Method and apparatus for predicting substrate images

Abstract

A method for training a machine learning model is described herein, wherein the machine learning model is configured to predict a substrate image corresponding to a printed pattern of the substrate as measured by a metrology tool, the method comprising: obtaining a training data set, the training data set comprising (i) measurement data of the metrology tool for measuring the printed pattern of the substrate, and (ii) a mask pattern for imaging the printed pattern onto the substrate; and training the machine learning model based on the training data set to predict the substrate image of the substrate as measured by the metrology tool, such that a cost function is improved; wherein the cost function comprises a relationship between the predicted substrate image and the measurement data.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 62 / 829,270, filed on April 4, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present description relates to methods and apparatus for detection, registration, and high-resolution quantification of images corresponding to a printed substrate undergoing a patterning process. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. For example, a lithographic apparatus can be used in the manufacture of integrated circuits (ICs). In this case, a pattern forming device (alternatively referred to as a mask or reticle) can be used to produce a circuit pattern corresponding to a single layer of the IC, and the pattern can be imaged on a target portion (e.g., a portion including a die, one or several dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will include a network of adjacent target portions that are exposed in succession. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing the entire pattern to the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern along a given direction (the "scanning" direction) by the beam, while simultaneously scanning the substrate in a direction parallel or anti-parallel to the direction. Different portions of the circuit pattern on the pattern forming device are progressively transferred to a target portion. Since typically the lithographic projection apparatus will have a magnification factor M (typically <1), the speed F at which the substrate is moved will be M times the speed at which the projection beam scans the patterning device. More information on the lithographic apparatus described herein can be found, for example, in U.S. Patent No. 6,046,792, which is incorporated herein by reference.

[0005] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various processes, such as priming, resist coating and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the circuit pattern after transfer. This array of processes is used as the basis for manufacturing a single layer of a device such as an IC. The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are expected to eventually complete a single layer of the device. If several layers are needed in the device, the entire process or its variation is repeated for each layer. Eventually, there will be a device in each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, so that a separate device can be mounted on a carrier, connected to a pin, etc.

[0006] As noted, microlithography is a core step in the fabrication of integrated circuits, where patterns formed on a substrate define the functional elements of the IC, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007] As semiconductor manufacturing processes continue to advance, the size of functional elements has been continuously reduced over the decades, while the number of functional elements (such as transistors) per device has been steadily increasing following a trend generally referred to as "Moore's Law." In the case of the prior art, the layers of the device are manufactured by using a lithographic projection device that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, thereby producing individual functional elements having a size well below 100 nm, i.e., the size of the functional element is less than half the wavelength of the radiation of the illumination source (e.g., a 193 nm illumination source).

[0008] The process of printing features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus is often referred to as low-k1 lithography, and is based on the resolution formula CD=k1×λ / NA, where λ is the wavelength of radiation employed (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (usually the smallest feature size printed), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it becomes to replicate a pattern on a wafer (similar to the shape and dimensions designed by a circuit designer to achieve specific electrical functions and performance). To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus and the design layout. These include, for example, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifted patterning devices, optical proximity correction (OPC, sometimes referred to as "optical and process correction") in the design layout, or other methods often defined as "resolution enhancement techniques (RET)". The term "projection optical element" as used herein should be broadly interpreted to include various types of optical systems, including, for example, refractive optical devices, reflective optical devices, apertures, and refractive-reflective optical devices. The term "projection optical element" may also collectively or individually include components that operate according to any of these design types for guiding, shaping, or controlling a radiation projection beam. The term "projection optical element" may include any optical component in a lithographic projection device, regardless of where the optical component is located on the optical path of the lithographic projection device. Projection optical elements may include optical components for shaping, adjusting, and / or projecting radiation from a source before the radiation passes through a pattern forming device, and / or optical components for shaping, adjusting, and / or projecting radiation after the radiation passes through a pattern forming device. Projection optical elements typically do not include a source and a pattern forming device. Summary of the invention

[0009] During the patterning process, it is desirable to frequently measure the resulting structure, for example for process control and verification. Typically, one or more parameters of the structure are measured or determined, such as a critical dimension of the structure, an overlay error between successive layers formed in or on the substrate, and the like. There are various techniques for measuring the microstructures formed during the patterning process. Various tools for making such measurements are known, including but not limited to scanning electron microscopes (SEMs), which are often used to measure critical dimensions (CDs).

[0010] In order to enable, for example, improved model recognition, defect detection, process control, etc., it is desirable to provide a technology for processing one or more images of one or more structures produced using a patterning process, and obtain a model that predicts the resulting pattern (e.g., after development, after etching, etc.) based on the design pattern used in the patterning process.

[0011] In an embodiment, a method for training a machine learning model is provided, the machine learning model being configured to predict a substrate image corresponding to a printed pattern of a substrate as measured via a metrology tool. The method comprises: obtaining a training data set, the training data set comprising (i) metrology data of the metrology tool for measuring the printed pattern of the substrate, and (ii) a mask pattern for imaging the printed pattern onto the substrate; and training a machine learning model based on the training data set to predict the substrate image of the substrate as measured by the metrology tool, such that a cost function is improved; wherein the cost function comprises a relationship between a predicted substrate image and the metrology data.

[0012] In addition, a method for predicting a substrate image corresponding to a printed pattern of a substrate is provided. The method comprises: obtaining a mask pattern of a patterning process and the trained machine learning model; and using the mask pattern as input, predicting the substrate image to be measured by the metrology tool via the trained machine learning model.

[0013] In addition, a computer program product is provided, the computer program product comprising a non-transitory computer-readable medium, on which instructions are recorded, and when the instructions are executed by a computer, the method according to any one of the above claims is executed. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0015] Figure 1 schematically depicts an embodiment of a lithographic apparatus according to an embodiment;

[0016] Figure 2 schematically depicts an embodiment of a lithography cell or cluster according to an embodiment;

[0017] Figure 3 schematically depicts an embodiment of a scanning electron microscope (SEM) according to an embodiment;

[0018] Figure 4 schematically depicts an overview of an example model prediction system according to an embodiment;

[0019] Figure 5 is a flow chart of a method for training a machine learning model configured to predict an image of a printed pattern of a substrate subjected to a patterning process according to an embodiment;

[0020] Figure 6 is a flow chart of an example method for predicting a substrate image of the substrate based on a trained machine learning model according to an embodiment;

[0021] Figure 7 The diagram shows the use of Figure 5 Example training of deep learning models using the methods in ;

[0022] Figure 8 illustrates an example of a pixelated input image for training a deep learning model according to an embodiment;

[0023] Fig. 9A Figure illustrates an example of a dilated kernel for training the deep learning model according to an embodiment;

[0024] Fig. 9B Figure illustrates example weights of a dilated kernel for training the deep learning model according to an embodiment;

[0025] Fig. 10A illustrates an example convolution operation with a first dilated kernel for training the deep learning model according to an embodiment;

[0026] Fig. 10B illustrates an example convolution operation with a second dilated kernel for training the deep learning model according to an embodiment;

[0027] Fig. 10C illustrates an example convolution operation with a third dilated kernel for training the deep learning model according to an embodiment;

[0028] Fig.11 is an example plot of local derivatives, i.e., partial derivatives, of a cost function according to an embodiment;

[0029] Fig. 12A illustrates application of a trained machine learning model using a first mask pattern according to an embodiment;

[0030] Fig. 12B According to the use of the embodiment Fig. 12A SEM image of the actual printed pattern imaged by the mask pattern shown in FIG;

[0031] Fig.13A illustrates application of a trained machine learning model using a second mask pattern according to an embodiment;

[0032] Fig. 13BAccording to the use of the embodiment Fig.13A SEM image of the actual printed pattern imaged by the mask pattern shown in FIG;

[0033] Fig.14 schematically depicts an embodiment of an electron beam inspection apparatus according to an embodiment;

[0034] Fig.15 is a block diagram of an example computer system according to an embodiment.

[0035] Fig.16 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0036] Fig.17 is a schematic diagram of another lithography projection apparatus according to an embodiment.

[0037] Fig.18 According to the embodiment Fig.17 A more detailed view of the devices in .

[0038] Fig.19 According to the embodiment Fig.17 and Fig.18 A more detailed view of the source collector module SO of the device.

[0039] Embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples so that those skilled in the art can practice the embodiments. It is noteworthy that the following figures and examples are not intended to limit the scope to a single embodiment, but other embodiments are possible by means of the interchange of some or all of the elements described or illustrated. Wherever convenient, the same reference numerals will be used throughout the drawings to refer to the same or similar parts. In the case where certain elements of these embodiments can be implemented partially or completely using known components, only those parts of these known components that are necessary for understanding the embodiments will be described, and detailed descriptions of other parts of these known components will be omitted so as not to make the description of the embodiments unclear. In this specification, embodiments showing a single component should not be considered restrictive; rather, unless otherwise explicitly stated in the present invention, the scope is expected to cover other embodiments including multiple identical components, and vice versa. In addition, the applicant does not intend to attribute any term in this specification or claims to an uncommon or specific meaning unless so explicitly stated. In addition, the scope covers the current and future known equivalents of the components mentioned in the present invention by means of illustration. DETAILED DESCRIPTION

[0040] Before describing the embodiments in detail, it is instructive to provide an exemplary environment in which the embodiments may be implemented.

[0041] Figure 1A lithographic apparatus LA is schematically depicted. The apparatus comprises:

[0042] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. DUV radiation or EUV radiation);

[0043] 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;

[0044] a substrate table (e.g. wafer stage) WTa 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

[0045] - a projection system (e.g. a refractive projection lens system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (e.g. comprising one or more dies).

[0046] The 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, to direct, shape or control radiation.

[0047] The pattern forming device support structure holds the pattern forming device in a manner that depends on the orientation of the pattern forming device, the design of the lithographic equipment, and other conditions such as whether the pattern forming device is held in a vacuum environment. The support structure of the pattern forming device can hold the pattern forming device using mechanical, vacuum, electrostatic or other clamping techniques. The support structure of the pattern forming device can be a frame or a table, for example, which can be fixed or movable as required. The support structure of the pattern forming device can ensure that the pattern forming device is located in a desired position (for example, relative to the projection system). Any term "reticle" or "mask" used herein may be considered to be synonymous with the more general term "pattern forming device".

[0048] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a pattern in the cross-section of the radiation beam so as to produce a pattern in the target portion of the 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 (for example if the pattern includes phase-shifting features or so-called assist features). Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) produced in the target portion.

[0049] The pattern forming device can be transmissive or reflective. Examples of pattern forming devices include masks, programmable mirror arrays, and programmable LCD (liquid crystal display) panels. Masks are well known in lithography and include mask types such as binary mask types, alternating phase shift mask types, attenuated phase shift mask types, and various hybrid mask types. An example of a programmable mirror array uses a matrix arrangement of small mirrors, each of which can be tilted individually to reflect an incident radiation beam in different directions. The tilted mirrors impart a pattern to the radiation beam reflected by the mirror matrix. More information about mirror arrays can be collected, for example, from U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference. An example of a programmable LCD array construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0050] The term "projection system" as used herein should be broadly interpreted to include any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation used, or other factors such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0051] As depicted here, the device is of the transmissive type (eg, employing a transmissive mask). Alternatively, the device may be of the reflective type (eg, using a programmable mirror array of the type mentioned above, or using a reflective mask).

[0052] The lithographic apparatus may be of a type having two tables (dual-stage) or more tables (e.g., two or more substrate tables, two or more patterning device supports, or a substrate table and a metrology table). In such a "multi-stage" machine, the additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for pattern transfer. For example, a dual-stage lithographic projection apparatus is described in US5,969,441, which is incorporated herein by reference.

[0053] The lithographic apparatus may also be of a type in which at least a portion of the substrate may also be covered by a liquid having a relatively high refractive index (e.g. water) so as to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as the space between the mask and the projection system. It is well known in the art that immersion techniques are used to increase the numerical aperture of a projection system. The term "immersion" as used herein does not mean that structures such as the substrate W must be immersed in liquid, but rather "immersion" only means that liquid is located between the projection system PS and the substrate W during exposure.

[0054] refer to Figure 1 , the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such a case, the source is not considered to constitute a part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, suitable directional reflectors and / or a beam expander. In other cases, the source may be an integral part of the lithographic apparatus (for example, when the source is a mercury lamp). The source SO and the illuminator IL, together with the beam delivery system BD provided when necessary, may be referred to as a radiation system.

[0055] The illuminator IL may comprise an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial extent and / or the 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. Furthermore, the illuminator IL may comprise various other components, such as an integrator IN and a condenser CO. The illuminator may be used to adjust the radiation beam so as to have a desired uniformity and intensity distribution in its cross-section.

[0056] The radiation beam B is incident on and patterned by the patterning device (e.g. mask) MA, which is held on the patterning device support (e.g. mask table MT). After having traversed the patterning device (e.g. mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position sensor IF (e.g. an interferometric measurement device, a linear encoder, a 2D encoder or a capacitive sensor), the substrate table WTa can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and the further position sensor ( Figure 1 The first positioner PM (not explicitly shown in the figure) is used to accurately position the pattern forming device (e.g. mask) MA relative to the path of the radiation beam B. In general, movement of the pattern forming device support (e.g. mask table) MT may be achieved with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) which form part of the first positioning device PM. Similarly, movement of the substrate table WTa may be achieved 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 pattern forming device support (e.g. mask table) MT may be connected to a short-stroke actuator only, or may be fixed.

[0057] The pattern forming device (e.g., mask) MA and substrate W can be aligned by using mask alignment marks M1, M2 and substrate alignment marks Pl, P2. Although the illustrated substrate alignment marks occupy dedicated target portions, they can be located in the spaces between multiple target portions (these are called scribe alignment marks). Similarly, in the case where more than one die is set on the pattern forming device (e.g., mask) MA, the mask alignment marks can be located between the dies. Small alignment marks can also be included within the die, between the device features, in which case it is desired that the marks are as small as possible and do not require any patterning or process conditions that are different from adjacent features. An embodiment of an alignment system for detecting the alignment marks is further described below.

[0058] The depicted device can be used in at least one of the following modes:

[0059] In step mode, the entire pattern imparted to the radiation beam is projected at once onto a target portion C (i.e. a single static exposure) while the patterning device support (e.g. mask table) MT and the substrate table WTa are held substantially stationary. 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 that is imaged in a single static exposure.

[0060] - In scan mode, the pattern imparted to the radiation beam is projected onto a target portion C while the patterning device support (e.g. mask table) MT and the substrate table WTa are scanned synchronously (i.e. a single dynamic exposure). The speed and direction of the substrate table WTa relative to the patterning device support (e.g. 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 of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning movement determines the height of the target portion C (in the scanning direction).

[0061] - In another mode, the patterning device support (e.g. mask table) MT is held substantially fixed and the substrate table WTa / WTb is moved or scanned as a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WTa or between successive radiation pulses during a scan. This mode of operation may readily be applied in maskless lithography using a programmable patterning device such as a programmable mirror array of the type mentioned above.

[0062] Combinations and / or variations of the above-described modes of use, or entirely different modes of use, may also be employed.

[0063] The lithographic apparatus LA is of a so-called dual-platform type having two tables WTa, WTb (e.g., two substrate tables) and two stations—an exposure station and a measurement station—between which the two tables can be exchanged. For example, while a substrate on one table is being exposed at the exposure station, another substrate can be loaded onto another substrate table at the measurement station and various preparatory steps performed. The preparatory steps may include mapping the surface control of the substrate using a level sensor LS and measuring the position of alignment marks on the substrate using an alignment sensor AS, both sensors being supported by a reference frame RF. If the position sensor IF cannot measure the position of the table when the table is at the measurement station and at the exposure station, a second position sensor may be provided to enable the position of the table to be tracked at both stations. As another example, while a substrate on one table is being exposed at the exposure station, another table without a substrate is waiting at the measurement station (where a measurement action may optionally occur). The other table has one or more measuring devices and may optionally have other tools (e.g., a cleaning device). When the substrate has finished exposure, the stage without the substrate moves to the exposure station to perform, for example, measurement, and the stage with the substrate moves to a location (for example, the measurement station) where the substrate is unloaded and another substrate is loaded. These multiple stage arrangements can significantly increase the throughput of the apparatus.

[0064] like Figure 2 As shown in , the lithography equipment LA can form part of a lithography unit LC, and is sometimes referred to as a lithography cell or lithography cluster, and the lithography unit also includes equipment for performing one or more pre-pattern transfer processes or post-pattern transfer processes on a substrate. Conventionally, these equipment include: one or more spin coaters SC for depositing a resist layer, one or more developers DE for developing the patterned resist, one or more chilling plates CH and one or more baking plates BK. The substrate transport device or robot RO picks up the substrate from the input / output ports I / O1, I / O2, moves the substrate between different process devices, and then transfers the substrate to the feed station LB of the lithography equipment. These devices are generally collectively referred to as tracks or coating and development systems, and are controlled by a track control unit TCU, which is itself controlled by a management control system SCS, which also controls the lithography equipment via a lithography control unit LACU. Therefore, different equipment can be operated to maximize production volume and processing efficiency.

[0065] In order for substrates processed (e.g., exposed) by the lithographic apparatus to be processed correctly and consistently, it is desirable to inspect the processed substrates to measure one or more properties, such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. If an error is detected, the processing of one or more subsequent substrates can be adjusted. For example, this may be particularly useful in cases where the inspection can be completed quickly and quickly enough so that another substrate of the same batch is still pending. In addition, processed substrates can be stripped and reworked (to improve yield) or discarded, thereby avoiding pattern transfer to substrates that are known to be defective. In the case where only some target portions of the substrate are defective, further pattern transfer can be performed only on those target portions that are good. Another possibility is to debug the settings of subsequent processing steps to compensate for the errors, for example, the timing of the trim etching step can be adjusted to compensate for the substrate-to-substrate CD variations produced by the lithographic process steps.

[0066] An inspection device is used to determine one or more properties of a substrate, in particular to determine how one or more properties of different substrates or different layers of the same substrate vary between different layers and / or across substrates. The inspection device may be integrated into the lithographic apparatus LA or the lithographic cell LC, or may be an independent device. In order to achieve the fastest measurement, it is desirable that the inspection device measures one or more properties in the patterned resist layer immediately after pattern transfer. However, the latent pattern in the resist may have a very low contrast—for example, there is only a very small refractive index difference between the portion of the resist that has been exposed to radiation and the portion that has not been exposed to radiation—and not all inspection devices may have sufficient sensitivity to make useful measurements of the latent pattern. Therefore, measurements may be made after a post-exposure bake step (PEB), which is typically the first step performed on the patterned substrate and increases, for example, the contrast between the exposed and unexposed portions of the resist. At this stage, the pattern in the resist may be referred to as semi-latent. Measurements can also be made on a developed resist image, for example at a point where the exposed or unexposed parts of the resist have been removed, or after a pattern transfer step such as etching. The latter possibility limits the possibility of reworking defective substrates, but can still provide useful information, for example for process control purposes.

[0067] In some embodiments, the inspection device may be a scanning electron microscope (SEM) that obtains images of structures (eg, some or all structures of a device) exposed or transferred onto the substrate. Figure 3Depicted is an embodiment of a SEM 200. A primary electron beam 202 emitted from an electron source 201 is converged by a condenser lens 203 and then passes through a beam deflector 204, an EB deflector 205, and an objective lens 206 to irradiate a substrate 100 on a substrate stage 101 at a focal point.

[0068] When the substrate 100 is irradiated with the electron beam 202, secondary electrons are generated from the substrate 100. The secondary electrons are deflected by the E×B deflector 205 and detected by the secondary electron detector 207. A two-dimensional electron beam image can be obtained by detecting the electrons generated from the sample in synchronization with, for example, two-dimensionally scanning the electron beam by the beam deflector 204 or repeatedly scanning the electron beam 202 in the X direction or the Y direction by the beam deflector 204, and continuously moving the substrate 100 in the other of the X direction or the Y direction by the substrate stage 101.

[0069] The signal detected by the secondary electron detector 207 is converted into a digital signal by an analog / digital (A / D) converter 208, and the digital signal is sent to the image processing system 300. In an embodiment, the image processing system 300 may have a memory 303 for storing all or part of the digital image for processing by the processing unit 304. The processing unit 304 (e.g., specially designed hardware or a combination of hardware and software) is configured to convert or process the digital image into a data set representing the digital image. In addition, the image processing system 300 may have a storage medium 301 configured to store the digital image and the corresponding data set in a reference database. The display device 302 can be connected to the image processing system 300 so that the operator can perform necessary operations of the equipment with the help of a graphical user interface.

[0070] As mentioned above, SEM images can be processed to extract contours in the image that describe the edges of objects representing device structures. These contours are then quantified via indicators such as CD. Thus, images of device structures are usually compared and quantified via simplistic indicators such as distance between edges (CD) or simple pixel differences between images. Typical contour models that detect the edges of objects in images in order to measure CD use image gradients. In practice, those models rely on strong image gradients. But in practice, images are usually noisy and have discontinuous boundaries. Techniques such as smoothing, adaptive thresholding, edge detection, erosion and dilation can be used to process the results of image gradient contour models to address noisy and discontinuous images, but will ultimately result in low-resolution quantization of high-resolution images. Thus, in most instances, mathematical processing of images of device structures to reduce noise and automated edge detection will result in a loss of resolution of the image, thereby resulting in a loss of information. Therefore, the result is a low-resolution quantization equivalent to an oversimplified representation of a complex high-resolution structure.

[0071] Thus, it is desirable to have a mathematical representation that can preserve resolution and can also describe the general shape of a structure (e.g., a circuit feature, an alignment mark, or a portion of a measurement target (e.g., a grating feature), etc.) produced or expected to be produced using a patterning process, whether, for example, the structure is in a latent resist image, in a developed resist image, or in a layer transferred to a substrate, such as by etching. In the context of a lithography or other patterning process, the structure can be a device being manufactured or a portion thereof, and the image can be a SEM image of the structure. In some cases, the structure can be a feature of a semiconductor device (e.g., an integrated circuit). In this case, the structure can be referred to as a pattern or expected pattern that includes multiple features of the semiconductor device. In some cases, the structure can be an alignment mark or a portion thereof (e.g., a grating of an alignment mark) used in an alignment measurement process to determine the alignment of an object (e.g., a substrate) with another object (e.g., a patterning device), or a measurement target or a portion thereof (e.g., a grating of a measurement target) used to measure parameters of the patterning process (e.g., overlay, focus, dose, etc.). In an embodiment, the measurement target is a diffraction grating used to measure (e.g.,) overlay.

[0072] refer to Figure 4 , depicts a schematic diagram of an example model prediction system according to an embodiment. In an embodiment, Figure 4 The implementation system is an adaptive state estimation and model predictive control system for a patterning process (e.g., both the lithography and etching processes of the patterning process). In the following discussion, the model predictive system (and associated techniques) will be described with respect to a patterning process involving an optical lithography process. In another embodiment, a different patterning process may be used, such as one involving imprint lithography. And therefore, for such a different patterning process, as will be appreciated by those skilled in the art, one or more different parameters / variables may be involved.

[0073] At 400, certain inputs to the model prediction system are provided. For example, nominal values ​​of focal length, dose, optical aberrations, illumination modes (e.g., spatial distributions such as annular, dipole, quadrupole, etc.), etc., may be input. Additionally, a design pattern for generating the structure using the patterning process is input. In a typical embodiment, the design pattern is a patterning device (e.g., mask) pattern. In combination, the input values ​​define a particular patterning process. As will be appreciated, different combinations of parameters / variables may define different patterning processes.

[0074] At 410, a mathematical model of at least a portion of the patterning process receives the input. The model generates an output 420, as further described below. In an embodiment, the model may predict the structure (as produced using the patterning process) as a latent image in the resist. In an embodiment, the model may predict the structure (as produced using the patterning process) as an image in the resist after development of the resist but before etching. In an embodiment, the model may predict the structure (as produced using the patterning process) after etching. As will be discussed further hereinafter, in an embodiment, the model is a machine learning model configured to predict the shape of a pattern on a product, for example, after a lithography step of the patterning process or after an etching step of the patterning process. In an embodiment, the machine learning model is trained to predict an SEM image of the structure. In an embodiment, the machine learning model is trained based on the input (such as at 400), the input including but not limited to an SEM image, dose, focal length, metrology parameters, etc.

[0075] At 420, the model generates one or more outputs reflecting predictions of the structure being produced using the patterning process. In an embodiment, the output is a predicted image of the structure predicted to be produced using the patterning process. In an embodiment, the output is a predicted parameter (e.g., CD) related to the image or structure predicted to be produced using the patterning process.

[0076] At 430, the state of the model can be estimated. In an embodiment, on-product measurements of the pattern shape as actually produced using the patterning process can be used to identify the model (e.g., a machine learning model) and estimate its parameters. Via state estimation, in an embodiment, the model can be continuously and recursively updated so that the model predictions match the measured outputs when the patterning process is running. This is advantageous because there will most likely be a mismatch between the open-loop model predictions and the measured reality; for example, the lithography equipment behaves differently than expected, the etching tool behaves differently than expected, process drift, other perturbations that may cause such a mismatch, etc. The mismatch degrades the yield of the patterning process, and therefore, in an embodiment, the mismatch is estimated during execution of the patterning process to control the patterning process. As can be seen, in Figure 44, the estimation of the state at 430 may take as input the predicted output 420 from the model 410 and one or more of the patterning process inputs 400. The estimation of the state at 430 may produce one or more parameters of the mathematical model 410. In an embodiment, the estimation of the state at 430 may receive as input the measurement results of one or more patterning process disturbances.

[0077] At 440, the model prediction system may adjust the pattern output to one or more targets 450. The one or more targets 450 may specify a certain desired value of a parameter / variable (e.g., desired CD, etc.). The adjuster at 440 may make appropriate changes or corrections to one or more inputs 400 to the model prediction system.

[0078] An example model 410 (e.g., of a lithography process and / or a lithography-etching process) is discussed in PCT Patent Publication No. WO2018108528A1 filed on December 16, 2016, the entire contents of which are incorporated herein by reference. This model 410 is a logical model that predicts a binary image or binarized image of the pattern shape of the structure produced after the lithography or etching process. This logical model is based on a small number of engineering features, resulting in a near-perfect binary product prediction. However, the output of the model is strictly binary, and further improvements in the prediction of the pattern shape of the structure can be made, as will be discussed in this disclosure.

[0079] In an embodiment of the present disclosure, a modeling method involves semantic segmentation of an image to enable pixel-level or pixel-grade prediction of multi-class labels (e.g., corresponding to one or more pattern shapes of the structure to be printed by the patterning process). This allows any image measured by the scanning electron microscope / electron beam to be converted into a pixel-level or pixel-level multi-class image. In an embodiment, the categories involve grayscale values. In addition, the semantic segmentation can be modified to improve the segmentation to uniquely identify pattern types (e.g., by coloring power lines or small lines differently), or to allow multiple patterning. In addition, the machine learning model is configured to predict a multi-class semantically segmented image, which is also converted into a grayscale image similar to that which can be measured by a measurement tool (e.g., a SEM tool). In an embodiment, assuming a mask image used to print the pattern shape of the structure at the measurement site, the machine learning model (e.g., which can be used as Figure 4 410) predicts the image as measured by the SEM / EB.

[0080] (For example, via Figure 3 SEM images (captured by a SEM in a SEM) typically contain non-informative measurement noise. In an embodiment, the machine learning model is configured to predict an image representing a semantic segmentation of a SEM image without noise. In an embodiment, such noise-free prediction can be achieved because the multi-category semantic segmentation is converted into a grayscale image similar to that which will be produced by the SEM imaging process. Conversion to grayscale involves binning or grouping of selected pixels with a predefined range of pixel values ​​and assigning specific labels to specific groups of pixels. For example, the grouping is uniform, wherein the range of pixel values ​​[0, 255] is evenly divided into 10 groups (or 10 labels). In an embodiment, the grouping is based on user-defined features of the pattern, and / or pixel values ​​corresponding to the desired pattern shape of the structure.

[0081] According to an embodiment, the training of the machine learning model is based on one or more deep learning architectures and algorithms. Deep learning involves training a neural network comprising multiple layers, which can be supervised or unsupervised. In one embodiment, the deep learning model can be based on architectures such as residual nets, convolutional neural networks, deep belief networks, and recursive neural networks. In a convolution-based architecture, each layer performs certain convolution operations based on one or more kernels (usually defined by weights associated with the kernels). During the training process, the deep learning model can be modified by adjusting the kernels (i.e., changing the kernel weight values).

[0082] A convolutional neural network typically consists of several layers linked together in a continuous manner so that information flows from input to output. In practice, each layer absorbs a tensor Tin and outputs a new tensor Tout. The input tensor is convolved with a kernel tensor W, the resulting convolution may be increased with a bias vector, and passed through an activation function such as a rectifier linear unit (ReLU). In the present disclosure, one or more dilated kernels or dilated kernels may be used to increase the receptive field without performing maximum pooling (as it may reduce spatial resolution). A dilated kernel or dilated kernel is a kernel used for dilation operations. Typically, maximum pooling is an operation that uses the maximum value of each of the neuron clusters from the previous layer.

[0083] The deep learning model needs to be trained, and the object (or feature within the image) labels may be domain specific. Thus, in an embodiment, a training data set is generated or obtained as a reference truth or basic truth (ground truth), for example, the reference truth may include a set of original input images (e.g., SEM images) corresponding to the mask pattern. In an embodiment, for training purposes, pixels are assigned object labels (e.g., gray levels, i.e., grayscale levels).

[0084] The following disclosure describes a method for training a deep learning model that performs semantic segmentation of an image (e.g., a grayscale SEM image). For example, the method assigns a label L(x) from a predetermined set of labels L to each image pixel x via a convolutional neural network (deep learning), and specifically via an expanded residual neural network. In the present disclosure, the term "label" is used interchangeably with a feature or class label of a wafer (which may be interchangeably referred to as a substrate) to generally refer to a specific feature of a wafer. In an embodiment, the class label is a grayscale level or grayscale grade, wherein each class level is associated with a range of grayscale values ​​(e.g., between [0, 255]).

[0085] Figure 5 is a flow chart of an exemplary method for training a machine learning model according to an embodiment of the present disclosure, the machine learning model being configured to predict an image of a printed pattern of a wafer undergoing a patterning process. The predicted image corresponds to measurement data obtained from a metrology tool (e.g., a SEM) (e.g., a SEM image including structures printed on the wafer). The predicted image corresponds to a SEM image (e.g., a SEM image of a structure printed on the wafer). Figure 7 The predicted image has substantially low or no noise compared to the noise seen in 701 in FIG. Thus, more accurate measurements (e.g., CD, EPE, etc.) of the structure (in an embodiment, pattern) can be obtained from the predicted image compared to measurements obtained directly from the corresponding SEM image.

[0086] The method involves, in process P501, obtaining a training data set, including: (i) measurement data 501 of the measurement tool for measuring the printed pattern on the wafer, and (ii) a pattern forming device pattern 502 used for imaging the printed pattern on the wafer via a lithography device (hereinafter referred to as a mask pattern 502 (or its mask image) for better readability).

[0087] In an embodiment, the training data set includes a plurality of SEM images obtained from the SEM tool. In an embodiment, the training data set may also include parameters of the measurement tool. For example, the parameters of the scanning electron microscope are at least one of: electron beam intensity; angle of incidence; or sampling site information. In an embodiment, the training data set may also include values ​​of one or more parameters of the patterning process. In an embodiment, the one or more parameters of the patterning process include at least one of dose, focal length, intensity, irradiation mode, etc. Thus, after training, the trained machine learning model may also receive the parameters of the measurement tool and the patterning process to make more accurate predictions of wafer images.

[0088] In an embodiment, the metrology data 501 includes an image (e.g., a SEM image) of the printed pattern on the wafer captured via the metrology tool. Such an image may include noise, deformation, and other image-related issues caused by the metrology tool and the measurement process. In an embodiment, the metrology options (e.g., intensity, incident angle, etc.) of the metrology tool are used during the measurement of the printed pattern on the wafer.

[0089] In an embodiment, a mask pattern 502 is obtained in the form of an image or other equivalent representation. In an embodiment, the mask pattern 502 is an image of a design layout, and / or a design layout including structures corresponding to OPC (e.g., SRAF, SERIF). In an embodiment, the mask pattern 502 is a binary image, e.g., Figure 7 702 in the OPC'd mask image. In an embodiment, the mask image includes a SRAF placed around (ie, placed around) the OPC'd original features.

[0090] At process P503, the method involves training a machine learning model based on the training data set to predict the wafer image 510 measured by the measurement tool so that a cost function is improved. In an embodiment, the cost function includes a relationship between the predicted wafer image 510 and the measurement data 501. For example, the relationship of the cost function is the difference between the labeled SEM image of 501 and the label of the predicted wafer image 510. In an embodiment, the cost function is a generalized sawing loss, which can be reduced (in an embodiment, minimized) during the training process. The sawing loss function can evaluate multiple class segmentations using a single score. For example, the sawing loss function evaluates multiple class segmentations of the predicted image 510 relative to the SEM image of the measurement data 501. An example sawing loss function is given as follows:

[0091]

[0092] In the generalized sawing loss (GDL) equation described above, N is the number of pixels, L is the number of labels (e.g., 2 labels in a two-label classification problem), and r ln is the pixel value corresponding to a specific label l (e.g., ground truth label or reference pixel) assigned to the nth pixel, p ln is an image element associated with the probability that a pixel belongs to a particular label (e.g., the pixel has label l assigned to the nth pixel), w l is used to provide invariance for different tag set properties. In an embodiment, When selecting the weights, the contribution of each label is corrected by the inverse of its area, thus reducing the well-known correlation between region size and sawing score. In an embodiment, when training using a gradient descent method, relative to p ln The gradient of the cost function is determined, and the weights of each layer are determined based on the gradient such that the cost function is reduced (in an embodiment, minimized).

[0093] In an embodiment, the machine learning model outputs the predicted image 510, which may be a pixelated image. The pixelated image may be further segmented to produce a segmented image. In an embodiment, a class label of the plurality of class labels is assigned to each pixel based on the probability of the pixel belonging to a particular class among the plurality of class labels. In an embodiment, each class label of the plurality of class labels corresponds to a grayscale level. In an embodiment, the trained machine learning model directly outputs a segmented image of a printed wafer corresponding to the mask pattern. The segmented image includes a plurality of class labels assigned to pixels of the predicted image of the printed pattern, wherein the pixels correspond to particular features of the printed pattern.

[0094] In an embodiment, in the context of the output of the machine learning model (e.g., a pixelated image), the image may be projected to a logistic model comprising a sigmoid function, i.e., an S-shaped curve function, in the form of, for example:

[0095]

[0096] In the logistic model above, P(x, y) is the probability that a pixel belongs to a particular class, the image a(x, y) is the output of the machine learning model as described above, γ determines the slope of the sigmoid function, and τ is a threshold for determining a for the case where P=0.5 (the probabilities of belonging to a particular class are equal). Thus, in an embodiment, the probability P∈[0,1]. In this example, the maximum value of the logistic model is 1, in which case τ is a threshold for determining a for the case where P is half of the maximum value. Therefore, the probabilities of different pixels correspond to particular classes or labels. Thus, when assigning a label to a pixel (i.e., predicting the pixel), the associated probability gives additional information about the degree of certainty / accuracy of the label assignment. For example, when more labels have very similar probabilities, it indicates that more data (e.g., an augmented training set) is needed.

[0097] In an embodiment, the gray level is an integer value indicating a grouping of a range of gray values. In an embodiment, the grouping of the gray values ​​is based on: uniform grouping; pixels corresponding to specific features of the mask pattern desired to be printed on the wafer; pixels corresponding to specific features of the printed pattern; and / or weighted pixel grouping, where higher weights are assigned to gray values ​​of features that occur more frequently than other features of the mask pattern (or printed pattern) or its image. For example, uniform grouping involves dividing the gray values ​​[0, 255] into L labels (e.g., for 10 labels, the first label L1 corresponds to gray values ​​0 to 25, the second label L2 corresponds to gray values ​​26 to 51, etc.). Another example of grouping is by equal histogram splitting, where the range is selected so that each bin of the histogram has a similar number of entries.

[0098] In an embodiment, the training of the machine learning model is an iterative process. In the iteration, it involves: determining the values ​​of the model parameters of the convolutional neural network based on the measurement data 501 and the mask pattern 502; and adjusting the values ​​of the model parameters until the cost function of the convolutional neural network is improved. For example, the weights and / or biases associated with one or more layers of the CNN can be changed during the backpropagation algorithm. In an embodiment, the adjustment of the weights can be guided by a (stochastic) gradient descent method, in which the gradient descent of the cost function (e.g., generalized sawing loss) is evaluated and the weights are adjusted so that the cost function is minimized. The reduction or minimization of the cost function makes the predicted output (e.g., predicted image) close to the reference truth image (e.g., manually segmented SEM image).

[0099] In an embodiment, Figure 5 The method further involves determining a characteristic of the printed pattern of the wafer based on the predicted wafer image. In an embodiment, the characteristic is a critical dimension, a profile of the feature, and / or an edge placement error.

[0100] In an embodiment, the method further comprises: acquiring real-time (eg, Figure 4 ) measurement data on the product discussed in ; updating a trained machine learning model based on the real-time measurement data and the mask pattern 502 used during the patterning process.

[0101] In the following, about Figure 7 , using examples to provide additional details Figure 5 Those skilled in the art will understand that Figure 7The training process in is not limited to the deep learning model 730 or images 701 and 702. The model 730 and images 701 and 702 are only used for illustration purposes and to better convey the concept of the present disclosure.

[0102] Figure 7 FIG. 7 shows an example training of the deep learning model 730 according to an embodiment of the present disclosure. Figure 5 As shown, the deep learning model includes a convolutional neural network having several layers, which are linked together in a continuous manner. Each layer performs a (e.g., dilated) kernel (e.g., using Figure 8 , FIG. 9A to FIG. 9B , FIG. 10A to FIG. 10C The convolution operation of the image is discussed in detail above. The dilation kernel enlarges the receptive field of the input image and maintains the spatial resolution of the input image and thereby the features within the input image. This enables accurate annotation of even the smallest features of the wafer. In this way, the trained deep learning model is able to detect and accurately annotate features of small size, such as less than 20 nm. In other words, in embodiments, the model can segment the image at a pixel level or pixel level, which can be significantly less than 5 nm, preferably less than about 2 nm.

[0103] The trained deep learning model can be used to perform semantic segmentation of, for example, SEM images obtained during the patterning process, and determine various features and parameters of the patterning process by performing measurements of features identified in segmented images of the SEM images. According to the present disclosure, the semantic segmentation is based on grayscale levels, i.e., gray levels (0, 1, 2, 3, ..., nth level) and a generalized sawing loss function. The grayscale levels are labels assigned to the pixels based on their grayscale values ​​and groupings of the grayscale values, as previously described in Figure 5 As discussed in .

[0104] In the current embodiment, the input image includes a SEM image 701 and a mask pattern 702 in the form of a pixelated image, which can be represented in the form of a tensor or vector to enable various mathematical operations (e.g., convolution, addition, multiplication, rotation, scaling, etc.), statistical analysis, and / or other suitable operations for each pixel of the input image. In addition, based on the analysis, each pixel can be labeled (e.g., using one or more gray levels).

[0105] In an embodiment, the input images 701 and 702 may be represented as input tensors with dimensions (b, w, h, c), where b represents the batch size (e.g., the total number of images used for training), w represents the width of the input image (or tensor), h represents the height of the input image (or tensor), and c represents the channel (i.e., the number of categories / labels / features). In an embodiment, each pixel of the SEM image may have a grayscale value, such as Figure 8 Pixelated input image 800 is shown in FIG.

[0106] like Figure 7 As shown in , the deep learning model 730 receives as input the set of categories (e.g., grayscale levels), and the SEM image 701 of the printed pattern and the mask pattern 702. In addition, on the input, the model 730 performs convolution with a dilated kernel during the training process (e.g., through modeling and / or simulation). The model 730 is trained so that the trained deep learning model predicts different features of any input image (e.g., design layout, mask image, or OPCed mask image), and annotates each feature within the predicted image to produce a segmented image 740 that accurately mimics the SEM image 701 (e.g., greater than 99% match, minimizes the average sawing score, etc.). The predicted image is compared to an SEM image obtained from a SEM (e.g., Figure 3 ) with reduced or no noise compared to the conventional method.

[0107] The neural network of the model 730 includes a plurality of layers linked together in a continuous manner. Each layer of the plurality of layers may include a plurality of interconnected nodes including an activation function. The activation function maps elements of an input tensor (e.g., values ​​associated with pixels of an input image) to an output tensor in a nonlinear manner. For example, the activation function a may be a nonlinear function, such as a rectified linear unit (ReLU). An example activation function is as follows:

[0108]

[0109] In the above activation function, (i) a is the activation function, which may be a sigmoid function (e.g., in an embodiment, at the lowest layer), (ii) w i is the weight of the ith element of the input tensor, (iii) x iis the value of the i-th element of the input tensor, and (iv) θ is a bias. The set of all weights and biases may also be referred to as model parameters. Such an activation function is typically a nonlinear function that enables the deep learning model 730 to generalize or adapt to a variety of data (e.g., different pixels of the input tensor). The nonlinear activation function allows for the definition of a rich class of models that contain effective models (e.g., for computer vision-based tasks). The present disclosure is not limited to one type of activation function.

[0110] During the training process, the weights may be initialized to random values ​​(e.g., based on a Gaussian distribution between 0 and 1), and during the training process, such weights may be optimized via backpropagation and a specific update rule (e.g., an Adam update rule). In the present disclosure, optimization using a cost function and backpropagation is discussed below. The weights may be updated to accurately identify specific features of the input image, such as the SEM image 701 and the mask pattern 702, so that the trained deep learning model can predict features corresponding to different mask patterns.

[0111] The training involves forward propagating the input (e.g., 701 and 702) through different layers of the neural network (e.g., the first layer, the second layer that produces output tensors 730a to 730h) to reach the output (e.g., layer 730h). At the output layer (e.g., the final layer of 730h), an output tensor representing the predicted image is obtained.

[0112] During the forward propagation, at each layer, a convolution operation with a dilated kernel is performed. The convolution operation includes: superimposing a portion of the input images 701 and 702 with the dilated kernel; taking the product between each superimposed element, each superimposed element including the weight of the dilated kernel and the value of the pixel of the input images 701 and 702; and summing the results of the products. For example, in Fig. 10A , a first 3x3 dilated kernel 1010 is superimposed with a pixelated input tensor 1000, with each of the elements of the dilated kernel being superimposed with a pixel of the input tensor. Then, the product of the value of each of the superimposed elements (e.g., the value of the pixel and the weight of the kernel) can be calculated, and further, the products can be summed to determine an element of the output tensor. In addition, the first dilated kernel can then be shifted by a stride (e.g., one pixel column to the right), and a similar convolution operation is performed on the new superimposed elements of the input tensor and the kernel elements (i.e., weights) to determine a second element of the output tensor.

[0113] In an embodiment, iteratively performing the convolution may include: for an input tensor (e.g., Figure 7The input images 701 and 702 in Figure 8 800 in the representation 800 of FIG. 8 , and performing a plurality of convolution operations on one or more dilated kernels within the layer. For example, a first layer may receive the input tensor (e.g., a representation of the input image, such as Figure 8 800 in ). On the input tensor, the first layer uses a first dilated kernel to perform a convolution operation. The first dilated kernel has (for example, Fig. 9B The result of the convolution is a first output tensor (e.g., Figure 7 730a in ), the first output tensor is passed to the second layer through the first activation function of the first layer. Similar to the first layer, the second layer also uses a second dilated kernel to perform a convolution operation. The second dilated kernel has a second set of weights, which can be the same as or different from the first set of weights of the first kernel. The output of the second layer can be a second output tensor (e.g., Figure 7 730b) in, etc. In an embodiment, the first kernel and the second kernel themselves may be different, which will result in different output tensors. The present disclosure is not limited to one convolution operation with one dilated kernel per layer.

[0114] The training process may include convolution of the input tensor with multiple dilated kernels at each layer of the deep learning model 730, thereby generating multiple output tensors. Figure 7 , the first layer may output four different output tensors (e.g., four tensors 730a to 730d), each resulting from a convolution with a different dilation kernel, such as a first dilation kernel with a dilation rate of 1 and a depth of 2c and a second dilation kernel with a dilation rate of 2 and a depth of 2c. Similarly, the second layer may output four different output tensors 730e, 730f, 730g, and 730h, each resulting from a convolution with a different corresponding dilation kernel, such as a third dilation kernel with a dilation rate of 2 and a depth of 4c, and a fourth dilation kernel with a dilation rate of 4 and a depth of 4c.

[0115] In an embodiment, the dilation kernel may be characterized by a plurality of weights, a depth (i.e., classes), a dilation rate, or a combination thereof. In an embodiment, the dilation rate is a parameter related to the model / architecture, which may be considered a hyperparameter. In an embodiment, the "optimal" value of the dilation rate is determined empirically, for example by considering different architectures and selecting the value for which the model / architecture performs best with respect to the cost function (e.g., GDL). In a first pass or first pass, the weights may be randomly assigned (e.g., based on a Gaussian distribution between 0 and 1) and later modified during the training process. The dilation rate may be, for example, an integer value between 1 and 10, which may be selected at the beginning of the training process and kept fixed during the training process. For example, Fig. 9A The figure shows a dilated kernel 900 in the form of a 3x3 grid, each element of which has a specific weight (e.g., w1 to w9). The dilated kernel 900 also has a depth D (e.g., the total number of features (e.g., the depth D is equal to the number of categories at the final layer)). Any dilated kernel (such as 900) can also be represented in tensor form, also called a weight tensor (or weight kernel). In another example, FIG. 10A to FIG. 10C The figure shows examples of different dilation kernels, such as the first 3x3 dilation kernel 1010 ( Fig. 10A ), a second 3x3 dilation kernel 1020 with a dilation rate of 2 ( Fig. 10B ), and with a dilation rate of 3 ( Fig. 10C The third 3x3 expansion kernel 1030 of FIG.

[0116] During the training process, the weights of the one or more dilated kernels may be iteratively modified and / or assigned. Iteratively assigning the weights may be performed to improve the prediction of one or more features of the output tensor (e.g., 730h). During the training process, such weight assignment is done based on local derivatives of a cost function (discussed later in this disclosure), such as using backpropagation. In an embodiment, iteratively assigning weights may include assigning / adjusting a set of weights of the dilated kernel to take into account, for example, aberrations of a projection system of a device of the patterning process. In an embodiment, iteratively assigning weights may include assigning / adjusting a set of weights of the dilated kernel to characterize an aspect of the patterning process.

[0117] The predicted image 740 (i.e., the image representation of the output vector) includes elements (i.e., pixels) corresponding to pixels of the input image (e.g., the mask pattern 702), each pixel of the predicted image having a value associated with the set of categories (i.e., a gray level corresponding to one or more features of the wafer), which can be assigned a unique label (i.e., a gray level corresponding to each of the contact holes, lines, bars, etc.). In an embodiment, assigning a category from the set of categories to an element of the predicted image 740 can be based on a comparison of the predicted image 740 with the reference truth image 701 or truth tensor. In an embodiment, the elements of the predicted image 740 include a set of probabilities associated with each category of the set of categories (or a probability distribution per category per pixel). The probability value indicates the probability that a particular element of the predicted image 740 belongs to a particular category. Based on the probability, a label can be assigned to each pixel, wherein the label corresponds to the category with the maximum probability for the element. For example, the probability of the first element associated with one of the 10 categories (e.g., line category, gate bar category, contact hole category, etc.) may have the following probability values ​​represented by the vector [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 0.95]. In an embodiment, the vector may have normalized probability values ​​such that their sum is 1.

[0118] In the first forward pass, the output at the final layer may deviate from the ground truth (e.g., SEM image 701). This deviation is determined by a cost function (e.g., as previously described in Figure 5 The generalized sawing loss mentioned in the method of ) is characterized to quantify the amount of deviation between the predicted image 740 and the input images 701 and 702. For example, the features of the reference truth image (e.g., 701) may not match the features of the output image. In order to minimize the deviation, the loss gradient relative to the weight is back-propagated through the different layers of the network (i.e., from the final layer to the first layer of the neural network). In this way, the local derivative of the cost function relative to the weight at a specific layer (e.g., the output of the 15th layer out of 25 layers of the neural network) can be determined. Based on the derivative of the local function, the weight of the specific layer (e.g., the 15th layer) can be adjusted to minimize the cost function. In other words, minimize the deviation in the output.

[0119] Backward propagation through the deep learning model 730 may involve a reverse mapping of the output tensor of a layer (e.g., the 25th layer) to the input tensor of the particular layer or multiple previous layers. For example, the output tensor of a layer (e.g., the 25th layer) may be reverse mapped through multiple layers to, for example, the input tensor of the fifth layer. In another example, the backward propagation may involve a reverse mapping of the output tensor of the 25th layer to the input tensor of the 25th layer (i.e., the output of the 24th layer), the output of the 24th layer to the input tensor of the 24th layer (i.e., the output of the 23rd layer), and so on. At each step during the backward propagation (i.e., at the output of a particular layer), a local derivative of the cost function may be calculated. The local derivative of the cost function may be further plotted as a mapping graph (e.g., see Fig.11 ) in order to graphically determine the direction of changing the weights of a layer. For example, up to 2 dimensions may be plotted for illustrative purposes. Gradient descent changes the weights such that the loss decreases. In an embodiment, one of different optimization methods (such as gradient descent) may be used to determine the optimal weights such that the output tensor (e.g., the predicted image 740) accurately depicts the input image 701.

[0120] Fig.11 The figure shows an exemplary mapping diagram of the local derivatives at a specific layer according to an embodiment of the present disclosure, wherein the local derivatives are obtained relative to the weights w1 and w2 of the dilated kernel. The weights can then be updated based on an optimization method (e.g., a gradient descent method) that produces a more optimal weight for the specific layer so as to minimize the cost given the specific layer.

[0121] In an embodiment, the cost function may be defined such that the error in identifying a particular feature is reduced (preferably, minimized). For example, the cost function may weight a particular feature (e.g., a contact hole) in the predicted image more than other features, resulting in a greater emphasis on improving the separation of the parts. Note that different image features are represented by different classes, and as such, different class weights allow for feature-dependent contributions to the cost function.

[0122] Figure 6 6 is a flowchart of an exemplary method for predicting a wafer image of the wafer based on a trained machine learning model (e.g., 530 / 730) according to an embodiment of the present disclosure. The method involves, in process P601, obtaining a mask pattern 602 of a patterning process and a trained machine learning model (e.g., about Figure 5 and Figure 7 discussed).

[0123] Process P603 uses the mask pattern 602 as input to predict a wafer image 620 to be measured by the metrology tool via the trained machine learning model 530. The predicted wafer image 620 is similar to the image of the printed wafer captured by the metrology tool. For example, the predicted wafer image 620 mimics the SEM image captured by the SEM. Since the predicted image does not include noise or deformation, such a predicted image 620 can provide accurate measurement results, which can be further used to optimize the patterning process or the metrology process (e.g., hot spot identification, sampling scheme, measurement matching scheme, etc.).

[0124] The method further involves determining a characteristic of the printed pattern of the wafer based on the predicted wafer image in process P605. In an embodiment, the characteristic is a critical dimension, a profile of the feature, and / or an edge placement error.

[0125] The method further involves optimizing an aspect of the patterning process based on the predicted wafer image in process P605. In an embodiment, the optimization of the aspect of the patterning process involves: optimizing a mask pattern of the patterning process via a mask optimization process and the predicted mask pattern; and / or optimizing a process window via a process window optimization process and the predicted mask pattern; and / or optimizing a metrology profile of the metrology tool based on the predicted mask pattern.

[0126] Fig. 12A The figure illustrates the application of an exemplary trained machine learning model (e.g., 530 or 730). The trained machine learning model 530 (or 730) receives the mask image 1210 as input and predicts a wafer image 1220. The mask image 1210 is a binary image that includes patterns such as horizontal and vertical lines along with OPC. When such a mask pattern (of 1210) is used to image onto a wafer, a printed pattern is imaged onto the wafer. Fig. 12B 1230 of the actual printed pattern is shown in FIG. Comparing the predicted wafer image 1220 and the SEM image 1230 shows that the predicted image 1220 is substantially similar to the SEM image 1230, and advantageously does not include the noise seen in the SEM image 1230. Thus, the trained machine learning model can accurately predict a wafer image corresponding to an image of an input mask pattern, or an image of the mask pattern.

[0127] In an embodiment, the trained machine learning model 530 / 730 may also predict features that are not present in the mask pattern during the training process. For example, the trained machine learning model may be trained based on a mask pattern that includes lines, bars, or other features in addition to contact holes. However, the trained machine learning model 530 / 730 is able to predict contact holes. For example, Fig.13A As shown in FIG. 1 , the trained machine learning model 530 / 730 predicts a wafer image 1320 including, in particular, contact holes in the mask image 1310 corresponding to contact holes of the mask pattern.

[0128] Fig. 13B is an actual SEM image 1330 of a printed wafer imaged using the mask pattern 1310. Comparing the predicted image 1320 and the actual SEM image 1330 shows that the predicted image is very similar to the SEM image and advantageously does not include the noise seen in the SEM image. Thus, the trained machine learning model can accurately predict wafer images corresponding to the input mask pattern, or images of the mask pattern, even including features not included in the training data set.

[0129] In an embodiment, the noise-free predicted image (e.g., Fig. 12A 1220 and Fig.13A 1320) can have various applications, including but not limited to, determining more accurate measurements of features of the printed wafer, hot spot detection, mask pattern optimization, optimization of parameters of the patterning process, and the like.

[0130] Given the model and estimates of the model parameters, the model's output predictions may not match the observed facts. This may be caused by disturbances, which may have various sources, such as model mismatch, parameter drift, processing equipment offset, etc.

[0131] Therefore, in an embodiment, in a closed loop system, the state of the system is adjusted such that these disturbances can be removed. In an embodiment, a closed loop state estimation process may be provided.

[0132] In an embodiment, (for example, Figure 4 The state estimator provided at 430 may be configured to estimate the state so that the prediction output (As from Figure 4 410, which may be a predicted SEM image obtained by a trained machine learning model) and a measured output (e.g., in Figure 4The state estimate is updated recursively using the Bayesian formula. In other words, the state estimate is based on the most recent measurement (e.g., SEM image), and the machine learning model is updated to match the predicted output with the SEM image.

[0133] With the model (e.g., trained machine learning model, combined model, etc.) and its parameters and reference Figure 4 , the model can then be used to change, design, adjust, etc. 440 the parameters / variables of the patterning process towards a target 450. For example, given the model parameters and / or the model state estimate 430, an optimization problem can be solved to determine one or more inputs 400 so that the model prediction achieves the defined target 450. In an embodiment, the optimization can utilize a model that is updated regularly as the measurement results of the physical structure arrive. The adjustment can be done in various ways. For example, in an embodiment, one or more optimal equipment (e.g., lithography equipment) settings, such as focus and / or dose, are controlled. This can be done relatively quickly and in conjunction with the execution of the patterning process (e.g., between exposures or between substrate batches). In an embodiment, one or more optimal illumination mode settings (e.g., angular or spatial distribution characteristics) can be determined. Those settings can be changed, for example, between different substrate batches. In an embodiment, one or more characteristics of the designed pattern can be changed (e.g., adding optically adjacent features, such as auxiliary features, feature biases, wiring, etc.). In an embodiment, the patterning process parameters include one or more selected from: focal length, irradiation dose, numerical aperture, thin film stack properties, projection system optical aberrations, radiation coherence, irradiation intensity distribution, position in the image field, and / or position on the substrate.

[0134] In an embodiment, the model can be used to identify defects when the design pattern is processed by the patterning process. For example, the model can identify CDs that do not meet or exceed a defined threshold. If so, the patterning process can be stopped, the problematic substrate reworked, etc.

[0135] In embodiments of the present disclosure, the models and / or model prediction systems may be used for defect detection (and appropriate actions in response thereto), model identification, existing model calibration, defect grading, defect estimation, process monitoring, process control, process design, design pattern design, and the like.

[0136] Thus, the techniques described herein can enable defect detection, model representation, existing model calibration, defect grading, defect estimation, process monitoring, process control, process design, design pattern design, etc. based on review of images. In some embodiments, based on review of such images, such as individual pixels of the images as independent results, a model can be generated based on these images of the patterning process, the model recognition (e.g., the effectiveness of forming a portion of a device according to one or more patterning process parameters).

[0137] In an embodiment of the present disclosure, the model can be used to measure structures of patterned structures created, for example, for production. For example, the model can be used to predict certain parameter values ​​of certain structures (e.g., a specific width), and then one or more production-created versions of the patterned structure can be measured using, for example, a scatterometer to compare with the prediction. If the measurement results and the prediction match sufficiently, the structure can be considered "good". Otherwise, the structure can be reprocessed or scrapped. In addition, data from the comparison can be fed back into the predictive analysis (as data for establishing correlations, updating model parameters, etc.) and can be used to affect changes in the process (e.g., an insufficient match between the measurement results and the prediction (e.g., occurring a certain number of times) can be an indicator that a change in the process is needed).

[0138] Current computational patterning process models rely on many parameters in order to make correct predictions. Such existing models can be complex and cumbersome and can be difficult to discern; as a result, they often do not predict the product structure in production very well. They can also be too cumbersome for optimization purposes. The technology herein implements a relatively simple model (e.g., a logical model) that can accurately predict the physical structure configuration.

[0139] In addition, current methods aim to match simulated contours with contours extracted from images, relying on deviations from the contours to identify the parameters of the model. Contouring inherently introduces inaccuracies. In addition, measurement gauges can be used to identify the model. However, these are not the product structures themselves, and therefore the models derived from the measurement gauges may be inherently disconnected or separated from the patterning process. The techniques for evaluating image pixels according to embodiments of the present disclosure can achieve robust (i.e., robust) and accurate model parameter and / or model state estimation.

[0140] In an embodiment, pixels in an image (e.g., an electron beam or SEM image) are considered to be conditionally independent of common parameters. To this end, image data such as measured by a SEM or other tool can be processed into a pixelated form (e.g., a grayscale level image). A machine learning model is proposed (e.g., for a portion of the patterning process, such as a lithography model to obtain a resist image or structure, or an etching model to obtain a post-etching structure), which calculates the probability that a pixel is at a certain level (e.g., a grayscale level). As mentioned above, when assigning a label to a pixel (i.e., predicting the pixel), the associated probability gives additional information about the degree of certainty / accuracy of the label assignment.

[0141] As noted above, given a measured image of a physical structure, the machine learning model can be identified as a function of one or more descriptive features (e.g., aerial image blur, aerial image curvature) and its parameters. Using this learning model, one or more parameters of the physical structure (e.g., shape, CD, etc.) produced by the modeled patterning process can be predicted given the design pattern.

[0142] In an embodiment, one or more known patterning process input parameters (such as focus, dose, substrate position, one or more irradiation conditions, one or more etching conditions, etc.) may be input to the model. Thus, the model may be used to predict the response to these process conditions.

[0143] In an embodiment, a relatively simple model is provided that can be advantageously and quickly deployed in, for example, a production environment. In an embodiment, the model can be recursively updated (e.g., based on measurements during production) in order to monitor and control the physical structure obtained during production, and thus monitor and control the yield.

[0144] In an embodiment, the model may be inverted relatively easily for design pattern modifications and / or other optimization problems (such as lithography equipment and / or etch tool adjustments).

[0145] Additionally, in an embodiment, the model is derived based on comparing all pixels of the finished structure with the derived contour.Since the model is identified using a physical structure, the model can directly predict the behavior of the patterning process.

[0146] The term "value" may be data such as numbers, symbols, letters, etc.

[0147] As used herein, the terms "optimize" and "optimization" refer to or mean adjusting a pattern forming device (e.g., a lithographic device), a patterning process, etc., so that the result and / or process has more desired characteristics, such as higher projection accuracy of the design layout on the substrate, a larger process window, etc. Thus, the terms "optimizing" and "optimization" as used herein by ASML refer to or mean a process of identifying one or more values ​​for one or more parameters that provides an improvement (e.g., a local optimum) in at least one relevant metric compared to an initial set of one or more values ​​for those one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In an embodiment, the optimization steps may be applied iteratively to provide further improvements in one or more metrics.

[0148] Fig.14 Another embodiment of the inspection apparatus is schematically illustrated. The system is used to inspect a sample 90 (such as a substrate) on a sample platform 89 and includes a charged particle beam generator 81, a condenser lens module 82, a probe forming objective lens module 83, a charged particle beam deflection module 84, a secondary charged particle detector module 85, and an image forming module 86.

[0149] The charged particle beam generator 81 generates a primary charged particle beam 91. The condenser lens module 82 condenses the generated primary charged particle beam 91. The probe forming objective lens module 83 focuses the converged primary charged particle beam into a charged particle beam probe 92. The charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the surface of the area of ​​interest on the sample 90 fastened on the sample platform 89. In an embodiment, the charged particle beam generator 81, the condenser lens module 82 and the probe forming objective lens module 83 or their equivalent designs, alternatives or any combination thereof together form a charged particle beam probe generator that generates a scanning charged particle beam probe 92.

[0150] The secondary charged particle detector module 85 detects secondary charged particles 93 emitted from the sample surface after being bombarded by the charged particle beam probe 92 (and possibly together with other reflected or scattered charged particles from the sample surface) to generate a secondary charged particle detection signal 94. An image forming module 86 (e.g., a computing device) is coupled to the secondary charged particle detector module 85 to receive the secondary charged particle detection signal 94 from the secondary charged particle detector module 85 and to form at least one scan image accordingly. In an embodiment, the secondary charged particle detector module 85 and the image forming module 86 or their equivalent designs, alternatives, or any combination thereof together form an image forming device that forms a scan image from the detected secondary charged particles emitted by the sample 90 bombarded by the charged particle beam probe 92.

[0151] Fig.15 A block diagram of a computer system 100 is provided to illustrate a method and process for performing the optimization disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information; and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106 (such as a random access memory (RAM) or other dynamic storage device) coupled to the bus 102 for storing information and instructions executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110 (such as a magnetic disk or optical disk) is provided and coupled to the bus 102 for storing information and instructions.

[0152] The computer system 100 may be coupled to a display 112 (such as a cathode ray tube (CRT) or a flat panel or touch panel display) via the bus 102 for displaying information to a computer user. An input device 114 (including alphanumeric keys and other keys) is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor controller 116 (such as a mouse, trackball, or cursor direction keys) for communicating direction information and command selections to the processor 104 and for controlling cursor movement on the display 112. This input device typically has two degrees of freedom in two axes (a first axis (e.g., x) and a second axis (e.g., y)), which allows the device to specify a position in a plane. A touch panel (screen) display may also be used as an input device.

[0153] According to one embodiment of the present invention, part of the optimization process can be performed by the computer system 100 in response to the processor 104 for executing one or more sequences of one or more instructions contained in the main storage 106. Such instructions can be read into the main storage 106 from another computer-readable medium (such as storage device 110). The execution of the sequence of instructions contained in the main storage 106 causes the processor 104 to perform the method steps described herein. One or more processors in a multi-processing arrangement can also be used to execute the sequence of instructions contained in the main storage 106. In an alternative embodiment, hard-wired circuits can be used to replace software instructions or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuits and software.

[0154] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including wires that include bus 102. Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cassettes, carrier waves as described below, or any other media that a computer can read.

[0155] Various forms of computer readable media may be involved in transmitting one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially appear on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 may receive data on the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector connected to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 transmits the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may be optionally stored on storage device 110 before or after execution by processor 104.

[0156] The computer system 100 may also preferably include a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupled to a network link 120, which is connected to a local network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem for providing data communication connected to a corresponding type of telephone line. As another example, the communication interface 118 may be a local area network (LAN) card for providing data communication connected to a compatible LAN. A wireless link may also be implemented. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0157] Typically, network link 120 provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection to a host computer 124 or data equipment operated by an Internet Service Provider (ISP) 126 through a local network 122. ISP 126 in turn provides data communication services through a global packet data communication network (now commonly referred to as the "Internet") 128. Both local network 122 and Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118 carry the digital data to and from computer system 100, which is an exemplary form of a carrier wave used to transport the information.

[0158] The computer system 100 can send information and receive data, including program code, through the network, network link 120 and communication interface 118. In the example of the Internet, the server 130 can send a request code for an application through the Internet 128, ISP 126, local area network 122 and communication interface 118. One such downloaded application can provide for, for example, irradiation optimization of an embodiment. When it is received and / or stored in the storage device 110 or other non-volatile storage for later execution, the received code can be executed by the processor 104. In this way, the computer system 100 can obtain the application code in the form of a carrier wave.

[0159] Fig.16 An exemplary lithographic projection apparatus is schematically described, whose illumination source can be optimized using the method described herein. The apparatus comprises:

[0160] 1. An illumination system IL, which is used to condition the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO;

[0161] 2. a first stage (e.g., mask stage) MT having a patterning device holder for holding a patterning device MA (e.g., a reticle) and connected to a first positioner for accurately positioning the patterning device relative to the device PS;

[0162] 3. a second stage (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the apparatus PS;

[0163] 4. A projection system ("lens") PS (eg, a refractive, reflective or catadioptric optical system) for imaging the illuminated portion of the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0164] As depicted in the present invention, the device is of the transmissive type (i.e., with a transmissive mask). However, in general, it may also be of the reflective type, for example (with a reflective mask). Alternatively, the device may use another class of patterning devices as an alternative to using a classical mask; examples include a programmable mirror array or an LCD matrix.

[0165] A source SO (e.g. a mercury lamp or an excimer laser) generates a radiation beam. The beam is fed into an illumination system (illuminator) IL, for example directly or after having traversed an adjustment member such as a beam expander Ex. The illuminator IL may include adjustment members AD for setting the outer radial extent and / or the inner radial extent (commonly referred to as σouter and σinner, respectively) of the intensity distribution in the beam. In addition, the illuminator IL will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0166] about Fig.16 It should be noted that the source SO can be within the housing of the lithographic projection device (which is usually the case when the source SO is, for example, a mercury lamp), but it can also be remote from the lithographic projection device, the radiation beam it produces being guided into the device (for example with the aid of appropriate guide mirrors); this latter case is often the case when the source SO is an excimer laser (for example based on KrF, ArF or F2 laser action).

[0167] The beam PB then intercepts the patterning device MA which is held on the patterning device table MT. Having traversed the patterning device MA, the beam B passes through a lens PL which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and the interferometry means IF), the substrate table WT can be accurately moved, for example in order to position a different target portion C in the path of the beam PB. Similarly, the first positioning means can be used to accurately position the patterning device MA relative to the path of the beam B, for example after mechanically obtaining the patterning device MA from a patterning device library or during scanning. Typically, the patterning device MA will be accurately positioned with the aid of the interferometry means not in the patterning device library. Fig.16 Movement of the stage MT, WT is achieved by a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) explicitly depicted in the figure. However, in the case of a wafer stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to the short-stroke actuator only, or may be fixed.

[0168] The depicted tools can be used in two different modes:

[0169] in step mode, the patterning device table MT is held substantially stationary and the entire patterning device image is projected once (i.e. a single “flash”) onto a target portion C. The substrate table WT is then shifted in the x-direction and / or y-direction so that a different target portion C can be illuminated by the beam PB;

[0170] In scan mode, essentially the same situation applies, but a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT is movable in a given direction (the so-called "scanning direction", e.g. the y-direction) at a speed v, so that the projection beam B is scanned across the patterning device image; at the same time, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or =1 / 5). In this way, a relatively large target portion C can be exposed without having to compromise resolution.

[0171] Fig.17 Another exemplary lithographic projection apparatus LA is schematically depicted, the illumination source of which may be optimized using the methods described herein.

[0172] The lithography projection apparatus LA comprises:

[0173] Source collector module SO;

[0174] an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation);

[0175] a support structure (eg, mask table) MT configured to support a patterning device (eg, mask or reticle) MA and connected to a first positioning device PM configured to accurately position the patterning device;

[0176] a substrate table (eg, a wafer table) WT configured to hold a substrate (eg, a resist-coated wafer) W and connected to a second positioning device PW configured to accurately position the substrate; and

[0177] • A projection system (eg a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0178] As shown here, the apparatus LA is reflective (e.g., employing a reflective mask). It should be noted that since most materials are absorptive in the EUV wavelength range, the mask can have a multilayer reflector, including multiple stacks of, for example, molybdenum and silicon. In one example, the multilayer reflector has 40 layers of paired molybdenum and silicon, each layer being a quarter wavelength thick. Even smaller wavelengths can be produced with X-ray lithography. Since most materials are absorptive in EUV and X-ray wavelengths, a thin sheet of absorbing material patterned on the patterning device topography (e.g., a TaN absorber on top of a multilayer reflector) defines areas where features will be printed (positive resist) or not (negative resist).

[0179] Reference Fig.17 , the illuminator IL receives the extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state, the material having at least one element having one or more emission lines in the EUV range, such as xenon, lithium, or tin. In one such method, generally referred to as laser produced plasma ("LPP"), the desired plasma can be generated by irradiating a fuel, such as a droplet, a beam, or a cluster of a material having an emission line element, with a laser beam. The source collector module SO may be a laser (in Fig.17 The laser and source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation.

[0180] In this case, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, commonly referred to as a DPP source.

[0181] The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent (generally referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. Furthermore, the illuminator IL may comprise various other components, such as a faceted field mirror arrangement and a faceted pupil mirror arrangement. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0182] The radiation beam B is incident on the patterning device (e.g. mask) MA held on a support structure (e.g. mask table) MT and is patterned by the patterning device. After having been reflected by the patterning device (e.g. mask) MA, the radiation beam B passes through a projection system PS which focuses the radiation beam onto a target portion C of the substrate W. With the help of a second positioning device PW and a position sensor system PS2 (e.g. interferometer device, linear encoder or capacitive sensor), the substrate table WT can be precisely moved, for example in order to position a different target portion C in the path of the radiation beam B. Similarly, the first positioning device PM and a further position sensor system PS1 can be used to precisely position the patterning device (e.g. mask) MA relative to the path of the radiation beam B. The patterning device (e.g. mask) MA and the substrate W can be aligned using pattern shape device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0183] The depicted device LA may be used in at least one of the following modes:

[0184] In step mode, the support structure (e.g. mask table) MT and the substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam is projected once onto a target portion C (i.e. a single static exposure). The substrate table WT is then moved in the X and / or Y direction so that a different target portion C can be exposed.

[0185] In scan mode, the support structure (e.g. mask table) MT and the substrate table WT are scanned synchronously 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 support structure (e.g. mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0186] In another mode, the support structure (e.g. mask table) MT holding the programmable patterning device is held substantially stationary 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 typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applicable to maskless lithography using a programmable patterning device (e.g. a programmable mirror array of the type described above).

[0187] Fig.18 The apparatus LA is shown in more detail, including a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment is maintained within an enclosure 220 of the source collector module SO. A plasma 210 for emitting EUV radiation may be formed by a discharge-generated plasma source. EUV radiation may be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein an extremely high temperature plasma 210 is formed to emit radiation in the EUV range of the electromagnetic radiation spectrum. The extremely high temperature plasma 210 is formed, for example, by a discharge that causes at least partially ionized plasma. For example, a partial pressure of 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required to effectively generate radiation. In one embodiment, an excited plasma of tin (Sn) is provided to generate EUV radiation.

[0188] The radiation emitted by the high temperature plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via a gas barrier or contaminant trap 230 (referred to in some cases as a contaminant barrier or fin trap) optionally positioned within or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further shown herein includes at least a channel structure, as known in the prior art.

[0189] The collector cavity 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation passing through the collector CO may be reflected off the grating spectral filter 240 to be focused at a virtual source point IF along the optical axis indicated by the dashed line 'O'. The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near the opening of the enclosing structure 220. The virtual source point IF is an image of the plasma 210 for emitting radiation.

[0190] The radiation then passes through an illumination system IL which may comprise a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and a desired uniformity of radiation intensity at the patterning device MA. When the radiation beam 21 is reflected at the patterning device MA held by the support structure MT, a patterned beam 26 is formed and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0191] There may typically be more elements present in the illumination optics unit IL and the projection system PS than are shown. The grating spectral filter 240 may be optionally provided, depending on the type of lithographic apparatus. Furthermore, there may be more mirrors than are shown in the figures, for example, there may be more than 100 mirrors in the projection system PS. Fig.18 1-6 additional reflective elements beyond the elements shown.

[0192] Collector optics CO, such as Fig.18 As shown, a nested collector with grazing incidence reflectors 253, 254 and 255 is shown in the figure as just one example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are arranged axially symmetrically around the optical axis O. This type of collector optical device CO is preferably used in conjunction with a discharge produced plasma source, usually called a DPP source.

[0193] Alternatively, the source collector module SO may be as follows Fig.19 A portion of the LPP radiation system shown. The laser LA is arranged to inject laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of several tens of eV. The high-energy radiation generated during the deexcitation and recombination of these ions is emitted by the plasma, collected by the near normal incidence collector optics CO and focused onto an opening 221 of the enclosing structure 220.

[0194] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features, and may be particularly useful with the advent of imaging technologies capable of producing ever shorter wavelengths. Existing technologies already in use include EUV (extreme ultraviolet) lithography, which can produce 193 nm wavelengths with ArF lasers, and even 157 nm wavelengths with fluorine lasers. In addition, EUV lithography can produce wavelengths in the 20-5 nm range by using a synchrotron or by bombarding materials (solid or plasma) with high energy electrons to produce photons in this range.

[0195] The embodiments may be further described using the following aspects.

[0196] 1. A method for training a machine learning model, the machine learning model being configured to predict a substrate image corresponding to a printed pattern of the substrate as measured via a metrology tool, the method comprising:

[0197] obtaining a training data set, the training data set comprising (i) metrology data of the metrology tool for measuring the printed pattern of the substrate, and (ii) a mask pattern for imaging the printed pattern onto the substrate; and

[0198] training a machine learning model based on the training data set to predict the substrate image of the substrate as measured by the metrology tool such that a cost function is improved;

[0199] The cost function includes predicting a relationship between a substrate image and the metrology data.

[0200] 2. The method according to aspect 1, wherein the measurement data comprises:

[0201] an image of the printed pattern on the substrate captured by the metrology tool; and / or

[0202] A metrology option for the metrology tool used during measurement of the printed pattern on the substrate.

[0203] 3. The method of clause 2, wherein the metrology tool is a scanning electron microscope and the image is a scanning electron microscope image.

[0204] 4. The method of aspect 2, wherein the metrology tool is the scanning electron microscope and the metrology profile includes one or more parameters of the scanning electron microscope.

[0205] 5. The method according to aspect 4, wherein the one or more parameters of the scanning electron microscope are at least one of the following:

[0206] Electron beam intensity;

[0207] Angle of incidence; or

[0208] Sampling site information.

[0209] 6. A method according to any one of aspects 1 to 5, wherein the predicted image of the machine learning model is a segmented image.

[0210] 7. The method of clause 6, wherein the segmented image comprises a plurality of class labels assigned to features of the printed pattern.

[0211] 8. A method according to clause 7, wherein the predicted image is a pixelated image, wherein a class label from the plurality of class labels is assigned to each pixel based on a probability that the pixel belongs to a particular class from the plurality of class labels.

[0212] 9. A method according to any one of aspects 5 to 7, wherein each class label of the plurality of class labels corresponds to a grayscale level.

[0213] 10. The method of clause 9, wherein the gray levels are groupings of gray value ranges.

[0214] 11. A method according to clause 10, wherein the grouping of the grayscale values ​​is based on:

[0215] Evenly grouped;

[0216] pixels corresponding to specific features of the printed pattern; and / or

[0217] Weighted pixel grouping.

[0218] 12. A method according to any one of aspects 1 to 11, wherein the machine learning model is a convolutional neural network.

[0219] 13. The method according to clause 12, wherein training the machine learning model is an iterative process, the iteration comprising:

[0220] determining values ​​of model parameters of the convolutional neural network based on the measurement data and the mask pattern; and

[0221] The values ​​of the model parameters are adjusted until the cost function of the convolutional neural network is improved.

[0222] 14. The method according to any one of aspects 1 to 13, wherein the cost function is a generalized sawing loss.

[0223] 15. The method according to aspects 1 to 14, wherein the value of the model parameter is adjusted so that the generalized sawing loss is reduced.

[0224] 16. The method according to any one of aspects 1 to 15, further comprising:

[0225] Characteristics of the printed pattern of the substrate are determined based on the predicted substrate image.

[0226] 17. The method of clause 16, wherein the characteristic is a critical dimension, a profile of the feature, and / or an edge placement error.

[0227] 18. The method according to any one of aspects 1 to 17, wherein the training data further comprises:

[0228] Values ​​of one or more parameters of the patterning process.

[0229] 19. The method of clause 17, wherein the one or more parameters of the patterning process include at least one of dose, focus, intensity, or illumination mode.

[0230] 20. The method according to any one of aspects 13 to 18, further comprising:

[0231] acquiring real-time measurement data during or just after the patterning process via the metrology tool,

[0232] A trained machine learning model is updated based on the mask pattern used during the patterning process and the real-time metrology data.

[0233] 21. A method for predicting a substrate image corresponding to a printed pattern of a substrate, the method comprising:

[0234] Obtaining a mask pattern of a patterning process and a trained machine learning model; and

[0235] The substrate image to be measured by a metrology tool is predicted via a trained machine learning model using the mask pattern as input.

[0236] 22. The method according to aspect 21, further comprising:

[0237] Characteristics of the printed pattern of the substrate are determined based on a predicted substrate image.

[0238] 23. The method of clause 22, wherein the characteristic is a critical dimension, a profile of the feature, and / or an edge placement error.

[0239] 24. The method according to any one of aspects 21 to 23, further comprising:

[0240] An aspect of the patterning process is optimized based on the predicted substrate image.

[0241] 25. The method of aspect 21, wherein optimizing the aspect of the patterning process comprises:

[0242] optimizing a mask pattern of the patterning process via a mask optimization process and the predicted mask pattern; and / or

[0243] optimizing a process window via a process window optimization process and the predicted mask pattern;

[0244] A metrology profile of the metrology tool is optimized based on the predicted mask pattern.

[0245] 26. A computer program product, comprising a non-transitory computer-readable medium, wherein instructions are recorded on the non-transitory computer-readable medium, and when the instructions are executed by a computer, the method according to any one of the above aspects is performed.

[0246] 27. The non-transitory computer-readable medium of any one of clauses 1 to 26, wherein the predicted substrate image is substantially free of noise compared to an actual substrate image as measured by the metrology tool.

[0247] Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system, for example, a lithography imaging system for imaging on substrates other than silicon wafers.

[0248] The above description is intended to be illustrative rather than limiting.Thus, it will be appreciated by those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth hereinafter.

Claims

1. A method for training a machine learning model, comprising: obtaining a training data set comprising (i) metrology data of a metrology tool for measuring a printed pattern on a substrate, and (ii) a representation of a mask pattern used to image the printed pattern onto the substrate; as well as training the machine learning model based on the training data set, the machine learning model operable to predict a substrate image of the substrate as measured by the metrology tool based on a cost function, wherein the substrate image corresponds to the printed pattern of the substrate as measured via the metrology tool; The predicted substrate image generated by the machine learning model includes a segmented image.

2. The method according to claim 1, wherein the measurement data comprises: an image of the printed pattern on the substrate captured by the metrology tool; and / or A metrology option for the metrology tool used during measurement of the printed pattern on the substrate.

3. The method of claim 2, wherein the metrology tool is a scanning electron microscope and the image is a scanning electron microscope image, and the metrology options of the scanning electron microscope include at least one of: Electron beam intensity; Angle of incidence; and Sampling site information. The method of claim 1 , wherein the cost function comprises a relationship between the predicted substrate image and the metrology data.

5. The method of claim 1, wherein the segmented image is associated with a plurality of class labels assigned to features of the printed pattern.

6. The method of claim 5, wherein the predicted image is a pixelated image, wherein a class label from the plurality of class labels is assigned to each pixel based on a probability that the pixel belongs to a particular class from the plurality of class labels. 7 . The method of claim 5 , wherein each of the plurality of category labels corresponds to a grayscale level, the grayscale level comprising one or more grayscale values.

8. The method of claim 7, wherein the one or more grayscale values ​​are grouped into the grayscale levels based on: Evenly grouped; pixels corresponding to specific features of the printed pattern; and / or Weighted pixel grouping.

9. The method of claim 1, wherein the machine learning model is a convolutional neural network, wherein training the machine learning model comprises an iterative process, an iteration of the iterative process comprising: determining values ​​of model parameters of the convolutional neural network based on the measurement data and the mask pattern; and The values ​​of the model parameters are adjusted to improve the cost function of the convolutional neural network.

10. The method according to claim 1, further comprising: Characteristics of the printed pattern of the substrate are determined based on the predicted substrate image, wherein the characteristics include critical dimensions, profiles of features, and / or edge placement errors.

11. The method according to claim 1, wherein the training data further comprises: Values ​​of one or more parameters of a patterning process, wherein the one or more parameters of the patterning process include at least one of dose, focus, intensity, or illumination mode.

12. The method according to claim 11, further comprising: acquiring additional metrology data during or after the patterning process via the metrology tool, The trained machine learning model is updated based on the mask pattern used during the patterning process and / or the additional metrology data.

13. The method according to claim 1, further comprising: obtaining another mask pattern of the patterning process and the trained machine learning model; and Another substrate image originating from the metrology tool is predicted via the trained machine learning model using the another mask pattern as input.

14. The method according to claim 13, further comprising: An aspect of the patterning process is optimized based on the further substrate image, wherein the aspect of optimizing the patterning process comprises one or more of: optimizing a mask pattern of the patterning process via a mask optimization process and a predicted mask pattern; optimizing a process window via a process window optimization process and the predicted mask pattern; and A metrology profile of the metrology tool is optimized based on the predicted mask pattern.

15. The method of claim 1, wherein the predicted substrate image is substantially free of noise compared to an actual substrate image as measured by the metrology tool.

16. A method for predicting a substrate image corresponding to a printed pattern of a substrate, the method comprising: Obtaining a mask pattern of a patterning process and a trained machine learning model; and Using the mask pattern as input, predicting the substrate image to be measured by a metrology tool via a trained machine learning model, Wherein the substrate image corresponds to the printed pattern of the substrate as measured via the metrology tool, and the predicted substrate image generated by the machine learning model comprises a segmented image.

17. The method according to claim 16, further comprising: Characteristics of the printed pattern of the substrate are determined based on a predicted substrate image.

18. The method of claim 17, wherein the characteristic is a critical dimension, a profile of a feature, and / or an edge placement error.

19. The method according to any one of claims 16 to 18, further comprising: An aspect of the patterning process is optimized based on the predicted substrate image.

20. The method of claim 16, wherein said step of optimizing said patterning process comprises: optimizing a mask pattern of the patterning process via a mask optimization process and the predicted mask pattern; and / or optimizing a process window via a process window optimization process and the predicted mask pattern; A metrology profile of the metrology tool is optimized based on the predicted mask pattern.

21. A computer program product, comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions for executing the method according to any one of the preceding claims when executed by a computer.

22. The method of any one of claims 16 to 20, wherein the predicted substrate image is substantially free of noise compared to an actual substrate image as measured by the metrology tool.

23. A computer-readable medium having recorded thereon instructions, which when executed by a computer, perform the method according to any one of claims 1 to 20 and 22.

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