Measurement of surface roughness and profile of nanosheets

Abstract

The inspection system 100 includes a controller 124 which includes a memory 128 that stores program instructions and one or more processors 126 configured to execute program instructions. The program instructions cause one or more processors to perform the following: generate a geometric model of the structure of the sample 104; generate an optical response function model of the structure of the sample 104 to illumination 108, at least based on the geometric model; receive measurement data from the detector 116; generate a parametric substructure model based at least on the optical response function model and the measurement data; and extract one or more parameters of the structure based on the measurement data.

Description

【Technical Field】 【0001】 The present disclosure relates generally to spectroscopic measurement, and more particularly to spectroscopic measurement of nanosheets. 【Background Art】 【0002】 Advances in the semiconductor manufacturing industry are placing increasingly greater demands on yield management, particularly measurement and inspection systems. While the critical dimensions are shrinking, the wafer size is increasing. Due to economics, the industry is forced to shorten the time to achieve high yield and high value-added production. Minimizing the total time from detecting a yield problem to fixing it determines the return on investment of semiconductor manufacturers. 【0003】 Measurement can be used to perform various measurements of, for example, semiconductor wafers or reticles during semiconductor manufacturing. Measurement tools can be used to measure the structural and material properties associated with various semiconductor manufacturing processes. For example, a measurement tool can measure the material composition, or can measure the dimensional properties of structures and films such as film thickness, critical dimension (CD) of a structure, or overlay. These measurements are used to facilitate process control and / or yield efficiency during the manufacture of semiconductor dies. 【Prior Art Documents】 【Patent Documents】 【0004】 【Patent Document 1】 U.S. Patent Application Publication No. 2014 / 0019097 【Patent Document 2】 U.S. Patent Application Publication No. 2014 / 0297211 【Summary of the Invention】 【Problems to be Solved by the Invention】 【0005】 As semiconductor device pattern dimensions continue to shrink, smaller measurement targets are often required. Furthermore, the requirements for measurement accuracy and matching with actual device characteristics increase the need for device-like targets and measurements within and even on the device. Therefore, it would be advantageous to provide devices, systems, and methods that address the aforementioned shortcomings. [Means for solving the problem] 【0006】 An inspection system is described according to one or more embodiments of the present disclosure. The inspection system comprises a controller. The controller comprises memory for maintaining program instructions. The controller comprises one or more processors configured to execute program instructions. The program instructions cause one or more processors to generate a geometric model of the structure of a sample. The structure comprises a nanosheet profile having surface roughness. The geometric model approximates the surface roughness. The program instructions cause one or more processors to generate an optical response function model of the structure of the sample to illumination, at least partially based on the geometric model. The optical response function model simulates the optical response of the nanosheet profile having surface roughness to illumination. The program instructions cause one or more processors to receive measurement data from a detector. The measurement data comprises a measurement spectrum of the structure detected by the detector. The program instructions cause one or more processors to generate a parametric substructure model based at least on the optical response function model and the measurement data. The program instructions cause one or more processors to extract one or more parameters of the structure based on the measurement data. 【0007】 In some embodiments, the geometric model approximates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a roughness layer. The roughness layer is a wrapper around the homogeneous layer. 【0008】 In some embodiments, one or more parameters include the standard deviation of the surface roughness. 【0009】 In some embodiments, the homogeneous layer comprises a material. The homogeneous layer comprises one or more dispersion parameters associated with the material, the one or more dispersion parameters comprising a refractive index (n) and an extinction coefficient (k). 【0010】 In some embodiments, the roughness layer includes one or more dispersion parameters determined using the effective medium approximation. These one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). 【0011】 In some embodiments, the roughness layer is a mixture of a first material and a second material in a certain ratio, wherein the first material is different from the second material. 【0012】 In some embodiments, the ratio is a fixed ratio. 【0013】 In some embodiments, program instructions cause the ratio to float to one or more processors. 【0014】 In some embodiments, the roughness layer is isotropic, and the surface roughness is anisotropic. 【0015】 In some embodiments, the geometric model approximates surface roughness using building blocks. The height of the building blocks varies along the direction. 【0016】 In some embodiments, the height of a building block is defined by multiple segments. 【0017】 In some embodiments, each of the multiple segments includes a segment height at a critical dimension along the direction. 【0018】 In some embodiments, the segment height is defined as either a fixed segment height or a percentage segment height. 【0019】 In some embodiments, the critical dimension is defined as either a fixed critical dimension or a percentage critical dimension from an edge. 【0020】 In some embodiments, the plurality of segments are slabs and the building block includes a stepped shape. 【0021】 In some embodiments, the program instructions cause one or more processors to adjust the resolution of the height of the building block by adjusting the quantity of the plurality of segments. 【0022】 In some embodiments, the height of the building block is defined by one or more polynomial functions. 【0023】 In some embodiments, the nanosheet profile includes a first surface and a second surface. The first surface is on the opposite side of the second surface, and the first surface is defined by a first polynomial function. The second surface is defined by a second polynomial function. The height of the building block is defined by the first polynomial function and the second polynomial function. 【0024】 In some embodiments, the first polynomial function is different from the second polynomial function. 【0025】 In some embodiments, the one or more parameters include roughness amplitude and correlation length. 【0026】 In some embodiments, the one or more parameters include height profiles at a plurality of positions along a direction. 【0027】 In some embodiments, the inspection system includes a user input source. The program instructions cause one or more processors to receive user input from the user input source. The one or more processors generate a geometric model at least partially based on the user input. 【0028】 In some embodiments, the inspection system includes an optical imaging subsystem. The optical imaging subsystem includes an illumination source and a detector. The illumination source generates illumination. The detector is communicatively coupled to a controller. 【0029】 In some embodiments, the optical imaging subsystem includes at least one of a spectroscopic ellipsometer, a reflectometer, a small-angle X-ray scattermeter, a scanning electron microscope, or a transmission electron microscope. 【0030】 In some embodiments, the nanosheet profile includes at least one of a diamond cross-section, an elliptical cross-section, a triangular cross-section, a rectangular cross-section, or a trapezoidal cross-section. 【0031】 In some embodiments, the structure is a gate-all-around (GAA) transistor. 【0032】 In some embodiments, the nanosheet profile includes a thickness of 5 nanometers or less. 【0033】 In some embodiments, program instructions cause one or more processors to generate an optical response function model using exact coupled-wave analysis (RCWA). 【0034】 In some embodiments, the parametric substructure model is a neural network model trained using an optical response function model and measurement data. 【0035】 A method is described according to one or more embodiments of the present disclosure. The method includes generating a geometric model of the structure of a sample. The structure includes a nanosheet profile having surface roughness. The geometric model approximates the surface roughness. The method includes generating an optical response function model of the structure of the sample to illumination, at least partially based on the geometric model. The optical response function model simulates the optical response of the nanosheet profile having surface roughness to illumination. The method includes receiving measurement data from a detector. The measurement data includes a measurement spectrum of the structure detected by the detector. The method includes generating a parametric substructure model based at least on the optical response function model and the measurement data. The method includes extracting one or more parameters of the structure based on the measurement data. 【0036】 In some embodiments, the geometric model approximates surface roughness by representing the nanosheet profile as a homogeneous layer and a roughness layer. The roughness layer is a wrapper around the homogeneous layer. 【0037】 In some embodiments, the roughness layer includes one or more dispersion parameters determined using the effective medium approximation. These one or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). 【0038】 In some embodiments, the roughness layer is a mixture of a first material and a second material in a certain ratio, wherein the first material is different from the second material. 【0039】 In some embodiments, the roughness layer is isotropic. The surface roughness is anisotropic. 【0040】 In some embodiments, the geometric model approximates surface roughness using building blocks. The height of the building blocks varies along the direction. 【0041】 In some embodiments, the height of a building block is defined by multiple segments, each of which includes a segment height with a critical dimension along its direction. 【0042】 In some embodiments, the segment height is defined as either a fixed segment height or a percentage segment height. The critical dimension is defined as either a fixed critical dimension or a percentage critical dimension from the edge. 【0043】 In some embodiments, the height of a building block is defined by one or more polynomial functions. 【0044】 In some embodiments, the nanosheet profile includes a first surface and a second surface. The first surface is opposite the second surface. The first surface is defined by a first polynomial function. The second surface is defined by a second polynomial function. The height of the building block is defined by the first and second polynomial functions. 【0045】 In some embodiments, one or more parameters include at least one of the standard deviation of surface roughness, roughness amplitude and correlation length, and height profile. 【0046】 It will be understood that both the above general description and the following detailed description are illustrative and descriptive only and do not necessarily limit the invention as described in the claims. The accompanying drawings incorporated herein and forming part thereof illustrate embodiments of the invention and, together with the general description, are helpful in illustrating the principles of the invention. 【0047】 Many of the advantages of this disclosure can be better understood by those skilled in the art by referring to the accompanying drawings. [Brief explanation of the drawing] 【0048】 [Figure 1A] A block diagram of an inspection system according to one or more embodiments of this disclosure is shown. [Figure 1B] A simplified schematic diagram of an inspection system suitable for optical measurement according to one or more embodiments of the present disclosure is shown. [Figure 1C] A simplified schematic diagram of an inspection system suitable for optical measurement according to one or more embodiments of the present disclosure is shown. [Figure 2A] A diagram shows the structure of a sample containing one or more nanosheets according to one or more embodiments of the present disclosure. [Figure 2B] One or more embodiments of this disclosure show nanosheets having surface roughness. [Figure 3] The following are block diagrams of model building and analysis engines according to one or more embodiments of the present disclosure. [Figure 4A] The diagrams show effective medium approximation (EMA) model profiles according to one or more embodiments of the present disclosure. [Figure 4B] The following shows plots of the variance parameters of the EMA model profile according to one or more embodiments of this disclosure. [Figure 4C] The following shows plots of the variance parameters of the EMA model profile according to one or more embodiments of this disclosure. [Figure 5A] One or more embodiments of the present disclosure show a building block including segments. [Figure 5B] One or more embodiments of this disclosure show building blocks including surfaces defined by polynomial functions. [Figure 6] A flowchart of a method according to one or more embodiments of this disclosure is shown. [Modes for carrying out the invention] 【0049】 Hereinafter, we refer in detail to the subject matter disclosed as shown in the accompanying drawings. This disclosure is shown and described in particular with respect to certain embodiments and their particular features. The embodiments described herein are to be construed as illustrative and not limiting. Those skilled in the art will readily understand that various changes and modifications in form and detail can be made without departing from the spirit and scope of this disclosure. 【0050】 Because the target structures for next-generation thin FinFETs or gate-all-around FETs are more sophisticated in terms of both composite materials and geometry (size, shape, material interfaces, etc.), current approaches cannot accommodate all the measurement steps necessary to ensure high measurement quality and, consequently, high yield. 【0051】 Nanostructures may contain surface roughness. Surface roughness can introduce anisotropy into nanostructures. In gate-all-around (GAA) semiconductor manufacturing processes, nanosheet surface roughness is a critical concern for the final device performance. As nanosheet thicknesses are reduced to less than 5 nm and gate lengths approach 10 nm, atomic-specific scale variations due to surface roughness must be monitored, controlled, and minimized due to their significant impact on performance variations from one nanosheet to another. 【0052】 Nanoscale surface topography methods for surface roughness include transmission electron microscopy (TEM) and atomic force microscopy (AFM). However, TEM and AFM have many drawbacks. TEM is a destructive technique. TEM is unsuitable for inline measurements. TEM requires the preparation of a surface preservation cross section and the deposition of thin-film materials, such as coatings, on the surface. Sample preparation from GAA wafers is very time-consuming. TEM requires image analysis to extract roughness parameters. TEM does not guarantee preservation of the original surface. In other words, the measurement itself modifies the target parameters. TEM can produce potential inaccuracies and artifacts due to pre-measurement sample preparation. Similarly, AFM is destructive and can damage the sample. AFM is a contact-mode measurement. The sample may be degraded from tip contact by the AFM. The scanning speed of AFM is another limitation. AFM is considered ultra-low throughput because a typical scan requires several minutes. AFM can introduce artifacts unless a high-quality tip is used. AFM can sometimes introduce image distortion due to lateral forces. AFM may encounter difficulties with probes on steep walls, side walls, overhangs, etc. AFM is also unsuitable for arbitrary inline measurements. 【0053】 Measurement techniques such as spectroscopy or scatterometry-based measurements provide alternative methods for nanoscale surface topography. These techniques characterize the parameters of semiconductor wafers during the manufacturing process. In practice, light is directed towards periodic gratings formed on the semiconductor wafer. The spectrum of the reflected light is measured and analyzed to characterize the grating parameters. Various parameters can be determined, including critical dimension (CD), thin film thickness, optical properties and composition, overlay, and lithography focus / dose. These various parameters typically require a geometric model of the underlying structure being measured. 【0054】 Measurement techniques require significant prior knowledge of the periodic structure in question. Any type of roughness is a potential source of error or uncertainty in measurements. Roughness is a source of error for periodic structures and is a parameter of interest. The roughness of nanosheets leads to non-periodic three-dimensional nanosheet properties. As a result, solving Maxwell's equations becomes significantly more difficult by considering randomly rough surfaces. Therefore, approximation methods are preferred. 【0055】 Optical scatterometry measurement data is sensitive to both the geometric features of the measured transistor structure and the optical properties of the underlying material. The geometric features of the measured transistor structure include surface roughness. The effect of surface roughness can be decorrelated with other contributing factors such as the optical and material properties of other structures captured in the measurement. 【0056】 The method involves designing and implementing a flexible surface geometry model of a nanosheet that can measure sheet-specific roughness in GAA. This flexible surface geometry model, also known as a surface geometry building block, is an innovative and highly precise coupled-wave (RCWA) model. Combined with appropriate inference techniques and machine learning (ML) algorithms, the method demonstrates accurate and robust measurement of nanoscale surface roughness. 【0057】 A method and system for generating measurement models having a flexible surface morphology of nanosheets are presented herein. The flexible surface morphology of nanosheets enables the generation of substantially simpler, less error-prone, and more accurate measurement models. As a result, the time to useful measurement results is significantly reduced, especially when modeling nanosheet structures. The flexible surface morphology of nanosheets is useful for generating measurement models for measurement systems. A measurement system employing a measurement model is then configured to measure structural and material properties associated with the nanosheet (e.g., material composition, structure, and dimensional properties of the film). 【0058】 The surface profile of nanosheets must be monitored, controlled, and minimized due to its significant impact on performance variations from one nanosheet to another. Actual nanosheet profiles include non-uniform sheet heights. To measure sheet surface roughness in an optical critical dimension (CD) exact coupled wave (RCWA) model, the ability to control individual heights in different lateral segments within a single nanosheet building block is required. An RCWA modeling building block with a physically aided machine learning method enabling nanosheet surface roughness measurement for foundry in-line processes is described. 【0059】 Measurement solutions for determining the roughness and profile of nanosheets are described. These measurement solutions are non-destructive, relatively fast, and introduce minimal artifacts. Specially designed optical methods with appropriate algorithms and methods, such as scatterometry, can be potential candidates due to their speed advantages, enabling higher sampling rates, non-contact modes, non-destructiveness, and avoidance of wafer damage. The controller accurately extracts the surface roughness and surface profile of the nanosheet from the spectroscopic optical response. 【0060】 The measurement solution includes methods and models employing an EMA approach, algorithms, a set of RCWA flexible building blocks, and / or methods and models. The measurement solution can be designed to address different process measurement requirements, including, but is not limited to, nanosheet roughness (t standard deviation), nanosheet roughness amplitude (δ) and correlation length (Γ), and / or nanosheet continuous height profile. Any of these measurement requirements can be selected depending on the application and use case. 【0061】 The nanosheet approximation can be modeled as anisotropic or isotropic. An isotropic EMA can model interfacial roughness in ellipsometry measurements. Because this type of roughness has a preferred orientation, the EMA can be extended to a more accurate and generalized anisotropic model. The preferred orientation may be due to silicon-germanium (SiGe) wet etching. In some embodiments, the isotropic EMA includes representing the nanosheet as two layers (e.g., a roughness layer and a homogeneous layer). Alternatively, the anisotropic approximation may model interfacial roughness in ellipsometry measurements. The anisotropic approximation may be desirable due to a higher level of accuracy. In some embodiments, the anisotropic approximation includes representing the nanosheet as one or more segments. In some embodiments, the anisotropic approximation includes representing the surface of the nanosheet using a polynomial equation. 【0062】 U.S. Patent Nos. 10,458,912, titled "Model based optical measurements of semiconductor structures with anisotropic dielectric permittivity"; U.S. Patent Nos. 11,573,077, titled "Scatterometry based methods and systems for measurement of strain in semiconductor structures"; U.S. Patent Nos. 11,036,898, titled "Measurement models of nanowire semiconductor structures based on re-useable sub-structures"; U.S. Patent Nos. 11,555,689, titled "Measuring thin films on grating and bandgap on grating"; U.S. Patent Nos. 11,156,548, titled "Measurement methodology of advanced nanostructures"; U.S. Patent Nos. 10,794,839, titled "Visualization of three-dimensional semiconductor structures"; U.S. Patent Publication No. 2014 / 0297211, titled "Statistical model-based metrology"; "Differential methods and apparatus for metrology of semiconductor U.S. Patent Publication No. 2015 / 0046118, titled "targets", U.S. Patent Publication No. 2016 / 0109375, titled "Measurement Of Small Box Size Targets", "System,U.S. Patent Publication No. 2016 / 0141193, entitled “Method and computer program product for combining raw data from multiple metrology tools,” U.S. Patent Publication No. 2016 / 0282105, entitled “Model-Based Single Parameter Measurement,” U.S. Patent Publication No. 2014 / 0316730, entitled “On-device metrology,” U.S. Patent Publication No. 2015 / 0046118, entitled “Differential methods and apparatus for metrology of semiconductor targets,” U.S. Patent Nos. 11,378,451, entitled “Bandgap measurements of patterned film stacks using spectroscopic metrology,” and U.S. Patent Nos. 11,156,548, entitled “Measurement methodology of advanced nanostructures,” are all incorporated herein by reference in their entirety. 【0063】 Next, with reference to Figures 1A to 6, a system and method for optical inspection according to one or more embodiments of the present disclosure will be described in more detail. 【0064】 Figure 1A is a block diagram of an inspection system 100 according to one or more embodiments of the present disclosure. In the field of semiconductor measurement, the inspection system 100 may include an optical imaging subsystem 102. The optical imaging subsystem 102 includes an illumination subsystem 106 for illuminating a target and an acquisition subsystem 112 for capturing relevant information provided by the interaction (or lack thereof) of the illumination subsystem 106 with the target, device, or feature. The inspection system 100 also includes a controller 124 (e.g., a processing system) for analyzing the acquired information using one or more algorithms. 【0065】 The inspection system 100 may include any type of measurement system known in the art that is suitable for providing measurement signals associated with measurement targets on a sample. The optical imaging subsystem 102 may include one or more hardware configurations. For example, the optical imaging subsystem 102 may include, but is not limited to, a spectrometer, a spectro-ellipsometer with one or more illumination angles, a spectro-ellipsometer for measuring Müller matrix elements (e.g., using a rotational compensator), a single-wavelength ellipsometer, an angle-resolved ellipsometer (e.g., a beam-profile ellipsometer), a spectroreflectometer (e.g., a broadband reflectance spectrometer), a single-wavelength reflectometer, an angle-resolved reflectometer (e.g., a beam-profile reflectometer), a pupil imaging system, a spectral imaging system, or a scatterometer (e.g., a speckle analyzer). The hardware configurations may be separated into individual operating systems. Alternatively, one or more hardware configurations may be combined with the inspection system 100. For example, multiple measurement heads may be integrated into the inspection system 100. 【0066】 In one embodiment, the inspection system 100 is configured to provide a spectral signal that exhibits one or more optical properties (e.g., one or more dispersion parameters, etc.) of a measurement target at one or more wavelengths. In one embodiment, the inspection system 100 includes an image-based measurement tool that measures measurement data based on the generation of one or more images of the sample. In another embodiment, the inspection system 100 includes a scatterometry-based measurement system that measures measurement data based on the scattering of light (reflection, diffraction, diffuse scattering, etc.) from the sample. 【0067】 In one embodiment, the inspection system 100 includes one or more optical imaging subsystems 102 (e.g., optical imaging tools). In some embodiments, the inspection system 100 may include a single optical imaging subsystem 102 or multiple optical imaging subsystems 102 (e.g., Figures 1B and 1C). If the inspection system 100 is a spectroscopic imaging system, the multiple optical imaging subsystems 102 of the spectroscopic imaging system may include a broadband spectroscopic ellipsometer, a spectroscopic ellipsometer with a rotational compensator, a beam profile ellipsometer, a beam profile reflectometer, a broadband reflectance spectrometer, a deep ultraviolet reflectance spectrometer, and the like. It is further intended that the optical imaging subsystem 102 includes a number of optical elements in such a system, including certain lenses, collimators, mirrors, quarter-wave plates, polarizers, detectors, cameras, apertures, and / or light sources. 【0068】 One or more of the optical imaging subsystems 102 are configured to generate one or more images of the sample 104. For example, the optical imaging subsystem 102 may include an illumination subsystem 106 configured to illuminate the sample 104 with illumination 108 from an illumination source 110, and an acquisition subsystem 112 configured to generate an image of the sample 104 in response to light emitted from the sample in response to the illumination 108 (e.g., sample light 114) using a detector 116. 【0069】 The illumination subsystem 106 includes one or more illumination sources 110. Examples of suitable light sources include white light sources, ultraviolet (UV) lasers, arc lamps or electrodeless lamps, laser-sustained plasma (LSP) light sources, supercontinuum sources (such as broadband laser light sources), or shorter wavelength light sources such as X-ray light sources or extreme ultraviolet light sources, or any combination thereof. 【0070】 The illumination source 110 can generate illumination 108. Illumination 108 can have only one wavelength (i.e., monochromatic light), several discrete wavelengths (i.e., polychromatic light), multiple wavelengths (i.e., broadband light), and / or sweep wavelengths by continuously or hopping between wavelengths (i.e., tunable or swept light source). For example, illumination 108 can include wavelengths that vary from approximately 120 nm to 3 microns. Illumination 108 can include luminance, and in some cases can have luminance greater than approximately 1 W / (nm cm2 Sr). Illumination 108 can be polarization-decomposed, unpolarized, etc. 【0071】 Sample 104 may include a substrate formed from a semiconductor or non-semiconductor material (e.g., a wafer). For example, the semiconductor or non-semiconductor material may include, but is not limited to, single-crystal silicon, gallium arsenide, and indium phosphide. Sample 104 may further include one or more layers disposed on the substrate. For example, such layers may include, but is not limited to, resists, dielectric materials, conductive materials, and semiconductor materials. Many different types of such layers are known in the art, and the term sample, as used herein, is intended to encompass samples on which all such types of layers may be formed. One or more layers formed on the sample may be patterned or not. For example, the sample may include multiple dies, each having repeatable patterned features. The formation and processing of such material layers may ultimately result in a finished device. Many different types of devices can be formed on the sample, and the term sample, as used herein, is intended to encompass samples on which any type of device known in the art has been manufactured. 【0072】 Sample 104 may include one or more targets. Targets may also be called measurement targets. Targets are examined by the inspection system 100. Targets may include certain constant regions of interest that are inherently periodic, such as gratings within a memory die. Measurement targets may include multiple layers (e.g., films) whose thickness can be measured by the inspection system 100. Targets may include target designs that are placed (or already exist) on a semiconductor wafer for use in alignment and / or overlay registration operations. Furthermore, targets can be placed at multiple sites on the semiconductor wafer. For example, targets can be placed within scribe lines (e.g., between dies) and / or on the die itself. In certain embodiments, multiple targets are measured (simultaneously or at different times) by the same or multiple measurement tools. 【0073】 The optical imaging subsystem 102 can generate one or more images of the sample 104 using any technique known in the art. In some embodiments, the optical imaging subsystem 102 is an optical imaging subsystem 102, where the illumination source 110 is a light source configured to produce illumination 108 in the form of light, and the acquisition subsystem 112 images the sample 104 based on the light emitted from the sample 104. In some embodiments, the imaging subsystem 102 is a particle imaging subsystem 102, where the illumination source 110 is a particle source configured to produce illumination 108 in the form of particles. For example, the particle illumination 108 can be in the form of an electron beam, an ion beam (e.g., a focused ion beam), or a neutral particle beam. Furthermore, the acquisition subsystem 112 can image the sample 104 based on particles (e.g., backscattered electrons) emitted from the sample 104. In some cases, the particle inspection system 100 can also image the sample 104 based on the light emitted from the sample 104 in response to the incident particle illumination 108 (for example, based on photoluminescence). 【0074】 The optical imaging subsystem 102 can, but is not required, measure the composition of one or more layers of a multilayer stack (e.g., a planar multilayer stack, a multilayer grating, etc.) or one or more defects on or within a sample. Multiple targets can be measured simultaneously or sequentially by the same or multiple measurement tools. In certain embodiments, multiple targets are measured (simultaneously or at different times) by the same or multiple optical imaging subsystems 102. Data from such measurements can be combined. 【0075】 The optical imaging subsystem 102 can provide various types of measurements related to semiconductor manufacturing. For example, the optical imaging subsystem 102 can provide one or more measurement metrics of one or more measurement targets, such as measurement metrics. In this respect, the optical imaging subsystem 102 may also be called a measurement tool. The measurement metrics may include, but are not limited to, structural and material properties of the sample 104, band gap, critical dimensions (e.g., width of a manufactured feature at a selected height), overlays of two or more layers, sidewall angles, film thickness, or process-related parameters (e.g., focal position of the sample during a lithography step, exposure dose of illumination during a lithography step, etc.). The structural properties of the sample 104 may include, but are not limited to, structural and film dimensional properties (such as film thickness and / or critical dimensions of the structure, overlays, etc.) associated with various semiconductor manufacturing processes. Material properties may include, but are not limited to, material compositions associated with various semiconductor manufacturing processes. The measurement metrics are used to facilitate process control and / or yield efficiency in the manufacturing of semiconductor dies. It is recognized herein that semiconductor processes performed by semiconductor process tools (e.g., film deposition, lithography steps, etching steps, etc.) may drift over time. Drift may result from numerous factors, including, but not limited to, tool wear or drift in process-associated control algorithms. Furthermore, drift may affect one or more properties of a sample, which in turn may affect one or more measurement (e.g., measurement metrics proportional to the bandgap, critical dimension measurements, etc.). In this regard, measurement can provide diagnostic information associated with one or more steps in the manufacturing process. Measurement data can be utilized in the semiconductor manufacturing process for, for example, feedforward, feedback word, and / or feedside way correction to the process (e.g., lithography steps, etching steps, etc.) to provide a complete process control solution. 【0076】 In some embodiments, the inspection system 100 includes a controller 124. The optical imaging subsystem 102 is communicatively coupled to the controller 124. In this regard, the controller 124 can be configured to receive data including, but not limited to, measurement data (e.g., spectral signals, target images, pupil images, etc.) or measurement metrics (e.g., measurement metrics proportional to the bandgap of a multilayer grating, critical dimensions, film thickness, composition, overlay accuracy, tool-induced shift, sensitivity, diffraction efficiency, focus pass-through slope, sidewall angle, etc.). In some embodiments, the measurement data includes indications of the measured spectral response of a sample (e.g., measured intensity as a function of wavelength) based on one or more sampling processes from a spectrometer (e.g., the optical imaging subsystem 102). 【0077】 The controller 124 can use data from the optical imaging subsystem 102 in the semiconductor manufacturing process to perform, for example, feedforward, feedback word, and / or feedside way corrections to the process (e.g., lithography, etching), thus potentially resulting in a complete process control solution. 【0078】 The controller 124 may include one or more processors 126 configured to execute program instructions held in memory 128 (e.g., a memory medium). In this regard, one or more processors 126 of the controller 124 may execute any of the various process steps described throughout this disclosure. The controller 124 may be communicatively coupled to one or more optical inspection subsystems 102. The controller 124 may receive images from the optical inspection subsystems 102. For example, the controller 124 may receive images from a detector 116. 【0079】 One or more processors 126 of the controller 124 may include any processing elements known in the art. In this sense, one or more processors 126 may include any microprocessor-type device configured to execute algorithms and / or instructions. In one embodiment, one or more processors 126 may consist of a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other computer system (e.g., a networked computer) configured to execute a program configured to operate the inspection system 100 as described throughout this disclosure. It is further recognized that the term “processor” can be broadly defined to include any device having one or more processing elements that execute program instructions from non-temporary memory 128. 【0080】 Memory 128 can include any storage medium known in the art that is suitable for storing program instructions executable by one or more associated processors 126. For example, memory 128 can include a non-temporary memory medium. As another example, memory 128 can include, but is not limited to, read-only memory, random-access memory, magnetic or optical memory devices (e.g., disks), magnetic tape, solid-state drives, etc. It should be further noted that memory 128 can be housed in a controller housing common to one or more processors 126. In one embodiment, memory 128 can be located remotely from the physical locations of one or more processors 126 and controller 124. For example, one or more processors 126 of controller 124 can access remote memory (e.g., a server) accessible via a network (e.g., the Internet, an intranet, etc.). Thus, the above description should be interpreted as merely illustrative and not as a limitation to the invention. 【0081】 Figure 1B is a simplified schematic diagram of an optical imaging subsystem 102 according to one or more embodiments of the present disclosure. 【0082】 The illumination source 110 may include any type of illumination source known in the art that is suitable for generating optical illumination 108, and the optical illumination 108 may be in the form of one or more illumination beams. Furthermore, the illumination 108 may have any spectrum, including, but not limited to, extreme ultraviolet (EUV) wavelengths, ultraviolet (UV) wavelengths, visible wavelengths, or infrared (IR) wavelengths. In addition, the illumination source 110 may be a broadband light source, a narrowband light source, and / or a tunable light source. 【0083】 In some embodiments, the illumination source 110 includes a broadband plasma (BBP) illumination source. In this regard, the illumination 108 may include radiation emitted by the plasma. For example, the BBP illumination source 110 may include, but is not required to include, one or more pump sources (e.g., one or more lasers) configured to focus within a volume of gas and cause the gas to absorb energy in order to generate or maintain a plasma suitable for emitting radiation. Furthermore, at least a portion of the plasma radiation can be utilized as illumination 108. In another embodiment, the illumination source 110 may include one or more lasers. For example, the illumination source 110 may include any laser system known in the art that is capable of emitting radiation in the infrared, visible, or ultraviolet portion of the electromagnetic spectrum. 【0084】 The illumination source 110 can generate illumination 108. Illumination 108 can have any time profile. For example, illumination 108 can include continuous wave (CW) illumination, pulsed illumination, or modulated illumination. Furthermore, illumination 108 can be delivered from the illumination source 110 via free-space propagation or induced light (e.g., optical fiber, light pipe, etc.). 【0085】 The illumination subsystem 106 and / or the optical imaging subsystem 102 may include a variety of components for directing illumination 108 towards the sample 104, including but not limited to lenses 118 and mirrors. Furthermore, such components may be reflective or transmissive. Thus, the depiction of lens 118 as a transmissive component in Figure 1B is illustrative and not limiting. The illumination subsystem 106 may further include one or more optical elements 120 for modifying and / or adjusting light in the associated optical path, for example, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. In embodiments, the illumination subsystem 106 and / or the optical imaging subsystem 102 includes a beam splitter 130 oriented to simultaneously direct illumination 108 towards the sample 104 and to collect sample light 114 emitted from the sample 104. In this respect, the illumination 108 and the sample light 114 can share the same path between the beam splitter 130 and the sample 104. 【0086】 In some embodiments, the inspection system 100 includes a translation stage 122 for fixing and / or positioning the sample 104 during imaging. For example, the translation stage 122 may include any combination of linear actuators, rotary actuators, angular actuators, tip / tilt stages, etc. The translation stage 122 can position the sample 104 using any number of degrees of freedom. In this regard, the translation stage 122 can position the sample 104 within the measurement field of view of the illumination 108. 【0087】 The optical imaging subsystem 102 may include various components for collecting at least a portion of the sample light 114 emission from the sample 104 (for example, sample light in the case of the optical imaging subsystem 102), and for directing at least a portion of the sample light 114 to the detector 116 to generate an image. 【0088】 The inspection system 100 can further image the sample 104 using any technique known in the art. In some embodiments, the inspection system 100 generates an image of the sample 104 in scan mode by focusing illumination 108 onto the sample 104 as a spot or line, capturing a point or line image, and scanning the sample 104 to construct a two-dimensional image. In this configuration, scanning can be achieved by moving the sample 104 relative to the illumination 108 (e.g., using a translation stage 122), moving the illumination 108 relative to the sample 104 (e.g., using a movable mirror, etc.), or a combination thereof. Scanning may include scanning the sample 104 along a scan path to generate a swath of the scan path. In some embodiments, the inspection system 100 generates an image of the sample 104 in static mode by directing illumination 108 onto the sample 104 in a two-dimensional field of view and capturing a two-dimensional image directly with a detector 116. 【0089】 The images generated by the inspection system 100 can be any type of image known in the art, including, but not limited to, bright-field images, dark-field images, phase-contrast images, etc. In some embodiments, the image may be a raw image from the optical imaging subsystem 102. In this configuration, the inspection image may include various patterned features on the sample. Furthermore, the images may be stitched together to form a composite image of the sample 104 or a part thereof, but this is not intended to be an limitation of the disclosure. Although the images are described as including patterned features, this is not intended to be an limitation of the disclosure. It is further intended that the images may be from a sample or wafer that does not have patterned features. 【0090】 The detector 116 may include any type of sensor known in the art that is suitable for measuring the sample light 114. For example, the detector 116 may include, but is not limited to, a multi-pixel sensor, including a charge-coupled device (CCD), a complementary metal-oxide-semiconductor (CMOS) device, a line sensor, or a time-delay integral (TDI) sensor. As another example, the detector 116 may include, but is not limited to, two or more single-pixel sensors, such as a photodiode, an avalanche photodiode, a photomultiplier tube, or a single-photon detector. In some embodiments, the detector 116 may include a TDI sensor. The TDI sensor may include multiple pixel rows and readout rows. The TDI sensor may include a clocking signal that moves charge continuously from one pixel row to the next until the charge reaches the readout row, at which point a row of the image is generated. By synchronizing the charge transfer (e.g., based on the clocking signal) with the movement of the sample along the scanning direction, charge can be continuously accumulated across the entire pixel row, providing a relatively high signal-to-noise ratio compared to a line sensor. 【0091】 The optical inspection mode can correspond to any combination of parameters used to generate an image of the sample 104, including, but not limited to, the nature of the illumination directed onto the sample 104 or the light collected from the sample 104. Furthermore, imaging in different optical inspection modes can generally be performed in any number of optical imaging subsystems 102. In some embodiments, one or more optical imaging subsystems 102 can be configured to image the sample 104 in multiple optical inspection modes. 【0092】 The optical inspection modes provided by the optical imaging subsystem 102 can be controlled based on the control of any combination of components within the illumination subsystem 106 or the acquisition subsystem 112. For example, control of illumination 108 directed onto the sample 104 can be provided directly by the illumination source 110 and / or by an optical element 120, the optical element 120 being, but not limited to, a spectral filter for controlling the wavelength of illumination 108, a polarizer for controlling the polarization of illumination 108, or an apodizer (e.g., at the illumination pupil plane) for controlling the angular distribution of illumination 108 on the sample 104. As another example, control of the sample light 114 collected from the sample 104 and passed to the detector 116 can be provided by an optical element 120, which is, but not limited to, a spectral filter for controlling the wavelength of the sample light 114 passed to the detector 116, a polarizer for controlling the polarization of the sample light 114 passed to the detector 116, or an apodizer (e.g., at the collection pupil) for controlling the angular distribution of the sample light 114 passed to the detector 116. 【0093】 For example, a particular optical inspection mode may correspond to illumination 108 having a selected spectrum (such as described by bandwidth and / or center wavelength) and a selected polarization directed onto the sample at a selected angle of incidence (such as defined by an illumination aperture or apodizer). The optical inspection mode may further correspond to a specific spectrum and polarization of sample light 114 directed onto the detector 116 (both of which may be the same as or different from the illumination 108 incident on the sample 104). 【0094】 Furthermore, any of the illumination source 110 and / or optical elements 120 can be made adjustable so that the inspection system 100 can be configured to provide different optical inspection modes. For example, any of the optical elements 120 can be made directly adjustable and / or controllable by an actuator to provide different optical inspection modes. In some embodiments, the controller 124 generates drive signals for any of the illumination source 110 and / or optical elements 120 to selectively provide different optical inspection modes. 【0095】 In the embodiment, the optical imaging subsystem 102 can generate one or more images. The images may include inspection images and reference images, as further described herein. In the embodiment, the optical imaging subsystem 102 can generate one or more images using one or more optical modes. 【0096】 Defects on a sample may respond differently to imaging in different optical modes, and consequently, defect analysis or identification can be improved by considering images generated in different optical modes, as intended herein. Additional embodiments of this disclosure relate to inspection systems suitable for performing multimode optical inspection. It is intended herein that multimode inspection can provide substantially better performance (e.g., identification between defects and background signals) than single-mode inspection techniques. Furthermore, increasing the number of inspection modes can generally improve inspection performance. However, it is further recognized herein that it may be desirable to balance the number of optical inspection modes used during inspection, particularly when such multimode inspection requires multiple imaging scans and is therefore time-consuming to perform. 【0097】 In some embodiments, a single optical imaging subsystem 102 can be configured to image the sample 104 simultaneously or sequentially in multiple optical inspection modes. In some embodiments, different optical imaging subsystems 102 are used to provide at least several different optical inspection modes. 【0098】 In some embodiments, the inspection system 100 provides a series of images in different optical inspection modes. For example, the inspection system 100 can provide a series of images of the sample 104 in different optical inspection modes by continuously switching between different optical imaging subsystems 102 and / or adjusting the parameters of the optical imaging subsystems 102. 【0099】 In some embodiments, the optical imaging subsystem 102 can be configured to simultaneously provide two or more images in different optical inspection modes. For example, the optical imaging subsystem 102 may include two or more acquisition channels, each having a separate detector 116. The optical imaging subsystem 102 may then have one or more beam splitters for splitting the sample light 114 into various channels, and / or additional optical elements 120 (e.g., separate spectral filters, polarizers, etc.) for providing separate control over the properties of the sample light 114 directed to the associated detector 116 within each channel. 【0100】 Figure 1C is a simplified schematic diagram of an optical imaging subsystem 102 according to one or more embodiments of the present disclosure. 【0101】 In one embodiment, the optical imaging subsystem 102 includes an illumination source 110 for generating illumination 108. Illumination 108 may include, but is not limited to, one or more selected wavelengths of light, including ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. For example, illumination source 110 may include, but is not limited to, one or more narrowband laser sources, one or more broadband laser sources, one or more supercontinuum laser sources, one or more white light laser sources, etc. In this regard, illumination source 110 can provide illumination 108 having high coherence (e.g., high spatial coherence and / or temporal coherence). In another embodiment, illumination source 110 may include, but is not limited to, a laser-driven light source (LDLS), such as a laser-sustained plasma (LSP) light source. For example, illumination source 110 may include, but is not limited to, an LSP lamp, an LSP bulb, or an LSP chamber suitable for housing one or more elements that can emit broadband illumination when excited to a plasma state by a laser light source, etc. In another embodiment, illumination source 110 includes a lamp light source. As another example, the illumination source 110 may include, but is not limited to, arc lamps, discharge lamps, electrodeless lamps, etc. In this regard, the illumination source 110 can provide illumination 108 having low coherence (e.g., low spatial coherence and / or temporal coherence). 【0102】 In another embodiment, the illumination source 110 is configured to provide illumination having wavelengths that surround the expected band gap of a test layer of a multilayer grating structure (but not limited to, a "high-k" insulating layer having a band gap in the UV spectral region or a layer of a memory structure having a band gap in the IR spectral region). For example, the illumination source 110 may include, but is not required to include, an LDLS that provides wavelengths in the spectral range between about 120 nanometers and 3 micrometers. As another example, the illumination source 110 may provide wavelengths greater than about 150 nanometers, which are suitable for determining the band gap of an insulating layer. As yet another example, the illumination source 110 may provide wavelengths greater than about 700 nanometers, which are suitable for determining the band gap of a layer of a memory structure. 【0103】 In another embodiment, the illumination source 110 provides adjustable illumination 108. For example, the illumination source 110 may include adjustable illumination sources (e.g., one or more adjustable lasers). As another example, the illumination source 110 may include a broadband illumination source coupled to an adjustable filter. 【0104】 The illumination source 110 can further provide illumination 108 having any time profile. For example, illumination 108 may have a continuous time profile, a modulated time profile, a pulsed time profile, and so on. 【0105】 In another embodiment, the illumination source 110 directs illumination 108 to the sample 104 via the illumination path of the illumination subsystem 106 and collects radiation emitted from the sample via the collection path of the collection subsystem 112. The illumination path may include one or more beam tuning components suitable for modifying and / or adjusting illumination 108. For example, one or more beam tuning components may include, but are not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers, or one or more lenses. 【0106】 In another embodiment, the illumination subsystem 106 may utilize one or more lenses 118 to focus the illumination 108 onto the sample 104. The illumination subsystem 106 may further include one or more optical elements 120 for modifying and / or adjusting the light in the associated optical path, for example, but not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. 【0107】 In another embodiment, the collection subsystem 112 may include one or more lenses 118 for collecting radiation from the sample 104. The collection subsystem 112 may further include one or more optical elements 120 for modifying and / or adjusting the light in the associated optical path, for example, but not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. 【0108】 In another embodiment, the optical imaging subsystem 102 includes a detector 116 configured to capture radiation emitted from the sample 104 through the collection path. For example, the detector 116 can receive radiation reflected or scattered from the sample 104 (e.g., via specular reflection, diffuse reflection, etc.). As another example, the detector 116 can receive radiation generated by the sample 104 (e.g., emission associated with the absorption of illumination 108). As yet another example, the detector 116 can receive one or more diffraction orders of radiation from the sample 104 (e.g., 0th order diffraction, ±1st order diffraction, ±2nd order diffraction, etc.). 【0109】 The detector 116 may include any type of optical detector known in the art that is suitable for measuring the illumination received from the sample 104. For example, the detector 116 may include, but is not limited to, a CCD detector, a CMOS detector, a TDI detector, a photomultiplier tube (PMT), an avalanche photodiode (APD), etc. In another embodiment, the detector 116 may comprise a spectroscopic detector suitable for identifying the wavelength of radiation emitted from the sample 104. 【0110】 The acquisition subsystem 112 may further include, but is not limited to, one or more lenses, one or more filters, one or more polarizers, or one or more phase plates, any number of acquisition beam tuning elements for directing and / or modifying the illumination to be collected. In this regard, the optical imaging subsystem 102 may be configured as, but is not limited to, any type of measurement tool such as a spectroscopic ellipsometer having one or more illumination angles, a spectroscopic ellipsometer for measuring Müller matrix elements (e.g., using a rotational compensator), a single-wavelength ellipsometer, an angle-resolved ellipsometer (e.g., a beam profile ellipsometer), a spectroreflectometer, a single-wavelength reflectometer, an angle-resolved reflectometer (e.g., a beam profile reflectometer), an imaging system, a pupil imaging system, a spectral imaging system, or a scatometer. 【0111】 Furthermore, it is noted herein that the described optical imaging subsystem 102 can facilitate multi-angle illumination of the sample 104 and / or two or more illumination sources 110 coupled to one or more additional detectors. In this regard, the optical imaging subsystem 102 can perform multiple measurement operations. 【0112】 In another embodiment, one or more optical components can be mounted on a rotating arm (not shown) that pivots around the sample 104, and as a result, the incident angle of illumination 108 on the sample 104 can be controlled by the position of the rotating arm. In another embodiment, the optical imaging subsystem 102 may include multiple detectors (e.g., associated with multiple beam paths generated by one or more beam splitters) to facilitate multiple measurements (e.g., multiple measurement tools) by the optical imaging subsystem 102. 【0113】 Figure 2A is a perspective view of a structure 200 of sample 104 according to one or more embodiments of the present disclosure. Structure 200 generally refers to one or more structures, specimens, measurement targets, etc. of sample 104. In some embodiments, the structure under measurement includes two or more geometric features, each manufactured from a different material. Geometric features can define various semiconductor transistors. For example, structure 200 may include, but is not limited to, thin-film stacks, fin field-effect transistors (FinFETs), gate-all-around (GAA) transistors (e.g., GAA FETs), partially fabricated transistor structures, and future-generation DRAM and 3D flash memory structures. As shown, structure 200 is a post-nanosheet-release GAA model (unit cell). 【0114】 In embodiments, the structure 200 may include one or more nanosheets 202. The nanosheets 202 can be two-dimensional nanostructures having a thickness in the range of 1 to 100 nm. For example, the nanosheets 202 may include nanosheet profiles having a thickness of 5 nanometers or less. In the illustrated example, the structure 200 is a GAA FET, and the nanosheets 202 are silicon nanosheets that function as conductive channels in the GAA transistor, but this is not intended to be limiting. The nanosheets 202 are wrapped all around by a set of materials that form the gate of the device. The wrapper materials include materials such as silicon dioxide, hafnium oxide, titanium nitride, and tantalum nitride. The wrapper materials are deposited on the nanowire using an atomic layer deposition process to form a gate that wraps all around the nanowire channel. 【0115】 When the thickness of the nanosheet 202 in the transistor reaches less than 5 nanometers (sub-5 nm), local thickness variations on the nanometer scale become critical to the performance of sample 104. If the nanosheet thickness is non-uniform, several undesirable effects may occur, but are not limited to: performance variations from one transistor to another, performance variations from one nanosheet to another within the same transistor, threshold voltage drift in the drive current from the design expectation, and / or changes in off-state leakage. 【0116】 In some embodiments, local thickness variations in the nanosheet 202 are induced by the surface roughness of the nanosheet 202. In some embodiments, carrier mobility is thickness-sensitive. If the vertical dimension of roughness is sufficiently large compared to the average thickness of the horizontal nanosheet, carrier mobility may vary significantly throughout the channel. Carrier velocity and other dynamic parameters also vary from point to point within the cross-section of the nanosheet due to surface heterogeneity. 【0117】 Much of this disclosure is described in the context of nanosheets, but this is not intended to be a limitation of this disclosure. Embodiments of nanosheets are further intended to be equally applicable to transistors having nanowires. In this regard, nanosheets and nanowires can be used interchangeably as described herein. 【0118】 Referring specifically to Figure 2B, a diagram of nanosheet 202 is shown, including roughness with mean thickness (t), roughness amplitude (δ), and correlation length (wavelength) Γ. Surface roughness can be quantified in terms of the root mean square of the roughness amplitude δ and the correlation length (wavelength) Γ. In this example, nanosheet 202 is in a post-nanosheet release process, but this is not intended as a limitation. As illustrated, the surface roughness of nanosheet 202 is anisotropic. 【0119】 In the case of GAA transistors, the nanosheet is relatively narrow, subject to large fluctuations in subband energy. The energy of the confined carriers is a function of the nanosheet thickness t, and the associated discrete energy is given by: 【0120】 【number】 【0121】 Here, E is the energy within the nanosheet, 【number】 π is Planck's constant, n is an integer quantum number, m is the effective carrier mass, and k is the wave vector associated with each energy level (k = nπ / t). The energy within the quantum nanosheet is inversely proportional to the square of the nanosheet thickness t. 【0122】 The effective mass and mobility μ are linked by the following: 【0123】 μ = qτ / m 【0124】 Here, q is the carrier charge and τ is the carrier lifetime. 【0125】 The perturbation of the nanosheet thickness from t to t+δ is directly translated into a variation in the energy level En across the nanosheet, which manifests as a variation in the effective mass and carrier mobility μ. n Such random fluctuations in scatter electron and hole carriers, resulting in mobility that varies depending on the nanosheet thickness given by the following: 【0126】 【number】 【0127】 The formula for carrier mobility μ is valid for materials with low effective mass, such as Si (0.187 m0 for electrons). The formula establishes a direct and quantitative relationship between carrier mobility and random variations in nanosheet thickness due to interface or surface roughness. Any strong variation in roughness leads to degradation of device performance. 【0128】 The primary cause of abnormal surface roughness occurs during the post-nanosheet release process. Optimization of the GAA process from superlattice stack to nanosheet release, particularly wet etching, should be carried out in a way that keeps the nanosheet surface as flat as possible. Therefore, a non-destructive, high-throughput, and accurate measurement method is needed to monitor nanosheet roughness and subsequently mitigate it to ensure that the final device performance meets design specifications. 【0129】 The profile of nanosheet 202 may include at least one of the following cross-sections: diamond, elliptical, triangular, rectangular, or trapezoidal. The profile of nanosheet 202 may have a thickness of 5 nanometers or less. 【0130】 Referring here to Figure 3, a model building and analysis engine 300 according to one or more embodiments of the present disclosure is described. The controller 124 is configured to run the model building and analysis engine 300. The model building and analysis engine 300 is a set of program instructions stored in memory 128. The program instructions are executed by one or more processors 126 to realize model building and analysis functions. 【0131】 The model building and analysis engine 300 is configured to receive one or more inputs, including, but not limited to, user input 302 and / or measurement data 304. In some embodiments, the controller 124 is configured to receive user input 302 from a user input source 306 of the inspection system 100, such as a graphical user interface or keyboard. In some embodiments, the controller 124 is configured to receive measurement data 304 from the detector 116. The measurement data 304 may include, but not limited to, the measurement spectrum of the structure 200 of the sample 104 detected by the detector 116. The measurement data 304 may include various values ​​for a given set of measurement system parameter values ​​(e.g., angle of incidence, azimuth angle, illumination polarization, electric field orientation, etc.). 【0132】 In some embodiments, the model building and analysis engine 300 includes a structural model building module 308. The structural model building module 308 generates a structural model 310. The structural model building module 308 can generate the structural model 310 based at least partially on user input 302. In some embodiments, the structural model building module 308 is implemented in the AcuShape software product manufactured by KLA Corporation in Milpitas, California, USA. In one example, the AcuShape software includes a set of geometric features (e.g., 1D layers, 2D trapezoids, 3D posts, etc.) that are coupled and parameterized to simulate a structure under measurement. In addition, the AcuShape software includes a set of building blocks available to the user to assign material behavior to any of the modeled structural features. Thus, the user input 302 may include a selection of which material (i.e., which part of the modeled structure) will be characterized with dispersion properties. 【0133】 In some embodiments, the structural model 310 is of the structure of sample 104 (e.g., structure 200). For example, the structural model 310 can be a nanosheet and / or nanowire-based semiconductor structure. In some embodiments, the structural model 310 also includes the material properties of the target. In some embodiments, the structural model 310 includes characterization of one or more optical dispersion properties of these different materials. In general, the structural model 310 can include any optical dispersion model. Non-limiting examples of dispersion models include the Bruggemann effective medium approximation (EMA) (BEMA) model, the Cody-Lorentz model, the Tauk-Lorentz model, the harmonic oscillator model, and the point-to-point dispersion model. 【0134】 A component of semiconductor measurement in a device or on a device-like target is the modeling of the optical interaction between the incident beam and the sample using an electromagnetic solver. In some embodiments, the model building and analysis engine 300 includes an optical response function building module 312. A structural model 310 is received as input to the optical response function building module 312. The optical response function building module 312 generates an optical response function model 314 based at least partially on the structural model 310. In some embodiments, the optical response function building module 312 characterizes the optical interaction between the incident beam and the structure under measurement using an electromagnetic solver employing algorithms such as exact coupled-wave analysis (RCWA), finite element method (FEM), method of moments, surface integral method, volume integral method, finite difference, time-domain (FDTD) method, and other simulation algorithms. Any of the simulation algorithms may depend on the predetermined variance of the individual components of the measurement target. Given a geometric model 310 along with dispersion parameters (e.g., n and k) for different parts of the structure, the optical response function construction module 312 can solve some form of Maxwell's equations and / or Schrödinger's equation. Such a solution can then be used to derive a simulated signal. The RCWA method can determine the structure from the measured spectrum by solving Maxwell's equations by expanding the dielectric function of the structure as a Fourier series. The RCWA method requires the measurement of a periodic structure. Therefore, RCWA assumes that the electric field interacts with a repeating lattice. In some embodiments, the optical dispersion models described herein are implemented in the Film Thickness Measurement Library (FTML) of Offline Spectroscopic Analysis (OLSA) standalone software available from KLA, Inc., Milpitas, California, USA. 【0135】 The optical response function model 314 can be the modeled optical response of sample 104 and / or target (e.g., structure 200). The modeled optical response can include various values ​​determined for a given set of measurement system parameter values ​​(e.g., angle of incidence, azimuth angle, illumination polarization, electric field orientation, etc.). 【0136】 In some embodiments, the model building and analysis engine 300 includes a fitting analysis module 316. The optical response function model 314 and / or measurement data 304 are received as input to the fitting analysis module 316. In some examples, the fitting analysis module 316 resolves at least one sample parameter value by performing a fitting analysis on the measurement data 304 using the optical response function model 314. 【0137】 The fitting analysis module 316 analyzes the measurement data 304 using any number of different data fitting and optimization techniques. As a non-limiting example, the fitting analysis module 316 can implement library matching techniques, fast degenerate-order modeling techniques, machine learning algorithms such as regression and neural networks, dimensionality reduction algorithms such as support vector machines (SVM), principal component analysis (PCA), independent component analysis (ICA), and local linear embedding (LLE), sparse representation techniques such as Fourier or wavelet transform techniques, Kalman filtering, and algorithms that facilitate matching between the same or different tool types. Fitting spectral measurement data is advantageous for any type of optical technique that provides sensitivity to the geometric and / or material parameters of the subject. Sample parameters can be deterministic (e.g., CD, SWA, etc.) or statistical (e.g., rms height of sidewall roughness, roughness correlation length, etc.), as long as a suitable model describing the interaction between the optical beam and the sample is used. 【0138】 Regression can be used to minimize an error function (e.g., the square of the difference between the simulated signal and the measured signal) over a space of unknown parameters (e.g., geometric parameters, material parameters, other parameters). In one example, unknown parameters are repeatedly inferred until the simulated spectrum in the optical response function model 314 and the measured spectrum in the measured data 304 agree sufficiently. In a machine learning example, a model can be trained based on a simulator that can output unknown parameters from a given spectrum. Once the model is available, the measured spectrum can be fed into the model to output the resulting values ​​for the unknown parameters. 【0139】 The fitting analysis module 316 compares the optical response function model 314 with the corresponding measurement data 304 to generate a parametric substructure model 318. The parametric substructure model 318 can be a structural model of the target (e.g., a nanosheet or nanowire-based semiconductor structure under measurement). The parametric substructure model 318 can be considered reusable. The parametric substructure model 318 may include optical property values ​​of the sample 104, geometric properties of the sample 104, and / or material properties of the sample 104. 【0140】 In some embodiments, the parametric substructure model 318 is a machine learning-based model (e.g., a neural network model, a linear model, a polynomial model, a response surface model, a support vector machine model, a random forest model, or other types of models). The machine learning-based model is trained on spectral signals collected from a measurement target having a known geometric profile, for example, the geometric profile is precisely measured by a reference measurement system such as the aforementioned X-ray and electron-based measurement system. In some embodiments, the parametric substructure model 318 is determined based on measured training data (e.g., spectra collected from a Design of Experiments (DOE) wafer). The parametric substructure model 318 can then be used to compute process parameter values, structural parameter values, or both, directly from measurement data (e.g., spectra) collected from other wafers. 【0141】 Therefore, the controller 124 is configured to generate a structural model 310 (e.g., a geometric model, a material model, or a combined geometric and material model) of the measured structure of the sample 104, generate an optical response model 314 that includes at least one geometric parameter from the structural model 310, and resolve at least one parameter value by performing a fitting analysis between the optical measurement data 304 and the optical response model 314. 【0142】 In some embodiments, the inspection system 100 is configured to store a parametric substructure model 318 in memory 128. The parametric substructure model 318 can then be one of a library of pre-calculated models for determining the value of at least one parameter associated with the sample 104. 【0143】 In some embodiments, the controller 124 is configured to access model parameters in real time by employing real-time critical dimension measurement (RTCD), or it can access a library of pre-calculated models to determine the value of at least one parameter associated with the sample 104. Using some form of CD engine, the difference between the assigned CD parameter and the CD parameter associated with the measurement data 304 of the sample 104 can be evaluated. The controller 124 uses the model building and analysis engine 300 to compare the simulated optical response signal with the measurement data 304, thereby enabling the determination of the geometric and material properties of the sample 104. 【0144】 Referring here to Figure 4A, an effective medium approximation (EMA) model profile 400 according to one or more embodiments of the present disclosure is described. The EMA model profile 400 is an example of a structural model 310 provided to the optical response function construction module 312. The EMA model profile 400 is an isotropic EMA. The isotropic EMA approximates the surface roughness of the nanosheet 202 profile using two layers. The EMA model profile 400 includes a homogeneous layer 402 and a rough layer 404. The nanosheet 202 is represented by the homogeneous layer 402 and the rough layer 404. In this respect, the nanosheet 202 is represented by two parts. 【0145】 The homogeneous layer 402 includes a thickness obtained by subtracting the surface roughness from the thickness of the nanosheet 202. A dispersion parameter (e.g., the usual Si dielectric function) is assigned to the homogeneous layer 402. 【0146】 The roughness layer 404 may also be referred to as the surface layer or interface layer. The roughness layer 404 is heterogeneous and contains a mixture of materials resulting from the surface roughness. The roughness layer 404 is isotropic. The roughness layer 404 is a wrapper around the homogeneous layer 402. The roughness layer 404 contains a thickness coupled with the amplitude of roughness. The roughness layer 404 contains dispersion parameters simulated using the Effective Medium Approximation (EMA). The dispersion relation then approximates the dispersion of surface roughness. The EMA is possible when the local variation in dielectric constant associated with the surface roughness is small compared to the wavelength of light interacting with the medium. The roughness layer 404 contains an EMA determined as a function of the material of the nanosheet 202 and a second material. For example, the material of the nanosheet 202 may be silicon and the second material may be air, but this is not intended as an limitation. The dispersion parameters are simulated as a mixture of silicon and air. A mixture of silicon and air can be kept constant and / or floated. 【0147】 In some embodiments, the silicon-air mixture is constant. For example, the EMA dielectric function can be simulated as a 50% Si-50% air mixture. A 50% Si-50% air mixture can pose a risk to roughness accuracy measurements because the actual medium is not in a 50:50 ratio. These inaccuracies are not insignificant for nanosheet thicknesses on the order of 5 nm. 【0148】 In some embodiments, the EMA ratio is floated within the model and constrained by the roughness thickness standard deviation σ. The conversion coefficient between the EMA ratio and σ is determined experimentally through design of experiments, where σ is the standard deviation of nanosheet thickness measured at multiple locations along the gate. An RCWA-based model is then constructed that links the EMA to the roughness index σ. Roughness extraction reduces to a solution of Maxwell's equations using the modeled dielectric function of the structure containing the EMA. An assumption verified by the actual process is that the roughness index is periodic within the measurement spot. 【0149】 Therefore, the EMA model profile 400 can be used as the geometric model 310 to approximate the surface roughness of the nanosheet 202 profile. The optical response function model 314 of the structure 200 of sample 104 to illumination 108 is generated at least partially based on the geometric model 310 (e.g., the EMA model profile 400). The optical response function model 314 then simulates the optical response of the nanosheet 202 profile with surface roughness to illumination 108. For example, the optical response function model 314 simulates the optical response using the dispersion parameters of the homogeneous layer 402 and the rough layer 404. Because the roughness parameter is low-sensitivity, the optical response function model 314 is provided to generate a parametric substructure model 318 (e.g., a machine learning model) based at least on the optical response function model 314. Because the volume of roughness is small compared to the whole structure, it becomes difficult to detect its variation from other high-sensitivity parameters. In this respect, the conventional RCWA model is used to simulate the underlying process variability. 【0150】 Here, we describe an experiment using EMA model profile 400. Using EMA model profile 400 with varying nanosheet thicknesses of 3 sigma (3σ) from 0.3 nm to 2.6 nm, a set of 400 synthetic spectra was generated. This set of synthetic spectra was used to train a parametric substructure model 318 (e.g., a neural network model). The parametric substructure model 318 was then validated with a blind test set of 50 spectra. The parametric substructure model 318 was determined by extracting the nanosheet roughness 3σ from the blind test set to an acceptable R-squared accuracy level of 0.97. For example, EMA model profile 400 was experimentally determined using Fullmüller matrix spectroscopy to an R-squared accuracy level between 0.9718 and 0.9777. 【0151】 Referring here to Figures 4 to 4C, plots 406a to 406b of the dispersion parameters of the EMA model profile 400 according to one or more embodiments of the present disclosure are depicted. Dispersion parameters can also be referred to as optical properties over one or more illumination wavelengths. Plots 406a to 406b include the dispersion parameters of the homogeneous layer 402 and the dispersion parameters of the rough layer 404. Plots 406a to 406b are plotted over a range of illumination wavelengths. For example, plots 406a to 406b are plotted over a range of 150 to 950 nm, but this is not intended to be limiting. 【0152】 Plot 406a depicts the real component of the dispersion parameter, also known as the refractive index (n). Plot 406a includes plot lines 408a and 410a. Plot line 408a depicts the refractive index (n) of the roughness layer 404 over the illumination wavelength. Plot line 410a depicts the refractive index (n) of the homogeneous layer 402 over the illumination wavelength. 【0153】 Plot 406b depicts the imaginary component of the variance parameter, also known as the extinction coefficient (k). Plot 406b includes plot lines 408b and 410b. Plot line 408b depicts the extinction coefficient (k) of the roughness layer 404 over the illumination wavelength. Plot line 410b depicts the extinction coefficient (k) of the homogeneous layer 402 over the illumination wavelength. 【0154】 In this example, plot lines 408a and 408b are for a rough layer 404 having a mixture of 50% air and 50% silicon. Plot lines 408a and 408b can be determined using the effective medium approximation (EMA) of the rough layer 404. Plot lines 410b and 410b are for a homogeneous layer of silicon (Si). Plot lines 410b and 410b can also be referred to as the ordinary Si dielectric function or the dispersion relation of the homogeneous layer 402. 【0155】 Referring here to Figures 5A and 5B, a building block 500 according to one or more embodiments of the present disclosure is described. The building block 500 is an example of a structural model 310 provided for the optical response function construction module 312. The building block 500 is anisotropic and includes a height that varies along the direction. The building block 500 approximates the surface roughness of the nanosheet 202 profile by varying the height. 【0156】 The Building Block 500 can also be referred to as a surface-shaped building block, a flexible-shaped building block, or a nanosheet building block. The Building Block 500 supports detailed surface profile control. It can reduce time to results and provide accurate data. The Building Block 500 is an RCWA-based approach for measuring nanosheet height along channels. The Building Block 500 is intended to provide modeling flexibility for applications such as GAAs, fork-sheet transistors, and complementary field-effect transistors (CFETs). 【0157】 The building block 500 defines the nanosheet 202 using one or more parameters. The building block provides flexibility in a wide range of height shapes, which are fully defined by the parameter values. The parameters can be received as user input 302 to the structural model building module 308. In some embodiments, the building block 500 may include a profile design modeled by a segment 502 and / or a polynomial function 506. The parameters may include any parameters for defining the segment and / or the polynomial function 506. 【0158】 Referring specifically to Figure 5A, the building block 500 includes segments 502. Parameters may include the number of segments 502, the height HT(i) of each segment 502, and / or the height ratio HTRatio(i) of each segment 502. The height HT(i) and / or the height ratio HTRatio(i) can be floated to design a building block profile that approximates the nanosheet 202 profile. The number of segments 502, the height HT(i) of each segment 502, and / or the height ratio HTRatio(i) of each segment 502 can be received as user input 302. The height HT(i) may also be referred to as the segment height. The height ratio HTRatio(i) may also be referred to as the critical dimension along the direction. The segment height is defined by the critical dimension along the direction. 【0159】 Segment 502 may include shapes. It is intended that segment 502 may include diamond-shaped primitive nanowire building blocks, elliptical-shaped primitive nanowire building blocks, triangular-shaped primitive nanowire building blocks, square-shaped primitive nanowire building blocks, trapezoidal-shaped primitive nanowire building blocks, cylindrical-shaped primitive nanowire building blocks, rectangular or slab-shaped primitive nanowire building blocks, hexagonal-shaped primitive nanowire building blocks, step-shaped primitive nanowire building blocks, elongated primitive nanowire building blocks, or any combination thereof. As shown in the illustration, segment 502 is a slab and building block 500 includes step shapes, but this is not intended to be limiting. A step approximation is applied in each segment 502. 【0160】 In some embodiments, the building block 500 supports combinations of multiple types of shapes along a direction. In this regard, the segment 502 may include any combination of diamond-shaped primitive nanowire building blocks, elliptical-shaped primitive nanowire building blocks, triangular-shaped primitive nanowire building blocks, square-shaped primitive nanowire building blocks, trapezoidal-shaped primitive nanowire building blocks, cylindrical-shaped primitive nanowire building blocks, rectangular or slab-shaped primitive nanowire building blocks, hexagonal-shaped primitive nanowire building blocks, step-shaped primitive nanowire building blocks, elongated primitive nanowire building blocks, and so on. 【0161】 The junctions between shapes can be specified in terms of one or more critical dimensions. The critical dimensions may include height HT(i) and / or height ratio HTRatio(i). 【0162】 The height ratio HTRatio(i) for each segment 502 can be reported as a fixed width or a percentage width. In some embodiments, the height ratio HTRatio(i) can be defined as a percentage of the critical dimension of the nanosheet 202 from the edge along the direction, and is also referred to as the percentage critical dimension from the edge. For example, the height ratio HTRatio(3) can be defined as 50% from the edge along the x direction. In some embodiments, the height ratio HTRatio(i) can be defined as a fixed position from the edge along the direction, and is also referred to as the fixed critical dimension from the edge. For example, the height ratio HTRatio(3) can be defined as 5 nm from the edge along the x direction. 【0163】 The height HT(i) of each segment 502 can be reported as a fixed height or a percentage height. In some embodiments, the height HT(i) can be defined as a percentage of the height or thickness of the nanosheet 202 and is also referred to as the percentage segment height. For example, the height ratio HT(3) can be defined as 100% of the nanosheet thickness. In some embodiments, the height ratio HT(i) can be defined as a fixed height and is also referred to as the fixed segment height. For example, the height HT(3) can be defined as a thickness of 5 nm. 【0164】 The resolution of the building block 500 can be adjusted by adjusting the number of segments 502. For example, the resolution can be increased by increasing the number of segments 502. If computing resources are available, the number of segments, as well as the resolution, can be increased. By increasing the resolution, the building block 500 can better match the morphology of the nanosheet 202. As shown in the illustration, the building block includes a resolution of five segments 502, but this is not intended to be an limitation of this disclosure. The building block is intended to include a resolution of 20 segments, 50 segments, or more. The resolution is implemented to control surface variation / horizontal slicing within the building block. 【0165】 Referring specifically to Figure 5B, the building block 500 is defined by one or more polynomial functions 506. The building block 500 includes a surface 504. The polynomial function 506 defines the surface 504. The height of the surface can be defined as the delta height (dHT) as a function of a critical dimension (CD) along the direction. As shown in the figure, the polynomial function 506 is defined as the critical dimension (CD) in the x-direction. xIt is further intended that the polynomial function 506 can be defined for critical dimensions in the x and / or y directions. In this regard, the delta height (dHT) can be defined as a polynomial function that varies as a function of CD along x or y. It is intended that the polynomial function 506 can include any polynomial function to describe all possible surface shapes of the nanosheet 202. The polynomial function 506 for surface 504 can be received as user input 302. 【0166】 The building block 500 includes surfaces 504a and 504b. Surface 504a is on the opposite side of surface 504b. Surface 504a is defined by polynomial function 506a, and surface 504b is defined by polynomial function 506b. The height of the building block 500 is defined by polynomial function 506a and polynomial function 506b. Polynomial function 506a can be the same as and / or different from polynomial function 506b. User input 302 can include any polynomial function 506a for surface 504a, and then the same or different polynomial function 506b for surface 504b. Polynomial function 506 then defines the nanosheet surface shape along the channel. 【0167】 Generally, referring again to Figures 5A and 5B, the building block 500 is described. The building block 500 can therefore be used as the geometric model 310 to approximate the surface roughness of the nanosheet 202 profile. The optical response function model 314 of the structure 200 of the sample 104 to illumination 108 is generated at least partially based on the geometric model 310 (e.g., the building block 500). The optical response function model 314 then simulates the optical response of the nanosheet 202 profile with surface roughness to illumination 108. For example, the optical response function model 314 runs RCWA on the building block 500 to generate a synthesized spectrum with pre-layer process variability that mimics actual in-line measurement performance. The advantage of using the building block 500 is that it is no longer necessary to approximate the surface roughness with an effective medium approximation. The optical response function model 314 is provided to generate a parametric substructure model 318 (e.g., a machine learning model) based at least on the optical response function model 314. 【0168】 The parametric substructure model 318 can enable the measurement of sheet-specific roughness (e.g., roughness amplitude and correlation length) and / or height along the nanosheet. 【0169】 In some embodiments, the parameter of interest may be the surface roughness of the nanosheet 202. The surface roughness of the nanosheet 202 can be defined by the roughness amplitude (δ) and the correlation length (Γ). The roughness can be quantified through the standard deviation of the height along the nanosheet. In this regard, the building block 500 provides a method for measuring the sheet-specific roughness using the building block 500. 【0170】 Here, we describe an experiment using Building Block 500 to determine nanosheet roughness. A set of 450 synthetic spectra was generated by varying the underlying parameters. The parameters were varied to mimic actual in-line measurements. The set of synthetic spectra was used to train a parametric substructure model 318. The parametric substructure model 318 was then validated with a blind test set of 50 spectra. The height standard deviation was independently varied for each nanosheet between 0.5 and 2.6 nm. The parametric substructure model 318 was determined to extract nanosheet roughness 3σ from the blind test set to an acceptable accuracy level of R-squared 0.97. For example, a Full Müller matrix combining a suitable model such as Building Block 500 can experimentally track individual nanosheet roughness 3σ to an accuracy level of R-squared values ​​between 0.9700 and 0.9819. 【0171】 In some embodiments, the parameter of interest can be one or more heights along the nanosheet 202. The building block 500 enables the parametric substructure model 318 to report heights. User input 302 may include heights at a position from the edge of the nanosheet 202. The parametric substructure model 318 receives measurement data 304 and can report heights at a position from the edge of the nanosheet 202 based on the measurement data 304. Heights can be considered the parameter of interest. For example, the parametric substructure model 318 reports a height of 5 nm from the edge. In this regard, the building block 500 provides a method for measuring sheet-specific shape continuous profiles using the building block 500. 【0172】 Here, we describe an experiment using building blocks 500 to determine the height at five locations along the nanosheet 202. A set of 400 synthetic spectra was generated while varying the underlying parameters. The parameters were varied to mimic actual in-line measurements. The set of synthetic spectra was used to train a parametric substructure model 318. The parametric substructure model 318 was then validated with a blind test set of 50 spectra. In some embodiments, the parametric substructure model 318 can track the height of a nanosheet with a thickness of 5 nm with an accuracy of 0.5 nm. It was determined that the parametric substructure model 318 could extract the height from the blind test set to an acceptable accuracy level of R-squared of 0.90. For example, it was experimentally determined that building block 500 includes an R-squared value of 0.9083 for the height at the first position, an R-squared value of 0.9265 for the height at the second position, an R-squared value of 0.9376 for the height at the third position, an R-squared value of 0.9250 for the height at the fourth position, and an R-squared value of 0.9073 for the height at the fifth position. 【0173】 Figure 6 is a flowchart illustrating the steps performed in Method 600 according to one or more embodiments of the present disclosure. The embodiments and enabling techniques described herein in the context of the inspection system 100, the EMA model profile 400, and the building block 500 should be interpreted as extending to Method 600. However, it should be further noted that Method 600 is not limited to the inspection system 100, the EMA model profile 400, and the building block 500. 【0174】 In step 610, a geometric model of the sample structure is generated. The structure includes a nanosheet profile with surface roughness. The geometric model approximates the surface roughness of the nanosheet profile. In some embodiments, user input can be received from a user input source. The geometric model of the structure can be generated at least partially based on user input. 【0175】 In some embodiments, the geometric model approximates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a roughness layer. The roughness layer is a wrapper around the homogeneous layer. The roughness layer is isotropic, and the surface roughness is anisotropic. The homogeneous layer contains the material. The homogeneous layer contains one or more dispersion parameters associated with the material. One or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). Similarly, the roughness layer contains one or more dispersion parameters determined using the effective medium approximation. One or more dispersion parameters include the refractive index (n) and the extinction coefficient (k). The roughness layer is a mixture of a first material and a second material in a certain ratio. The first material is different from the second material. The ratio is a fixed ratio and / or a floating ratio. 【0176】 In some embodiments, the geometric model approximates the surface roughness of the nanosheet profile using building blocks. The height of the building blocks varies along the direction. 【0177】 In some embodiments, the height of a building block is defined by multiple segments. Each of the multiple segments includes a segment height at a critical dimension along the direction. The segment height can be defined as either a fixed segment height or a percentage segment height. The critical dimension is defined as either a fixed critical dimension or a percentage critical dimension from the edge. The multiple segments can be slabs, and the building block can include step shapes. The resolution of the building block height is adjusted by adjusting the number of multiple segments. 【0178】 In some embodiments, the height of the building block is defined by one or more polynomial functions. The nanosheet profile includes a first surface and a second surface. The first surface is opposite to the second surface. The first surface is defined by a first polynomial function, and the second surface is defined by a second polynomial function. The height of the building block is defined by the first polynomial function and the second polynomial function. The first polynomial function may or may not be different from the second polynomial function. 【0179】 In step 620, an optical response function model of the structure to illumination is generated, at least partially based on the geometric model. The optical response function model simulates the optical response of a nanosheet profile with surface roughness to illumination. In some embodiments, the optical response function model is generated using exact coupled wave analysis (RCWA). 【0180】 In step 630, measurement data is received from the detector. The measurement data includes the measurement spectrum of the structure detected by the detector. 【0181】 In step 640, a parametric substructure model is generated based on at least the optical response function model and the measurement data. In some embodiments, the parametric substructure model is a neural network model trained using the optical response function model and the measurement data. 【0182】 In step 650, one or more parameters of the structure are extracted based on the measurement data. One or more parameters may include the standard deviation of surface roughness, roughness amplitude, correlation length, and / or height profiles at multiple locations along the direction. 【0183】 Generally, we will again refer to Figures 1A to 6. Each step of any of the various methods can be performed by one or more controllers (e.g., controller 124) which can be configured according to any of the embodiments described herein. In addition, the method can be performed by any of the systems. The method may also include one or more additional steps which can be performed by the controllers or any system embodiments described herein. 【0184】 In some examples, measurements based on optical scatterometry involve using the measurement data to determine the dimensions of the sample by an inverse method of a predetermined measurement model. This inverse method may include, but is not limited to, model-based regression, tomography, machine learning, or any combination thereof. In this way, the target profile parameters are estimated by solving for values ​​in the parameterized measurement model that minimize the error between the measured light intensity and the modeled result. 【0185】 When used throughout this disclosure, the term “sample” generally refers to a substrate formed from a semiconductor or non-semiconductor material comprising one or more “layers” or “films,” and a patterned structure typically selected to be periodic for optical measurement. For example, semiconductor or non-semiconductor materials include, but are not limited to, single-crystal silicon, gallium arsenide, and indium phosphide. Layers formed on the substrate may include, but are not limited to, resists, dielectric materials, conductive materials, or semiconductor materials. Many different types of sample layers are known in the art, and when used herein, the term sample is intended to encompass the substrate and any type of layer formed thereon. Furthermore, for the purposes of this disclosure, the terms sample and wafer should be construed as interchangeable. In addition, for the purposes of this disclosure, the terms patterning device, mask, and reticle should be construed as interchangeable. 【0186】 All methods described herein may include storing the results of one or more steps of an embodiment of the method in memory. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results are stored, they may be accessed in memory, used by any of the embodiments of the method or system described herein, formatted for display to a user, used by another software module, method or system, etc. Furthermore, the results may be stored "permanently," "semi-permanently," "temporarily," or over a period of time. For example, the memory may be random-access memory (RAM), and the results do not necessarily have to persist indefinitely in memory. 【0187】 Each embodiment of the above-described method is further intended to include any other step of any other method described herein. In addition, each embodiment of the above-described method can be carried out by any of the systems described herein. 【0188】 Those skilled in the art will recognize that the components, actions, devices, objects, and accompanying discussions described herein are used as examples for conceptual clarity, and that various configuration variations are intended. Therefore, when used herein, the specific examples and accompanying discussions described are intended to represent their more general class. In general, the use of any particular example is intended to represent its class, and the exclusion of specific components, actions, devices, and objects should not be interpreted as limitation. 【0189】 When used herein, terms indicating direction, such as “top,” “bottom,” “up,” “down,” “upper,” “upward,” “lower,” and “downward,” are intended to indicate relative positions for illustrative purposes and not to specify an absolute reference system. Various modifications to the embodiments described herein will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments. 【0190】 With regard to the use of substantially any plural and / or singular terms herein, those skilled in the art can convert from plural to singular and / or singular to plural as appropriate to the context and / or use. Various singular / plural substitutions are not explicitly stated herein for the sake of clarity. 【0191】 The subject matter described herein sometimes refers to different components that are included in or connected to other components. It should be understood that the architectures described herein are merely examples, and in practice, numerous other architectures can be implemented to achieve the same function. Conceptually, any arrangement of components that achieve the same function is effectively “associated” in such a way that the desired function is achieved. Thus, any two components combined herein to achieve a particular function can be recognized as “associated” with each other, independently of architecture or intermediate components, in such a way that the desired function is achieved. Similarly, any two components thus associated can also be considered “connected” or “joined” with each other to realize the desired function, and any two components that can be associated in such a way can also be considered “joinable” with each other to achieve the desired function. Specific examples of “joinable” include, but are not limited to, physically matable and / or physically interacting components, as well as / or wirelessly interactable and / or wirelessly interacting components, and / or logically interacting and / or logically interactable components. 【0192】 Furthermore, it should be understood that the present invention is defined by the appended claims. In general, it will be understood by those skilled in the art that the terms used herein and especially in the appended claims (e.g., in the text of the appended claims) are intended to be "open" terms (for example, the term "includes" should be interpreted as "includes but not limited to," the term "has" should be interpreted as "has at least," and the term "includes" should be interpreted as "includes but not limited to," etc.). It will further be understood by those skilled in the art that if a specific number of claims to be introduced is intended, such intention will be explicitly stated in that claim, and if such statement is not made, such intention does not exist. For example, for the sake of understanding, the following appended claims may include introducing the claims using the introductory phrases "at least one" and "one or more." However, even if the same claim includes an introductory phrase such as "one or more" or "at least one" and an indefinite article such as "a" or "an" (for example, "a" and / or "an" should typically be interpreted as meaning "at least one" or "one or more"), the use of such phrases should not be interpreted as meaning that the introduction of a claim description by the indefinite article "a" or "an" limits any particular claim containing such introduced description to an invention containing only one such description, and the same applies to the use of a definite article used to introduce a claim description. In addition, even if a specific number of claims to be introduced is explicitly listed, a person skilled in the art will recognize that such description should typically be interpreted as meaning at least the number listed (for example, a bare list of "two lists" without other modifiers typically means at least two lists, or two or more lists).Furthermore, in cases where a conventional expression similar to "at least one of A, B, and C, etc." is used, such configurations are generally intended in a way that a person skilled in the art would understand the conventional expression to be (for example, "a system having at least one of A, B, and C" is not limited to but includes systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or systems having both A, B, and C). In cases where a conventional expression similar to "at least one of A, B, or C, etc." is used, such configurations are generally intended in a way that a person skilled in the art would understand the conventional expression to be (for example, "a system having at least one of A, B, or C" is not limited to but includes systems having only A, only B, only C, both A and B, both A and C, and / or systems having both A, B, and C). It will be further understood by those skilled in the art that virtually any separate words and / or phrases that present two or more alternative terms should be understood, wherever they appear in the description, claims, or drawings, as construing the possibility of including one of those terms, either of those terms, or both of those terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.” 【0193】 The present disclosure and its numerous accompanying advantages are to be understood from the foregoing description, and it will be clear that various modifications can be made to the form, structure, and arrangement of the components without departing from the disclosed subject matter or sacrificing all of the substantial advantages of the disclosed subject matter. The described forms are merely illustrative, and the following claims are intended to imply and encompass such modifications. Furthermore, it will be understood that the present invention is defined by the appended claims.

Claims

[Claim 1] It is an inspection system, The controller is equipped with a controller, Memory that holds program instructions, The system comprises one or more processors configured to execute the program instructions, and the instructions are to be performed by the one or more processors. The method involves generating a geometric model of the structure of a sample, wherein the structure includes a nanosheet profile having surface roughness, and the geometric model approximates the surface roughness. Based at least partially on the geometric model, a model of the optical response function of the structure of the sample to illumination is generated, wherein the optical response function model simulates the optical response of the nanosheet profile having the surface roughness to illumination. Receiving measurement data from a detector, wherein the measurement data includes the measurement spectrum of the structure detected by the detector. At least the generation of a parametric substructure model based on the optical response function model and the measurement data, Extracting one or more parameters of the structure based on the measurement data, An inspection system characterized by performing the following. [Claim 2] An inspection system according to claim 1, wherein the geometric model approximates the surface roughness of the nanosheet profile by representing the nanosheet profile as a homogeneous layer and a roughness layer, and the roughness layer is a wrapper around the homogeneous layer. [Claim 3] An inspection system according to claim 2, characterized in that one or more parameters include the standard deviation of the surface roughness. [Claim 4] An inspection system according to claim 2, wherein the homogeneous layer comprises a material, the homogeneous layer comprises one or more dispersion parameters associated with the material, and the one or more dispersion parameters comprises a refractive index (n) and an extinction coefficient (k). [Claim 5] An inspection system according to claim 2, wherein the roughness layer includes one or more dispersion parameters determined using the effective medium approximation, and the one or more dispersion parameters include a refractive index (n) and an extinction coefficient (k). [Claim 6] An inspection system according to claim 5, wherein the roughness layer is a mixture of a first material and a second material in a certain ratio, and the first material is different from the second material. [Claim 7] An inspection system according to claim 6, characterized in that the ratio is a fixed ratio. [Claim 8] An inspection system according to claim 6, wherein the program instruction causes the ratio to float on one or more processors. [Claim 9] An inspection system according to claim 5, characterized in that the roughness layer is isotropic and the surface roughness is anisotropic. [Claim 10] An inspection system according to claim 1, wherein the geometric model approximates the surface roughness with building blocks, and the height of the building blocks varies along the direction. [Claim 11] An inspection system according to claim 10, characterized in that the height of the building block is defined by a plurality of segments. [Claim 12] An inspection system according to claim 11, wherein each of the plurality of segments includes a segment height at a critical dimension along the direction. [Claim 13] An inspection system according to claim 12, characterized in that the segment height is defined as either a fixed segment height or a percentage segment height. [Claim 14] An inspection system according to claim 12, characterized in that the critical dimension is defined as either a fixed critical dimension from the edge or a percentage critical dimension. [Claim 15] An inspection system according to claim 11, wherein the plurality of segments are slabs, and the building block includes a step shape. [Claim 16] An inspection system according to claim 11, wherein the program instruction causes one or more processors to adjust the resolution of the height of the building block by adjusting the number of the plurality of segments. [Claim 17] An inspection system according to claim 10, characterized in that the height of the building block is defined by one or more polynomial functions. [Claim 18] An inspection system according to claim 17, wherein the nanosheet profile includes a first surface and a second surface, the first surface is on the opposite side from the second surface, the first surface is defined by a first polynomial function, the second surface is defined by a second polynomial function, and the height of the building block is defined by the first polynomial function and the second polynomial function. [Claim 19] An inspection system according to claim 18, characterized in that the first polynomial function is different from the second polynomial function. [Claim 20] An inspection system according to claim 10, characterized in that one or more parameters include roughness amplitude and correlation length. [Claim 21] An inspection system according to claim 10, wherein one or more parameters include height profiles at a plurality of positions along the direction. [Claim 22] An inspection system according to claim 1, comprising a user input source, wherein a program instruction causes one or more processors to receive user input from the user input source, and the one or more processors generate the geometric model at least partially based on the user input. [Claim 23] An inspection system according to claim 1, comprising an optical imaging subsystem, wherein the optical imaging subsystem includes an illumination source and a detector, the illumination source generates the illumination, and the detector is communicably coupled to the controller. [Claim 24] An inspection system according to claim 23, wherein the optical imaging subsystem includes at least one of a spectroscopic ellipsometer, a reflectometer, a small-angle X-ray scattermeter, a scanning electron microscope, or a transmission electron microscope. [Claim 25] An inspection system according to claim 1, wherein the nanosheet profile includes at least one of a diamond cross-section, an elliptical cross-section, a triangular cross-section, a rectangular cross-section, or a trapezoidal cross-section. [Claim 26] A testing system according to claim 1, wherein the structure is a gate-all-around (GAA) transistor. [Claim 27] An inspection system according to claim 1, characterized in that the nanosheet profile includes a thickness of 5 nanometers or less. [Claim 28] An inspection system according to claim 1, characterized in that the program instruction causes one or more processors to generate the optical response function model using exact coupled-wave analysis (RCWA). [Claim 29] An inspection system according to claim 1, characterized in that the parametric substructure model is a neural network model trained using the optical response function model and the measurement data. [Claim 30] It is a method, The method involves generating a geometric model of the structure of a sample, wherein the structure includes a nanosheet profile having surface roughness, and the geometric model approximates the surface roughness. Based at least partially on the geometric model, a model of the optical response function of the structure of the sample to illumination is generated, wherein the optical response function model simulates the optical response of the nanosheet profile having the surface roughness to illumination. Receiving measurement data from a detector, wherein the measurement data includes the measurement spectrum of the structure detected by the detector. At least the generation of a parametric substructure model based on the optical response function model and the measurement data, Extracting one or more parameters of the structure based on the measurement data, A method characterized by including the following. [Claim 31] A method according to claim 30, wherein the geometric model approximates the surface roughness by representing the nanosheet profile as a homogeneous layer and a roughness layer, the roughness layer being a wrapper around the homogeneous layer. [Claim 32] A method according to claim 31, characterized in that the roughness layer includes one or more dispersion parameters determined using the effective medium approximation, the one or more dispersion parameters including a refractive index (n) and an extinction coefficient (k). [Claim 33] A method according to claim 32, characterized in that the roughness layer is a mixture of a first material and a second material in a certain ratio, wherein the first material is different from the second material. [Claim 34] A method according to claim 32, characterized in that the roughness layer is isotropic and the surface roughness is anisotropic. [Claim 35] A method according to claim 30, characterized in that the geometric model approximates the surface roughness with building blocks, and the height of the building blocks varies along the direction. [Claim 36] A method according to claim 35, characterized in that the height of the building block is defined by a plurality of segments, each of which includes a segment height at a critical dimension along the direction. [Claim 37] A method according to claim 36, characterized in that the segment height is defined as either a fixed segment height or a percentage segment height, and the critical dimension is defined as either a fixed critical dimension from the edge or a percentage critical dimension. [Claim 38] A method according to claim 35, characterized in that the height of the building block is defined by one or more polynomial functions. [Claim 39] A method according to claim 38, characterized in that the nanosheet profile includes a first surface and a second surface, the first surface is opposite to the second surface, the first surface is defined by a first polynomial function, the second surface is defined by a second polynomial function, and the height of the building block is defined by the first polynomial function and the second polynomial function. [Claim 40] A method according to claim 30, characterized in that the one or more parameters include at least one of the standard deviation of the surface roughness, the roughness amplitude and correlation length, and the height profile.

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