Metrology accuracy improvement using reference geometric parameter

Abstract

Improved methods and apparatus for correcting measurements on an inspection image for a wafer inspection system are provided. An improved method comprises acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.

Description

METROLOGY ACCURACY IMPROVEMENT USING REFERENCE GEOMETRIC PARAMETERCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23219572.7 which was filed on 22 December 2023 and which is incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] The embodiments provided herein generally relate to a measurement correction technique, and more particularly, to a metrology accuracy improvement technique utilizing a reference geometric parameter.BACKGROUND

[0003] In manufacturing processes of integrated circuits (ICs), unfinished or finished circuit components are inspected to ensure that they are manufactured according to design and are free of defects. Inspection systems utilizing optical microscopes or charged particle (e.g., electron) beam microscopes, such as a scanning electron microscope (SEM) can be employed. 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 of patterns / structures measured from a SEM image can be used for identifying defects of manufactured ICs.SUMMARY

[0004] In some embodiments, an apparatus for correcting measurements on an inspection image for a wafer inspection system is provided. The apparatus comprises a memory storing a set of instructions; and at least one processor configured to execute the set of instructions to cause the apparatus to perform: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.

[0005] 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 a method for correcting measurements on an inspection image for a wafer inspection system is provided. The method comprises acquiring a first measurement for a firstdimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.

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

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

[0008] FIG. 1 is a schematic diagram illustrating an example charged-particle beam inspection system, consistent with embodiments of the present disclosure.

[0009] 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 inspection system of FIG. 1.

[0010] 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 inspection system of FIG. 1.

[0011] FIG. 3 is a block diagram of an example measurement correction system, consistent with some embodiments of the present disclosure.

[0012] FIG. 4 shows an example inspection image for illustrating a measurement correction technique, consistent with some embodiments of the present disclosure.

[0013] FIG. 5A is a graph illustrating simulation results of variations of measurements.

[0014] FIG. 5B is a graph illustrating simulation results of variations of corrected measurements, consistent with some embodiments of the present disclosure.

[0015] FIG. 6A are graphs illustrating measurements according to process parameter changes.

[0016] FIG. 6B are graphs illustrating corrected measurements according to process parameter changes, consistent with some embodiments of the present disclosure.

[0017] FIG. 7 are graphs comparing noise reduction efficiencies of a conventional method and a measurement correction method consistent with some embodiments of the present disclosure.

[0018] FIG. 8A illustrates an example spacer double patterning structure.

[0019] FIG. 8B is a graph illustrating measurements for a spacer double patterning structure.

[0020] FIG. 8C is a graph illustrating corrected measurements for a spacer double patterning structure, consistent with some embodiments of the present disclosure.

[0021] FIG. 9A illustrates a measurement distribution as a wafer plot for a spacer double patterning structure.

[0022] FIG. 9B illustrates a corrected measurement distribution as a wafer plot for a space double patterning structure, consistent with some embodiments of the present disclosure.

[0023] FIG. 10 are graphs comparing noise reduction efficiencies of a conventional method and a measurement correction method consistent with some embodiments of the present disclosure.

[0024] FIG. 11 is a flow chart illustrating an example method for correcting measurements, consistent with some embodiments of the present disclosure.DETAILED DESCRIPTION

[0025] 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.

[0026] 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.

[0027] 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.

[0028] 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 ascanning 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.

[0029] 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 of patterns / structures measured from a SEM image can be used for identifying defects of manufactured ICs. 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 dimensions 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 is limited by a 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), etc. 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.

[0030] According to some embodiments of the present disclosure, a measurement correction technique is provided. In some embodiment, precision of one or more critical dimension measurements can be achieved by utilizing a known geometric parameter value that is associated with the one or more critical dimension measurements. In some embodiments, measurement errors of one or more critical dimension measurements can be estimated based on reference data for the one or more critical dimension measurements. In some embodiments, measurement errors of one or more measurements can be corrected using a known reference value associated with the one or more measurements. In some embodiments, reference data can remain unchanged despite various noise sources such as inspection tool error, process noise, measurement errors, etc.

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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.

[0035] 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 secondpressure, the wafer is subject to inspection by beam tool 104. Beam tool 104 may be a single-beam system or a multi-beam system.

[0036] A controller 109 is electronically connected to beam tool 104. 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.

[0037] 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.

[0038] 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 random-access memory (RAM), a read-only memory (ROM), an optical disc, a magnetic disk, a hard drive, a solid-state drive, a flash drive, a security digital (SD) card, a memory stick, a compact flash (CF) card, or any type of storage device. The codes 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.

[0039] 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.

[0040] Beam tool 104A 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.

[0041] 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 104 A. Secondary optical system 242 and charged-particle detection device 244 can be aligned with a secondary optical axis 252 of apparatus 104A.

[0042] 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.

[0043] 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 microdeflectors 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.

[0044] 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 beamlimit 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.

[0045] 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 ofbeamlets 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] 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. Forexample, 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 104A 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.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] 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.

[0054] 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 150 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 emanatedfrom 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.

[0055] 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 post-processed 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.

[0056] 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.

[0057] 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.

[0058] 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 adetector 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.

[0059] The images generated by SCPM may be used for defect inspection. 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.

[0060] In some embodiments, machine learning may be employed in the generation 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 the measurement correction method, e.g., method 1100 of FIG. 11, in association with, e.g., a measurement correction system 300 of FIG. 3, which will be described below. 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.

[0061] If the model(s) include one or more discriminative models, the discriminative model(s) may have any suitable architecture or configuration known in the art. Discriminative models, also called conditional models, are a class of models used in machine learning for modeling the dependence of an unobserved variable “y” on an observed variable “x.” Within a probabilistic framework, this may be done by modeling a conditional probability distribution P(ylx), which can be used for predicting y based on x. Discriminative models, as opposed to generative models, may notallow 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.

[0062] 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.

[0063] 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.

[0064] 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.

[0065] 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.

[0066] Neural networks typically consist of multiple layers, and the signal path traverses from front to back. The goal of the neural network is to solve problems in the same way that the human brain would, although several neural networks are much more abstract. Modern neural network projects typically work with a few thousand to a few million neural units and millions of connections. The neural network may have any suitable architecture or configuration known in the art.

[0067] 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.

[0068] Reference is now made to FIG. 3, which is a block diagram of an example measurement correction system, consistent with some embodiments of the present disclosure. In some embodiments, measurement correction system 300 can comprise one or more processors and memories. It is appreciated that in various embodiments measurement correction system 300 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, measurement correction system 300 may include one or more components (e.g., software modules) that can be implemented in controller 109 or systems 290 or 199 as discussed herein. As shown in FIG. 3, measurement correction system 300 may comprise a measurement acquirer 310, a reference data acquirer 320, and measurement corrector 330.

[0069] According to some embodiments of the present disclosure, measurement acquirer 310 can be configured to acquire measurement data from at least one inspection image 301. In some embodiments, inspection image 301 is a SCPM image of a sample or a wafer. In some embodiments, inspection image 301 can be an inspection image generated by, e.g., EBI system 100 of FIG. 1 or electron beam tool 104A of FIG. 2A or 104B of FIG. 2B. In some embodiments, inspection image 301 may be obtained from a storage device or system storing the inspection image. In some embodiments, inspection image 301 can be an image of structures in the region of interest of the wafer. In some embodiments, inspection image 301 can be an image of structures having at least two critical dimensions that may be utilized to identify defects. In some embodiments, inspection image 301 can have one or more lines and one or more trenches as shown in FIG. 4 as an example inspection image. In some embodiments, inspection image 301 can have a plurality of inspection images of device structures corresponding to the same pattern design.

[0070] According to some embodiments of the present disclosure, measurement acquirer 310 is configured to acquire measurements of structure dimensions on inspection image 310. According to some embodiments of the present disclosure, measurements of structure dimensions can include first measurement 311 and second measurement 322. In some embodiments, first measurement 311 andsecond measurement 322 can be associated with reference data, e.g., reference data 321 acquired by reference data acquirer 320.

[0071] FIG. 4 shows an example inspection image for illustrating a measurement correction mechanism, consistent with some embodiments of the present disclosure. As shown in FIG. 4, inspection image 301 can be an inspection image of device structures including a plurality of lines. In this example, each of the plurality of lines of device structures is designed to have the same width along its length and to be uniformly spaced from the neighboring line along its length. However, as shown in FIG. 4, inspection image 301 illustrates line edge roughness on a plurality of lines 401 and trenches 402 between neighboring lines 401 as a noise source. Therefore, measurements of dimensions based on inspection image 301 are influenced by this noise source. For example, measurements for a line width LW along one line 401 can vary according to its measuring position. The same goes with a trench width TW. In some embodiments, first measurement 311 can include one or more first measurements 311 of line width LW along line 401. In some embodiments, the one or more first measurements 311 can be measurements measured along a first measurement box 410 in FIG. 4. Similarly, in some embodiments, second measurement 312 can include one or more second measurements 312 of trench width TW along trench 402. In some embodiments, the one or more second measurements 312 can be measurements measured along a second measurement box 420 in FIG. 4.

[0072] Referring back to FIG. 3, reference data acquirer 320 is configured to acquire reference data associated with measurements (e.g., first measurement 311 or second measurement 312) acquired in measurement acquirer 310. In some embodiments, reference data 321 associated with first measurement 311 or second measurement 312 can have a property that tends to remain constant on inspection image 310 while first measurement 311 or second measurement varies along the measurement points. In some embodiments, reference data 321 can be a known geometric parameter value such as a pitch. In some embodiments, reference data 321 can be a pitch between two neighboring lines 401. Because the pitch is a geometric parameter of the corresponding pattern on the reticle, which is then transferred to a wafer as device structures, the pitch value may not be dependent on a process variation (e.g., focus or dose) of a scanner, line-edge roughness noise, inspection tool error, measurement error, etc. Even when a line width may change due to scanning process variations, the pitch remains the same. Further, because inspection tools generally generate inspection images at a sub-ppm magnificent error level, it can be assumed in the present disclosure that errors on the 100 nm level pitch caused by inspection tool’s magnificent error is considered negligible.

[0073] In some embodiments, reference data 321 can be obtained from a layout file for a wafer design corresponding to the inspection image, e.g., inspection image 301 of FIG. 4. The layout file can be in a Graphic Database System (GDS) format, Graphic Database System II (GDS II) format, an Open Artwork System Interchange Standard (OASIS) format, a Caltech Intermediate Format (CIF), etc. The wafer design may include patterns or structures for inclusion on the wafer. The patterns orstructures can be mask patterns used to transfer features from the photolithography masks or reticles to a wafer. In some embodiments, a layout in GDS or OASIS format, among others, may comprise feature information stored in a binary file format representing planar geometric shapes, text, and other information related to the wafer design.

[0074] According to some embodiments of the present disclosure, measurement corrector 330 can be configured to correct measurements (e.g., first measurement 311 or second measurement 312) acquired in measurement acquirer 310. In some embodiments, measurement corrector 330 can correct first measurement 311 or second measurement 312 based on reference data 321. In an example shown in FIG. 4, a measured pitch PM can be represented as below:LWM+ TWM= PMHere, LWM represents first measurement 311, which is a measured line width, and TWM represents second measurement 312, which is a measured trench width.

[0075] In some embodiments, it can be inferred that a difference between a reference pitch, e.g., reference data 321 and the measured pitch PM results from noise included in first measurement 311 and second measurement 312. The pitch measurement error Np in the measured pitch PM can be represented as below:Np = PM ~ PRHere, PR represents reference data 321, i.e., a reference pitch. Because errors in first measurement 311 and second measurement 312 contribute to pitch measurement error Np in the measured pitch PM, line measurement error NL in first measurement 311 and trench measurement error NT in second measurement 312 can be estimated based on pitch measurement error Np. In some embodiments, a relationship among pitch measurement error Np, line measurement error NL, and trench measurement error NT can be represented as below:NP= NL+ NT, where:NL= WiNp (Equation 1)NT= W2NP(Equation 2)Here, W i represents a first weight, which is a contribution ratio of line measurement error NL to pitch measurement error Np. Similarly, W2 represents a second weight, which is a contribution ratio of trench measurement error Np to pitch measurement error Np. Here, Wi+W2=l. In an example shown in FIG. 4, it is assumed that the magnitudes of line measurement error NL and trench measurement error Np are equal, and thus both first weight W 1 and second weight W2 are set to 0.5. That is, in some embodiments, it is assumed that a line measurement and a trench measurement have the same degree of uncertainty so that both the first weight and the second weight are set to have the same weight, e.g., 1 / 2. In some embodiments, a first weight and a second weight can have different values according to their respective contribution ratios. For example, a line measurement and a trench measurement may not have the same degree of uncertainty depending the recipe setting on how to conduct the edge detection. In some embodiments, error contributions can be different for each measurement and thus weights can be set according to each measurement’ s contribution to the pitch measurement error, e.g., by measuring variations of each measurement. In some embodiments, reference data 321 can be associated with more than two dimensions, e.g., three or more dimensions (e.g., described later referring to FIG. 8A). In such scenarios, error contribution weights can be similarly set according to each measurement’s contribution to the pitch measurement error while maintaining the sum of all weights to be 1.

[0076] According to some embodiments of the present disclosure, measurement corrector 330 can correct first measurement 311 based on the estimated line measurement error N = WiNp and correct second measurement 312 based on the estimated trench measurement error NT = W2NP, respectively, as below:LWC= LWM- W^p (Equation 3)TWC= TWM- W2NP(Equation 4)Here, LWc represents a corrected line width measurement and TWc represents a corrected trench width measurement.

[0077] While correcting one set of first measurement 311 and second measurement 312 has been described, it will be appreciated that measurement acquirer 310 can acquire a plurality of sets of first measurement 311 and second measurement 312, and measurement corrector 330 can correct each set of first measurement 311 and second measurement 312 similarly. For example, measurement acquirer 310 can acquire a plurality of first measurements 311 along line 401 in first box 410 of FIG. 4 and a plurality of second measurements along trench 402 in second box 420. In some embodiments, after correcting the plurality of first measurements 311, a critical dimension of a line width of line 401 can be determined by averaging the plurality of corrected first measurements. Similarly, in someembodiments, after correcting the plurality of second measurements 312, a critical dimension of a trench width of trench 402 can be determined by averaging the plurality of corrected second measurements.

[0078] While some embodiments have been described utilizing known reference data 321, e.g., reference pitch PR from design data, it will be appreciated that the present disclosure can be applied when reference data 321 is not known. In some embodiments, reference data 321 can be obtained by adding a line measurement and a trench measurement. In some embodiments, reference data 321 can be obtained by averaging a plurality of measurements. For example, in an example shown in FIG. 4, an average of a plurality of first measurements 311 can be obtained and an average of second measurements 312 can be obtained. And a sum of the average of first measurements 311 and the average of second measurements 312 can be used as a reference pitch, e.g., reference data 321. In some embodiments, reference data 321 can be obtained by measuring a distance corresponding to a reference dimension, e.g., pitch. For example, in an example shown in FIG. 4, a measurement for a distance between two rising edges of two lines 401, e.g., neighboring two lines can be used as reference data 321. Similarly, a measurement for a distance between two falling edges of two lines 401, e.g., neighboring two lines can be used as reference data 321. Each of these measurements, i.e., a measurement for two rising edges and a measurement for two falling edges, can be referred to as an edge-to-edge measurement in this disclosure. When measuring critical dimensions, systematic measurement errors in a rising edge may be different from systematic measurement errors in a falling edge, and thus the errors in the rising edge and the errors in the falling edges may accumulate when a distance between the rising edge and the falling edge is measured. In contrast, the systematic measurement errors can be canceled out in the edge-to-edge measurement because it only measures a distance between the same edges, e.g., between two rising edges or between two falling edges. In some embodiments, reference data 321 can be obtained by averaging a plurality of edge-to-edge measurements.

[0079] FIG. 5A illustrates simulation results of variations of measurements. In this experiment, to simulate measured line widths and measured trench width with noise, two sets of normally distributed 1000 random numbers are generated. In FIG. 5A, plot 510 represents random numbers generated to simulate line width measurements LW«, which have a mean value ML and a standard deviation o of 1. Similarly, plot 520 represents random numbers generated to simulate trench width measurements TWM, which have a mean value MT and a standard deviation o of 1. As shown in FIG. 5A, most of simulated line width measurements LWM in plot 510 vary from its mean value ML and such variations from mean value ML can be considered noise in the simulated line width measurements. Similarly, most of simulated trench width measurements TWM in plot 520 vary from its mean value MT, and such variations from mean value MT can be considered noise in the simulated trench width measurements. In FIG. 5A, plot 530 represents simulated pitch measurements PM, which are generated by summing simulated line width measurements of plot 510 and simulated trenchwidth measurements in plot 520. In this experiment, simulated pitch measurements PM of plot 530 has a mean value Mp= ML+ MT and a standard deviation o ~ v / 2, which can be expected from mean value ML and a standard deviation G= I of plot 510 and mean value MT and a standard deviation o=l of plot 520. In FIG. 5A, variations of simulated pitch measurements PM from its mean value Mp can be considered noise, and variations of simulated line width measurements LWM and variations of simulated trench width measurements TWM contribute to variations of simulated pitch measurements PM-

[0080] FIG. 5B illustrates simulation results of variations of corrected measurements, consistent with embodiments of the present disclosure. In this experiment, a sum of mean value ML of simulated line width measurements LWM and mean value MT of simulated trench width measurements TWM is used as reference pitch PR. Thus, plot 560 representing reference pitch PR in FIG. 5B has a constant value of ML and does not present variations, which means no noise. In this experiment, simulated line width measurements LWM are corrected according to Equation 3 with first weight Wi=l / 2 and reference pitch PR, and corrected line width measurements LWc are shown as plot 540 of FIG. 5B. Similarly, simulated trench width measurements TWM are corrected according to Equation 4 with second weight W 2=1 / 2 and reference pitch PR, and corrected trench width measurements TWc are shown as plot 550 of FIG. 5B. In this experiment, variations of the corrected line width measurements of plot 540 and corrected trench width measurements of plot 550 are reduced by a factor of about 2, which is equivalent to 30% of noise reduction.

[0081] It will be noted that the line edge roughness and measurement equipment errors are not the only source of noise in measurement data. Various factors can be a noise source of critical dimension measurement data. While line widths or trench widths can vary systematically or randomly over a wafer, it is noted that reference data, e.g., pitch of the lines and trenches remain constant over the varying line widths and trench widths. In some embodiments, process parameters in the lithography process for manufacturing structure devices on a wafer can cause critical dimension variations, which can be presented as line edge error roughness on inspection images. In some embodiments, the process parameters can include various parameters such as a focus, a exposure dose, etc.

[0082] FIG. 6A are graphs illustrating variations of measurements as a function of focus and exposure dose. In this experiment, real data measurements (i.e., line width measurements and trench width measurements) are obtained on inspection images (e.g., inspection image 301 in FIG. 4) that are obtained under various focus-exposure dose conditions. In FIG. 6A, real data measurements are plotted as measurements versus for different exposure doses, e.g., as focus-exposure matrix, in graph 610 and 620 in FIG. 6A. In FIG. 6A, in each graph 610, 620, and 630, the x-axis represents a focus parameter, and the y-axis represents a measurement value corresponding to a certain focus value. Graph 610 shows line width measurements LWM under a corresponding focus parameter for differentexposure doses. In graph 610, each horizontally extended line connects measurement data having the same exposure dose. As shown in graph 610, line width measurements LW« vary according to a focus change, dose change, or focus-dose combination change. Similarly, graph 620 shows trench width measurements TWM under a corresponding focus parameter for different exposure doses. In graph 620, each horizontally extended line connects measurement data having the same exposure dose. As shown in graph 620, it is shown that trench width measurements TWM vary according to a focus change, dose change, or focus-dose combination change. Graph 630 represents pitch measurements PM, which are generated by summing line width measurements LWM of graph 610 and trench width measurements TWM of graph 620. In graph 630, each horizontally extended line corresponds to a certain exposure dose and can be generated by summing line width measurements of graph 610 and trench width measurements of graph 620 for the certain exposure dose. As shown in graph 630, the measured pitch PM is noisy, which is illustrated as variations (or fluctuations) in graph 630. It is also noted that the noise is especially visible at the edge of the process window, e.g., each graph 610, 620, and 630 presents greater variations on the top side, bottom side, left side, and right side of the window than the center.

[0083] FIG. 6B illustrates simulation results of variations of corrected measurements according to focus and dose changes, consistent with embodiments of the present disclosure. In this experiment, a constant reference value is used as reference pitch PR. Thus, graph 660 representing reference pitch PR in FIG. 6B has a constant value and does not show variations along various focus-dose combinations, which means no noise. In this experiment, line width measurements LWM are corrected according to Equation 3 with first weight Wi= 1 / 2 and reference pitch PR, and corrected line width measurements LWc are shown as graph 640 of FIG. 6B. Similarly, trench width measurements TWM are corrected according to Equation 4 with second weight W 2=1 / 2 and reference pitch PR, and corrected trench width measurements TWc are shown as graph 650 of FIG. 6B. Compared to the direct measurements LWM and TWM in graphs 610 and 620 of FIG. 6A, corrected measurements LWc and TWc present less variations, especially at the edges of the process window. In this experiment, to quantitatively evaluate how much noise is suppressed by a measurement correction mechanism according to some embodiments of the present disclosure, a fit has been performed on the measurement data or corrected measurement data, and residual values have been analyzed. As a fit function, 3rdorder dose and 2ndorder focus dependency has been assumed. It is noted that a measurement correction mechanism according to some embodiments of the present disclosure has improved from 3.4 to 3.2 nm in 3o fit residuals for line measurements and from 4.0 to 3.2 nm for trench measurements.

[0084] FIG. 7 are graphs comparing noise reduction efficiencies of a conventional method and a measurement correction method consistent with some embodiments of the present disclosure. In this experiment, noise of direct measurements and noise of corrected measurements according to some embodiments of the present disclosure are compared. In the conventional method, directmeasurements are utilized as critical dimension measurements without correcting the measurements with the measurement correcting mechanism using a measurement correcting system, e.g., system 300 of FIG. 3. In FIG. 7, bar graph 710 represents an experiment result for measurements of a longer measurement box and bar graph 720 represents an experiment result for measurements of a shorter measurement box. In this experiment, the shorter measurement box is a half-size of the longer measurement box, which means that the number of direct measurements along the shorter measurement box is the half of the number of direct measurements along the longer measurement box. For example, the longer measurement box can correspond to measurement box 430 of FIG. 4 in length and the shorter measurement box can correspond to measurement box 410 of FIG. 4 in length. For bar graph 710, a plurality of line width measurements LW« and trench width measurements TWM are taken along a longer measurement box, e.g., measurement box 430 of FIG. 4. In bar graph 710, the y-axis represents quantified noise (variation) in data, and the lower value presents lower noise. Noise (or variation) of line width measurements LW« and trench width measurements TWM are quantified as bar 711 and 713, respectively. Similarly, noise of corrected line width measurements LWM and noise of corrected trench width measurements TWM are quantified as bar 712 and 714. As shown in bar graph 710, corrected measurements present reduced noise than direct measurement data for both the line width and trench width.

[0085] Similarly, for bar graph 720, a plurality of line width measurements LWM and trench width measurements TWM are taken along a shorter measurement box, e.g., measurement box 410 of FIG. 4. Noise (or variation) of line width measurements LWM and trench width measurements TWM are quantified as bar 721 and 723, respectively. Similarly, noise of corrected line width measurements LWM and noise of corrected trench width measurements TWM are quantified as bar 722 and 724. As shown in bar graph 720, corrected measurements present reduced noise than direct measurement data for each of the line width and trench width along the shorter measurement box.

[0086] It is noted that noise can be generally reduced by measuring critical dimensions along a longer measurement box. Based on experiment results in FIG. 7, it is also be noted that the correction method consistent with some embodiments of the present disclosure shows the almost same effect on noise reduction as the conventional method using a double sized measurement box. For example, bar 722 in bar graph 720 for corrected linewidth measurements along the shorter measurement box has the similar noise amount to bar 711 in bar graph 710 for direct linewidth measurements along the longer measurement box. Similarly, bar 724 in bar graph 720 for corrected trench width measurements along the shorter measurement box has the even lower noise amount than bar 713 in bar graph 710 for direct measurements along the longer measurement box.

[0087] While some embodiments of the present disclosure have been described with inspection image 301 having regularly spaced lines as shown in FIG. 3, it will be appreciated that present disclosure can be applied to any device structures when it has a stable dimension regardless of measurement equipment noise, process variations, line edge roughness, measurement errors, etc.FIG. 8A illustrates an example spacer double patterning structure. As shown in FIG. 8A, spacer double patterning structure 801 includes a plurality of lines having the same line width L and includes two trenches having different trench widths T1 and T2 between neighboring lines. In some embodiments, spacer double patterning structure 801 can be generated by a spacer double patterning process. For example, first trench width T1 can be defined by a lithography, line width L can be defined by a space formation process, and second trench width T2 can be the remaining trench width. In this example, reference pitch PR can be represented as PR=2L+T1+T2.

[0088] FIG. 8B is a graph illustrating measurements for a spacer double patterning structure. In this experiment, real data measurements (i.e., line width measurements and trench width measurements) are obtained on an inspection image corresponding to spacer double patterning structure 801 of FIG. 8A. In FIG. 8B, plots 810, 820, and 830 represent 40 direct measurements for each of line width L, first trench width Tl, and second trench width T2. In FIG. 8B, plot 840 represents pitch measurements PM, which are generated by summing line width measurements of plot 810 twice, first trench width measurements of plot 830, and second trench width measurements of plot 840. In FIG. 8B, it can be seen that each line width L, first trench width Tl, second trench width T2, and pitch measurements PM are all noisy as they show variations throughout measurements.

[0089] FIG. 8C is a graph illustrating corrected measurements for a spacer double patterning structure, consistent with embodiments of the present disclosure. In this experiment, a constant reference value is used as reference pitch PR. Thus, plot 880 representing reference pitch PR in FIG. 8C has a constant value and does not show variations. In this experiment, line width measurements L are corrected according to the measurement correction, and corrected line width measurements are shown as plot 850 of FIG. 8C. Similarly, trench width measurements Tl and T2 are corrected according to the measurement correction method and corrected trench width measurements are shown as plots 860 and 870 of FIG. 8C, respectively. In this experiment, error contribution weights 0.25, 0.25, and 0.25 have been used as the error contribution weights for line width measurements L, first trench width measurement Tl, and second trench width measurement T2, respectively. As the line width measurements L are added twice for the measured pitch PM, a weight for one line width measurement L can be determined 0.25. In this experiment, variations of the corrected line width measurements of plot 850 and corrected trench width measurements of plots 860 and 870 are reduced compared to direct measurements in FIG. 8B. It is noted that the present measurement correction technique can be applied to different structures other than a structure having regularly spaced lines.

[0090] FIG. 9A illustrates a measurement distribution as a wafer plot for a spacer double patterning structure. In FIG. 9A, line width measurements in plot 810 of FIG. 8B are marked on corresponding position on the wafer plot and values for the rest of the wafer space are interpolated based the marked direct line width measurements. In the wafer plot in FIG. 9A, the brighter section presents measurements with less noise as it is closer to a mean value, i.e., values around mean value 18 and the darker section presents measurements with more noise as it is farther from the mean value.As shown in FIG. 9A, the measurements are noisier at the center and at the edge of the wafer, which is indicated as dark. FIG. 9B illustrates a corrected measurement distribution as a wafer plot for a space double patterning structure, consistent with embodiments of the present disclosure. In FIG. 9B, corrected line width measurements in plot 850 of FIG. 8C are marked on corresponding position of a wafer and values for the rest of the wafer space are interpolated based the marked corrected line width measurements. Similarly, FIG. 9B also illustrates that the corrected measurements are noisier at the center and at the edge of the wafer. But it is noticed that the area of the darker section becomes reduced and brighter compared to the wafer plot of FIG. 9A. It is noted that the measurement noise imbalance on a wafer can also be improved according to the measurement correction mechanism consistent with some embodiments of the present disclosure.

[0091] FIG. 10 are graphs comparing noise reduction efficiencies of a conventional method and a measurement correction method consistent with some embodiments of the present disclosure. In this experiment, noise of direct measurements in FIG. 8B of conventional methods and noise of corrected measurements according to some embodiments of the present disclosure in FIG. 8C are compared. In FIG. 10, the y-axis represents quantified noise (variation) in data, and the lower value presents lower noise. Noise (or variation) of line width measurements L and trench width measurements T1 and T2 are quantified as bar 1011, 1013, and 1015, respectively. Similarly, noise of corrected line width measurements corresponding to line width measurements L and noise of corrected trench width measurements corresponding to trench width measurements T1 and T2 are quantified as bar 1012, 1014, and 1016, respectively. As shown in FIG. 10, corrected measurements present reduced noise than direct measurements for both the line width and trench widths. It is notable that the measurement correction mechanism according to some embodiments of the present disclosure has improved from 1.9 to 1.4 nm in 3o fit residuals for line measurements.

[0092] While some embodiments have been described using a pattern having lines and trenches, it will be appreciated that the present disclosure can be applied to any types of patterns including contact holes, pillars, lines with reduced length, staggered lines, lines or trenches with various widths, overlay patterns, etc. as long as the pattern includes two or more critical dimensions associated with its reference data. For example, in the contact hole patterns, a distance from a center of a contact hole to a center of a neighboring contact hole can be used as reference data, i.e., a pitch value, and a diameter measurement of a contact hole and a distance measurement between two nearest edges of two neighboring contact holes can be used as two measurements associated with the reference data. In some embodiments, a value corresponding to N time of a pitch value can also be utilized as reference data. In some embodiments, a measurement correction mechanism can be applied at various stages, e.g., on the measured data directly (See example cases) or incorporated in the fit algorithm. Noise reduction performance of a measurement correction mechanism according to some embodiments of the present disclosure can also be used as an indicator for the contribution of line edge roughness, another noise source, etc. to the measurement noise.

[0093] FIG. 11 is a flow chart illustrating an example method for correcting measurements, consistent with embodiments of the present disclosure. The steps of method 1100 can be performed by a system (e.g., system 300 of FIG. 3) executing on or otherwise using the features of a computing device, e.g., controller 109 of FIG. 1. It is appreciated that the illustrated method 1100 can be altered to modify the order of steps and to include additional steps.

[0094] In step S 1110, a first measurement for a first dimension and a second measurement for a second dimension are acquired. Step S 1110 can be performed by, for example, measurement acquirer 310, among others. In some embodiments, the first measurement and second measurement can be measurements on an inspection image 301. In some embodiments, a first measurement can include one or more first measurements 311 of line width LW along line 401 , e.g., shown in FIG. 4. In some embodiments, the one or more first measurements 311 can be measurements measured along a first measurement box 410 in FIG. 4. Similarly, in some embodiments, a second measurement can include one or more second measurements 312 of trench width TW along trench 402. In some embodiments, the one or more second measurements 312 can be measurements measured along a second measurement box 420 in FIG. 4.

[0095] In step S 1120, reference data is acquired. Step S 1120 can be performed by, for example, reference data acquirer 320, among others. In some embodiments, reference data 321 is associated with first measurement 311 or second measurement 312 and can have a property that tends to remain constant on inspection image 310 while first measurement 311 or second measurement vary along the measurement points. In some embodiments, reference data 321 can be a known geometric parameter value such as a pitch. In some embodiments, reference data 321 can be a pitch between two neighboring lines 401. Because the pitch is a geometric parameter of the corresponding pattern on the reticle, which is then transferred to a wafer as device structures, the pitch value may not be dependent on a process variation (e.g., focus or dose) of a scanner, line-edge roughness noise, inspection tool error, measurement error, etc. In some embodiments, reference data 321 can be obtained from a layout file for a wafer design corresponding to the inspection image, e.g., inspection image 301 of FIG. 4.

[0096] In step S 1130, a first measurement error for first measurement 311 and a second measurement error for second measurement 312 are estimated. Step SI 130 can be performed by, for example, measurement corrector 330, among others. According to some embodiments of the present disclosure, the first measurement error and second measurement error can be estimated based on first measurement 311, second measurement 312, and reference data 321. The procedure for estimating for first measurement error NL and second measurement error NT is described in detail with respect to the procedure for obtaining Equation 1 and Equation 2, and thus the repetitive explanation for the estimation procedure will be omitted here for simplicity.

[0097] In step SI 140, first measurement and second measurement are corrected based on the estimated first measurement error and second measurement error. Step S 1140 can be performed by, for example, measurement corrector 330, among others. According to some embodiments of thepresent disclosure, first measurement 311 can be corrected based on the estimated first measurement error NL= WiNp, second measurement 312 can be corrected based on the estimated second measurement error NT = W2Np. respectively. The procedure for correcting the first measurement and second measurement is described in detail with respect to the procedure for obtaining Equation 3 and Equation 4, and thus the repetitive explanation for the correction procedure will be omitted here for simplicity.

[0098] 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 1100. 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.

[0099] The embodiments may further be described using the following clauses:1. A method for correcting measurements on an inspection image for a wafer inspection system, comprising: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.2. The method of clause 1, wherein the reference data is a reference value associated with the first dimension and the second dimension.3. The method of clause 1 or 2, wherein the first dimension is a line width, and the second dimension is a trench width.4. The method of any one of clauses 1 to 3, further comprising: summing the first measurement and the second measurement; determining a pitch measurement based on the sum; and estimating a pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.5. The method of clause 4, further comprising: determining a first contribution ratio of the first measurement to the estimated pitch measurement error; and determining a second contribution ratio of the second measurement to the estimated pitch ratio.6. The method of clause 5, wherein estimating the first measurement error for the first measurement and the second measurement error for the second measurement based on the reference data comprises: estimating the first measurement error based on the first contribution ratio and the estimated pitch; and estimating the second measurement error based on the second contribution ratio and the estimated pitch.7. The method of any one of clauses 1 to 6, wherein acquiring reference data associated with the first dimension and the second dimension comprises: acquiring a plurality of first measurements for the first dimension and a plurality of second measurements for the second dimension; averaging the plurality of first measurements to generate a first average measurement; averaging the plurality of second measurements to generate a second average measurement; and determining a sum of the first average measurement and the second average measurement as the reference data.8. The method of any one of clauses 1 to 6, wherein the reference data is obtained based on an edge- to-edge measurement of patterns on the inspection image.9. The method of clause 8, wherein the edge-to-edge measurement is for a distance between two rising edges of the patterns or for a distance between two falling edges of the patterns.10. The method of clause 8 or 9, wherein the patterns comprise at least one of a contact hole, a pillar, a line, or a trench.11. The method of any one of clauses 1 to 6, wherein the reference data is obtained from design data corresponding to the inspection image.12. The method of any one of clauses 1 to 11, further comprising: determining a critical dimension of the first dimension based on the corrected first measurement.13. A method for correcting measurements on an inspection image for a wafer inspection system, comprising: acquiring a line width measurement for a line on the inspection image and a trench width measurement for a trench on the inspection image; determining a pitch measurement error based on a sum of the line width measurement and the trench width measurement and reference data;correcting the line width measurement based on the pitch measurement error and a contribution ratio of the line width measurement to the pitch measurement error; and correcting the trench width measurement based on the pitch measurement error and a contribution ratio of the trench width measurement to the pitch measurement error.14. The method of clause 13, wherein the reference data is a pitch between two neighboring lines having the trench in between.15. The method of clause 13 or 14, wherein determining the pitch measurement error comprises: summing the line width measurement and the trench width measurement; determining a pitch measurement based on the sum of the line width measurement and the trench width measurement; and determining the pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.16. The method of any one of clauses 13 to 14, further comprising: acquiring a plurality of line width measurements and a plurality of trench width measurements; averaging the plurality of line width measurements to generate an average line width measurement; averaging the plurality of trench width measurements to generate an average trench width measurement; and determining a sum of the average line width measurement and the average trench width measurement as the reference data.17. The method of any one of clauses 13 to 15, wherein the reference data is obtained based on an edge-to-edge measurement of two lines on the inspection image.18. The method of clause 17, wherein the edge-to-edge measurement is for a distance between two rising edges of the two lines or for a distance between two falling edges of the two lines.19. The method of any one of clauses 13 to 15, wherein the reference data is obtained from design data corresponding to the inspection image.20. An apparatus for correcting measurements on an inspection image for a wafer inspection system, 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: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension;estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.21. The apparatus of clause 20, wherein the reference data is a reference value associated with the first dimension and the second dimension.22. The apparatus of clause 20 or 21, wherein the first dimension is a line width, and the second dimension is a trench width.23. The apparatus of any one of clauses 20 to 22, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: summing the first measurement and the second measurement; determining a pitch measurement based on the sum; and estimating a pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.24. The apparatus of clause 23, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: determining a first contribution ratio of the first measurement to the estimated pitch measurement error; and determining a second contribution ratio of the second measurement to the estimated pitch ratio.25. The apparatus of clause 24, wherein, in estimating the first measurement error for the first measurement and the second measurement error for the second measurement based on the reference data, the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: estimating the first measurement error based on the first contribution ratio and the estimated pitch; and estimating the second measurement error based on the second contribution ratio and the estimated pitch.26. The apparatus of any one of clauses 20 to 25, wherein, in acquiring reference data associated with the first dimension and the second dimension, the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: acquiring a plurality of first measurements for the first dimension and a plurality of second measurements for the second dimension; averaging the plurality of first measurements to generate a first average measurement; averaging the plurality of second measurements to generate a second average measurement; anddetermining a sum of the first average measurement and the second average measurement as the reference data.27. The apparatus of any one of clauses 20 to 25, wherein the reference data is obtained based on an edge-to-edge measurement of patterns on the inspection image.28. The apparatus of clause 27, wherein the edge-to-edge measurement is for a distance between two rising edges of the patterns or for a distance between two falling edges of the patterns.29. The apparatus of clause 27 or 28, wherein the patterns comprise at least one of a contact hole, a pillar, a line, or a trench.30. The apparatus of any one of clauses 20 to 25, wherein the reference data is obtained from design data corresponding to the inspection image.31. The apparatus of any one of clauses 20 to 30, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: determining a critical dimension of the first dimension based on the corrected first measurement.32. An apparatus for correcting measurements on an inspection image for a wafer inspection system, 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: acquiring a line width measurement for a line on the inspection image and a trench width measurement for a trench on the inspection image; determining a pitch measurement error based on a sum of the line width measurement and the trench width measurement and reference data; correcting the line width measurement based on the pitch measurement error and a contribution ratio of the line width measurement to the pitch measurement error; and correcting the trench width measurement based on the pitch measurement error and a contribution ratio of the trench width measurement to the pitch measurement error.33. The apparatus of clause 32, wherein the reference data is a pitch between two neighboring lines having the trench in between.34. The apparatus of clause 32 or 33, wherein, in determining the pitch measurement error, the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: summing the line width measurement and the trench width measurement; determining a pitch measurement based on the sum of the line width measurement and the trench width measurement; and determining the pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.35. The apparatus of any one of clauses 32 to 33, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: acquiring a plurality of line width measurements and a plurality of trench width measurements; averaging the plurality of line width measurements to generate an average line width measurement; averaging the plurality of trench width measurements to generate an average trench width measurement; and determining a sum of the average line width measurement and the average trench width measurement as the reference data.36. The apparatus of any one of clauses 32 to 34, wherein the reference data is obtained based on an edge-to-edge measurement of two lines on the inspection image.37. The apparatus of clause 36, wherein the edge-to-edge measurement is for a distance between two rising edges of the two lines or for a distance between two falling edges of the two lines.38. The apparatus of any one of clauses 32 to 34, wherein the reference data is obtained from design data corresponding to the inspection image.39. 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 a method for correcting measurements on an inspection image for a wafer inspection system, the method comprising: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.40. The computer readable medium of clause 39, wherein the reference data is a reference value associated with the first dimension and the second dimension.41. The computer readable medium of clause 39 or 40, wherein the first dimension is a line width, and the second dimension is a trench width.42. The computer readable medium of any one of clauses 39 to 41, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to further perform: summing the first measurement and the second measurement; determining a pitch measurement based on the sum; andestimating a pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.43. The computer readable medium of clause 42, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to further perform: determining a first contribution ratio of the first measurement to the estimated pitch measurement error; and determining a second contribution ratio of the second measurement to the estimated pitch ratio.44. The computer readable medium of clause 43, wherein, in estimating the first measurement error for the first measurement and the second measurement error for the second measurement based on the reference data, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: estimating the first measurement error based on the first contribution ratio and the estimated pitch; and estimating the second measurement error based on the second contribution ratio and the estimated pitch.45. The computer readable medium of any one of clauses 39 to 44, wherein, in acquiring reference data associated with the first dimension and the second dimension, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: acquiring a plurality of first measurements for the first dimension and a plurality of second measurements for the second dimension; averaging the plurality of first measurements to generate a first average measurement; averaging the plurality of second measurements to generate a second average measurement; and determining a sum of the first average measurement and the second average measurement as the reference data.46. The computer readable medium of any one of clauses 39 to 44, wherein the reference data is obtained based on an edge-to-edge measurement of patterns on the inspection image.47. The computer readable medium of clause 46, wherein the edge-to-edge measurement is for a distance between two rising edges of the patterns or for a distance between two falling edges of the patterns.48. The computer readable medium of clause 46 or 47, wherein the patterns comprise at least one of a contact hole, a pillar, a line, or a trench.49. The computer readable medium of any one of clauses 39 to 44, wherein the reference data is obtained from design data corresponding to the inspection image.50. The computer readable medium of any one of clauses 39 to 49, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: determining a critical dimension of the first dimension based on the corrected first measurement.51. 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 a method for correcting measurements on an inspection image for a wafer inspection system, the method comprising: acquiring a line width measurement for a line on the inspection image and a trench width measurement for a trench on the inspection image; determining a pitch measurement error based on a sum of the line width measurement and the trench width measurement and reference data; correcting the line width measurement based on the pitch measurement error and a contribution ratio of the line width measurement to the pitch measurement error; and correcting the trench width measurement based on the pitch measurement error and a contribution ratio of the trench width measurement to the pitch measurement error.52. The computer readable medium of clause 51, wherein the reference data is a pitch between two neighboring lines having the trench in between.53. The computer readable medium of clause 51 or 52, wherein, in determining the pitch measurement error, the set of instructions that is executable by at least one processor of the computing device cause the computing device to perform: summing the line width measurement and the trench width measurement; determining a pitch measurement based on the sum of the line width measurement and the trench width measurement; and determining the pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.54. The computer readable medium of any one of clauses 51 to 52, wherein the set of instructions that is executable by at least one processor of the computing device cause the computing device to further perform: acquiring a plurality of line width measurements and a plurality of trench width measurements; averaging the plurality of line width measurements to generate an average line width measurement; averaging the plurality of trench width measurements to generate an average trench width measurement; anddetermining a sum of the average line width measurement and the average trench width measurement as the reference data.55. The computer readable medium of any one of clauses 51 to 53, wherein the reference data is obtained based on an edge-to-edge measurement of two lines on the inspection image.56. The computer readable medium of clause 55, wherein the edge-to-edge measurement is for a distance between two rising edges of the two lines or for a distance between two falling edges of the two lines.57. The computer readable medium of any one of clauses 51 to 53, wherein the reference data is obtained from design data corresponding to the inspection image.

[0100] 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 in a schematic diagram may represent certain arithmetical or logical operation processing that may be implemented using hardware such as an electronic circuit. Blocks may also represent a module, segment, or portion of code that comprises one or more executable instructions for implementing the specified logical functions. It should be understood that in some alternative implementations, functions indicated in a block may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed 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.

[0101] 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

CLAIMS1. An apparatus for correcting measurements on an inspection image for a wafer inspection system, 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: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.

2. The apparatus of claim 1, wherein the reference data is a reference value associated with the first dimension and the second dimension.

3. The apparatus of claim 1, wherein the first dimension is a line width, and the second dimension is a trench width.

4. The apparatus of claim 1, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: summing the first measurement and the second measurement; determining a pitch measurement based on the sum; and estimating a pitch measurement error of the pitch measurement based on the pitch measurement and the reference data.

5. The apparatus of claim 4, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to further perform: determining a first contribution ratio of the first measurement to the estimated pitch measurement error; and determining a second contribution ratio of the second measurement to the estimated pitch ratio.

6. The apparatus of claim 5, wherein, in estimating the first measurement error for the first measurement and the second measurement error for the second measurement based on the reference data, the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: estimating the first measurement error based on the first contribution ratio and the estimated pitch; and estimating the second measurement error based on the second contribution ratio and the estimated pitch.

7. The apparatus of claim 1, wherein, in acquiring reference data associated with the first dimension and the second dimension, the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: acquiring a plurality of first measurements for the first dimension and a plurality of second measurements for the second dimension; averaging the plurality of first measurements to generate a first average measurement; averaging the plurality of second measurements to generate a second average measurement; and determining a sum of the first average measurement and the second average measurement as the reference data.

8. The apparatus of claim 1, wherein the reference data is obtained based on an edge-to-edge measurement of patterns on the inspection image.

9. The apparatus of claim 8, wherein the edge-to-edge measurement is for a distance between two rising edges of the patterns or for a distance between two falling edges of the patterns.

10. The apparatus of claim 8, wherein the patterns comprise at least one of a contact hole, a pillar, a line, or a trench.

11. The apparatus of claim 1, wherein the reference data is obtained from design data corresponding to the inspection image.

12. The apparatus of claim 1, wherein the at least one processor is configured to execute the set of instructions to cause the apparatus to perform: determining a critical dimension of the first dimension based on the corrected first measurement.

13. 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 a method for correcting measurements on an inspection image for a wafer inspection system, the method comprising: acquiring a first measurement for a first dimension and a second measurement for a second dimension on the inspection image; acquiring reference data associated with the first dimension and the second dimension; estimating a first measurement error for the first measurement and a second measurement error for the second measurement based on the reference data; and correcting the first measurement based on the estimated first measurement error and the second measurement based on the estimated second measurement error.

14. The computer readable medium of claim 13, wherein the reference data is a reference value associated with the first dimension and the second dimension.

15. The computer readable medium of claim 13, wherein the reference data is obtained based on an edge-to-edge measurement of patterns on the inspection image.

Images