Method for performing metrology, method for training a machine learning model, method for providing a layer comprising a two-dimensional material, metrology apparatus

Abstract

A method for performing metrology is disclosed. In one configuration, a substrate is provided having a layer formed thereon. The layer comprises a two-dimensional material. A target portion of the layer is illuminated with a radiation beam, and a distribution of the radiation at a pupil plane is detected to obtain measurement data. The measurement data is processed to obtain metrology information for the target portion of the layer. The illumination, detection, and processing are performed for a plurality of different target portions of the layer to obtain metrology information for the plurality of target portions of the layer.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to European Patent Application Publication No. 20196358.4, filed September 16, 2020, and European Patent Application Publication No. 21191255.5, filed August 13, 2021, both of which are incorporated by reference in their entireties.

[0002] The present invention relates to performing metrology on layers comprising two-dimensional materials. [Background technology]

[0003]

[0003] There is great interest in using two-dimensional materials to form device structures, such as circuit elements, as part of the semiconductor manufacturing process. Various deposition techniques exist for creating two-dimensional materials. Such deposition techniques include chemical vapor deposition (CVD) and atomic layer deposition (ALD). For quality and / or process control during the fabrication of device structures, it is important to be able to assess the quality of the deposited two-dimensional materials and / or structures or patterns formed from the two-dimensional materials. Achieving quality assessment while maintaining an optimal balance between accuracy and speed has proven difficult. Summary of the Invention

[0004]

[0004] An object of embodiments of the present disclosure is to improve the characterization of two-dimensional materials.

[0005]

[0005] According to one aspect of the present invention, there is provided a method for performing metrology, the method comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; illuminating target portions of the layer with a radiation beam and detecting a distribution of radiation redirected by the target portions of the layer at a pupil plane to obtain measurement data; and processing the measurement data to obtain metrology information for the target portions of the layer, wherein the illumination, detection and processing are performed for a plurality of different target portions of the layer to obtain metrology information for a plurality of target portions of the layer.

[0006]

[0006] Thus, a non-destructive method is provided that allows for rapid and efficient acquisition of metrology information about two-dimensional materials over large areas. This technique can be conveniently implemented using optical equipment similar to that used to perform conventional metrology processes in the context of semiconductor lithography. Using the distribution of detected radiation in the pupil plane (rather than the image plane) has proven to be very sensitive to small signals, allowing information about defects such as grain boundaries to be extracted even in the presence of large background signals, as may be the case in connection with bright-field imaging, for example.

[0007] In one embodiment, the processing of the measurement data uses a machine learning model to derive metrology information from the distribution of detected radiation in the pupil plane. The use of machine learning allows detailed information to be obtained from the measurement data without having to perform additional measurements, such as those used to train the machine learning model, which can be relatively costly and / or time-consuming.

[0008]

[0008] According to one aspect of the present invention, there is provided a method for training a machine learning model, the method comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; obtaining a training data set for a plurality of different target portions of the layer by performing a first measurement process on the target portions of the layer; and training a machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information for a new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion.

[0009] In one embodiment, a training dataset for training a machine learning model is obtained by performing a first measurement process and a second measurement process. In one embodiment, the first measurement process includes detecting an image in a bright-field imaging mode, and the second measurement process includes detecting an image in a dark-field imaging mode. The inventors have found that dark-field imaging is particularly sensitive to defects of interest, such as grain boundaries. In dark-field imaging, an ideal tabular crystal would appear mostly dark (only edges scatter light) in the absence of grain boundaries or defects. Any type of discontinuity (e.g., surface defects, grain boundaries, surface topology) serves as a scattering site, thereby contributing to a detectable signal. Grain boundaries are of particular interest because they are predicted to degrade the performance of devices formed from two-dimensional materials. Grain boundaries represent imperfections in the crystalline structure and therefore contribute to the scattering of charge carriers. Charge carrier scattering dissipates energy and / or reduces charge carrier mobility, both of which typically negatively impact device performance. Bright-field imaging has advantages in terms of increased acquisition speed, smaller spot size, and / or additional or alternative filtering options (e.g., based on polarization). Training machine learning models using a combination of bright-field and dark-field imaging allows leveraging the benefits of both techniques.

[0010] In one embodiment, the layer including the two-dimensional material used to obtain the training data set is supported on a non-planar support surface, the surface topography of which is configured to provide a predetermined defect distribution in the layer. Alternatively or additionally, the layer including the two-dimensional material used to obtain the training data set is supported on a support surface having a non-uniform composition, the spatial variation of the composition within the support surface being configured to provide a predetermined defect distribution in the layer. This approach can ensure that the training data set effectively trains the machine learning model over a desired range of defect distributions without requiring the training set to be excessively large. Furthermore, controlling the defect distribution in this manner can avoid or reduce the need for a separate calibration measurement of the defect distribution to provide labels for the machine learning process, thereby increasing efficiency. Thus, if the machine learning model is a supervised machine learning model, the predetermined defect distribution can be directly used to provide labels for measurement data from a first measurement process in the training data set.

[0011]

[0011] According to one aspect of the present invention, there is provided a metrology apparatus configured to perform metrology on a substrate, the metrology apparatus including: a measurement system configured to illuminate target portions of a layer of two-dimensional material on the substrate and detect a distribution of radiation redirected by the target portions in a pupil plane to obtain measurement data; and a data processing system configured to control the measurement system to obtain measurement data for a plurality of different target portions and to use a machine learning model to obtain metrology information for the target portions from the distribution of each detected radiation in the pupil plane.

[0012]

[0012] According to one aspect of the present invention, there is provided a metrology apparatus configured to train a machine learning model, the metrology apparatus including: a measurement system configured to perform a first measurement process and a second measurement process on a target portion of a layer of two-dimensional material for a plurality of different target portions of the layer; and a data processing system configured to train the machine learning model using a training data set derived from the first measurement process and the second measurement process, whereby the machine learning model is able to derive metrology information for a new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion.

[0013]

[0013] According to one aspect of the present invention, there is provided a method for performing metrology, comprising providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; illuminating target portions of the layer with an incoherent radiation beam and detecting radiation redirected by the target portions of the layer to obtain measurement data; and processing the measurement data to obtain metrology information for the target portions of the layer, wherein the illumination, detection and processing are performed for a plurality of different target portions of the layer to obtain metrology information for a plurality of target portions of the layer.

[0014]

[0014] Thus, a non-destructive method is provided that allows for rapid and efficient acquisition of metrology information about two-dimensional materials over large areas. The use of incoherent radiation allows for low-cost and high-speed implementation of this technique. This approach can also be conveniently implemented using optical equipment similar to that used to perform conventional metrology processes in the context of semiconductor lithography.

[0015] In one embodiment, the measurement data includes data derived from a detected image formed in a dark-field imaging mode. The inventors have found that dark-field imaging is particularly sensitive to defects of interest, such as grain boundaries. In dark-field imaging, an ideal tabular crystal would appear mostly dark (only edges scatter light) in the absence of grain boundaries or defects. Any type of discontinuity (e.g., surface defects, grain boundaries, surface topology) acts as a scattering site, thereby contributing to the detectable signal. Grain boundaries are of particular interest because they are predicted to degrade the performance of devices formed from two-dimensional materials. Grain boundaries represent imperfections in the crystalline structure and therefore contribute to the scattering of charge carriers. Charge carrier scattering dissipates energy and / or reduces charge carrier mobility, both of which typically negatively impact device performance.

[0016] In one embodiment, the measurement data comprises data derived from the distribution of detected radiation in the pupil plane. This detection mode has been shown to be very sensitive to small signals and is able to extract information about defects such as grain boundaries even in the presence of large background signals expected in bright-field imaging.

[0017]

[0017] According to one aspect of the present invention, there is provided a method for performing metrology, the method comprising providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; performing dark-field holographic microscopy on target portions of the layer to obtain measurement data; and processing the measurement data to obtain metrology information for the target portions of the layer, wherein the dark-field holographic microscopy and processing are performed for a plurality of different target portions of the layer to obtain metrology information for a plurality of target portions of the layer.

[0018]

[0018] Thus, a method is provided that allows metrology information about two-dimensional materials to be obtained with high sensitivity and speed. The advantages of dark-field imaging discussed above are combined with the ability of holographic microscopy to discern phase information to provide high sensitivity and precision.

[0019] In some embodiments, at least a majority of the plurality of target portions are positioned within a distance from the outer radial edge of the substrate closest to the target portion, the distance being less than 20% of the average spacing between the outer radial edge and the center of gravity of the substrate. Preferentially locating the target portions near the outer radial edge of the substrate ensures that the target portions efficiently sample available information about the spatial distribution of defects, particularly when the defects of interest are grain boundaries.

[0020] In one embodiment, the target portions vary in size and / or shape as a function of position on the substrate. The variation in size and / or shape may be selected, for example, taking into account the expected defect distribution in layer 30. This may facilitate finding an optimal balance between quality and speed of the measurement process used.

[0021]

[0021] According to one aspect of the present invention, there is provided a method for training a machine learning model, the method including: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; performing a first measurement process on a target portion of the layer to obtain first measurement data, and performing a second measurement process on the target portion of the layer to obtain second measurement data, the first measurement process and the second measurement process being performed on a plurality of different target portions of the layer to obtain a training data set; and training a machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information for a new target portion of the layer comprising the two-dimensional material from the measurement data obtained by performing the first measurement process on the new target portion.

[0022]

[0022] Accordingly, there is provided a method for training a machine learning model, which allows for obtaining more information from measurement data relating to a new target portion of the layer, obtained using a first measurement process, without the need to additionally perform a second measurement process (which may be a relatively costly and / or time-consuming technique, such as electron microscopy or second harmonic imaging microscopy).

[0023] In one embodiment, a layer including a two-dimensional material used to obtain a training data set is supported on a non-planar support surface, the surface topography of the non-planar support surface being configured to provide a predetermined defect distribution in the layer. This approach can ensure that the training data set effectively trains a machine learning model over a desired range of defect distributions without the training set needing to be excessively large.

[0024]

[0024] In one embodiment, a method for providing a layer including a two-dimensional material on a substrate includes: forming a layer including the two-dimensional material on the substrate using a formation process; performing metrology on the layer including the two-dimensional material using a method for performing metrology described in any of the embodiments disclosed herein; modifying one or more process parameters of the formation process based on the obtained metrology information; and repeating the formation process to form a layer including the two-dimensional material on a new substrate. Thus, any of the methods for performing metrology of the disclosed embodiments can be used to help control a manufacturing process for producing a layer (patterned or unpatterned) including a two-dimensional material. Thus, more consistent and / or higher quality layers can be produced, which can improve the overall efficiency and / or yield of device manufacturing.

[0025]

[0025] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which: [Brief explanation of the drawings]

[0026] [Figure 1]

[0026] A lithographic apparatus is depicted. [Figure 2]

[0027] 1 shows a lithography cell or cluster. [Figure 3]

[0028] 1 shows a scatterometer used in metrology; [Figure 4]

[0029] A framework for performing metrology using an incoherent radiation beam is presented. [Figure 5]

[0030] 1 is a schematic cross-sectional side view of a substrate having a layer comprising a two-dimensional material formed thereon. [Figure 6]

[0031] We present a framework for how to perform metrology using dark-field holographic microscopy. [Figure 7]

[0032] 1 illustrates an exemplary configuration for performing dark-field holographic microscopy. [Figure 8]

[0033] We present a framework for how to train machine learning models to derive metrology information. [Figure 9]

[0034] 1 is a schematic top view of a support surface having training zones of different compositions. [Figure 10]

[0035] 1 shows a framework for a method for providing a layer comprising a two-dimensional material on a substrate. DETAILED DESCRIPTION OF THE INVENTION

[0027]

[0036] This specification discloses one or more embodiments incorporating the features of the present invention. The disclosed embodiments are merely exemplary of the invention. The scope of the invention is not limited to the disclosed embodiments. The invention is defined by the claims appended hereto.

[0028]

[0037] References to the described embodiments and to "one embodiment," "embodiment," "exemplary embodiment," etc. herein indicate that the described embodiment may include a particular feature, structure, or characteristic, but not all embodiments necessarily include the particular feature, structure, or characteristic. Moreover, such descriptions do not necessarily refer to the same embodiment. Furthermore, when a particular feature, structure, or characteristic is described in connection with one embodiment, it is understood that it is within the knowledge of one skilled in the art that such feature, structure, or characteristic also occurs in connection with other embodiments, whether or not explicitly described.

[0029]

[0038] However, before describing such embodiments in more detail, it is beneficial to present an exemplary environment in which embodiments of the present disclosure can be implemented.

[0030]

[0039] 1 schematically depicts a lithographic apparatus LA comprising: an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV or DUV radiation), a support structure (e.g. mask table) MT configured to support a patterning device (e.g. mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters, a substrate table (e.g. wafer table) WT configured to hold a substrate (e.g. resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters, and a projection system (e.g. refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning the device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0031]

[0040] An illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping or controlling radiation.

[0032]

[0041] The support structure supports (i.e. bears the weight of) the patterning device. The support structure holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, and may for example be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms "reticle" or "mask" herein may be considered as synonymous with the more general term "patterning device".

[0033]

[0042] The term "patterning device", as used herein, should be interpreted broadly as referring to any device that can be used to impart a beam with a pattern in its cross-section so as to create a pattern in a target portion of a substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate if, for example, the pattern includes phase-shifting features or so-called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0034]

[0043] A patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern to the radiation beam, which is reflected by the mirror matrix.

[0035]

[0044] The term "projection system" as used herein should be interpreted broadly to encompass various types of projection systems, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate to the exposure radiation being used or other factors, such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein can be considered as synonymous with the more general term "projection system".

[0036]

[0045] In this embodiment, the apparatus may be of a transmissive type (e.g. employing a transmissive mask) or alternatively may be of a reflective type (e.g. employing a programmable mirror array of a type as referred to above, or employing a reflective mask).

[0037]

[0046] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables, and, for example, two or more mask tables. In such a "multiple stage" machine, the additional tables may be used in parallel, or preparatory steps for one or more tables may be carried out, while one or more other tables are being used for exposure.

[0038]

[0047] The lithographic apparatus may be of a type in which at least a portion of the substrate may be covered with a liquid having a relatively high refractive index, for example water, so as to fill a space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, for example between the mask and the projection system. Immersion techniques for increasing the numerical aperture of projection systems are well known in the art. As used herein, the term "immersion" does not imply that a structure such as the substrate must be immersed in liquid, but simply that there is a liquid between the projection system and the substrate during exposure.

[0039]

[0048] Referring to Figure 1, the illuminator IL receives a radiation beam from a radiation source SO. The radiation source and the lithographic apparatus may be separate entities, for example when the radiation source is an excimer laser. In such cases, the radiation source is not considered to form part of the lithographic apparatus and the radiation beam is transmitted from the source SO to the illuminator IL by a beam delivery system BD comprising, for example, appropriate directing mirrors and / or beam expanders. In other cases, the radiation source may be part of the lithographic apparatus, for example when the radiation source is a mercury lamp. The radiation source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0040]

[0049] The illuminator IL may include an adjusting device AD ​​for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. In addition, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam so that it has a desired uniformity and intensity distribution in its cross-section.

[0041]

[0050] The radiation beam B is incident on a patterning device (e.g., mask MA), which is held on a support structure (e.g., mask table MT), and is patterned by the patterning device. Having passed the mask MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate table WT can be accurately moved, for example, to position different target portions C in the path of the radiation beam B, using a second positioner PW and a position sensor IF (e.g., an interferometer device, a linear encoder, a 2-D encoder, or a capacitive sensor). Similarly, the first positioner PM and further position sensors (not explicitly shown in FIG. 1 ) can be used to accurately position the mask MA with respect to the path of the radiation beam B, for example after mechanical retrieval from a mask library or during a scan. In general, movement of the mask table MT can be realized using a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT can be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the mask table MT may be connected to a short-stroke actuator only, or may be fixed. The mask MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, they may be located in spaces between the target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks may be located between the dies.

[0042]

[0051] The depicted apparatus could be used in at least one of the following modes: 1. In step mode, the mask table MT and substrate table WT are kept essentially stationary while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure. 2. In scan mode, the mask table MT and the substrate table WT are scanned simultaneously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the mask table MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, while the length of the scanning movement determines the height (in the scanning direction) of the target portion. 3. In another mode, the mask table MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is generally employed, with the programmable patterning device being updated as required after each movement of the substrate table WT, or between successive pulses of radiation during a scan. This mode of operation is readily adaptable to maskless lithography employing a programmable patterning device, such as a programmable mirror array of the type referred to above.

[0043]

[0052] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0044]

[0053] As shown in FIG. 2, the lithography apparatus LA forms part of a lithography cell LC, sometimes referred to as a lithocell or cluster, which also includes equipment for performing pre-exposure and post-exposure processes on a substrate. Conventionally, these include a spin coater SC for depositing a resist layer, a developer DE for developing exposed resist, a chill plate CH, and a bake plate BK. A substrate handler or robot RO picks up substrates from input / output ports I / O1 and I / O2, moves them between different process tools, and then delivers them to the loading bay LB of the lithography apparatus. These devices, often collectively referred to as the track, are under the control of a track control unit TCU, which is itself controlled by a supervisory control system SCS, which also controls the lithography apparatus via a lithography control unit LACU. Thus, different tools can be operated to maximize throughput and processing efficiency.

[0045]

[0054] To ensure correct and consistent exposure of substrates exposed by a lithography apparatus, it is desirable to inspect exposed substrates to measure properties such as overlay error between subsequent layers, line thickness, critical dimension (CD), etc. If errors are detected, adjustments can be made, for example, to the exposure of subsequent substrates, especially if inspection can be performed early and quickly enough that other substrates from the same batch have not yet been exposed. Also, substrates that have already been exposed can be stripped and reworked or possibly discarded to improve yield, thereby avoiding performing exposures on substrates that are known to be in a bad state. If only some of the target portions of a substrate are in a bad state, further exposures can be performed only on those target portions that are deemed to be in a good state.

[0046]

[0055] Inspection systems, also known as metrology systems, are used to determine substrate characteristics, particularly how the characteristics of different substrates or different layers of the same substrate vary from layer to layer. The inspection system may be integrated into a lithography system (LA) or lithocell (LC) or may be a standalone device. To enable the most rapid measurements, it is desirable for the inspection system to measure the properties of the exposed resist layer immediately after exposure. However, the latent image of the resist has very low contrast (the difference in refractive index between the radiation-exposed and unexposed resist is negligible), and not all inspection systems are sensitive enough to make useful measurements of the latent image. Therefore, measurements can be taken after a post-exposure bake step (PEB), which is typically the first step performed on an exposed substrate to increase the contrast between the exposed and unexposed portions of the resist. At this stage, the resist image can be referred to as semi-latent. Measurements can also be made of developed resist images (at which point either the exposed or unexposed portions of the resist have been removed) or after a pattern transfer step such as etching. The latter possibility limits the possibility of reworking a defective substrate, but can still provide useful information.

[0047]

[0056] FIG. 3 is a schematic diagram of an optical apparatus in the form of a scatterometer suitable for performing metrology in conjunction with the lithocell of FIG. 2. The apparatus may be used to measure critical dimensions of lithographically formed features, measure overlay between layers, etc. Product features or dedicated metrology targets are formed on a substrate W. The apparatus may be a standalone device or may be integrated into a lithography apparatus LA, for example, in either a measurement station or a lithographic cell LC. An optical axis with several branches throughout the apparatus is indicated by a dotted line O. In this apparatus, light emitted by a radiation source 11 is directed to the substrate W via optical element 15 by a beam splitter including lenses 12, 14, and an objective lens 16. These lenses are arranged in a two-stage 4F configuration. Different lens configurations can be used, provided they still provide an image of the radiation source on the substrate while allowing access to an intermediate pupil plane for spatial frequency filtering. Therefore, the angular range at which radiation impinges on the substrate can be selected by defining a spatial intensity distribution in a plane, referred to herein as the (conjugate) pupil plane, that represents the spatial spectrum at the substrate plane. In particular, this can be achieved by inserting an aperture plate 13 of appropriate form between lenses 12 and 14 in a plane that is a back-projected image of the objective lens pupil plane. For example, as shown, aperture plate 13 can take various forms, two of which are labeled 13N and 13S, that allow various illumination modes to be selected. The illumination system in this illustrated example forms an off-axis illumination mode. In the first illumination mode, aperture plate 13N provides off-axis illumination from a direction designated "north (N)" for illustrative purposes only. In the second illumination mode, aperture plate 13S is used to illuminate from a similar but opposite direction, labeled "south (S)." Other illumination modes are possible using various apertures. Any unwanted light other than the desired illumination mode will interfere with the desired measurement signal, so it is desirable to have the remainder of the pupil plane dark.

[0048]

[0057] At least the zeroth order and one of the -1st and +1st orders diffracted by the target on the substrate W are collected by the objective lens 16 and directed back through the beam splitter 15. A second beam splitter 17 splits the diffracted beam into two measurement branches. In the first measurement branch, an optical system 18 uses the zeroth and first-order diffracted beams to form a diffraction spectrum (pupil plane image) of the target on a first sensor 19 (e.g., a CCD or CMOS sensor). Because each diffracted order strikes a different part of the sensor, image processing allows the orders to be compared and contrasted. The pupil plane image captured by the sensor 19 can be used to focus the metrology device and / or normalize the intensity illuminance measurements of the first-order beam. The pupil plane image can be used for many measurement purposes, such as reconstruction.

[0049]

[0058] In the second measurement branch, the optical system 20, 22 forms an image of the target on a sensor 23 (e.g., a CCD or CMOS sensor). In the second measurement branch, an aperture stop 21 is provided in a plane conjugate with the pupil plane. The aperture stop 21 functions to block the zeroth-order diffracted beam, so that the image of the target formed on the sensor 23 is formed only from the −1 or +1 first-order beam. Therefore, the image detected by the sensor 23 is also called a “dark-field” image. It should be noted that the term “image” is used in a broad sense here. If only one of the −1 and +1 orders is present, no image of the grating lines is formed.

[0050]

[0059] The images captured by sensors 19 and 23 are output to an image processor and controller PU, the function of which depends on the particular type of measurement being made.

[0051]

[0060] Examples of scatterometers and techniques can be found in U.S. Patent Application Publication No. 2006 / 066855A1, WO 2009 / 078708, WO 2009 / 106279 and U.S. Patent Application Publication No. 2011 / 0027704A, all of which are incorporated herein by reference in their entirety.

[0052]

[0061] FIG. 4 illustrates a framework for a method of performing metrology. In step S1, a substrate W is provided having a layer 30 formed thereon, as shown in FIG. 5. The layer 30 comprises, consists essentially of, or consists of a two-dimensional material. A two-dimensional material is a material that exhibits significant anisotropic properties laterally within the plane of the material compared to a direction perpendicular to the plane of the material. The group of two-dimensional materials may also be referred to as monolayer materials and may include crystalline materials consisting of an atomic monolayer or a few overlapping atomic monolayers. In some embodiments, the two-dimensional material includes one or more of graphene, hexagonal boron nitride (hBN), and transition metal dichalcogenides (TMDs). The layer 30 may be ostensibly uniform (e.g., unpatterned) on the substrate W or on selected regions of the substrate W. Alternatively, the layer 30 may be patterned to define features relevant, for example, to the fabrication of functional devices incorporating the two-dimensional material.

[0053]

[0062] In some embodiments, the method includes step S2 of illuminating a target portion 32 of the layer 30 with an incoherent radiation beam. Step S2 further includes detecting radiation redirected (e.g., scattered) by the target portion 32 of the layer 30 to obtain measurement data. The illumination may be performed using radiation having a wavelength in the range of 10 nm to 1000 nm, for example 400 nm to 900 nm. In one embodiment, the method is performed using an optical apparatus of the type described above with reference to FIG. 3 . The illumination in this case is provided by a light source 11 and an optical system between the light source 11 and the substrate W.

[0054]

[0063] In some embodiments, the method includes a step S3 of processing the measurement data obtained in step S2 to obtain metrology information about the target portion 32 of the layer 30.

[0055]

[0064] In some embodiments, the method includes performing steps S2 and S3 for a plurality of different target portions to obtain metrology information for a plurality of target portions 32 of layer 30. The metrology information for the plurality of target portions may be used to construct (e.g., by compiling in software the information from each of the target portions 32) a map of metrology information across an area of ​​substrate W covered by the plurality of portions 32 of layer 30. The map of metrology information may also be referred to as a fingerprint.

[0056]

[0065] The method may include a final step S4 of outputting the metrology information, for example as an output data stream (eg for use as feedback to a manufacturing process) or as information displayed on a screen.

[0057]

[0066] In one embodiment, the measurement data includes data derived from a detected image formed in a dark-field imaging mode. The detected image can be obtained, for example, using sensor 23 in the optical apparatus of FIG. 3. Aperture stop 21 provides the dark-field imaging mode by preventing scattered zero-order radiation from reaching sensor 23. Image processing techniques can be used to convert the detected dark-field image into a pattern representative of defect distribution, such as a pattern indicating the location of grain boundaries or a pattern indicating spatial variations in grain boundary density on substrate W. Image processing techniques can include the use of pattern recognition algorithms. Algorithms can also be used to remove or reduce unwanted noise resulting from imperfections in the optical elements and / or the sensor.

[0058]

[0067] In one embodiment, the measurement data includes data derived from the distribution of detected radiation at the pupil plane. The distribution of detected radiation at the pupil plane can be obtained, for example, using sensor 19 in the optical device of FIG. 3. Optical system 18 is configured to form a pupil plane image of the target on sensor 19. In some embodiments, the measurement data is preprocessed before being used to obtain metrology information (e.g., input to a trained machine learning model). For example, information about a defect of interest (e.g., a grain boundary) may be concentrated (e.g., have a stronger signal) in a subset of pixels at the pupil plane. In such a case, the preprocessing may include selecting a subset of pixels at the pupil plane and obtaining the metrology information using only that subset of pixels. Alternatively or additionally, the preprocessing may include extracting an antisymmetric radiation distribution of the radiation distribution at the pupil plane. This approach may be advantageous when the presence of a defect of interest disrupts the overall symmetry and therefore the defect of interest appears more strongly in the antisymmetric radiation distribution of the radiation distribution at the pupil plane.

[0059]

[0068] Figure 6 shows an alternative framework for a method of performing metrology. The method comprises step S11 of providing a substrate W having a layer 30 formed thereon, as shown in Figure 5. The layer 30 may take any of the forms described above with reference to Figures 4 and 5.

[0060]

[0069] In some embodiments, the method includes a step S12 of performing dark-field holographic microscopy on the target portion 32 of the layer 30 to obtain measurement data. Holographic microscopy can be performed using radiation having a wavelength ranging from 10 nm to 1000 nm, e.g., 400 nm to 900 nm. Unlike the embodiments described above with reference to FIGS. 4 and 5, the method according to this embodiment requires illumination with coherent radiation, e.g., from a laser. Those skilled in the art will recognize various ways of performing dark-field holographic microscopy. FIG. 7 schematically illustrates an exemplary configuration to illustrate the general principle. A radiation source 40, e.g., a laser, provides a coherent radiation beam. The radiation beam is split by a first beam splitter 41 (e.g., a polarizing beam splitter) into a reference beam 42 and an illumination beam 43. The illumination beam 43 passes through an optical path length adjustment device 44 before being directed onto the target portion 32 of the layer 30. Scattered zero-order radiation is discarded in a beam dump 45. The scattered non-zero order radiation is recombined with the reference beam 42 at a second beam splitter 46 (e.g., a polarizing beam splitter). The resulting interference pattern caused by the interference of the scattered radiation with the reference beam 42 is detected by a sensor 47.

[0061]

[0070] In some embodiments, the method includes a step S13 of processing the measurement data obtained from the dark-field holographic microscopy of step S12 to obtain metrology information about the target portion 32 of the layer 30.

[0062]

[0071] In some embodiments, the method includes performing steps S12 and S13 for a plurality of different target portions 32 to obtain metrology information for the plurality of target portions 32 of layer 30. The metrology information for the plurality of target portions may be used to construct (e.g., by compiling in software information from each of the target portions 32) a map of metrology information across an area of ​​the substrate covered by the plurality of portions 32 of layer 30. The map of metrology information may also be referred to as a fingerprint.

[0063]

[0072] The obtained metrology information may include information about the distribution of defects in the layer 30. Embodiments of the present disclosure are particularly applicable when the defect distribution includes information about the spatial distribution of grain boundaries. Information about the spatial distribution of grain boundaries may include information about the spatial distribution of grain boundary density. Various metrics may be used to quantify the grain boundary density. For example, the metrics may be based on one or more of the total length of grain boundaries per unit area, the number of grain boundaries per unit area, and the percentage of surface area occupied by grain boundaries per unit area. Information about the rate of change of the metric as a function of position can be obtained to quantify the gradient of the grain boundary distribution (e.g., to obtain the positional rate of change of grain boundary density). Grain boundaries in two-dimensional materials can disrupt the properties of the two-dimensional material that are relevant to the functionality provided in the device being fabricated. For example, if the two-dimensional material forms part of an electrically functional element, increased resistivity caused by grain boundaries can degrade device performance. The detection modes described above with reference to Figures 4-7 (based on incoherent radiation scattering and dark-field holographic microscopy) facilitate the detection of grain boundaries with sufficient sensitivity to provide high-quality information about the spatial distribution of grain boundaries.

[0064]

[0073] In some embodiments, the obtained information about the defect distribution may include other information related to the quality of the two-dimensional material, such as one or more of variations in layer thickness, distribution of islands of additional layers (e.g., areas where a second or third layer is erroneously present on a first layer), distribution of defects in a pattern formed in the two-dimensional material (e.g., causing variations in the critical dimension (CD) and / or edge quality in the pattern), and distribution of delaminations.

[0065]

[0074] The inventors have found that the spatial density of grain boundaries and other defects often increases toward the outer edge of the substrate W. This increase in spatial density may occur, for example, due to a radial distribution of substrate temperature that occurs during a deposition process (such as chemical vapor deposition). Based on this insight, in some embodiments, the target portions 32 are arranged so that at least a majority of the target portions 32 are positioned within a distance from the outer radial edge of the substrate W that is closest to the target portions 32, where this distance is less than 20%, optionally less than 15%, and optionally less than 10% of the average spacing between the outer radial edge and the center of gravity of the substrate W. In some embodiments, the target portions 32 are all positioned closer to the outer edge of the substrate W than the center of gravity of the substrate W. In other embodiments, several target areas are positioned at or near the center of gravity of the substrate W to provide reference target areas. The substrate W can, in principle, take on a variety of shapes. If the substrate W is a circular disk, the center of gravity corresponds to the axis of the disk, and the outer radial edge corresponds to the periphery of the disk. By preferentially providing the target portions 32 toward the radially outer edge of the substrate W in the manner described above, it is ensured that the target portions 32 efficiently sample usable information regarding the spatial distribution of defects, particularly when the defects of interest are grain boundaries. For example, the target portions 32 typically contain more defects of interest than target portions 32 located closer to the center of gravity of the substrate W. Therefore, fewer and / or smaller target portions 32 may need to be measured to provide useful information regarding the defect distribution. The risk of spending a long time measuring target portions 32 that do not contain (or insufficiently contain) defects of interest may be reduced. In embodiments in which a reference target area is also located at or near the center of gravity of the substrate W, as described above, a useful comparison may be between the reference target area (which may typically contain no defects or fewer defects) and a target area closer to the radially outer edge (where more defects are expected). The reference target area may provide information regarding background signals unrelated to the presence of defects of interest, for example.

[0066]

[0075] In some embodiments, the target portions 32 may be fabricated such that their size and / or shape vary as a function of position on the substrate W. The variation in size and / or shape may be selected, for example, taking into account the expected defect distribution in the layer 30. For example, if a higher density of defects is expected at the radially outer edges of the substrate W, the target portions 32 may be arranged such that their average surface area monotonically decreases as a function of increasing distance from the center of gravity of the substrate W. In this way, the variation in the amount of grain boundaries between different target portions 32 may be reduced (e.g., by providing smaller target portions 32 in areas with a higher grain boundary density, and vice versa), which may facilitate finding an optimal balance between quality and speed of the measurement process used (e.g., based on incoherent radiation scattering or dark-field holographic microscopy).

[0067]

[0076] Various techniques can be used to process the measurement data (e.g., in step S3 of FIG. 4 or step S13 of FIG. 6). Pattern recognition algorithms can be used to automatically identify features of interest. Segmentation algorithms can be used to classify different regions of the image, for example, to distinguish between pixels that correspond to grain boundaries and pixels that do not correspond to grain boundaries.

[0068]

[0077] In embodiments in which the defects of interest include grain boundaries, processing of the measurement data may use pattern recognition or segmentation algorithms to determine one or more of the spatial distribution of grain boundary density, the spatial distribution of grain boundary density gradient.

[0069]

[0078] In some embodiments, processing the measurement data (e.g., in step S3 of FIG. 4 or step S13 of FIG. 6) includes using a trained machine learning model to derive metrology information from the measurement data. Examples of how to train such a machine learning model are described below with reference to FIGS. 8 and 9. The use of a machine learning model has been found to be particularly effective when the measurement data includes a distribution of detected radiation in a pupil plane.

[0070]

[0079] Figure 8 shows the framework of a method for training a machine learning model. The method comprises the step S21 of providing a substrate W having thereon a layer 30 comprising a two-dimensional material, as shown in Figure 5. The layer 30 may take any of the forms described above with reference to Figures 4 to 7.

[0071]

[0080] In some embodiments, the method includes obtaining a training data set by performing a first measurement process on a target portion 32 of the layer 30 for a plurality of different target portions 32 of the layer 30. In some embodiments, as illustrated in FIG. 8 , obtaining the training data set further includes performing a second measurement process on each of the target portions 32. Thus, the method may include step S22 of performing the first measurement process on the target portion 32 of the layer 30 to obtain first measurement data. The method may further include step S23 of performing the second measurement process on the target portion 32 of the layer 30 to obtain second measurement data. The method may further include step S24, in which the first measurement process and the second measurement process are performed on a plurality of different target portions 32 of the layer 30 to obtain the training data set. The first measurement process and the second measurement process may also be performed for a plurality of different layers 30 (e.g., on a plurality of different respective substrates W).

[0072]

[0081] The obtained training data set is used to train a machine learning model, whereby the trained machine learning model is able to derive metrology information about the new target portion 32 (e.g., a target portion 32 that was not used to train the machine learning model) from measurement data obtained by performing the first measurement process on the new target portion 32. In the example of Figure 8, the training data set obtained in step S24 is used in step S25 to train the machine learning model.

[0073]

[0082] In one embodiment, the first measurement process (performed in step S22) involves illuminating each target portion 32 of the layer 30 with an incoherent radiation beam and detecting radiation redirected by the target portions 32. The first measurement process may therefore be performed using any of the techniques described above with reference to step S2 of FIG. 4. The first measurement process may, for example, include obtaining a detected image formed in a dark-field imaging mode. The detected image may, for example, be obtained using the sensor 23 in the optical apparatus of FIG. 3. The apparatus of FIG. 3 is therefore an example of a measurement system suitable for carrying out the method.

[0074]

[0083] In one embodiment, the first measurement process (performed in step S22) includes obtaining a distribution of detected radiation in a pupil plane (e.g., in bright-field imaging mode). The distribution of detected radiation in the pupil plane can be obtained, for example, using sensor 19 in the optical apparatus of Figure 3. The apparatus of Figure 3 is therefore an example of a measurement system suitable for carrying out the method.

[0075]

[0084] In one embodiment, the first measurement process (performed in step S22) includes dark-field holographic microscopy, and thus may be performed using any of the techniques described above with respect to step S12 of FIG.

[0076]

[0085] In some embodiments, the second measurement process is a process that can provide more detailed information about defects of interest in layer 30, such as grain boundaries, than the first measurement process. However, the second measurement process may be more costly and / or time-consuming than the first measurement process. By training the machine learning model based on measurement data from both the first and second measurement processes, the machine learning model learns to obtain more useful information from future measurement data obtained from only the first measurement process. For example, the machine learning model may learn how to correlate subtle features in the first measurement data with features identified as defects of interest in the second measurement data. The machine learning model enables high-quality information to be obtained from new measurements of layer 30 using only the first measurement process. Therefore, high-quality information can be obtained efficiently (e.g., at low cost and / or high speed).

[0077]

[0086] In some embodiments, the machine learning model comprises a supervised (e.g., fully supervised or semi-supervised) machine learning model. The measurement data from the second measurement process is processed to obtain metrology information about the target portion 32 of the layer 30. The metrology information obtained using the measurement data from the second measurement process provides labels for training the supervised machine learning model using the measurement data from the first measurement process. The combination of the measurement data from the first and second measurement processes may be considered a calibration. The first and second measurement processes provide pairs of data units to a training data set. The first measurement process provides measurement data corresponding to that obtained when measuring a new target portion, and the second measurement process associates those measurements with metrology information of interest (e.g., grain boundary density). The labels may take various forms depending on the nature of the metrology information of interest. Each label may include or consist of, for example, one of the metrics discussed above for quantifying the density of grain boundaries corresponding to the measured target portion. Each label obtained by applying the second measurement process to a particular target portion is assigned to measurement data obtained by applying the first measurement process to the same target portion or target portions in close proximity to that target portion (e.g., the target portions closest to and / or overlapping that target portion). The first measurement process can be performed on any region of the substrate where two-dimensional material is present, including where devices may be fabricated. The second measurement process can be destructive, if desired. Note that a second measurement process is not necessarily required for training, for example, if a predefined defect distribution is induced as described below (e.g., by spatially varying surface topography and / or surface composition). The nature of the predefined defect distribution allows the defect distribution to be known in advance. The known defect distribution can be used directly to provide labels for the measurement data from the first measurement process in the training dataset (without an additional measurement step).

[0078]

[0087] In some embodiments, either or both of the first and second measurement processes include illuminating each target portion 32 of the layer 30 with an incoherent radiation beam and detecting radiation redirected by the target portion 32. In an exemplary implementation, the first measurement process includes detecting an image in a bright-field imaging mode, and the second measurement process includes detecting an image in a dark-field imaging mode. The signals obtained from dark-field imaging and bright-field imaging, which may also be referred to as dark-field and bright-field signals, respectively, can be viewed as different response functions from the illuminated area. Each response function can be expressed as a distribution of radiation at an image plane (e.g., detected using sensor 23 in the optical device of FIG. 3 ) or a pupil plane (e.g., detected using sensor 19 in the optical device of FIG. 3 ). Bright-field imaging has various practical advantages over dark-field imaging. For example, bright-field imaging may facilitate faster acquisition speeds and / or the use of smaller spot sizes. Alternative and / or additional modes of filtering, such as filtering based on polarization properties, may be available for bright-field imaging. Such filtering options may, for example, improve contrast. On the other hand, many target defects, such as grain boundaries, may be difficult to recognize in bright-field images. Dark-field imaging may be more sensitive to certain types of defects, such as grain boundaries. According to this embodiment, dark-field imaging is used to train a machine learning model to interpret the bright-field image (e.g., to provide labels for a training dataset used to train a supervised machine learning model). This makes it possible to achieve a desirable combination of advantages. It is possible to benefit from the practical advantages of bright-field imaging (e.g., increased acquisition speed, reduced spot size, filtering, etc.) and the improved defect sensitivity of dark-field imaging described above. This approach works particularly effectively when the first measurement process includes obtaining a distribution of detected radiation in a pupil plane (i.e., when a pupil plane representation of the response function is used).

[0079]

[0088] In one embodiment, the second measurement process comprises electron microscopy, such as scanning electron microscopy.

[0080]

[0089] In one embodiment, the second measurement process includes second-harmonic imaging microscopy. Second-harmonic imaging microscopy can be particularly effective for detecting defects of interest when the microscopy employs dark-field imaging. Second-harmonic imaging microscopy can also use the distribution of detected radiation at the pupil plane. Second-harmonic imaging microscopy as a general technique is known in the art and can be implemented using a variety of optical configurations. This technique relies on exploiting variations in the layer 30's ability to generate second-harmonic light to provide contrast in the image. Different (e.g., more) second-harmonic light can be generated at defects, such as grain boundaries, compared to regions of the layer 30 away from the defects. This effect allows for a clearer visualization of defects than would be possible using conventional optical microscopy techniques that rely on detecting changes in optical density, optical path length, or refractive index. In some embodiments, second-harmonic imaging microscopy is implemented using an optical arrangement of the type discussed above with reference to FIG. 3, except that the light source 11 is configured to be a coherent radiation source (e.g., a laser). If a dark field imaging mode is used, this can be obtained using sensor 23 in the optical apparatus of Figure 3. If a detected radiation distribution at a pupil plane is used, the radiation distribution can be obtained using sensor 19 in the optical apparatus of Figure 3. In some embodiments, an optical apparatus of the type discussed above with reference to Figure 3 is configured to operate in two different modes, the apparatus performing a first measurement process (e.g., using incoherent radiation) in the first mode, and a second measurement process (e.g., using second harmonic imaging microscopy) in the second mode.An exemplary demonstration of dark-field second-harmonic imaging used to detect grain boundaries in transition metal dichalcogenides (TMDs) is presented in the paper: “Nonlinear Dark-Field Imaging of One-Dimensional Defects in Monolayer Dichalcogenides”; Bruno R. Carvalho, Yuanxi Wang, Kazunori Fujisawa, Tianyi Zhang, Ethan Kahn, Ismail Bilgin, Pulickel M. Ajayan, Ana M. de Paula, Marcos A. Pimenta, Swastik Kar, Vincent H. Crespi, Mauricio Terrones, and Leandro M. Malard; Nano Letters 2020 20 (1), 284-291. In this work, dark-field second-harmonic imaging microscopy was used to obtain images of two-dimensional crystals of MoS2, MoSe2, and WS2 formed as monolayers on quartz substrates. In the example described, the samples were excited with energies of 1.38 eV (900 nm) for MoSe2 and 1.42 eV (873 nm) for MoS2 and WS2, respectively. A broadband laser between 750 and 950 nm was used, but a more narrowband laser, e.g., between 870 and 900 nm, should be sufficient to stimulate second-harmonic generation in MoS2, MoSe2, and WS2.

[0081]

[0090] In some embodiments, the layer 30 used to obtain the training dataset is intentionally engineered to produce predefined variations in defect distribution. This approach can ensure that the training dataset effectively trains a machine learning model across a desired range of defect distributions without requiring the training set to be excessively large (which could otherwise rely on more random variations in defect distribution in the training set). Alternatively or additionally, this approach can be used to enable labeling of data in the training dataset without individual measurement of defect distribution. In some embodiments, this is achieved by arranging the layer 30 to be supported on a non-planar support surface, the surface topography of which is configured to provide a predetermined defect distribution in the layer 30. For example, grain boundary formation is predicted to be favored in regions where the slope of the support changes rapidly (e.g., along sharp ridges, etc.). In some embodiments, lithographic techniques are used to provide the non-planar support surface. Lithographic techniques offer a high degree of local precision and control. Thus, training zones with different topologies can be created with a high degree of freedom and precision. Such high-quality training zones facilitate the effective and reliable training of machine learning models.

[0082]

[0091] Alternatively or additionally, in some embodiments, the layer 30 used to obtain the training data set is supported on a support surface having a non-uniform composition, and the spatial variation in composition within the support surface is configured to provide a predetermined defect distribution in the layer 30.

[0083]

[0092] 9 , the support surface 50 is configured to provide a substantially uniform defect distribution in each of a plurality of different training zones 51-54, where the substantially uniform defect distribution is substantially different in each of the training zones 51-54. The defect distribution in each training zone 51-54 may be established using a non-planar topography (e.g., formed using lithography) and / or using different surface compositions in the different training zones 51-54, as described above. In the illustrated example, the support surface 50 may be such that when the layer 30 is formed on the support surface 50, the topography and / or composition of the training zones 51-54 may be such that the lowest density of grain boundaries occurs in training zone 51, the highest density of grain boundaries occurs in training zone 52, the highest density of grain boundaries occurs in training zone 53, and the highest density of grain boundaries occurs in training zone 54.

[0084]

[0093] In some embodiments, the substrate is pretreated to make defects, such as grain boundaries, more easily identifiable. Pretreatment may be applied prior to any of the methods for performing metrology described above with reference to FIGS. 4 and 6. Alternatively or additionally, pretreatment may be applied to enhance training of a machine learning model in the manner described with reference to FIG. 8. For example, pretreatment may be applied as part of the second measurement process. Pretreatment may include chemically modifying the defects, for example, by applying an oxidation process (e.g., using heating and / or O vapor) to selectively oxidize the defects. Alternatively or additionally, self-assembled monolayer functionalization may be applied to enhance the contrast between the defects and other regions of the two-dimensional material. Alternatively or additionally, an additional thin layer (e.g., a monolayer) may be applied on the layer 30 comprising the two-dimensional material to enhance the contrast between the defects and other regions of the two-dimensional material.

[0085]

[0094] FIG. 10 illustrates the framework of a method for providing a layer 30 comprising a two-dimensional material on a substrate W, as illustrated in FIG. 5 . The layer 30 may take any of the forms described above with reference to FIGS. 4-9 . The method includes a step S31 of forming a layer comprising a two-dimensional material on the substrate W using a formation process. The method further includes a step S32 of performing metrology on the layer 30 using, for example, any of the methods described above with reference to FIGS. 4 and 6 . The method further includes a step S33 of modifying one or more process parameters of the formation process based on the obtained metrology information, and a step S34 of repeating the formation process to form a layer comprising a two-dimensional material on a new substrate. The obtained metrology information can thus be used in a control loop to control one or more process parameters that affect the metrology information of interest, e.g., affecting defect distribution, such as grain boundary distribution. The modified process parameters may include, for example, parameters of a deposition process configured to deposit two-dimensional material, including process parameters of a patterning process and / or an etching process involving localized deposition (e.g., direct radiation-induced deposition of material in a desired pattern), such as temperature gradients, or any other parameters in the manufacturing tool that affect the associated defect distribution. The control loop may, for example, correct for process drift and improve yield.

[0086]

[0095] An apparatus may be provided for performing any of the above-described methods. For example, a measurement system may be provided for illuminating a target portion 32 of a layer 30 of two-dimensional material on a substrate. The measurement system may be configured to detect radiation redirected by the target portion 32, such as a distribution of radiation in a pupil plane, to obtain measurement data. The apparatus described above with reference to FIG. 3 is an example of such a measurement system. A data processing system may be provided. The data processing system may be realized using any suitable combination of data processing hardware. The image processing unit and controller PU of FIG. 3 are an example of such a data processing system. The data processing system may be configured to control the measurement system to obtain measurement data for a plurality of different target portions 32. The data processing system may further be configured to use a machine learning model to obtain metrology information for the target portion 32 from the detected radiation, for example, the distribution of each detected radiation in a pupil plane. In some embodiments, the measurement system is configured to perform both a first measurement process and a second measurement process on the target portion 32 of the layer 30 of two-dimensional material for a plurality of different target portions 32 of the layer 30. The measurement system may be configured to perform, for example, a first measurement process that includes detecting an image in a bright-field imaging mode and a second measurement process that includes detecting an image in a dark-field imaging mode, and the data processing system may be configured to train a machine learning model using training data sets derived from the first and second measurement processes, such that the machine learning model is able to derive metrology information for the new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion.

[0087]

[0096] The following clauses may be used to further describe the embodiments. 1. A method of performing metrology, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; illuminating a target portion of the layer with an incoherent radiation beam and detecting radiation redirected by the target portion of the layer to obtain measurement data; processing the measurement data to obtain metrology information about the target portion of the layer; wherein the illumination, detection and processing are performed for a plurality of different target portions of the layer to obtain metrology information for the plurality of target portions of the layer. 2. The method of clause 1, wherein the measurement data includes data derived from a detected image formed in a dark-field imaging mode. 3. The method of clause 1, wherein the measurement data includes data derived from the distribution of detected radiation in a pupil plane. 4. The method according to any one of clauses 1 to 3, wherein the illumination is carried out using radiation having a wavelength in the range of 10 nm to 1000 nm. 5. A method of performing metrology, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; performing dark-field holographic microscopy on a target portion of the layer to obtain measurement data; processing the measurement data to obtain metrology information about the target portion of the layer; wherein dark-field holographic microscopy and processing is performed for a plurality of different target portions of the layer to obtain metrology information for the plurality of target portions of the layer. 6. A method according to any one of clauses 1 to 5, wherein at least a majority of the plurality of target portions are positioned within a distance from the radially outer edge of the substrate closest to the target portion, the distance being less than 20% of the average spacing between the radially outer edge and the center of gravity of the substrate. 7. The method of any one of clauses 1-6, wherein the plurality of target portions are all positioned closer to the nearest outer edge of the substrate than to the center of gravity of the substrate. 8. The method of any one of clauses 1 to 7, wherein the plurality of target portions vary in size and / or shape as a function of position on the substrate. 9. The method of clause 8, wherein the average surface area of ​​the target portions monotonically decreases as a function of increasing spacing from the center of gravity of the substrate. 10. The method of any one of clauses 1-9, further comprising using a trained machine learning model to derive metrology information from the measurement data. 11. The method of clause 10, wherein the machine learning model is trained using first measurement data from a first measurement process and second measurement data from a second measurement process. 12. The method of clause 11, wherein the first measurement process includes detecting an image in bright-field imaging mode. 13. The method of clause 11 or 12, wherein the second measurement process includes detecting the image in a dark-field imaging mode. 14. The method of any one of clauses 1 to 13, wherein the obtained metrology information includes information about the distribution of defects in the layer. 15. The method of claim 14, wherein the information about the defect distribution includes information about the spatial distribution of grain boundaries. 16. The method of clause 15, wherein the information about defect distribution includes information about the spatial distribution of grain boundary density. 17. The method of clause 15 or 16, wherein processing the measurement data includes using a pattern recognition algorithm or a segmentation algorithm to determine one or more of the spatial distribution of grain boundary density, the spatial distribution of grain boundary density gradient. 18. The method of any one of clauses 14 to 17, wherein the obtained information on the defect distribution comprises information on one or more of the following: variation in layer thickness, distribution of islands in the additional layer, distribution of defects in a pattern formed in the two-dimensional material, distribution of delaminations. 19. The method of any one of clauses 1-18, further comprising using metrology information obtained for multiple target portions of the layer to construct a map of metrology information across an area of ​​the substrate covered by multiple portions of the layer. 20. A method for training a machine learning model, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; performing a first measurement process on the target portion of the layer to obtain first measurement data; and performing a second measurement process on the target portion of the layer to obtain second measurement data; obtaining a training dataset, wherein the first measurement process and the second measurement process are performed on a plurality of different target portions of the layer; training a machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information regarding the new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; A method comprising: 21. The method of clause 20, wherein the first measurement process includes illuminating each target portion of the layer with an incoherent radiation beam and detecting radiation redirected by the target portion. 22. The method of clause 21, wherein the first measurement process includes obtaining a detected image formed in a dark-field imaging mode. 23. The method of clause 21, wherein the first measurement process includes obtaining a distribution of detected radiation in a pupil plane. 24. The method of clause 20, wherein the first measurement process includes dark-field holographic microscopy. 25. The method of any one of clauses 20 to 24, wherein the second measurement process comprises electron microscopy. 26. The method of any one of clauses 20 to 25, wherein the second measurement process comprises second harmonic imaging microscopy. 27. The method of clause 26, wherein second harmonic imaging microscopy uses dark field imaging. 28. The method of clause 20 or 21, wherein the first measurement process includes detecting an image in bright-field imaging mode. 29. The method of clause 28, wherein the second measurement process includes detecting the image in a dark-field imaging mode. 30. A method according to any one of clauses 20 to 29, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a non-planar support surface, the surface topography of the non-planar support surface being configured to provide a predetermined defect distribution in the layer. 31. A method according to any one of clauses 20 to 30, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a support surface having a non-uniform composition, and the spatial variation of the composition within the support surface is configured to provide a predetermined defect distribution in the layer. 32. The method of clause 30 or 31, wherein the support surface is configured to provide a defect distribution that is substantially uniform in each of a plurality of different training zones, and the substantially uniform defect distribution is substantially different in each of the training zones. 33. The method of any one of clauses 30 to 32, wherein the predetermined defect distribution includes a predetermined grain boundary distribution. 34. The method of any one of clauses 1 to 19, further comprising deriving metrology information from the measurement data using a machine learning model, the machine learning model being trained according to the method of any one of clauses 20 to 33. 35. A method of providing a layer comprising a two-dimensional material on a substrate, comprising: forming a layer comprising a two-dimensional material on a substrate using a formation process; performing metrology on a layer comprising a two-dimensional material using the method of any one of clauses 1 to 19; and modifying one or more process parameters of the formation process based on the obtained metrology information, and repeating the formation process to form a layer comprising the two-dimensional material on the new substrate. A method comprising: 36. The method of clause 35, wherein the modified process parameters include one or more of parameters of a deposition process configured to deposit a two-dimensional material and parameters of a patterning process configured to impart a pattern to the two-dimensional material.

[0088]

[0097] The following clauses may be used to further describe the embodiments. 1. A method of performing metrology, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; illuminating a target portion of the layer with a radiation beam and detecting a distribution of radiation redirected by the target portion of the layer in a pupil plane to obtain measurement data; processing the measurement data to obtain metrology information about the target portion of the layer; wherein the illumination, detection and processing are performed for a plurality of different target portions of the layer to obtain metrology information for the plurality of target portions of the layer. 2. The method according to clause 1, wherein the processing of the measurement data uses a machine learning model to obtain metrology information from the distribution of detected radiation in the pupil plane. 3. How to train a machine learning model providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; obtaining a training data set by performing a first measurement process on the target portions of the layer for a plurality of different target portions of the layer; training a machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information regarding the new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; 3. The method according to clause 2, comprising: 4. A method for training a machine learning model, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; obtaining a training data set by performing a first measurement process on the target portions of the layer for a plurality of different target portions of the layer; training a machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information regarding the new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; A method comprising: 5. The method of clause 3 or 4, wherein obtaining the training dataset further comprises performing a second measurement process for each of the target portions. 6. The machine learning model is a supervised machine learning model, The measurement data from the second measurement process is processed to obtain metrology information about the target portion of the layer; and 6. The method of clause 5, wherein metrology information obtained using measurement data from the second measurement process provides labels for training a supervised machine learning model using measurement data from the first measurement process. 7. The method of clause 5 or 6, wherein either or both of the first measurement process and the second measurement process include illuminating each target portion of the layer with an incoherent radiation beam and detecting radiation redirected by the target portion. 8. The first measurement process includes detecting an image in a bright-field imaging mode; and 8. The method of clause 7, wherein the second measurement process includes detecting the image in a dark-field imaging mode. 9. The method of any one of clauses 3 to 8, wherein the first measurement process includes obtaining a distribution of detected radiation in a pupil plane. 10. The second measurement process is detecting an image formed in a dark field imaging mode; electron microscopy, Second harmonic imaging microscopy, and Dark-field holographic microscopy 10. The method of clause 9, comprising one or more of: 11. The method of any one of clauses 3 to 10, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a non-planar support surface, and the surface topography of the non-planar support surface is configured to provide a predetermined defect distribution in the layer. 12. The method of any one of clauses 3 to 11, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a support surface having a non-uniform composition, and the spatial variation of the composition within the support surface is configured to provide a predetermined defect distribution in the layer. 13. The method of clause 11 or 12, wherein the machine learning model is a supervised machine learning model, and the predetermined defect distribution is used directly to provide labels for measurement data from the first measurement process in the training dataset. 14. A method according to any one of clauses 11 to 13, wherein the support surface is configured to provide a defect distribution that is substantially uniform in each of a plurality of different training zones, and the substantially uniform defect distribution is substantially different in each of the training zones. 15. The method of any one of clauses 11 to 14, wherein the predetermined defect distribution comprises a predetermined grain boundary distribution. 16. A method according to any one of clauses 1 to 15, wherein the illumination is carried out using radiation having a wavelength in the range of 10 nm to 1000 nm. 17. A method according to any one of clauses 1 to 16, wherein at least a majority of the plurality of target portions are positioned within a distance from the radially outer edge of the substrate closest to the target portion, the distance being less than 20% of the average spacing between the radially outer edge and the center of gravity of the substrate. 18. The method of any one of clauses 1-17, wherein the plurality of target portions are all positioned closer to a nearest outer edge of the substrate than to a center of gravity of the substrate. 19. The method of any one of clauses 1-18, wherein the plurality of target portions vary in size and / or shape as a function of position on the substrate. 20. The method of clause 19, wherein the average surface area of ​​the target portions monotonically decreases as a function of increasing spacing from the center of gravity of the substrate. 21. The method of any one of clauses 1 to 20, wherein the obtained metrology information includes information about the distribution of defects in the layer. 22. The method of clause 21, wherein the information about the defect distribution includes information about the spatial distribution of grain boundaries. 23. The method of clause 22, wherein the information about defect distribution includes information about the spatial distribution of grain boundary density. 24. The method of clause 22 or 23, wherein processing the measurement data includes using a pattern recognition algorithm or a segmentation algorithm to determine one or more of the spatial distribution of grain boundary density, the spatial distribution of grain boundary density gradient. 25. The method of any one of clauses 21 to 24, wherein the obtained information on the defect distribution comprises information on one or more of the following: variation in layer thickness, distribution of islands in the additional layer, distribution of defects in a pattern formed in the two-dimensional material, distribution of delaminations. 26. The method of any one of clauses 1-25, further comprising using metrology information obtained for multiple target portions of the layer to construct a map of metrology information across an area of ​​the substrate covered by multiple portions of the layer. 27. The method of any one of clauses 1-26, wherein the two-dimensional material comprises one or more of graphene, hexagonal boron nitride, and transition metal dichalcogenides. 28. A method of providing a layer comprising a two-dimensional material on a substrate, comprising: forming a layer comprising a two-dimensional material on a substrate using a formation process; performing metrology on a layer comprising a two-dimensional material using the method of any one of clauses 1 to 27; and modifying one or more process parameters of the formation process based on the obtained metrology information, and repeating the formation process to form a layer comprising the two-dimensional material on the new substrate. A method comprising: 29. A metrology apparatus configured to perform metrology on a substrate, comprising: a measurement system configured to illuminate a target portion of a layer of two-dimensional material on a substrate and to detect a distribution of radiation redirected by the target portion in a pupil plane to obtain measurement data; 1. A data processing system comprising: controlling the measurement system to obtain measurement data for a plurality of different target portions; Using a machine learning model to obtain metrology information of the target portion from the distribution of each detected ray in the pupil plane; a data processing system configured to: metrology equipment including: 30. A metrology apparatus configured to train a machine learning model, comprising: a measurement system configured to perform a first measurement process and a second measurement process on a target portion of the layer of the two-dimensional material for a plurality of different target portions of the layer; a data processing system configured to train a machine learning model using training data sets derived from the first measurement process and the second measurement process, whereby the machine learning model is capable of deriving metrology information for the new target portion of the layer comprising the two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; and metrology equipment including: 31. The first measurement process includes detecting an image in a bright-field imaging mode; and 31. The apparatus of clause 30, wherein the second measurement process includes detecting the image in a dark-field imaging mode.

[0089]

[0098] While specific reference may be made herein to the use of lithography apparatus in the manufacture of ICs, it should be understood that the lithography apparatus described herein may have other applications, such as the manufacture of integrated optics, magnetic domain memory guidance and detection patterns, flat panel displays, liquid crystal displays (LCDs), and thin-film magnetic heads. Those skilled in the art will appreciate that, in connection with such alternative applications, any use of the terms "wafer" or "die" herein can be considered synonymous with the more general terms "substrate" or "target portion," respectively. Substrates referred to herein may be processed, pre- or post-exposure, by, for example, a track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), a metrology tool, and / or an inspection tool. Where applicable, the disclosure herein may also apply to such and other substrate processing tools. Furthermore, a substrate may be processed multiple times, for example, to manufacture multi-layer ICs; as a result, the term "substrate," as used herein, may also refer to a substrate that already includes multiple processed layers.

[0090]

[0099] Although specific reference may be made above to the use of embodiments of the invention in relation to optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and is not limited to optical lithography, where circumstances permit. In imprint lithography, a topography of a patterning device defines the pattern to be formed on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate and the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is then moved away from the resist after the resist has been cured, leaving a pattern in the resist.

[0091]

[0100] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having wavelengths of 365, 355, 248, 193, 157, or 126 nm or thereabouts) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5 to 20 nm), soft x-rays, and particle beams such as ion beams or electron beams.

[0092]

[0101] The term "lens", where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components.

[0093]

[0102] The foregoing description of specific embodiments fully reveals the general nature of the present invention so that others, by applying knowledge within the skill of those skilled in the art, can readily modify and / or adapt such specific embodiments for various uses without undue experimentation and without departing from the general concept of the present invention. Accordingly, such adaptations and modifications are intended to be within the spirit and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It should be understood that the terminology used herein is for the purpose of description and not of limitation, and that the terminology used herein should be interpreted by those skilled in the art in light of the teaching and guidance.

[0094]

[0103] The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

1. 1. A method of performing metrology, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; illuminating a target portion of the layer with a radiation beam and detecting a distribution of radiation redirected by the target portion of the layer in a pupil plane to obtain measurement data; processing the measurement data to obtain metrology information about the target portion of the layer; and wherein the illuminating, detecting, and processing are performed for a plurality of different target portions of the layer to obtain metrology information of the plurality of different target portions of the layer.

2. The method of claim 1 , wherein the processing of the measurement data uses a machine learning model to derive the metrology information from the distribution of the detected radiation in the pupil plane.

3. The method for training the machine learning model includes: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; obtaining a training data set by performing a first measurement process on the target portions of the layer for a plurality of different target portions of the layer; training the machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information for the new target portion of a layer comprising a two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; The method of claim 2 , comprising:

4. 1. A method for training a machine learning model, comprising: providing a substrate having a layer formed thereon, the layer comprising a two-dimensional material; obtaining a training data set by performing a first measurement process on the target portions of the layer for a plurality of different target portions of the layer; training the machine learning model using the obtained training data set, whereby the trained machine learning model is capable of deriving metrology information for the new target portion of a layer comprising a two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; A method comprising:

5. The method of claim 3 or 4, wherein obtaining the training data set further comprises performing a second measurement process on each of the target portions.

6. 6. The method of claim 5, wherein either or both of the first measurement process and the second measurement process include illuminating each target portion of the layer with an incoherent radiation beam and detecting radiation redirected by the target portion.

7. The first measurement process includes detecting an image in a bright-field imaging mode; and The method of claim 6 , wherein the second measurement process includes detecting an image in a dark-field imaging mode.

8. the first measurement process includes obtaining a distribution of detected radiation in a pupil plane; The method according to any one of claims 3 to 7.

9. 9. The method of claim 3, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a non-planar support surface, the surface topography of the non-planar support surface providing a predetermined defect distribution in the layer.

10. 10. The method of claim 3, wherein the layer comprising the two-dimensional material used to obtain the training data set is supported on a support surface having a non-uniform composition, wherein a spatial variation of the composition within the support surface provides a predetermined defect distribution in the layer.

11. 11. The method of claim 9 or 10, wherein the machine learning model is a supervised machine learning model, and the predetermined defect distribution is used directly to provide labels for measurement data from the first measurement process in the training dataset.

12. 1. A method of providing a layer comprising a two-dimensional material on a substrate, the method comprising: forming a layer comprising a two-dimensional material on a substrate using a formation process; performing metrology on said layer comprising said two-dimensional material using the method of any one of claims 1 to 11; modifying one or more process parameters of the formation process based on the obtained metrology information, and repeating the formation process to form a layer comprising the two-dimensional material on a new substrate; A method comprising:

13. 1. A metrology apparatus for performing metrology on a substrate, comprising: a measurement system configured to illuminate a target portion of a layer of two-dimensional material on a substrate and to detect a distribution of radiation redirected by said target portion in a pupil plane to obtain measurement data; 1. A data processing system comprising: controlling the measurement system to obtain the measurement data for a plurality of different target portions; using a machine learning model to derive metrology information of the target portion from the distribution of each detected radiation in the pupil plane; and a data processing system that performs metrology equipment including:

14. 1. A metrology apparatus for training a machine learning model, comprising: a measurement system configured to perform a first measurement process and a second measurement process on a target portion of a layer of two-dimensional material for a plurality of different target portions of the layer; a data processing system that uses training data sets derived from the first measurement process and the second measurement process to train a machine learning model, whereby the machine learning model is capable of deriving metrology information for the new target portion of a layer comprising a two-dimensional material from measurement data obtained by performing the first measurement process on the new target portion; and metrology equipment including:

15. The first measurement process includes detecting an image in a bright-field imaging mode; and The apparatus of claim 14 , wherein the second measurement process includes detecting an image in a dark-field imaging mode.

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