Methods and samples to determine charged-particle beam spot size

Abstract

Samples and methods for determining a beam spot size include scanning a pattern on the sample with a charged-particle beam to generate an image. The pattern may include at least one inclined side edge and a top surface. The at least one inclined side edge may have an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees. The beam spot size may be determined based on an imaging profile of the at least one inclined side edge derived based on the image.

Description

METHODS AND SAMPLES TO DETERMINE CHARGED-PARTICLE BEAM SPOT SIZECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of US application 63 / 611,078 which was filed on December 15, 2023 and which is incorporated herein in its entirety by reference.TECHNICAL FIELD

[0002] The description herein generally relates to methods and samples for measuring the primary beam size, or resolution, of a charged-particle beam in a charged-particle beam apparatus.BACKGROUND

[0003] In manufacturing processes of integrated circuits (ICs), unfinished or finished circuit components are inspected or measured to ensure that features are fabricated according to design and are free of defects. Inspection and / or measurement systems utilizing charged particle (e.g., electron) beam microscopes, such as a scanning electron microscope (SEM) can be employed. As feature sizes of IC components continue to shrink, determination of the resolution of the particle beam (e.g., electron beam) becomes important, for example, for the accurate determination of feature sizes.SUMMARY

[0004] Some embodiments provide a method of determining a beam spot size. The method may include scanning a pattern on a sample with a charged-particle beam to generate an image. The pattern may include at least one inclined side edge and a top surface. The at least one inclined side edge may have an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees. The method may also include determining the beam spot size based on an imaging profile of the at least one inclined side edge derived based on the image.

[0005] Some embodiments provide a method of determining a beam spot size. The method may include scanning a pattern on a sample with a charged-particle beam to generate an image. The pattern may include at least one inclined side edge and a top surface. The at least one inclined side edge has an inclination angle between about 40-80 degrees and a slope width greater than or equal to about 2.3 times an estimated beam spot size based on a simulation. The method may also include determining the beam spot size based on an imaging profile of an inclined side edge of the at least one inclined side edge derived based on the image.

[0006] Some embodiments provide a sample for determining beam spot size of a charged-particle beam. The sample may include a substrate formed of an electrically conductive material and a pattern disposed on the substrate. The pattern may be formed of an electrically conductive material and may include at least one inclined side edge and a top surface. The at least one inclined side edge may havean inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees.

[0007] Some embodiments provide 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 determining a beam spot size. The method may comprise scanning a pattern on a sample with a charged-particle beam to generate an image. The pattern may include at least one inclined side edge and a top surface. The at least one inclined side edge may have an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees. The method may also include determining the beam spot size based on an imaging profile of the at least one inclined side edge derived based on the image.

[0008] 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

[0009] 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.

[0010] FIG. 1 is a schematic illustration of an exemplary charged particle beam inspection or metrology system, consistent with some embodiments of the present disclosure.

[0011] FIG. 2A is a schematic illustration of an exemplary multi-beam tool that may be part of the charged particle beam inspection system of FIG. 1.

[0012] FIG. 2B is a schematic illustration of an exemplary single -beam tool that may be part of the charged particle beam inspection system FIG. 1.

[0013] FIG. 3A is a schematic illustration of a primary electron beam landing on a surface of a sample, consistent with some embodiments of the present disclosure.

[0014] FIG. 3B illustrates an exemplary relationship between the secondary electron yield of a sample and the landing angle of the primary electron beam on the sample, consistent with some embodiments of the present disclosure.

[0015] FIG. 4A is a schematic illustration of the secondary electron yield when a single electron scans over an exemplary pattern on a sample, consistent with some embodiments of the present disclosure.

[0016] FIG. 4B is a schematic illustration of the secondary electron yield signal when a primary electron beam scans over an exemplary pattern on a sample, consistent with some embodiments of the present disclosure.

[0017] FIG. 4C is a schematic illustration of measuring resolution from the secondary electron yield signal of FIG. 4B, consistent with some embodiments of the present disclosure.

[0018] FIG. 5A illustrates a cross-sectional view of an exemplary resolution-measurement sample with an exemplary pattern having an inclined edge.

[0019] FIG. 5B illustrates the effect of the width of the inclined edge on the resolution and measurement error in the resolution-measurement sample of FIG. 5A.

[0020] FIG. 6 is an illustration of the edge-proximity effect when a primary electron beam lands on an inclined edge of a pattern, consistent with some embodiments of the present disclosure.

[0021] FIG. 7A is a schematic illustration of an exemplary resolution-measurement sample with multiple patterns, consistent with some embodiments of the present disclosure.

[0022] FIGs. 7B-7C are illustrations of exemplary resolution-measurement samples having various patterns, consistent with some embodiments of the present disclosure.

[0023] FIGs. 8A-8D illustrate top-down views of resolution-measurement samples with exemplary patterns arranged in different orientations, consistent with some embodiments of the present disclosure.

[0024] FIGs. 9A-9B illustrate exemplary resolution-measurement samples with exemplary patterns arranged in two orthogonal orientations, consistent with some embodiments of the present disclosure.

[0025] FIG. 10A illustrates an exemplary resolution-measurement sample with multiple patterns arranged in a field of view (FOV), consistent with some embodiments of the present disclosure.

[0026] FIG. 10B illustrates the scanning an exemplary pattern with the scanning direction different from the edge direction of the pattern, consistent with some embodiments of the present disclosure.

[0027] FIGs. 11A-11B illustrate exemplary resolution-measurement samples configured to measure beam size at different locations in a FOV, consistent with some embodiments of the present disclosure.

[0028] FIGs. 12A-12D illustrate exemplary resolution-measurement samples with a dense layout of patterns arranged in different orientations in a FOV, consistent with some embodiments of the present disclosure.

[0029] FIGs. 13A-13C illustrate exemplary resolution-measurement samples with dense groups of patterns arranged in different orientations in a FOV, consistent with some embodiments of the present disclosure.

[0030] FIG. 13B illustrate an exemplary resolution-measurement sample with dense groups of patterns arranged in the same orientation in a FOV, consistent with some embodiments of the present disclosure.

[0031] FIGs. 14A-14F illustrate some exemplary shapes of patterns, consistent with some embodiments of the present disclosure.

[0032] FIGs. 15A-15D illustrate exemplary resolution-measurement samples with different types of patterns arranged in a FOV, consistent with some embodiments of the present disclosure.

[0033] FIG. 16A is a flow chart illustrating an exemplary method of fabricating a resolutionmeasurement sample, consistent with some embodiments of the present disclosure.

[0034] Fig. 16B is a flow chart illustrating an exemplary method of using a resolution-measurement sample to measure the resolution and beam size, consistent with some embodiments of the present disclosure.DETAILED DESCRIPTION

[0035] 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.

[0036] 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.

[0037] 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.

[0038] 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 conducted using a scanning charged particle microscope (“SCPM”). For example, an SCPM may be a scanning electron microscope (SEM). A SCPM can be used to image these extremely small structures, in effect, taking a “picture” of the structures of the wafer. The image can be used to determine if the structure was formed properly in the proper location. If the structure is defective, then the process can be adjusted, so the defect is less likely to recur.

[0039] As the physical sizes of IC components continue to shrink, accuracy and yield in defect detection becomes more and more important. In the context of an SEM used for inspection in semiconductor fabrication, resolution refers to the microscope’s ability to distinguish and display fine details in the sample being observed. Resolution is typically described in terms of spatial resolution, which is the smallest distance between two points on a sample's surface that can be distinguished as separate entities in the SEM image. The resolution of an SEM is a critical performance parameters in the semiconductor industry where extremely small features need to be accurately characterized. As feature sizes continue to decrease, accurately measuring the resolution of an electron beam apparatus is important to ensure that the device is capable of providing the level of detail required for specific applications and to ensure that feature sizes are accurately measured. Conventional methods of measuring the resolution of an electron beam apparatus include using taking measurements on samples with a pattern of lines having sharp edges or a pattern of particles (e.g., nanoparticles) on a substrate. However, these samples may not be accurate and suitable for measuring the resolution in some applications. For example, due to shape and configuration of the particles and the lines, data measured on such samples may not correspond satisfactorily to a known resolution. Consequently, the error in the resolution measured using such samples may be large. Embodiments of the present disclosure provide methods and samples to accurately measure the resolution of an electron beam in an electron-beam apparatus (or a particle beam in a particle beam apparatus).

[0040] 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.

[0041] 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.

[0042] All relative terms such as “about,” “substantially,” “approximately,” etc., indicate a possible variation of ±10% (unless noted otherwise or another variation is specified). For example, a featuredisclosed as being about “w” units wide (or long, thick, etc.) may vary in width from (w - O.lw) to (w + O.lw) units. Similarly, a width within a range of about A-B units can have a width between (A - 10%) and (B + 10%). Further, a width varying from, or between, A-B units includes the endpoints (i.e., A and B). In some cases, the specification and / of figures provide context to some of the relative terms used.

[0043] FIG. 1 illustrates an exemplary 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.

[0044] One or more robotic arms (not shown) in EFEM 106 may transport the wafers to load / lock chamber 102. Load / lock chamber 102 is connected to a load / lock vacuum pump system (not shown) which removes gas molecules in load / lock chamber 102 to reach a first pressure below the atmospheric pressure. After reaching the first pressure, one or more robotic arms (not shown) may transport the wafer from load / lock chamber 102 to main chamber 101. Main chamber 101 is connected to a main chamber vacuum pump system (not shown) which removes gas molecules in main chamber 101 to reach a second pressure below the first pressure. After reaching the second pressure, the wafer is subject to inspection by beam tool 104. Beam tool 104 may be a single-beam system or a multi-beam system.

[0045] 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.

[0046] In some embodiments, controller 109 may include one or more processors (not shown). A processor may be a generic or specific electronic device capable of manipulating or processing information. For example, the processor 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), and any type circuit capable of data processing. The processor may also be a virtualprocessor that includes one or more processors distributed across multiple machines or devices coupled via a network.

[0047] In some embodiments, controller 109 may further include one or more memories (not shown). A memory may be a generic or specific 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.

[0048] 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.

[0049] Beam tool 104 A comprises a charged particle source 202, a gun aperture 204, a condenser lens 206, a primary charged particle beam 210 emitted from charged particle source 202, a source conversion unit 212, a plurality of beamlets 214, 216, and 218 of primary charged particle beam 210, a primary projection optical system 220, a motorized wafer stage 280, a wafer holder 282, multiple secondary charged particle beams 236, 238, and 240, a secondary optical system 242, and a charged particle detection device 244. Primary projection optical system 220 can comprise a beam separator 222, a deflection scanning unit 226, and an objective lens 228. Charged particle detection device 244 can comprise detection sub-regions 246, 248, and 250.

[0050] Charged particle source 202, gun aperture 204, condenser lens 206, source conversion unit 212, beam separator 222, deflection scanning unit 226, and objective lens 228 can be aligned with a primary optical axis 260 of apparatus 104A. Secondary optical system 242 and charged particle detection device 244 can be aligned with a secondary optical axis 252 of apparatus 104A.

[0051] 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.

[0052] 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.

[0053] Condenser lens 206 can focus primary charged particle beam 210. The electric currents of beamlets 214, 216, and 218 downstream of source conversion unit 212 can be varied by adjusting the focusing power of condenser lens 206 or by changing the radial sizes of the corresponding beam-limit apertures within the array of beam-limit apertures. Objective lens 228 can focus beamlets 214, 216, and 218 onto a wafer 230 for imaging, and can form a plurality of probe spots 270, 272, and 274 on a surface of wafer 230.

[0054] Beam separator 222 can be a beam separator of Wien filter type generating an electrostatic dipole field and a magnetic dipole field. In some embodiments, if they are applied, the force exerted by the electrostatic dipole field on a charged particle (e.g., an electron) of beamlets 214, 216, and 218 can be substantially equal in magnitude and opposite in a direction to the force exerted on the charged particle by magnetic dipole field. Beamlets 214, 216, and 218 can, therefore, pass straight through beam separator 222 with zero deflection angle. However, the total dispersion of beamlets 214, 216, and 218 generated by beam separator 222 can also be non-zero. Beam separator 222 can separate secondary charged particle beams 236, 238, and 240 from beamlets 214, 216, and 218 and direct secondary charged particle beams 236, 238, and 240 towards secondary optical system 242.

[0055] 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 (energies50 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.

[0056] 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 interests 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.

[0057] 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.

[0058] In some embodiments, image processing system 290 may include an image acquirer 292, a storage 294, and a controller 296. Image acquirer 292 may comprise one or more processors. For example, image acquirer 292 may comprise a computer, server, mainframe host, terminals, personal computer, any kind of mobile computing devices, or the like, or a combination thereof. Image acquirer 292 may be communicatively coupled to charged particle detection device 244 of beam tool 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 someembodiments, image acquirer 292, storage 294, and controller 296 may be integrated together as one control unit.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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 emanated from the wafer surface may be collected by detector 144 to determine intensity of the beam and so that an image of an area of interest on wafer 150 may be reconstructed.

[0064] 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 withimage acquirer 120 and may be used for saving scanned raw image data as original images, and postprocessed images. Image acquirer 120 and storage 130 may be connected to controller 109. In some embodiments, image acquirer 120, storage 130, and controller 109 may be integrated together as one electronic control unit.

[0065] 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.

[0066] 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.

[0067] FIB. 2B illustrates a charged particle beam apparatus that may use a single primary beam configured to generate secondary electrons by interacting with wafer 150. Detector 144 may be placed along optical axis 105, as in the embodiment shown in FIG. 2B. The primary electron beam may be configured to travel along optical axis 105. Accordingly, detector 144 may include a hole at its center so that the primary electron beam may pass through to reach wafer 150. FIG. 2B shows an example of detector 144 having an opening at its center. However, some embodiments may use a detector placed off-axis relative to the optical axis along which the primary electron beam travels. For example, as in the embodiment shown in FIG. 2A, 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.

[0068] Thus, in embodiments of an SEM-based e-beam apparatus, an image of a sample (e.g., wafer 230 of FIG. 2A and wafer 150 of FIG. 2B) is formed by detecting secondary electrons generated and emitted from the sample that is scanned by a focused primary beam (e.g., electron beam 161 of FIG. 2B). Typically, the detection efficiency of detector 144 may be over 90% and, in some embodiments, very close to 100%. The image signal (h) is the convolution of the current density distribution of the primary electron beam spot, or probe spot 170, on the wafer 150 and the secondary electron yield signal (Io), as shown in Equation (1) below. The convolution (denoted by the symbol “*”) of two signals is a mathematical operation that combines two signals to produce a third signal. The current density distribution of the primary electron beam spot (or probe spot 170) is called as point spread function (PSF) or the beam profile. The PSF of an electron beam describes how an electron source isimaged by the electron optics of the microscope on the sample. It characterizes the blurring or spreading of primary electrons in the electron source image. In electron microscopy, when a focused primary electron beam interacts with wafer 150 (or another sample), electrons of the beam are scattered inside wafer and generate secondary electrons, which are detected to form an image of wafer 150. However, due to various physical and optical factors, the resulting image of the source is not a sharp point but rather a spread-out spot. The PSF is a mathematical description of how the source image is spread out and is a critical factor in determining the achievable resolution of an electron microscope. For example, PSF is used to determine the smallest features that can be accurately resolved in an image of a sample. Secondary electron yield (8) is a material property that characterizes how many secondary electrons are emitted from a material when it is bombarded with primary electrons. For example, if a material has a secondary electron yield of 2, it means that, on average, two secondary electrons are emitted for every primary electron that hits the material. The secondary electron yield signal (Io) is the actual signal that is generated and detected in the microscope (e.g., by detector 144) due to the emission of secondary electrons. In other words, the secondary electron yield signal (Io) is a signal indicative of the number of secondary electrons emitted from wafer 150 in response to being bombarded by primary electrons. li (x, y) = PSF (x, y) * Io(x, y) (Eqn. 1)

[0069] Based on equation 1, how the image signal ( ) resembles the secondary electron yield signal (Io) depends on the PSF. For example, if the PSF is a delta function (or a Dirac delta distribution), f will be the same as Io(i.e., h (x, y) = Io(x, y)). A delta function is a theoretical construct used to describe a spike or impulse at a point. It represents an infinitely tall, infinitely thin spike at one point, while being zero everywhere else. For a delta function, the area under the curve is always equal to 1. However, practically, because of the non-zero size and non-zero energy spread of the primary electron beam (for example, due to the geometric aberration coefficients, waveform diffraction, electron interactions in the electron optics system of the apparatus, etc.), all the electrons will not be focused on one position and PSF will not be a delta function. If PSF is known, the secondary electron yield signal (Io) can be calculated from equation 1 by deconvoluting PSF from the image signal (F). Deconvolution is a mathematical operation used to reverse or undo the convolution of two signals. When two signals are convolved, their information becomes combined or blended together. Deconvolution aims to separate this combined information and retrieve the original signals.

[0070] Typically, the PSF of an electron optics system is very close to a Gaussian distribution as shown in equation (2) above. A property that may be used to describe, or quantify, how spread out a PSF. This property indicates that if a circle is drawn around the central peak of the PSF with a diameter equal to twice the beam radius (rb), the integrated intensity within this circle will be approximately 63% of the total intensity of the PSF. In other words, a circle with a diameter equal to 2rb includes about 63% of the current inside the PSF. In some embodiments, 2rb may be used as the e- beam spot size for the PSF. In other embodiments, a circle with a different diameter may be used as the e-beam spot size. For example, in some embodiments, a circle with a diameter equal to 1.916 rb that includes about 60% of the current may be used as the e-beam spot size. In some embodiments, FWHM (Full Width at Half Maximum) is used as the e-beam spot size, which corresponds to a circle with a diameter equal to 1.664 rb that includes about 50% of the current.

[0071] Numerical simulations may be used to determine or predict the expected PSF (and resolution) of an SEM apparatus. For example, the design configuration of an electron optical system may be simulated and the primary electron distribution of the primary electron beam on the sample and the resolution of the system may be determined based on the simulations. However, the actual resolution of an electron beam apparatus may be different from the value obtained from simulations. For example, some electron optical elements (e.g., lens, deflectors, etc.) may have mechanical errors, and the electronic elements may have electronic noise and drift that may contribute to the variation of the actual resolution from the value predicted from simulations. Moreover, in some cases, the electron optical elements may not be well aligned with the optical axis (e.g., optical axis 105 of FIG. 2B) of the system and this may contribute to the variation. Therefore, it is desirable to experimentally measure the resolution of an electron optical system. However, since the PSF is very small, it typically cannot be experimentally measured directly to determine its resolution. However, since secondary electron yield (8) depends on the local tilt of the sample, in embodiments of the current disclosure, PSF may be measured indirectly from the secondary electron image based on the impact of secondary electron yield (8) on the local topographic contrast (e.g., local tilt) of the sample. The secondary electron yield signal (Io) is proportional to secondary electron yield (8) of a sample, and can simply be regarded as the secondary electron yield (8). That is, Io ~ 8.

[0072] Secondary electron yield (8) strongly depends on the landing energy and the angle 0 of the primary electron beam on the sample and, for landing energies less than about 5keV, slightly depends on the sample material. As illustrated in FIG. 3A, the landing angle (0) of the primary electron beam 300 is measured with respect to the surface normal of the landing location of beam 300 on sample320. Equation 3 shows the relationship between the secondary electron yield (8) of a sample and its surface topography, and FIG. 3B is a graph that plots the ratio 8(0) / 8(0=O) versus the landing angle (0). In equation 3 and FIG. 3B, “n” is a material parameter (that describes the dependence of yield on the landing angle) that is equal to 1.3 for light elements, equal to 1 for elements with an atomic number of 30, and equal to 0.8 for heavy elements. As evident from FIG. 3Btsecondary electron yield (8) is very sensitive to the surface topography of the sample.

[0073] The sample 320 of FIG. 3A includes an exemplary pattern 340 or structure (e.g., line, etc.) formed on the surface of a substrate 330 (wafer, die, etc.). As illustrated in this figure, pattern 340 includes two inclined (or slant) edges si and s2 on opposite sides of a relatively flat top. FIG. 4A schematically illustrates the resulting secondary electron yield (8) when a single electron 300' (e.g., a point) scans over the pattern 340 on sample 320. As shown in FIG. 4A, the secondary electron yield (8) is a rectangular function with respect to each pattern edge. Thus, in an SEM image, the secondary electron yield (8) distribution is indicative of the cross-sectional profile of the pattern 340.

[0074] FIG. 4A illustrates the resulting secondary electron yield (8) when a hypothetical ray of a single electron scans over the pattern 340. When a primary electron beam (that includes many electrons) scans over the pattern 340, the total secondary electron yield (8t) will be the sum of the secondary electron yield (8) of all the electrons in the primary beam. As explained previously, PSF is a mathematical description of the current density distribution of the primary electron beam.Therefore, as shown in equation 4 below, when a primary electron beam scans over the pattern 340, the total secondary electron yield (8t) is equal to the convolution of PSF (Gaussian function) and the single secondary electron yield (8) (rectangular function). The image signal I is proportional to the total secondary electron yield (8t) and may be considered to be the same as 8t. h ~ 8t = PSF * 8 (Eqn. 4)

[0075] Thus, when a primary electron beam scans over the pattern 340, each step-type side of the rectangular function distribution in the profile of FIG. 4A blurs to an error function distribution, as shown in FIG. 4B. The image signal (h) for the inclined edge si of pattern 340 is shown in equation (5) below by assuming that the distance (x3-x2) is so large that the influence of the inclined edge s2 on the image signal of inclined edge si is negligible. In equation 5, Ao depends on 8n, Ai depends on 812-811, and A2depends on 812-813.I;= Ao+ A, ■ | ■ [1 + erf f^)] - A2■ | ■ [1 + erf (^)] (Eqn. 5)

[0076] In FIG. 4B, the sharpness of each blurred side (si, s2) depends on the PSF of the primary electron beam 300. With reference to FIG. 4C, taking the left side inclined edge si of pattern 340 (which corresponds to the region labelled pl in FIG. 4C) as an example, the resolution (or sharpness) of the image may be considered as the distance S2575 between the points I_25% (= I2+O.25 x (I1-I2)) and I_75% (= I2+ 0.75 x (I1-I2)) intensity within intensity range (I1-I2) from maximum (Ii) to minimum (I2). For the image signal h in equation (5), if the distance X2-X1 is large enough in comparison with the PSF of the primary electron beam 300 (such as, for example, 5.2X of rb), the image signal h may be contributed by mainly the first error function in equation (5). In this case S2575 will be equal to 0.954 rb, as shown in equation (6). 2575 — 0-954 ■ rb(Eqn. 6)

[0077] From an SEM image of sample 320, distance S2575 value can be directly measured from the signal profile of the edge (e.g., inclined edge si) of the pattern 340, and rb value may be determined from equation (6). In some embodiments, the determined distance S2575 may be regarded as the resolution of the system and rb (or a multiple of rb, such as, for example 2rb, 1.916rb, etc.) may be regarded as the beam size. In some embodiments, rb may regarded as the resolution of the system. The difference between the resolution values obtained experimentally and from simulations may be used as feedback to adjust the electron optical system (e.g., adjust the electron optical devices, improve alignment the system, etc.) of the SEM to reduce the difference in the measured and expected values.

[0078] In embodiments of the current disclosure, samples with selected resolution measurement patterns with an inclined edge having a controlled profile are provided to accurately measure the beam size (e.g., PSF size, radius rb, or a multiple of rb) and resolution (e.g., distance S2575, etc.) of an SEM-based e-beam apparatus. FIG. 5A illustrates a cross-sectional view of an exemplary sample 400 having a resolution measurement pattern 440 formed on a substrate 330. In a 3-dimensional or a perspective view, the pattern 440 of FIG. 5A will appear as a line (see, e.g., FIG. 14A). Pattern 440 may be formed on substrate 330 using any known semiconductor fabrication technique (deposition, photolithography, etching, etc.). Both substrate 330 and pattern 440 may include, or be formed of, an electric conductive material. Any electrically conductive material (e.g., a metal, a doped semiconductor having a surface resistivity < 0.01 ohm-cm, etc.) may be used. Substrate 330 and pattern 440 may be made of the same electrically conductive material or of different electrically conductive materials. For example, in some embodiments, both substrate 330 and pattern 440 may be formed of the same electrically conductive material, such as, for example, a metal (e.g., copper) or doped silicon. While in some embodiments, the substrate 330 may be formed of a first electricallyconductive material (e.g., doped silicon) and the pattern 440 may be formed of a different electrically conductive material (e.g., a metal).

[0079] The geometry of the pattern 440 formed on substrate 330 is designed to make changes in the secondary electron yield (8) due to an edge distinct and obvious as an electron beam 300 scans the pattern. As shown in FIG. 5A, in some embodiments, pattern 440 of sample 400 includes two inclined edges si and s2 on opposite sides of a relatively-flat top-surface fl. As used herein, relatively-flat surface merely indicates that the surface is not designed or intended to have an inclination. However, it should be appreciated that surface fl may still have a tilt or non-flatness that results from the fabrication process used. Inclined edge si may be fabricated to have an inclination angle (<[>) and a slope width W 1. Inclination angle (<[>) is designed to be between about 40° ~ 80°. An inclination angle (<[>) within this range makes the changes in secondary electron yield (8) distinct and obvious, and mitigates the strong edge effect . The secondary yield is impacted by the landing angle (0 in equation 3) and also the edge effect of a pattern edge. It is preferred to use the landing angle impact not the edge effect. The larger the inclination angle (<[>) of the pattern edge sidewall, the stronger is the edge effect of the pattern edge. Slope width W1 (which corresponds to X2-X1 of FIG. 4A) may be selected based on the PSF size (e.g., rb) to reduce the influence of the second error function in equation (5) (i.e., Az- 1 / 2- [ 1 +erf((x-X2) / rb )]), for example, to an acceptable level.

[0080] FIG. 5B is a graph that illustrates the effect of slope width W1 on the S2575 distance (sharpness, resolution, etc.) and measurement error. As can be seen in this figure, the error is less than about 10% when W1 is selected to be greater than or equal to (>) about 2.3rb. Therefore, to ensure the difference of S2575 (and rb) < 10%, width W1 of pattern 440 may be selected to be > about 2.3rb. In some embodiments, to ensure that the measurement error is less than about 1%, W1 may be selected to be about > 3.8rb. Similarly, in some embodiments, to ensure that the measurement error is less than about 0.1%, W1 may be selected to be > 5rb. The combination of inclination angle (<[>) and slope width W 1 may be selected to make the edge height Hl less than the depth of focus (DOF) of the electron beam. Depth of focus (DOF) refers to the range of distances along the optical axis over which the sample remains in acceptable focus.

[0081] In some embodiments, to ensure that signals from both the inclined surfaces or edges si and s2 may be used for beam width measurements, similar to the selection of width W 1 (see FIG. 5A), the top surface width W2 and the slope width W3 may both be selected to beabout 2.3rb to keep the measurement error than about 10%, or > about 3.8rb to keep the measurement error <1% , orabout 5rb to keep the measurement error < 0.1%. Similarly, inclination angle (<[>') of inclined surface s2 may also be selected to be between about 40° ~ 80° to make the changes in secondary electron yield (8) distinct and obvious when the electron beam scans inclined surface s2. However, this is not a requirement. For example, in some embodiments, only the inclination angle (<[>) and width W 1 may be selected to be within the above-described ranges (i.e., <[> = about 40° ~ 80°, and W1 about 2.3rbor about 3.8rb orabout 5rb). In some embodiments, in addition to inclination angleWl and W2 may both be selected to be within the above-described range. And in some embodiments, the inclination angles <f>, (|)', Wl, W2, and W3 may each be selected to be within the above described ranges. It should be noted that although inclination angle (<f> ') and slope width W3 of inclined edge s2 may be the same inclination angle (<[>) and slope width (Wl), respectively, of inclined edge si, they do not have to be.

[0082] As schematically illustrated in FIG. 6, when a primary electron beam 300 is incident on inclined edge si of pattern 440, in addition to the secondary electrons released from edge si, secondary electrons may also be released from the opposite inclined edge s2 if the primary electrons penetrates too deep inside the sample. The secondary electrons exiting the inclined side s2 may also get recorded by the detector 144 (see FIG. 2B). This phenomena may be referred to edge cross-talk or edge proximity effect. The effect of the secondary electrons exiting inclined edge s2 when the primary electron beam 300 scans over inclined edge si may cause an error in the measurement of the beam size. For example, the secondary electrons exiting inclined edge s2 may increase the secondary electron yield in the recorded data of inclined edge si and result in an error in the determined beam size. Therefore, to avoid the negative effects of edge cross-talk, in some embodiments, width W2 of sample 400 may be selected to be larger than the electron beam penetration depth. For example, if pattern 440 is made of silicon and the primary electron beam 300 has an energy of 2keV, width W2 may be selected to be greater than or equal to (>) about lOOnm to avoid edge cross-talk. Similarly, if the electron beam has 5keV energy, width W2 may be selected to be > about 400nm to avoid edge cross-talk. Thus, in some embodiments of the current disclosure, in addition to the inclination angle (<[>) and width Wl being selected to be within the previously described ranges (e.g., <[> between about 40° ~ 80°, and Wlabout 2.3rborabout 3.8rborabout 5rb), width W2 may be selected to be the larger of the value determined based on rb(see FIG. 5B) (i.e., greater than or equal to 2.3rb, 3.8rb, or 5rbbased on the acceptable measurement error) and the value determined based on e-beam penetration depth. For example, in an exemplary embodiment of a sample 400 with a silicon pattern 440 designed to measure a beam size rbof about 5 nm (e.g., simulated value) using a primary electron beam 300 having energy of about 5keV, W2 based on rbmay be determined to be5rb(i.e., > 25 nm) to keep the measurement error less than 0.1% and400 nm to minimize edge cross-talk.Therefore, in this exemplary embodiment, width W2 may be selected to be greater than or equal to 400 nm (the larger of 25 nm and 400 nm).

[0083] It should be noted that although a sample 400 with two opposite inclined edges si and s2 are illustrated in FIGs. 4A and 5A, this is only exemplary. It is contemplated that, in some embodiments, the pattern may only have one inclined edge (e.g., edge si). For example, in some embodiments, a sample may include a pattern (e.g., in the form of a metal coating on a substrate) with a single inclined edge having an inclination angle (<[>) between about 40° ~ 80° and slope width Wl aboutabout 5rb (based on acceptable measurement error). Width W2 of the coating may be substantially (e.g., 1000 times, etc.) greater than its thickness to make width W2 theoretically infinite.

[0084] In contrast with the disclosed samples 400 with patterns 440 having an inclined edge with a controlled profile (e.g., having an edge with an inclination angle (<[>) between about 40° ~ 80° and slope width about 2.3rb orabout 3.8rb orabout 5rb based on acceptable measurement error), conventional samples used for resolution measurement include gold particles on a substrate or a line pattern with a sharp edges formed on a substrate. See, e.g., “Scanning Electron Microscopy (2nd edition)”, Chapter 4, Peter W. Hawkes. However, for a particle-type sample, the single electron yield (8) is not a rectangular function (as in FIG. 4A) due to the roundness of the particles, and therefore, the image signal f (see Eqn. (5)) will not be an error function distribution and the sharpness S2575 will not be equal to 0.954 rb (see Eqn. (6)). For a line pattern with a sharp edge (see, for example, the sharp right edge s2 of FIG. 4A), because of the sharpness of the edge, the slope width (x4-x3 of FIG. 4A) will not be large enough in comparison with rb. Consequently, the secondary electron yield signal (see FIG. 4C) corresponding to this sharp edge will not have a flat top part (as in the flat top part p2 of the signal corresponding to the inclined left edge si in FIG. 4C) that demarcates the regions p4 and p5. Therefore, the signals in regions p4 and p5 will merge with each other, and the secondary electron yield (8) will not be a rectangular function. Instead, the secondary electron yield (8) for this sharp edge will be more like a delta function for the PSF, and consequently, the S2575 distance will be significantly smaller than 0.954*rb.

[0085] Although an exemplary sample 400 with a single pattern 440 has been described above, this is only exemplary. In some embodiments, a sample 400 may include multiple patterns thereon. For example, FIG. 7A illustrates an exemplary sample 400 with two patterns 440A, 440B formed thereon. When there are multiple patterns in a sample 400, as illustrated in FIG. 7A, the space W4 between two adjacent patterns 440A, 440B may be selected to be > 2.3rb to keep the measurement error < 10%, or > 3.8rb to keep the measurement error < 1% , or > 5rb to keep the measurement error < 0.1% as described with reference to FIG. 5B. In some embodiments, aspect ratio H / W4 of the patterns may be selected to be < 1 to avoid secondary electrons generated from one pattern (e.g., pattern 440A) being blocked by an adjacent pattern 440 (e.g., pattern 440B). This phenomena may be referred to as the pattern proximity effect. To avoid potential impact from an adjacent pattern, in some embodiments, W4 may also be selected to be larger than the e-beam penetration depth inside the substrate 330. For example, if substrate 330 is made of silicon and the primary electron beam has 5keV energy, W4 may be selected to be > 400 nm to avoid negative effects due to e-beam penetration. Thus, in some embodiments, the spacing W4 between adjacent patterns 440A, 440B may be selected to be the larger of the value determined based on rb (as described with reference to FIG. 5B), the value determined based on pattern proximity effect (H / W4 < 1), and the value determined based onthe e-beam penetration depth. For example, in an exemplary sample designed to measure an expected (e.g., from simulations, etc.) beam size rb) of about 5 nm with an electron beam having 5keV energy, W4 may be determined to be > 25 nm based on rb (e.g., 5n,), > 50 nm if H is designed to be 50nm, and > 400 nm in terms of the electron beam penetration depth. Thus, in such embodiments, W4 may be selected to be > 400 nm (i.e., the largest value of 25 nm, 50 nm, and 400 nm).

[0086] Although the opposite edges si and s2 of the patterns 440, 440A, 440B in the exemplary samples 400 illustrated in FIGs. 5A, and 7A are shown to be inclined in opposite directions, this is only exemplary. In some embodiments, as illustrated in FIGs. 7B and 7C, the opposite edges si and s2 may be inclined in the same direction. The discussion above made with reference to samples having the configuration of FIGs. 5A and 7A are also applicable to samples having the configuration of FIGs. 7B and 7C. In some cases, it may be possible to fabricate samples with patterns 440, 440A, 440B having the configuration of FIGs. 7B and 7C easier than samples with patterns having the configuration of FIGs. 5A and 7A. The inclination angles (<[>, <[>') and the widths Wl, W2, and W4 of the patterns 440, 440 A, 440B of FIGs. 7B and 7C may be selected in the same manner as described with reference to patterns 440 of FIGs. 5A and 7A. For example, if the sample 400 is designed to measure an expected beam size rb(e.g., determined from simulations, calculations, etc.), of about 4.5 nm with a primary electron beam having about 2keV energy, then Wl may be selected to be > 22.5 nm (e.g., 5rb to keep measurement error < 0.1%), and W2 may be selected to be > lOOnm (the larger value of 22.5 nm based on rb and 100 nm based on e-beam penetration depth at 2keV). In this case, if pattern height H is 50 nm and slant angle <[> = 65°, then W 1= H / tan((|)) = 23.3 nm, which is > 22.5 nm. Thus, in some embodiments, W2 may be selected to be > 100 nm, which is the larger one of 23.3 nm and 100 nm. Therefore, in some embodiments, patterns 440A, 440B having a pitch P of about 750 nm and a pattern width W 1+W2 = 200 nm may be selected to meet the foregoing requirements.

[0087] As explained above (e.g., with reference to FIGs. 7 A, 7C), in some cases, when scanning a first pattern 440A on a sample 400, an adjacent second pattern 440B may have some effect on the signals recorded from the first pattern 440A. In some embodiments, to completely avoid the effect of an adjacent pattern (or proximity effect of an adjacent pattern), adjacent patterns 440A, 440B on a sample 400 may separated by large gaps. For example, in some embodiments of samples, a single pattern 440 or line may be provided in the scanning area, or field of view (FOV), of the primary electron beam. The field of view (FOV) refers to the area of the sample 400 that is imaged (or is visible) by the primary electron beam at any given time. FIG. 8A illustrates the top view of the exemplary sample 400 illustrated in FIG. 5A. Note that FIG. 5A illustrates the cross-sectional view (e.g., in the XZ plane) of the pattern 440 on sample 400 while FIG. 8A illustrates its top-down view (e.g., in the orthogonal XY plane) showing the pattern 440 as a line on the substrate 330. With reference to FIGs. 5A and 8A, a direction perpendicular to the pattern 440 (i.e., the line in the top- down view) that passes through its two opposite inclined edges si and s2 is referred to herein as theedge direction A of the pattern 440. In the example shown in FIGs. 5A and 8A, the pattern 440 is arranged such that the edge direction A is aligned with the X-axis of the sample 400 and that the angle (a) between the edge direction A and the X-axis is zero. As illustrated in FIG. 8A, in some embodiments of samples 400, a single pattern 440 may be provided in the FOV 500.

[0088] In some embodiments, the direction of scanning (or scanning direction B) of the primary electron beam 300 may be aligned with the X-axis. For example, the electron beam 300 may start at one corner of FOV 500 and scan across the surface of sample 400 in a horizontal line along the X- axis, and once beam 300 reaches the opposite end of FOV 500, it moves up or down (e.g., in the Y- axis) slightly and starts scanning the next line. This process continues until the entire FOV 500 has been scanned in a series of parallel lines. In the example of FIG. 8A (and FIG. 5A), the electron beam 300 scans the pattern 440 along, or parallel to, the edge direction A. When beam 300 scans the pattern 440, the beam size in the scanning direction B is measured. In some embodiments, the PSF of the primary electron beam 300 may not be round because of aberrations and manufacturing variations in the optical elements of the SEM. To evaluate the size of a non-round PSF in different directions, the primary electron beam 300 may scan patterns 440 in different orientations, along the edge direction A, as illustrated in FIGs. 9A and 9B. FIGs. 9A and 9B show both the cross-sectional view and the top-down view of an exemplary pattern 440. In FIG. 9A, the pattern 440 extends as a line in the Y-direction (similar to the configuration illustrated in FIG. 8A), while in FIG. 9B the pattern 440 extends as a line in the X-direction. In both embodiments (FIGs. 9A and 9B), the scanning direction B of the beam 300 is along (or parallel to) the edge direction A of the pattern. For example, while the beam 300 scans the sample 400 of FIG. 9A left to right (and right to left) to measure the size of the beam in one direction (left-right direction or X-axis direction), the scanning direction of the beam 300 may be rotated to scan the sample 400 of FIG. 9B in the top-bottom direction to measure the size of the beam in another direction (top-bottom direction of the Y-axis direction). Thus, using the samples 400 of FIGs. 9A and 9B, the beam size in two orthogonal directions may be measured.

[0089] As explained with reference to pattern 440 of FIG. 8A (which illustrates the same configuration of the pattern in FIG. 9A), pattern 440 of FIG. 9A is oriented such that the angle (a) between the edge direction A and the X-axis is zero. In FIG. 9B (which illustrates the same configuration of the pattern illustrated in FIG. 8B), pattern 440 is oriented such that the angle (a) between the edge direction A and the X-axis is 90°. Samples 400 of the current disclosure may also include patterns 440 oriented in other directions to measure the beam size in other directions. For example, FIG. 8C illustrates a sample 400 with a pattern 440 oriented such that angle (a) is 45°, and FIG. 8D illustrates a sample 400 with a pattern 440 oriented such that angle (a) is 135°. Angle (a) may be measured (or defined) with respect to any common axis (e.g., the X-axis). In some embodiments, as illustrated in FIG. 8D, the common X-axis may be defined as an axis extending between the center of a wafer (e.g., wafer 150 (of FIG. 2B) upon which pattern 440 may be formed)and a notch (or a flat) provided on the periphery of the wafer (e.g., as a reference point for alignment, handling, etc.). An electron beam 300 may scan the samples of FIGs. 8A-8D with its scanning direction B parallel to the edge direction A to measure the size of beam 300 in different directions (e.g., arranged 45° apart). It should be noted that the specific orientations illustrated in FIGs. 8A-8D are merely exemplary and, in general, the patterns 440 may be oriented in any direction (i.e., at any angle (a)). Regardless of its orientation, the inclination angles (<f>, <f>') and widths Wl, W2, and W3 of the patterns 440 may be selected as described previously (e.g., with reference to FIG. 5A).

[0090] In the example samples illustrated in FIGs. 8A-8D, the patterns 440 on each sample are spaced apart such that there is only one pattern 440 in the FOV 500 to avoid measurement errors resulting from the proximity effect of adjacent patterns. In some embodiments, as illustrated in FIG. 10A, a sample 400 may include multiple isolated patterns 440A-440F (or lines) spaced apart in a single FOV 500. As shown in FIG. 10A, the patterns 440A-440F may be oriented such that the edge direction A of each pattern may make a different angle (a) with the X-axis to measure the beam size in different directions as the beam scans the FOV 500. Regardless of the orientation of the patterns 440A-440F, the inclination angles (<[>, <[>') and widths Wl, W2, W3, and W4 of the patterns 440A- 440F may be selected as described previously (e.g., with reference to FIGs. 5A and 7A). When an electron beam scans the FOV 500, in some cases, the scanning direction B of the beam may not be parallel to the edge direction of all the patterns 440A-440F in the FOV 500. In such cases, as shown in FIG. 10B, the beam size will be measured in the edge direction, but the pixel size in the SEM image will be in the scanning direction B. Therefore, the pixel size may need to be converted to the edge direction A of each pattern 440A-440F. Pixel size refers to the size of an individual pixel in the final digital image and may be determined by the step size used during the scanning process. The pixel size (PS) may be converted from one direction (e.g., scanning direction B) to another direction (e.g., edge direction A) based on the angle (|3) between the two directions (such as, for example, PSA = PSB COS (|3) ) . It is also contemplated that, in some such embodiments, as described with reference to FIGs. 9A and 9B, the scanning direction B of the electron beam may be changed as it scans over some patterns 440A-440F in the FOV 500 to make the scanning direction B parallel to the edge direction A of each pattern 440A-440F.

[0091] Resolution (e.g., S2575 distance) and beam size of a primary electron beam may not be the same at all locations in a large FOV (such as, for example, 100 Ltrn x 100 Ltrn). To measure the resolution and beam size at all locations of the FOV 500, in some embodiments, isolated patterns may be provided at different locations of the FOV 500. FIGs. 11A and 11B illustrate exemplary samples 400 that may be used to measure the beam size at different locations of a large FOV 500. In some embodiments, as illustrated in FIG. 11 A, a pattern 440C may be provided at the center of the FOV 500, and a pattern 440A, 440B, 440D, 440E may be provided at each corner of the FOV to independently measure the resolution and beam size at these locations using the different patterns. Itshould be noted that the specific locations of the patterns illustrated in FIG. 11A are only exemplary. In general, the patterns may be provided at any location in the FOV. In the embodiment of FIG. 11B, the two patterns on the same side of the FOV are combined to form one single pattern (e.g., patterns 440A and 440D of FIG. 11A are combined to form pattern 440A of FIG. 11B and patterns 440B and 440E of FIG. 11A are combined to form pattern 440C of FIG. 11B). Compared with sample 400 of FIG. 11B, sample 400 of FIG. 11A may be easier to fabricate since it may be easier (such as taking less writing time, e.g., by using an e-beam writer) to prepare the mask used to make this sample.

[0092] To increase signal / noise ratio, in some embodiments, a denser layout of patterns may be provided in a FOV, and the measurement results (of beam size) may be averaged across the different patterns. FIGs. 12A-12D illustrate exemplary samples 400 with a dense layout of patterns 440A- 440D in different orientations in a FOV 500. As explained with reference to FIG. 10A, the electron beam size or PSF may not be round, and to measure the beam size in different directions, patterns 440A-440D may be oriented such that the edge direction A of the patterns may make a different angle (a) with the X-axis. In general, if the FOV size is small (e.g., 10 pm x 10 pm), the beam size may be almost the same at all locations in the FOV and the average beam size (e.g., obtained by averaging the results from all the patterns in a dense pattern layout) may be used. For example, the average beam size obtained from the four patterns 440A-440D of FIG. 12A may be taken as the beam size in one direction and the average beam size obtained from the four patterns 440A-440D of FIG. 12B may be taken as the beam size in the orthogonal direction. As described with reference to FIGs. 9A and 9B, the scanning direction B of the electron beam 300 may be changed as it scans over the patterns 440A- 440D of FIGs. 12A-12D to make the scanning direction B parallel to the edge direction A of the patterns 440A-440D. In the denser pattern layouts of FIGs. 12A-12D, the inclination angles (<[>, <[>') and widths Wl, W2, W3, and W4 of the patterns 440A-440D may be selected as described previously (e.g., with reference to FIGs. 5A and 7A).

[0093] In some embodiments, to evaluate the beam size in different directions in a FOV 500, a sample 400 may include groups 440' of denser patterns 440A-440D in different orientations (e.g., different angle a) in a FOV 500 as shown in FIG. 13A. In this case, as similarly described above with reference to FIGs. 10A and 10B, the electron beam scanning direction B may not be parallel to the edge directions A of all the patterns in the FOV 500. In such embodiments, the pixel size (which is in the scanning direction) may be converted to the pixel size in the edge direction based on the angle between the two directions. If the size of the FOV 500 is large enough such that the beam size is not uniform over the FOV, the beam size measurement results at a local area (e.g., the FOV center, FOV corner, etc.) may be averaged. For example, in some exemplary embodiments of samples 400, as illustrated in FIG. 13B, a denser group 440' of patterns 440A-440D in one orientation (e.g., at one angle a) may be provided at different locations of the FOV and the results at each location may be averaged. It should be noted that although FIG. 13B illustrates a sample where groups of patterns440A-440D oriented at an angle a = 0 are provided, in general, the patterns 440A-440D may be oriented at any angle (a). In some embodiments, to measure the beam size in different directions at different location of a FOV 500, as illustrated in FIG. 13C, a sample 400 may include a group 440' of patterns 440A-440F at different locations (e.g., center, corners, etc.) of the FOV 500, and different patterns 440A-440F in each group 440' may be oriented at a different angle (a). In the embodiment of FIG. 13C, as described with reference to FIGs. 10A and 10B, the electron beam scanning direction B may not be parallel to the edge direction A of all the patterns 440A-440F in a group of patterns. In such embodiments, as explained previously, the pixel size of the SEM image (which is measured in the scanning direction B) may be converted to the edge direction A of each pattern 440A-440F based on the angle between the two directions. In the pattern layouts of FIGs. 13A-13C, the inclination angles (<[>, <f> ') and widths Wl, W2, W3, and W4 of the patterns may be selected as described previously (e.g., with reference to FIGs. 5A and 7A).

[0094] In the example patterns described above, as illustrated in FIG. 14A, the shape (e.g., the cross-sectional shape) of the pattern 440 in one plane (e.g., the XZ plane) may be approximately trapezoidal with two opposing inclined edges, and the shape of the pattern in an orthogonal plane (e.g., XY plane) resembles a line. And to measure the beam size in different directions, the pattern is oriented such that edge direction A of the pattern 440 makes different angles (a) with respect to the X-axis. However, such a configuration of the pattern is only exemplary. In some embodiments, a pattern having multiple edges oriented in more than one direction may be used. For ease of description, such a pattern may be referred to herein as a two-dimensional or 2D pattern. FIG. 14B illustrates an exemplary octagon-shaped pattern 440 with multiple edges oriented in different directions. Specifically, pattern 440 includes four pairs of opposing edges (si & s2, s3 & s4, s5 & s6, and s7 & s8) with each pair of edges oriented in a different direction. For example, edges si & s2 are oriented along a first edge direction Al, edges s3 & s4 are oriented along a second edge direction A2, edges s5 & s6 are oriented along a third edge direction A3, and edges s7 & s8 are oriented along a fourth edge direction A4. In some embodiments, the inclination angle <[> of each inclined edge and its slope width may be selected as described previously with reference to FIG. 5A. For example, the inclination angle (<[>) of each inclined edge sl-s8 may be between about 40° ~ 80° to make the changes in secondary electron yield (8) distinct and obvious and mitigates the strong edge effect as described previously with reference to FIG. 5A. The width of each of the inclined edges sl-s8 (which corresponds to Wl and W3 of FIG. 5A), and the distance between the opposing inclined edges (i.e., si & s2, s3 & s4, s5 & s6, and s7 & s8) may be selected to beabout 2.3rb to make the measurement error less than about 10%, or3.8rb to make the measurement error less than about 1%, or5rb to make the measurement error less than about 0.1%. The combination of inclination angle (<[>) and slope width may be selected to make the edge height less than the depth of focus (DOF) of the electron beam. By scanning over the pattern 440 using an electron beam with the scanning direction parallelto (or along) the different edge directions (Al, A2, A3, and A4), the beam size in different directions can be measured. In some embodiments, the scanning direction of the beam may be changed to be parallel to the different edge directions. However, as explained previously with reference to FIGs. 10A and 10B, in some embodiments, it may not be possible to make the scanning direction parallel to all the edge directions. In such embodiments, the pixel size (which is in the scanning direction) may be converted to the non-parallel edge directions based on the angles between these edges and the scanning direction.

[0095] It should be noted that the octagonal-shaped pattern 440 illustrated in FIG. 14B is only exemplary. In general, pattern 440 may include any polygonal shape (in a top-down view of the sample) with the inclined edges forming the sides of the polygon shape. For example, FIGs. 14C-14 F illustrate some exemplary 2D patterns 440 having multiple inclined edges. FIG. 14C illustrates a triangular pattern 440 with three inclined edges sl-s3, FIG. 14D illustrates a quadrilateral pattern 440 with four inclined edges sl-s4, FIG. 14E illustrates a hexagonal shaped pattern 440 with six inclined edges sl-s6, and FIG. 14E illustrates a heptagonal pattern 440 with seven inclined sides sl-s7. It should be noted that these 2D pattern shapes are merely exemplary and other pattern shapes (e.g., pentagonal shape, nonagonal shaped, decagonal shaped, etc.) are also contemplated. The inclination angle (<[>), the slope width, and the distance between the opposite edges of each of these patterns 440 may be selected as described previously (e.g., with reference to FIGs. 5A and 7A). As described previously, to measure the beam size in different directions in one FOV 500, a 2D pattern 440 having multiple edges oriented in different directions (such as, for example, a pattern 440 of FIGs. 14B-14F) may be provided in the FOV 500. For example, FIG. 15A illustrates an exemplary embodiment of a sample 400 where an octagonal pattern 440 (as illustrated in FIG. 14B) is provided in a FOV 500. By scanning over the pattern 440 using an electron beam with the scanning direction parallel to the different edge directions (A1-A4, see FIG. 14B), the beam size in different directions can be measured. The scanning direction may be made parallel to each edge direction by changing the scanning direction of the beam as it scans over each pair of opposing edges. If it is not possible to make the scanning direction parallel to all the different edge directions, as described with reference to FIGs. 10A and 10B, the pixel size (which is in the scanning direction) may be converted to each nonparallel edge direction based on the angle between the edge direction and the scanning direction.

[0096] To account for the differences in beam size at different locations of the FOV, multiple multiedge 2D patterns may be provided at different locations of the FOV 500. FIG. 15B illustrates an exemplary sample 400 with an octagonal pattern 440B at the center and an octagonal pattern 440A, 440C, 440D, 440E at each corner of the FOV 500. In the embodiment of FIG. 15B, the orientation of the pattern 440A-440E at each location in the FOV 500 may be the same. However, this is not a requirement. In some embodiments, even if the same configuration of pattern is used at different locations, the orientation of the patterns may be changed at different locations of the FOV 500. For example, FIG. 15C illustrates an exemplary sample 400 with pentagonal patterns 440A-440E withdifferent orientations at different locations of the FOV 500. Different configurations of patterns may also be provided at different locations of the FOV 500. For example, FIG. 15D illustrates an exemplary sample 400 with an octagonal pattern 440C at the FOV center, two quadrilateral patterns 440A, 440B with different orientations at two FOV corners, one pentagon pattern 440D at the third FOV corner and one hexagonal pattern 440E at the fourth FOV corner. In each of these samples (e.g., of FIGs. 15B-15D), the inclination angles (<t>), the slope width, and the distance between the opposite edges, and the spacing between adjacent patterns may be selected as described previously.

[0097] In the current disclosure, electron beam size (e.g., n>) is measured using samples with patterns fabricated to have an edge profile having a known and controlled inclination angle and slope width. The beam size measured using such samples is expected to improve the measurement accuracy, for example, by as much as 30% (see FIG. 5B). Exemplary methods of fabricating resolutionmeasurement samples and methods of measuring the resolution (S2575) and the beam size using such samples will now be described.

[0098] FIG. 16A illustrates an exemplary method 600 of fabricating an exemplary resolutionmeasurement sample. In step S610, the primary electron beam size (e.g., rb) of an SEM may be predicted or determined using, for example, simulations. In some embodiments, the predicted (or estimated) size of the electron beam (or beam spot) may be a sharpness S2575 or a Gaussian radius. Any suitable simulation technique (e.g., Monte Carlo simulations, Gaussian beam models, Finite element analysis, etc.) may be used to predict the beam size in step S610. Samples 400 with a pattern 440 having a controlled edge profile as described previously may be fabricated in step S620. For example, the inclination angle (<[>) of the edge may be between about 40° ~ 80°, and the slope width of the inclined edge may beabout 2.3rb (for less than about 10% measurement error) or3.8rb (for less than about 1% measurement error), or5n> (for less than about 0.1% measurement error). As explained previously, such a controlled edge profile makes the changes in secondary electron yield (8) distinct and obvious with less or even minimal effect from other surfaces of pattern. In some embodiments, this pattern 440 may include a line having a cross-sectional shape as illustrated in FIG. 5A extending on the surface of a substrate 330. With additional reference to FIG. 5A, the fabricated pattern 440 in step S620 may have a pair of inclined edges si and s2 each having an angle of inclination (<[>, <[>') between about 40° ~ 80° and a slope width (Wl, W3)about 5 times the beam size (rb) determined in step S610. The pattern 440 may be fabricated using known semiconductor fabrication techniques in step S620. For example, the pattern 440 may be formed on the substrate using know photo-lithography techniques. Samples having any of the patterns 440 described previously may be fabricated using method 600.

[0099] FIG. 16B illustrates an exemplary method 700 of measuring the resolution (S2575) and determining the beam size of a primary electron beam of an SEM using the exemplary resolutionmeasurement sample (e.g., the sample fabricated using method 600). In some exemplaryembodiments, method 700 may be performed by controller 109 (of FIG. 1), image processing systems 290, 199 (of FIGs. 2A, 2B) of any other controller associated with the SEM system. In step S710, the resolution-measurement sample with a pattern 440 (e.g., the pattern 440 illustrated in FIG. 5A) may be scanned using the primary electron beam of an SEM to obtain a signal (e.g., see FIG. 4C). With additional reference to FIGs. 4C and 5A, from the signal corresponding to the inclined edge si (having an inclination angle (<[>) between about 40° ~ 80° and a slope width (Wlabout 5 n,), the S2575 distance (i.e., resolution, sharpness, etc.) may be measured as explained previously in step S720. For example, the maximum and minimum (Imax and Imin) of the vertical axis values of the signal is obtained and the difference between the X-axis positions corresponding to 25% and 75% of Imax-Imin may be measured as the S2575 distance. The beam size (rb) may then be determined based on the measured S2575 distance in step S730. In some embodiments, in step S730, rb may be determined as S2575 / 0.954 (e.g., based on equation 6). In some embodiments, rb may be determined to be equal to S2575 (i.e., S2575 / 1.0). In general, rb may be determined as S2575 / A, where A is any value between 0.9 and 1.0. It should be noted that although beam size is described as rb, this is only exemplary. In general, beam size may be selected as any multiple of rb, such as, for example, 2rb, 1.916rb, etc.

[0100] In some embodiments, instead of scanning the resolution-measurement sample in step S710 to measure the S2575 distance (e.g., resolution) and determine the beam size, an SEM image of the resolution-measurement sample may be used to determine the resolution and beam size. For example, an SEM image of a resolution-measurement sample may be input into an SEM image analysis software (e.g., ImageJ, FIJI, Image Pro Plus, DigitalMicrograph, AnalySIS, Avizo, etc.) and the profile of an edge (e.g., an edge having a controlled inclination profile as explained with reference to FIG. 5A) in the SEM image may be selected and used to measure the beam size and resolution (e.g., as explained with reference to steps S720 and S730 of method 700). In some exemplary embodiments, method 700 may be performed by controller 109 (of FIG. 1), image processing systems 290, 199 (of FIGs. 2A, 2B) of any other controller associated with the SEM system.

[0101] In some embodiments, 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, stage positioning, beam focusing, electric field adjustment, beam bending, condenser lens adjusting, activating charged particle source, beam deflecting, measuring the resolution and beam size of a primary electron beam, and methods 700 and 800. 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 flashmemory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0102] The embodiments may further be described using the following clauses:1. A method of determining a size of a beam spot of a charged-particle beam, comprising: scanning a pattern on a sample with a charged-particle beam to generate an image, wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle that is controlled during manufacture of the sample to be between about 40- 80 degrees; and determining the size of the beam spot on the sample based on an imaging profile of the at least one inclined side edge derived based on the image.2. The method of clause 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 2.3 times an estimated size of the beam spot .3. The method of clause 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 3.8 times an estimated size of the beam spot.4. The method of clause 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 5 times an estimated size of the beam spot.5. The method of any one of clauses 2-4, wherein the estimated size of the beam spot is a predetermined value based on a simulation.6. The method of any one of clauses 1-4, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.7. The method of clause 6, wherein the first inclined side edge and the second inclined side edge have a slope width greater than or equal to about 2.3 times an estimated size of the beam spot.8. The method of any one of clauses 1-4, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times an estimated size of the beam spot.9. The method of clause 8, wherein the sample includes only a single pattern in a field of view of the charged-particle beam.10. The method of any of clauses 1-4, wherein the pattern is a first pattern and the sample further includes a second pattern spaced apart from the first pattern, the second pattern having a second inclined side edge having an inclination angle between about 40-80 degrees, wherein the first pattern and the second pattern are positioned in a field of view of the charged-particle beam.11. The method of clause 10, wherein the first pattern and the second pattern are spaced apart by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot.12. The method of clause 11, wherein the second pattern is oriented on the sample differently from the first pattern.13. The method of any of clauses 1-4, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.14. The method of clause 13, wherein the pattern is a first pattern and the sample further includes a second pattern and a third pattern in a field of view of the charged-particle beam, and wherein the second pattern and the third pattern are spaced apart from the first pattern by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot.15. The method of clause 14, wherein at least one of the second pattern and the third pattern is (a) oriented on the sample differently than the first pattern, or (b) has a different number of sides than the first pattern.16. A method of determining a size of a beam spot of a charged-particle beam, comprising: scanning a pattern on a sample with a charged-particle beam to generate an image, wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle between about 40-80 degrees and a slope width greater than or equal to about 2.3 times an estimated size of the beam spot based on a simulation; and determining the size of the beam spot based on an imaging profile of an inclined side edge of the at least one inclined side edge derived based on the image.17. The method of clause 16, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.18. The method of clause 16, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.19. The method of any of clauses 16-18, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times the estimated size of the beam spot.20. The method of any of clauses 16-18, wherein the sample includes the pattern formed on a substrate, wherein the substrate and the pattern includes an electrically conductive material, and wherein at least one of the substrate and the pattern includes a metal or doped silicon.21. A sample for determining a size of a beam spot of a charged-particle beam, comprising: a substrate formed of an electrically conductive material, and a pattern disposed on the substrate, wherein the pattern is formed of an electrically conductive material, and wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees.22. The sample of clause 21, wherein the at least one inclined side edge has a slope width greater than or equal to about 2.3 times an estimated size of the beam spot based on a simulation.23. The sample of clause 21, wherein the at least one inclined side edge has a slope width greater than or equal to about 3.8 times an estimated size of the beam spot based on a simulation.24. The sample of clause 21, wherein the at least one inclined side edge has a slope width greater than or equal to about 5 times an estimated size of the beam spot based on a simulation.25. The sample of any one of clauses 21-24, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.26. The sample of clause 25, wherein the first inclined side edge and the second inclined side edge have a slope width greater than or equal to about 2.3 times an estimated size of the beam spot.27. The sample of any one of clauses 22-24, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times the estimated size of the beam spot.28. The sample of clause 27, wherein the sample includes only a single pattern in a field of view of the charged-particle beam.29. The sample of any of clauses 22-24, wherein the pattern is a first pattern and the sample further includes a second pattern spaced apart from the first pattern, the second pattern having a second inclined side edge having an inclination angle between about 40-80 degrees, wherein the first pattern and the second pattern are positioned in a field of view of the charged-particle beam.30. The sample of clause 29, wherein the first pattern and the second pattern are spaced apart by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times the estimated size of the beam spot.31. The sample of clause 30, wherein the second pattern is oriented on the sample differently from the first pattern.32. The sample of any of clauses 22-24, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.33. The sample of clause 32, wherein the pattern is a first pattern and the sample further includes a second pattern and a third pattern in a field of view of the charged-particle beam, and wherein the second pattern and the third pattern are spaced apart from the first pattern by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times the estimated size of the beam spot.34. The sample of clause 33, wherein at least one of the second pattern and the third pattern is (a) oriented on the sample differently than the first pattern, or (b) has a different number of sides than the first pattern.35. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for determining a size of a beam spot of a charged-particle beam, the operations comprising: scanning a pattern on a sample with a charged-particle beam to generate an image, wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees; and determining the size of the beam spot based on an imaging profile of the at least one inclined side edge derived based on the image.36. The non-transitory computer readable medium of clause 35, wherein the at least one inclined side edge has a slope width greater than or equal to about 2.3 times an estimated size of the beam spot.37. The non-transitory computer readable medium of clause 35, wherein the at least one inclined side edge has a slope width greater than or equal to about 3.8 times an estimated size of the beam spot.38. The non-transitory computer readable medium of clause 35, wherein the at least one inclined side edge has a slope width greater than or equal to about 5 times an estimated size of the beam spot.39. The non-transitory computer readable medium of any one of clauses 35-38, wherein the estimated size of the beam spot is a predetermined value based on a simulation.40. The non-transitory computer readable medium of any one of clauses 35-38, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.41. The non-transitory computer readable medium of clause 40, wherein the first inclined side edge and the second inclined side edge have a slope width greater than or equal to about 2.3 times an estimated size of the beam spot.42. The non-transitory computer readable medium of any one of clauses 35-38, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times an estimated size of the beam spot.43. The non-transitory computer readable medium of clause 42, wherein the sample includes only a single pattern in a field of view of the charged-particle beam.44. The non-transitory computer readable medium of any of clauses 35-38, wherein the pattern is a first pattern and the sample further includes a second pattern spaced apart from the first pattern, the second pattern having a second inclined side edge having an inclination angle between about 40-80 degrees, wherein the first pattern and the second pattern are positioned in a field of view of the charged-particle beam.45. The non-transitory computer readable medium of clause 44, wherein the first pattern and the second pattern are spaced apart by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot.46. The non-transitory computer readable medium of clause 45, wherein the second pattern is oriented on the sample differently from the first pattern.47. The non-transitory computer readable medium of any of clauses 35-38, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.48. The non-transitory computer readable medium of clause 47, wherein the pattern is a first pattern and the sample further includes a second pattern and a third pattern in a field of view of the charged- particle beam, and wherein the second pattern and the third pattern are spaced apart from the first pattern by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot.49. The non-transitory computer readable medium of clause 48, wherein at least one of the second pattern and the third pattern is (a) oriented on the sample differently than the first pattern, or (b) has a different number of sides than the first pattern.50. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for determining a size of a beam spot of a charged-particle beam, the operations comprising: scanning a pattern on a sample with a charged-particle beam to generate an image, wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle between about 40-80 degrees and a slope width greater than or equal to about 2.3 times an estimated size of the beam spot based on a simulation; and determining the size of the beam spot based on an imaging profile of an inclined side edge of the at least one inclined side edge derived based on the image.51. The non-transitory computer readable medium of clause 50, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.52. The non-transitory computer readable medium of clause 50, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.53. The non-transitory computer readable medium of any of clauses 50-52, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times the estimated size of the beam spot.54. The non-transitory computer readable medium of any of clauses 50-52, wherein the sample includes the pattern formed on a substrate, wherein the substrate and the pattern includes an electrically conductive material, and wherein at least one of the substrate and the pattern includes a metal or doped silicon.

[0103] Block diagrams in the figures may illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer hardware or software productsaccording 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.

[0104] 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. A non-transitory computer readable medium that stores a set of instructions that is executable by at least on processor of a computing device to cause the computing device to perform operations for determining a size of a beam spot of a charged-particle beam, the operations comprising: scanning a pattern on a sample with a charged-particle beam to generate an image, wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees; and determining the size of the beam spot based on an imaging profile of the at least one inclined side edge derived based on the image.

2. The non-transitory computer readable medium of claim 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 2.3 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation.

3. The non-transitory computer readable medium of claim 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 3.8 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation.

4. The non-transitory computer readable medium of claim 1, wherein the at least one inclined side edge has a slope width greater than or equal to about 5 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation..

5. The non-transitory computer readable medium of claim 1, wherein the at least one inclined side edge includes a first inclined side edge and a second inclined side edge disposed on opposite sides of the top surface.

6. The non-transitory computer readable medium of claim 5, wherein the first inclined side edge and the second inclined side edge have a slope width greater than or equal to about 2.3 times an estimated size of the beam spot.

7. The non-transitory computer readable medium of claim 1, wherein a width of the top surface is greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 2.3 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation.

8. The non-transitory computer readable medium of claim 7, wherein the sample includes only a single pattern in a field of view of the charged-particle beam.

9. The non-transitory computer readable medium of claim 1, wherein the pattern is a first pattern and the sample further includes a second pattern spaced apart from the first pattern, the second pattern having a second inclined side edge having an inclination angle between about 40-80 degrees, wherein the first pattern and the second pattern are positioned in a field of view of the charged- particle beam.

10. The non-transitory computer readable medium of claim 9, wherein the first pattern and the second pattern are spaced apart by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation.

11. The non-transitory computer readable medium of claim 10, wherein the second pattern is oriented on the sample differently from the first pattern.

12. The non-transitory computer readable medium of claim 1, wherein the pattern is polygonal shaped in a top-down view of the sample, and the at least one inclined side edge includes multiple inclined side edges, and wherein each inclined side edge of the multiple inclined side edge forms a side of the polygonal shaped pattern.

13. The non-transitory computer readable medium of claim 12, wherein the pattern is a first pattern and the sample further includes a second pattern and a third pattern in a field of view of the charged-particle beam, and wherein the second pattern and the third pattern are spaced apart from the first pattern by a distance greater than or equal to larger of (i) a penetration depth of the charged-particle beam on the sample and (ii) about 5 times an estimated size of the beam spot, wherein the estimated size of the beam spot is a predetermined value based on a simulation.

14. The non-transitory computer readable medium of claim 13, wherein at least one of the second pattern and the third pattern is (a) oriented on the sample differently than the first pattern, or (b) has a different number of sides than the first pattern.

15. A sample for determining a size of a beam spot of a charged-particle beam, comprising: a substrate formed of an electrically conductive material, anda pattern disposed on the substrate, wherein the pattern is formed of an electrically conductive material, and wherein the pattern includes at least one inclined side edge and a top surface, wherein the at least one inclined side edge has an inclination angle that is controlled during manufacture of the sample to be between about 40-80 degrees.

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