WO2025201837A1

WO2025201837A1 - Metrology improvement for pattern-edge based measurements

Info

Publication number: WO2025201837A1
Application number: PCT/EP2025/056185
Authority: WO
Inventors: Yiming LEI; Kangsheng QIU; Hongquan ZUO; Ying Luo; Lingling Pu; Qiang Li
Original assignee: ASML Netherlands BV
Current assignee: ASML Netherlands BV
Priority date: 2024-03-26
Filing date: 2025-03-06
Publication date: 2025-10-02
Anticipated expiration: 2026-09-26
Also published as: TW202544949A

Abstract

A method for metrology may include receiving an inspection image of a structure on a sample, extracting a gray level value profile associated with the structure from the received inspection image, and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value. The threshold value may be determined from multiple gray level value profiles associated with the structure and may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. And each gray level value profile of the multiple gray level value profiles may be associated with a different apparatus setting.

Description

METROLOGY IMPROVEMENT FOR PATTERN-EDGE BASED MEASUREMENTS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63/570,221 which was filed on March 26, 2024 and which is incorporated herein in its entirety by reference.

TECHNICAL FIELD

[0002] The embodiments provided herein generally relate to metrology improvement, and more particularly, to a metrology improvement technique for pattern-edge based measurements.

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. Charged particle beam based systems such as charged particle (e g., electron) beam microscopes, such as a scanning electron microscope (SEM) can be employed. Metrology, in the context of a charged particle beam system, refers to the science and technology of measurement of micro and nanoscale structures using the system. As the physical sizes of IC components continue to shrink, accuracy and repeatability in metrology and defect detection becomes more and more important. Metrology and defect inspection involves measurements of semiconductor device structures using inspection images during the device fabrication processes, and then the measurements are further processed to identify possible defects on the wafer.

SUMMARY

[0004] In some embodiments, an apparatus for metrology is disclosed. The apparatus may comprise a memory storing a set of instructions and at least one processor configured to execute the set of instructions to cause the apparatus to perform operations. These operations may comprise receiving an inspection image of a structure on a sample and extracting a gray level value profile associated with the structure from the received inspection image. The operations may also comprise determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value. The threshold value may be determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. Each gray level value profile of the multiple gray level value profiles may be associated with a different apparatus setting.

[0005] In some embodiments, an apparatus for metrology is disclosed. The apparatus may comprise a memory storing a set of instructions and at least one processor configured to execute the set of instructions to cause the apparatus to perform operations. The operations may comprise receiving multiple inspection images of a structure on a sample. Each inspection image of the multiple inspection images may be an image of the sample acquired at a different apparatus setting. The operations may also comprise obtaining multiple gray level value profiles from the multiple inspection images. Each gray level value profile of the multiple gray level value profiles may be associated with the structure in a different inspection image of the multiple inspection images. The method may also comprise determining a threshold value from the multiple gray level value profiles. The threshold value may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. The operations may further comprise determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

[0006] In some embodiments, a non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology is disclosed. The operations may comprise receiving an inspection image of a structure on a sample and extracting a gray level value profile associated with the structure from the received inspection image. The operations may also comprise determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value. The threshold value may be determined from multiple gray level value profiles associated with the structure and may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. Each gray level value profile of the multiple gray level value profiles may be associated with a different apparatus setting.

[0007] In some embodiments, a non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology is disclosed. The operations may comprise receiving multiple inspection images of a structure on a sample. Each inspection image of the multiple inspection images may be an image of the sample acquired at a different setting of an apparatus. The operations may also comprise obtaining multiple gray level value profiles from the multiple inspection images. Each gray level value profile of the multiple gray level value profiles may be associated with the structure in a different inspection image of the multiple inspection images. The operations may also comprise determining a threshold value from the multiple gray level value profiles. The threshold value may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. The operations may further comprise determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

[0008] In some embodiments, a method for metrology is disclosed. The method may comprise receiving an inspection image of a structure on a sample and extracting a gray level value profile associated with the structure from the received inspection image. The method may also comprise determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value. The threshold value may be determined from multiple gray level value profiles associated with the structure and may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. Each gray level value profile of the multiple gray level value profiles may be associated with a different apparatus setting.

[0009] In some embodiments, a method for metrology is disclosed. The method may comprise receiving multiple inspection images of a structure on a sample. Each inspection image of the multiple inspection images may be an image of the sample acquired at a different setting of an apparatus. The method may also comprise obtaining multiple gray level value profiles from the multiple inspection images. Each gray level value profile of the multiple gray level value profiles may be associated with the structure in a different inspection image of the multiple inspection images. The method may also comprise determining a threshold value from the multiple gray level value profiles. The threshold value may be indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum. The method may further comprise determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

[0010] Other advantages of the embodiments of the present disclosure will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of the present invention.

BRIEF DESCRIPTION OF FIGURES

[0011] The above and other aspects of the present disclosure will become more apparent from the description of exemplary embodiments, taken in conjunction with the accompanying drawings.

[0012] Fig. 1 is a schematic diagram illustrating an example charged-particle beam system, consistent with embodiments of the present disclosure.

[0013] Fig. 2A is a schematic diagram illustrating an example multi-beam tool, consistent with embodiments of the present disclosure that can be a part of the example charged-particle beam system of Fig. 1.

[0014] Fig. 2B is a schematic diagram illustrating an example single-beam tool, consistent with embodiments of the present disclosure that can be a part of the example charged-particle beam system of Fig. 1.

[0015] Fig. 3 illustrates an exemplary technique to determine a critical dimension of a structure, consistent with embodiments of the present disclosure.

[0016] Fig. 4A is a block diagram of an example metrology system, consistent with some embodiments of the present disclosure. [0017] Fig. 4B is a flow chart of an exemplary process used by the metrology system of Fig. 4A to determine a critical dimension of a structure, consistent with some embodiments of the present disclosure.

[0018] Fig. 5 illustrates an exemplary inspection image showing a plurality of structures on a sample, consistent with embodiments of the present disclosure.

[0019] Fig. 6 is a schematic illustration of a gray level value profile across a selected structure on the sample of Fig. 5 overlaid on a cross-section of the structure.

[0020] Figs. 7A and 7B illustrate gray level value profiles across the selected structure at different variations in tool performance, in an example case consistent with the present disclosure.

[0021] Figs. 8A and 8B illustrate the effect of variations in tool performance on an exemplary critical dimension, in an example case consistent with the present disclosure.

[0022] Fig. 9 illustrates critical dimension values of an exemplary structure over time, in an example case consistent with the present disclosure.

DETAILED DESCRIPTION

[0023] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent all implementations. Instead, they are merely examples of apparatuses and methods consistent with aspects related to the disclosed embodiments as recited in the appended claims. For example, although some embodiments are described in the context of utilizing electron beams, the disclosure is not so limited. Other types of charged particle beams (e.g., including protons, ions, muons, or any other particle carrying electric charges) may be similarly applied. Furthermore, other imaging systems may be used, such as optical imaging, photon detection, x-ray detection, ion detection, etc.

[0024] Electronic devices are constructed of circuits formed on a piece of semiconductor material called a substrate. The semiconductor material may include, for example, silicon, gallium arsenide, indium phosphide, or silicon germanium, or the like. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. The size of these circuits has decreased dramatically so that many more of them can be fit on the substrate. For example, an IC chip in a smartphone can be as small as a thumbnail and yet may include over 2 billion transistors, the size of each transistor being less than 1/1000th the size of a human hair.

[0025] Making these ICs with extremely small structures or components is a complex, timeconsuming, 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.

[0026] One component of improving yield is monitoring the chip-making process to ensure that it is producing a sufficient number of functional integrated circuits. One way to monitor the process is to inspect the chip circuit structures at various stages of their formation. Inspection can be carried out using a scanning charged-particle microscope (“SCPM”). For example, an SCPM may be a scanning electron microscope (SEM). A SCPM can be used to image these extremely small structures, in effect, taking a “picture” of the structures of the wafer. The image can be used to determine if the structure was formed properly in the proper location. If the structure is defective, then the process can be adjusted, so the defect is less likely to recur.

[0027] As the physical sizes of IC components continue to shrink, accuracy and yield in defect detection becomes more and more important. Defect inspection involves measurements of device structures using inspection images during wafer fabrication processes, and then the measurements are further processed to identify possible defects on the wafer. Critical dimensions (CDs) of pattems/structures measured from a SEM image can be used for identifying defects of manufactured ICs. The term critical dimensions refer to any geometric parameters or features (e.g., line width, space width, thickness, aspect ratio, overlay accuracy, etc.) of the device structure that, for example, may affect the functionality and performance of the device. For example, shifts between patterns or edge placement variations, which are determined from measured critical dimensions, can be helpful in identifying defects. Without accurate metrology of critical dimension of device structures, accurate defect identification is hardly possible. Therefore, accuracy and yield in defect detection is fundamentally based on accurate measurements of critical dimensions of device structures. However, measurement accuracy and repeatability of the measurement is limited by metrology tool error (e g., calibration ruler error), process variations (e.g., leading to line-width roughness or trench-width roughness), measurement error (e.g., alignment variation), a measurement tool noise (e.g., a limited number of electrons when inspecting a line/edge), limitations of the metrology, etc.

[0028] In conventional systems, noise reduction of SCPM type metrology is achieved by averaging over multiple measurements. For example, a line width as a critical dimension can be determined by averaging multiple measurements measured from a section of a line or from multiple lines. In such systems, critical dimension measurement precision can be improved by increasing the number of measurements to be averaged. Currently, measurement of a critical dimension (CD) is based on locating edges of a structure or a pattern (e.g., a trace) from a gray level value (GLV) profile obtained from an electron-beam (e-beam) image. Gray level value profile represents the variation of pixel intensity values along a line in the image. Pixels with intensity values above a default threshold are considered part of the pattern, while pixels below this threshold are considered background.

[0029] According to some embodiments of the present disclosure, a critical dimension measurement technique is provided where a threshold value that is relatively insensitive to expected variations in the performance of the tool is selected and used. Precision and repeatability of critical dimension measurements may be improved by using a threshold value that is determined to be insensitive to tool performance.

[0030] 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. Other objects and advantages of the disclosure may be realized by the elements and combinations as set forth in the embodiments discussed herein. However, embodiments of the present disclosure are not necessarily required to achieve such exemplary objects or advantages, and some embodiments may not achieve any of the stated objects or advantages.

[0031] Without limiting the scope of the present disclosure, some embodiments may be described in the context of providing scanning deflection systems and scanning deflection methods in systems utilizing electron beams (“e-beams”). Some scanning deflection systems may use electric fields to influence a charged particle beam. However, the disclosure is not so limited. Other types of charged particle beams may be similarly applied. For example, systems and methods may be applicable with optics, photons, x-rays, and ions, etc. Deflection may be used to scan a beam over a surface in, for example, cathode ray tubes (CRTs), lithography machines, scanning charged-particle microscopes (SCPMs), or other analytical instruments. While some embodiments are discussed with reference to deflection systems that use electric field to influence a beam, deflection may also be achieved with magnetic fields, for example.

[0032] 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 includes A or B, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or A and B. As a second example, if it is stated that a component includes A, B, or C, then, unless specifically stated otherwise or infeasible, the component may include A, or B, or C, or A and B, or A and C, or B and C, or A and B and C. Expressions such as “at least one of’ do not necessarily modify an entirety of a following list and do not necessarily modify each member of the list, such that “at least one of A, B, and C” should be understood as including only one of A, only one of B, only one of C, or any combination of A, B, and C. The phrase “one of A and B” or “any one of A and B” shall be interpreted in the broadest sense to include one of A, or one of B.

[0033] Fig. 1 illustrates an example electron beam inspection (EBI) system 100 consistent with embodiments of the present disclosure. EBI system 100 may be used for imaging. As shown in Fig. 1, EBI system 100 includes a main chamber 101, a load/lock chamber 102, a beam tool 104, and an equipment front end module (EFEM) 106. Beam tool 104 is located within main chamber 101. EFEM 106 includes a first loading port 106a and a second loading port 106b. EFEM 106 may include additional loading port(s). First loading port 106a and second loading port 106b 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). A “lot” is a plurality of wafers that may be loaded for processing as a batch.

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

[0035] A controller 109 (or control unit) is electronically connected to beam tool 104. In the context of a charged particle beam apparatus, the controller may be responsible for managing and regulating various aspects of the beam generation, manipulation, and delivery processes of EBI system 100. Controller 109 may include circuits (or circuitry) that enables various functionalities. Some exemplary circuits and their related functionalities will be described. For example, in some embodiments, controller 109 may include circuitry that enables it to control one or more of the intensity, focus, energy, and direction of the charged particle beam in beam tool 104. The controller may adjust these parameters according to the requirements of the specific application. Alternatively, or additionally, the controller may also include circuitry that enables it to manage mechanisms for steering and deflecting the charged particle beam. These steering or deflecting circuits may activate electromagnetic fields or use other techniques to manipulate the trajectory of the beam. For example, these circuits may include power supplies, electromagnetic coils, electrostatic lenses, or other mechanisms for controlling the trajectory and direction of the beam.

[0036] In some embodiments, controller 109 may additionally or alternatively include circuits that enable it to continuously monitors the stability of the beam and adjust parameters to maintain suitable performance of beam tool 104. These circuits may include sensors, detectors, and feedback loops to measure parameters such as beam current, position, energy, intensity, etc. in real-time. These circuits may incorporate feedback systems to detect deviations from desired beam characteristics and make real-time corrections. For example, the feedback system may compare measured beam parameters with desired setpoints and adjust control signals to minimize deviations and ensure consistent beam quality. In some embodiments, controller 109 may also include circuits that enable data acquisition and analysis, allowing users to collect and analyze data generated by the charged particle beam interactions with the sample.

[0037] It should be noted that it is not a requirement that controller 109 include circuits corresponding to all, or any, of the above-described exemplary functionalities. In other words, controller 109 include circuitry that enables it to control some aspects of EBI system 100. In some embodiments, controller 109 may 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, it is appreciated that controller 109 may be a part of the structure.

[0038] In some embodiments, controller 109 may include one or more processors (not shown). A processor may be an electronic device capable of manipulating or processing information. For example, the processor may include any combination of any number of a central processing unit (or “CPU”), a graphics processing unit (or “GPU”), an optical processor, a programmable logic 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), a neural processing unit (NPU), and any other type of circuit capable of data processing. The processor may also be a virtual processor that includes one or more processors distributed across multiple machines or devices coupled via a network.

[0039] In some embodiments, controller 109 may further include one or more memories (not shown). A memory may be an electronic device capable of storing codes and data accessible by the processor (e.g., via a bus). For example, the memory may include any combination of any number of a randomaccess memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or any type of storage device. The codes and data may include an operating system (OS) and one or more application programs (or “apps”) for specific tasks. The memory may also be a virtual memory that includes one or more memories distributed across multiple machines or devices coupled via a network.

[0040] Fig. 2A illustrates a schematic diagram of an example multi -beam beam tool 104A (also referred to herein as apparatus 104A) and an image processing system 290 that may be configured for use in EBI system 100 (Fig. 1), consistent with embodiments of the present disclosure.

[0041] Beam tool 104 A comprises a charged-particle source 202, a gun aperture 204, a condenser lens 206, a primary charged-particle beam 210 emitted from charged-particle source 202, a source conversion unit 212, a plurality of beamlets 214, 216, and 218 of primary charged-particle beam 210, a primary projection optical system 220, a motorized wafer stage 280, a wafer holder 282, multiple secondary charged-particle beams 236, 238, and 240, a secondary optical system 242, and a charged- particle detection device 244. 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.

[0042] 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 apparatus 104A. Secondary optical system 242 and charged-particle detection device 244 can be aligned with a secondary optical axis 252 of apparatus 104A.

[0043] Charged-particle source 202 can emit one or more charged particles, such as electrons, protons, ions, muons, or any other particle carrying electric charges. In some embodiments, charged- particle source 202 may be an electron source. For example, charged-particle source 202 may include a cathode, an extractor, or an anode, wherein primary electrons can be emitted from the cathode and extracted or accelerated to form primary charged-particle beam 210 (in this case, a primary electron beam) with a crossover (virtual or real) 208. For ease of explanation without causing ambiguity, electrons are used as examples in some of the descriptions herein. However, it should be noted that any charged particle may be used in any embodiment of this disclosure, not limited to electrons. Primary charged-particle beam 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 effect. The Coulomb effect may cause an increase in size of probe spots.

[0044] 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 beam 210. 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. 2A, embodiments of the present disclosure are not so limited. For example, in some embodiments, the apparatus 104A may be configured to generate a first number of beamlets. In some embodiments, the first number of beamlets may be in a range from 1 to 1000. In some embodiments, the first number of beamlets may be in a range from 200-500. In some embodiments, an apparatus 104A may generate 400 beamlets.

[0045] 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. 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.

[0046] Beam separator 222 can be a beam separator of Wien filter type generating an electrostatic dipole field and a magnetic dipole field. In some embodiments, if they are applied, the force exerted by the electrostatic dipole field on a charged particle (e.g., an electron) of beamlets 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 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.

[0047] 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 may be emitted from wafer 230. Secondary charged-particle beams 236, 238, and 240 may comprise charged particles (e.g., electrons) with a distribution of energies. For example, secondary charged-particle beams 236, 238, and 240 may 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 may 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 an inspection image of structures on or underneath the surface area of wafer 230.

[0048] The generated signals may represent intensities of secondary charged-particle beams 236, 238, and 240 and may 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 may be synchronized and coordinated with the beam deflections controlled by deflection scanning unit 226, such that the movement of the scan probe spots (e.g., scan probe spots 270, 272, and 274) may orderly cover regions of interest on the wafer 230. The parameters of such synchronization and coordination may be adjusted to adapt to different materials of wafer 230. For example, different materials of wafer 230 may have different resistance-capacitance characteristics that may cause different signal sensitivities to the movement of the scan probe spots.

[0049] The intensity of secondary charged-particle beams 236, 238, and 240 may vary according to the external or internal structure of wafer 230, and thus may indicate whether wafer 230 includes defects. Moreover, as discussed above, beamlets 214, 216, and 218 may 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 may 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 may reconstruct an image that reflects the characteristics of internal or external structures of wafer 230.

[0050] In some embodiments, image processing system 290 may include an image acquirer 292, a storage 294, and a controller 296. Image acquirer 292 may comprise one or more processors. For example, image acquirer 292 may comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, or the like, or a combination thereof. Image acquirer 292 may be communicatively coupled to charged-particle detection device 244 of beam tool 104 A through a medium such as an electric conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or a combination thereof. In some embodiments, image acquirer 292 may receive a signal from charged-particle detection device 244 and may construct an image. Image acquirer 292 may thus acquire inspection images of wafer 230. Image acquirer 292 may also perform various post-processing functions, such as generating contours, superimposing indicators on an acquired image, or the like. Image acquirer 292 may be configured to perform adjustments of brightness and contrast of acquired images. In some embodiments, storage 294 may be a storage medium such as a hard disk, flash drive, cloud storage, random access memory (RAM), other types of computer-readable memory, or the like. Storage 294 may be coupled with image acquirer 292 and may be used for saving scanned raw image data as original images, and postprocessed images. Image acquirer 292 and storage 294 may be connected to controller 296. In some embodiments, image acquirer 292, storage 294, and controller 296 may be integrated together as one control unit.

[0051] In some embodiments, image acquirer 292 may acquire one or more inspection images of a wafer based on an imaging signal received from charged-particle detection device 244. An imaging signal may correspond to a scanning operation for conducting charged particle imaging. An acquired image may be a single image comprising a plurality of imaging areas. The single image may be stored in storage 294. The single image may be an original image that may be divided into a plurality of regions. Each of the regions may comprise one imaging area containing a feature of wafer 230. The acquired images may comprise multiple images of a single imaging area of wafer 230 sampled multiple times over a time sequence. The multiple images may be stored in storage 294. In some embodiments, image processing system 290 may be configured to perform image processing steps with the multiple images of the same location of wafer 230.

[0052] In some embodiments, image processing system 290 may include 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 any defects that may exist in the wafer.

[0053] In some embodiments, the charged particles may be electrons. 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 may penetrate the surface of wafer 230 for a certain depth, interacting with particles of wafer 230. Some electrons of primary charged-particle beam 210 may elastically interact with (e.g., in the form of elastic scattering or collision) the materials of wafer 230 and may 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). Some electrons of primary charged-particle beam 210 may 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 may cause electron excitation and transition of atoms of the materials. Such inelastic interaction may also generate electrons exiting the surface of wafer 230, which may be referred to as secondary electrons (SEs). Yield or emission rates of BSEs and SEs depend on, e.g., the material under inspection and the landing energy of the electrons of primary charged-particle beam 210 landing on the surface of the material, among others. The energy of the electrons of primary charged-particle beam 210 may 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. 2A). The quantity of BSEs and SEs may be more or fewer (or even the same) than the injected electrons of primary charged-particle beam 210.

[0054] Another example of a charged particle beam apparatus will now be discussed with reference to Fig 2B. Beam tool 104B (also referred to herein as apparatus 104B) may be an example of beam tool 104 and may be similar to beam tool 104A shown in Fig. 2A. However, different from apparatus 104A, apparatus 104B may be a single-beam tool that uses only one primary electron beam to scan one location on the wafer at a time.

[0055] As shown in Fig. 2B, apparatus 104B includes a wafer holder 136 supported by motorized stage 134 to hold a wafer 150 to be inspected. Beam tool 104B includes an electron emitter, which may comprise a cathode 103, an anode 121, and a gun aperture 122. Beam tool 104B further includes 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, in some embodiments, may be a modified SORIL lens, which includes 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 may be accelerated by anode 121 voltage, pass through gun aperture 122, beam limit aperture 125, condenser lens 126, and be focused into a probe spot 170 by the modified SORIL lens and impinge onto the surface of wafer 150. Probe spot 170 may be scanned across the surface of wafer 1 0 by a deflector, such as deflector unit 132c or other deflectors in the SORIL lens. Secondary or scattered particles, such as secondary electrons or scattered primary electrons emanated from the wafer surface may be collected by detector 144 to determine intensity of the beam and so that an image of an area of interest on wafer 150 may be reconstructed. [0056] There may also be provided an image processing system 199 that includes an image acquirer 120, a storage 130, and controller 109. Image acquirer 120 may comprise one or more processors. For example, image acquirer 120 may comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, and the like, or a combination thereof. Image acquirer 120 may connect with detector 144 of beam tool 104B through a medium such as an electrical conductor, optical fiber cable, portable storage media, IR, Bluetooth, internet, wireless network, wireless radio, or a combination thereof. Image acquirer 120 may receive a signal from detector 144 and may construct an image. Image acquirer 120 may thus acquire images of wafer 150. Image acquirer 120 may also perform various post-processing functions, such as image averaging, generating contours, superimposing indicators on an acquired image, and the like. Image acquirer 120 may be configured to perform adjustments of brightness and contrast, etc. of acquired images. Storage 130 may be a storage medium such as a hard disk, random access memory (RAM), cloud storage, other types of computer readable memory, and the like. Storage 130 may be coupled with image acquirer 120 and may be used for saving scanned raw image data as original images, and postprocessed images. Image acquirer 120 and storage 130 may be connected to controller 109. In some embodiments, image acquirer 120, storage 130, and controller 109 may be integrated together as one electronic control unit.

[0057] In some embodiments, image acquirer 120 may acquire one or more images of a sample based on an imaging signal received from detector 144. An imaging signal may correspond to a scanning operation for conducting charged particle imaging. An acquired image may be a single image comprising a plurality of imaging areas that may contain various features of wafer 150. The single image may be stored in storage 130. Imaging may be performed on the basis of imaging frames.

[0058] The condenser and illumination optics of the electron beam tool may comprise or be supplemented by electromagnetic quadrupole electron lenses. For example, as shown in Fig. 2B, electron beam tool 104B may comprise a first quadrupole lens 148 and a second quadrupole lens 158. In some embodiments, the quadrupole lenses may be used for controlling the electron beam. For example, first quadrupole lens 148 may be controlled to adjust the beam current and second quadrupole lens 158 may be controlled to adjust the beam spot size and beam shape.

[0059] Fig. 2B illustrates a charged particle beam apparatus that may use a single primary beam configured to generate secondary electrons by interacting with wafer 150. Detector 144 may be placed along optical axis 105, as in the embodiment shown in Fig. 2B. The primary electron beam may be configured to travel along optical axis 105. Accordingly, detector 144 may include a hole at its center so that the primary electron beam may pass through to reach wafer 150. Fig. 2B shows an example of detector 144 having an opening at its center. However, some embodiments may use a detector placed off-axis relative to the optical axis along which the primary electron beam travels. For example, as in the embodiment shown in Fig. 2B, discussed above, a beam separator 222 may be provided to direct secondary electron beams toward a detector placed off-axis. Beam separator 222 may be configured to divert secondary electron beams toward an electron detection device 244, as shown in Fig. 2A.

[0060] The images generated by SCPM may be used for defect inspection on a sample being imaged. For example, a generated image capturing a test device region of a wafer may be compared with a reference image capturing the same test device region. The reference image may 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 may be identified. For another example, the SCPM may 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 may be compared with each other. If a difference between the multiple images exceeds a tolerance level, a potential defect may be identified.

[0061] In some embodiments, the images generated by SCPM may be used for metrology, such as, for example, determining feature sizes of structures (e.g., circuits, etc.) on the sample being imaged. For example, to measure a critical dimension or CD (e g., width, pitch, thickness, spacing, etc.) of structures on the sample surface. To measure a critical dimension of a pattern such as a circuit line or a trace on the sample surface, a pattern edge gray level value (GLV) profile of the captured image may be used. Pattern edge gray level value (GLV) profile refers to the variation in grayscale intensity (or gray scale values) along the edge of a pattern within the captured image. In an exemplary application, the SEM image of the trace or pattern on the sample surface is captured. Then, suitable algorithms (e.g., edge detection algorithms) may be applied to identify the boundary or edge of the trace. The grayscale intensity values of the pixels along the detected edge are then analyzed.

Grayscale intensity typically corresponds to the contrast or brightness of the pixels in the image and may be represented on a scale from 0 (black) to 255 (white) in an 8-bit grayscale image. A curve or profile may then be generated by plotting the grayscale intensity values along a line across the width of the trace. This profile represents the variation in grayscale intensity (or gray scale values (GLVs)) across the width of the trace. By analyzing the gray level value profile, measurements such as the distance between specific intensity thresholds may be used to determine a critical dimension (CD) (e.g., the width) of the trace.

[0062] Fig. 3 illustrates an exemplary gray level value (GLV) profile 300 (which may also be referred to herein as GLV curve 300) across a pattern or a structure (e.g., a circuit line) in an imaged sample. In some embodiments, as illustrated in Fig. 3, a two pattern-edges based metrology may be used to measure the critical dimension of the structure. For example, a user may set the measurement point on the two sides (or edges) of the profile based on a default threshold value (such as, for example, 50%, etc.). Theoretically, any value between 0% - 100% (where 0% and 100% correspond to the minimum and maximum gray level values) may be selected as the default threshold value. Pixels with intensity values above this default threshold value are considered part of the structure, while pixels below the threshold are considered background. During operation, an algorithm (e g., an image processing algorithm) may find the minimum gray level value (GLV) point 310_L, 31 OR and the maximum gray level value point 320L, 320R on the left and right-side edges of the , and then based on the default threshold value, select the measurement points 330L, 330R at the left and right-side edges. As illustrated in Fig. 3, the x-axis values corresponding to the left-side and right-side selection points 330L, 330R may be xi and xj. The critical dimension (CD) of the structure may then be determined as a function of xi and X2 (e.g., CD = /(xl, x2)).

[0063] The repeatability and stability of the two pattern-edges based metrology with a default threshold, as described above, may be affected by expected variations in the tool performance during normal operation. Such variations in tool performance during the course of normal operation of the tool may include, for example, variations in resolution, alignment, sample positioning, stigmata settings, etc. And these variations in tool performance may result in variations in the determined critical dimension. The drive towards smaller feature sizes in the semiconductor industry necessitates critical dimensions of features to be determined with a high degree of repeatability and stability (e.g., < 0.1 nanometer variation). Even with comprehensive and periodic tool calibration protocols, repeatability and stability in critical dimension measurement may be difficult to attain when preset default thresholds are used. Repeatability refers to the ability of a measurement tool to provide consistent results when measuring the same feature multiple times under the same or similar conditions. In other words, if a critical dimension of a feature is measured multiple times using the same tool, repeatability indicates how close those measurements are to each other. A high level of repeatability means that the measurements cluster closely around a central value. Stability refers to the consistency of critical dimension measurements over time or under changing environmental conditions. It assesses how well the measurement tool maintains its accuracy and precision over extended periods of use. When a charged particle beam tool is used for metrology applications, high repeatability and stability of the tool is important for ensuring product quality, process control, and yield optimization since variations in critical dimensions can directly impact the performance and reliability of semiconductor devices.

[0064] Critical dimension measurement methodologies of the current disclosure are configured to minimize the impact of expected variations in tool performance (e.g., resolution, alignment, sample placement, etc.) on the determined critical dimension (CD). The insensitivity of the determined critical dimension to expected tool variations improves the repeatability and stability of the tool. In embodiments of the current disclosure, instead of using a default threshold value, a threshold value that is insensitive to expected variations in tool performance is first determined based on analysis, simulation, or experimentation. This determined threshold value is then used to determine the left-side and right-side selection points (e.g., 330L, 330R in Fig. 3) from a pattern gray level value profile of the structure (e.g., GLV curve 300 of Fig. 3). Since these determined selection points are insensitive to expected variations in tool performance, the critical dimension determined based on these selection points will also be insensitive to variations in tool performance. [0065] It should be noted that, as used herein, the term “insensitive” (and insensitivity, etc.) is used synonymously with “relatively insensitive” or “substantially insensitive.” This means that a measured parameter that is described as being insensitive to variations in tool performance will be practically unaffected, or minimally affected, by changes or variations in the tool performance. In other words, even if the measurement tool experiences variations, fluctuations, or instabilities within the range considered normal for its operation, the measured parameter remains relatively unaffected and maintains its accuracy and reliability. However, it is important to note that while the measured parameter is insensitive to, or is minimally affected by, the normally expected performance instabilities of the measurement tool, some variations may still occur due to practical reasons. For example, every metrology system has some degree of noise, which can arise from electronic components of the system, environmental factors, or inherent limitations of the metrology. While the measured parameter may be minimally affected by this noise, it can still introduce minor fluctuations in the measured parameter. The resolution of the measurement tool can affect the precision of the measured parameter. While the parameter may be insensitive to (or relatively insensitive to) variations in resolution within the normal operating range of the measurement tool, changes in resolution can still introduce minor fluctuations in the measured parameter, especially for fine or small-scale features. Periodic calibration is essential for maintaining the accuracy of measurement tools. While the measured parameter may be minimally affected by variations in calibration during normal operation, deviations from the calibrated state can still occur over time, leading to potential fluctuations or minor changes in the measured parameter. Changes in environmental conditions, such as temperature, humidity, or vibration, can affect the performance of measurement tools. While the measured parameter may be relatively robust and insensitive to these environmental variations, they can still introduce minor fluctuations in the measured parameter. These possible minor fluctuations may be negligible in practice. The specification provides context to the fluctuations that may be expected in a measured parameter that is described as being insensitive to expected variations in tool performance. For example, Fig. 9 shows variations in the determined critical dimension (e g., the curves using 85% threshold for the x-direction scan and the y-direction scan) over time that may be observed in some embodiments of the current disclosure. These observed variations are considered to be insensitive to expected variations in tool performance.

[0066] In some embodiments, machine learning may be employed in the generation and analysis of inspection images, reference images, or other images associated with apparatus 100, 104A, or 104B. For example, in some embodiments, a machine learning system may be operated in association with, e.g., controller 109 or 296, image processing system 199 or 290, image acquirer 120 or 292, or storage unit 130 or 294 of Figs. 1-2B. In some embodiments, machine learning may be employed in metrology (e g., as described with reference to Fig. 3). For example, a machine learning algorithm (or an algorithm that employs machine learning) may analyze gray level value profiles (such as, for example, GLV curve 300 of Fig. 3, 6001-600n of Figs. 7A-7B, etc.) to determine critical dimensions. In some embodiments, a machine learning system may comprise a discriminative model. In some embodiments, a machine learning system may include a generative model. For example, learning can feature two types of mechanisms: discriminative learning that may be used to create classification and detection algorithms, and generative learning that may be used to actually create models that, in the extreme, can render images. For example, as described further below, a generative model may be configured for generating an image from a design clip that resembles a corresponding location on a wafer in a SEM image. This may be performed by 1) training the generative model with design clips and the associated actual SEM images from those locations on the wafer; and 2) using the model in inference mode to feed the model design clips in locations for which simulated SEM images are desired. Such simulated images can be used as reference images in, e.g., die-to-database inspection. [0067] If the model(s) include one or more discriminative models, the discriminative model(s) may have any suitable architecture or configuration known in the art. Discriminative models, also called conditional models, are a class of models used in machine learning for modeling the dependence of an unobserved variable “y” on an observed variable “x.” Within a probabilistic framework, this may be done by modeling a conditional probability distribution P(y |x), which can be used for predicting y based on x. Discriminative models, as opposed to generative models, may not allow one to generate samples from the joint distribution of x and y. However, for tasks such as classification and regression that do not require the joint distribution, discriminative models may yield superior performance. On the other hand, generative models are typically more flexible than discriminative models in expressing dependencies in complex learning tasks. In addition, most discriminative models are inherently supervised and cannot easily be extended to unsupervised learning. Application specific details ultimately dictate the suitability of selecting a discriminative versus generative model.

[0068] A generative model can be generally defined as a model that is probabilistic in nature. In other words, a “generative” model is not one that performs forward simulation or rule-based approaches and, as such, it may not be necessary to model the physics of the processes involved in generating an actual image or output (for which a simulated image or output is being generated). Instead, the generative model can be learned (in that its parameters can be learned) based on a suitable training set of data. Such generative models may have a number of advantages for the embodiments described herein. In addition, the generative model may be configured to have a deep learning architecture in that the generative model may include multiple layers, which may perform a number of algorithms or transformations. The number of layers included in the generative model may depend on the particular use case. For practical purposes, a suitable range of layers is from 2 layers to a few tens of layers.

[0069] Deep learning is a type of machine learning. Machine learning can be generally defined as a type of artificial intelligence (Al) that provides computers with the ability to learn without being explicitly programmed. Machine learning focuses on the development of computer programs that can teach themselves to grow and change when exposed to new data. Machine learning explores the study and construction of algorithms that can learn from and make predictions on data — such algorithms overcome following strictly static program instructions by making data driven predictions or decisions, through building a model from sample inputs.

[0070] The machine learning described herein may be further performed as described in “Introduction to Statistical Machine Learning,” by Sugiyama, Morgan Kaufmann, 2016, 534 pages; “Discriminative, Generative, and Imitative Learning,” Jebara, MIT Thesis, 2002, 212 pages; and “Principles of Data Mining (Adaptive Computation and Machine Learning)” Hand et al., MIT Press, 2001, 578 pages; which are incorporated by reference as if fully set forth herein. The embodiments described herein may be further configured as described in these references.

[0071] In some embodiments, a machine learning system may comprise a neural network. For example, a model may be a deep neural network with a set of weights that model the world according to the data that it has been fed to train it. Neural networks can be generally defined as a machine learning approach that is based on a collection of connected artificial neurons, inspired by a biological brain, that learns to solve problems from data. Each neural unit is connected with many others, and links can be enforcing or inhibitory in their effect on the activation state of connected neural units. These systems are self-learning and trained rather than explicitly programmed and excel in areas where the solution or feature detection is difficult to express in a traditional computer program.

[0072] Neural networks typically consist of multiple layers, and the signal path traverses from front to back. The goal of the neural network is to solve problems in the same way that the human brain would, although several neural networks are much more abstract. Modem neural network projects typically work with a few thousand to a few million neural units and millions of connections. The neural network may have any suitable architecture or configuration known in the art.

[0073] In some embodiments, a model may comprise convolutional and deconvolution neural network. For example, the embodiments described herein can take advantage of learning concepts such as a convolution and deconvolution neural network to solve the normally intractable representation conversion problem (e.g., rendering). The model may have any convolution and deconvolution neural network configuration or architecture known in the art.

[0074] Reference is now made to Fig. 4A, which is a block diagram of an example metrology system 400, consistent with some embodiments of the present disclosure. System 400 may comprise one or more processors and memories. It is appreciated that in various embodiments system 400 may be part of, or may be separate from, a charged-particle beam inspection system (e.g., EBI system 100 of Fig. 1). In some embodiments, metrology system 400 may include one or more components (e.g., algorithms, software modules) that can be implemented in controller 109 or systems 290 or 199 as discussed herein.

[0075] Fig. 4B is a flow chart of an exemplary process 450 used by metrology system 400 to determine a critical dimension of a structure. In the discussion below, reference will be made to Figs. 4A and 4B to describe the operation of system 400 to determine an exemplary critical dimension 410 (e.g., width) of an exemplary structure (e.g., a circuit line).

[0076] During operation, metrology system 400 may receive or acquire one or more inspection images 405 in step 452. Each inspection image 405 may be a scanning charged-particle microscope (SCPM) image of a sample with one or more patterns or structures (line or trace, plane, trench, bond pad, etc.) having at least one critical dimension. Inspection images 405 may be generated by any charged-particle beam tool (such as, for example, EBI system 100 of Fig. 1, electron beam tool 104 A of Fig. 2A, 104B of Fig. 2B, etc.). In some embodiments, inspection image 405 may be obtained from a storage device or system that stores inspection images. Fig. 5 illustrates an exemplary inspection image 405 showing a plurality of spaced-apart lines 502 on the surface of an exemplary sample 500. These lines 502 may have associated critical dimensions such as, for example, the width W, pitch P, etc. In the discussion below, system 400 (of Fig. 4 A) will be described as being used to determine the width (W) of a selected line 502A on sample 500 of Fig. 5.

[0077] Referring back to Figs. 4A and 4B, the inspection images 405 received by system 400 in step 452 may include images 405 of sample 500 acquired at different tool settings (e g., different column aperture positions, different resolutions, different sample positions, different alignment settings, different times (e.g., to capture drift of tool settings over time), different environmental conditions, etc.). These different tool settings may represent different expected variations in tool performance during normal operation. Charged particle beam tools, such as a scanning electron microscope (SEM), are highly sensitive instruments used for imaging samples at very high magnification. Several factors can cause variations in images obtained by an SEM during normal operation. These variations may occur as a result of, for example, alignment errors, variations in sample positioning, variations in stigmata settings, charging effects of the sample, instrument drift, detector characteristics, beam damage to sample, sample preparation artefacts, variations in environmental magnetic field or vibrations, operation of nearby tools, ambient temperature changes, operator variations or error, and other similar practical variations that may cause changes in the beam spot size. In other words, the images 405 received by metrology system 400 may include images of sample 500 that represent expected variations of tool performance. For example, a first image of images 405 may be the image of sample 500 at a first resolution setting (e.g., at a first column aperture position) and a second image may be the image of sample 500 at a second resolution setting (e.g., at a second column aperture position), where the first and second resolution settings represent are expected variations in the resolution of the tool during normal operation.

[0078] In step 454, metrology system 400 may analyze each image 405 of the received images 405 to profile the gray level values (e.g., map GLV curves 300 similar to Fig. 3) across one or more structures in the image. For example, with reference to Fig. 5, metrology system 400 may analyze image 405 to determine the gray level value profile across the selected line 502A (e.g., along line A) in the image. Fig. 6 is a schematic illustration of the determined gray level value profile 600 from an image 405 overlaid on a cross-section of line 502A. The x-axis of the gray level value profile 600 represents pixel values and the y-axis represents intensity (e.g., gray level value). System 400 may similarly extract the gray level value profiles from each image 405 to determine multiple gray level value profiles across line 502A corresponding to different variations of tool performance. In other words, in step 454, system 400 may analyze the received images 405 acquired at different tool settings that correspond to different variations of tool performance to determine the variations in the gray level value profiles across line 502A that result from these variations in tool performance.

[0079] Figs. 7A and 7B illustrate exemplary gray level value profiles (600i - 600_n) across line 502A determined by system 400 from multiple images 405 each acquired at a different variation in tool performance. In these figures, the x-axis represents pixel values, and the y-axis represents normalized intensity. The different gray level value profiles (600i - 600_n) of Figs. 7A and 7B were obtained from images collected by changing the column aperture position of an electron beam tool to simulate expected variations in the resolution of the tool during normal operation. However, collecting multiple images at different column aperture positions in merely exemplary. Multiple images that simulate expected variations in tool performance may be collected in any suitable manner (e.g., at different alignment settings, at different sample stage positions, at different stigmata settings, etc.). The different gray level value profiles 600i-600_n are overlaid in Fig. 7A and 7B to illustrate the differences in these profiles. Fig. 7A illustrates a portion of the gray level value profiles 600i-600_n that correspond to the first edge (see Fig 6) of line 02A, and Fig 7B is an enlarged view of a portion of the gray level value profiles 600i-600_n shown in Fig. 7A.

[0080] In step 456, metrology system 400 may analyze the gray level value profiles that result from different expected variations in tool performance to determine or extract a threshold value that is insensitive to these variations in tool performance. For example, with reference to Fig. 7B, system 400 may determine the Y -axis value (or normalized intensity) at the location where the different gray level value profiles (or curves) 600i-600_n meet or intersect. In some embodiments, in this step, system 400 may determine the normalized intensity (or range of intensities) corresponding to the location(s) where the different curves 600i-600_n are closest to each other. In other words, system 400 may determine the normalized intensity (or range of intensities) corresponding to the location(s) where the variation between the different curves 600i-600_n is a minimum. For example, in the example curves 600i -600_n illustrated in Fig. 7B, the curves 600i-600_n converge towards each other and intersect, or are closest to each other, at a range of normalized intensities (or Y-axis range) between about 0.84- 0.86 (or 84-86%). Between this range, the gray level value profiles corresponding to different resolutions of the tool (that are expected during normal operation) overlap with, or are closest to, each other. Therefore, selecting a value within this range will result in a threshold value that is insensitive to expected variations in tool performance.

[0081] In some embodiments, system 400 may determine a value between this range (84-86%) of normalized intensities as the threshold value that is insensitive to variations in tool performance for the first edge (see Fig. 6) of line 502A. Any value from 84% to 86% may be selected. In some embodiments, the minimum value in this range (e.g., 84%) may be selected as the threshold value. In some embodiments, the maximum value in this range (86%) may be selected as the threshold value. In some embodiments, the average of the range (e.g., 85%) may be selected as the threshold value. In some embodiments, system 400 may select the same value selected as the threshold value for the first edge (e.g., a value from 84% to 86%) as the threshold value for the second edge of line 502A. In some embodiments, system 400 may independently determine the threshold value for the second edge of line 502 A using a process similar to that described above. For example, system 400 may analyze the region of curves 600i-600_n corresponding the second edge of line 502A to determine the Y-axis location where the different curves intersect or are closest to each other and select the normalized intensity corresponding to this location as the threshold value for the second edge of line 502A.

[0082] System 400 may use any suitable algorithm (e g., bisection algorithms, Newton-Raphson algorithms, curve-fitting algorithms, interpolation algorithms, optimization algorithms, graph traversal algorithms, geometric algorithms, etc.) to determine the Y-axis location where the curves intersect or are closest to each other. In some embodiments, a machine learning algorithm may assist in the determination of the Y-axis location where the curves intersect or are closest to each other.

[0083] In step 458, system may then determine a desired critical dimension using the threshold value(s) determined in step 456. In general, the critical dimension may be determined as a function of the determined threshold values for the first edge and the second edge. In some embodiments, the width (W) of line 502A (see Fig. 5) may be determined using the two pattern-edges based metrology previously discussed with reference to Fig. 3. For example, with reference to Fig. 6, a first measurement point 610 may be selected in the region of profile 600 corresponding to the first edge of line 502 A using the determined threshold value for the first edge. And a second measurement point 620 may be selected in the region of profile 600 corresponding to the second edge of line 502A using the determined threshold value for the second edge. The width (W) may then be determined as a function of the x-axis locations of the first and second measurement points 610, 620. Since system 400 determines the first and second selection points 610, 620 using threshold values that were determined to be insensitive to expected variations in tool performance in step 456, the critical dimension (e.g., width (W)) determined in step 458 using these threshold values will also be insensitive to expected variations in tool performance during normal operation.

[0084] In some embodiments, after a threshold value is determined using steps 452-456 of process 450, this determined threshold value may be stored and used for the determination of the critical dimension of multiple samples. For example, inspection images 405 of a selected line 502A on sample 500 is acquired at different tool settings and used to determine the threshold value for the determination of an exemplary critical dimension (e.g., width (W)) in steps 452-456. This threshold value may then be used to determine the critical dimension of other lines of sample 500 and lines of other samples. To ensure that the determined threshold values (in step 456) remain accurate and results in stable critical dimension measurements over time, steps 452-456 may be repeated periodically (e.g., at a predetermined schedule, after a selected number of samples, etc.) to update the threshold values. The frequency of these periodic updates may depend on factors such as, for example, the tool’s usage, environmental conditions, and the specific requirements of the metrology application.

[0085] Figs. 8A and 8B are curves that illustrate the effect of expected variations in tool performance on the critical dimension (e.g., width of line 502A of Fig. 5) determined using different threshold values in an example case consistent with the current disclosure. As in Figs. 7A and 7B, the expected variations in tool performance in Figs. 8 A and 8B were simulated by changing the column aperture position of an electron beam tool relative to its baseline column aperture position. As explained previously, changing the column aperture positions simulates expected variations in the resolution of the tool during normal operation, and are representative of expected variations in tool performance during normal operation of the tool.

[0086] In Fig. 8A, the X-axis indicates the column aperture position, with “0” representing the baseline column aperture position. Values on the left side of “0” indicate column aperture positions shifted in the -Z direction of the tool (e.g., towards the sample) from the baseline position and values on the right side of “0” indicate column aperture positions shifted in the +Z direction (e.g., away from the sample) from the baseline position. The Y-axis in Fig. 8 A indicates the difference (in nanometers) in the critical dimension determined in each case from that determined at the baseline column aperture position (e.g., ACD). The different curves in Fig. 8A represent ACD values when the critical dimension was determined using five different threshold values (e.g., 25%, 50%, 75%, 80%, and 85%). Note that 80% was the threshold value that was determined to be insensitive to expected variations in tool performance by system 400 using process 450 (see Figs. 4A-4B). As evident from Fig. 8A, shifting the column aperture position from its baseline position (in the +Z direction or the -Z direction) increases ACD. Since the curve obtained using a threshold value of 85% is flatter than those obtained using other threshold values, the variation in critical dimension (from the baseline value) at different column aperture positions is smaller when a threshold value of 85% is used to determine the critical dimension.

[0087] Fig. 8B illustrates the critical dimensions (Y -axis) determined using the five different threshold values (e.g., 25%, 50%, 75%, 80%, and 85%) at different tool resolutions (X-axis). As evident from Fig. 8B, the magnitude of the critical dimensions determined using different threshold values differ. However, the variation of the critical dimension at different tool resolutions is smaller when it is determined using a threshold value of 85%. Thus, Figs. 8A and 8B demonstrate that the critical dimension determined using a threshold value extracted using process 450 (of Fig. 4B) is insensitive to expected variations in tool performance during normal operation and produces stable and consistent results. As explained previously, although the critical dimension is described as being insensitive to expected variations in tool performance, as evident from Figs. 8A and 8B, these performance variations may introduce minor and practically -negligible variations in the critical dimension.

[0088] Repeatability and stability in the determination of critical dimensions is important because it provides confidence in the consistency of the measurements over time and across different operators or instruments. In semiconductor manufacturing, where consistency and reliability are important, repeatability ensures that the measurements can be trusted.

[0089] Fig. 9 is an exemplary graph that shows critical dimension values determined in an exemplary critical dimension monitoring study conducted over several days. In Fig. 9, the X-axis indicates the time at which an inspection image (e.g., image 405 of Fig. 4A) was taken for the determination of the critical dimension, and the Y-axis indicates the magnitude of the measured critical dimension. The values determined using two different threshold values (e.g., a default threshold valve of 50% and a threshold value of 85% determined using process 450 of Fig. 4B) on both a horizontal and a vertical pattern edge (e.g., an X direction scan and a Y direction scan) are plotted in Fig. 9. As evident from Fig. 9, for both the X direction scan and the Y direction scan, the critical dimensions determined using a threshold value insensitive to variations in tool performance (e.g., 85%) is more stable and repeatable with less variations over time. In Figs. 7A- 9, an exemplary e-beam landing energy of 500 eV was used to obtain the data plotted. It is expected that critical dimensions determined using a threshold value that is insensitive to variations in tool performance will result in more stable and repeatable critical dimensions for other electron beam landing energies also.

[0090] While some embodiments have been described using a pattern having lines and trenches (e.g., see Fig. 5), it will be appreciated that the present disclosure can be applied to any type of patterns including vias, pillars, contact pads, lines with reduced length, staggered lines, lines or trenches with various widths, overlay patterns, etc. that includes one or more associated critical dimensions. For example, in an exemplary via pattern, a threshold value that is determined to be insensitive to variations in tool performance may be used to determine critical dimensions, such as, for example, a diameter of a via, pitch of the vias, etc.

[0091] In some embodiments of the current disclosure, a non-transitory computer readable medium may be provided that stores instructions for a processor of a controller (e.g., controller 109 of Fig. 1) to carry out, among other things, image inspection, image acquisition, image processing, stage positioning, beam focusing, electric field adjustment, beam bending, condenser lens adjusting, activating charged-particle source, beam deflecting, and the functionalities described above and including method 450 of Fig. 4B. 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.

[0092] The embodiments may further be described using the following clauses:

1. An apparatus for metrology, the apparatus comprising: a memory storing a set of instructions; and at least one processor configmed to execute the set of instructions to cause the apparatus to perform operations comprising: receiving an inspection image of a structure on a sample; extracting a gray level value profile associated with the structure from the received inspection image; and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value, wherein the threshold value is determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum, and wherein each gray level value profile of the multiple gray level value profiles is associated with a different apparatus setting.

2. The apparatus of clause 1, wherein the multiple gray level value profiles comprises a first gray level value profile and a second gray level value profile, wherein the first gray level value profile is extracted from a first image of the structure obtained at a first apparatus setting, and the second gray level value profile is extracted from a second image of the structure obtained at a second apparatus setting different from the first apparatus setting.

3. The apparatus of clause 2, wherein the multiple gray level value profiles comprises a third gray level value profile extracted from a third image of the structure obtained at a third apparatus setting different from the first and second apparatus settings.

4. The apparatus of clause 1, wherein the apparatus setting includes at least one of resolution, sample position, alignment, or stigmata.

5. The apparatus of clause 1, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

6. The apparatus of clause 1, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

7. The apparatus of clause 1, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

8. An apparatus for metrology, the apparatus comprising: a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform operations comprising: receiving multiple inspection images of a structure on a sample, each inspection image of the multiple inspection images being an image of the sample acquired at a different apparatus setting; obtaining multiple gray level value profiles from the multiple inspection images, wherein each gray level value profile of the multiple gray level value profiles is associated with the structure in a different inspection image of the multiple inspection images; determining a threshold value from the multiple gray level value profiles, wherein the threshold value is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum; and determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

9. The apparatus of clause 8, wherein the multiple inspection images comprises a first inspection image and a second inspection image, wherein the first inspection image is obtained at a first apparatus setting, and the second inspection image is obtained at a second apparatus setting.

10. The apparatus of clause 9, wherein the multiple inspection images further comprises a third inspection image obtained at a third apparatus setting different from the first and second apparatus settings.

11. The apparatus of clause 8, wherein the apparatus setting includes at least one of resolution, sample position, alignment, or stigmata.

12. The apparatus of clause 8, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

13. The apparatus of clause 8, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

14. The apparatus of clause 8, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

15. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology, the operations comprising: receiving an inspection image of a structure on a sample; extracting a gray level value profile associated with the structure from the received inspection image; and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value, wherein the threshold value is determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum, and wherein each gray level value profile of the multiple gray level value profiles is associated with a different apparatus setting.

16. The non-transitory computer readable medium of clause 15, wherein the multiple gray level value profiles comprises a first gray level value profile and a second gray level value profile, wherein the first gray level value profile is extracted from a first image of the structure obtained at a first apparatus setting, and the second gray level value profile is extracted from a second image of the structure obtained at a second apparatus setting different from the first apparatus setting.

17. The non-transitory computer readable medium of clause 16, wherein the multiple gray level value profiles further comprises a third gray level value profile extracted from a third image of the structure obtained at a third apparatus setting different from the first and second apparatus settings.

18. The non-transitory computer readable medium of clause 15, wherein the apparatus setting includes at least one of resolution, sample position, alignment, or stigmata.

19. The non-transitory computer readable medium of clause 15, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

20. The non-transitory computer readable medium of clause 15, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

21. The non-transitory computer readable medium of clause 15, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

22. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology, the operations comprising: receiving multiple inspection images of a structure on a sample, each inspection image of the multiple inspection images being an image of the sample acquired at a different setting of an apparatus; obtaining multiple gray level value profiles from the multiple inspection images, wherein each gray level value profile of the multiple gray level value profiles is associated with the structure in a different inspection image of the multiple inspection images; Y1 determining a threshold value from the multiple gray level value profiles, wherein the threshold value is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum; and determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

23. The non-transitory computer readable medium of clause 22, wherein the multiple inspection images comprises a first inspection image and a second inspection image, wherein the first inspection image is obtained at a first apparatus setting, and the second inspection image is obtained at a second apparatus setting different from the first apparatus setting.

24. The non-transitory computer readable medium of clause 23, the multiple inspection images comprises a third inspection image obtained at a third apparatus setting different from the first and second apparatus settings.

25. The non-transitory computer readable medium of clause 22, wherein the setting of the apparatus includes at least one of resolution, sample position, alignment, or stigmata.

26. The non-transitory computer readable medium of clause 22, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

27. The non-transitory computer readable medium of clause 22, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

28. The non-transitory computer readable medium of clause 22, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

29. A method for metrology, comprising: receiving an inspection image of a structure on a sample; extracting a gray level value profile associated with the structure from the received inspection image; and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value, wherein the threshold value is determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum, and wherein each gray level value profile of the multiple gray level value profiles is associated with a different apparatus setting.

30. The method of clause 29, wherein the multiple gray level value profiles comprises a first gray level value profile and a second gray level value profile, wherein the first gray level value profile is extracted from a first image of the structure obtained at a first apparatus setting, and the second gray level value profile is extracted from a second image of the structure obtained at a second apparatus setting different from the first apparatus setting.

31. The method of clause 30, wherein the multiple gray level value profiles further comprises a third gray level value profile extracted from a third image of the structure obtained at a third apparatus setting different from the first and second apparatus settings.

32. The method of clause 29, wherein the apparatus setting includes at least one of resolution, sample position, alignment, or stigmata.

33. The method of clause 29, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

34. The method of clause 29, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

35. The method of clause 29, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

36. A method for metrology, comprising: receiving multiple inspection images of a structure on a sample, each inspection image of the multiple inspection images being an image of the sample acquired at a different setting of an apparatus; obtaining multiple gray level value profiles from the multiple inspection images, wherein each gray level value profile of the multiple gray level value profiles is associated with the structure in a different inspection image of the multiple inspection images; determining a threshold value from the multiple gray level value profiles, wherein the threshold value is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum; and determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

37. The method of clause 36, wherein the multiple inspection images comprises a first inspection image and a second inspection image, wherein the first inspection image is obtained at a first apparatus setting, and the second inspection image is obtained at a second apparatus setting different from the first apparatus setting.

38. The method of clause 37, wherein the multiple inspection images comprises a third inspection image obtained at a third apparatus setting different from the first and second apparatus settings.

39. The method of clause 36, wherein the setting of the apparatus includes at least one of resolution, sample position, alignment, or stigmata. 40. The method of clause 36, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

41. The method of clause 36, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

42. The method of clause 36, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

[0093] Block diagrams in the figures may illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer hardware or software products according to various exemplary embodiments of the present disclosure. In this regard, each block may represent one or multiple arithmetical or logical operation processing that may be implemented using hardware such as an electronic circuit. Blocks may also represent modules, segments, or portions of code that comprises one or more executable instructions for implementing the specified logical functions. It should be understood that in some alternative implementations, functions indicated in a block may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed or implemented substantially concurrently, or two blocks may sometimes be executed in reverse order, depending upon the functionality involved. Some blocks may also be omitted. It should also be understood that each block of the block diagrams, and combination of the blocks, may be implemented by special purpose hardware-based systems that perform the specified functions or acts, or by combinations of special purpose hardware and computer instructions.

[0094] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings, and that various modifications and changes may be made without departing from the scope thereof. The present disclosure has been described in connection with various embodiments, other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims

1. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology, the operations comprising: receiving an inspection image of a structure on a sample; extracting a gray level value profile associated with the structure from the received inspection image; and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value, wherein the threshold value is determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum, and wherein each gray level value profile of the multiple gray level value profiles is associated with a different apparatus setting.

2. The non-transitory computer readable medium of claim 1, wherein the multiple gray level value profiles comprises a first gray level value profile and a second gray level value profile, wherein the first gray level value profile is extracted from a first image of the structure obtained at a first apparatus setting, and the second gray level value profile is extracted from a second image of the structure obtained at a second apparatus setting different from the first apparatus setting.

3. The non-transitory computer readable medium of claim 2, wherein the multiple gray level value profiles further comprises a third gray level value profile extracted from a third image of the structure obtained at a third apparatus setting different from the first and second apparatus settings.

4. The non-transitory computer readable medium of claim 1, wherein the apparatus setting includes at least one of resolution, sample position, alignment, or stigmata.

5. The non-transitory computer readable medium of claim 1, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

6. The non-transitory computer readable medium of claim 1, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

7. The non-transitory computer readable medium of claim 1, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

8. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for metrology, the operations comprising: receiving multiple inspection images of a structure on a sample, each inspection image of the multiple inspection images being an image of the sample acquired at a different setting of an apparatus; obtaining multiple gray level value profiles from the multiple inspection images, wherein each gray level value profile of the multiple gray level value profiles is associated with the structure in a different inspection image of the multiple inspection images; determining a threshold value from the multiple gray level value profiles, wherein the threshold value is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum; and determining a critical dimension of the structure from a gray level value profile associated with the structure based on the determined threshold value.

9 The non-transitory computer readable medium of claim 8, wherein the multiple inspection images comprises a first inspection image and a second inspection image, wherein the first inspection image is obtained at a first apparatus setting, and the second inspection image is obtained at a second apparatus setting different from the first apparatus setting.

10. The non-transitory computer readable medium of claim 9, the multiple inspection images comprises a third inspection image obtained at a third apparatus setting different from the first and second apparatus settings.

11. The non-transitory computer readable medium of claim 8, wherein the setting of the apparatus includes at least one of resolution, sample position, alignment, or stigmata.

12. The non-transitory computer readable medium of claim 8, wherein the threshold value is indicative of gray level value at a location where at least some different gray level value profiles of the multiple gray level value profiles intersect.

13. The non-transitory computer readable medium of claim 8, wherein the threshold value is indicative of gray level value at a location where a distance between at least some different gray level value profiles of the multiple gray level value profiles is lowest.

14. The non-transitory computer readable medium of claim 8, wherein the structure includes at least one of a circuit line, a via, a pillar, a contact pad, a trench, or an overlay pattern.

15. A method for metrology, comprising: receiving an inspection image of a structure on a sample; extracting a gray level value profile associated with the structure from the received inspection image; and determining a critical dimension of the structure from the extracted gray level value profile based on a threshold value, wherein the threshold value is determined from multiple gray level value profiles associated with the structure and is indicative of gray level value at a location where a variation between different gray level value profiles of the multiple gray level value profiles is a minimum, and wherein each gray level value profile of the multiple gray level value profiles is associated with a different apparatus setting.