End-to-end mapping of near-field interaction patterns via physics-aware neural network and plasmon-assisted near-field structured illumination

Abstract

A defect detection system configured to control an energy source to transmit a deep ultraviolet (DUV) laser light at a wavelength along an incident path at different time periods; direct the laser light from an initial angle of transmission to obtain first angles of incidence of the laser light along the incident path at the different time periods; control a polarizer to generate polarized DUV laser light at the different time periods; obtain far-field images for each of the near-field interaction patterns with an image sensor based on the polarized DUV laser light; compare reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed patterned reflector transmitter (PRT) pattern with sub-micron features; and obtain an inference on nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference patterns.

Description

Atty. Docket No.: 4502-88500 (6000800PCT01)End-To-End Mapping of Near-Field Interaction Patterns via Physics-Aware Neural Network and Plasmon-Assisted Near-Field Structured IlluminationCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] None.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not applicable.REFERENCE TO A MICROFICHE APPENDIX

[0003] Not applicable.BACKGROUND

[0004] Current demands for high-resolution in optical imaging requires imaging on structures with submicron features. However, such demands require formation of device features with high precision and uniformity. Further, surface imaging of a structure is effective at a region of interest at the edge of the structure where a light beam can bend or spread out as it passes through an opening or moves around the edge. However, many structures of interest are of sizes and scales that are far below the diffraction limit of visible light. Several methods have been used, but tradeoffs between resolution, speed, field of view, sensitivity, and experimental complexity. Traditional structured illumination microscopy (SIM) has been used for optical imaging but the illumination structure in SIM is diffraction-limited, and the resolution is only about 3 -fold versus standard microscopy of imaged structures.SUMMARY

[0005] In an embodiment, the disclosure includes a defect detection system. The defect detection system includes one or more memories comprising instructions and one or more processors coupled to the one or more memories. In an embodiment, the one or more processors is configured to execute instructions to cause the defect detection system to control an energy source to transmit a deep ultraviolet (DUV) laser light at a wavelength along an incident path at different time periods; direct the laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; control aAtty. Docket No.: 4502-88500 (6000800PCT01) polarizer to generate polarized DUV laser light at the different time periods; obtain far- field images for each of the near-field interaction patterns with an image sensor; compare reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed PRT pattern; and obtain an inference on nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference pattern.

[0006] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to control incidence of the polarized DUV laser light onto a plasmon generating mask at the different time periods; and obtain high-spatial frequency plasmon interference patterns based on the polarized DUV laser light incident on the plasmon generating mask at the different time periods.

[0007] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to obtain near-field interaction patterns based on interaction of the high-spatial frequency plasmon interference patterns with a patterned reflector transmitter (PRT) at the different time periods, wherein the PRT comprises submicron features for interacting with DUV wavelengths, and wherein the plasmon generating mask is at a sub-wavelength distance to the PRT.

[0008] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to control a light steering system to direct the laser light from the initial angle of transmission to the first angles of transmission; control a polarizer to generate polarized DUV laser light at the different time; and control the polarizer to change the polarized angles of transmission to obtain polarized DUV laser light at polarized angles of incidence based on the first angles of transmission.

[0009] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to obtain the high- spatial frequency plasmon interference patterns based on the first angles of transmission and the polarized angles of incidence at the different time periods.

[0010] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to obtain the far-field images for each of the near-field interaction patterns at the different time periods based on interaction of the polarized DUV laser light via the first angles of transmission and the polarized angles of incidence at the different time periods; obtain a reference pattern that corresponds to the PRT;Atty. Docket No.: 4502-88500 (6000800PCT01) process the far-field images and the expected designed PRT through the neural network model; and infer defects in the PRT based on processing the far-field images and the expected designed PRT through the neural network model, wherein the neural network model is configured to infer defective distributions in the PRT.

[0011] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to train the neural network model using a training dataset, wherein the training dataset is obtained by obtaining a library of ideal binary PRT layouts based on randomized geometric parameters comprising pitch, orientation, and unit-cell motifs; creating defective distributions for defective PRT layouts by applying physically motivated defect operators to the ideal binary PRT layouts, and wherein the defect operators comprise stochastic edge roughness, bridges, breaks, and stitching errors; utilizing simulations to physically precompute near-field characteristic of DUV plasmonic interactions; obtaining physically simulated far-field images; and training the neural network model using the physically simulated far-field images and each of the expected designed PRT patterns as training inputs, and the defective distributions as training ground truth.

[0012] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to train the neural network model using the physically simulated far-field images by using the near-field characteristic of DUV plasmonic interactions comprising physically precomputed near-field Poynting flux (Sz) distributions, wherein the simulations comprise a method selected from one or more of finite different time domain (FDTD) method, a rigorous coupled wave analysis (RCWA) method, or a finite element (FEM) method, and obtaining the physically simulated far-field images by modulating the defective distributions with the precomputed near-field Poynting vector distributions and convolving a result with a physical aperture-limited Point Spread Function (PSF).

[0013] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to train the neural network model using a training dataset, wherein the training dataset is obtained by obtaining a library of ideal binary PRT layouts based on designed geometric parameters comprising pitch, orientation, and unit-cell motifs; obtaining a physical PRT based on the ideal binary PRT layouts; characterizing defective distributions in the physical PRT using nanometer resolution methodology; physically acquiring far-field images; training the neural network model using theAtty. Docket No.: 4502-88500 (6000800PCT01) far-field images and each of the ideal binary PRT layouts as training input; characterizing the defective distributions on the physical PRT as training ground truth.

[0014] Optionally, in any of the preceding aspects, another implementation of the aspect provides instructions to further cause the processor to be configured to cause the defect detection system to train the neural network model using a physics-aware dataset comprising training input and ground truth. In an embodiment, the training input and ground truth is obtained by synthetic training data. For instance, the training input and ground truth is obtained by obtaining a library of ideal binary PRT layouts based on randomized geometric parameters comprising pitch, orientation, and unit-cell motifs; creating defective distributions for defective PRT layouts by applying physically motivated defect operators to the ideal binary PRT layouts, and wherein the defect operators comprise stochastic edge roughness, bridges, breaks, and stitching errors; utilizing simulations to physically precompute near-field characteristic of DUV plasmonic interactions; obtaining physically simulated far-field images; and training the neural network model using the physically simulated far-field images and each of the expected designed PRT patterns as training inputs, and the defective distributions as training ground truth.

[0015] In another embodiment, the training input and ground truth is obtained by measurements. For example, the training input and ground truth is obtained by obtaining a library of ideal binary PRT layouts based on designed geometric parameters comprising pitch, orientation, and unit-cell motifs; obtaining a physical PRT based on the ideal binary PRT layouts; characterizing near-field defects in the physical PRT using nanometer resolution methodology; physically acquiring far-field images; training the neural network model using the far-field images and each of the ideal binary PRT layouts as training input; characterizing the near-field defects on the physical PRT as training ground truth. In an embodiment, the training input is obtained through synthetic training data and measurements.

[0016] In an embodiment, the disclosure includes a method for defect detection. The method comprises controlling an energy source to transmit a deep ultraviolet (UV) laser light at a wavelength along an incident path at different time periods; directing the laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; controlling a polarizer to generate polarized DUV laser light at the different time periods; obtaining far-field images for each of the near-field interaction patternsAtty. Docket No.: 4502-88500 (6000800PCT01) with an image sensor; comparing reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed patterned reflector transmitter (PRT) pattern with sub-micron features; and obtaining an inference on nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference pattern.

[0017] Optionally, in any of the preceding aspects, another implementation of the aspect includes providing a plasmon generating mask includes aluminum material; controlling incidence of the polarized DUV laser light onto the plasmon generating mask at the different time periods; and obtaining high-spatial frequency plasmon interference patterns based on the polarized DUV laser light incident on the plasmon generating mask at the different time periods.

[0018] Optionally, in any of the preceding aspects, another implementation of the aspect provides positioning a patterned reflector transmitter (PRT) comprising submicron features at a sub-wavelength distance to the plasmon generating mask; and obtaining near-field interaction patterns based on interaction of the high-spatial frequency plasmon interference patterns with the PRT at the different time periods.

[0019] Optionally, in any of the preceding aspects, another implementation of the aspect provides controlling a light steering system to direct the DUV laser light from the initial angle of transmission to the first angles of transmission; controlling a polarizer to generate polarized DUV laser light at the different time periods; and controlling the polarizer to change the polarized angles of transmission to obtain polarized DUV laser light at polarized angles of incidence based on the first angles of transmission.

[0020] Optionally, in any of the preceding aspects, another implementation of the aspect provides obtaining the far-field images for each of the near- field interaction patterns at the different time periods based on interaction of the polarized DUV laser light via the first angles of transmission and the polarized angles of incidence at the different time periods; obtaining a reference pattern that corresponds to the PRT; process the far-field images and the expected designed PRT through a neural network model; and inferring defective distributions in the PRT based on processing the far-field images and the expected designed PRT through the neural network model, wherein the neural network model is configured to infer defective distributions in the PRT.Atty. Docket No.: 4502-88500 (6000800PCT01)

[0021] In an embodiment, the disclosure includes a non-transitory computer-readable medium. In an embodiment, the non-transitory computer-readable medium stores computer-executable instructions that, when executed by one or more processors, cause a defect detection system to control an energy source to transmit a deep ultraviolet (DUV) laser light at a wavelength along an incident path at different time periods; direct the laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; control a polarizer to generate polarized DUV laser light at the different time periods; obtain far- field images for each of the near- field interaction patterns with an image sensor; compare reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed PRT pattern; and obtain an inference on defective distributions in the PRT based on comparing the far-field images with the reference pattern.

[0022] For the purpose of clarity, any one of the foregoing embodiments may be combined with any one or more of the other foregoing embodiments to create a new embodiment within the scope of the present disclosure.

[0023] These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0024] For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts.

[0025] FIG. 1 is a schematic diagram of a defect detection system in accordance with an embodiment of the disclosure.

[0026] FIG. 2 is a schematic diagram illustrating a DUV localized plasmonic structured illumination microscopy (LPSIM) setup for showing a DUV localized plasmonic structure interacting with PRT in near-field in accordance with an embodiment.

[0027] FIG. 3 is a schematic diagram illustrating a method for identifying defects in a nanopattern using a neural network in accordance with an embodiment of the disclosure.

[0028] FIG. 4 is a schematic diagram of training a neural network for identifying defects in a patterned reflector transmitter in accordance with an embodiment of the disclosure.Atty. Docket No.: 4502-88500 (6000800PCT01)

[0029] FIG. 5 is a flowchart of a method for identifying defects in a patterned reflector transmitter using a neural network in accordance with an embodiment of the disclosure.

[0030] FIG. 6 is a schematic diagram of a network device according to various embodiments of the disclosure.

[0031] FIG. 7 is a schematic diagram illustrating a means for defect detection according to various embodiments of the disclosure.DETAILED DESCRIPTION

[0032] It should be understood at the outset that although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and / or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents.

[0033] Disclosed herein are embodiments of a defect detection system that may be implemented for detecting defects in a patterned reflector / transmitter (PRT) that are to be inspected using structured illumination microscopy (SIM) in accordance with an embodiment. In an embodiment, the PRT is a nanopattern with an arrangement of structures and features on a surface where at least one dimension is in the nanoscale, typically ranging from 1 to 200 nanometers (nm). In an embodiment, the PRT comprises submicron features. As will be more fully explained below, structured illumination microscopy (SIM) of the PRT is used with a physics-aware neural network model to provide an inference on defective distributions in the PRT. In an example, physics-aware refers to a set of machine learning (ML) methodologies that incorporates physical laws, governing equations (for example, partial differential equations), and boundary / initial conditions directly into a model's training process. The inference may be obtained from far-field images using near-field interaction patterns generated by a plasmon generating mask. The near-field interaction patterns include high-spatial frequency information. In an embodiment, the defect detection system may use an energy source, for example, may use deep ultraviolet (DUV) laser light that is input into a polarizer to obtain polarized DUV laser light in an incident path of the defect detection system. In embodiments, the deep UV laser light is 193 nm or 248 nm. The angle of transmission of the UVAtty. Docket No.: 4502-88500 (6000800PCT01) laser light and the angle of incidence of the polarized DUV laser light may be tuned to obtain multiple near-field interaction patterns during a collection path of the defect detection system. The polarized DUV laser light are incident on a plasmon generating mask to emit near-field plasmon interference patterns, which are modulated by the PRT to obtain near-field interaction patterns. The PRT is placed at a sub-wavelength spacing (for example around approximately 200 nm) from the plasmon generating mask. The plasmon interference patterns travel through the PRT in positive z-direction to create near-field interaction patterns. These near-field interaction patterns are collected by an image sensor and processed to obtain far-field images. In an embodiment, a trained neural network receives the far-field images and provides, using the far-field images and reference patterns, an inference on defective distributions in the PRT. In an embodiment, the reference patterns are defect-free ideal PRT layouts.

[0034] Referring now to the figures, FIG. 1 depicts a schematic diagram of defect detection system 100 using localized plasmonic structured illumination microscopy (LPSIM) according to an embodiment of the disclosure. In an embodiment, the defect detection system 100 comprises an incident path 102, a collection path 104, and a controller 126. In an embodiment, the incident path 102 defines an arrangement of optical components such as an optical energy source 106, a light steering system 108 and polarizer 114, a plasmon generating mask 116, and a patterned reflector transmitter (PRT) 118.

[0035] In an embodiment, the optical energy source 106 is a laser device that generates and transmits optical energy as a deep ultraviolet (DUV) laser light (for example, DUV optical beam). In an embodiment, the optical energy source 106 is controlled by the controller 126 to transmit the DUV laser light under excitation having a wavelength in a range from about 100 nanometer (nm) to about 300 nm along the incident path 102. In an embodiment, the DUV laser light is about 193 nm. In another embodiment, the DUV laser light is about 248 nm. In an embodiment, an excitation wavelength of the DUV laser light is selected based on a metal-dielectric interface that is used in a plasmon generating mask 116. In another example, the optical energy source 106 may be a lamp. In an example, the DUV laser light is incident along an incident path 102.

[0036] In an embodiment, the light steering system 108 includes controllable mirrors, lenses, quarter wave plate, and prisms along an incident path 102 of the laser light. In an embodiment, the optical energy source 106 is controlled by the controller 126 to transmit laser light. In embodiments, the laser device is controlled by either direct modulation to emit the DUV laserAtty. Docket No.: 4502-88500 (6000800PCT01) light, by external modulation to emit the DUV laser light, or similar methods to emit the DUV laser light. In direct modulation, an electrical current feeding the laser device is varied to change characteristics (for example, intensity) of the laser light. In external modulation, the optical energy source 106 stays on at a constant intensity, and an external shutter or crystal manipulates the DUV laser light before or after it exits the laser device. In an embodiment, the laser light from the optical energy source 106 is transmitted at an initial angle of transmission at different time periods and directed to different angles by the light steering system 108 (for example, the laser light from the optical energy source 106 includes tunable angles of transmission). In an example, the light steering system 108 is controlled by controller 126 to steer, split or otherwise control the angle of transmission of the laser light from an initial transmitted angle that is directed to the polarizer 114. In an embodiment, the controller 126 controls the angles and position of mirrors and lenses of the light steering system 108 to direct the incident light from the optical energy source 106 to desired angles. In some embodiments, the controller 126 may control the light steering system 108 to redirect the laser light from the initial angle of transmission of the laser light at different time periods to at least three different angles of transmission (for example, transmitted laser light is directed at angle al, angle a2, or angle a3 as shown in FIG. 1) at the different time periods. In an embodiment, the three different angles al, a2, and a3 represents directed laser light at the different angles that is directed out from light steering system 108. However, more or less angles of transmission of the directed laser light may also be contemplated for use in defect detection system 100. A polarizer 114 is positioned between light steering system 108 and plasmon generating mask 116. In an embodiment, the polarizer 114 is positioned before the light steering system 108. The directed laser light is incident on the polarizer 114 in order to create polarized DUV laser light from the directed laser light. The polarized DUV laser light is tuned by the controller 126 (for example, polarization angle of the polarized DUV laser light may be adjusted) to generate a polarized DUV laser light having at least two polarization angles at different time periods. In an embodiment, the controller 126 controls the polarizer 114 to align the directed laser light relative to the plane of incidence. The at least two polarization angles are shown as bl and b2 in FIG. 1. In an example, for each angle of incidence of the directed laser light (for example, al, a2, or a3 as shown in FIG. 1) that is received at the polarizer 114, the polarizer 114 generates polarized DUV laser light at angles bl or b2, which are the polarized angles of incidence. Further, the polarized DUV laser light from the polarizer 114 that is incident on the plasmon generating mask 116 at theAtty. Docket No.: 4502-88500 (6000800PCT01) different time periods includes the polarized DUV laser light with at least two polarization angles (for example, polarized angles of incidence bl or b2). For instance, for each angle of transmission of the directed laser light, the polarizer 114 is tuned to generate at least two different angles of polarized DUV laser light that is incident on the plasmon generating mask 116 to generate at least 6 different plasmonic interference patterns.

[0037] In an embodiment, the plasmon generating mask 116 is a localized plasmonic structure that is positioned at a sub-wavelength distance from the PRT 118. In an example, the localized plasmonic structure includes a metal with a LPSIM substrate. In an embodiment, the subwavelength distance is around 200 nm. In an example, the plasmon generating mask 116 includes a metal with a dielectric interface, such as an optically thick metal film on glass, or a metal with a dielectric multilayer on glass. In an example, the metal in the plasmon generating mask 116 is an aluminum material. In an embodiment, the plasmon generating mask 116 includes an arrangement of surface features arranged in a hexagonal lattice having a symmetrical structure. In an embodiment, each hexagonal lattice includes a repeating arrangement of metal pillars in a sixsided, honeycomb-like pattern that is embedded in a substrate. In embodiments, the plasmon generating mask 116 includes periodic aluminum pillars embedded in a magnesium fluoride (MgF2) substrate. In an embodiment, aluminum metal is selected as the metal layer since aluminum metal has high plasmon frequency and low loss at DUV wavelengths and may create interference patterns that are more suitable for defect detection using deep UV light in the 100 - 300 nm range.

[0038] In an embodiment, the aluminum material of the plasmon generating mask 116 and the features in the plasmon generating mask 116 are dimensioned, shaped, and arranged to generate plasmon interference patterns (or localized surface plasmon polaritons (SPPs)) from the polarized DUV laser light from the polarizer. In an embodiment, polarized DUV laser light causes the plasmon generating mask 116 to emit plasmon interference patterns based on structured excitation of the plasmon generating mask 116. For instance, the plasmon generating mask 116 emits plasmon interference patterns when the polarized DUV laser light is directed on the surface features of the plasmon generating mask 116. In an embodiment, the hexagon structure of the substrate of the plasmon generating mask 116 generates three symmetrical plasmon interference patterns for each incident angle of the polarized DUV laser light. In an embodiment, with three different angles of incidence of the directed laser light that is redirected by the polarizer 114, atAtty. Docket No.: 4502-88500 (6000800PCT01) least 18 plasmon interference patterns are created by the plasmon generating mask 116. Tn an example, the 18 far- field images are based on 3 angles of the directed laser light x 2 angles of the polarized DUV laser light x 3 plasmon interference patterns with symmetry (for example, at 0 degrees and 30 degrees in hexagonal) of the plasmon generating mask 116. In an embodiment, plasmon interference patterns with non-symmetry are also selected (for example, at 20 degrees). In an embodiment, the incident angles of transmission of the energy source 106 and the polarizer 114 are tuned to different angles than disclosed herein. In an example, the plasmon interference patterns have a periodicity that is shorter than the wavelength of the optical light beam. In an embodiment, characteristics of the plasmon interference patterns are controlled by configuring the plasmon generating mask 116 in a pre-determined manner (i.e., selecting the plasmon generating mask material and geometry). Additionally, in an example, the plasmon interference patterns that are obtained are further controlled / determined by controlling the wavelength of the incident light (for example, wavelength of the laser light from the energy source 106), angle of incidence of the polarized DUV laser light relative to the metal / dielectric interface of the plasmon generating mask 116, and the plasmon interference patterns of the excitation energy from different polarized DUV laser light.

[0039] In an embodiment, the PRT 116 is positioned at a sub-wavelength distance to the plasmon generating mask 116. The PRT 116 is a nanopattern with a pitch for interacting with the polarized DUV laser light and includes submicron features. In an embodiment, the PRT 116 is a real-fabricated photomask (for example, PRT 116 is a photomask of a physical specimen being examined). In an embodiment, sub-wavelength spacing of the PRT 118 from the plasmon generating mask 116 causes the plasmon interference patterns (for example, Poynting vector distributions along a direction of wave propagation in the positive z direction) to interact with the PRT 116. In an embodiment, high-spatial frequency Poynting vector distributions in the z direction (for example, distribution of high-spatial frequency Sz vectors) interact with features of the PRT 118 and are modulated (for example, point -wise multiplication) by the PRT 118 to produce near-field interaction patterns. In an embodiment, each polarized DUV laser light that is incident on the plasmon generating mask 116 at a time period produces a near-field interaction pattern. In an embodiment, the near-field interaction pattern includes high frequency information.

[0040] In an embodiment, the collection path 104 is defined by an image sensor 124. The image sensor 124 receives the light from the near-field interaction patterns. The image sensor 124 directsAtty. Docket No.: 4502-88500 (6000800PCT01) and converts the near-field interaction patterns into the far-field digital images. In an embodiment, the image sensor 124 comprises an objective lens and a tube lens (not shown) to direct the near-field interaction patterns. In an embodiment, the image sensor 124 comprises a capturing apparatus, such as a charge coupled device (CCD) camera that captures the far-field images of each near-field interaction pattern. In an example, the far-field images are inputted by the controller 126 into a trained neural network 128 for obtaining an inference of defective distributions 130 in the PRT 116.

[0041] In embodiments, the trained neural network is based on a trained convolutional neural network (CNN) structure or other similarly trained deep neural network model. In an embodiment, the neural network 128 is trained on a physics-aware training dataset. In an embodiment, the physics-aware training dataset includes a diverse library of ideal binary photomask layouts of expected designed PRT that are procedurally synthesized using randomized geometric parameters such as, for example, pitch, orientation, and / or unit-cell motifs. The ideal binary photomask layouts are defect-free ideal PRT layouts (also referred to as a reference pattern) that is synthesized or computer-generated. The training data set also includes corresponding defective distributions for defective PRT layouts (for example, defective binary photomask layouts with defective distributions) that are created / synthesized by applying physically motivated defect operators such as, for example, stochastic edge roughness, bridges, breaks, and stitching errors to the ideal binary photomask layouts. As used herein, “applying a physical operator” may include incorporating operators consistent with known laws of physics, material properties, or inherent physical dynamics into the neural network model to improve accuracy, efficiency, and generalization. Further, in an example, optical physics is integrated into the model by utilizing Finite-Difference Time-Domain (FDTD) simulations to precompute near-field Poynting vector (Sz) distributions characteristic of Deep Ultraviolet (DUV) plasmonic interactions. In embodiments, other simulations are also contemplated such as rigorous coupled wave analysis (RCWA), and finite element method (FEM). In an embodiment, in order to synthesize the final training inputs, the defective distributions for defective binary photomask layouts are modulated by precomputed plasmonic interference patterns (for example, precomputed near-field Poynting vectors) and convolved with a numerical aperturelimited Point Spread Function (PSF) to yield simulated defect far-field images that refer to actual optical measurements. The simulated defect far-field images are physics-consistent far-field images. In an embodiment, the neural network is subsequently supervised trained using the simulated defect far-field images and the ideal binary photomask layouts as whole inputs. In an embodiment, theAtty. Docket No.: 4502-88500 (6000800PCT01) simulated defective distributions are a ground truth that represents a verified output image that the neural network is being trained to predict.

[0042] In an embodiment, the neural network model is trained using a training dataset that is obtained by creating or obtaining a library of ideal binary PRT layouts based on randomized geometric parameters comprising pitch, orientation, and unit-cell motifs; creating defective distributions for defective PRT layouts by applying physically motivated defect operators to the ideal binary PRT layouts, and wherein the defect operators comprise stochastic edge roughness, bridges, breaks, and stitching errors; utilizing simulations to physically precompute near-field Poynting flux (Sz) distributions characteristic of DUV plasmonic interactions; obtaining physically simulated far- field images by modulating the defective distributions with the precomputed near-field Poynting vector distributions and convolving a result with a physical aperture-limited Point Spread Function (PSF). The neural network model is trained using the physically simulated far-field images as inputs and each of the expected designed PRT patterns as ground truth references. In embodiments, the simulations include methods selected from one of finite different time domain (FDTD) method, a rigorous coupled wave analysis (RCWA) method, or a finite element (FEM) method.

[0043] In another embodiment, the neural network model is trained using a training dataset that is obtained by obtaining a library of ideal binary PRT layouts based on designed geometric parameters comprising pitch, orientation, and unit-cell motifs; obtaining a physical PRT based on the ideal binary PRT layouts; characterizing defective distributions in the physical PRT using nanometer resolution methodology; physically acquiring far-field images; training the neural network model using the far-field images and each of the ideal binary PRT layouts as training input; characterizing the defective distributions on the physical PRT as training ground truth. In an embodiment, the ground truth references are obtained using scanning electron microscopy (SEM), scanning electron microscopy (SEM), atomic force microscopy (AFM), and scanning near-field microscopy (SNOM).

[0044] In an embodiment, the training input and ground truth is obtained by synthetic training data. For instance, the training input and ground truth is obtained by obtaining a library of ideal binary PRT layouts based on randomized geometric parameters comprising pitch, orientation, and unit-cell motifs; creating defective distributions for defective PRT layouts by applying physically motivated defect operators to the ideal binary PRT layouts, and wherein the defect operators comprise stochastic edge roughness, bridges, breaks, and stitching errors; utilizing simulations toAtty. Docket No.: 4502-88500 (6000800PCT01) physically precompute near-field characteristic of DUV plasmonic interactions; obtaining physically simulated far-field images; and training the neural network model using the physically simulated far- field images and each of the expected designed PRT patterns as training inputs, and the defective distributions as training ground truth. In an embodiment, in addition to the synthetic training data, the training input and ground truth is also obtained by obtaining a library of ideal binary PRT layouts based on designed geometric parameters comprising pitch, orientation, and unit-cell motifs; obtaining a physical PRT based on the ideal binary PRT layouts; characterizing near-field defects in the physical PRT using nanometer resolution methodology; physically acquiring far-field images; training the neural network model using the far-field images and each of the ideal binary PRT layouts as training input; characterizing the near-field defects on the physical PRT as training ground truth.

[0045] The controller 126 uses the neural network model 128 to obtain an inference on pixel level defective distributions on the PRT 116 using the far-field images. In an embodiment, the controller 126 inputs the far-field images and a reference pattern into the neural network model 128. The reference pattern is an expected designed PRT pattern representing an image of an ideal pattern of a defect free PRT layout that is synthesized or computer-generated (for example, an ideal binary photomask layout). In an embodiment, the controller 126 obtains an inference from the neural network model 128 that includes whether the PRT 116 includes defective distributions. In an example, the defect detection system 100 uses any trained deep neural network models with the far- field images and expected designed PRT pattern to obtain an inference on pixel level defective distributions on a PRT 116 based on the far-field images obtained from the near-field interaction patterns.

[0046] FIG. 2 is a schematic diagram illustrating an LPSIM setup 200 of FIG. 1 in accordance with an embodiment. In an embodiment, the LPSIM setup 200 illustrates a DUV localized plasmonic structure interacting with PRT in near-field. In an embodiment, the LPSIM setup 200 comprises a plasmon generating mask 116 that is positioned at a sub-wavelength distance to the plasmon generating mask 116. In an embodiment, the sub-wavelength distance is around approximately 200 nm. In an embodiment, a polarized DUV laser light 204 from the polarizer 114 (FIG. 1) is incident on the plasmon generating mask 116 at an incident angle b2. In an example, the angle b2 is 40 degrees. The polarized DUV laser light 204 creates plasmon interference patterns 206 based on structured excitation of structures in the plasmon generating mask 116. In an embodiment, high-spatial frequency Poynting vector distributions 208 of the plasmon interferenceAtty. Docket No.: 4502-88500 (6000800PCT01) patterns 206 in a positive z-direction are incident on the PRT 118 based on the sub-wavelength spacing of the PRT 118 from the plasmon generating mask 116. The high-spatial frequency Sz vectors 208, that are applied to the PRT 118 (for example, applied to features of the nanopattern in the PRT 118) are modulated (for example, through point -wise multiplication) by the PRT 118 to produce near-field interaction patterns 210.

[0047] FIG. 3 is a schematic diagram illustrating a method 300 for identifying defects in a real- fabricated PRT 302 using a neural network in accordance with an embodiment of the disclosure. With continued reference to FIG. 1, the PRT 302 is PRT 118 in FIG. 1 that is a real-fabricated that is positioned at a sub-wavelength distance from a plasmon generating mask 116. The PRT 302 receives high-spatial frequency Poynting vector distributions in positive z-direction (for example, high-spatial frequency Sz vectors) from the plasmon generating mask 116, which interact with the features of the PRT 302 to produce near-field interaction patterns 306. In an embodiment, the near- field interaction patterns 306 travel to an image sensor (for example, image sensor 124 in FIG. 1), which captures these images as far-field images 308. The far-field images 308 have high frequency information of the surface features of the PRT 116. The far-field images 308 are inputted into a physics-aware neural network model 310. In an embodiment, the physic-aware neural network model 310 is the trained neural network model 128 in FIG. 1. In an embodiment, an expected design PRT 304 layout represents a defect-free binary photomask layout (for example, an image of an ideal PRT pattern). In an example, the trained neural network model 310 compares the far-field images 308 and defect-less ideal binary photomask layout to obtain an inference on defective distributions in the PRT 302. In an embodiment, the trained neural network model 128 is configured to infer defective distributions in the PRT 302 by comparing the defect-less ideal binary photomask layout with the far-field images.

[0048] FIG. 4 is a schematic diagram for training a physics-aware neural network 400 for defective distribution detection of photomasks in accordance with an embodiment. In an example, the trained CNN 400 algorithm (for example, a CNN model) is used with defect detection system 100 (FIG. 1) to obtain an inference of defective distributions in a real fabricated PRT. In an embodiment, other neural networks for defective distribution detection that may be used include a U-Net convolutional neural network, having a contracting path (encoder), an expanding path (decoder), and skip connections.Atty. Docket No.: 4502-88500 (6000800PCT01)

[0049] In an example, the neural network 400 algorithm is trained on a physics-aware training dataset for a defect detection neural network. The physics-aware training dataset receives a diverse library of ideal binary photomask layouts of ideal PRT that are procedurally synthesized using randomized geometric parameters, such as pitch, orientation, and unit-cell motifs. The ideal binary photomask layouts are defect-less expected designed binary photomask layouts. The training data set also includes corresponding defective distributions (for example, defective distributions for defective photomask layouts) that are created / synthesized by applying physically motivated defect operators such as, for example, stochastic edge roughness, bridges, breaks, and stitching errors to the ideal binary photomask layouts. Further, in an example, optical physics is integrated into the model by utilizing Finite-Difference Time-Domain (FDTD) simulations to precompute near-field Poynting vector (Sz) distributions characteristic of Deep Ultraviolet (DUV) plasmonic interactions. In embodiments, other simulations are also contemplated such as rigorous coupled wave analysis (RCWA), and finite element method (FEM). To synthesize the final training inputs, these defective distributions for defective binary photomask layouts are modulated by the precomputed plasmonic interference patterns (for example, precompute near-field Poynting vectors) and convolved with a numerical aperture-limited Point Spread Function (PSF) to yield simulated far-field images that refer to actual optical measurements. The simulated far-field images are physics-consistent far-field images.

[0050] In an embodiment, the neural network is subsequently supervised trained using the physics-consistent far-field images and the ideal binary photomask layouts as whole inputs, while the simulated pixel-level defective distribution is a ground truth that represents a verified output image that the neural network is being trained to predict. In an embodiment, a GPU synthesizes a binary photomask layout with a physical sampling of nm_per_pixel = 2.0 (default) and a fixed canvas of 256 pixels x256 pixels (for a 512 x 512 nm2 photomask). Expected designed patterns are drawn from a library of ID gratings (line-space, double-duty, super-lattice) and 2D Bravais lattices classified by the shape and symmetry of unit cells (for example, square, hexagonal, and oblique) with diverse unit-cell motifs (rectangle, ellipse, plus, T, herringbone, saw-tooth edge). For each sample image, in an embodiment, physically meaningful parameters are randomized such as, for example, parameters like pitch in wavelength ~ U[80, 120] nm, feature size ~ U[40, 60] nm (or equivalent thickness fractions), orientation e [0°, 180°], and optional chirp / phase — then an exact 0 / 1 mask (for example, using a float32 precision) is rendered on the target device, with coordinatesAtty. Docket No.: 4502-88500 (6000800PCT01) in nanometers. As used herein, “U” is a uniform distribution. The optical resolution of the far-field image received by the image sensor is defined by a numerical aperture (NA)-limited point spread function (PSF) from wavelength / NA that convolves the near-field illumination patters (and / or multiply by precomputed plasmonic Sz patterns before convolution) to synthesize far-field images consistent with the optical resolution limit. In an embodiment, synthesized photomasks are divided into a training set for training the CNN model 400, a validation set to tune the model’s hyperparameters and evaluate performance during training, and a test set to evaluate the final trained model on unseen data.

[0051] As shown, CNN 400 includes an input layer 410, a convolutional layer / pooling layer 420, and a neural network layer 430. In an embodiment, the pooling layer is optional. In an embodiment, a structure including the convolutional layer / pooling layer 420 and the neural network layer 430 comprises a first convolutional layer and a second convolutional layer. The input layer 410 is coupled to the convolutional layer / pooling layer 420, the convolutional layer / pooling layer 420 is coupled to the neural network layer 430, an output of the neural network layer 430 is an input to an activation layer, and the activation layer performs non-linear processing on the output of the neural network layer 430.

[0052] Convolutional layer / Pooling layer 420: As shown in FIG. 4, the convolutional layer / pooling layer 420 includes layers 421, 422, 423, 424, 425, and 426. In an implementation, the layer 421 is a convolutional layer, the layer 422 is a pooling layer, the layer 423 is a convolutional layer, the layer 424 is a pooling layer, the layer 425 is a convolutional layer, and the layer 426 is a pooling layer. In another implementation, the layers 421 and 422 are convolutional layers, the layer 423 is a pooling layer, the layers 424 and 425 are convolutional layers, and the layer 426 is a pooling layer. That is, an output of a convolutional layer is used as an input of a subsequent pooling layer, or is used as an input of another convolutional layer to continue a convolution operation.

[0053] The convolutional layer 421 is used as an example. The convolutional layer 421 includes a plurality of convolution operators. A convolution operator is also referred to as a kernel. In image processing, the convolution operator functions as a filter that extracts specific information from an input image matrix. The convolution operator comprises a weight matrix, and the weight matrix can be predefined. In a process of performing a convolution operation on a training image, the weight matrix is used to process pixels at a granularity level of one pixel (or two pixels, which depends on a value of a stride (stride)) in a horizontal direction on the input image, to extract a specific featureAtty. Docket No.: 4502-88500 (6000800PCT01) from the image. A size of the weight matrix should be related to a size of the image. It should be noted that a depth dimension (depth dimension) of the weight matrix is the same as a depth dimension of the input image. In a process of performing a convolution operation, the weight matrix extends to an entire depth of the input image. Therefore, a convolution output of a single depth dimension is generated by performing convolution with a single weight matrix. However, in most cases, a plurality of weight matrices of a same dimension rather than a single weight matrix is applied. Outputs of the weight matrices are stacked to form a depth dimension of a convolutional image. Different weight matrices are used to extract different features of the image. For example, one weight matrix is used to extract edge information of the image, another weight matrix is used to extract a specific color of the image, still another weight matrix is used to blur an unnecessary noise in the image, and so on. Because the plurality of weight matrices has the same dimension, feature maps extracted by using the plurality of weight matrices with the same dimension also have a same dimension. Then, the plurality of extracted feature maps with the same dimension are combined to form an output of the convolution operation.

[0054] Weight values in these weight matrices are obtained during training. The weight matrices are formed based on the weight values that are obtained through training, and are used to extract information from the input image after training is completed to help the CNN 400 perform correct prediction.

[0055] When the CNN 400 has a plurality of convolutional layers, a large quantity of general features is extracted at an initial convolutional layer (for example, 421). The general feature is referred to as a low-level feature. As a depth of the CNN 400 increases, a feature extracted at a later convolutional layer (for example, 426) is more complex, for example, a higher-level semantic feature. A higher semantic feature is more applicable to a to-be-resolved problem.

[0056] Convolutional / Pooling layer 420: Because a quantity of training parameters usually needs to be reduced, a pooling layer is periodically introduced after a convolutional layer, namely, the layers 421 to 426 shown in 420. One convolutional layer is followed by one pooling layer, or a plurality of convolutional layers are followed by one or more pooling layers.

[0057] Neural network layer 430: As described above, at the convolutional layer / pooling layer 420, only a feature is extracted, and parameters resulting from an input image are reduced. However, to generate final output information (for example, image segmentation information), the CNN 400 uses the neural network layer 430 to generate an output of a pixel-wise mask with every pixel withAtty. Docket No.: 4502-88500 (6000800PCT01) a defect is colored. Therefore, the neural network layer 430 includes a plurality of hidden layers (431, 432, and 43n shown in FIG. 4) and an output layer 440. Parameters included in the plurality of hidden layers are obtained during pre-training based on image training data for image segmentation.

[0058] The plurality of hidden layers in the neural network layer 430 are followed by the output layer 440, namely, the last layer of the entire CNN 400. The output layer 440 has a loss function value similar to classification cross entropy, and the loss function value is used to calculate a prediction error. This loss function measures the difference between the model's prediction and the true ground-truth label. The goal of training is to minimize this value (e.g., Cross-Entropy Loss for classification). Once forward propagation (for example, propagation from the layer 410 to the layer 440 is forward propagation) of the entire CNN 400 is completed, back propagation (for example, propagation from the layer 440 to the layer 410 in FIG. 4 is back propagation) is started to update weight values and deviations of the layers to reduce a loss of the CNN 400 and an error between a result output (for example, a pixel-wise mask) by the CNN 400 through the output layer and an ideal result. In some examples, a Stochastic Gradient Descent algorithm or Adam algorithm is used to adjust the CNN’s internal weights and biases based on the loss function's gradient. The CNN 400 is one example of a neural network suitable for implementing the disclosed methods. In an example, the convolutional neural network alternatively exists in a form of another network prediction model, for example, a model in which a plurality of convolutional layers / pooling layers are parallel, and extracted features are all input to the neural network layer 430 for processing.

[0059] In an embodiment, the CNN 400 is not limited to a single forward propagation path but further includes a lateral propagation mechanism for feature fusion. In an embodiment, the input layer 410 receives a combination of far-field images and reference pattern, wherein different far- field images and reference pattern contain distinct optical information (e.g., diverse illumination conditions, phases, or focus depths). The CNN 400 processes these images through parallel convolutional branches to extract respective feature maps. These feature maps are subsequently transmitted to a feature fusion module. The feature fusion module 427 is configured to give lateral combination of the features extracted from the different far-field images, using operations such as concatenation, element-wise addition, or weighted averaging. This fused feature representation, which integrates complementary information from the plurality of far-field images, is then input into the neural network layer 430. By jointly reasoning over the fused features, the neural network layerAtty. Docket No.: 4502-88500 (6000800PCT01)430 generates a final output indicating a defective distribution with higher accuracy than inferring from a single image source.

[0060] In another embodiment, the structure of the convolutional layer / pooling layer 426 is further optimized to be a normalization layer, such as a Batch Normalization (BN) layer or a Layer Normalization (LN) layer. The normalization layer is typically coupled between convolutional layer and an activation function, or between a convolutional layer and a pooling layer. The normalization layer is configured to normalize the output distribution of the previous layer, thereby accelerating convergence and reducing the vanishing gradient problem. Furthermore, the architecture of the CNN 400 may be constructed by stacking a plurality of processing blocks. Each processing block functions as a modular unit comprising a specific sequence, such as 421-426. The depth of the CNN 400 is adjusted by increasing or decreasing the quantity of these stacked processing blocks. This modular design allows the CNN 400 to learn features of varying complexities at different depths while maintaining training stability through normalization.

[0061] During training, the CNN 400 iteratively processes the training image data and updates its internal weights. In some embodiments, during a forward pass, a batch of training data is fed into the CNN 400. Data flows from the input layer through all the convolutional and pooling layers to produce a prediction (output). The loss function compares the prediction to the ground-truth label and computes a single loss value. The calculated loss is used to compute the gradient of the loss with respect to every weight in the CNN 400. This involves propagating the error signal backward through the CNN 400. The optimizer uses the gradients and the learning rate to adjust the weights and biases of the CNN 400. The CNN 400 iteratively repeats the forward pass, calculates the loss function, and updates the weights for every batch in the training set (one epoch). Training typically runs for many epochs until the CNN 400 improves identification of far-field defects in the synthetic photomask. The performance of CNN 400 is evaluated during training using the validation set. If the training loss function decreases but the validation loss function increases, the model is overfitting and is adjusted (e.g., more regularization, data augmentation, or a simpler model). Once trained, the CNN 400 is used to detect defects in images by comparing a reference pattern with far field images obtained from near-field interaction patterns.

[0062] FIG. 5 is a flowchart of a method 500 for implementing a defect detection technique in accordance with an embodiment of the disclosure. In an embodiment, the method 500 is implemented by defect detection system 100 (FIG. 1). In an embodiment, a controller in defectAtty. Docket No.: 4502-88500 (6000800PCT01) detection system 100 of FIG. 1 implements method 500 using instructions stored in one or more memories of the controller. In some embodiments, portions of method 500 are implemented or processed by remote servers in communication with the controller.

[0063] At block 502, the method 500 includes obtaining a trained neural network model 128. In an embodiment, the trained neural network model 128 is obtained by training a convolutional neural network algorithm on physically simulated far-field images, expected designed PRT patterns as training inputs, and defective distributions for defective PRT layouts as training ground truth. In an example, the physically simulated far-field images, expected designed PRT patterns as training inputs, and defective distributions for defective PRT layouts as training ground truth are synthesized in a graphics processing unit (GPU). The training images representing the PRT layouts may have defects (for example, defective distributions of defective PRT layouts) or may be without defects (ideal PRT layout). The physically simulated far-field images, expected designed PRT patterns as training inputs, and defective distributions for defective PRT layouts as training ground truth are input as image into the training model for training. In an embodiment, the neural network model is obtained by training a neural network algorithm as shown in FIG. 4.

[0064] At block 504, the method 500 includes transmitting a laser light along an incident path. In an embodiment, an optical energy source is a laser device that emits a deep ultraviolet (UV) laser light under excitation with a wavelength in a range from about 100 nanometer (nm) to about 300 nm along the incident path to a plasmon generating mask. In some embodiments, the laser device is selected to emit a deep UV laser light at about 193 nm or, alternatively, the laser device is selected to emit the UV laser light at about deep 248 nm. In an embodiment, the excitation wavelength of the laser light is adjusted based on the metal-dielectric interface selected for use in the plasmon generating mask. In an embodiment, the transmission angle of the laser light from the optical energy source is transmitted at different transmission angles. In an example, an light steering system steers, splits, or otherwise changes the transmission angle of the laser light that is transmitted from the energy source to a polarizer by varying the transmission angle of the laser light by at least three different angles. Further, the polarizer may be controlled by the controller to transmit a tunable polarized DUV laser light to the plasmon generating mask

[0065] At block 506, the method 500 includes obtaining plasmon interference patterns from a plasmon generating mask. In an embodiment, plasmon interference patterns are high-spatial- frequency pointing flux vectors patterns emitted by the plasmon generating mask when polarizedAtty. Docket No.: 4502-88500 (6000800PCT01)DUV laser light strikes the plasmon generating mask substrate of the plasmon generating mask. The polarized DUV laser light causes the plasmon generating mask to emit the plasmonic interference patterns when the polarized DUV laser light interacts with the surface features of the plasmon generating mask. In an embodiment, the hexagon structure of the plasmon generating mask substrate generates three plasmon interference patterns for each angle of polarization of the polarized DUV laser light, and with three different angles of transmission of the directed laser light that are received and adjusted at the polarizer 114, at least 18 plasmon interference patterns are created by the plasmon generating mask 116.

[0066] At block 508, the method 500 includes obtaining near-field interaction patterns by modulating the plasmon interference patterns. In an embodiment, Poynting vector distributions in the positive z-direction are applied to a nanopattern of a PRT, and modulated by the nanopattern of the PRT 118 to produce near-field interaction patterns without fluorescence. In an embodiment, each tuned angle of light (for example, incident angle of polarized DUV laser light) that is incident at a time period produces a near-field interaction pattern that includes high frequency information.

[0067] At block 510, the method 500 includes obtaining far-field images of the near-field interaction patterns at image sensor. In an embodiment, an objective lens receives the light from the near-field interaction patterns and directs these near-field interaction patterns to be collimated. These beams are directed to the far-field and captured by an image sensor. In an embodiment, the image sensor captures resultant digital far-field images of each near-field interaction patterns.

[0068] At block 512, the method 500 includes comparing reference patterns with the far-field images for inference of defective distributions. In an embodiment, the reference patterns include defective distributions for defective PRT layouts as training ground truth. In an embodiment, a controller 126 inputs the far-field images into a trained neural network model 128 for obtaining an inference of nanometer scale defective distributions in a PRT 118. In an embodiment, a controller uses a trained neural network model 128 to compare the far-field images with reference patterns. In an embodiment, the reference patterns are an image of expected designed PRT patterns. In an example, the neural network model 128 is trained on a physics-aware training dataset for a defect detection neural network. In an embodiment, the physics-aware training dataset receives a diverse library of ideal binary photomask layouts of ideal PRT that are procedurally synthesized using randomized geometric parameters. The ideal binary photomask layouts are defect-less ideal / reference binary photomask layouts. The training data set also includes correspondingAtty. Docket No.: 4502-88500 (6000800PCT01) defective samples (defective photomask layouts) that are created / synthesized by applying physically motivated defect operators such as, for example, stochastic edge roughness, bridges, breaks, and stitching errors to the ideal binary photomask layouts. Further, in an example, optical physics is integrated into the model by utilizing Finite-Difference Time-Domain (FDTD) simulations to precompute near-field Poynting vector distributions characteristic of Deep Ultraviolet (DUV) plasmonic interactions. In embodiments, other simulations are also contemplated such as rigorous coupled wave analysis (RCWA), and finite element method (FEM). To synthesize the final training inputs, these defective binary photomask layouts are modulated by the precomputed plasmonic interference patterns (for example, precompute near-field Poynting vectors) and convolved with a numerical aperture-limited Point Spread Function (PSF) to yield simulated far-field images that refer to actual optical measurements. The simulated far-field images are physics-consistent far-field images. In an embodiment, the neural network is subsequently supervised trained using the physicsconsistent far-field images and the ideal binary photomask layouts as whole inputs, while the simulated pixel-level defective distribution image is a ground truth that represents a verified output image that the neural network is being trained to predict. In an embodiment, synthesized photomasks are divided into a training set for training the neural network model 128, a validation set to tune the model’s hyperparameters and evaluate performance during training, and a test set to evaluate the final trained model on unseen data. The controller 126 uses the neural network model 128 to obtain an inference on pixel level defective distributions on the PRT 116 using the far-field images. In an embodiment, the controller 126 inputs the far-field images and reference patterns into the neural network model 128. Each reference pattern is an expected designed PRT pattern representing an image of an ideal pattern of a defect free PRT layout that is synthesized or computer-generated (for example, an ideal binary photomask layout). In an embodiment, the controller 126 obtains an inference from the neural network model 128 that identifies defective distributions in a real- fabricated PRT 116. In an example, the defect detection system 100 uses any trained deep neural network models with the far-field images and expected designed PRT pattern to obtain an inference on pixel level defective distributions on a PRT 116 based on the far-field images obtained from the near-field interaction patterns.

[0069] FIG. 6 is a schematic diagram of a network device 600 (e.g., a defect detection system) according to an embodiment of the disclosure. FIG. 6 is a schematic diagram of a network device 600 in defect detection system 100 according to various embodiments of the disclosure. InAtty. Docket No.: 4502-88500 (6000800PCT01) embodiments, network device 600 may be implemented as any one of network nodes such as controller 126. Network Device 600 is suitable for implementing the disclosed embodiments as described herein. The network device 600 comprises ingress ports 610 and receiver units (Rx) 620 for receiving data; a processor, logic unit, or one or more central processing units (CPU) 630 to process the data; transmitter units (Tx) 640 and egress ports 650 for transmitting the data; and one or more memories 660 for storing the data. The network device 600 may also comprise optical-to- electrical (OE) components and electrical-to-optical (EO) components coupled to the ingress ports 610, the receiver units 620, the transmitter units 640, and the egress ports 650 for egress or ingress of optical or electrical signals.

[0070] The one or more processors 630 is implemented by hardware and software. The one or more processors 630 may be implemented as one or more central processing unit (CPU) and / or graphics processing unit (GPU) chips, logic units, cores (e.g., as a multi-core processor), field- programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), and digital signal processors (DSPs). The one or more processors 630 is in communication with the ingress ports 610, receiver units 620, transmitter units 640, egress ports 650, and one or more memories 660. The one or more processors 630 comprises a defect detection module 670. The defect detection module 670 is implemented by the one or more processors 630 to execute the steps of methods 502- 512 and instructions for implementing various embodiments described herein. For instance, the defect detection module 670 implements, processes, prepares, or provides the various neural network functions, image segmentation functions, image acquisition functions, and synthesized image generation functions. The inclusion of the defect detection module 670 therefore provides a substantial improvement to the functionality of the network device 600 and effects a transformation of the network device 600 to a different state. Alternatively, the defect detection module 670 is implemented as instructions stored in the one or more memories 660 and executed by the one or more processors 630. In embodiments, the network device 600 is a non-transitory computer- readable medium configured to store a computer program product comprising computer executable instructions that, when executed by the one or more processors 630, cause the one or more processors 630 to implement the steps of method 300. For example, the defect detection module 670 is configured to forward data on a path in system 100. The inclusion of the neural network 128 (FIG. 1) also provides an improvement to the functionality of the network device 600 and other devices in system 100 by minimizing the processing overheads and processing intensive calculations in defectAtty. Docket No.: 4502-88500 (6000800PCT01) detection while ensuring that the system 100 (FIG. 1) may provide an inference on defects of fabricated PRT with a high accuracy. The defect detection module 670 also effects a transformation of plasmon interference patterns and near-field interaction patterns to a different state. Alternatively, the defect detection module 670 is implemented as instructions stored in the one or more memories 660.

[0071] The network device 600 may also include input and / or output (I / O) devices 680 for communicating data to and from a user. The VO devices 680 may include output devices such as a display for displaying video data, speakers for outputting audio data, etc. The VO devices 680 may also include input devices, such as a keyboard, mouse, trackball, etc., and / or corresponding interfaces for interacting with such output devices.

[0072] The one or more memories 660 comprises one or more disks, tape drives, and solid-state drives and may be used as an over-flow data storage device, to store programs when such programs are selected for execution, and to store instructions and data that are read during program execution. The one or more memories 660 may be volatile and / or non-volatile and may be read-only memory (ROM), random-access memory (RAM), ternary content-addressable memory (TCAM), and / or static RAM (SRAM).

[0073] The one or more processors 630 may be implemented by hardware and software. The one or more processors 630 may be implemented as one or more central processing unit (CPU) and / or graphics processing unit (GPU) chips, logic units, cores (e.g., as a multi-core processor), field- programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), and digital signal processors (DSPs). The one or more processors 630 is in communication with the ports 610, 650, Tx / Rx 620, 640, and one or more memories 660. The defect detection module 670 is implemented by the one or more processors 630 to execute the steps of methods 502-512 and the instructions for implementing various embodiments discussed herein. In embodiments, the network device 600 is a non-transitory computer-readable medium configured to store a computer program product comprising computer executable instructions that, when executed by the one or more processors 630, cause the one or more processors to implement the steps of methods 502-512. For example, the defect detection module 670 is configured to fuse a reference image with far-field images. The inclusion of the defect detection module 670 provides an improvement to the functionality of the network device 600. Alternatively, the defect detection module 670 is implemented as instructions stored in the one or more memories 660.Atty. Docket No.: 4502-88500 (6000800PCT01)

[0074] The one or more memories 660 comprises one or more of disks, tape drives, or solid- state drives and may be used as an over-flow data storage device, to store programs when such programs are selected for execution, and to store instructions and data that are read during program execution. The one or more memories 660 may be volatile and non-volatile and may be read-only memory (ROM), random- access memory (RAM), ternary content-addressable memory (TCAM), and static random-access memory (SRAM).

[0075] It is understood that by programming and / or loading executable instructions onto the network device 600, at least one of the one or more processors 630 and / or one or more memories 660 are changed, transforming the network device 600 in part into a particular machine or apparatus, e.g., a multi-core forwarding architecture, having the novel functionality taught by the disclosure. It is fundamental to the electrical engineering and software engineering arts that functionality that can be implemented by loading executable software into a computer can be converted to a hardware implementation by well-known design rules. Decisions between implementing a concept in software versus hardware typically hinge on considerations of stability of the design and numbers of units to be produced rather than any issues involved in translating from the software domain to the hardware domain. Generally, a design that is still subject to frequent change may be preferred to be implemented in software, because re-spinning a hardware implementation is more expensive than re-spinning a software design. Generally, a design that is stable that will be produced in large volume may be preferred to be implemented in hardware, for example in an ASIC, because for large production runs the hardware implementation may be less expensive than the software implementation. Often a design may be developed and tested in a software form and later transformed, by well-known design rules, to an equivalent hardware implementation in an ASIC that hardwires the instructions of the software. In the same manner as a machine controlled by a new ASIC is a particular machine or apparatus, likewise a computer that has been programmed and / or loaded with executable instructions may be viewed as a particular machine or apparatus.

[0076] FIG. 7 is a schematic diagram of embodiments of a means for defect detection 700 in a network in accordance with various embodiments of the invention. In embodiments, the means for defect detection 700 is implemented in a network apparatus 702 (e.g., controller 126). The network apparatus 702 includes receiving means 701. The receiving means 701 is configured to receive a data packet or to receive a data stream to route to a destination network element. The network apparatus 702 includes transmission means 707 coupled to the receiving means 701. TheAtty. Docket No.: 4502-88500 (6000800PCT01) transmission means 707 is configured to transmit or forward the data packet or data stream to another network element.

[0077] The network apparatus 702 includes a storage means 703. The storage means 703 is coupled to at least one of the receiving means 701 or the transmission means 707. The storage means 703 is configured to store instructions. The network apparatus 702 also includes processing means 705. The processing means 705 is coupled to the storage means 703. The processing means 705 is configured to execute the instructions stored in the storage means 703 to perform the methods disclosed herein.

[0078] While several embodiments have been provided in the present disclosure, it should be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented.

[0079] In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and could be made without departing from the spirit and scope disclosed herein.

Claims

Atty. Docket No.: 4502-88500 (6000800PCT01)CLAIMSWhat is claimed is:

1. A defect detection system, comprising: one or more memories comprising instructions; and one or more processors coupled to the one or more memories and configured to execute the instructions to cause the defect detection system to : control an energy source to transmit a deep ultraviolet (UV) laser light at a wavelength along an incident path at different time periods; direct the laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; control a polarizer to generate polarized DUV laser light at the different time periods; obtain far-field images of near-field interaction patterns with image sensor; compare reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed PRT pattern; and obtain an inference on nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference patterns.

2. The defect detection system of any of claims 1 or 2, wherein the one or more processors is further configured to execute the instructions to cause the defect detection system to: control incidence of the polarized DUV laser light onto a plasmon generating mask at the different time periods; and obtain high-spatial frequency plasmon interference patterns based on the polarized DUV laser light incident on the plasmon generating mask at the different time periods.

3. The defect detection system of claim 2, wherein the plasmon generating mask includes aluminum material.

4. The defect detection system of any of claims 2-3, wherein the one or more processors is further configured to execute the instructions to cause the defect detection system to obtain near- field interaction patterns based on interaction of the high-spatial frequency plasmon interferenceAtty. Docket No.: 4502-88500 (6000800PCT01) patterns with a patterned reflector transmitter (PRT) at the different time periods, wherein the PRT comprises submicron features for interacting with DUV wavelengths, and wherein the plasmon generating mask is at a sub-wavelength distance to the PRT.

5. The defect detection system of any of claims 1-4, wherein the one or more processors is further configured to execute the instructions to cause the defect detection system to: control a light steering system to direct the laser light from the initial angle of transmission to the first angles of transmission; control a polarizer to generate polarized DUV laser light at the different time; and control the polarizer to change the polarized angles of transmission to obtain polarized DUV laser light at polarized angles of incidence based on the first angles of transmission.

6. The defect detection system of any of claims 1-5, wherein the first angles of transmission include at least three angles, wherein the polarized angles of incidence include at least two angles, and wherein the one or more processors are further configured to execute the instructions to cause the defect detection system to obtain the high-spatial frequency plasmon interference patterns based on the first angles of transmission and the polarized angles of incidence at the different time periods.

7. The defect detection system of any of claims 1-6, wherein the one or more processors are further configured to execute the instructions to cause the defect detection system to: obtain the far-field images for each of the near-field interaction patterns at the different time periods based on interaction of the polarized DUV laser light via the first angles of transmission and the polarized angles of incidence at the different time periods; obtain a reference pattern that corresponds to the PRT; process the far-field images and the expected designed PRT through the neural network model; and infer defects in the PRT based on processing the far-field images and the expected designed PRT through the neural network model, wherein the neural network model is configured to infer defective distributions in the PRT.Atty. Docket No.: 4502-88500 (6000800PCT01)8. The defect detection system of any of claims 1 to 7, wherein the one or more processors are further configured to execute the instructions to cause the defect detection system to train the neural network model using a training dataset, wherein the training dataset is obtained by synthetic training data by: obtaining a library of ideal binary PRT layouts based on randomized geometric parameters comprising pitch, orientation, and unit-cell motifs; creating defective distributions for defective PRT layouts by applying physically motivated defect operators to the ideal binary PRT layouts, and wherein the defect operators comprise stochastic edge roughness, bridges, breaks, and stitching errors; utilizing simulations to physically precompute near-field characteristic of DUV plasmonic interactions; obtaining physically simulated far-field images; and training the neural network model using the physically simulated far-field images and each of the expected designed PRT patterns as training inputs, and the defective distributions as training ground truth.

9. The defect detection system of claim 8, wherein the one or more processors are further configured to execute the instructions to train the neural network model using the physically simulated far-field images by: using the near-field characteristic of DUV plasmonic interactions comprising physically precomputed near-field Poynting flux (Sz) distributions, wherein the simulations comprise a method selected from one or more of finite different time domain (FDTD) method, a rigorous coupled wave analysis (RCWA) method, or a finite element (FEM) method, and obtaining the physically simulated far-field images by modulating the defective distributions with the precomputed near-field Poynting vector distributions and convolving a result with a physical aperture-limited Point Spread Function (PSF) and random noise.

10. The defect detection system of any of claims 1 to 7, wherein the one or more processors are further configured to execute the instructions to cause the defect detection system to train the neural network model using a training dataset, wherein the training dataset is obtained by measurement by:Atty. Docket No.: 4502-88500 (6000800PCT01) obtaining a library of ideal binary PRT layouts based on designed geometric parameters comprising pitch, orientation, and unit-cell motifs; obtaining a physical PRT based on the ideal binary PRT layouts; characterizing near-field defects in the physical PRT using nanometer resolution methodology; physically acquiring far-field images; training the neural network model using the far-field images and each of the ideal binary PRT layouts as training input; characterizing the near-field defects on the physical PRT as training ground truth.

11. The defect detection system of claim 10, wherein the nanometer resolution methodology is based on one or more of scanning electron microscopy (SEM), atomic force microscopy (AFM), and scanning near-field microscopy (SNOM).

12. The defect detection system of any of claims 1 to 7, wherein the one or more processors are further configured to execute the instructions to cause the defect detection system to train the neural network model using a physics-aware dataset comprising training input and ground truth, wherein the training input and ground truth is obtained by a combination of the synthetic training data and the measurements.

13. The defect detection system of any of claims 1-12, wherein the wavelength of the polarized DUV laser light is 193 nanometer.

14. The defect detection system of any of claims 1-12, wherein the wavelength of the polarized DUV laser light is 248 nanometer.15 A method comprising: controlling an energy source to transmit a deep ultraviolet (UV) laser light at a wavelength along an incident path at different time periods;Atty. Docket No.: 4502-88500 (6000800PCT01) directing the DUV laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; controlling a polarizer to generate polarized DUV laser light at the different time periods; obtaining far-field images for each of the near-field interaction patterns with image sensor; comparing reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed PRT pattern; and obtaining an inference on nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference patterns.

16. The method of claim 15, further comprising: providing a plasmon generating mask made of an aluminum material; controlling incidence of the polarized DUV laser light onto the plasmon generating mask at the different time periods; and obtain high-spatial frequency plasmon interference patterns based on the polarized DUV laser light incident on the plasmon generating mask at the different time periods.

17. The method of any of claims 15-16, further comprising: positioning a patterned reflector transmitter (PRT) comprising submicron features at a subwavelength distance to the plasmon generating mask; and obtaining near-field interaction patterns based on interaction of the high-spatial frequency plasmon interference patterns with the PRT at the different time periods.

18. The method of any of claims 15-17, further comprising: controlling a light steering system to direct the DUV laser light from the initial angle of transmission to the first angles of transmission; controlling a polarizer to generate polarized DUV laser light at the different time periods; and controlling the polarizer to change the polarized angles of transmission to obtain polarized DUV laser light at polarized angles of incidence based on the first angles of transmission.Atty. Docket No.: 4502-88500 (6000800PCT01)19. The method of any of claims 15-18, further comprising: obtaining the far-field images for each of the near-field interaction patterns at the different time periods based on interaction of the polarized DUV laser light via the first angles of transmission and the polarized angles of incidence at the different time periods; obtaining a reference pattern that corresponds to the PRT; process the far-field images and the expected designed PRT through a neural network model; and inferring defects in the PRT based on processing the far-field images and the expected designed PRT through the neural network model, wherein the neural network model is configured to infer defective distributions in the PRT.

20. A non-transitory computer-readable medium storing computer-executable instructions that, when executed by one or more processors, cause a defect detection system to: control an energy source to transmit a deep ultraviolet (UV) laser light at a wavelength along an incident path at different time periods; direct the laser light from an initial angle of transmission at the different time periods to obtain first angles of transmission of the laser light along the incident path at the different time periods, wherein each of the first angles of transmission is different; control a polarizer to generate polarized DUV laser light at the different time periods; obtain far-field images of near-field interaction patterns with image sensor; compare reference patterns with the far-field images in a neural network model, wherein each of the reference patterns is an image of an expected designed PRT pattern; and obtain an inference on near nanometer scale defective distributions in the PRT based on comparing the far-field images with the reference patterns.

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