image 510 (FIG. 5)). The information of edge-extracted contour 517 can be converted into power spectral density (PSD) spectrum 606 (or simply spectrum 606) (dashed black plot). Numerous graphs similar to FIG. 6 can be generated, but for each edge-extracted contour identified in the SEM images. For the conversion, a fast Fourier transform (FFT) or other suitable spectral conversion method can be used. Edge-extracted contours can be obtained in a similar manner for each of SEM images 506, 508, and 512 for different f. The resulting spectra are shown as spectrum 602 (f, = 2.88 kHz) (solid black plot), spectrum 604 (f = 5.76 kHz) (solid gray plot), and spectrum 608 (f = 21.48 kHz) (dotted gray plot). The vertical axis of graph 600 represents the power spectral density. The horizontal axis of graph 600 represents the frequency.

[0084] Candidate noise features can be determined based on a noise floor threshold condition. Noise features can include noise peaks 610 (in spectrum 602, fs= 2.88 kHz), 612 (in spectrum 604, fs= 5.76 kHz), 614 (in spectrum 606, fs= 11.36 kHz), and 616 (in spectrum 608, fs= 21.48 kHz). Noise peak 610 occurs at 1.159 kHz. Noise peak 612 occurs at 1.631 kHz. Noise peak 614 occurs at 4.393 kHz. Noise peak 616 occurs at 5.748 kHz. It is noted that the acquisition of set of SEM images 500 is performed such that the sole difference between the SEM images is the line sampling rate. In the case that the noise isindependent of the sampling rate, it is expected that an identified noise frequency would be consistent across the SEM images. From this understanding, it is inferred that the difference in the noise peaks (difference of frequencies) is indicative of frequency aliasing.

[0085] As explained earlier, aliasing (false signals) can occur if a signal (e.g., noise signal) that interacts with a measurement (e.g., SEM image acquisition) has a frequency that is higher than the Nyquist frequency associated with the sampling rate of the measurement (e.g., line sampling rate A). In the example for line sampling frequencies of 2.88 kHz, 5.76 kHz, 11.36 kHz, and 21.48 kHz, their respective Nyquist frequencies are 1.44 kHz, 2.88 kHz, 5.68 kHz, and 10.74 kHz. In this example, if the source of the noise has a characteristic frequency below a given Nyquist frequency, then it can be trusted that the corresponding noise peak is indeed a true (non-aliased) noise signal and its frequency position along the horizontal frequency axis is accurate.

[0086] However, certain situations can arise in which the noise signal is determined or suspected to have a frequency higher than the Nyquist frequency (e.g., via process of elimination in consideration of active elements in an SEM). In such situation, de-aliasing should be performed. Described below are some embodiments that provide de-aliasing operations for use with data obtained from edge extraction as described in reference to FIGS. 4 and 5.

[0087] In some embodiments, the frequency corresponding to an aliased noise peak is denoted by fauas (e.g., faiias= 1.159 kHz for noise peak 610, if indeed noise peak 610 is an alias). The alias frequency, the sampling frequency, and the true noise frequency f„oise are related as in equation 1:> > << <

[0088] Using equation 1, the true noise frequency f„riKeof a noise signal can be ascertained. In equation 1, n is a positive integer (e.g., n = 1, 2, 3, ...). The noise peak frequency fauasis assumed to be an aliased frequency. Equation 1 is a branch function. Selecting an appropriate branch of the function can be based on which condition of the branches is satisfied by a given value of fnoise. For example, ripple edges or image blurring is observed in an SEM image, indicating a presence of noise. Then, active components in an SEM, whether mechanical or electrical, can be ranked according to their likelihood of causing the noise in the captured image. Based on the ranking of the active components, it is supposed that the true noise frequency is within the range 0.5ancl 1 MHz. While this example begins with a suspected noise frequency (to illustrate an example), it is to be appreciated that the method is even more powerful in the context of unknown noise sources, as will be described further below at the conclusion of the example.

[0089] The algorithmic operations disclosed herein can be used to recover one or more true (non-aliased) frequencies of the noise. Continuing with the example above, it is deemed likely that the true noise frequency is 27.1 kHz (e.g., due to the RPM of an actuator) based on the rankings. Since 27.1 kHz is higher than the Nyquist frequencies associated with SEM images 500 (FIG. 5), it is determined that oneor more of noise peaks 610, 612, 614, and 616 can be aliased signals that correspond to the potential true noise frequency of 27.1 kHz (recall that respective Nyquist frequencies are 1.44 kHz, 2.88 kHz, 5.68 kHz, and 10.74 kHz). Based on the above determination, the algorithm can set f„oiseas in equation 2:fnoise = 27.1 kHz Eq. 2.

[0090] Equation 2 represents an arbitrary setting of the noise frequency using a stand-in or proxy value. It is to be appreciated that, at this stage of the algorithm, it is not yet known whether 27.1 kHz is a true noise frequency. Analyzing the particulars off', = 2.88 kHz (corresponds to SEM image 506 (FIG. 5) and noise peak 610), it can be determined that the fulfdled branch condition is the upper branch of equation 1, as verified by equation 3, where n = 9:9 / s < fnoise (27.1 kHz) < 9.5fsEq. 3.

[0091] Using the selected branch of equation 1, the alias frequency of fnoisecan be calculated as in equation 4:f alias fnoise fs 1.18 kHz Eq. 4.

[0092] The calculated alias frequency f alias = 1.18 kHz is within 1.72% (margin of error) of the measured frequency of 1.159 kHz of noise peak 610. Therefore, it can be determined with a high degree of confidence that noise peak 610 is an aliased signal corresponding to a true noise signal having a frequency fnoise= 27.1 kHz.

[0093] The above steps of the algorithm can be repeated for each of SEM images 508, 510, and 512 (FIG.5) and corresponding noise peaks 612, 614, and 616 (respective sampling frequencies are 5.76 kHz, 11.36 kHz, and 21.48 kHz). The results are shown in equation 5 (including the results of equation 4):^5.62 kHz compare to 5.748 kHz) , fs= 21.48 kHzI 4.38 kHz (compare to 4.393 kHz) , fs= 11.36 kHzf alias Eq. 5.I 1.70 kHz (compare to 1.631 kHz) , fs= 5.76 kHz11.18 kHz (compare to 1.159 kHz) , fs= 2.88 kHz

[0094] The respective margins of error can be given by equation 6.(-2.26% , fs= 21.48 kHz-0.23% , fs= 11.36 kHzmargin of error, 6 = Eq. 6.+4.30% , fs= 5.76 kHz1+1.72% , fs= 2.88 kHz

[0095] A technical significance of the algorithmic technique described above can be appreciated better in situations where the source of true noise(s) is unknown. The operations described above with setting a range (upper and lower boundaries) for fnoise. Since the true noise source is unknown, a wide range can be selected (e.g., 100 Hz to 1 MHz). This selection can be based on all active components of the SEM tool and their respective frequencies of operation. The algorithm described above can then be iterated by using a proxy value for fnoiseand incrementing its value in finite steps. For example, step increments set to 100 Hz would have the algorithm iteratively perform the above operations for fnoise= 100 Hz, 200 Hz, ... , 0.9999 MHz, and 1 MHz. Some of these proxy values of f„oisecan result in very large margins of error. Other proxy values of fmisecan result in very small margins of error. Based on this behavior, it can be determined that the calculated alias frequencies having the smallest total relative error are the ones associated with the true noise frequency. As an alternative to the smallest total relative error (or additionally), threshold conditions for margins of error (e.g., exceeds a certain value) can be used to determine whether one or more calculated alias frequencies are associated with one or more true noise frequencies. The smallest total relative error can itself be considered a threshold condition.

[0096] Using the results of the algorithm (e.g., true noise likely at f„oise= 27.1 kHz), subsequent actions can be taken to mitigate the source of the noise, such as identifying the active component that causes oscillations at 27.1 kHz and implementing mitigation measures (e.g., install isolation and damping, electrical shielding, or the like).

[0097] Another reason the above-noted algorithm is useful is that the method allows identification of noise sources in a self-contained manner. The technique described above analyzes the inspection results (images) generated by the SEM tool without resorting to modification of the inspection tool (e.g., adding noise-sensing devices). It is to be appreciated that the examples above relate to an SEM device and that above-described algorithm operations can be performed on images acquired by other types of imaging inspection devices.

[0098] The determination of noise can be made more robust by analyzing an aggregate (e.g., average) of contours. The example above illustrated the process in relation to contour 517 (FIG. 5). Since each SEM image can contain numerous contours, numerous spectra can be generated (e.g., per identified contour) and the iterative algorithmic process can be applied in relation to the noise peaks of each spectra. The results can be combined (e.g., averaged), thereby improving reliability of results (e.g., improve on the margin of error).

[0099] A similar true noise determination can be performed using the data of contour 317 (FIG. 3), which was obtained via image vibrational analysis, as opposed to the trigger-based edge extraction of FIG. 5. A limitation of image vibrational analysis is that one contour can be extracted from each of SEM images 300. The single contours can be subsequently transformed into spectral data similar to FIG.6. From the spectral data, candidate noise alias peaks can be determined. To analyze the spectral data, the above-described algorithmic operations with reference to equations 1-6 can be performed. The generated potential true noise frequencies are then fdtered (e.g., process of elimination) based on a comparison of the results from equation 1 and the candidate noise alias peaks (e.g., low margin of error). However, as alluded to earlier, the image vibrational analysis technique has a shortcoming of extracting one representative edge value, even if there are multiple edges present in a line of pixels of the SEM image. In some circumstances, high frequency noise information of multiple edges can undesirably cancel each other out. Embodiments described herein circumvent the above-noted shortcomings of image vibrational analysis and accurately extract high frequency noise by using equation 1 using edge-extracted contours .

[0100] FIG. 7 illustrates an example method 700 for determining a noise characteristic from images acquired using an inspection apparatus, consistent with embodiments of the present disclosure. The method can be executed using the devices and functions described above with reference to FIGS. 1-6.

[0101] In some embodiments, at operation 702, images are analyzed using a computing device (e.g., SEM images 300 or 500 (FIGS.3 and 5) analyzed by controller 109 (FIG. 1), image processing system 199 (FIG. 2A), image processing system 290 (FIG. 2B), or the like). The images can represent a same region of a substrate comprising device patterns (e.g., patterns 304 or 504 (FIGS. 3 or 5)). The images can comprise lines of pixels (e.g., row or line 316 (FIG. 3)). The images can be associated with different line sampling frequencies of the inspection apparatus (e.g., EBI system 100, beam tools 104 / 104A / 104B (FIGS. 1-2B)). The different line sampling frequencies can be set and adjusted as per the inspection apparatus’s capabilities and constraints (e.g., adjusting a scan speed of the probing electron beam). The analyzing at operation 702 can be further subdivided into multiple operations, for example, operations 704, 706, and 708.

[0102] At operation 704, position information of edges of the device pattern (e.g., contour 317 or edge-extracted contour 517 (FIGS. 3 and 5)) can be extracted from grayscale values of each pixel line of the images (e.g., as described in reference to FIG. 4).

[0103] At operation 706, the position information can be transformed into frequency domain information comprising aliased noise information (e.g., noise spectra of graph 600 (FIG. 6)).

[0104] At operation 708, a noise frequency (e.g., true noise frequency) higher than Nyquist frequencies can be determined based on the aliased noise information. The Nyquist frequencies can be associated with the different line sampling frequencies. In the non-limiting examples covered above, Nyquist frequencies 1.44 kHz, 2.88 kHz, 5.68 kHz, and 10.74 kHz respectively correspond to line sampling frequencies 2.88 kHz, 5.76 kHz, 11.36 kHz, and 21.48 kHz.

[0105] In some embodiments, method 700 includes further operations that correspond to devices and functions described above with reference to FIGS. 1-6 (e.g., histogram data generation, iterative algorithmic calculations of alias frequencies, or the like).

[0106] A non-transitory computer-readable medium may be provided that stores instructions for a processor of a controller (e.g., controller 109 in FIG. 1, image processing system 199 in FIG.2A, image processing system 290 (FIG. 2B), or the like) for determining a noise characteristic from images acquired using an inspection apparatus, according to the example flowcharts of FIG. 7 above, consistent with embodiments in the present disclosure. For example, the instructions stored in the non-transitory computer-readable medium may be executed by the circuitry of the controller for performing method 700 in part or entirely. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read-Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read-Only Memory (PROM), and Erasable Programmable Read-Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0107] Some embodiments may further be described using the following clauses:1. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to perform operations for determining a noise characteristic from images acquired using an inspection apparatus, the operations comprising:analyzing the images that represent a same region of a substrate comprising a device pattern, that comprise lines of pixels, and that are associated with different line sampling frequencies of the inspection apparatus, wherein the analyzing comprises:extracting position information of edges of the device pattern from grayscale values of each pixel line of the images; andtransforming the position information into frequency domain information comprising aliased noise information; anddetermining a noise frequency higher than Nyquist frequencies based on the aliased noise information.2. The non-transitory computer-readable medium of clause 1, wherein each of the Nyquist frequencies corresponds to each of the different line sampling frequencies.3. The non-transitory computer-readable medium of clauses 1 or 2, wherein extracting the position information comprises:generating histogram information of the grayscale values of each pixel line of the images; and determining histogram peaks based on the histogram information.4. The non-transitory computer-readable medium of clause 3, wherein extracting the position information further comprises:determining search boundaries for a pixel position of an edge of the device pattern based on the histogram peaks; andanalyzing the grayscale values between the histogram peaks to search for the pixel position of the edge of the device pattern.5. The non-transitory computer-readable medium of clauses 3 or 4, wherein extracting the position information further comprises:determining weighting coefficients based on the histogram peaks to determine a threshold grayscale value;determining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the threshold grayscale value.6. The non-transitory computer-readable medium of any one of clauses 3 to 5, wherein extracting the position information further comprises:determining an edge position trigger value based on the histogram peaks; anddetermining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the edge position trigger value.7. The non-transitory computer-readable medium of clause 6, wherein extracting the position information further comprises:determining a hysteresis threshold based on the histogram peaks; andmitigating a false trigger using the hysteresis.8. The non-transitory computer-readable medium of any one of clauses 1 to 7, wherein transforming the position information into frequency domain information is performed via a fast Fourier transform.9. The non-transitory computer-readable medium of any one of clauses 1 to 8, wherein determining the noise frequency comprises:invoking a branched function comprising a sampling frequency variable for the different line sampling frequencies and a proxy variable for the noise frequency;determining which branch of the branched function to select based on the different line sampling frequencies and a proxy value for the proxy variable.10. The non-transitory computer-readable medium of any one of clauses 1 to 9, wherein determining the noise frequency comprises:based on the different line sampling frequencies, determining alias frequencies associated with a proxy value for the noise frequency.11. The non-transitory computer-readable medium of clause 10, wherein determining the noise frequency further comprises:determining margins of error between the alias frequencies associated with the proxy value and the aliased noise information.12. The non-transitory computer-readable medium of clause 11, wherein determining the noise frequency is based on whether the margins of error satisfy a threshold condition.13. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to perform operations for determining a noise characteristic of a scanning electron microscopy (SEM) apparatus, the operations comprising:analyzing SEM images captured by the SEM apparatus to extract grayscale values of pattern edges from each pixel line of the SEM images, wherein the SEM images are associated with different line sampling frequencies of the SEM apparatus; andrecovering a noise frequency higher than Nyquist frequencies based on the aliased noise information using a recovery algorithm.14. The non-transitory computer-readable medium of clause 13, wherein each of the Nyquist frequencies corresponds to each of the different line sampling frequencies.15. The non-transitory computer-readable medium of clauses 13 or 14, wherein analyzing the SEM images to extract the grayscale values of the pattern edges comprises:generating histogram information of the grayscale values of each pixel line of the SEM images; anddetermining histogram peaks based on the histogram information.16. The non-transitory computer-readable medium of clause 15, analyzing the SEM images to extract the grayscale values of the pattern edges further comprises:determining search boundaries for a pixel position of a pattern edge based on the histogram peaks; andanalyzing the grayscale values between the histogram peaks to search for the pixel position of the pattern edge.17. The non-transitory computer-readable medium of clauses 15 or 16, analyzing the SEM images to extract the grayscale values of the pattern edges further comprises:determining weighting coefficients based on the histogram peaks to determine a threshold grayscale value;determining a pixel position of a pattern edge based on a transition of the grayscale values through the threshold grayscale value.18. The non-transitory computer-readable medium of any one of clauses 15 to 17, analyzing the SEM images to extract the grayscale values of the pattern edges further comprises:determining an edge position trigger value based on the histogram peaks; anddetermining a pixel position of a pattern edge based on a transition of the grayscale values through the edge position trigger value.19. The non-transitory computer-readable medium of clause 18, wherein analyzing the SEM images to extract the grayscale values of the pattern edges further comprises:determining a hysteresis threshold based on the histogram peaks; andmitigating a false trigger using the hysteresis.20. The non-transitory computer-readable medium of any one of clauses 13 to 19, wherein analyzing the SEM images to extract the grayscale values of the pattern edges comprises:transforming the position information of the pattern edges into frequency domain information is performed via a fast Fourier transform.21. The non-transitory computer-readable medium of clause 20, wherein transforming the position information of the pattern edges into frequency domain information is performed via a fast Fourier transform.22. The non-transitory computer-readable medium of any one of clauses 13 to 21, wherein recovering the noise frequency comprises:invoking a branched function comprising a sampling frequency variable for the different line sampling frequencies and a proxy variable for the noise frequency;determining which branch of the branched function to select based on the different line sampling frequencies and a proxy value for the proxy variable.23. The non-transitory computer-readable medium of any one of clauses 13 to 22, wherein recovering the noise frequency comprises:based on the different line sampling frequencies, determining alias frequencies associated with a proxy value for the noise frequency.24. The non-transitory computer-readable medium of clause 23, wherein determining the noise frequency further comprises:determining margins of error between the alias frequencies associated with the proxy value and the aliased noise information.25. The non-transitory computer-readable medium of clause 24, wherein recovering the noise frequency is based on whether the margins of error satisfy a threshold condition.26. A method of determining a noise characteristic from images acquired using a metrology system, comprising:analyzing the images that represent a same region of a wafer comprising a patterned structure, that comprise lines of pixels, and that are associated with different line sampling frequencies of the metrology system, and wherein the analyzing comprises:extracting position information of contours of the device pattern from grayscale values of each pixel line of the images; andtransforming the position information into frequency domain information comprising aliased noise information; anddetermining a noise frequency higher than Nyquist frequencies based on the aliased noise information.27. The method of clause 26, further comprising adjusting a property or design of the inspection apparatus based on the determined noise frequency.28. The method of clause 26 or 27, wherein each of the Nyquist frequencies corresponds to each of the different line sampling frequencies.29. The method of any one of clauses 26 to 28, wherein extracting the position information comprises:generating histogram information of the grayscale values of each pixel line of the images; and determining histogram peaks based on the histogram information.30. The method of clause 29, wherein extracting the position information further comprises:determining search boundaries for a pixel position of an edge of the device pattern based on the histogram peaks; andanalyzing the grayscale values between the histogram peaks to search for the pixel position of the edge of the device pattern.31. The method of clauses 29 or 30, wherein extracting the position information further comprises: determining weighting coefficients based on the histogram peaks to determine a threshold grayscale value;determining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the threshold grayscale value.32. The method of any one of clauses 29 to 31, wherein extracting the position information further comprises:determining an edge position trigger value based on the histogram peaks; anddetermining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the edge position trigger value.33. The method of clause 32, wherein extracting the position information further comprises:determining a hysteresis threshold based on the histogram peaks; andmitigating a false trigger using the hysteresis.34. The method of any one of clauses 26 to 33, wherein transforming the position information into frequency domain information is performed via a fast Fourier transform.35. The method of any one of clauses 26 to 34, wherein determining the noise frequency comprises: invoking a branched function comprising a sampling frequency variable for the different line sampling frequencies and a proxy variable for the noise frequency;determining which branch of the branched function to select based on the different line sampling frequencies and a proxy value for the proxy variable.36. The method of any one of clauses 26 to 35, wherein determining the noise frequency comprises: based on the different line sampling frequencies, determining alias frequencies associated with a proxy value for the noise frequency.37. The method of clause 36, wherein determining the noise frequency further comprises:determining margins of error between the alias frequencies associated with the proxy value and the aliased noise information.38. The method of clause 37, wherein determining the noise frequency is based on whether the margins of error satisfy a threshold condition.39. A system comprising:one or more processors; andone or more memory devices storing instructions that, when executed, cause the one or more processors to perform operations for determining a noise frequency from images acquired using an inspection apparatus, the operations comprising:analyzing the images that represent a same region of a wafer comprising a patterned structure, that comprise lines of pixels, and that are associated with different line sampling frequencies of the metrology system, and wherein the analyzing comprises:extracting position information of edges of the device pattern from grayscale values of each pixel line of the images; andtransforming the position information into frequency domain information comprising aliased noise information; anddetermining the noise frequency in a frequency range higher than Nyquist frequencies based on the aliased noise information.40. The system of clause 39, wherein each of the Nyquist frequencies corresponds to each of the different line sampling frequencies.41. The system of clauses 39 or 40, wherein extracting the position information comprises:generating histogram information of the grayscale values of each pixel line of the images; and determining histogram peaks based on the histogram information.42. The system of clause 41, wherein extracting the position information further comprises:determining search boundaries for a pixel position of an edge of the device pattern based on the histogram peaks; andanalyzing the grayscale values between the histogram peaks to search for the pixel position of the edge of the device pattern.43. The system of clauses 41 or 42, wherein extracting the position information further comprises:determining weighting coefficients based on the histogram peaks to determine a threshold grayscale value;determining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the threshold grayscale value.44. The system of any one of clauses 41 to 43, wherein extracting the position information further comprises:determining an edge position trigger value based on the histogram peaks; anddetermining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the edge position trigger value.45. The system of clause 44, wherein extracting the position information further comprises:determining a hysteresis threshold based on the histogram peaks; andmitigating a false trigger using the hysteresis.46. The system of any one of clauses 39 to 45, wherein transforming the position information into frequency domain information is performed via a fast Fourier transform.47. The system of any one of clauses 39 to 46, wherein determining the noise frequency comprises: invoking a branched function comprising a sampling frequency variable for the different line sampling frequencies and a proxy variable for the noise frequency;determining which branch of the branched function to select based on the different line sampling frequencies and a proxy value for the proxy variable.48. The system of any one of clauses 39 to 47, wherein determining the noise frequency comprises: based on the different line sampling frequencies, determining alias frequencies associated with a proxy value for the noise frequency.49. The system of clause 48, wherein determining the noise frequency further comprises:determining margins of error between the alias frequencies associated with the proxy value and the aliased noise information.50. The system of clause 49, wherein determining the noise frequency is based on whether the margins of error satisfy a threshold condition.

[0108] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings and that various modifications and changes may be made without departing from the scope thereof.

Claims

1. CLAIMS1. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an apparatus to perform operations for determining a noise characteristic from images acquired using an inspection apparatus, the operations comprising:3.analyzing the images that represent a same region of a substrate comprising a device pattern, that comprise lines of pixels, and that are associated with different line sampling frequencies of the inspection apparatus, wherein the analyzing comprises:4.extracting position information of edges of the device pattern from grayscale values of each pixel line of the images; and5.transforming the position information into frequency domain information comprising aliased noise information; and6.determining a noise frequency higher than Nyquist frequencies based on the aliased noise information.

2. The non-transitory computer-readable medium of claim 1, wherein each of the Nyquist frequencies corresponds to each of the different line sampling frequencies.

3. The non-transitory computer-readable medium of claim 1, wherein extracting the position information comprises:9.generating histogram information of the grayscale values of each pixel line of the images; and determining histogram peaks based on the histogram information.

4. The non-transitory computer-readable medium of claim 3, wherein extracting the position information further comprises:11.determining search boundaries for a pixel position of an edge of the device pattern based on the histogram peaks; and12.analyzing the grayscale values between the histogram peaks to search for the pixel position of the edge of the device pattern.

5. The non-transitory computer-readable medium of claim 3, wherein extracting the position information further comprises:14.determining weighting coefficients based on the histogram peaks to determine a threshold grayscale value;15.determining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the threshold grayscale value.

6. The non-transitory computer-readable medium of claim 3, wherein extracting the position information further comprises:16.determining an edge position trigger value based on the histogram peaks; and17.determining a pixel position of an edge of the device pattern based on a transition of the grayscale values through the edge position trigger value.

7. The non-transitory computer-readable medium of claim 6, wherein extracting the position information further comprises:19.determining a hysteresis threshold based on the histogram peaks; and20.mitigating a false trigger using the hysteresis.

8. The non-transitory computer-readable medium of claim 1, wherein transforming the position information into frequency domain information is performed via a fast Fourier transform.

9. The non-transitory computer-readable medium of claim 1, wherein determining the noise frequency comprises:23.invoking a branched function comprising a sampling frequency variable for the different line sampling frequencies and a proxy variable for the noise frequency;24.determining which branch of the branched function to select based on the different line sampling frequencies and a proxy value for the proxy variable.

10. The non-transitory computer-readable medium of claim 1, wherein determining the noise frequency comprises:26.based on the different line sampling frequencies, determining alias frequencies associated with a proxy value for the noise frequency.

11. The non-transitory computer-readable medium of claim 10, wherein determining the noise frequency further comprises:28.determining margins of error between the alias frequencies associated with the proxy value and the aliased noise information.

12. The non-transitory computer-readable medium of claim 11, wherein determining the noise frequency is based on whether the margins of error satisfy a threshold condition.

13. A method of determining a noise characteristic from images acquired using a metrology system, comprising:analyzing the images that represent a same region of a wafer comprising a patterned structure, that comprise lines of pixels, and that are associated with different line sampling frequencies of the metrology system, and wherein the analyzing comprises:31.extracting position information of contours of the device pattern from grayscale values of each pixel line of the images; and32.transforming the position information into frequency domain information comprising aliased noise information; and33.determining a noise frequency higher than Nyquist frequencies based on the aliased noise information.

14. The method of claim 13, further comprising adjusting a property or design of the inspection apparatus based on the determined noise frequency.

15. A system comprising:36.one or more processors; and37.one or more memory devices storing instructions that, when executed, cause the one or more processors to perform operations for determining a noise frequency from images acquired using an inspection apparatus, the operations comprising:38.analyzing the images that represent a same region of a wafer comprising a patterned structure, that comprise lines of pixels, and that are associated with different line sampling frequencies of the metrology system, and wherein the analyzing comprises:39.extracting position information of edges of the device pattern from grayscale values of each pixel line of the images; and40.transforming the position information into frequency domain information comprising aliased noise information; and41.determining the noise frequency in a frequency range higher than Nyquist frequencies based on the aliased noise information.

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